The Gold Standard and the Fren h Great Depression

Slim Bridji∗

February 14, 2010

Abstra t

The analysis of the Great Depression through the lens of the gold standard theory has been

mainly ondu ted from an international omparative perspe tive. As far as I know, there is no

stru tural model-based studies of the link between the malfun tioning of the gold standard and

the Great Depression. A su h analysis would be helpful to assess the role of gold standard in the

worldwide depression. Here, I intend to take step into this dire tion. I develop a gold standard

DSGE model whi h aims to emphasize the working of the gold standard and the link of the latter

with the real e onomy. The u tuations of the variables of the arti ial e onomy are driven by

one real and three nominal sho ks. The real sho k is assumed to be a produ tivity sho k in the

nal good se tor. The nominal sho ks are related to the working of the gold standard: a gold

ow sho k, a gold ba king sho k, and a money multiplier sho k. The two lastest nominal sho ks

alter the ratio of the urren y value of the monetary gold sto k to the nominal money sto k as

in Bernanke (1995, Journal of Money, Credit, and Banking). I, then, analyze the steady state

and dynami properties of the model in the ontext of the Fren h Great Depression.

Keywords: Gold Standard, Business Cy le model, Great Depression.

JEL Classi ations: E30, N14.

∗Université Paris Ouest-Nanterre la Défense and E onomiX. Email: sbridjiu-paris10.fr. I thank Fabien Tripier and

the team of the Chair of E onomi History Ulri h Woitek, Tobias Straumann, Alex Rathke and Samad Sarferaz

for their helpful guidan e, omments, and support. This work has been partly realized during my stays in the

University of Zuri h during the two following periods: September 2008-January 2009 and August-September 2009. I

would like to thank the Institute of Empri al Resear h in E onomi s (IEW) of the University of Zuri h for wel oming

me. In parti ular, I thank Sonja Verel for the help she has provided me. I also a knowledge the nan ial support of

the Globaleuronet program. All errors are mine.

1

1 Introdu tion

The Great Depression of the 1930s is seen as a vivid lesson for the ongoing global nan ial risis.

The auses and the transmission me hanisms of the Great Depression have attra ted the interest of

a onsiderable number of ma roe onomists. For re ent years, there is a body of literature, su h as

Cole and Ohanian (1999, 2004), Cole, Ohanian and Leung (2005), Bordo, Er eg and Evans (2000),

and, Christiano, Motto and Rostagno (2003), assessing the ability of Dynami Sto hasti General

Equilibrium (hereafter DSGE) models to repli ate the e onomi risis in the 1930s. However, few

of them have shed light on the international dimension of the Great Slump, but as Ei hengreen and

Sa hs (1985), Ei hengreen (1992, 2004), Bernanke and James (1991), Bernanke and Carey (1996),

and Bernanke (1995) argue, the worldwide nature of the e onomi risis should not be ignored. It

is ru ial to analyze the Great Depression as a global phenomenon and not as a ountry spe i

one to gain a deeper understanding. A ording to those authors, the Depression was triggered o

by a worldwide monetary ontra tion. The worldwide ollapse of money supplies resulted from an

ine ient management of the international monetary system that was at work during the interwar

period, i.e. the gold standard. The urrent work intends to introdu e the gold standard-based

explanation of the worldwide Great Depression into the new body of literature. Basi ally, I propose

a simple DSGE model e onomy in whi h the monetary poli y is ondu ted onsistently to the gold

standard monetary system. In order to analyze the properties of the gold standard model, I take

Fran e as a ase study. Thus, the urrent work aims to be a rst step into the use of DSGE models

as an evaluation tool of the gold standard-based explanation of the Great Depression.

Basi ally, the gold standard monetary system an be dened as follows. Countries whi h were

ommitted to the gold standard, were supposed to dene the pri es of their domesti urren ies in

terms of a xed weight of gold (Bordo 1981; Bordo et al. 2007). In other words, ountries on the gold

standard dened a xed pri e of gold in terms of their domesti urren ies. For example, during the

interwar gold standard, the fran poin aré weighted 65 milligrams of gold 0.900 ne1, or equivalently

1 grams of gold ne was worth 16.92 fran s poin aré2. In order to hold xed the urren y pri es of

gold, ountries on the gold standard a tually their entral banks are assumed to stand ready

to sell or pur hase any quantity gold demanded or supplied at that pri e. The gold standard was

an impure ommodity money system3. By denition, in an impure ommodity money system, the

medium of ex hange onsists not only of the ommodity money (e.g. gold oins) but also of laims

to units of the ommodity money (e.g. at money and du iary money). Ea h unit of those laims

an be ex hanged against gold at the xed urren y pri e of gold if desired. Countries on the gold

standard substituted at and du i iary money for gold oins as medium of ex hange be ause the

size of ex hanges of goods and servi es had be ome high and be ause the podu tion of gold was

demanding in terms of ressour es and hen efore ostly (Bordo 1981). The urren y value of the

additional instruments of payment at money and du iary money ould ex eed the urren y

value of gold. Nevertheless, the ratio of the at and du iary monies to gold should remain stable

over time in order to ensure that the maintenan e of the gold standard (Bordo 1981). Sin e the gold

standard was an international monetary system, gold was allowed to move freely from one ountry

to an other. More spe i ally, ountries on the gold standard were forbidden to prevent gold from

owing away.

The entral banks of the ountries involved in the gold standard, where they existed, were sup-

posed to ondu t their monetary poli ies in agreement with the so alled rules of the game in order

to ensure the ontinued good management of the gold standard. In parti ular, a entral banks had

to use its nominal interest rate so that the ee t of the ongoing gold ow in or out of the ountry

on the domesti money supply was strengthened. For example, the entral bank of a ountry

experien ing a gold outow (inow) had to raise (lower) its nominal interest rate so that the total

money supply was further redu ed (in reased). By raising (lowering) the nominal interest rate, the

entral bank led the ommer ial banks to de line (raise) their redit supply (that is du iary money

supply).

The gold standard monetary system took two forms during the last two enturies the 19th and

20th enturies. The rst form of the gold standard, alled the lassi al gold standard, was the one

1See the arti le 2 of the Fren h monetary law of June 25, 1928. This monetary law has been also published in the

Federal Reserve Bulletin of August 1928 (see Federal Reserve Board 1928).2The movements in the Fren h pri e of gold during the interwar period are reported in Annuaire Statistique (1966).3This expression is borrowed from M Callum (1989, p 250).

2

des ribed above. It operated over the 1821-1914 period, that is from the end of the Napoleoni Wars

to the onset of the World War 1. In the beginning of that period only few ountries were on the

lassi al gold standard, the main ountry being England. The lassi al gold standard were outspread

to a large part of the world between 1880 and 1914 (Bordo 1981; Bordo et al. 2007). The lassi al

gold standard were suspended at the beginning of the World War 1 in order to allow ountries

involved into the worldwide military oni t to fa e the war related expenditures. The gold standard

were restored during the interwar period under a new form following the re ommendations of the

Genoa Conferen e that took pla e in 1922 (Nurkes 1944). The main re ommendation stated that the

money issued by entral banks ould be ba ked not only by gold as it was during the lassi al gold

standard period but also by foreign ex hanges. Those foreign ex hanges spe i ally sterlings

and dollars were onvertible into gold. Thus the legal reserves of the entral banks onsisted of

gold and foreign ex hanges4. By dening the entral banks reserves in terms of both gold and foreign

ex hange rather than in terms of only gold, the parti ipants of the Genoa Conferen e expe ted to

to be able to deal with a possible shortage of the world gold sto k. in the future. The shortage of

world gold sto k might be aused by a redu tion in the world gold produ tion or an in rease of the

world money demand (Nurkse 1944). The gold standard that took pla e during the interwar period

was alled the gold ex hange standard.

Several authors, su h as Choudhri and Ko hin (1980), Ei hengreen and Sa hs (1985), Bernanke

and James (1991), and Bernanke (1995), provided some eviden es that the internation Great De-

pression took its roots in the gold standard. Choudhri and Ko hin (1980) showed that four small

European e onomies Belgium, Italy, Netherlands and Poland whi h were ommited to the

gold standard, experien ed large drops in output and pri es between 1928 and 1932. Instead, Spain,

whi h remained outside the gold standard during all the interwar period, was almost not ae ted by

the e onomi risis as its european neighbors: in 1932, the Spanish output and pri es were lose to

their respe tive 1928 level. In addition, Choudhri and Ko hin (1980) showed that three S andinavian

ountries Denmark, Finland and Norway whi h were in the gold standard in the beginning

the Great Depression then moved out5 from it 1931 along with the United Kingdom, experien ed

less severe ollapses in output and pri es than Belgium, Italy, Netherland and Poland did during

the 1928-1932 period. Ei hengreen and Sa hs (1985), using a sample of ten European ountries

Belgium, Denmark, Finland, Fran e, Germany, Italy, Netherlands, Norway, Sweden, and United

Kingdom , showed that the ountries whi h had left the gold standard got their industrial produ -

tions ba k to their 1929 levels qui kly after they had depre iated their urren ies. For example, the

industrial produ tions in Finland, Denmark, United Kingdom, Norway and Sweden those oun-

tries abondoned the gold standard in 1931 were well above their 1929 levels in 1935. In onstrast,

ountries whi h were still in the gold standard in the end of 1935 Fran e and Netherlands whi h

abandoned the gold standard in 1936 had their industrial produ tion below their 1929 levels in

1935. Similarly, Bernanke and James (1991), using a sample of 24 ountries, found that on average,

the industrial produ tion growth rates were higher in ountries whi h had left the gold standard in

1931 during the 1932-1935 period than those in ountries whi h were still in the gold standard in

1935. Additionally, Bernanke and James (1991) showed that all the ountries whi h were in the gold

standard on the onset of the Great Depression suered from a severe deation in the early 1930s. In

1933, the deationary movement of pri es slowed down or stopped in ountries whi h moved away

from the gold standard in 1931. Afterwards, the pri e level slightly in reased in those ountries. On

the ontrary, the pri e levels ontinued to drop after 1933 in ountries whi h remained ommited to

the gold standard until 1936. Bernanke and James (1991) also ompared the money supply behaviors

of the two groups of ountries the ountries whi h abandoned the gold standard in 1931 on the one

hand, the ountries whi h remained in the gold standard until 1936 on the other hand between

1930 and 1935. Before 1932, the two groups of ountries experien ed ontra tions in money supplies.

The ountries whi h left the gold standard in 1931, started to raise their money supply in 1933. The

money supplies de reased during all the 1930-1935 period in ountries whi h remained in the gold

standard until 1936. From this result, Bernanke and James (1991) pointed out that the ommitment

to the gold standard made it di ult for a ountry to raise its money supply and hen efore to restrain

the deationary movement of pri es. In other words, by abandoning the gold standard, a ountry

4The United Kingdom and the United States hold their reserves only in gold during the interwar period.5In general in this literature, represented here by Choudhri and Ko hin (1980), Ei hengreen and Sa hs (1985),

Bernanke and James (1991), and Bernanke (1995), a ountry is onsidered as abandoning the gold standard if either

it devalues its urren y, impose ex hange ontrols or o ially abandons the gold parity of its urren y.

3

ould more easily ondu t an expansionary monetary poli y6. These eviden es led those authors to

put forward the idea that several monetary sho ks, transmitted from one ountry to an other through

the gold standard monetary system, had aused pri es and output to ollapse in ountries on the

gold standard.

As stressed by Bernanke and Mihov (2000), the proponents of the gold standard-based explanation

of the Great Depression have suggested several sour es of the ollapse of national money supplies

during the 1930s: ontra tionary monetary poli y through the sterilization of gold osetting the

ee t of gold inow on the money supply ; ine ien y of the distribution or maldistribution of the

world gold among the ountries involved in the gold standard; the onversion of foreign ex hange

into gold by the entral banks; the ollapse of the money multiplier aused by su essive banking

rises; and the s ar ity of gold at the world level. The three rst fa tors of the ollapse of the money

supplies mainly resulted from the ine ien y or absen e of management of the gold standard during

the interwar period7. Bernanke (1995) and, Bernanke and Mihov (2000) suggest to de ompose, for

several ountries, the identity linking the money supply (spe i ally the monetary aggregate M1)

of a ountry ommitted to the gold standard to the gold sto k held by the entral bank of that

ountry into several ratios in order to identify quantitatively the main ontributors of the ollapse

of money supplies among the ontra tionary me hanisms proposed above. Those ratios are assumed

to ree t the banking rises (through the money multiplier ratio or the ratio of M1 to monetary

base), the sterilization of gold inow (through the gold ba king ratio or the ratio of international

reserves gold plus foreign ex hange to monetary base), and the onversion of foreign ex hange

(through the ratio of the international reserves to the gold sto k). From those studies, it result

that initially, period prior to 1931, the money supplies have fallen mainly be ause the ountries

whi h have attra ted massively gold mainly the United States, Germany and Fran e have

sterilized those gold inows ree ted by an in rease of the gold ba king ratio: the ountries from

where gold have own away toward the United States, Germany and Fran e have no hoi e than to

restri t their money supplies in order to keep safe their respe tive parity to gold. For the period

post 1931, the banking rises have been the main ulprit of the ollapse of the money supplies

ree ted by a de rease of the money multiplier8. Bernanke and Mihov (2000) have also shown that

the maldistribution of the world gold sto k has worsened after 1931, be oming an important fa tor

of the monetary ontra tions9.

Nonetheless, the presented eviden es of a possible link between the gold standard and the drop

of domesti money supplies leave open the question of the hannel through whi h the monetary

ontra tions have led domesti outputs to fall during the 1930s. Most of proponents of the gold

standard-base explanation of the Great Depression laim that the fall in the global money supply

has been transmitted to the real part of the world e onomy, mainly through nominal wage sti kiness.

Basi ally, the sti ky wage story of the Great Depression an be summarized as follows. Consequently

to a monetary ontra tion, pri es go down. Produ tion osts should de rease also in order to maintain

the level of produ tion. Thus, when nominal wages do not respond qui kly to the de rease in pri es

(due to labor market imperfe tions), rms lay o and produ e less. This results in an in rease

in unemployment and a drop in output. Ei hengreen and Sa hs (1985) and Bernanke and Carey

(1996) have provided some eviden es for the sti ky wage story. Ei hengreen and Sa hs (1985), using

a sample of 10 European ountries as said above, have shown that in 1935, ountries whi h have

left the gold standard earlier have displayed high industrial produ tion growth rates and low real

6Bordo, Choudhri and S hwartz (2002) laim that the proposition stating that the ommitment to the gold standard

makes it di ult for a ountry to ondu t an expansionary monetary poli y during the Great Depression holds only

for small open e onomies with little gold reserves. They laim that the U.S., whi h was a large e onomy and detained

large gold reserves, ould have raised its money supply before 1933 without putting in danger its ommitment to the

gold standard.7If during the prewar period, the gold standard system was well managed, this was not the ase during the interwar

period. England was the main nan ial pla e before World War 1, a position whi h was weakened after the war. By

onsequen e, after the majority of developed ountries was ba k on the gold standard, the position of nan ial leader

was free but no ountry was ready to ll it. Moreover, be ause of the war related questions of reparations and debts,

the relationships between ountries, su h as Fran e and Germany, were di ult.8Those ndings are also pointed out by Hamilton (1987).9Bernanke and Mihov (2000) dene an index of the maldistribution of gold as being approximately the ovarian e

between the ountry e onomi weights and log gold shares. The e onomi weight of a ountry orresponds to the

ratio of its urrent GDP to its 1928 GDP.

4

wages omparatively to the levels that those two variables have taken in 1929. In ontrast, in 1935,

ountries whi h have remained ommitted to the gold standard until its full dissolution in 1936, su h

as Fran e, have low industrial produ tion growth rates and high real wages in omparison with the

levels that those two variables have taken in 1929. Bernanke and Carey (1996), using a sample of 22 ountries, have found similar results to those of Ei hengreen and Sa hs (1985). In addition, Bernanke

and Carey (1996) have reported that in ountries where industrial produ tions have strongly fallen

over the 1931-1936 period ountries whi h have been on the gold standard until the break down

of that monetary system the nominal wages have adjusted slowly to movements in pri es. The

debt-deation hypothesis of Fisher (1933) is also onsidered as a possible hannel of transmission of

the monetary ontrations on real e onomies. The debt-deation story an be stated as follows. The

ollapse of money supplies ause pri es to de line. The deation raises the real value of the debts

ontra ted by rms. It results that the net worth positions of those rms be omes so weak that

they annot get a ess to new redits. Worst, the in rease of the real value of their debts might lead

them to lay o or go bankrupt. It follows that investment and employment de line. So does output

(Bernanke and James 1991; Bernanke 1995).

The analysis of the gold standard-based explanation of the Great Depression has been mostly

treated in a omparative international perspe tive10. In parti ular, the gold standard approa h of the

international Great Depression has re eived little theoreti al attention. Of ourse, several models

about the working of the lassi al gold standard have been developed and analyzed, su h as those of

Barro (1979), Barsky and Summers (1988), Goodfriend (1988)11. Barro (1979) developes a dynami

model to emphasize how the pri e level is determined under the gold standard. Barro (1979) re alls

that under the gold standard the money supply is dened upon the existing quantity of gold and the

pri e of the latter is set xed by the entral bank (or any monetary authority). In other words, gold

is a ommodity money whi h pri e is maintained xed12. It follows that the determination of the

pri e level pri e of other goods than gold is equivalent to the determination of the relative pri e

of the ommodity money the ratio of the xed pri e of gold to the pri e level. Hen e, the relative

pri e of gold is determined by the equilibrium on the gold market, whi h in turn orresponds to the

equality between the total demand for gold sto k gold demand for monetary and non-monetary

uses and the supply of gold sto k. The model of Barro (1979) presents the following features:

the gold standard model e onomy is dened as a lose e onomy; the real part of the gold standard

e onomy, represented by the output (or real in ome), is treated as exogenous; gold is not only held

for monetary purpose but also for non-monetary uses; the expe ted ination rate is assumed to be nil

in the steady state; only the non-monetary gold sto k depre iates over time (at a onstant rate); and

the supply of new gold is dened as a negative fun tion of the relative pri e of gold. Barro (1979)

uses its model to analyze the ee ts of a te hni al progress in the gold se tor, a hange in output

whi h an be interpreted as a hange of produ tivity in the output se tor , and a hange in

the ratio of monetary gold sto k to nominal money sto k onsidered as the gold ba king ratio in

the model on the pri e level and gold sto ks. The analysis is ondu ted with the use of a phase

diagram. An in rease of the produ tivity in the gold produ tion su h as a dis overy of a new

gold sour e leads the pri e level, monetary gold sto k and non-monetary gold sto k to in rease.

In other words, following an in rease of gold produ tion, the gold standard e onomy moves to a new

steady state where the levels of pri e level and gold sto ks are higher. Barro (1979) shows that an

in rease in output leads the gold standard e onomy towards a new steady state hara terized by

a lower pri e level and higher non-monetary gold sto k. However, the net ee t of an in rease of

output on the monetary gold sto k is generally ambiguous. From this, Barro (1979) argues that sin e

te hni al progresses are expe ted to materialized more often in the output se tor than in the gold

se tor, deationary episodes are likely to happen under the gold standard monetary system. Then,

Barro (1979) evaluates whether lowering the gold ba king ratio an dampen the deationary for es

of the gold standard13. Barro (1979) nds that even though the de rease of the gold ba king ratio

leads the pri e level to in rease, this ee t is only transitory. Indeed, the de line of the gold ba king

ratio leads the gold standard e onomy to new steady state where only the level of monetary gold has

10The expression is borrowed from Bernanke and Carey (1996).11There are also the models of Dowd and Sampson (1993) and Chappell and Dowd (1997).12For a dis ussion on the ommodity money of see Friedman (1951).13A ording to Barro (1979), this evaluation is based on the idea that the reation of paper gold, representing gold

promises, would allow shield ountries ommitted to the gold standard against the deationary for es of the gold

standard.

5

hanged it takes a lower value. From this, Barro (1979) on ludes that lowering the gold ba king

ratio annot weaken the deationary for es of the gold standard.

Barsky and Summers (1988) provides some eviden e that the Gibson paradox the positive

orrelation between the pri e level and nominal interest rates an be observed over the period

during whi h the gold standard monetary system has prevailed. Hen e, those authors develope a gold

standard model in order to demonstrate that the Gibson paradox is losely related to the working

of the gold standard. The model of Barsky and Summers (1988) is similar to the one developed by

Barro (1979). However, while the real money demand depends on the expe ted ination in the Barro

(1979)'s model, the real money demand is fun tion of the nominal interest rate in the Barsky and

Summers (1988)'s model.

Goodfriend (1988) uses an intertemporal, rational expe tations, asset pri ing model to study the

monetary poli ies ondu ted by entral banks under the lassi al gold standard. Goodfriend (1988)

bases its gold standard analysis on an asset pri ing model be ause it provides a rational expe tation-

based framework for the private valuation of money and gold sto ks, that is the pri ing of those two

assets. Goodfriend (1988) analyzes how a entral bank an ae t the pri ing of money and gold

sto ks behaviors, through money and gold poli y rules, so that the money pri e of gold is maintained

xed. The Goodfriend (1988)'s model represents a losed e onomy whi h onsists of two types of

agents: an innitely-lived representative household and a entral bank (or a government). In this

e onomy there are four assets: apital sto k, money sto k, gold sto k and bond sto k. The household

gets satisfa tion from onsuming goods (others than gold and apital) and holding real money and

gold sto k for non-monetary purposes. The household hooses sequen es for onsumption and assets

so that it maximizes its expe ted intertemporal utility fun tion subje t to its budget onstraint. The

produ tion of onsumption good is treated as exogenous in the model. Indeed, there is no labor

in the e onomy and the apital sto k is assumed to be xed to unity in the equilibrium. Hen e,

the produ tion of the onsumption good is driven by an exogenous sto hasti produ tivity sho k.

The e onomy is endowed on e for all with a xed sto k of gold. Ea h period, this total gold sto k is

ex hanged between the household and the entral bank. The latter holds gold for monetary purposes.

The entral bank is assumed to ondu t two poli ies in terms of gold and money: a pure gold poli y

whi h onsists of buying/selling gold from the household and a pure monetary poli y whi h onsists

of supply or destru tion of money. Both poli ies are nan ially supported through the pur hases or

sales of bonds to the household. Goodfriend (1988) shows formally how the entral bank an use

either of its two poli ies to ensure the xity of the money pri e of gold14, whi h in turn is dened as

the ratio of the real pri e of gold that is onsumption pri e of gold to real pri e of money

that is the onsumption pri e money or inverse of the pri e level. This author demonstrates that if

the entral bank ommits itself not only to ensure the xity of the money pri e of gold but also to

keep the ratio of monetary gold to money onstant over time, it annot additionally ondu t poli ies

ae ting the pri e level or the nominal interest rate behavior in the e onomy. However, a ording

to Goodfriend (1988), the entral bank an both satises the gold standard rule on the xity of the

money pri e of gold and inuen es the behavior of the pri e level or the one of the nominal interest

rate15 if it relaxes temporally the onstraint on the monetary gold-money ratio the monetary

gold-money ratio is allowed to u tuate around a narrowed range.

As it an be noted, those models oer a good des ription of the working of the gold standard in

terms of money, pri e and interest rate. However, the impli ations of the working of the gold standard

on the real part of the e onomy are not well emphasized. Thus, they are not very useful if one wants

to analyze the Great Depression through the lens of the gold standard theory. More re ently, Bordo

et al. (2007) have developed a DSGE model representing a losed gold standard e onomy16. In this

model, the nal good produ tion se tor and the gold produ tion se tor are both expli itly dened.

The produ tions of the nal good and gold require the use of labor and apital as inputs. The

produ ed gold sto k an be held for three dierent purposes in this e onomy: utility purpose

holding gold yields utility to the household , monetary purpose, and produ tion purpose gold

is used as apital in both nal good and gold se tors. In this e onomy, the household needs money

14Basi ally, the entral bank stands ready to ex hange gold for mney or money for gold at a xed money pri e of

gold.15The pri e level and nominal interest rate poli ies onsidered in Goodfriend (1988) are pri e level smoothing and

nominal interest rate smoothing poli ies.16Bordo et al. (2007) use a DSGE model to study and ompare the dynami behaviors of the pri e level under

dierent monetary systems for example the gold standard monetary system and at monetary system.

6

be ause it allows to de rease the time spent into transa tion a tivities. The e onomy in ludes also a

entral bank whi h ontrols the money supply through an interest rate rule. Still, this model seems

not suitable for a formal analysis of the gold standard-based explanation of the Great Depression.

The Bordo et al. (2007) model seems not to expli it the link between the monetary gold sto k and the

money supply as for example in Barro (1979) and Goodfriend (1988)17. Hen e, it would be di ult

to re on ile this model with the works of Bernanke and its oauthors.

A ordingly to the above dis ussion on gold standard models, I propose to develop a new DSGE

model whi h would emphasize the working of the gold standard and its link to the real e onomy. I

essentially rely on the works of barro (1979) and Goodfriend (1988) when I dene the nominal part

of the gold standard arti ial e onomy. The model is basi ally a monetary business y le model with

a ommodity money. In parti ular, it in orporates the following features. The gold standard model

represents a lose e onomy in whi h there are ve ompetitive markets nal good market, labor

market, gold market, money market and bond market and four assets gold, money, bonds,

and physi al apital. The gold standard arti ial e onomy is populated by three types of agents:

households, nal good produ ers, and a entral bank. The supply of new gold is treated as exogenous

and in terms of ows rather than in terms of produ tion. Note that the supply of new gold an be

either positive (inow of gold) or negative (outow of gold). In the e onomy, gold has two fun tions:

the households gets satisfa tion from holding money (non-monetary gold sto k) and the entral bank

bases its money supply de ision on the value of its gold sto k (monetary gold sto k). The entral

bank is ommitted to pur hase of sell any quantity of gold in ex hange of money that households

asks for at a xed pri e: the urren y pri e of gold is assumed to be onstant over time. Households

hold money in order to redu e the transa tions osts. Indeed, those transa tions osts introdu e a

distortive wedge in the optimal de isions of the households. In parti ular, the transa tion ost wedge

ae ts the real part of e onomy as a negative preferen e sho k to onsumption. The physi al apital

sto k and the non-monetary gold sto k are assumed to depre iate over time at onstant rates. In

the steady state the ination rate is assumed to be zero so that there are no growths in the gold

and money sto ks. The arti ial gold standard e onomy an be perturbated through two exogenous

sto hasti sho ks: the produ tivity sho k in the nal good se tor and the gold ow sho k. In addition,

the entral bank an ae t the state of the e onomy through two monetary poli ies. Spe i ally,

the monetary authority an modify the gold-money ratio through the money multiplier and the gold

ba king ratio (dened as in Bernanke 1995 and Bernanke and Mihov 2000)18. This gold standard

model in ludes two hannels of transmission through whi h the perturbations in any nominal sho k

gold ow sho k, gold ba king sho k, and money multiplier sho k is transmitted to the real

part of the e onomy: the transa tion ost wedge and the optimal ondition on the non-monetary

gold sto k. The transa tion ost wedge represents a bridge between the nominal and the real parts

of the arti ial e onomy be ause it is endogenously linked to the gross nominal interest rate. The

optimal ondition on the non-monetary gold sto k an be interpreted also as a bridge between the

real and the nominal part of the e onomy be ause this optimal ondition states that any hange in

the working of the gold standard hanges in the nominal part of the e onomy would ae t the

onsumption de ision of the households.

Then, I evaluate, through simulation exer ises, whether the gold standard model is useful for the

study of the Great Depression under the gold standard fo us. I on entrate this work on the Fren h

experien e of the Great Depression over the 1929-1936 period. Fran e is an interesting ase study

be ause this ountry has experien ed a deep and long-lasting depression during the 1930s and has

been one the lastest ountry to abandon the gold standard monetary system. Fran e has legally

returned to the gold standard in 1928 with the approval of the monetary law of June 1928. The

fren h monetary law has dened the pri e of the fran in terms of a xed weight of gold19. It has

restored the onvertibility of the fran in gold20. It has imposed a legal minimum for the ratio of

17The link between the money supply and the monetary gold sto k might exist in the Bordo et al. (2007)'s model,

but I do not manage to identify it so far.18A tually, the entral bank annot ontrol, at least dire tly, the money multiplier of the e onomy. In the urrent

framework, sin e the ommer ial banks are not modelized, I treat the money multiplier as a monetary poli y instrument

of the entral bank.19Arti le 2: The fran , the Fren h monetary unit, shall ontain 65.5 milligrams of gold 0.900 ne [.... See Federal

Reserve Board (1928).20Arti le 3: The Bank of Fran e shall guarantee the onvertibility in gold of its notes to bearer and at sight [....

See Federal Reserve Board (1928).

7

monetary gold sto k to the monetary base: the gold reserves of the Bank of Fran e are required

to represent at least 35 per ent of the monetary base21. The monetary law has also forbidden the

Bank of Fran e pur hasing additional foreign ex hanges. Fran e has left the gold standard with the

devaluation its urren y in September 1936. In the literature, the monetary poli ies that Fran e

has undertaken during the interwar period are often onsidered as responsible, at least partly, for

the malfun tioning of the gold standard and hen efore for the worldwide Great Depression. In

parti ular, Fran e is blamed for attra ting too mu h gold to the detriment of other ountries and to

sterilized the gold inows22. The massive gold ows into Fran e and their sterilization would have

exa erbated the de line of money supplies and pri es elsewhere (Nurkse 1944; Ei hengreen 1986;

Bordo and Ma Donald 2003). This leads me to wonder whether those Fren h monetary poli ies are

also responsible for the depression that the ountry has experien ed in the 1930s. The developed

gold standard model might be helpful to answer to this question.

Before onfronting the predi tions of the gold standard model to the Fren h histori al data, I

examine the dynami properties of the model through the impulse response fun tions to the real and

nominal sho ks. The results of the exer ise an be summarized as follows. A transitory in rease of

the gold ow sho k leads the monetary and non-monetary gold sto ks, nominal money and the pri e

level to in rease. The gold ow sho k displays no liquidity ee t as the in rease of the money supply

is not followed by a de line of the nominal interest rate. The ee ts of the gold ow sho k on the

nominal part of the e onomy are strong and highly persistent. The in rease of the gold ow sho k

does ae t the real e onomy. In parti ular, it auses a re ession as output, onsumption, labor and

investment de line. One reason of this is that the in rease of the nominal interest rate raises the

transa tion ost wedge, whi h in turn dis ourages onsumption. However, the ee ts of the gold ow

sho k on the real e onomy are relatively small. A non-permanent de rease of the gold ba king ratio

leads the money sto k and the pri e level to in rease. The monetary gold sto k de lines while the

non-monetary gold sto k rises when the gold ba king is lowered. Contrary to gold ow sho k, the

gold ba king sho k displays a liquidity ee t. The ee ts of the gold ba king sho k on the nominal

part of the e onomy are weaker and less persistent than those of the gold ow sho k. Lowering the

gold ba king ratio leads the real part of the e onomy towards an expansion as output, onsumption,

investment and labor in rease. The expansionary ee t of the de rease of the gold ba king sho k is

partly due to the following me hanism: be ause of the liquidity ee t, the transa tion ost wedge

de lines and hen efore stimulates the households' onsumption. Nevertheless, the ee ts of the gold

ba king sho k on the real part of the e onomy are very weak. I nd that the ee ts of a transitory

in rease of the money multiplier on the e onomy both real and nominal parts of the e onomy

are qualitatively similar to those of a transitory drop in the gold ba king ratio. However, there

are some quantitative dieren es between the ee ts of a de rease of the gold ba king ratio on the

e onomy and those of an in rease of the money multiplier, notably in terms of persisten e. Not

surprisingly, the transitory in rease of the produ tivity sho k has an expansionary ee t on the real

part of the e onomy. Besides, raising the produ tivity in the nal good se tor leads the pri e level,

nominal interest rate the monetary gold sto k and the money sto k to de line. The non-monetary

gold sto k in reases following the produ tivity improvement in the nal good se tor.

In order to onfront the predi tions of the model to the Fren h histori al data, I onstru t time

series for the dierent sho ks onsidered in the arti ial e onomy. I nd that the histori al measures

of the produ tivity sho k, gold ow sho k, gold ba king sho k and money multiplier sho k deviate

strongly from their respe tive 1929 level during the 1930s. Then, I feed the histori al measures of the

real and nominal sho ks, one at a time and in ombination, into the gold standard model to simulate

the latter. The simulation results an be summarized as follows. I nd that the nominal part of

the arti ial gold standard e onomy is mainly ae ted by the histori al nominal sho ks gold ow

sho k, gold ba king sho k and money multiplier while the real part of that arti ial e onomy is

mainly ae ted by the histori al produ tivity sho k. However, with all the histori al sho ks taken

together, the gold standard model is not able to repli ate the Fren h Great Depression. Hen e, in

its state, the model suers from two important problems. First, the hannels of transmission of the

nominal sho ks to the real part of the e onomy are too weak to allow the model to repli ate an

21Arti le 4: The Bank of Fran e shall maintain a metalli reserve in gold bullion and gold oin equal at the minimum

of 35 per ent of the ombined amount of its notes in ir ulation and its liabilities on urrent a ount [.... See Federal

Reserve Board (1928).22The United States fa es the same riti s. A ording to Ei hengreen (1986), more than 60 per ent of the world

monetary gold sto k are in the hands of Fran e and the United States in 1931.

8

histori al event su h as the Great Depression. Se ond, the working of the gold standard in Fran e

during the 1930s seems not to be well aptured by the model. Indeed, for example, the gold standard

model predi ts that the histori al nominal sho ks ause the nominal money sto k and the pri e level

to de line more than what it is observed in the histori al data. As well, in the arti ial gold standard

e onomy, the histori al nominal sho ks lead the nominal interest rate to follows a dierent pattern

to the one followed by the a tual nominal interest rate.

Hen e, the proposed gold standard model is too stylized to be used for an evaluation of the gold

standard-based explanation of the Great Depression in general and in Fran e in parti ular. The

model needs to be improved in several aspe ts. For example, in order to reinfor e the non-neutrality

of the nominal sho ks in the gold standard model, one an introdu e nominal wage regidity in the

model. Besides, the model an be extended to a small open e onomy framework in order to better

apture the international dimension of the gold standard.

The remainder of the paper is organized as follows. Se tion 2 presents in details the gold standard

model. Se tion 2 des ribes the onstru tion of the Fren h histori al data, in luding the measures of

the real and nominal sho ks. Se tion 4 outlines the method used to solve the model, dis usses the

alibration pro edure, and analyzes the steady state properties of the model. Se tion 5 presents the

quantitative analysis of the model to the Fren h Great Depression. Se tion 6 on ludes.

2 A Basi Gold Standard Model

This se tion des ribes the gold standard model and its equilibrium.

2.1 The arti ial e onomy

The arti ial e onomy onsists of three se tors households, nal good produ ers and a entral

bank and of ve ompetitive markets nal good market, labor market, redit (bonds) market,

money market and gold market. In the following, I dis uss ea h se tor and the gold market in

details. Sin e the members of ea h se tor are in large number and identi al, I fo us my attention

on the behavior of a representative member of ea h se tor. Thus, all the variables of the model are

expressed in per apita terms. Besides, I assume that there is no growth in the e onomy.

2.1.1 Central bank

In the lassi al gold standard system, the medium of ex hange, namely money, is partially or

fully dened as laims to units of the ommodity money, that is monetary gold. Those laims an

take the form of bank notes and ommer ial bank deposits. The value of the money sto k an be

larger than the value of the monetary gold sto k, up to a eiling value. I assume that the monetary

gold sto k an be held only by the monetary authority of the e onomy, that is the entral bank23.

The main goal of the entral bank, under the gold standard system, is to defend the onvertibility

of its urren y into gold at a xed pri e. To do so, the entral bank is ommited to buy or sell any

quantity of gold in ex hange of money that private agents ask for, at a xed pri e. Formally, the

money supply rule, under the gold standard system, is stated as follows (see Barro, 1979):

M st =

1

µt

PGGm,t 0 ≤ µt ≤ 1 (1)

where M st denotes the nominal money supply money aggregate M1 , Gm,t the monetary gold

sto k and PG the xed pri e of gold. The variable µt indi ates how mu h the money supply is

tightening up on the monetary gold sto k. The monetary gold sto k is assumed not to depre iate

over time.

Following Bernanke (1995), I de ompose the money-monetary gold ratio, measured by1µt, in two

terms:1

µt

=M s

t

M bt

M bt

Gm,t

(2)

23When the gold standard has been rebuilt after the World War 1, the publi has been asked to bring their monetary

gold sto k ( oins and bullions) to entral banks in order to deal with the s ar ity of the money ommodity.

9

where M bt denotes the monetary base24. The rst term in equation (2), the ratio of money supply

to monetary base, is alled the money multiplier and is assumed to be larger than one. Indeed,

in e onomies with a fra tional-reserve banking system the total amount of money supply money

aggregate M1 ex eeds the amount of monetary base. A ording to Bernanke (1995), the money

multiplier is an indi ator of the degree of development of the nan ial system of an e onomy: Closer

to unity the money multiplier is, less the nan ial system is developed.

The se ond term of equation (2), the ratio of monetary base to monetary gold, is alled the inverse

of gold ba king ratio or alled the overage ratio. The inverse of gold ba king ratio is reglemented by

the publi authority. In parti ular, the monetary base-monetary gold ratio is bounded by a eiling

value. For example, in Fran e, following the monetary law of June 1928, the value of the monetary

gold sto k of the Bank of Fran e must be larger or equal to 35 per ent of the amount of its monetary

base. Nonetheless, as noted by Bernanke (1995), the overage ratio is not bounded by a oor.

Hen e, the gold standard money supply rule, presented in equation (1), an be restated as follows

M st =

1

µ1,t

1

µ2,t

PGGm,t 0 ≤ µ1,t, µ2,t ≤ 1

with1

µ1,t

≡ M st

M bt

,1

µ2,t

≡ M bt

Gm,t

(3)

In equation (3), µ1,t denotes the inverse of the money multiplier and µ2,t the gold ba king ratio.

Sin e, the nan ial-banking se tor is not expli itely introdu ed in the model, variables µ1,t and µ2,t

are taken exogenously. The exogenous sto hasti pro ess followed by µ1,t and µ2,t, are des ribed

below.

2.1.2 Households

The representative household gets satisfa tions from having a onsumption good, having leisure

and holding a gold sto k for non-monetary purposes. Households are about non-monetary gold

sto k be ause they reap a benet from the latter in the form of, for example, jewelry, ornamentation

or safe asset. Several authors, su h as Goodfriend (1988), Velde and Weber (2000), and Bordo et al.

(2007), make the assumption that non-monetary gold sto k yields satisfa tion to households. Gold is

introdu ed in the model for non-monetary uses be ause, together with gold produ tion, it represents a

major ausal fa tor of the monetary gold sto k. Barro (1979) emphasizes this point, refering to Irvin

Fisher25. In addition, following Barro (1979), the non-monetary gold sto k is assumed to depre iate

over time at a onstant rate. A ording to M Callum (1989), the depre iation of non-monetary gold

sto k measures the unavoidable losses to whi h the total gold sto k is subje t. Leisure is measured

as the share of the representative household's total time endowment, normalized to unity, spent in

non-market a tivities.

Thus, the household's preferen es are stated over onsumption, denoted Ct, non-monetary gold

sto k, denoted Gc,t, and leisure time, denoted 1− ht where ht is labor supply. Those preferen es are

des ribed by an expe ted intertemporal utility fun tion of the form

E0

∞∑

t=0

βtU (Ct − bCt−1, Gc,t, 1 − ht) 0 ≤ b < 1 (4)

where Et denotes the expe tation operator onditional on the period-t information set, β is a sub-

je tive dis ount fa tor and U (·) is a period-t utility measure. Note that the period-t information set

of the representative household in ludes the realizations of all endogenous variables of the e onomy,

24Bernanke (1995) onsiders a more general de omposition of the money-monetary gold ratio:

1

µt

=Ms

t

M bt

M bt

Rest

Rest

Gm,t

where Rest is the international reserves of the Central Bank, in luding monetary gold and foreign assets.25As stressed by Fisher, [..., the two key determinants of the monetary gold sto k in a dynami ontext are gold

produ tion and the extent to whi h gold is held for non-monetary purposes. Quoted from Barro (1979).

10

as well as the exogenous sho ks, through period t. Note that the parameter b introdu es internal

habit formation in onsumption when it is stri tly positive. Several authors, among them Fuhrer

(2000), Christiano et al. (2001), argue that habit formation in onsumption is helpful to under-

stand the monetary propagation me hanism for the post-war period. Spe i ally, those authors nd

that a positive money supply sho k auses a de rease in the real interest rate and a hump-shaped

in rease in onsumption. A ording to those authors, introdu ing internal habit formation in on-

sumption allows monetary models to repli ate those fa ts. Indeed, in absen e of habit formation in

onsumption, the optimal hoi es of households lead the urrent onsumption to be larger than the

(expe ted) next period onsumption when the real interest rate de reases. With internal habit for-

mation in onsumption, households are about the variations in onsumption rather than about the

level of onsumption. Therefore, in that ase, the optimal hoi es of households state that the urrent

hange in onsumption is higher than the next period hange in onsumption when the real interest

rate falls. It follows that the response of onsumption to a money supply sho k is hump-shaped.

Furthermore, as it will be shown below, habit formation in onsumption allows investment to be

pro y li al following an in rease of the gold ow sho k or the inverse of money multiplier sho k even

though the latter are not highly persistent. Finally, the utility fun tion, U (Ct − bCt−1, Gc,t, 1 − ht),satises the following standard properties

U1,t ≡∂U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (Ct − bCt−1)> 0, U11,t ≡

∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (Ct − bCt−1)2 < 0

U2,t ≡∂U (Ct − bCt−1, Gc,t, 1 − ht)

∂Gc,t

> 0, U22,t ≡∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂G2c,t

< 0

U3,t ≡∂U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (1 − ht)> 0, U33,t ≡

∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (1 − ht)2 < 0

U12,t ≡∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (Ct − bCt−1) ∂Gc,t

= U21,t ≤ 0, U13,t ≡∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂ (Ct − bCt−1) ∂ (1 − ht)= U31,t ≤ 0

U23,t ≡∂2U (Ct − bCt−1, Gc,t, 1 − ht)

∂Gc,t∂Gc,t

= U32,t ≤ 0

Hen e, the utility fun tion is stri tly in reasing in its three arguments, and stri tly on ave. Addi-

tionally, the preferen es are allowed to be non-separable over onsumption, non-monetary gold sto k

and leisure.

In the beginning of ea h period, the representative household is endowed with the new gold ow,

gst , whi h value is given by PGgs

t . This new ow of gold is added to the net of depre iation non-

monetary gold sto k of the household. Then, the representative household de ides how mu h of

the newly a umulated non-monetary gold sto k is going to be ex hanged against money with the

entral bank, at the xed pri e PG, a ordingly to the money supply rule (3) and how mu h is going

to be used for its own satisfa tion. Therefore, variable Gc,t represents the sto k of non-monetary gold

on e the gold-money trade between the household and the entral bank is realized. For the sake of

simpli ity, I assume that the osts of minting gold to spe ies that is osts of onverting gold to

monetary gold are negligeable.

Households demand money be ause it fa iliates the a ess to the onsumption good. Indeed,

households fa e transa tions osts whi h are inherent to the pur hase of the onsumption good.

Those transa tions osts in rease proportionally to the volume of the onsumption good. Households

an redu e the transa tions osts by holding money. In other words, the transa tions osts rise with

the onsumption-based velo ity of money. The latter, denoted vt, is formally dened as follows:

vt =PtCt

Mdt

(5)

where Pt is the pri e level, Mdt denotes the nominal money sto k demanded by the representative

household.

Following S hmitt-Grohé and Uribe (2004, 2006), the transa tion ost fun tion, denoted L (vt),is assumed to satisfy the following properties:

11

(i) L (vt) is non-negative and twi e ontinuously dierentiable;

(ii) there exists a satiation level of onsumption-based velo ity of money, denoted v > 0, su h that

L (v) = L′ (v) = 0;

(iii) (v − v) L′ (v) > 0 for v 6= v;

(iv) 2L′ (v) + vL′′ (v) > 0 for v ≥ v.

Assumption (ii) ensures that a zero nominal interest rate Friedman rule does not mean that

the demand of money is innite. Besides, this assumption makes the ost of transa tions as well as

the implied distortions fade away when the nominal interest rate takes a value of zero. Assumption

(iii) states that the equilibrium onsumption-based money velo ity is always larger than the satiation

level v. Assumption (iv) garantees that the demand of money falls when the nominal interest rate

rises26.

Moreover, ea h period, households an get an other asset, that is a full set of nominal state-

ontingent bonds, at ost Bt. The nominal pay-o for bonds is given by qt−1Bt−1, where qt represents

the gross nominal interest rate.

The representative household also pur hases an investment good, denoted It, at pri e Pt and uses

it to a umulate its sto k of apital, Kt, as follows,

Kt = (1 − δk) Kt−1 + It (6)

where δk is the apital depre iation rate. The representative household rents its sto k of apital to

the nal good produ ers at the rental pri e Rt.

Ea h period, the representative household supplies its labor for e to the representative nal good

produ er and re eives, in ounterpart from the latter, a wage bill of total amount Wtht, where Wt

denotes the nominal hourly wage rate.

In addition, households are assumed to own rms whi h produ e the nal good. Therefore,

households re eive the prots realized by the produ ers.

The intratemporal budget onstraint of the representative household is given by

PtCt (1 + L (vt)) + PGGc,t + PtIt + Bt + Mdt + Tt ≤

Wtht + RtKt−1 + qt−1Bt−1 + Mdt−1 + (1 − δg) PGGc,t−1 + Φt + PGgs

t + TRt

(7)

Φt denotes the prots realized by the nal good produ ers. δg indi ates the non-monetary gold

depre iation rate. Tt represents a lump-sum transfer from households to the entral bank inherent to

the gold-money trade. TRt is a lump-sum transfer from the entral bank to households. The purposes

of the two transfers, Tt and TRt, are dis ussed below. The left-hand side of the budget onstraint

des ribes the uses of the representative household wealth: Pur hases of onsumption good, investment

good and state- ontingent bonds, holdings of non-monetary gold and money sto ks, payment of the

transa tions osts and payment of the lump-sum transfer to the entral bank. The right-hand side

des ribes the sour es of wealth: Labor and apital in omes, prots from nal good produ ers, interests

on bonds a quired in the previous period, money sto k and net of depre iation non-monetary gold

sto k brought from the previous period, new ow of gold, and the re eipt of lump-sum transfer from

the entral bank.

The representative household is supposed to hoose sequen es for Ct, Gc,t, It, ht, Mdt , Kt and Bt

whi h maximize its expe ted intertemporal utility fun tion (4), subje t to its intratemporal budget

onstraint (7), the apital a umulation law (6) and the expression of the onsumption-based velo ity

of money (5), and taking pri e level, Pt, pri e of gold PG, nominal wage, Wt, nominal apital rental

pri e, Rt, gross nominal interest rate on bonds, qt, rms prots, Φt, newly produ ed gold, gst , lump-

sum transfer, Tt, and the initial onditions, C−1, Gc,−1, K−1, Md−1, B−1, as given.

26For more details on this spe i ation of the transa tion ost fun tion, the reader is referred to S hmitt-Grohé and

Uribe (2004, 2006)

12

2.1.3 Final good produ ers

The representative rm makes use of a onstant return to s ale te hnology to produ e its nal

good,

Yt ≤ ztF (Kt−1, ht) (8)

The fa tor inputs used by this te hnology are apital, Kt−1, and labor, ht. Yt denotes the quantity

of the nal good, or output, produ ed by the representative rm. zt represents a sto hasti neutral

produ tivity sho k to the nal good produ tion te hnology. Hereafter, I refer to zt as the produ tivity

sho k. It is determined exogenously by a sto hasti pro ess, whi h I spe ify below. The produ tion

fun tion F (·) is assumed to satisfy the following standard properties:

F1,t ≡∂F (Kt−1, ht)

∂Kt−1

> 0, F11,t ≡∂2F (Kt−1, ht)

∂K2t−1

< 0

F2,t ≡∂F (Kt−1, ht)

∂ht

> 0, F22,t ≡∂2F (Kt−1, ht)

∂h2t

< 0

Hen e, the produ tion fun tion is stri tly in reasing in its two arguments and is stri tly on ave.

The representative rm makes prots

Φt = PtYt − Wtht − RtKt−1 (9)

by selling its output, Yt, at the market pri e, Pt, and paying its labor and apital inputs, Kt−1 and

ht, at their respe tive market pri e, Wt and Rt.

The representative rm hooses the quantities of apital and labor inputs, Kt−1 and ht, to max-

imize its prots, (9), subje t to the te hnology of produ tion onstaint, (8), taking the pri e level,

Pt, the nominal rental rate of apital, Rt, and the nominal hourly wage, Wt, as given.

2.1.4 Gold market

In this model, the gold mining se tor is not dened. Instead and as a simpli ation, I onsider the

gold supply in terms of gold ow between the e onomy and a no identied pla e outside the e onomy.

In addition, the gold ows are taken exogenously by the agents of the e onomy. In parti ular, ea h

period, a new ow of gold is exogenously shipped to (from) households from (to) a pla e outside the

e onomy. Therefore, the demand for new gold is onstrained by the supply side.

In this e onomy, gold has two fun tions: (i) Gold is used by households for non-monetary purpose,

Gc,t; (ii) the entral bank bases its monetary poli y on its gold reserves, Gm,t. Thus, the total demand

for gold in the e onomy, denoted Gdt , is given by the sum of non-monetary gold sto k and monetary

gold sto k:

Gdt = Gm,t + Gc,t (10)

It follows that the total demand for new gold, denoted gdt , is given by

gdt = Gd

t − Gdt−1 + δgGc,t−1 (11)

The supply of new gold, denoted gst , is assumed to follow an exogenous sto hasti pro ess that I

spe ify the form below.

Note that the supply of new gold, gst , an be either positive or negative. In the former ase, there

is a gold inow in the e onomy while in the latter ase there is an outow of gold from the e onomy.

2.1.5 Exogenous sho ks

The arti ial e onomy is subje t to four exogenous sto hasti sho ks. These are the produ tivity

sho k, zt, the inverse of money multiplier sho k, µ1,t, the gold ba king sho k, µ2,t, and the gold ow

sho k, gst .

I assume that the exogenous variables zt, µ1t, µ2,t and gst are orthogonal to ea h other and follow

autoregressive pro esses of order one. The latters are dened su h that:

ln zt = (1 − ρz) ln z + ρz ln zt−1 + εz,t (12)

13

where εz,t ; i.i.d. (0, σ2z) and z−1 is given.

ln µ1,t = (1 − ρµ1) ln µ1 + ρµ1 ln µ1,t−1 + εµ1,t (13)

where εµ1,t ; i.i.d.(0, σ2

µ1

)and µ1,−1 is given.

ln µ2,t = (1 − ρµ2) ln µ2 + ρµ2 ln µ2,t−1 + εµ2,t (14)

where εµ2,t ; i.i.d.(0, σ2

µ2

)and µ2,−1 is given.

gst = (1 − ρgs) gs + ρgsgs

t−1 + εgs,t (15)

where εgs,t ; i.i.d.(0, σ2

gs

)and gs

−1 is given. The variables written without time subs ript denote

the steady state levels.

The produ tivity sho k, zt, measures the e ien y with whi h the fa tor inputs are used in the

nal good se tor. The inverse of the money multiplier sho k, µ1,t, measures the degree of development

of the nan ial-banking system of the e onomy. In other words, an in rease of the money multiplier

a de rease of µ1,t means that the e onomy is able to provide a larger volume of instruments of

payment (in addition to bank notes) to the e onomi agents. The gold ba king sho k, µ2,t, represents

the poli y instrument of the entral bank in terms of money supply. By rising the gold ba king ratio,

the entral bank would ondu t a restri tive monetary poli y: Following a positive sho k to the gold

ba king ratio, the size of the issued money is redu ed. Hereafter, I onsider the inverse of the money

multiplier sho k, µ1,t, and the gold ba king sho k, µ2,t, as being two money supply sho ks. The gold

ow sho k, gst , indi ates whether the e onomy is subje t to an entry of new gold or an exit of existing

gold.

2.2 Solving the agents' optimization problems

The agents' optimization problems stated above fo us only on interior solutions, that is all the

quantities of endogenous variables are supposed to be stri tly positive. In this subse tion, I present

the solutions of these problems and the asso iated market learing onditions.

2.2.1 Household's optimization problem

After ombining the household's budget onstraint (7), the apital a umulation law (6) and the

expression of onsumption-based velo ity of money (5), the representative household's optimization

problem an be stated as follows

maxCt,Gc,t,ht,M

dt ,Bt,Kt

E0

∞∑

t=0

βtU (Ct − bCt−1, Gc,t, 1 − ht)

subje t to

PtCt

(

1 + L

(PtCt

Mdt

))

+ PGGc,t + Pt [Kt − (1 − δk) Kt−1] + Bt + Mdt + Tt

= Wtht + RtKt−1 + qt−1Bt−1 + Mdt−1 + (1 − δg) PGGc,t−1 + Φt + PGgs

t + TRt

(16)

The Lagrangian asso iated to the representative household's optimization problem is given by

LH =∞∑

t=0

βt

U (Ct − bCt−1, Gc,t, 1 − ht) +λt

Pt

[Wtht + RtKt−1 + qt−1Bt−1 + Md

t−1 + (1 − δg) PGGc,t−1+

+Φt + PGgst + TRt − PtCt

(

1 + L

(PtCt

Mdt

))

− PGGc,t − Pt [Kt − (1 − δk) Kt−1] − Bt − Mdt − Tt

]

14

whereλt

Ptis the Langrange multiplier asso iated to the budget onstraint. The rst order onditions

of (16) with respe t to Ct, Gc,t, ht, Mdt , Bt and Kt, in that order, are

λt [1 + L (vt) + vtL′ (vt)] = U1,t − bβEt (U1,t+1) (17)

λt

PG

Pt

= U2,t + β (1 − δg) Et

(

λt+1PG

Pt+1

)

(18)

U3,t = λt

Wt

Pt

(19)

λt = λtv2t L

′ (vt) + βEt

(

λt+1Pt

Pt+1

)

(20)

λt = qtβEt

(

λt+1Pt

Pt+1

)

(21)

λt = βEt

(

λt+1

[Rt+1

Pt+1

+ 1 − δk

])

(22)

The onsumption-based velo ity of money denition, (5), the apital a umulation law, (6), and

the household's intertemporal budget onstraint, (7), holding with equality, omplete the set of

household's optimization problem rst order onditions. There are also transversality onditions

whi h an be ignored in regards to the purpose of the study.

The optimality ondition (17) states that the expe ted marginal utility of urrent onsumption,

U1,t − bβEt (U1,t+1), must be equal to the opportinity ost of the additional onsumption in period t,λt [1 + L (vt) + vtL

′ (vt)]. From that equation, note that the transa tions osts put a wedge between

the expe ted marginal utility of onsumption and the marginal utility of wealth, λt. A ording to the

properties of the transa tion ost fun tion, presented above, this wedge vanishes if the onsumption-

based velo ity of money is at its satiation level.

The optimality ondition (18) states that the marginal benet of an additional unit of non-

monetary gold in period t must be equal to the opportunity ost of holding that additional unit of

non-monetary gold, in terms of expe ted marginal utility of urrent onsumption, λtPG

Pt, in period

t. The marginal benet of an additional unit of non-monetary gold omes from, on the one hand,

the marginal utility brought by the non-monetary gold sto k, U2,t, on the other hand, the present

expe ted value of that additional unit of non-monetary gold net of depre iation brought to the

household's resour es in the next period, measured in terms of expe ted marginal utility of future

onsumption, β (1 − δg) Et

(

λt+1PG

Pt+1

)

.

The optimality ondition (19) states that the marginal utility of urrent leisure, U3,t, has to be

set equal to the opportinity ost of that additional leisure at time t, evaluated in terms of expe ted

marginal utility of urrent onsumption, λtWt

Pt.

The optimality ondition (20) states that the marginal benet of an additional unit of money in

period t must be equal to the opportunity ost of holding that additional unit of money, in terms

of expe ted marginal utility of urrent onsumption, λt, in period t. The marginal benet of an

additional unit of money onsists of two elements. First, holding additional money redu es the

transa tions osts. This rst marginal benet, measured in terms of expe ted marginal utility of

urrent onsumption, is given by λtv2t L

′ (vt). Se ond, holding additional money brings resour es to

the household's budget in the future. This se ond marginal benet, measured in terms of expe ted

marginal utility of future onsumption, is evaluated in the urrent period by βEt

(

λt+1Pt

Pt+1

)

.

The optimality ondition (21) states that the present expe ted value of a marginal unit of bond

brought to the household's resour es in the next period, measured in terms of expe ted marginal

utility of future onsumption, qtβEt

(

λt+1Pt

Pt+1

)

, must equal the opportunity ost of holding that

marginal unit of bond in the urrent period, evaluated in terms of expe ted marginal utility of

urrent onsumption, λt.

15

The optimality ondition (22) states that the expe ted value of future apital returns, in terms

of expe ted marginal utility of future onsumption, βEt

(

λt+1

[Rt+1

Pt+1+ 1 − δk

])

, has to be set equal

to the opportunity ost of holding that additional apital in the urrent period, in terms of expe ted

marginal utility of urrent onsumption, λt.

In the following, I denote κt the wedge introdu ed by the transa tions osts:

κt = 1 + L (vt) + vtL′ (vt) (23)

A ording to the properties of the transa tion ost fun tion, the wedge, κt, in reases with the

onsumption-based velo ity of money. This wedge resembles to a onsumption tax rate in the way it

distorts the representative household's optimization problem. The fri tions that transa tions osts

introdu e in the e onomy represent a transmission hannel of the gold ow sho ks and the two money

supply sho ks to the real part of the e onomy. Indeed, as it will be shown later, the transa tion ost

wedge is endogenously driven by the gross nominal interest rate, qt.

Combining equations (17) and (18) leads to

[U1,t − bβEt (U1,t+1)

κt

]PG

Pt

− U2,t = β (1 − δg) Et

([U1,t+1 − bβEt (U1,t+2)

κt+1

]PG

Pt+1

)

(24)

Hen e, equation (24) denes a non-monetary gold pri ing fun tion. Note that the pri ing of non-

monetary gold is expressed in terms of onsumption good: The key pri e variable in equation (24)

isPG

Pt, that is the relative pri e of gold or real pri e of gold. Goodfriend (1988) derives a similar

non-monetary gold pri ing fun tion. Besides, the transa tions osts alter the optimal non-monetary

gold demand de ision.

Combining equations (17) and (19) leads to

U3,t

U1,t − bβEt (U1,t+1)κt =

Wt

Pt

(25)

From equation (25), one an observe that the existen e of transa tions osts prevents the expe ted

marginal rate of substitution of onsumption for leisure,U3,t

U1,t−bβEt(U1,t+1), from being equal to the real

wage,Wt

Pt. Spe i ally, the transa tions osts alter the optimal behavior of households in terms of

onsumption and labor supply. Hen e, given the real wage and if preferen es are non-separable

the non-monetary gold sto k, a higher onsumption-based velo ity of money (higher wedge) leads

households to onsume less and to redu e their labor supply.

Combining equations (17) and (20) leads to

v2t L

′ (vt) = 1 − βEt

([U1,t+1 − bβU1,t+2

U1,t − bβU1,t+1

]κt

κt+1

Pt

Pt+1

)

(26)

Equation (26) represents a pri ing equation for money. Note that the transa tions osts distort the

pri ing equation for money.

Combining equations (17) and (21) leads to

1

qt

= βEt

([U1,t+1 − bβU1,t+2

U1,t − bβU1,t+1

]κt

κt+1

Pt

Pt+1

)

(27)

Equation (27) represents a pri ing equation for the nominal bonds. This equation states that the

gross nominal interest rate, qt, is in reasing with the expe ted next period ination, Et

(Pt

Pt+1

)

, and

in reasing with the expe ted marginal rate of substitution of future onsumption for urrent on-

sumption, Et

(U1,t−bβU1,t+1

U1,t+1−bβU1,t+2

)

. In other words, the gross real interest rate, qtEt

(Pt

Pt+1

)

, is in reasing

with the expe ted marginal rate of substitution of future onsumption for urrent onsumption. In

addition, one an note that the transa tions osts distort the pri ing equation for nominal bonds.

16

Combining equations (17) and (21) leads to

1 = βEt

([U1,t+1 − bβU1,t+2

U1,t − bβU1,t+1

]κt

κt+1

[Rt+1

Pt+1

+ (1 − δk)

])

(28)

From equation (28), one an note that the transa tions osts introdu e an intertemporal wedge,

Et

(κt

κt+1

)

, between the expe ted marginal rate of substitution of future onsumption for urrent

onsumption, Et

(U1,t−bβU1,t+1

U1,t+1−bβU1,t+2

)

, and the real interest rate, Et

(Rt+1

Pt+1+ 1 − δk

)

.

From the previous Euler equations (24), (26), (27) and (28), one an observe that the weight

that the representative household puts on the present omparatively to the future is higher when it

determines optimally the sequen e of non-monetary gold sto k than when it determines optimally the

sequen es of money, bond and apital sto ks. The household behaves so be ause the non-monetary

gold depre iates over time27. While it uses the subje tive dis ount fa tor, β, when it determines

the optimal sequen es of money, bonds and apital, it dis ounts the future with β (1 − δg) when it

hooses the optimal sequen e of non-monetary gold sto k. Hen e, higher the non-monetary gold

depre iation rate is, lower the value of non-monetary gold be omes in the future omparatively to its

urrent value.

The household's optimal de ision on the non-monetary gold holding happens to be an additional

hannel through whi h the gold ow sho k and the two money supply sho ks are transmitted to

the real part of the e onomy. Indeed, as shown in equation (24), the household's optimal de isions

in terms of onsumption and non-monetary gold are linked to ea h other. It is worth to note that

if preferen es are non-separable in onsumption, leisure and non-monetary gold, then labor and

non-monetary gold also feature in the Euler equations (24), (26), (27) and (28). Therefore, the

non-separability hypothesis on the household's utility fun tion may reinfor e this hannel.

Besides, from ombining (26) and (27), one an get the following expression

1 − 1

qt

= v2t L

′ (vt) (29)

The left-hand side of (29), dening the opportunity ost of holding money instead of bonds, is an

in reasing fun tion of the gross nominal interest rate qt. The right-hand side of (29) is an in reasing

fun tion of the onsumption-based velo ity of money, vt, a ording to the assumptions made on the

transa tion ost fun tion L (·). One an interpret this equation as a liquidity preferen e fun tion

whi h is de reasing with gross nominal interest rate and has an elasti ity in onsumption of one (see

S hmitt-Grohé and Uribe, 2006).

Furthermore, rearranging terms in equation (24),

1 =Pt

PG

U2,t

U1,t − bβEt (U1,t+1)κt + (1 − δg) βEt

([U1,t+1 − bβEt (U1,t+2)

U1,t − bβEt (U1,t+1)

κt

κt+1

]PG

Pt+1

Pt

PG

)

and using equation (27), one gets

1 =Pt

PG

U2,t

U1,t − bβEt (U1,t+1)κt + (1 − δg)

1

qt

⇔ PG

Pt

(

1 − 1 − δg

qt

)

= κt

U2,t

U1,t − bβEt (U1,t+1)(30)

Hen e, equation (30) shows that the expe ted marginal rate of substitution of onsumption for non-

monetary gold,U2,t

U1,t−bβEt(U1,t+1), depends not only on the real pri e of gold,

PG

Pt, but also on the gross

nominal interest rate, qt. In parti ular, the expe ted marginal rate of substitution of onsumption for

27The apital sto k also depre iates over time. However, the apital depre iation rate is used to dene the real return

on apital rather than to dis ount the future. Indeed, apital is remunetated, whi h is not the ase of non-monetary

gold.

17

non-monetary gold is in reasing with the real pri e of gold and the gross nominal interest rate. Note

that the transa tions osts alter the onsumption-non-monetary gold margin through the wedge, κt.

I have stressed that the transa tion ost wedge and the optimal de ision on non-monetary gold

holding represent two hannels of transmission of the gold ow sho k and the two money supply

sho ks to the real part of the arti ial e onomy. I dis uss these two hannels of transmission more

in details when I analyse the dynami properties of the gold standard model.

2.2.2 Final good produ er's problem

The representative nal good produ er's problem an be stated as follows,

maxht,Kt−1

PtYt − RtKt−1 − Wtht

subje t to Yt ≤ ztF (Kt−1, ht)(31)

The rst order onditions of (31) with respe t to ht and Kt−1, in that order, are

Wt

Pt

= ztF2,t (32)

Rt

Pt

= ztF1,t (33)

Hen e, equation (32) states that rms hire workers until the point where the marginal produ t

of labor, ztF2,t, is equal to the real wage,Wt

Pt. As well, equation (33) states that rms use apital

servi es until the point where the marginal produ t of apital, ztF1,t, is equal to the real rental pri e

of apital.Rt

Pt.

The te hnology onstraint, (8), holding with equality, ompletes the set of nal good produ er's

problem rst order onditions:

Yt = ztF (Kt−1, ht) (34)

2.2.3 Market learing onditions

Here, I dis uss the market learing onditions in the gold market, money market, bond market

and nal good market.

2.2.3.1 Market learing ondition in the gold market

In the equilibrium, the gold market must satisfy the following equation

gdt = gs

t (35)

Hen e, in the equilibrium, the gold ow demand, gdt , is supposed to be equal to the gold ow supply,

gst .

Using equation (11), the previous gold market equilibrium ondition an be restated as an a u-

mulation equation

Gdt − Gd

t−1 = gst − δgGc,t−1 (36)

The left-hand side of the gold market learing equation represents the hange of the total gold sto k

demand, while the right-hand side represents the ow of new gold net of the non-monetary gold

depre iation. Besides, equation (36) states that, in any period t, the total gold sto k in reases

(de reases) if, at the equilibrium relative pri e of gold,PG

Pt, the new gold ow, gs

t , is larger (lower)

than the depre iation of the non-monetary gold sto k, δgGc,t−1.

18

2.2.3.2 Market learing onditions in the money market and bond market

The market learing onditions in the money market and the bond market are dened as follows:

Mdt = M s

t = Mt (37)

Bt = Bt−1 = 0 (38)

Hen e, equation (37) states simply that, in the equilibrium, money supply and money demand

must oin ide. In turn, equation (38) states that the representative household does not hold bonds

in the equilibrium, sin e the bond market is omplete.

2.2.3.3 Market learing ondition in the nal good market

The resour e onstraint of the e onomy, dening how the output is absorbed in the equilibrium,

is dedu ed from the household's budget onstraint, (7), holding with equality.

Hen e, ombining equations (9), (10), (36), (37) and (38) with the household's budget onstraint

(7), one gets

PtCt (1 + L (vt)) + PtIt + Tt = PtYt + PG (Gm,t − Gm,t−1) − (Mt − Mt−1) + TRt

As said above, the gold trade between the representative household and the entral bank leads to a

lump-sum transfer from the former to the latter, Tt. In parti ular, this transfer is supposed to over

the dieren e between the value of the new ow of monetary gold and the value of the new ow of

money: Tt = PG (Gm,t − Gm,t−1)−(Mt − Mt−1). An additional lump-sum transfer is realized between

the representative household and the monetary authority, whi h, this time, goes from the latter to

the former. More pre isely, following Kim and Subramanian (2006), I assume that the entral bank

pays ba k the transa tions osts to households in a lump-sum way: TRt = PtCtL (vt). Therefore,

the resour e onstraint of the e onomy is given by

Yt = Ct + It (39)

Thus, output is absorbe by onsumption and investment. The transa tions osts are rebated to

households be ause they are onsidered as a private ost and not as a so ial ost28.

2.2.4 Fun tional forms

I use the following fun tional form for the households' preferen es:

U (Ct − bCt−1, Gc,t, 1 − ht) =

h

(Ct−bCt−1)φ1 (1−ht)

φ2Gφ3c,t

i1−φ4−1

1−φ4if φ4 6= 1

φ1 ln (Ct − bCt−1) + φ2 ln (1 − ht) + φ3 ln (Gc,t) if φ4 = 1

where φ1 + φ2 + φ3 = 1 and φ4 > 0.It follows from the denition of household preferen es that the partial derivatives of the utility

fun tion with respe t to its arguments are

U1,t = φ1Ω1−φ4

t

Ct − bCt−1

U3,t = φ2Ω1−φ4

t

1 − ht

U2,t = φ3Ω1−φ4

t

Gc,t

28In addition, this assumption allows to eliminate the wealth ee t. The reader is refered to Kim and Subramanian

(2006) for more details.

19

where Ωt = (Ct − bCt−1)φ1 (1 − ht)

φ2 Gφ3c,t.

I assume that the produ tion fun tion used by nal good produ ers is a Cobb-Douglas of the

form:

F (Kt−1, ht) = Kθt−1h

1−θt

where 0 < θ < 1.It follows from the denition of the produ tion te hnology of nal good produ ers that the partial

derivatives of the produ tion fun tion with respe t to its arguments are

F1,t = θKθ−1t−1 h1−θ

t

= θF (Kt−1, ht)

Kt−1

F2,t = (1 − θ) Kθt−1h

−θt

= (1 − θ)F (Kt−1, ht)

ht

Following S hmitt-Grohé and Uribe (2004), I assume the following fun tional form for the trans-

a tions osts

L (vt) = γ1vt + γ21

vt

− 2√

γ1γ2

Thus, some useful expressions with the derivative of the transa tion ost fun tion are given below

L′ (vt) = γ1 − γ21

v2t

vtL′ (vt) = γ1vt − γ2

1

vt

v2t L

′ (vt) = γ1v2t − γ2

It is worth to note the satiation level of onsumption-based velo ity of money v is given by

L′ (v) = 0

⇔ γ1 − γ21

v2= 0

⇔ 1

v2=

γ1

γ2

⇔ v =

(γ2

γ1

) 12

2.3 Equilibrium

The stationary non-linear equilibrium equations of the gold standard e onomy are (3), (5), (6),

(10), (23), (24), (25), (26), (28), (29), (32), (33), (34), (36), (37) and (39).

Below, I restate the stationary non-linear equilibrium equations using the fun tional forms dened

above. Before doing so, I pro eed to the following hange of variables:

wt =Wt

Pt

, rt =Rt

Pt

, pg,t =PG

Pt

, mt =Mt

Pt

(40)

whi h denotes, respe tively, real wage, real rental pri e of apital, real pri e of gold and real money

balan es. Indeed, wage and rental pri e of apital are always expressed in real terms in the rst order

onditions of households and rms. Besides, it is onvenient for the analysis of the gold standard

model to fo us on the real pri e of gold rather than on the pri e level. Therefore, it is also onvenient

20

to express money in real terms in the equilibrium equations29. Anyway, sin e the pri e of gold is

assumed xed, it is easy to ome ba k to denition of the pri e level.

The money supply rule, (3), is restated as follows

mt =1

µ1,t

1

µ2,t

pg,tGm,t (41)

The onsumption-based velo ity of money, (5), is restated as follows

vt =Ct

mt

(42)

The apital a umulation law is

Kt = (1 − δk) Kt−1 + It (6)

The total gold sto k demand is

Gdt = Gc,t + Gm,t (10)

The transa tion ost wedge, (23), is restated as follows

κt = 1 + 2γ1vt − 2√

γ1γ2 (43)

The non-monetary gold pri ing equation, (24), is restated as follows

pg,t

κt

[

(1 − ht)φ2 G

φ3c,t

]1−φ4

(Ct − bCt−1)1−φ1(1−φ4)

− bβEt

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

−

− φ3

φ1

[

(Ct − bCt−1)φ1 (1 − ht)

φ2

]1−φ4

G1−φ3(1−φ4)c,t

= (1 − δg) βEt

(pg,t+1

κt+1

×

×

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

− bβ

[

(1 − ht+2)φ2 G

φ3

c,t+2

]1−φ4

(Ct+2 − bCt+1)1−φ1(1−φ4)

(44)

The optimal labor supply ondition, (25), is restated as follows

φ2

φ1

[

(Ct − bCt−1)φ1 G

φ3c,t

]1−φ4

(1 − ht)1−φ2(1−φ4)

[

(1 − ht)φ2 G

φ3c,t

]1−φ4

(Ct − bCt−1)1−φ1(1−φ4)

− bβEt

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

−1

=wt

κt

(45)

The Euler equation for money demand, (26), is restated as follows

γ1v2t − γ2 = 1 − βEt

κt

κt+1

pg,t+1

pg,t

[

(1 − ht)φ2 G

φ3c,t

]1−φ4

(Ct − bCt−1)1−φ1(1−φ4)

− bβ

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

−1

×

×

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

− bβ

[

(1 − ht+2)φ2 G

φ3

c,t+2

]1−φ4

(Ct+2 − bCt+1)1−φ1(1−φ4)

(46)

29For example, if the pri e level is expressed only relatively to the gold pri e, money must be stated in real terms

to make the money supply rule, (3), onsistent.

21

The optimal intertemporal onsumption de ision, (28), is restated as follows

1

κt

[

(1 − ht)φ2 G

φ3c,t

]1−φ4

(Ct − bCt−1)1−φ1(1−φ4)

− bβEt

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

=

= βEt

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

− bβ

[

(1 − ht+2)φ2 G

φ3

c,t+2

]1−φ4

(Ct+2 − bCt+1)1−φ1(1−φ4)

[rt+1 + 1 − δk

κt+1

]

(47)

The liquidity preferen e fun tion, (29), is restated as follows

γ1v2t − γ2 = 1 − 1

qt

(48)

The optimal labor demand ondition, (32), is restated as follows

wt = (1 − θ)Yt

ht

(49)

The optimal apital demand ondition, (33), is restated as follows

rt = θYt

Kt−1

(50)

The produ tion te hnology onstraint is

Yt = ztKθt−1h

1−θt (51)

The total gold sto k a umulation law is

Gdt = Gd

t−1 − δgGc,t−1 + gst (36)

The resour e onstraint of the e onomy is

Yt = Ct + It (39)

In addition, I dene the real interest rate equilibrium equation

rt = qtEt

(pg,t+1

pg,t

)

(52)

Besides, I re apitulate the exogenous sto hasti pro esses

ln zt = (1 − ρz) ln z + ρz ln zt−1 + εz,t (12)

ln µ1,t = (1 − ρµ1) ln µ1 + ρµ1 ln µ1,t−1 + εµ1,t (13)

ln µ2,t = (1 − ρµ2) ln µ2 + ρµ2 ln µ2,t−1 + εµ2,t (14)

gst = (1 − ρgs) gs + ρgsgs

t−1 + εgs,t (15)

Hen e, a stationary ompetitive equilibrium is a set of pro esses

Yt, Ct, It, Kt, ht, wt, Gc,t, Gm,t, G

dt ,mt, rt, qt, rt, pg,t, vt, κt

22

satisfying the following non stationary equilibrium equations (41), (42), (6), (10), (43), (44), (45),

(46), (47), (48), (49), (50), (51), (36), (39) and (52), given the exogenous sto hasti pro esses for

zt, µ1,t, µ2,t and gst , (12), (13), (14) and (15), and initial onditions K−1, C−1, Gc,−1, Gd

−1.

If the preferen es over onsumption, non-monetary gold and leisure are separable, φ4 = 1, andthe preferen es over onsumption are time separable, b = 0, then equilibrium equations (44), (45),

(46) and (47), in that order, take the following simpler forms:

pg,t

κtCt

− φ3

φ1

1

Gc,t

= (1 − δg) βEt

(pg,t+1

κt+1Ct+1

)

(44')

φ2

φ1

Ctκt

1 − ht

= wt (45')

γ1v2t − γ2 = 1 − βEt

(Ctκt

Ct+1κt+1

pg,t+1

pg,t

)

(46')

1

Ctκt

= βEt

(1

Ct+1κt+1

[rt+1 + 1 − δk]

)

(47')

The expressions of the remaining equilibrium equations, (41), (42), (6), (10), (43), (48), (49), (50),

(51), (36), (39) and (52), are not modied when φ4 = 1 and b = 0.It is worth to note from the equilibrium equations (44), (45), (46) and (47) that the transa tion

ost wedge, κt, ae ts the e onomy as a negative preferen e sho k to onsumption would do. It is

easier to observe this in the ase where φ4 = 1 and b = 0. Several authors, su h as Baxter and King

(1991), have studied the ee t of preferen e sho ks on the business y le. Thus, in Baxter and King

(1991), the equilibrium ondition on labor supply and the Euler equation on apital are similar to

the equilibrium equations (45') and (47'). In parti ular, the transa tion ost wedge manifests itself

as a negative preferen e sho k in (45') and (47'). Hen e, the transa tion ost wedge reates an urge

to slow down onsumption.

As shown in equation (48), the onsumption-based velo ity of money, vt, u tuates dire tly with

the gross nominal interest rate, qt. As a result, the u tuations in the transa tion ost wedge, κt, are

driven, endogenously, by the gross nominal interest rate.

From the expression of the liquidity preferen e fun tion (48) and the expression of the

onsumption-based velo ity of money (42), I an derive the expression of the real money demand

fun tion. Spe i ally, I plug (42) into (48), then I get the expression of money demand fun tion

(Ct

mt

)2

=γ2

γ1

+1

γ1

qt − 1

qt

⇔ mt = Ct

(γ2

γ1

+1

γ1

qt − 1

qt

)−

12

(53)

Hen e, real money balan es are in reasing with onsumption and de reasing with nominal interest

rate.

Besides, writing the money demand expression in logarithm,

ln mt = ln Ct −1

2ln

(γ2

γ1

+1

γ1

− 1

γ1

1

qt

)

one an note that the elasti ity of money demand with respe t to onsumption is equal to unity

∂ ln mt

∂ ln Ct

= 1

23

The optimal ondition on the marginal rate of substitution of onsumption for non-monetary

gold, (30), an be restated as follows

pg,t

(

1 − 1 − δg

qt

)

= κt

φ3

φ1

Ω1−φ4t

Gc,t

1

Ω1−φ4t

Ct−bCt−1− bβEt

(Ω

1−φ4t+1

Ct+1−bCt

) (54)

To analyse how onsumption and non-monetary gold sto k intera t, I fo us, here, on the simple ase

where preferen es are separable, φ4 = 1, and display no habit formation in onsumption , b = 030.Therefore, equation (54) be omes

pg,t

(

1 − 1 − δg

qt

)

= κt

φ3

φ1

Ct

Gc,t

(54')

Then, I log-linearize (54') in the neighborhood of the steady state:

Ct −(

pg,t + Gc,t

)

+ κt = ωqt (55)

⇔ Ct −(

pg,t + Gc,t

)

= ϕqt (56)

where ω = β(1−δg)

1−β(1−δg), ϕ = ω− β

vκand xt = ln

(xt

x

), x = q, C, pg, Gc. The move from equation (55) to

equation (56) is done be ause the transa tion ost wedge is linked only to the gross nominal interest

rate (a tually through the onsumption-based velo ity of money, as shown in equilibrium equations

(43) and (48)). Thus, both equations (55) and (56) point out how the nominal sho ks the gold

ow sho k and the two money supply sho ks are propagated to the real part of the e onomy.

The me hanism of transmission works through the transa tion ost wedge, on the one hand, the

non-monetary gold sto k optimal hoi e, on the other hand. Written that way, equations (55) and

(56), refer to the optimal ondition on the marginal rate of substitution of onsumption, Ct, for real

non-monetary gold, pg,tGc,t, rather than on the marginal rate of substitution of onsumption, Ct, for

non-monetary gold. Hen e, in equilibrium, the marginal rate of substitution of onsumption for real

non-monetary gold must be equal to a linear fun tion of the nominal interest rate. However, the

transa tions osts introdu e a wedge, κt, in that optimal ondition. Clearly, equation (55) is more

onvenient than equation (56) if one wants to highlight the role of the transa tion ost wedge in the

optimal ondition on the marginal rate of substitution of onsumption for real non-monetary gold.

Under reasonable alibration, the oe ients ω and ϕ are more likely to be stri tly positive. From

both equations (55) and (56) one an note that the ee ts of the nominal sho ks on onsumption an

be ambigous. Indeed, the responses of onsumption to the nominal sho ks depend on how the gross

nominal interest rate, the real pri e of gold, the non-monetary gold sto k and the transa tion ost

wedge intera t between themselves. Assuming that ω, ϕ > 0 (and hen efore ω > ϕ), the transa tions osts ome to weaken the positive ee t of the gross nominal interest rate on onsumption.

Besides, from equation (56), one an note that for any given onsumption, Ct, if following a

positive nominal sho k an in rease of gold ow sho k, gst , or a de rease of money supply sho ks,

µi,t i = 1, 2 the real non-monetary gold sto k, pg,tGc,t, in reases, the gross nominal interest rate, qt,

has to de line. I all the negative ee t of the nominal sho ks on the gross nominal interest rate, the

non-monetary gold liquidity ee t. Indeed, it resembles the standard liquidity ee t31. The liquidity

ee t and the non-monetary gold liquidity ee t are interelated: When the latter arises, the former

shows up too.

As well, equations (55) and (56) point out how the real sho k the produ tivity sho k is

transmitted to the nominal part of the e onomy.

The equilibrium equation (52) represents the Fisher equation whi h relates the real and nominal

interest rates to the expe ted ination32. The real interest rate, rt, is linked to the apital gross real

rate of return as follows: rt = Et (rt+1 + 1 − δk).

30The non-separability of the preferen es and habit formation in onsumption hypotheses do not alter the main

points of the following analysis.31In the literature, one alls liquidity ee t, the negative ee t of money supply on the gross nominal interest rate.

The liquidity ee t takes pla e when both the nominal money and real money in rease.32Here, the gross ination rate is dened with the real pri e of gold rather than with the pri e level.

24

3 The Data

The aim of this work is to evaluate the ability of the gold standard model to repli ate the

u tuations of Fren h key ma roe onomi variables over the 1929-1936 period. Therefore, this se tion

presents the onstru tion of the histori al Fren h data on output, onsumption, investment, apital,

labor, real wage, nominal money, real money, monetary gold, real pri e of gold, gross nominal interest

rate and gross real interest rate. In addition, it dis usses the onstru tion of the four sho ks onsidered

in the model: Produ tivity sho k, inverse of money multiplier sho k, gold ba king sho k and gold

ow sho k. All those data histori al and sho ks are onstru ted onsistenly to the model.

3.1 Raw data

Table 1 provides a des ription of the Fren h raw data used to onstru t the histori al data and

sho ks. Thus, in the urrent analysis, I use dierent sour es for the data: The data olle ted by Villa

(1993)33, Saint-Mar (1983), Banque de Fran e34, INSEE and, Jones and Obstfeld (2001). Note that

the raw data are mainly available at the annual frequen y35. Therefore, I ondu t the analysis on

the basis that the model period is the year.

Before going through the onstru tion of the histori al data and sho ks, I need to ensure that

all the raw data, but hourly nominal wage in rms, money market rate and weekly average hours

worked per worker, are dened are measured in a same unit, i.e. in billions. In parti ular, the

raw data data dened in thousands series dhe, emp and pop must be divided by 1 000 000.The raw data dened in units series Billets au porteur en ir ulation, Compte ourant

du Trésor, Compte ourant de la Caisse Autonome d'Amortissement, Comptes ourants et

omptes de dépts de fonds, Dispositions et autres engagements à vue and En aisse Or

must be divided by 1 000 000 000.Even though the histori al data might display a determinist trend, I do not remove it. Indeed,

for onvenien e, I have assumed that the gold standard model exhibits no growth: No deterministi

growth rate has been introdu ed in the model. Nevertheless, this point is not ru ial sin e I am

interested in a very short window of the histori al time span, that is the period going from 1929 to

1936. Bordo et al. (2001) argue that introdu ing a deterministi trend term in a model might not

be appropriate if that model intends to explain an histori al event su h the Great Depression. As a

onsequen e, removing a deterministi trend from the histori al data might not be justied neither.

Those authors laims if there is a deterministi trend to remove from data that over the Great

Depression period, it may be a negative one instead of a positive one.

3.2 Histori al data

In this subse tion, I present and dis uss the onstru tion of annual histori al Fren h data on

output, onsumption, investment, apital, labor, real wage, nominal money, real money, monetary

gold, real pri e of gold, nominal interest rate and real interest rate. The histori al data set overs

the interwar period.

3.2.1 Output and its omponents

The histori al measure of onsumption is assumed to be equal to the real household onsumption

time series (series zm). In turn, the histori al measure of investment is obtained by adding together

the real household investment time series (series izm) and the real rm investment time series (series

ize). Consistently to the baseline and learning model, the histori al measure of output is got by

taking the sum of the histori al measures of onsumption and investment.

Be ause output variable and its omponents onsumption and investment are dened in

per apita terms in the gold standard model, their respe tive empiri al measures are divided by the

population measure (series pop). Then, I deate the per apita measures of output, onsumption

33The Villa (1993)'s data are freely available in the website of the CEPII: www. epii.fr.34The Banque de Fran e ara available in its website: www.banque-fran e.fr35As far as I know, there are no Fren h ma roe onomi data, ex ept for money, monetary gold and interest rate

variables, available at a higher frequen y.

25

Table 1: Fren h Raw Data

Name Sour e Coverage period

Labor market and populationWeekly average hours worked per worker Villa P., 1993 (dh) Annual 1919-1939 and 1946-1985Total employment (in thousand), Villa P., 1993 (emp) Annual 1890-1913, 1919-1939

and 1946-1985Hourly nominal wage in rms (prudhommes) Villa P., 1993 (whpe) Annual 1913 and 1920-1939Total population (in thousand) Villa P., 1993 (pop) Annual 1890-1985

National in ome a ountReal household onsumption (in billion fran of 1938) Villa P., 1993 ( zm) Annual 1896-1939Real household investment (in billion fran of 1938) Villa P., 1993 (izm) Annual 1890-1985Real rm investment (in billion fran of 1938) Villa P., 1993 (ize) Annual 1890-1985Real rm apital sto k (in billion fran of 1938) Villa P., 1993 (kze) Annual 1890-1985Nominal household onsumption (in billion fran ) Villa P., 1993 ( m) Annual 1896-1939Nominal household investment (in billion fran ) Villa P., 1993 (im) Annual 1890-1985Nominal rm investment (in billion fran ) Villa P., 1993 (ie) Annual 1890-1985

Money, gold and interest rateNotes in i ulation (in fran ) Banque de Fran e Weekly 14/04/1898-21/03/1974

(Billets au porteur en ir ulation)Current a ount of the Treasury (in fran ) Banque de Fran e Weekly 14/04/1898-21/03/1974

(Compte ourant du Trésor)Current a ount of the autonomous sinking fund (in fran ) Banque de Fran e Weekly 28/06/1928-29/12/1949

(Compte ourant de la CaisseAutonome d'Amortissement)

Current a ount and deposits (in fran ) Banque de Fran e Weekly 28/06/1928-29/12/1949(Comptes ourants et

omptes de dépts de fonds)Other liabilities on urrent a ount (in fran ) Banque de Fran e Weekly 28/06/1928-29/12/1949

(Dispositions et autresengagements à vue)

Commer ial banks and Banque de Fran e's sight deposits Saint-Mar M. (1983) Annual 1807-1952(in billion fran ) ( ol. Dépts à vue, pp.36-38)Gold reserve ( oin and bullion) (in fran ) Banque de Fran e Weekly 14/04/1898-21/03/1974

(En aisse Or)Net gold exports (in million fran ) Jones M. and M. Obstfeld (2001) Annual 1850-1938Net gold exports (in million fran 1928) INSEE, Annuaire Statistique (1966) Annual 1910-1913 and 1920-1938

(Mouvements d'or in balan edes paiements, p.365)

Money market rate (in per ent) Villa P., 1993 (txmm) Annual 1890-1985

26

and investment by the 1929 value of the per apita measure of output. As a onsequen e, output,

for example, is evaluated to unity in 1929. By doing so, I ensure that the histori al data on output,

onsumption and investment are dened in the same s ale as the data generated by the model.

The empiri al measures of output and its omponents over the 1919-1939 period.

3.2.2 Labor

I onstru t the empiri al measure of labor as follows. First, I ompute the total number of hours

worked ea h year of the interwar period, using data on total employment (series emp) and weekly

average number of hours worked per worker (series dh), and assuming that a year onsists in 52 weeks.

Se ond, I express the total number of hours worked in per apita terms using data on population

(series pop). Finally, I divide the per apita total number of hours worked series by the total time an

individual is endowed ea h year, on average, in order to get an empiri al measure of labor onsistent

with the model. In parti ular I assume that a household an allo ate 4992 hours per year between

market and non-market a tivities.

The empiri al measure of labor overs the 1919-1939 period.

3.2.3 Capital

In the reported raw data there is a series of rms' real apital sto k (series kze). However, the

onstru ted data on investment in ludes not only the investment made by rms but also those realized

by households. Therefore, the raw data on apital may not ree t orre tly all the investment done

in the Fren h e onomy during the interwar period. Thus, I onstru t a new series for apital using

the apital a umulation law dened in the gold standard model (equations (6) and the onstru ted

investment series. To generate a series of apital with the a umulation law equation, I still need

an initial value for apital and to assign a value to the apital depre iation rate, δk. To do so, rst

I divide the raw data on rms' apital (series kze) by the population series (series pop). Then, I

divide the per apita series of rms' apital by the 1929's value of per apita output. Se ond, I

alibrate the apital depre iation rate using the steady state expression of the apital a umulation

law, together with the per apita rms' apital sto k, denoted kft , and the empiri al measure of

investment, denoted idt ,

δk =

(i

kf

)

where(

ikf

)denotes the sample mean of the investment-rm's apital ratio,

idt

kft

, over the 1896-1939

period. Thus, δk is evaluated to 0.0752. Third, I generate a new apital series over the 1896-1939

period, using the apital a umulation law, a apital depre iation rate of 7.5 per ent and the 1896's

rms apital value as an initial value. Finally, I extra t the 1919-1939 sample from the new apital

time series.

3.2.4 Interest rate, wage and real pri e of gold

I take the nominal market rate (series txmm) as a measure of the nominal interest rate. In

parti ular, I onstru t a gross nominal interest rate time series, onsistently to the model, over the

1919-1939 period as follows

qdt = 1 +

mmrt

100∀ t = 1919, · · · , 1939

where qdt denotes the empiri al measure of nominal interest rate and mmrt orresponds to the raw

series txmm.

I need a measure of pri e to in order to onstru t the series of real wage and gross real interest

rate. To get a measure of pri e, I al ulate the output deator, that is the ratio of nominal output

to real output. I get a measure of nominal output in the same way as I al ulate the real output,

using data on nominal household onsumption (series m), nominal household investment (series im)

and nominal rm investment (series ie). Then, the obtained output deator is redened su h that

it takes the value of 100 in 1929. Besides, as output, it overs the 1919-1939 period.

27

Thus, the histori al measure of real wage is omputed as the ratio of the hourly nominal wage in

rms series (series whpe) to the output deator series. The onstru ted series of real wage overs the

1920-1939 period

In turn, I al ulate the histori al measure of gross real interest rate, over the 1919-1939 period,

using the following formula

rdt =

qdt

πdt+1

, πdt+1 =

pdt+1

pdt

, ∀ t = 1919, · · · , 1939

where rdt denotes the real interest rate and pd

t the output deator.

Re all that under the gold standard monetary system, the pri e of gold is assumed to be xed. As

a simpli ation and without loss of generality, I normalize the pri e of gold to unity. It follows that

the real pri e of gold is dened as the inverse of the pri e level. Therefore, I onstru t an empiri al

measure of real pri e of gold by taking the inverse of the output deator: pdg,t = 1

pdt

. Sin e the pri e of

gold has been maintained xed between June 1928 and September 1936 in Fran e36, the onstru ted

real pri e of gold series overs the 1928-1936 period.

3.2.5 Monetary gold and money

Note that sin e I normalize the xed pri e of gold to unity, the monetary gold sto k is evaluated

in nominal terms. The time series of nominal monetary gold sto k owned by the Banque de Fran e

(En aisse Or) is provided by that institution. Being available at a weekly frequen y, I need to

onvert the data on monetary gold to annual frequen y. Sin e monetary gold is a sto k data, I do

the onversion as follows

Gadm,t = Gwd

m,τt, ∀ t = 1898, · · · , 1939

where Gadm,t denotes the annual monetary gold sto k series and Gwd

m,t the weekly monetary gold sto k

series. The time index τt indi ates the last week of the year t. In words, for example, the 1920

value of the annual monetary gold sto k series is equal to the last week of de ember 1920 value

of the weekly monetary gold sto k. Besides, note that Fran e experien es a devaluation in 1928.

In parti ular, the monetary law of June 1928 brings a new denition of the Fren h urren y: The

fran poin aré. Hen e, 1 fran germinal (old urren y denition) is equal to 4.925 fran poin aré.

Therefore, I revaluate the monetary gold sto k series in fran poin aré using that onversion rate.

Note that the monetary gold sto k series needs to be onverted only for the 1898-1927 period:

Gd,fpm,t = 4.925 × G

d,fgm,t , ∀ t = 1898, · · · , 1927

where Gd,fpm,t denotes the value of monetary gold sto k in fran poin aré and G

d,fgm,t the value of monetary

gold sto k in fran germinal.

In the gold standard model, the nominal money variable is identied as being the monetary

aggregate M1. Thus, I onstru t the monetary aggregate M1 by taking the sum of notes in ir ulation

issued by the Banque de Fran e (Billets au porteur en ir ulation) and total sight deposits

(Dépts à vue). I ex lude metalli oins from the denition of the monetary aggregate M1. Indeed,

in Fran e, during the gold standard period ( lassi al gold standard period and gold-ex hange standard

period), a large part of the metalli oins are in gold and silver (Fran e has been in a bimetallism

monetary system before joining the gold standard monetary system). A ording to Saint-Mar (1983),

oins in opper or bronze happen to be the main metalli oins in Fran e only after 1936, that is

on e the ountry left the gold standard monetary system.

The time series of notes in ir ulation is provided by the Banque de Fran e. As Saint-Mar

(1983) emphasizes it, the histori al data on notes in ir ulation are of good quality sin e the Banque

de Fran e has always ausiously kept its note issues in book-re ord. Be ause the data on notes in

ir ulation are reported at a weekly frequen y, I have to onvert them to annual frequen y. To do

so, I pro eed as for the monetary gold data.

36In Fran e, the pri e of gold is set to 19.96 fran s poin aré over the period going from June 1928 to September

1936.

28

A time series of the Fren h sight deposits, over the period 1807-1952, is provided by Saint-

Mar (1983). Those data in lude the sight deposits in the Bank of Fran e, the sight deposits in all

ommer ial banks and the postal urrent a ounts.

A ording to Saint-Mar (1983), the value of sight deposits in the Bank of Fran e is orre tly

evaluated over the full period sin e, as said above, that institution kept its banking a tivities in

book-re ord. The postal urrent a ounts exist only sin e 1920. Nonetheless, the value of the postal

urrent a ounts is well measured sin e the institution managing those assets has always kept its

a titivities in book-re ord too.

However, there are no good or o ial evaluation of the value of ommer ial banks' sight deposits

for the full period. In parti ular, Saint-Mar (1983) tells that the regulation of the banking a tivity

is reglemented only sin e the World War 2 in Fran e. The rst evaluations of the Fren h banking

a tivity start in 1900 and the o ial re ordings in 1942. Therefore, Saint-Mar (1983) proposes her

own evaluation of the sight deposits of ommer ial banks. To do so, the author pro eeds methodi ally

by subperiods. Sin e, the urrent work fo uses only on the interwar period, I des ribe briey her

method for the post 1900 (in luded) period. Saint-Mar (1983) uses the measure of total deposits

onstru ted by the INSEE37 for the period going from 1900 to 1950. Substra ting the time series

of the Bank of Fran e's sight deposits from the INSEE's time series, the author dedu es the value

of ommer ial banks' sight deposits over the post-1900 period. The auhtor laims that the INSEE's

data have to be taken with ausious be ause they have been overevaluated.

In addition, I onstru t a time series of the real money variable. To do so, I simply divide the

time series of monetary aggregate M1 by the measure of pri e level, pdt .

Finally, the onstru ted data on nominal money, real money and nominal monetary gold sto k

are divided by the population series then s aled by the 1929s' value of per apita output. The

nal empiri al measures of nominal money, real money and nominal monetary gold sto k over the

1919-1939 period.

3.2.6 Summary

To summarize this subse tion, Figures 1 and 2 display the annual histori al data onstru ted

above, over the 1928-1936 period. The histori al data are plotted in log-deviation from their respe -

tive 1929 level.

1928 1930 1932 1934 1936−20

−15

−10

−5

0

5

perc

ent d

evia

tion

Output

1928 1930 1932 1934 1936−7

−6

−5

−4

−3

−2

−1

0

perc

ent d

evia

tion

Consumption

1928 1930 1932 1934 1936−80

−60

−40

−20

0

20

perc

ent d

evia

tion

Investment

1928 1930 1932 1934 1936−5

0

5

10

perc

ent d

evia

tion

Capital

1928 1930 1932 1934 1936−20

−15

−10

−5

0

perc

ent d

evia

tion

Labor

1928 1930 1932 1934 1936−10

0

10

20

30

40

perc

ent d

evia

tion

Real wage

Figure 1: Fren h histori al data, 1929 = 0 (a).

37The Institut National de la Statistique et des Études É onomiques is the Fren h national institute on statisti s

and e onomi studies.

29

From Figure 1, one an observe that output and investment fall dramati ally from 1930 onwards.

Consumption starts to de rease one year earlier than output and investment. However, the former

experien es a milder ollapse than the latters. The apital sto k starts to de line when investment

moves below its 1929 level. Nonetheless, sin e investment rises strongly before 1930, apital remains

above its 1929 level until 1936. Labor de lines signi antly between 1929 and 1932. Then it remains

at a low level until 1936. Real wage rises strongly over all the 1928-1936 period.

1928 1930 1932 1934 1936−40

−20

0

20

40

60

80

perc

ent d

evia

tion

Monetary gold

1928 1930 1932 1934 1936−10

−5

0

5

10

15

20

perc

ent d

evia

tion

Nominal money

1928 1930 1932 1934 1936−1.5

−1

−0.5

0

0.5

perc

ent d

evia

tion

Nominal interest rate

1928 1930 1932 1934 1936−5

0

5

10

15

20

25

perc

ent d

evia

tion

Real price of gold

1928 1930 1932 1934 19360

5

10

15

20

25

perc

ent d

evia

tion

Real money

1928 1930 1932 1934 19360

1

2

3

4

5

6

7

perc

ent d

evia

tion

Real interest rate

Figure 2: Fren h histori al data, 1929 = 0 (b).

As it an be noted from Figures 2, the monetary gold sto k in reases strongly between 1928 and

1932. Then, it de lines until 1936. Nonetheless, the monetary gold sto k remains above its 1929

level between 1929 and 1936. Nominal money also rises between 1928 and 1931. It is worth to note

that the nominal money in rease is milder than the monetary gold sto k one. From 1931 to 1935,

nominal money de lines signi antly. It moves below its 1929 level between 1934 and 1935. Besides,

the real pri e of gold drops between 1928 and 1930. After what it rises until 1936. Note that the

real pri e of gold moves above its 1929 level as soon as the nominal money starts to fall. The gross

nominal interest rate ollapses between 1929 and 1931. Then, it moves upwards again, rea hing ba k

its 1929 level in 1935. The 1930-1935 ination in the real pri e of gold drives upwards the gross real

interest rate during that period. As well, the real money rises between 1929 and 1936.

3.3 Sho ks

In this subse tion, I present and dis uss the onstru tion of the four sho ks onsidered in the

model over the interwar period.

3.3.1 Produ tivity sho ks

Here, I de ribe and dis uss the onstru tion of a histori al sequen e of produ tivity sho ks. They

are dened as being movements in output whi h are not explained by movements in fa tor inputs.

Note that the produ tivity sho ks are not dire tly observable in the ma roe onomi data. Never-

theless, they an be measured onditionally to the form of the ma roe onomi produ tion fun tion. In

parti ular, a measure of te hnology sho ks, zdt , asso iated to a onstant return to s ale Cobb-Douglas

produ tion fun tion with two inputs apital and labor an be generated, for the interwar period,

as follows

zdt =

ydt

(kd

t−1

)θ (hd

t

)1−θ∀, t = 1920, · · · , 1939 (57)

30

where ydt , kd

t and hdt denote the histori al measures of, respe tively, output, apital and labor.

3.3.2 Gold ow sho ks

Here, I des ribe and dis uss the onstru tion of a histori al sequen e of gold ow sho ks. They

are dened as being the entry/exit ows of gold in/out of the e onomy.

The INSEE, in its Annuaire Statistique (1966), reports the net exports of gold in Fran e for the

interwar period, evaluated in fran poin aré. However, there are missing observations in 1925 and

1926. Jones and Obstfeld (2001) propose also a measure of net gold exports from 1850 to 1938.

Those authors spli e together dierent data on gold exports over that period. In parti ular, their

data between 1930 and 1938 are taken from Annuaire Statistique (1966). Thus, I ll the missing

observations of the net gold export series of Annuaire Statistique (1966) with those olle ted by

Jones and Obstfeld (2001)38. Note that the 1925 and 1926's values of net gold exports, taken from

Jones and Obstfeld (2001), are onverted in fran poin aré in order to make them onsistent with

the data of Annuaire Statistique (1966). Note that there are some dieren es between the Annuaire

Statistique (1966)'s data and those olle ted by Jones and Obstfeld (2001) for the 1920-1930 period.

Here, to onstru t a time series of gold ow sho ks, I favor the data from Annuaire Statistique (1966)

rather than those from Jones and Obstfeld (2001) be ause the formers are dire tly originated from

Fran e.

In the gold standard model, the gold ow variable an be interpreted as a net gold inow. There-

fore, I onstru t the gold ow sho k series by taking the minus net gold export time series over the

1920-1938 period. In addition, the onstru ted gold ow sho k series is divided by the population

series then s aled by the 1929's value of per apita output.

3.3.3 Money supply sho ks

Here, I des ribe and dis uss the onstru tion of histori al sequen es of the two money supply

sho ks onsidered in the gold standard model: The inverse of money multiplier sho ks and the gold

ba king sho ks. The formers represent the ratio of monetary base to monetary aggregate M1. The

latters represent the ratio of monetary gold to monetary base. Therefore, I need a measure of the

monetary base.

The monetary base is dened as being the sum of notes in ir ulation and the Banque de Fran e

liabilities on urrent a ount. Spe i ally the Banque de Fran e liabilities on urrent a ount on-

sist in the urrent a ount of the Treasury (Compte ourant du Trésor), the urrent a ount of

the autonomous sinking fund (Compte ourant de la Caisse Autonome d'Amortissement), ur-

rent a ount and deposits (Dispositions et autres engagements à vue), and other liabilities on

urrent a ount (Dispositions et autres engagements à vue). Note that this denition of the

Banque de Fran e liabilities on urrent a ount is essentially based on the monetary law of June 1928

and parti ularly on the new balan e sheet of the Banque de Fran e. Indeed, from Table 1, one an

observe that only the data on the urrent a ount of Treasury are available before 1928. A ording

to Morant (1951), the urrent a ount of the autonomous sinking fund has been introdu ed in 1926.

However, in the website of the Banque de Fran e the data on the urrent a ount of the autonomous

sinking fund are available only starting from mid-1928. As a onsequen e, for the period pre-1928

(ex luded), I onstru t the monetary base time series by taking the sum of notes in ir ulation and

urrent a ount of the Treasury. Note that the obtained measure of monetary base is, at this stage,

dened at a weekly frequen y sin e the raw data used to ompute it are displayed at this frequen y.

Hen e, I onvert that measure of monetary base to annual frequen y following the same pro edure

as for the monetary gold data.

The onstru ted time series of monetary base is divided by the population series then s aled by

the 1929's value of per apita output in order to make it onsistent with the time series on monetary

gold and monetary aggregate M1.

38For the period going from 1915 to 1930, Jones and Obstfeld (2001) take their data from those olle ted by the

League of Nations.

31

3.3.4 Summary

To summarize this subse tion, Figure 3 shows the realizations of the sho ks onstru ted above,

over the 1928-1936 period. The realizations of the te hnology sho k and those of the money supply

sho ks inverse of money multiplier sho ks and gold ba king sho ks are plotted in log-deviation

from their respe tive 1929 level. Instead, the realizations of the gold ow sho k are reported in

deviation from their 1929 level be ause they an take negative values.

1928 1930 1932 1934 1936−10

−8

−6

−4

−2

0

2

4

perc

ent d

evia

tion

Productivity

1928 1930 1932 1934 1936−8

−6

−4

−2

0

2

4

devi

atio

n

Gold flow

1928 1930 1932 1934 1936−5

0

5

10

15

perc

ent d

evia

tion

Inverse of money multiplier

1928 1930 1932 1934 1936−40

−20

0

20

40

60

80

100pe

rcen

t dev

iatio

n

Gold backing

deviation from 1929deviation from rule

Figure 3: Fren h histori al sho ks, 1929=100.

From Figure 3, one an observe that the produ tivity sho k follows the same pattern as output.

In parti ular, it starts to ollapse in 1930 where it is above its 1929 level. The produ tivity sho k

drop lasts until the end of the 1928- 1936 period. The inverse of money multiplier sho k in reases

during all the gold-ex hange standard period. As well, the gold ba king sho k rises between 1928

and 1934. After what, it de lines but still remains above its 1929 level until the end of the period.

The starred line in the subplot represents the log-deviation of the gold ba king sho k from that the

35 per ent rule on the monetary gold-monetary base ratio. Clearly the poli y rule is respe ted over

all the period. Note that the gold ba king sho k in rease happens to be larger than the inverse of

money multiplier sho k in rease. It is worth to note that, taking together, the movements in the two

money supply sho ks explain the relative weakness of the nominal money in rease omparatively to

the monetary gold rise.

As it an observed in Figure 4, the Fren h e onomy experien es a gold (net) inow between 1928

and 1933. The net imports of gold start to de line in 1932. From 1933 onwards, gold moves away

from the ountry. It is worth to note that as gold ows out of Fran e, the monetary gold reserve of

the Banque de Fran e de lines.

Bernanke and Mihov (2000) de ompose the identity that links the nominal money sto k of a

ountry to its monetary gold sto k into several ratios. They do that for several ountries that are

in the gold standard during the interwar period. For Fran e, they nd that the money muliplier

de reases strongly between 1928 and 1936 while the gold ba king ratio remains relatively stable

during that same period. Thus, my results ontrast with the ones of those authors: I nd that

the gold ba king sho k is signi antly more volatile than the inverse of money mutliplier sho k

between 1928 and 1936. The dieren e between my measure of the gold ba king ratio and the one

of Bernanke and Mihov (2000) is mainly due to the fa t these two measures of the gold ba king

ratio are not identi ally dened. Spe i ally, those authors dene the gold ba king ratio as the ratio

of the monetary base to the international reserves of the entral bank. The international reserves

onsist of the foreign ex hange and monetary gold held by the entral bank. In the onstru tion of

my measure of the gold ba king ratio, I do not in lude the foreign assets held by the entral bank.

32

1928 1929 1930 1931 1932 1933 1934 1935 1936−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05Gold flow

leve

l

Figure 4: Fren h gold ow sho k in level.

Indeed, even though the Fren h entral bank is allowed to hold foreign ex hange, they are not taken

into a ount in the denition of the legal minimum overage ratio. Spe i ally, the Bank of Fran e

is legally required to ensure that its gold sto k ex eeds or is equal to 35 per ent of its sight liabilities

(monetary base). An other sour e of dieren e an ome from the onstru tion of the monetary base.

In Bernanke and Mihov (2000), the monetary base is dened as the sum of notes in ir ulation and

bank reserves. However, they do not expli itly pre ise of what onsist the bank reserves in the ase

of Fran e. Nevertheless, my measure of the gold ba king ratio is onsistent with the one onstru ted

by Mouré (1991, Table 2.1, ol. Reserve ratio, pp. 55-56).

My measure of the money multiplier and the one of Bernanke and Mihov (2000) follow the same

denition: The money multiplier orresponds to the ratio of money aggregate M1 to monetary base.

The dieren e between the two measures of the money mutliplier an ome from two sour es. As said

above, I might not have onstru ted the monetary base as have done those authors. Furthermore, my

measure of the monetary aggregate M1 might be dierent from the one of Bernanke and Mihov (2000).

Indeed, those authors dene the nominal money sto k as being equal to the notes in ir ulation plus

the total ommer ial bank deposits. I have also in luded the private deposits held by the Bank of

Fran e in the denition of M1. Indeed, during the interwar period, the Fren h entral bank is also

involved into ommer ial banking a titivities.

4 Solution Method, Calibration and Steady State

In this se tion, I present the solution method used to derive the de ision rules of the gold standard

model. Then, I dis uss the alibration of the model's parameters and dene the steady state of the

arti ial e onomy.

4.1 Solution method

The system of equilibrium equations of the gold standard model are log-linearized in the neighbor-

hood of the deterministi steady state. Then, the obtained log-linear system of equilibrium equations

are solved using the method developed by Klein (2000). Nonetheless, in order to apply the solution

method of Klein (2000), I need to assign values to the parameters of the model and dene the steady

state of the e onomy. Appendix A reports in details the log-linearization of the system of equilibrium

equations.

33

4.2 Calibration and steady state

The model ontains 11 stru tural parameters, gathered in the set

Θ = β, δk, δg, φ1, φ2, φ3, φ4, θ, γ1, γ2, b

8 exogenous sto hasti pro ess parameters, gathered in the set

∆ = ρz, ρµ1 , ρµ2 , ρgs , σz, σµ1 , σµ2 , σgs

and 20 variables, whi h steady state levels are gathered in the set

Ξ =Y,C, I,K, h, w, r, q, r, pg, Gc, Gm, Gd,m, v, κ, z, µ1, µ2, g

s

In order to assign a value to ea h parameter and steady state variable of the model, I solve a

system formed by the deterministi steady-state expressions of the equilibrium equations and 23

additional onstraints. When I solve that system, I assume that the time unit in the model is the

year.

The deterministi steady state expressions of the equilibrium equations are

m =1

µ1

1

µ2

pgGm (58)

v =C

m(59)

K = (1 − δk,t) K + I (60)

Gd = Gc + Gm (61)

κ = 1 + 2γ1v − 2√

γ1γ2 (62)

pg

κ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

− φ3

φ1

[

(C − bC)φ1 (1 − h)φ2

]1−φ4

G1−φ3(1−φ4)c

=

= (1 − δg) βpg

κ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

(63)

φ2

φ1

[

(C − bC)φ1 Gφ3c

]1−φ4

(1 − h)1−φ2(1−φ4)

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

−1

=w

κ(64)

γ1v2 − γ2 = 1 − β

κ

κ

pg

pg

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

−1

×

×

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

(65)

34

1

κ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

=

= β

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

[r + 1 − δk

κ

]

(66)

γ1v2 − γ2 = 1 − 1

q(67)

w = (1 − θ)Y

h(68)

r = θY

K(69)

Y = z Kθh1−θ(70)

Gd = Gd − δgGc + gs(71)

Y = C + I (72)

r = q

(pg

pg

)

(73)

The additional onstraints are put on the exogenous sto hasti pro ess parameters in luded in

∆, a subset of stru tural parameters

Θ = δk, δg, φ1, φ2, φ3, φ4, θ, b, γ1, γ2

and on a subset of steady state variable levels

Ξ = h, q, z, µ1, µ2, gs

I present and dis uss the restri tions below.

I rely partly on the onstru ted histori al data and partly on the business y le literature to

dene the additional restri tions on parameters and steady state levels of variables. The apital

share parameter, θ, is set to 0.34 as in Beaudry and Portier (2002). Those authors nd that 66per ent of the Fren h GDP goes to labor in the interwar pariod.

I restri t the sum of the preferen e parameters for onsumption, non-monetary gold and leisure to

be equal to unity: φ1+φ2+φ3 = 1. In addition, the preferen e parameter for gold parameter, φ3 is set

to 0.002. This assumption implies that households put relatively a smaller weight on non-monetary

gold than on onsumption and leisure. Two alternative values for the utility fun tion urvature

parameter, φ4, are onsidered. The rst value, φ4 = 1, orresponds to the ase where the household's

preferen es are separable in onsumption, leisure and non-monetary gold. The se ond value, φ4 = 2, orresponds to the ase where the household's preferen es are non-separable in onsumption, leisure

and non-monetary gold39. As well, the habit formation in onsumption parameter, b, an take two

alternative values. First, I onsider the ase where onsumption is not subje t to habit formation:

b = 0. Se ond, I onsider the ase where onsumption exhibits habit persisten e: b = 0.65. This

39For the non-separable preferen es' ase, I assign a value (stri tly) larger than 1 to φ4 rather than a value (stri ly)

lower than 1 in order to ensure the on avity of the utility fun tion.

35

value for the habit formation parameter, b, is quite standard in the business y le literature (see, for

example, S hmitt-Grohé and Uribe, 2005).

The apital depre iation rate, δk, has been alibrated above, when the onstru tion of an histori al

measure of apital sto k is presented. Spe i ally, I have set δk = 0.0752. As in Bordo et al. (2007),

the non-monetary gold sto k is assumed to depre iate annually at the onstant rate40 of δg = 0.02.I estime the liquidity preferen e fun tion (48), by the ordinary least square estimation pro edure

(OLS hereafter), to identify the transa tion ost parameters, γ1 and γ2, using the annual data on

nominal interest rate, qdt , onsumption, cd

t and real money, mdt . The results of the estimation,

performed over the 1920-1934 period are given by

(cdt

mdt

)2

= 1.3391︸ ︷︷ ︸

(2.2074)

+ 80.6615︸ ︷︷ ︸

(5.8569)

(qdt − 1

qdt

)

∀ t = 1920, · · · , 1934

R2 = 0.70

(74)

where the numbers in parentheses are the t-statisti s. The estimates are signi antly dierent from

zero a ording to the t-statisti s. Besides, the adjusted oe ient of determination, R2, is large

enough. Thus, the transa tion ost parameter γ1 is given by the inverse of the slop the regression,

that is γ1 = 0.0124. The transa tion ost parameter γ2 is equal to the inter ept of the regression

times γ1: γ2 = 0.0166. Nonetheless, those estimation results have to be taken with ausious sin e the

sample size is small. The hoi e of the sample, over whi h the estimation is done, is motivated by

te hni al reasons. Indeed, the estimation results based on larger samples still withing the interwar

war period be ome statisti ally not signi ant.

I restri t the steady state value of the nominal interest rate to be equal to its 1928's histori al

value. Indeed, 1928 an be onsidered as a normal year in Fran e be ause in June of that year,

the Poin aré's governement arries out a monetary law and introdu es a new denition of the Fren h

urren y, the fran poin aré, putting an end to a high ination period. Besides, that year omes

just before the onset of the worldwide Great Depression. Spe i ally, the steady state values of the

nominal interest rate is q = qd1928 = 1.0353. The steady state value of labor, h, is set to the sample

mean of its histori al measure over the interwar period: h = hdt , where the upperbar stands for the

sample mean over the 1919-1939 period.

The parameters of the exogenous sto hasti pro esses, gathered in ∆, are estimated by OLS, using

data on produ tivity sho k, zdt , inverse of money multiplier sho k, µd

1,t, gold ba king sho k, µd2,t and

gold ow sho k, gsdt . Be ause the evaluation of the gold standard model, with regard to the Fren h

Great Depression, will be done in terms of (log-)deviation from the 1929's levels, the estimations are

based on the autoregressive pro esses of the exogenous variables restated in (log-)deviation from the

1929's levels. The steady state values of the exogenous variables, z, µ1, µ2 and gs, are set equal to

the sample mean of their respe tive empiri al measure.

The estimation of the produ tivity sho k autoregressive pro ess of order 1 over the 1921-1939

period, leads to the following results

ln zdt − ln zd

τ = 0.6557︸ ︷︷ ︸

(6.3792)

(ln zd

t−1 − ln zdτ

)+ εz,t τ = 1929, ∀ t = 1922, · · · , 1939

σz = 0.0443, R2 = 0.3575, DW = 1.9583

(75)

The t-statisti of the autoregressive parameter's estimator appears in parenthesis. εz,t represents the

estimation residual. Hen e, the t-statisti being larger than 1.96 in absolute value, the autoregressive

parameter, ρz, is signi antly dierent from zero. Besides, the Durbin-Watson statisti test (DW),

being relatively lose to 2, suggests that the residuals are not auto orrelated. However, the adjusted oe ient of determination, R2, is small. The quality of estimation does not get better by in reasing

the number of lags in the autoregressive pro ess. Those estimation results have to be taken with

ausious sin e the sample size is small. I set the steady state level of produ tivity sho k equal to

40More pre isely, in their model, Bordo et al. (2007) assume that gold is also used as a apital in the produ tion

se tors gold se tor and goods se tor. Those authors assume that the gold apital depre iate over time at a quarterly

rate of 0.005.

36

the sample mean of its histori al measure over the estimation sample: z = zdt = 1.8716 where the

upperbar stands for the sample mean over the 1921-1939 period.

The estimation of the inverse of money multiplier sho k autoregressive pro ess of order 1, overthe 1926-1939 period, leads to the following results

ln µd1,t − ln µd

1,τ = 0.7904︸ ︷︷ ︸

(4.9975)

(ln µd

1,t−1 − ln µd1,τ

)+ εµ1,t τ = 1929, ∀ t = 1927, · · · , 1939

σµ1 = 0.0601, R2 = 0.6066, DW = 1.9286

(76)

The t-statisti of the autoregressive parameter's estimator appears in parenthesis. εµ1,t represents

the estimation residual. Hen e, the t-statisti being larger than 1.96 in absolute value, the autore-

gressive parameter, ρµ1 , is statisti ally signi ant. Besides, the Durbin-Watson statisti test, being

relatively lose to 2, indi ates that the residuals are not auto orrelated. The adjusted oe ient of

determination, R2, is not too small. Note that I do not estimate the exogenous sto hasti pro ess

of µ1,t over a larger sample still within the interwar period be ause otherwise the results with

regard to the t-statisti and DW be ome poorer. In addition, in reasing the number of lags in the

autoregressive pro ess does not improve the quality of the statisti al inferen e. Those estimation

results need to be taken ausiously be ause the sample is quite short. I set the steady state level of

the inverse of money multiplier sho k equal to the sample mean of its histori al measure over the

estimation sample: µ1 = µd1,t = 0.5974 where the upperbar stands for the sample mean over the

1926-1939 period.

Re all that the gold ba king sho k represents a monetary poli y instrument ree ting the om-

mitment of an e onomy to the gold standard system. Therefore, the exogenous sto hasti pro ess of

µ2,t must be dened only for the period during whi h Fran e has been in the gold-ex hange standard

system, that is for the 1928-1936 period. The estimation of the gold ba king sho k autoregressive

pro ess of order 1, over the 1928-1936 period, leads to the following results

ln µd2,t − ln µd

2,τ = 0.9065︸ ︷︷ ︸

(5.7502)

(ln µd

2,t−1 − ln µd2,τ

)+ εµ2,t τ = 1929, ∀ t = 1929, · · · , 1936

σµ1 = 0.1627, R2 = 0.3379, DW = 0.5185

(77)

The t-statisti of the autoregressive parameter's estimator appears in parenthesis. εµ2,t represents

the estimation residual. A ording to the standard error of the residuals, σµ1 , the un ertainty is quite

high for the realizations of µ2,t. Hen e, the t-statisti being larger than 1.96 in absolute value, the

autoregressive parameter, ρµ2 , is statisti ally signi ant. However, the Durbin-Watson statisti test,

being very small, indi ates that the residuals are auto orrelated. Besides, the adjusted oe ient of

determination, R2, is small too. Adding further lags to the sto hasti pro ess does not improve the

quality of the statisti al inferen e. Those estimation results are not satisfa tory be ause the sample

is very short. I set the steady state level of the gold ba king sho k equal to the sample mean of its

histori al measure over the estimation sample: µ2 = µd2,t = 0.6268 where the upperbar stands for the

sample mean over the 1928-1936 period.

The estimation of the gold ow sho k autoregressive pro ess of order 1, over the 1920-1937 period,leads to the following results

gsdt − gsd

τ = 0.8225︸ ︷︷ ︸

(5.3321)

(gsd

t−1 − gsdτ

)+ εgs,t τ = 1929, ∀ t = 1921, · · · , 1937

σgs = 0.0177, R2 = 0.4141, DW = 1.7322

(78)

The t-statisti of the autoregressive parameter's estimator appears in parenthesis. εgs,t represents the

estimation residual. Hen e, the t-statisti being larger than 1.96 in absolute value, the autoregressive

parameter, ρgs , is statisti ally signi ant. Besides, the Durbin-Watson statisti test, being relatively

lose to 2, indi ates that the residuals are not auto orrelated or weakly. The adjusted oe ient of

determination, R2, is quite small. In reasing the number of lags in the autoregressive pro ess does

not improve the quality of the statisti al inferen e. Nonetheless, those estimation results ought to be

taken ausiously be ause the sample is quite short. I set the steady state level of the gold ow sho k

37

equal to the sample mean of its histori al measure over the estimation sample: gs = gsdt = 0.0022

where the upperbar stands for the sample mean over the 1920-1937 period. Note that the steady

state value of gold ow sho k is positive: In the steady state, there is a ( onstant) gold inow.

The additional restri tions are summurized in Table 2.

Table 2: Additional restri tions

Capital share parameter θ = 0.34Degree of habit formation in onsumption parameter b = 0 or b = 0.65Preferen e for non-monetary gold parameter φ3 = 0.002Sum of preferen e parameters φ1 + φ2 + φ3 = 1Utility fun tion urvature parameter φ4 = 1 or φ4 = 2Non-monetary gold depre iation rate parameter δg = 0.02

Capital depre iation rate parameter δk =(

idt

kft

)

= 0.0752

Transa tion ost parameter γ1 = γols1 = 0.0124

Transa tion ost parameter γ2 = γols2 = 0.0166

Steady state nominal interest rate q = qd1928 = 1.0353

Steady state labor demand h = hdt = 0.2341

Steady state te hnology sho ks z = zdt = 1.8716

Steady state gold ow sho ks gs = gsdt = 0.0022

Steady state gold ba king sho ks µ1 = µd1,t = 0.5974

Steady state inverse of money multiplier sho ks µ2 = µd2,t = 0.6268

Produ tivity sho k sto hasti pro ess autoregressive pa-

rameter

ρz = ρolsz = 0.6557

Te hnology sho k sto hasti pro ess standard deviation

parameter

σz = σolsz = 0.0443

Inverse of money multiplier sho k sto hasti pro ess au-

toregressive parameter

ρµ1 = ρolsµ1

= 0.7904

Inverse of money multiplier sho k sto hasti pro ess

standard deviation parameter

σµ2 = σolsµ2

= 0.0601

Gold ba king sho k sto hasti pro ess autoregressive pa-

rameter

ρµ2 = ρolsµ2

= 0.9065

Gold ba king sho k sto hasti pro ess standard devia-

tion parameter

σµ2 = σolsµ2

= 0.1627

Gold ow sho k sto hasti pro ess autoregressive pa-

rameter

ρgs = ρolsgs = 0.8225

Gold ow sho k sto hasti pro ess standard deviation

parameter

σgs = σolsgs = 0.0177

Note that at this stage, the values of the following parameters

γ1, γ2, φ3, b, δk, δg, θ, ρz, ρµ1 , ρµ2 , ρgs , σz, σµ1 , σµ2 , σgs

and steady state variable levels

q, h, z, µ1, µ2, gs

are known.

38

I use the deterministi steady state equations and the additional restri tions to evaluate the

remaining parameters and steady state levels of the model variables

Y,C, I,K,w, r, r, Gc, Gm, Gd,m, pg, v, κ, β, φ1, φ2

Combining equations (65) and (67), I get the dis ount fa tor

β =1

q

From equation (66) I get the real rental pri e of apital

r =1

β− 1 + δk

From equation (67) I get the steady state value of the onsumption-based velo ity of money

v =

(γ2

γ1

+1

γ1

q − 1

q

) 12

From equation (62) I get the steady state value of the transa tion ost wedge

κ = 1 + 2γ1v − 2√

γ1γ2

Combining equations (69) and (70), I get the steady state value of apital

K =(r

θ

) 1θ−1

z1

1−θ h

From equation (69) I get the steady state value of output

Y =r

θK

From equation (60) I get the steady state value of investment

I = δkK

From equation (72) I get the steady state value of onsumption

C = Y − I

From equation (68) I get the steady state value of real wage

w = (1 − θ)Y

h

From equation (59) I get the steady state value of real money

m =C

v

From equation (71) I get the steady state value of non-monetary gold sto k

Gc =gs

δg

39

To al ulate the value of the preferen e parameters, φ1 and φ2, rst I express the latter in fun tion

of the former using equation (64)

φ2 =w (1 − h)

Cκ

1 − bβ

1 − bφ1 (*)

Se ond, I use (*) and the assumption that∑3

i=1 φi = 1, to get the value of φ1

φ1 = [1 − φ3]

[

1 +w (1 − h)

Cκ

1 − bβ

1 − b

]−1

Third, I dedu e the value of φ2 from (*).

From equation (63) I get the steady state value of the real pri e of gold

pg =φ3

φ1

Cκ

Gc

1 − b

1 − bβ(1 − (1 − δg) β)−1

From equation (58) I get the steady state value of the monetary gold sto k

Gm = µ1µ2m

pg

From equation (61) I get the steady state value of total gold sto k

Gd = Gc + Gm

Note that the steady state of the gold standard model is dened independently to the utility

fun tion urvature parameter, φ4, value. However, dierent values for the habit formation in on-

sumption parameter, b, lead to dierent steady state levels for the real pri e of gold and monetary

gold. Sin e for any alternative values of b, the steady state level of labor is restri ted to take one

and only one possible value, the values of the preferen e parameters φ1 and φ2 are onditional on the

value taken by b. Nonetheless, the dieren es are not large.

On an ompare the steady state impli ations of the gold standard model, in terms of ratios, with

the orresponding histori al quantities. This exer ise allows to assess the a ura y of the alibration.

The results of this exer ise are reported in Table 3. The rst olumn of Table 3 des ribes several

ratios under onsideration. The se ond and third olumns display the steady state values, implied

by the model, of those ratios, when b = 0 and b = 0.65 respe tively. The fourth olumns reports

the sample means of the ratios, al ulated using the histori al data, over the interwar period. The

last olumn reports the sample means of the ratios, al ulated using the histori al data, over the

gold-ex hange standard period. Hen e, a ording to Table 3, globally, the model reprodu es quite

well, in the steady state, the properties of the histori al data over the interwar and gold-ex hange

standard periods. Therefore, the alibration of the model, presented above, seems a eptable.

In appendix A, the alibration of the model parameters are summarized in Table 7.

4.3 Analysis of the steady state

Two properties of the steady state of the gold standard e onomy are worth to be emphasized.

The ination is impli itly set to zero in the steady state. Indeed, the real interest rate is set equal

to the nominal interest rate in the steady state: r = q. Besides, the steady state level of gold ow

sho k is just su ient to over the depre iation of the non-monetary gold sto k: gs = δgGc. Indeed,

by assumption, the total gold sto k, Gd, is neither in reasing nor de reasing in the steady state. It

follows that the relative pri e of gold, pg, is onstant in the steady state. So is the pri e level41.

Clearly, these two properties of the steady state are interelated.

41The fa t that the relative pri e of gold is onstant in the steady state implies that all the gold sto ks and nominal

money are onstant too.

40

Table 3: Steady state properties of the model vs histori al properties of the Fren h data

Ratio Model, b = 0 Model, b = 0.65 Fran e 1919-1939 Fran e 1928-1936

CY

0.7686 0.7686 0.8216 0.8106IY

0.2314 0.2314 0.1784 0.1894mY

0.3801 0.3801 0.4202 0.4537YK

0.3251 0.3251 0.4521 0.4398Kh

14.1850 14.1850 8.4549 9.4290IK

0.0752 0.0752 0.0814 0.0845Yh

4.6115 4.6115 3.7839 4.1188Cm

2.0222 2.0222 2.0172 1.8074GmY

0.1294 0.1315 0.1245 0.1619

Now, I ompare the steady states of the gold standard model assuming dierent values of the gold

ow sho k, the gold ba king sho k or the produ tivity sho k42. First, I study the impa t of a higher

steady state gold ow sho k on the steady state of the gold standard e onomy. Spe i ally, I double

the steady state value of gold ow sho k, the other exogenous sho ks being un hanged: gs′ = 0.0044.Then, I analyse the ee ts of a lower steady state gold ba king sho k on the steady state of the gold

standard e onomy. In parti ular, I de rease the steady state value of the gold ba king to its bottom

bound, the other exogenous sho ks being un hanged: µ′

2 = 0.35. Finally, I analyse the ee ts of a

25 per ent higher steady state produ tivity sho k on the steady state of the gold standard e onomy:

z′ = 2.34. In those exer ises, the stru tural parameters of the model are kept un hanged. Only the

endogenous steady state variables are allowed to hange.

Here, I onsider the ase where onsumption is not subje t to habit formation. The results of the

exer ises are reported in Table 4. The rst olumn displays the steady state variables. The se ond

olumn shows how the steady state variables are omputed analyti ally. The last three olumns

reports the numeri al values of the steady state variables in the initial state, with a higher gold ow

sho k and with a lower gold ba king sho k, respe tively.

A ording to Table 4, the steady state levels of nominal interest rate, real rental rate of ap-

ital, real interest rate, onsumption-based velo ity of money, transa tion ost wedge and labor

q, r, r, v, κ and h are dened independently to the values of the exogenous variables, z, µ1, µ2

and gs. The steady state levels of output, apital, investment, onsumption, real money and real

wage Y, K, I, C, m and w are subje t (positively) only to the produ tivity sho k. The steady

state level of non-monetary gold, Gc, an be ae ted only by the gold ow sho k. Otherwise, the

gold sto k variables (and hen efore nominal money and real pri e of gold) would grow in the steady

state. The steady state level of the real pri e of gold, pg, depends positively on the produ tivity

sho k (through onsumption) and negatively on the gold ow sho k (through non-monetary gold).

The steady state level of the monetary gold sto k, Gm, an be ae ted by the two money supply

sho ks and gold ow sho k. In parti ular, Gm in reases with the two money supply sho ks, µ1 and

µ2. As well, the steady state level of the monetary gold sto k rises with the gold ow sho k (through

the real pri e of gold). In a rst glan e, the steady state value of the monetary gold sto k seems to be

subje t the produ tivity sho k too. Indeed, an in rease of z would be transmitted to Gm, positively

through real money, m, and negatively through the real pri e of gold, pg. The omputation of the

derivative of the expression dening Gm with respe t to z show that one ee t ompensate for the

other one: The nal ee t of the produ tivity sho k to the steady state level of monetary gold sto k

is nil. Being dened as the sum of monetary and non-monetary gold sto ks, the steady state level of

the total gold sto k, Gd, is subje t to the money supply sho ks and gold ow sho k. Table 4 reports

also the steady state level of nominal money, M . Hen e, being equal to the ratio of real money to

real pri e of gold, M is subje t only to the gold ow sho k (positively through real pri e of gold). As

for the monetary gold sto k, the produ tivity sho k has no ee ts on nominal money. To summarize,

42In a steady state analysis of the gold standard model, the inverse of the money multiplier sho k plays a same role

as the gold ba king sho k.

41

Table 4: Changes in the steady state, with b = 0

Variable Expression Initial With gs′ > gs With µ′

2 < µ2 With z′ > z

steady state gs′ = 0.0044 µ′

2 = 0.35 z′ = 2.34

q 1β

1.0353 1.0353 1.0353 1.0353

r 1β− 1 + δk 0.1105 0.1105 0.1105 0.1105

r 1β

1.0353 1.0353 1.0353 1.0353

v(

γ2

γ1+ 1

γ1

q−1q

) 12

2.0222 2.0222 2.0222 2.0222

κ 1 + 2γ1v − 2√

γ1γ2 1.0214 1.0214 1.0214 1.0214

h

[

1 +φ2φ1

1−b1−bβ

κ( 1−β

(1−θ)β+δk)

1β−1+δk

]−1

0.2341 0.2341 0.2341 0.2341

Y z1

1−θ

[1θ

(1β− 1 + δk

)] θθ−1

h 1.0794 1.0794 1.0794 1.5136

K θ Y1β−1+δk

3.3202 3.3202 3.3202 4.6559

I δkK 0.2498 0.2498 0.2498 0.3503

C Y − I 0.8296 0.8296 0.8296 1.1633

m Cv

0.4102 0.4102 0.4102 0.5753

w (1 − θ) Yh

3.0436 3.0436 3.0436 4.2679

Gcgs

δg0.1085 0.2169 0.1085 0.1085

pgφ3Cκ(1−b)

φ1Gc(1−bβ)(1−(1−δg)β)1.0995 0.5498 1.0995 1.5418

Gm µ1µ2mpg

0.1397 0.2794 0.0780 0.1397

Gd Gc + Gm 0.2482 0.4969 0.1865 0.2482

M mpg

0.3731 0.7462 0.3731 0.3731

42

all the real variables are invariant a ross dierent values of µ1, µ2 or gs in the steady state be ause

neither nominal money nor gold sto k grow. In turn, all the nominal variables (in luding gold sto k

variables) but the real pri e of gold are dened independently to the produ tivity sho k in the steady

state.

Considering only the nominal variables, this analyti al steady state analysis of the gold standard

model is onsistent to the ndings of Barro (1979) and M Callum (1989). Those authors analyse

the working of the gold standard in parti ular the determination of the pri e level under the gold

standard taking the real part of the e onomy as exogenously given. They assume that expe ted

ination is ( orre tly) anti ipated to be nil in the steady state. In addition, the gold ow (or gold

produ tion) is an endogenous variable in their models. Spe i ally, the gold produ tion is assumed

to be an in reasing fun tion of the real pri e of gold and (exogenously) subje t to te hni al progress.

For the sake of simpli ation, they omit the nominal interest rate from their analysis. The former

author studies the working of the gold standard using a phase diagramm while the latter author does

a omparative stati analysis of the gold standard. Barro (1979) shows that following an upward

shift of the gold supply fun tion, gs, (be ause of te hni al progress in gold produ tion43) the e onomy

moves to a new steady state where the monetary and non-monetary gold sto ks are higher and the

real pri e of gld is lower. Sin e the steady state level of monetary gold sto k is larger, the nominal

money happens to be greater in the new steady state too, as shown by the gold standard money

supply rule.

In addition, Barro (1979) points out that following a de rease in the gold ba king ratio, µ2, the

e onomy shifts to a new steady state hara terised by a higher monetary gold sto k. The levels of

the real pri e of gold and non-monetary gold sto k remain un hanged in the new steady state. In

Barro (1979), the steady state level of the non-monetary gold sto k is altered by the hange in the

gold ba king ratio be ause the real pri e of gold is dened independently to µ2. Indeed, in Barro

(1979), the gold ow is fun tion of the real pri e of gold, so is the non-monetary gold sto k in the

steady state. Thus, the reason of the neutrality of hange in the gold ba king ratio with respe t

the non-monetary gold in Barro (1979) has to be ontrasted to the reason of that neutrality in the

urrent work. Barro (1979) nds that the steady state level of nominal money remains un hanged

following a hange in the gold ba king ratio be ause the in rease in the steady state monetary gold

ompensates for the drop in µ2. This explanation of the xity of the nominal money holds in the

present work too.

Barro (1979) also onsiders the impa t of an in rease in real in ome (or real output) whi h is

equivalent to an in rease in the produ tivity sho k in the urrent work on the steady state of the

gold standard e onomy. The author shows that raising the value of real in ome leads the real pri e

of gold to take a higher value in the steady state. Besides, the Barro (1979)'s model predi ts that an

in rease of real in ome implies a higher steady state value for the non-monetary gold sto k. However,

Barro (1979) laims that the ee t of an in rease in real in ome on the monetary gold sto k is in

general not lear44. The results obtained in the urrent study ontrast with those obtained by Barro

(1979) be ause I have assumed that the gold ow is exogenous whereas Barro (1979) has dened it as

being endogenous and fun tion to the real pri e of gold. In other words, in Barro (1979), the in rease

of the steady state level of the real pri e of gold, indu ed by the hange in real in ome, drives up the

steady state level of the gold ow. It follows that the steady state level of the non-monetary gold

sto k is raised too. Instead, in the present work, the gold ow sho k, being exogenously given and

orthogonal to the other sho ks, remains xed. Therefore, the steady state level of the non-monetary

gold sto k is not ae ted by the in rease in the produ tivity sho k.

A ording to four last olumns of Table 4, the numeri al exer ises onfort the analyti al anal-

ysis. The steady state levels of nominal interest rate, real rental rate of apital, real interest rate,

onsumption-based velo ity of money, transa tion ost wedge and labor are invariant to hanges in

the steady state values of any sho ks. In the steady state, the levels of output, apital, investment,

onsumption, real money and real wage be ome higher when the produ tivity sho k takes a larger

value. However, those real variables are invariant to hanges in the steady state values of the money

supply sho ks or gold ow sho k. Nonetheless, with a higher gold ow sho k, the monetary and

non-monetary gold sto ks in rease. So do the total gold sto k as well as the nominal money sto k.

43Te hni al progress in gold produ tion in Barro (1979) is equivalent to a positive gold ow sho k in the urrent

model.44Barro (1979) argues that the non-monetary gold sto k rises if and only if the sum of the pri e elasti ities of the

gold produ tion fun tion and non-monetary gold demand fun tion are larger than unity in absolute value.

43

However, the real pri e of gold be omes lower. When the gold ba king sho k is lowered to its mini-

mum value, the monetary gold sto k be omes smaller. The non-monetary gold sto k and real pri e of

gold are not modied. It follows that the total gold sto k de reases and the nominal money remains

un hanged. In the steady state, all the nominal variables but real pri e of gold are not ae ted by a

hange in the produ tivity sho k level.

As shown in Table 5, the results of the steady state analysis are not ae ted when habit formation

in onsumption is introdu ed in the model.

5 Quantitative Analysis

In this se tion, rst I examine the dynami properties of the gold standard model through the im-

pulse response fun tions, then I onfront the predi tions of this model for several key ma roaggregate

variables to the orresponding histori al data.

5.1 Impulse Response Fun tions

Here, I analyse the impulse responses fun tions (IRFs hereafter) of the gold standard model's

variables to the gold ow sho k, the money supply sho ks and to the produ tivity sho k. They

measure quantitatively the ee ts of a single (positive or negative) 1 per ent innovation to ea h

exogenous sho k, in terms of log-deviation from the steady state, on key model variables over Tperiods after the impa t.

In the dis ussion of the IRFs of the gold standard model's variables to ea h exogenous sho k, I

onsider three versions of the model. Spe i ally, the rst alternative model labelled baseline model

orresponds to a gold standard e onomy with separable preferen es and without habit formation

in onsumption (φ4 = 1, b = 0). The se ond alternative model labelled habit model orresponds

to a gold standard e onomy with separable preferen es and habit formation in onsumption (φ4 =1, b = 0.65). The last alternative model labelled omplete model orresponds to a gold standard

e onomy with non-separable preferen es and habit formation in onsumption (φ4 = 2, b = 0.65).The plots of the Fren h histori al data have shown that output and investment move in the same

dire tions during the 1929-1936 period. However, an innovation to either produ tivity sho k, gold

ow sho k, gold ba king sho k or the inverse of money multiplier sho k might generate, through the

transa tion ost wedge, ounter y li al investment in the baseline model. Re all that the transa tion

ost wedge a ts as a negative preferen e sho k. Baxter and King (1991) and Wen (2006) point out

that a standard RBC model an generate, through preferen e sho ks, ounter y li al investment

unless the preferen e sho k is highly persistent. Agreed, this would not be too mu h troublesome

if all the sho ks taken together would not generate ounter y li al investment. However, as it will

be shown, investment is more likely to be ounter y li al following an innovation to the gold ow

sho k or to either money supply sho k than following an innovation to the produ tivity sho k. Thus,

I need to ensure that hanges in the gold ow sho k and money supply sho ks do not lead output

and investment to move in opposite dire tions, at least initially, in order to assess the ability of

the gold standard model, through the gold ow sho k and the money supply sho ks, to explain the

Fren h Great Depression. Wen (2006) demonstrates that the introdu tion of either habit formation

in onsumption or non-separable preferen es into the standard RBC model an redu e the ne essary

degree of preferen e sho k persisten e in order to ensure the pro y li ality of investment. Hen e, I

also simulate the habit and omplete models in order to he k whether the ndings of Wen (2006)

are still relevant to the gold standard model or not. Simply put, I nd that, given the alibration of

the gold standard model, investment and output are ensured to move in opposite dire tions following

a hange in any of the sho ks, at least initially, in both habit and omplete models.

5.1.1 Impulse response fun tions to the gold ow sho k

Figures 5 and 6 display the impulse responses of the baseline and habit models to a single positive

innovation to the gold ow sho k. The IRFs of the basline model's variables are represented with

starred lines while the IRFs of the habit model are represented with ir le lines. In period 0, the goldow sho k is assumed to in rease by 1 per ent.

44

Table 5: Changes in the steady state, with b = 0.65

Variable Expression Initial With gs′ > gs With µ′

2 < µ2 With z′ > z

steady state gs′ = 0.0044 µ′

2 = 0.35 z′ = 2.34

q 1β

1.0353 1.0353 1.0353 1.0353

r 1β− 1 + δk 0.1105 0.1105 0.1105 0.1105

r 1β

1.0353 1.0353 1.0353 1.0353

v(

γ2

γ1+ 1

γ1

q−1q

) 12

2.0222 2.0222 2.0222 2.0222

κ 1 + 2γ1v − 2√

γ1γ2 1.0214 1.0214 1.0214 1.0214

h

[

1 +φ2φ1

1−b1−bβ

κ( 1−β

(1−θ)β+δk)

1β−1+δk

]−1

0.2341 0.2341 0.2341 0.2341

Y z1

1−θ

[1θ

(1β− 1 + δk

)] θθ−1

h 1.0794 1.0794 1.0794 1.5136

K θ Y1β−1+δk

3.3202 3.3202 3.3202 4.6559

I δkK 0.2498 0.2498 0.2498 0.3503

C Y − I 0.8296 0.8296 0.8296 1.1633

m Cv

0.4102 0.4102 0.4102 0.5753

w (1 − θ) Yh

3.0436 3.0436 3.0436 4.2679

Gcgs

δg0.1085 0.2169 0.1085 0.1085

pgφ3Cκ(1−b)

φ1Gc(1−bβ)(1−(1−δg)β)1.0820 0.5410 1.0820 1.5173

Gm µ1µ2mpg

0.1420 0.2839 0.0793 0.1420

Gd Gc + Gm 0.2504 0.5009 0.1817 0.2504

M mpg

0.3791 0.7583 0.3791 0.3791

45

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Gold demand

baselinehabit

0 50 1000

10

20

30

Year

perc

ent d

evia

tion

Non−monetary gold

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Monetary gold

0 50 100−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Nominal interest rate

0 50 100−15

−10

−5

0

5x 10

−3

Yearpe

rcen

t dev

iatio

n

Real interest rate

0 50 100−20

−15

−10

−5

0

Year

perc

ent d

evia

tion

Real gold price

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Nominal money stock

0 50 100−10

−5

0

5

Year

perc

ent d

evia

tion

Real money

0 50 1000

0.5

1

Year

devi

atio

n

Gold supply

Figure 5: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ow sho k (a).

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Output

baselinehabit

0 20 40−0.3

−0.2

−0.1

0

0.1

Year

perc

ent d

evia

tion

Consumption

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

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Figure 6: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ow sho k (b).

46

First, I fo us my attention on the dynami behavior of non-monetary gold sto k, monetary gold

sto k, total gold sto k, real pri e of gold, gross nominal interest rate, nominal money and real money.

As shown in Figure 5, the baseline and habit models display very similar IRFs for those variables.

Hen e, the existen e of habit formation in onsumption does not alter the impulse responses of those

variables to the single innovation to the gold ow sho k. In what follows, I onsider indierently the

baseline model or the habit model when I dis uss the IRFs of non-monetary gold sto k, monetary

gold sto k, total gold sto k, real pri e of gold, nominal interest rate, nominal money and real money.

Thus, following a positive innovation to the gold ow sho k, the inow of new gold, gst , be-

omes larger than the depre iation of the non-monetary gold sto k brought from the previous period,

δgGc,t−1. Therefore, the existing total gold sto k of the e onomy in reases. Hen e, gold be omes

relatively heaper. Indeed, as shown in Figure 5, on impa t, the total gold sto k, Gdt , rises and the

real pri e of gold (the pri e level) moves down (up). Sin e the pri e level is perfe tly exible, the

fall of the real pri e of gold is qui k. Be ause the gold ow sho k is positively serially orrelated

(ρgs > 0), households expe t that the innovation to that sho k, on e it is observed, is going to drive

the real pri e of gold above its steady state level in the subsequent periods. It follows that, under

full exibility of the pri e level assumption, the household redu es its demand for real money. In

addition, note that the gross nominal interest rate responds positively to the gold ow sho k. As

illustrated in Figure 5, the gross nominal interest rate, qt, rises on impa t, onsistently to the fall in

real money demand. As a result, the equilibrium real money, mt, de reases too (see Figure 5).

How the in rease in the total existing gold sto k is allo ated between monetary and non-monetary

uses? As shown in Figure 5, the model predi ts that both non-monetary and monetary gold sto ks

respond positively to the gold ow sho k. Sin e the real pri e of gold de lines, the value of gold

de reases relatively to the onsumption good. As a result, the representative household in reases

its demand for non-monetary gold sto k, Gc,t. On impa t, the real pri e of gold ollapses more

than the real money does. In other words, the household in reases its demand of nominal money.

Therefore, the household has to bring additional gold to the entral bank to satisfy its demand of

nominal money, the two money supply sho ks being un hanged. As a result, the monetary gold sto k,

Gm,t, and nominal money, Mt, in rease. It is worth to note that by holding gold for non-monetary

purpose, the household prevents the new gold inow from being fully aptured by the entral bank.

As a onsequen e, on impa t, the monetary gold sto k does not deviate from its steady state level as

mu h as the gold ow sho k does. Thus, less money is inje ted in the e onomy when the household

enjoys holding gold for non-monetary use omparatively to what would happen if gold brought no

satisfa tion to the household. Hen efore, the gold ow sho k generates a smaller pri e level rise when

the household gets satisfa tion from holding gold for non-monetary purpose omparatively to what

would happen if gold yields no utility to the household.

As one an observe from Figure 5, the in reases of nominal money and non-monetary gold are

not followed by a fall in the gross nominal interest rate: The positive innovation to the gold ow

sho k does not generate a liqudity ee t or a non-monetary gold liquidity ee t. Therefore, the real

non-monetary gold sto k an be de reasing though the non-monetary gold sto k is in reasing. As a

matter of fa t the real non-monetary gold sto k does de rease sin e the real pri e of gold deviates

more strongly from its steady state level on impa t than the non-monetary gold does.

Note that the impulse responses of the gold sto k variables, real pri e of gold variable and nominal

money variable are hump-shaped45. Even though the non-monetary gold sto k rea hs a higher

maximum than the monetary gold sto k, the latter moves up higher than the former on impa t. In

addition, those variables deviate strongly from their respe tive steady state level and move ba k very

slowly. Indeed, 100 years following the single innovation to the gold ow sho k, Gc,t, Gm,t, Gdt , pg,t and

Mt are still far from their respe tive steady state level. A ording to Friedman (1951), the movements

in gold sto ks are large and the adjustment me hanism is slow be ause the gold ow represents a small

fra tion of the existing gold sto k: Be ause urrent output of the urren y ommodity is generally

a small fra tion of the existing sto k, deviations from equilibrium an be substantial; and a relatively

long time may be required to orre t them46. As a matter of fa t, those results are sensitive to the

alibration of the non-monetary gold depre iation rate, δg. In parti ular, higher the non-monetary

gold depre iation rate is, higher the in rease of non-monetary gold sto k is on impa t. For example,

with δg = 0.1, the non-monetary gold sto k deviates from its steady state level substantially more

45Nonetheless, the impulse response of the real pri e of gold is not sluggish: It jumps below its steady state level

strongly on impa t.46The quotation is from Friedman (1951), p. 205

47

than the monetary gold sto k does on impa t. In addition, the latter rea hes a higher maximum

than the former. Instead, with a non-monetary gold depre iation rate almost nil, say δg = 10−9, the

non-monetary gold sto k responds negatively to the innovation to the gold ow sho k on impa t,

then moves above its steady state level. However, the monetary gold sto k in reases on impa t.

Note that this observation is onsistent with what I have said about the optimal behavior of the

representative household with respe t to the non-monetary gold. Pre isely, I have stressed that the

household dis ounts the future with (1 − δg) β rather than with β when it determines its optimal

sequen e of non-monetary gold sto k. Hen e, higher δg is, lower the value of non-monetary gold

is in the future omparatively to its urrent value. In other words, when the non-monetary gold

depre iation rate is larger, the household hooses the a umulate more non-monetary gold sto k in

the period during whi h the innovation to the gold ow sho k is realized than in the subsequent

periods. Furthermore, the speed at whi h the the gold sto k variables, real pri e of gold variable

and nominal money variable ome ba k to their respe tive steady state level, on e they deviate from

it, depends on δg too. Spe i ally, higher the non-monetary gold depre iation rate is, qui ker the

adjustment me hanism is. As an illustation to those omments, I report in Appendix B the impulse

response fun tions of non-monetary gold and monetary gold sto ks to an innovation to the gold ow

sho k for the ases where δg = 0.1 and δg = 10−9.

Se ond, I fo us my attention on the real sphere of the e onomy. In the gold standard model, the

gold ow sho k is onsidered as a nominal sho k be ause it ae ts the money supply of the e onomy

through the optimal household's de ision on non-moneatary gold holding and hen efore through the

monetary gold sto k. This leads to the following question: How an innovation to the gold ow sho k

is transmitted to the real part of the e onomy? The gold standard model in ludes two hannels

through whi h the innovation to the gold ow sho k is transmitted to the real part of the e onomy.

Spe i ally, those two hannels are the transa tion ost wedge, κt, and the optimal ondition on

the non-monetary gold sto k, Gc,t. The transa tion ost wedge represents a bridge between the

nominal and the real parts of the e onomy be ause it is endogenously linked to the gross nominal

interest rate. Indeed, the transa tion ost wedge is a (positive) fun tion of the onsumption-based

velo ity of money (see equation (43)) whi h in turn omoves (positively) with the gross nominal

interest rate (see equation (48)). As mensioned above, the transa tion ost wedge alters the optimal

de isions of the representative household in terms of onsumption, labor supply and apital47 that

is the household's optimization problem rst order onditions (17), (25) and (28). The optimal

ondition on non-monetary gold sto k represents also a bridge between the nominal and the real part

of the gold standard e onomy. This se ond hannel is made learer by the optimal ondition of the

(expe ted) marginal rate of substitution of onsumption for (real) non-monetary gold. As said above,

the intera tion between non-monetary gold sto k, real pri e of pri e and gross nominal interest rate

ae ts onsumption through the optimal ondition (56)48.

As shown in Figure 6, in the baseline model, onsumption, Ct, responds negatively to the in rease

of the gold ow sho k on impa t. Indeed, the in rease of the gross nominal interest rate, qt, raises the

transa tion ost wedge, κt, as reported in Figure 6. The rise of transa tions osts leads the household

to de rease its demand for onsumption good. Furthermore, the optimal ondition (56) states that

if the gross nominal interest rate moves up, the marginal rate of substitution of onsumption for real

non-monetary gold must in rease too. Spe i ally, this optimal ondition states that the de rease

of real non-monetary gold sto k, the in rease of nominal interest rate and hen efore the rise of

transa tion ost wedge following a positive innovation to the gold ow sho k, make it optimal for

the household to de rease its onsumption. I annot disentangle the ee t of the transa tion ost

wedge from the ee t of the optimal ondition on non-monetary gold sto k be ause those ee ts are

linked to ea h other as shown in equation (55). However, I an evaluate the importan e of the two

hannels through a redu tion of the variability of the transa tion ost wedge. Pre isely, I weaken

the link of the transa tion ost wedge to the onsumption-based velo ity of money by assigning

smaller values to γ1 and γ2. For example49, I set γ1 and γ2 to 10−9. The IRF of the baseline model's

onsumption with this alternative alibration of the transa tion ost parameters are reported in the

47See the omments on the rst order onditions of the household's problem.48See the omments on the optimal ondition on the marginal rate of substitution of onsumption for real non-

monetary gold.49Note that this alternative alibration is used only for a omparative analysis. Indeed, this alternative alibration

of the transa tion ost fun tion parameters leads the onsumption-based velo ity of money to take an unreasonable

high value in the steady state.

48

left window of Figure 750. Thus, onsumption still responds negatively to the innovation to the gold

ow sho k on impa t. However, quantitatively, this response of onsumption is signi antly weaker

omparatively to the response of onsumption in the ase where the transa tions osts are more

sensitive to the onsumption-based velo ity of money. Hen e, it seems that more the transa tion

ost wedge is sensitive to the onsumption-based velo ity of money, stronger the two hannels are.

0 10 20 30 40 50−2

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baselinewith high persistence

Figure 7: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ow sho k ( ).

In the baseline model, the in rease of the transa tion ost wedge, following the innovation to the

gold ow sho k, lowers the opportunity ost of leisure in terms of the marginal utility of onsumption,

making it optimal for the household to take more leisure. Consequently, labor and output ollapse on

impa t (see Figure 6). However, as shown in Figure 6, the baseline model predi ts that investment

responds positively on impa t to the rise of the gold ow sho k. As said above, the intertemporal

transa tion ost wedge,κt

κt+1, alters the optimal ondition on the intertemporal marginal rate of

substitution of onsumption, (28). In parti ular, that intertemporal wedge prevents the expe ted

marginal rate of substitution of future onsumption for urrent onsumption from being equal to

the gross real interest rate in the equilibrium. The baseline model predi ts that the transa tion

wedge wedge rises on impa t, then de reases toward its steady state level. Hen e, the intertemporal

transa tion ost wedge moves above its steady state level when the innovation to the gold ow sho k

is realized. Thus, the rise of the intertemporal transa tion ost wedge may have a rowding in

ee t on investment. Indeed, the upward shift of the intertemporal transa tion ost wedge may lead

onsumption to de rease more than output does, at least initially. The household would de rease that

mu h its onsumption by postponing it. By doing so, the household in reases its savings, whi h take

the form apital a umulation. Therefore, investment in reases. The in rease of the apital sto k,

50The impulse responses of the other variables of the baseline model with small transa tions osts to the innovation

to the gold ow sho k are reported in Figures 42 and 43 in appendix B. Note that the IRFs of the baseline model are

qualitatively similar to the IRFs of the baseline model with small transa tions osts. Nonetheless, output, onsumption,

investment, labor, apital, real wage and gross real interest rate are less ae ted by the gold ow in rease in the baseline

model with small transa tion ost than in the baseline model. On the ontrary, gold sto ks, money, real pri e of gold

and gross nominal interest rate are more volatile in the baseline model with small transa tions osts than in the baseline

model: The pi k responses of those variables are higher in the baseline model with small transa tions osts than in

the baseline model. Those variables onverge to their respe tive steady state level more qui kly in the baseline model

with small transa tions osts than in the baseline model. Thus, it seems that the transa tion ost wedge dampens

down the ee t of the gold ow sho k on gold sto ks, money, real pri e of gold and nominal interest rate.

49

together with the low level of future labor omparatively to its steady state level, leads the gross real

interest rate the apital gross rate of return to fall. The rowding in ee t is more likely to

happen if the innovation to the gold ow sho k has not a persistent ee t on the transa tion ost

wedge. Lower the interval of time, in whi h the transa tion ost wedge is above its steady state level,

is, larger the fri tions indu ed by the transa tions osts are, and more likely to happen the rowding

in ee t is. One way to step down the distortions introdu ed by the transa tions osts and hen efore

to generate a de reasing investment, is to raise the persisten e of the gold ow sho k. Indeed,

in reasing the persisten e of the gold ow sho k leads to rise the interval of time during whi h the

gross nominal interest rate and hen efore the transa tion ost wedge are above their respe tive steady

state level. Baxter and King (1991) and Wen (2006) show that the preferen e sho k to onsumption

an lead investment to be rowded out if this preferen e sho k is not su iently persistent: The

preferen e sho k generates ounter y li al investment. As said above, the transa tion ost wedge

alters the equilibrium of an e onomy the real part of the e onomy as a negative preferen e

sho k to onsumption does. Thus, the rowding out ee t des ribed by those authors is similar to

the rowding in ee t dis ussed in the urrent work.

In order to illustrate the dis ussion on the rowding in ee t of the (intertemporal) transa tion

ost wedge51 on investment, the IRFs of the baseline model's variables to an innovation to the gold

ow sho k are omputed with a highly persistent gold ow sho k. Spe i ally, the autoregressive

parameter of the gold ow sho k, ρgs , set to 0.95. The right window of Figure 7 shows that the

initial upward shift of the intertemporal transa tion ost wedge is milder when the gold ow sho k

is highly persistent omparatively to the ase where ρgs is set to its estimated value. Consequently,

onsumption in reases ba k smoothly toward its steady state level. In parti ular, as displayed in

Figure 8, the interval of time in whi h onsumption is below its steady state level is larger when ρgs =0.95 than when ρgs = 0.82, the latter being the estimated value of the gold ow sho k autoregressive

parameter. It follows that the household de rease its savings, at least initially. Therefore, investment

ollapses in response to the rise of the gold ow sho k. The gross real interest rate is still de reasing

on impa t when the gold ow sho k is highly persistent be ause the marginal produ tivity of apital

is lowered by a smaller level of future labor. The initial in rease of apital does not lead the gross

real interest rate to in rease be ause the former is not enough large to ountera t the ee t of future

labor. Indeed, apital responses to the rise of the gold ow sho k is hump-shaped. In other words,

apital rea ts only gradually to the upward shift of the gold ow sho k52. Note that later in the

impulse responses, investment moves above its steady state level while output and onsumption

are still below their respe tive steady state level. To fully eliminate the rowding in ee t of the

transa tion ost wedge on investment, the value of the parameter ρgs has to be larger than 0.995.This solution is not onvenient sin e I have initially alibrated the autoregressive parameter of the

gold ow sho k exogenous sto hasti pro ess a ording to the Fren h data. Below, I follow an other

strategy to ensure that investment de reases on impa t as output does.

Re all that in the gold standard model, the real wage is equal to the marginal produ tivity of

labor in the equilibrium. Sin e the produ tion fun tion is assumed to be a Cobb-Douglas, the log-

deviation of the real wage from its steady state level orresponds to the log-deviation of the average

labor produ tivity from its steady state level. From Figure 6, one an observe that on impa t labor

deviates from its steady state level more strongly than output does. It follows that the average labor

produ tivity in reases. So the real wage does (see Figure 6).

As shown in Figure 6, one period after the realisation of the innovation to the gold ow sho k,

output, onsumption, investment, labor and real wage move ba k to their respe tive steady state

level in the baseline model. Later in the impulse responses, output, onsumption and labor move

above their respe tive steady state level for some periods. The impulse response of apital to the

innovation to the gold ow sho k is hump-shaped in the baseline model. In parti ular, apital

ontinues to in rease after the impa t for several periods. Then, it de reases toward its steady state

51One an assume that the rowding in/out ee t on investment is generated by either the transa tion ost wedge

or the intertemporal wedge. Thus, in what follows, I onsider indierently that the rowing in/out ee t is reated by

the transa tion ost wedge or the by the intertemporal transa tion ost wedge.52The impulse responses of the other variables gold sto ks, real pri e of gold, nominal money, real money,

onsumption-based velo ity of money, real wage and rental rate of apital to the innovation to the gold ow sho k,

in the baseline model with highly persistent gold ow sho k, are reported in Figure 44 in appendix B. Note that all

those variables display more persistent and volatile responses in the baseline model with highly persistent gold ow

sho k than in the baseline model.

50

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Figure 8: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Baseline

model vs baseline model with highly persistent gold ow sho k.

level. Approximately forty years after the impa t, the real wage moves (weakly) below its steady

state level. Figure 5 shows that the gross real interest rate starts to in rease in the period following

the realization of the innovation to the gold ow sho k toward its steady state level. It is worth

to note that the rise of the gold ow sho k has a relatively small ee t on output, onsumption,

investment, labor, apital, real wage and gross real interest rate. As well, those variables onverge to

their respe tive steady state level more qui kly than the gold sto ks, real pri e of gold, real money,

nominal money and gross nominal interest rate variables do.

As said above, there is an other way to get investment de reasing following an innovation to the

gold ow sho k without in reasing the persisten e of that sho k. Spe i ally, as shown in Figure 6,

habit formation in onsumption has the ee t of making investment de reases on impa t. Indeed,

the innovation to the gold ow sho k generates a smoother and more persistent onsumption drop.

From Figure 6, one an observe that the impulse response of onsumption is inversely hump-shaped

when it is subje t to habit formation. Hen e, onsumption ontinues to de rease one period after

the innovation to the gold ow sho k is realized. As a onsequen e, the household nds optimal

to de rease its urrent investment in order to fa e the expe ted fall in its subsequent onsumption.

Even though the transa tion ost wedge behaves similarly in the two alternative models, it has not a

rowding in ee t on investment in the habit model. The habit formation in onsumption weakens the

rowding in ee t, at least initially. Indeed, the habit formation in onsumption leads the transa tion

ost wedge to have a more persistent ee t on onsumption. It follows that the household de reases its

savings and hen efore the investment, at least initially. The gross real interest rate drops on impa t

in the habit model be ause the marginal produ tivity of apital is de reased by a lower level of future

labor. Indeed, in the se ond period, labor is still below its steady state level. As in the baseline model

with highly persistent gold ow sho k, the initial in rease of apital is not enough large to ountera t

the ee t of the future labor on the gross real interest rate. Moreover, note that the trough response

of onsumption is less deeper in the habit model than in the baseline model. Wen (2006) laims

that habit formation in onsumption leads a transitory preferen e sho k to onsumption to have

persistent ee t on onsumption. Consequently, investment in reases following a positive innovation

to the preferen e sho k to onsumption. The persistent ee t of the transitory onsumption sho k is

endogenously generated by the habit formation in onsumption. Thus, in the urrent work, the same

me hanism is at work: The habit formation in onsumption in reases endogenously the persistent

ee t of the transa tion ost wedge on onsumption so that investment in reases initially. Output

and parti ularly labor deviate more strongly from their respe tive steady state on impa t in the

51

baseline model than in the model with habit. Consequently, the real wage in reases more in the

baseline model than in the habit model. Figure 5 shows that on impa t the gross real interest rate

de lines more strongly in the baseline model than in the habit model53.

Thus, the existen e of habit formation in onsumption leads investment to de rease on impa t

as output and onsumption do. However, the initial drop in investment is very weak. Indeed, one

period after the impa t, investment moves above its steady state level while output and onsumption

are still below their respe tive steady state level. Thus, in addition to habit formation in onsumption,

I assume that preferen es over onsumption, leisure and non-monetary gold sto k are non-separable

in order to get investment de reases for a longer period following an innovation to the gold ow sho k.

A ording to Wen (2006), onsumption and leisure are more likely move in opposite dire tions when

onsumption and leisure are better substitute. Thus, following an in rease of the gold ow sho k, the

household would be more willing to de rease its labor supply when the preferen es are non-separable.

Consequently, that the elasti ity of output supply would be ome higher in the omplete model

gold standard model featuring habit formation in onsumption and non-separable preferen es than

in the habit model and the ee t of the intertemporal transa tion ost wedge on investment would

be weakened. In other words, output would experien e a deeper de line in the omplete model than

in the habit model, implying a de rease of investment54. Indeed, Figure 9 shows that the omplete

model predi ts that a rise in the gold ow sho k leads investment to de rease on impa t and to

remain below its steady state level for one period after the realisation of the innovation. The initial

de rease of investment happens to be deeper in the omplete model than in the habit model. Indeed,

on impa t, labor and hen efore output experien e a deeper ollapse in the omplete model than in

the habit model55. On impa t, the onsumption drop is a little less severe in the omplete model than

in the habit model. On impa t, output, onsumption and labor de line more in the baseline model

than in the omplete model. Comparing Figure 6 with Figure 9, one an oberve that on impa t, the

real wage jumps higher in the omplete model than in the habit model. The ee t of the in rease

of the gold ow sho k on the real wage happens to be less persistent in the omplete model than in

the habit model. The initial in rease of the real wage is weaker in the omplete model than in the

baseline model. As reported in gures 5 and 10, the gold sto ks, money, gross nominal interest rate

and real pri e of gold respond similarly to the rise of the gold ow sho k a ross the three alternative

versions of the gold standard model. However, on impa t, the gross real interest rate de reases more

in the omplete model than in the habit model. The innovation to the gold ow sho k ae ts the

gross real interest rate less persistently in the omplete model than in the habit model. The initial

drop of the gross real interest rate is milder in the omplete model than in the baseline model.

5.1.2 Impulse response fun tions to the money supply sho ks

In the previous subsubse tion, I have found that an in rease of the gold ow sho k leads the

money supply to rise. There are other ways to make the money supply in reases endogenously. In

parti ular, a de rease of either the gold ba king sho k or the inverse of money multiplier sho k auses

the money supply to in rease. Thus, here, I study rst the ee t of a de rease of the gold ba king

sho k on the gold standard e onomy, then the ee t of a de line of the inverse of the money multiplier

sho k on the gold standard e onomy.

53This means that there must be dieren es between the impulse responses of the gross nominal interest rate and/or

the real pri e of gold a ross the alternative models. However, I have said above that they were similar when I have

dis ussed the nominal part of the e onomy. Indeed, for example, the dieren es between the impulse response of the

real pri e of gold in the baseline model and the one in the habit model are negligeable when only the nominal part of

the e onomy is onsidered. Sin e any hange in the gold ow sho k has little ee ts on the real part of the e onomy,

those dieren es be ome noti eable in the real part of the e onomy.54Wen (2006) explains why non-separable preferen es over onsumption and leisure an lead investment to behave

pro y li ally, in the ase where preferen es in onsumption are time-separable. The argument seems to hold in the

ase where preferen es in onsumption are time-separable.55The ee ts of habit formation in onsumption and non-separable preferen es on the behavior of investment are

not totally satisfa tory. Indeed, as shown in Figure 9, even tough investment de reases on impa t as output does, one

annot on lude that investment is pro y li al.

52

0 20 40−0.1

−0.05

0

0.05

0.1

Year

perc

ent d

evia

tion

Output

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Consumption

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Investment

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Labor

0 20 40−0.02

0

0.02

0.04

0.06

Yearpe

rcen

t dev

iatio

n

Capital

0 20 400

0.02

0.04

0.06

Year

perc

ent d

evia

tion

Real wage

0 20 40−0.1

−0.05

0

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−5

0

5

10

Year

perc

ent d

evia

tion

Velocity

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Wedge

Figure 9: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ow sho k:

Complete model (a).

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Gold demand

0 50 1000

10

20

30

Year

perc

ent d

evia

tion

Non−monetary gold

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Monetary gold

0 50 100−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Nominal interest rate

0 50 100−8

−6

−4

−2

0x 10

−3

Year

perc

ent d

evia

tion

Real interest rate

0 50 100−20

−15

−10

−5

0

Year

perc

ent d

evia

tion

Real gold price

0 50 1000

5

10

15

20

Year

perc

ent d

evia

tion

Nominal money stock

0 50 100−10

−5

0

5

Year

perc

ent d

evia

tion

Real money

0 50 1000

0.5

1

Year

devi

atio

n

Gold supply

Figure 10: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ow sho k:

Complete model (b).

53

5.1.2.1 Impulse response fun tions to the gold ba king sho k

Figures 11 and 12 report the impulse responses of the baseline and habit models to a single negative

innovation to the gold ba king sho k. The IRFs of the basline model's variables are represented with

starred lines whereas the IRFs of the habit model are represented with ir le lines. In period 0, thegold ba king sho k is assumed to de rease by 1 per ent.

0 20 40−0.06

−0.04

−0.02

0

Year

perc

ent d

evia

tion

Gold demand

baselinehabit

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.8

−0.6

−0.4

−0.2

0

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−0.03

−0.02

−0.01

0

0.01

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 400

2

4

6x 10

−4

Year

perc

ent d

evia

tion

Real interest rate

0 20 40−0.3

−0.2

−0.1

0

0.1

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Nominal money stock

0 20 40−0.1

0

0.1

0.2

0.3

Year

perc

ent d

evia

tion

Real money

0 20 40−1

−0.5

0

Year

perc

ent d

evia

tion

Gold backing

Figure 11: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ba king sho k

(a).

First, I analyze the dynami behavior of non-monetary gold sto k, monetary gold sto k, total gold

sto k, real pri e of gold, gross nominal interest rate, nominal money and real money. From Figure

11, one an note that the baseline and habit models generate, through the gold ba king sho k, very

similar IRFs for those variables. Consequently, the existen e of habit formation in onsumption

does not ae t the impulse responses of those variables to a single negative innovation to the gold

ba king sho k. In the following, I onsider indierently the baseline model or the habit model when

I omment the IRFs of non-monetary gold sto k, monetary gold sto k, total gold sto k, real pri e of

gold, gross nominal interest rate, nominal money and real money.

By lowering the gold ba king ratio, the entral bank lets the household knows that it is willing

to supply more money in ex hange of a same amount of monetary gold sto k. As a result, the value

of gold de lines. In other words, the innovation to the gold ba king sho k leads the real pri e of gold

(the pri e level) to fall (to rise) on impa t, as shown in Figure 11. Therefore, the household goes

to the entral bank to buy gold for non-monetary use. It follows, that the household in reases its

non-monetary gold holding and the entral bank de reases its monetary gold sto k. Indeed, from

Figure 11, one an observe that the de rease of the gold ba king sho k auses the non-monetary gold

sto k to move up on impa t and the monetary gold sto k to fall on impa t. Nonetheless, the gold

standard model predi ts that the de line of monetary gold is smaller in size than the de rease of the

gold ba king ratio. Therefore, the entral bank raises its money supply: As reported in Figure 11,

the nominal money in reases on impa t, onsistently to the in rease of the nominal money supply.

As shown in Figure 11, the total gold sto k existing in the e onomy remains at its steady state level

on impa t: In the urrent ase, the gold ow sho k sti ks to its steady state level so that on impa t it

is just su ient to over the depre iation of the non-monetary gold sto k brought from the previous

period.

Figure 11 shows that the in reases in the nominal money and the non-monetary gold sto k are

followed by a de line of the gross nominal interest rate. Hen e, the (negative) innovation to the gold

ba king sho k generates a liquidity ee t and a non-monetary gold liquidity ee t. The liquidity

54

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Output

baselinehabit

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Consumption

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Investment

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Labor

0 20 40−5

0

5

10

15x 10

−4

Year

perc

ent d

evia

tion

Capital

0 20 40−3

−2

−1

0x 10

−3

Year

perc

ent d

evia

tion

Real wage

0 20 400

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−0.3

−0.2

−0.1

0

0.1

Year

perc

ent d

evia

tion

Velocity

0 20 40−15

−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Wedge

Figure 12: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ba king sho k

(b).

ee t makes it optimal for the household to in rease its demand of real money. Indeed, the gold

standard model predi ts that the real money jumps in response to a de rease in the gold ba king

sho k, as displayed in Figure 11. As well, the non-monetary gold liquidity ee t leads the real non-

monetary gold sto k to in rease on impa t: As one an note from Figure 11, the (log-)deviation of

non-monetary gold from its steady state level is larger than the (log-)deviation of the real pri e of

gold from its steady state level.

From Figure 11, one an observe that non-monetary gold sto k, nominal money and real money

rea h their pi k response to the (negative) innovation to the gold ba king sho k on impa t. The

monetary gold sto k, real pri e of gold and gross nominal interest rate rea h their trough response

to fall of the gold ba king sho k on impa t too. Then, non-monetary gold sto k, monetary gold

sto k, total gold sto k, real pri e of gold, gross nominal interest rate, nominal money and real money

onverge to their respe tive steady state level. Nonetheless, the de rease of gold ba king sho k has

a relatively persistent ee t on those variables56. In parti ular, it takes approximately 25 years for

nominal money to rea h ba k its steady state level. Afterwhat, it even moves (weakly) below its

steady state level. Real money returns to its steady state level approximately 45 years after the

impa t. In turn, it takes around 30 years for non-monetary gold sto k and gross nominal interest

rate to ome ba k to their respe tive steady state level. 50 years after the innovation to the gold

ba king sho k hit the e onomy, the monetary gold sto k is still below its steady state level. The

real pri e of gold is the rst variable, among those onsidered here, to onverge to its steady state

level, that is around 20 years after the impa t. Then, it moves (weakly) above its steady state level.

From Figure 11, one an note the total gold sto k starts to de rease one period after the impa t

for approximately 30 years. As said above the total gold sto k in reases (de reases) if the inow

of gold is larger (lower) than the depre iation of the non-monetary gold sto k brought from the

previous period. In the urrent ase, the non-monetary gold sto k is above its steady state level for

approximately 30 years after the impa t while the gold ow sho k remains at its steady state level for

all that period. As a onseqen e, the gold inow happens to be not su ient to over the depre iation

of non-monetary gold sto k during all that period. Thus, the total gold sto k de reases. Thus, the

total gold sto k starts to move ba k to its steady state level one period after the non-monetary gold

sto k returns to its steady state level.

56The adjustment me hanism be omes qui ker if the depre iation rate of non-moneatry gold sto k is raised. The

explanation of that is the same as the one provided when the IRFs to gold ow sho k are dis ussed.

55

Se ond, I fo us my attention on the real part of the e onomy. In the gold standard model, the

gold ba king sho k an be interpreted as a nominal sho k sin e it inuen es the money supply of

the e onomy through the optimal household's de ision on non-moneatary gold sto k and hen efore

through the monetary gold sto k. As for the gold ow sho k, a hange in the gold ba king ratio

is transmitted to the real part of the e onomy through the transa tion ost wedge and the optimal

ondition on the non-monetary gold sto k.

As shown in Figure 12, the baseline model predi ts that the (negative) innovation to the gold

ba king sho k leads onsumption to rise on impa t. Be ause of the liquidity ee t implied by the

de rease in the gold ba king ratio, the transa tion ost wedge de lines on impa t: The de rease

of of the gold ba king ratio pushes the gross nominal interest rate down, whi h in turn leads the

transa tion ost wedge to de rease. The initial fall of transa tions osts makes it optimal for the

household to in rease its demand for onsumption good. Moreover, the optimal ondition (56) states

that if the gross nominal interest rate drops, the marginal rate of substitution of onsumption for

real non-monetary gold must de rease too. The non-monetary gold liquidity ee t leads the gross

nominal interest rate and the real non-monetary gold to move in opposite dire tions. Taking into

a ount the ollapse of the transa tion ost wedge, the in rease of the real non-monetary gold sto k

is suently larger in size than the de line of the nominal interest rate to make it optimal for the

household to in rease its onsumption.

In the baseline model, the de rease of the transa tion ost wedge, that follows the drop in the gold

ba king ratio, leads the opportunity ost of leisure, in terms of the marginal utility of onsumption,

to rise. Thus, it be omes protable for the household to redu e its leisure. It follows that labor

and output in rease on impa t, as shown in Figure 12. The left window of Figure 13 reports that

lowering the gold ba king ratio auses investment to in rease too in the baseline model. Note that the

transa tion ost wedge moves ba k to its steady state level after its initial drop. It follows that the

intertemporal transa tion ost wedge falls below its steady state level when the innovation to the gold

ba king sho k is realized. The de line of the intertemporal transa tion ost wedge does not have a

rowding out ee t on investment, at least initially. The gold ba king sho k is su iently persistent

so that the fri tions indu ed by the transa tions osts are small. The interval of time in whi h

the transa tion ost wedge is below its steady state level is su iently large so that the ee t of the

transa tion ost wedge on onsumption is persistent, at least initially. The household nds it optimal

to in rease initially its savings in order to ensure that its future onsumption is still su iently high.

By postponing its onsumption, the household a umulates more apital. Therefore, investment

in reases. However, the response of investment to the de line of the gold ba king sho k is very small.

Hen e, higher persisten e of the gold ba king sho k is required to in rease to volatility of investment.

As shown in Figure 12, the gross real interest rate in reases on impa t: Sin e future labor is still

well above its steady state level, the marginal produ tivity of apital is shifted upwards. The initial

in rease of apital is too small to push the marginal produ tivity of apital down. Figure 12 reports

that the de rease of the gold ba king sho k leads the average labor produ tivity to de rease be ause

labor in reases more than output does on impa t. As a result, the real wage de reases when the gold

ba king ratio is lowered.

Figure 12 shows that output, onsumption, investment, labor and real wage go ba k to their

respe tive steady state level one period after the innovation to the gold ba king sho k is realized in

the baseline model. Output, onsumption, labor and real wage return to their respe tive steady state

level aproximately 45 years after the impa t. Investment returns to its steady state level qui kly,

that is aproximately 6 years after the impa t. Then it moves below its steady state level. Later

in the impulse responses, output, onsumption and labor drop below their respe tive steady state

level. The impulse response of apital to the downward shift of the gold ba king ratio is hump-shaped.

Capital ontinues to in rease for four years after the impa t. Afterwhat it de reases toward its steady

state level. Later in the impulse response, as investment is de reasing below its steady state level,

it falls below its steady state level. As shown in Figure 11, one period after the impa t, the gross

real interest rate de reases ba k toward its steady state level. It gets ba k to its steady state level

aproximately 30 years after the realization of the innovation to the gold ba king sho k. It is worth to

note that the innovation to the gold ba king sho k has relatively little ee t on output, onsumption,

investment, labor, apital, real wage and gross real interest rate. Globally, those variables onverge

to their respe tive steady state as slowly as the gold sto ks, real pri e of gold, nominal money, real

money and gross nominal interest rate do.

As mentioned above, the response of investment to the (negative) innovation to the gold ba king

sho k is positive but is relatively weak. Figures 12 and 13 show that habit formation in onsumption

56

0 10 20 30 40 50−2

−1

0

1

2

3

4x 10

−4

Year

perc

ent d

evia

tion

Baseline model

0 10 20 30 40 50−2

0

2

4

6

8

10x 10

−3

Yearpe

rcen

t dev

iatio

n

Habit model

Figure 13: Impulse response fun tions of investment to a 1 per ent innovation to the inverse of money

multiplier sho k: Baseline model vs habit model.

amplies the ee t of a de rease of the gold ba king ratio on investment. Indeed, onsumption

ontinues to in rease for few periods after the impa t. Thus, expe ting onsumption in rease in

the subsequent periods, the household hooses to rise its savings through apital a umulation.

Consequently, investment in reases more strongly on impa t in the habit model than in the baseline

model. As said above, when the household is subje t to habit formation in onsumption, the ee ts of

the transa tion ost wedge on onsumption be ome more persistent so that the household hooses to

in rease its onsumption over several periods rather than over one single period. The initial response

of onsumption to the de rease of the gold ba king sho k is smaller in the habit model than in the

baseline model. As well, the pi k response of the onsumption is smaller in the habit model than

in the baseline model. Interestingly, as one an observe in Figure 12, the habit model generates a

hump-shaped impulse response of output to the innovation to the gold ba king sho k. Indeed, output

ontinues to in rease one period after the impa t. As for onsumption, the initial in rease of output

is smaller in the habit model than in the baseline model. When the innovation to the gold ba king

sho k is realized, labor in reases in the habit model but less strongly than in the baseline model,

whi h is onsistent with the impulse response of output in the habit model. The real wage de lines

in the habit model when the gold ba king ratio is lowered, as in the baseline model. Nonetheless,

the initial drop of the real wage is deeper in the baseline model than in the habit model. The gross

real interest rate moves above its steady state level when the innovation to the gold ba king sho k

is realized. However, the initial in rease of the gross real interest rate is milder in the habit model

than in the baseline model.

I have also omputed the IRFs of the omplete model gold standard model featuring habit

formation in onsumption and non-separable preferen es to a (negative) innovation to the gold

ba king sho k. Those IRFs are reported in Figures 14 and 15.

As said above, a ording to Wen (2006), onsumption and leisure are more likely to move in

opposite dire tion if the preferen es over onsumption and leisure are non-separable Thus, following

a de rease of the gold ba king ratio, in reasing labor supply should be less ostly to the household

when the preferen es are non-separable. Consequently, output would jump higher on impa t in

the omplete model than in the habit model, implying a higher initial in rease in investment too.

Comparing Figure 15 with Figure 11, one an note that on impa t, investment in reases higher in

the omplete model than in the habit model. Additionally, investment remains above its steady

state level afer the impa t for a longer time in the omplete model than in the habit model. Indeed,

the initial in reases of labor and hen efore output are stronger in the omplete model than in the

57

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Output

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Consumption

0 20 40−5

0

5

10

15x 10

−3

Year

perc

ent d

evia

tion

Investment

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Labor

0 20 40−1

0

1

2x 10

−3

Yearpe

rcen

t dev

iatio

n

Capital

0 20 40−3

−2

−1

0x 10

−3

Year

perc

ent d

evia

tion

Real wage

0 20 400

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Real interest rate

0 20 40−0.3

−0.2

−0.1

0

0.1

Year

perc

ent d

evia

tion

Velocity

0 20 40−15

−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Wedge

Figure 14: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ba king sho k:

Complete model (a).

0 20 40−0.06

−0.04

−0.02

0

Year

perc

ent d

evia

tion

Gold demand

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.8

−0.6

−0.4

−0.2

0

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−0.03

−0.02

−0.01

0

0.01

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 400

1

2

3

4x 10

−4

Year

perc

ent d

evia

tion

Real interest rate

0 20 40−0.3

−0.2

−0.1

0

0.1

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Nominal money stock

0 20 40−0.1

0

0.1

0.2

0.3

Year

perc

ent d

evia

tion

Real money

0 50 100−1

−0.5

0

Year

perc

ent d

evia

tion

Gold backing

Figure 15: Sele ted impulse response fun tions to a 1 per ent innovation to the gold ba king sho k:

Complete model (b).

58

habit model. Furthermore, when the innovation to the gold ba king sho k is realized, onsumption

in reases less strongly in the omplete model than in the habit model. Besides, the in reases of

output, onsumption, investment and labor are milder in the omplete model than in the baseline

model. As shown in Figures 12 and 14, the initial real wage drop is deeper in the omplete model

than in the habit model. Nonetheless, the larger initial ollapse of the real wage is generated by the

baseline model. Comparing Figure 15 with Figure 11, one an note that the gold sto ks, real pri e of

gold, nominal money, real money, gross nominal interest rate respond to the innovation to the gold

ba king sho k similarly a ross the three alternative versions of the gold standard model. On impa t,

the gross real interest rate in reases in the omplete model as mu h as in the habit model. However,

The initial jump of the gross real interest rate is higher in the baseline model than in the omplete

model. The innovation to the gold ba king sho k has a less persistent ee t on the gross real interest

rate in the omplete model than in the habit and baseline models.

If an in rease of the gold ow sho k or a de rease of the gold ba king sho k leads the entral bank

to raise the money supply, those two sho ks do not have the same ee ts on the e onomy. When

the in rease of the money supply results from a drop in the gold ba king ratio, a liquidity ee t

omes out: The in rease of the money supply is followed by a drop in the gross nominal interest

rate. Instead, when the money supply is shifted upwards be ause of an in rease of the gold inow,

the liquidity ee t does not happen. When there is a liquidity ee t, the transa tion ost wedge is

shifted upwards and hen efore ae ts the e onomy as a positive preferen e sho k to onsumption

does. The transa tion ost wedge auses an urge to onsume. If the liquidity ee t does not emerge,

the transa tion ost wedge moves below its steady state level and therefore leads the household

to de rease its onsumption. The transa tion ost wedge behaves as a negative preferen e sho k

to onsumption. Consequently, lowering the gold ba king ratio has an expansionary ee t on the

e onomy whereas in reasing the inow of gold has a re essive ee t on the e onomy. The dieren es

between the ee ts of an in rease of the gold ow sho k on the e onomy and the ee ts of a de rease

of the gold ba king sho k on the e onomy show up also in quantitative terms. Spe i ally, the ee ts

aused the positive innovation to the gold ow sho k on the e onomy are larger and more peristent

than the ee ts aused by a negative innovation to the gold ba king sho k on the e onomy. The fa t

that a de rease of the gold ba king sho k generates a liquidity ee t while an in rease of the gold ow

sho k does not is puzzling be ause the market onditions are not modied. Here, I put forward the

following possible explanation. Expe ting that the interval of time in whi h the real pri e of gold is

below its steady state level would be larger following a positive innovation to the gold ow sho k than

following a negative innovation to the gold ba king sho k, the household is more willing to in rease

its real money demand in response to the latter sho k than in response to the former. Therefore,

the gross nominal interest rate would have to drop in order to ensure that the real money demand

in reased following the de line of the gold ba king ratio. The gross nominal interest rate would not

have to de line following an in rease of the inow of gold sin e the real money demand de reased.

Agreed, those omments hold for an arti ial e onomy where the pri es real pri e of gold, nominal

wage and gross nominal interest rate are determined in ompetitive markets. The only fri tions

that appear in this e onomy are introdu ed by the transa tions osts. Thus, within this framework,

it seems that if the publi authorities want to drive the e onomy on a expansionary phase of the y le

through an in rease of the money supply, it would be better to lower the gold ba king ratio rather

than to import more gold in the e onomy. However, the monetary poli y onsisting in lowering the

gold ba king ratio has to be ondu ted ausiously. Indeed, if the gold ba king ratio is set to a very

low level, the additional quantity of non-monetary gold sto k that the household hooses to hold,

may be larger than the total quantity of monetary gold held by the entral bank. Consequently, the

monetary authority would not be able to stand ready to sell or buy gold at the same xed pri e of

gold, PG. The entral bank may have to raise the pri e of gold. This would lead the e onomy to

leave the gold standard system. In the urrent state of the model, I annot nd the level of the gold

ba king ratio, µ2,t, under whi h, the xity of the pri e gold, PG, annot be held. To do so, I should

have dened expli itly and separately the pri e level and the real pri e of gold so that the ondition

on the xity of the pri e of gold would have been, somehow, endogeneized. In the urrent work, I

assume that this ondition is always fullled57.

57The reader interested about this question is refered to Goodfriend (1988).

59

5.1.2.2 Impulse response fun tions to the inverse of money supply sho k

In the gold standard model, the inverse of money multiplier sho k and the gold ba king sho k are

expe ted, by denition, to have similar ee ts on the e onomy, at least qualitatively. Abviously, if the

degree of persisten e of the inverse of money multiplier sho k is dierent from the degree of persisten e

of the gold ba king sho k, those two sho ks will ae t dierently the e onomy from a quantitative

perspe tive. As a matter of fa t, a ording to the alibration of the autoregressive parameters of the

exogenous sto hasti pro esses, the inverse of money multiplier sho k is less persistent than the gold

ba king sho k. This dieren e in terms of persisten e might lead the two money supply sho ks to

have dierent impa ts on the e onomy quantitatively as well as qualitatively. Indeed, if the degree

of persisten e of the inverse of money multiplier sho k was not enough high, it would generate a

rowding out ee t on investment through the transa tion ost wedge. Thus, in what follows, I will

mainly fo us my attention on the dieren es between the ee ts of the two money supply sho ks on

the e onomy. The e onomi me hanisms behind the impulse responses of the model's variables to a

negative innovation to the inverse of money multiplier sho k are the same as those behind the impulse

responses of the model's variables to a negative innovation to gold ba king sho k. The usefulness of

the distin tion between the gold ba king sho k and the inverse of the money multiplier sho k may

not be lear at this stage of the analysis. A tually, this distin tion will make more sens when the

gold standard model is onfronted to the histori al data.

Figures 16 and 17 report the impulse responses of the baseline model and model with habit to a

single negative innovation to the inverse of money multiplier sho k. The IRFs of the basline model's

variables are represented with starred lines while the IRFs of the model with habit are represented

with ir le lines. In period 0, the inverse of money multiplier sho k is assumed to de rease by 1per ent.

0 20 40−0.03

−0.02

−0.01

0

Year

perc

ent d

evia

tion

Gold demand

baselinehabit

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.8

−0.6

−0.4

−0.2

0

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−0.04

−0.02

0

0.02

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 400

2

4

6x 10

−4

Year

perc

ent d

evia

tion

Real interest rate

0 20 40−0.15

−0.1

−0.05

0

0.05

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Nominal money stock

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Real money

0 20 40−1

−0.5

0

Year

perc

ent d

evia

tion

Inverse of money multiplier

Figure 16: Sele ted impulse response fun tions to a 1 per ent innovation to the inverse of money

multiplier sho k (a).

From Figure 16, one an note that the baseline and habit models generate, through the inverse of

money multiplier sho k, very similar IRFs for non-monetary gold sto k, monetary gold sto k, total

gold sto k, real pri e of gold, gross nominal interest rate, nominal money and real money. Therefore,

the existen e of habit formation in onsumption does not ae t the impulse responses of those

variables to a single negative innovation to the inverse money multiplier sho k. This nding has been

also obtained with a negative innovation to the gold ba king sho k. Thus, I onsider indierently the

baseline model or the habit model when I omment the IRFs of non-monetary gold sto k, monetary

gold sto k, total gold sto k, real pri e of gold, gross nominal interest rate, nominal money and real

60

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Output

baselinehabit

0 20 40−5

0

5

10

15x 10

−3

Year

perc

ent d

evia

tion

Consumption

0 20 40−15

−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Investment

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Labor

0 20 40−3

−2

−1

0

1x 10

−3

Year

perc

ent d

evia

tion

Capital

0 20 40−3

−2

−1

0x 10

−3

Year

perc

ent d

evia

tion

Real wage

0 20 400

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−0.4

−0.2

0

0.2

0.4

Year

perc

ent d

evia

tion

Velocity

0 20 40−0.02

−0.01

0

0.01

Year

perc

ent d

evia

tion

Wedge

Figure 17: Sele ted impulse response fun tions to a 1 per ent innovation to the inverse of money

multiplier sho k (b).

money. The signs of the impulse responses of gold sto ks, real pri e of gold, gross nominal interest

rate, nominal money and real money to the innovation to the inverse of the money multiplier sho k

are identi al to signs of the impulse responses of those variables to the innovation to the gold ba king

sho k. Nonetheless, there are some dieren es between the impulse responses of those variables to

a de rease of the inverse of money multiplier and the impulse responses of those variables to a drop

in the gold ba king ratio. Not suprisingly, the innovation to the inverse of money multiplier sho k

has a less persistent ee t on gold sto ks, real pri e of gold, nominal money, real money and gross

nominal interest rate than the innovation to the gold ba king sho k has. On impa t, the deviations

of non-monetary gold sto k, monetary gold sto k, total gold sto k, gross nominal interest rate, and

real money from their respe tive steady state level are slightly larger following a de line of the inverse

of money multiplier than following a drop in the gold ba king ratio. Instead, the drop of the real

pri e of gold is signi antly deeper when it is the gold ba king ratio whi h is lowered rather than the

inverse of the money multiplier. As well, on impa t, the jump of nominal money above its steady

state level is slightly higher following an downward shift of the gold ba king ratio than following a

de rease of the inverse of money multiplier.

Now, I fo us my attention on the real part of the e onomy. In the arti ial gold standard e onomy,

the inverse of the money multiplier sho k an be dened as a nominal sho k be ause it determines,

indire tly, the money supply of that e onomy, as the gold ba king sho k does. As for the gold ow

sho k and the gold ba king sho k, a hange in the inverse of money multiplier sho k is transmitted

to the real part of the e onomy through the transa tion ost wedge and the optimal ondition on the

non-monetary gold sto k. Considering only the baseline model predi tions, Figures 17 and 12 show

that the signs of the impulse responses of output, onsumption, labor, real wage and transa tion ost

wedge to the negative innovation to the inverse of the money multiplier sho k are identi al to signs of

the impulse responses of those same variables to the negative innovation to the gold ba king sho k.

However, investment and hen efore apital drop on impa t following a de rease of the inverse of

money multiplier whereas those two variables jump above their respe tive steady state when the gold

ba king ratio is lowered. Hen e, in the baseline model, the de rease of the inverse of money multiplier

leads the transa tion ost wedge to have a rowding out ee t on investment. The inverse of money

multiplier sho k is not su iently persistent to rule out the rowing out ee t of the transa tion

ost wedge on investment. Spe i ally, the innovation to the inverse of money multiplier sho k has

not enough persistent ee t on the transa tion ost wedge so that the distortions introdu ed by the

transa tion ost wedge are large. The initial drop of the transa tion ost wedge is larger following

61

a de rease of the inverse of money multiplier than following a de line of the gold ba king ratio:

The de rease of the inverse of money multiplier leads to a sign antly stronger urge to onsume

than a drop of the gold ba king ratio does. Consequently, the initial in rease of onsumption is

signi antly higher following a de rease of the inverse of money multiplier sho k than following a

drop in the gold ba king ratio. As a result, investment de lines when the inverse of money multiplier

is lowered. As well, the innovation to the inverse of money multiplier sho k has a less persistent

ee t on onsumption than the innovation to the gold ba king sho k has. In addition, the impulse

responses of labor and output to the innovation to the inverse of money multiplier sho k are less

persistent than the impulse responses of those two variables to the innovation to the gold ba king

sho k. The initial jumps of labor and output above their respe tive steady state level are slightly

higher following a de rease of the gold ba king ratio than following a drop of the inverse of money

multiplier. Globally, a ording to Figures 17, 12, 16 and 11, the impulse responses of the real wage

and the gross real interest rate to the innovation to the inverse of money multiplier sho k are similar

to the impulse responses of those same variables to the innovation to the gold ba king sho k.

As shown in Figure 17, introdu ing habit formation in onsumption in the baseline model allows to

weaken the rowding out ee t of the transa tion ost wedge on investment. Indeed, the habit model

predi ts that investment moves above its steady state level when the inverse money multiplier sho k is

de reased, at least intially. The rowding out ee t of the transa tion ost wedge on investment is even

more dampened down when the gold standard model features both habit formation in onsumption

and non-separable preferen es. Indeed, from Figures 18 and 17 one an observe that the initial

in rease of investment following a de line of the inverse of money multiplier sho k is higher in the

omplete model than in the habit model. As well, the interval of time in whi h investment is above

its steady state level is slightly larger in the omplete model than in the habit model. In both

habit and omplete models, the impulse response of onsumption to the innovation to the inverse of

money multiplier sho k is hump-shaped, as the impulse response of onsumption to the innovation

to the gold ba king sho k is. Nonetheless, in both habit and omplete models, the pi k response

of onsumption is higher following a drop of the gold ba king ratio than following a de rease of the

inverse of money multiplier. Additionally, in both habit and omplete models, the pi k response of

onsumption takes pla e later when the gold ba king ratio is lowered than when the inverse of money

multiplier is de reased. Output ontinues to in rease one period after the realization of the innovation

to the gold ba king sho k in the habit and omplete model whereas, it already de reases ba k to its

steady state level one period after the realization of the innovation to the inverse of money multiplier

sho k in the habit and omplete model. As well, onsidering both habit and omplete models, the

de rease of the inverse of money multiplier has less persistent ee ts on output and labor than the

drop of the gold ba king ratio does. The initial in reases of labor and real wage are higher following

a de rease of the gold ba king ratio than following a drop of the inverse of money multiplier in both

habit and omplete models.

Comparing Figure 19 with Figure 16, one an observe that the gold sto ks, real pri e of gold,

nominal money, real money, gross nominal interest rate respond to the negative innovation to the

inverse of money multiplier sho k similarly a ross the three alternative versions of the gold standard

model. This nding is identi al to the one obtained with the inverse of money multiplier sho k.

However, in all three versions of the gold standard model, the de rease of the inverse of money

multiplier sho k has less persistent ee ts on those variables than the drop of the gold ba king sho k.

Furthermore, onsidering baseline, habit and omplete models, the initial in rease of the gross real

interest rate is higher following a drop of the gold ba king ratio than following a de line of the inverse

of the money multiplier.

5.1.3 Impulse response fun tions to the produ tivity sho k

Now, I study the ee ts of an in rease of produ tivity on the arti ial gold standard e onomy.

Figures 21 and 20 display the impulse responses of the baseline model and model with habit to a

single positive innovation to the produ tivity sho k. The IRFs of the basline model's variables are

represented with starred lines while the IRFs of the model with habit are represented with ir le

lines. In period 0, the produ tivity sho k is assumed to in rease by 1 per ent.

First, I onsider the ee ts of an in rease of produ tivity on the baseline model. Figure 20

shows that the innovation to the produ tivity sho k does not ae t the non-monetary gold sto k,

monetary gold sto k, total gold sto k, nominal money and the gross nominal interest rate. However,

62

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Output

0 20 40−2

0

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Consumption

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Investment

0 20 40−5

0

5

10x 10

−3

Year

perc

ent d

evia

tion

Labor

0 20 40−5

0

5

10x 10

−4

Yearpe

rcen

t dev

iatio

n

Capital

0 20 40−3

−2

−1

0x 10

−3

Year

perc

ent d

evia

tion

Real wage

0 20 400

2

4

6x 10

−3

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−0.4

−0.2

0

0.2

0.4

Year

perc

ent d

evia

tion

Velocity

0 20 40−0.02

−0.01

0

0.01

Year

perc

ent d

evia

tion

Wedge

Figure 18: Sele ted impulse response fun tions to a 1 per ent innovation to the inverse of money

multiplier sho k: Complete model (a).

0 20 40−0.03

−0.02

−0.01

0

Year

perc

ent d

evia

tion

Gold demand

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.8

−0.6

−0.4

−0.2

0

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−0.04

−0.02

0

0.02

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 400

1

2

3

4x 10

−4

Year

perc

ent d

evia

tion

Real interest rate

0 20 40−0.15

−0.1

−0.05

0

0.05

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Nominal money stock

0 20 40−0.2

0

0.2

0.4

0.6

Year

perc

ent d

evia

tion

Real money

0 20 40−1

−0.5

0

Year

perc

ent d

evia

tion

Inverse of money multiplier

Figure 19: Sele ted impulse response fun tions to a 1 per ent innovation to the inverse of money

multiplier sho k: Complete model (b).

63

0 20 40−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Gold demand

0 20 40−0.1

0

0.1

0.2

0.3

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−15

−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 40−0.1

−0.05

0

0.05

0.1

Yearpe

rcen

t dev

iatio

n

Real interest rate

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

−0.1

0

0.1

0.2

Year

perc

ent d

evia

tion

Nominal money stock

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real money

0 20 400

0.5

1

Year

perc

ent d

evia

tion

Productivity

baselinehabit

Figure 20: Sele ted impulse response fun tions to a 1 per ent innovation to the produ tivity sho ks

(a).

0 20 400

0.5

1

1.5

2

Year

perc

ent d

evia

tion

Output

baselinehabit

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Consumption

0 20 40−2

0

2

4

6

Year

perc

ent d

evia

tion

Investment

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Labor

0 20 400

0.5

1

Year

perc

ent d

evia

tion

Capital

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real wage

0 20 40−1

0

1

2

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−0.15

−0.1

−0.05

0

0.05

Year

perc

ent d

evia

tion

Velocity

0 20 40−6

−4

−2

0

2x 10

−3

Year

perc

ent d

evia

tion

Wedge

Figure 21: Sele ted impulse response fun tions to a 1 per ent innovation to the produ tivity sho ks

(b).

64

as reported in Figures 21 and 20, the other variables58 real pri e of gold, gross real interest rate,

output, onsumption, investment, labor, apital, real wage and real rental rate of apital move

away from their respe tive steady state level following an in rease of the produ tivity sho k. The

transa tion ost wedge does not distort the e onomy following the in rease of the produ tivity sho k

when the baseline model is onsidered. The orthogonality of the gold sto ks, nominal money and gross

nominal interest rate to the produ tivity sho k is due to the log and time-separability spe ation of

the preferen es in the baseline model59. Nevertheless, it is still useful to analyze the ee t of a rise

of produ tivity on the baseline model.

The in rease of the produ tivity sho k raises the real wage, that is the marginal produ tivity

of labor. A knowledging that the urrent wage is higher than the expe ted subsequent real wages,

the household is more willing to in rease its labor supply when the innovation to the produ tivity

sho k is realized. Indeed, labor in reases on impa t in the baseline model, as shown in Figure 21.

The in reases of both produ tivity sho k and labor lead output to move above its steady state level

on impa t. As a result, the log-deviation output from its steady state level is larger than the log-

deviation of labor from its steady state level, onsistently to the in rease of the real wage. This

an be observed in Figure 21. The baseline model predi ts that the additional output is essentially

absorbed by investment. Indeed, Figure 21 reports that the 1.6 per ent rise of output is used to

in rease investment by 5.6 per ent. This allows the household to have a higher onsumption level

omparatively to its steady state level, in the urrent period as well as in the future periods. As

shown in Figure 21, the impulse response of onsumption to the innovation to the produ tivity sho k

is hump-shaped. In parti ular, onsumption rises mildly on impa t then ontinues to in rease for

two periods. Afterwhat it de reases ba k to its steady state level. One period after the impa t the

produ tivity sho k and labor are still above their respe tive steady state level so that the marginal

produ tivity of apital is in reased. The apital sto k moves above its steady state level on impa t

sin e investment is in reasing. However, the initial jump of apital is not enough high to oset the

ee ts of future produ tivity sho k and labor on the marginal produ t of apital. Therefore, the

gross real interest rate in reases on impa t, as reported in Figure 20. The initial in rease of the gross

real interest rate is onsistent with the hump-shaped impulse response of onsumption to the in rease

of the produ tivity sho k. The gross real interest rate moves below its steady state level when the

onsumption rea hes its pi k response.

As reported in Figure 21, output, labor and investment de rease ba k to their respe tive steady

state level one period after the impa t. Those three variables rea h ba k qui kly their respe tive

steady state level. In parti ular, output, labor and investment return to their respe tive steady state

level 30, 4 and 5 periods after the impa t, respe tively. Little apital sto k is a umulated through

investment so that the interval of time in whi h output remains above its steady state level is relatively

short. Consumption returns to its steady state level later than output does: Consumption rea hes

ba k its steady state level approximately 40 periods after the impa t. Indeed, the household hooses

to smooth its onsumption behavior in order to keep its onsumption above its steady state level for

a period of time as long as possible. Note that labor drops below its steady state level after having

returned to its steady state level. In parti ular, labor moves below its steady state level when apital

starts to de line ba k to its steady state level. Thus, few periods after the impa t, the household

hooses to enjoy higher onsumption and leisure levels omparatively to their respe tive steady state

level by taking advantage of the apital sto k, previously a umulated. Investment also moves below

its steady state level after having rea hed ba k its steady state level in order to keep onsumption

above its steady state level. The real wage de lines ba k to its steady state level one period after the

impa t. Nonetheless, the interval of time in whi h it remains above its steady state level is relatively

large: The real wage returns to its steady state level approximately 40 periods after the realiszation

of the innovation to the produ tivity sho k. Indeed, labor de reases ba k to its steady state level

58If the gross nominal interest rate does not respond to the innovation to the produ tivity sho k, the onsumption-

based velo ity of money and the transa tion ost wedge do not move away from their respe tive steady state level for

all the period following an in rease of produ tivity, onsistently to equations (48) and (43).59It is not easy to have a formal proof of this statement. However, I have simulated a monetary model with a

transa tion ost fun tion and log-separable preferen es. The household is not subje t to habit formation in onsump-

tion. There is no motive for the household to hold non-monetary gold sto k and the money supply is determined

independently of the monetary gold sto k of the entral ban k. In parti ular the money supply is exogenously dened

by a sto hasti pro ess. I have found that the gross nominal interest rate does not respond to an innovation to the

produ tivity sho k.

65

qui ker than output does so that the marginal produ tivity of labor is kept above its steady state

level for a relatively long time. The drop of labor below its steady state level has also maintained the

marginal produ tivity of labor above its steady state level. One reason why the produ tivity sho k

has not a strong persistent ee t on output, labor and investment is that the produ tivity sho k is

itself weakly persistent. Figure 20 shows that the produ tivity sho k returns to its steady state level

approximately 15 periods after the impa t. The la k of a strong internal propagation me hanism in

the baseline model also explains why output, labor and investment go ba k to their respe tive steady

state level so qui kly60.

As said above, the in rease of the produ tivity sho k ae ts also the real pri e of gold and

real money in the baseline model. More pre isely, the real pri e of gold and the real money respond

positively to the in rease of the produ tivity sho k. One way to understand why the innovation to the

produ tivity sho k raises the real pri e of gold, is to sket h out the working of e onomy is a standard

aggregate supply-aggregate demand diagram, where the pri e level is represented in the y-axis and

the aggregate supply and demand levels are represented in the x-axis. Thus, the aggregate supply

urve is upward slopping while the aggregate demand is downward slopping in this diagram. The

in rease of the produ tivity sho k shifts the aggregate supply urve rightward so that the aggregate

supply in reases. This leads to a downward movement along the aggragate demand urve so that

the pri e level drops. Hen e, the in rease of produ tivity sho k auses an in rease of output and a

de line of the pri e level. Sin e the pri e of gold is assumed xed, the de rease of the pri e level leads

the real pri e of gold to move above its steady state level, as shown in Figure 20. The initial in rease

of real money is driven only by the movement in the real pri e of gold sin e the nominal money does

not respond to the hange in the produ tivity sho k. From Figures 21 and 20, one an note that the

IRFs of the real pri e of gold and real money are identi al to the IRF of onsumption in the baseline

model. Indeed, if the gross nominal interest rate is set to its steady state level for every periods,

the de ision rules of output, onsumption, investment, apital, labor, real wage, real rental rate of

apital, real money, real pri e of gold and gross real interest rate an be derived from the equilibrium

equations (42), (6), (39), (45'), (46'), (47'), (49), (50), (51) and (52)61. The log-linearization of this

blo k of equilibrium equations shows that the gross growth rate of onsumption,Ct+1

Ct, and the gross

rate of real money,mt+1

mt, would deviate from their respe tive steady state level as mu h as the gross

growth rate of the real pri e of gold,pg,t+1

pg,t, would do following a hange in the produ tivity sho k62.

It would follow that Ct = mt = pg,t sin e, the nominal money sto k and the gross nominal interest

rate, do not respond to the innovation to the produ tivity sho k.

Re all that the produ tivity sho k does not ae t the gold sto ks, nominal money and gross

nominal interest rate in the baseline model. Thus, I modify the spe i ation of the utility fun tion in

order to allow the produ tivity sho k to be fully transmitted to the nominal part of the e onomy. In

parti ular, I introdu e habit formation in onsumption in the utility fun tion. Figure 20 shows that

non-monetary gold sto k, monetary gold sto k, total gold sto k, nominal money and gross nominal

interest rate respond to the hange in the produ tivity sho k in the habit model. Before going

through the analysis of the IRFs of non-monetary gold sto k, monetary gold sto k, total gold sto k,

nominal money, real money, real pri e of gold and gross nominal interest rate in the habit model, I

study how the existen e of habit formation in onsumption alters the ee ts of the in rease of the

produ tivity sho k on the real part of the gold standard e onomy.

As shown in Figure 21, the hump-shaped impulse response of onsumption to the innovation to

60Those ndings are similar to those obtained by King and Rebelo (1999) with the standard RBC model.61If the gross nominal interest rate is set to its steady state level for every periods, the onsumption-based velo ity

of money and the transa tion ost wedge are xed to their respe tive steady state level too, onsistently to equations

(48) and (43).62Spe i ally, the log-linearized form of equation (46') is given by

Et

(

Ct − Ct+1 + pg,t+1 − pg,t

)

= 0

sin e κt is assumed to be xed to its steady state level. Hen e, the log-deviation of the gross growth rate of onsumption

from its steady state level is equal to the log-deviation of the gross rate of the real pri e of gold from its steady state

level. Besides, a ording to (42), Ct = mt sin e vt = v by assumption. Therefore, the gross growth rate of real money

from its steady state level is equal to the log-deviation of the gross growth rate of onsumption from its steady state

level and hen efore to the log-deviation of the real pri e of gold from its steady state level.

66

the produ tivity sho k is more pronoun ed in the habit model than in the baseline model. Thus, the

household substitutes more future onsumption for urrent onsumption when it is subje t to habit

formation in onsumption so that the initial in rease of onsumption is lower in the habit model than

in the baseline model. Consequently, on impa t, investment jumps higher in the habit model than

it does in the baseline model. This allows the household to ontinue to in rease its onsumption

over four periods after the impa t in the habit model. Nonetheless, the interval of time in whi h

onsumption is above its steady state level is approximately identi al in both models. After the

impa t, investment behaves similarly in both models. The initial responses of output and labor to

the innovation to the produ tivity sho k are slightly lower in the habit model than in the baseline

model. On the ontrary, on impa t, the real wage in reases slightly higher in the habit model than

in the baseline model. However, after the impa t, the IRFs of output, labor and real wage are similar

a ross the two versions of the gold standard model. In the habit model, the transa tion ost wedge

moves away from its steady state level following a hange in the produ tivity sho k, as shown in

Figure 21. Pre isely, the transa tion ost wedge de lines on impa t. Then, it in reases ba k to its

teady state level. Later in the impulse response, the transa tion ost wedge moves slightly above its

steady state level. Nonetheless, the initial de rease of the transa tion ost is relatively weak so that it

does not alter signi antly the behavior of the real variables su h as onsumption and investment. It

might have played a se ondary role in the in rease of onsumption. The impulse response of the gross

real interest rate follows the same pattern in both models. There are two minor dieren es between

the IRF of the gross real interest rate in the habit model and the IRF of the gross real interest rate

in the baseline model. Spe i ally, the initial in rease of the gross real interest rate is slightly lower

in the habit model than in the baseline model. Later in the impulse response, the gross real interest

rate moves below its steady state level in both models. However, the gross real interest rate drop

below its steady state level is slightly deeper in the habit model than in the baseline model. Thus,

introdu ing the habit formation in onsumption in the baseline model does not lead the produ tivity

sho k to ae t the real part of the e onomy more persistenly.

Now, I fo us my attention on the nominal part of the e onomy. As shown in Figure 20, the impulse

response of the real pri e of gold to the innovation to the produ tivity sho k follows a pattern in the

habit model whi h is similar to one followed in the baseline model. The real pri e of gold jumps above

its steady state level following an in rease of the produ tivity sho k in the habit and baseline models.

Nonetheless, the initial in rease of the real pri e of gold is higher in habit model than in the baseline

model. The real pri e of gold ontinues to in rease after the impa t for two periods in both models.

The pi k response of the real pri e of gold is higher in the habit model than in the baseline model.

Then, the real pri e of gold de lines towards its steady state level in the habit model as it does in the

baseline model. The habit model predi ts that the gross nominal interest rate responds negatively

to the innovation to the produ tivity sho k. The intuition is that the in rease of the produ tivity

sho k leads the gross nominal interest rate to de line so that the transa tions osts are lowered. As

a result, onsumption is stimulated. However, the initial de rease of the gross nominal interest rate

is relatively weak. One period after the impa t, the gross nominal interest rate in reases ba k to

its steady state level. Later in the impulse response, it mildly moves above its steadys state level.

The de line of the gross nominal interest rate leads the household to raise its real money demand.

Indeed, as shown in Figure 20, the real money in reases on impa t. As in the baseline model, the

impulse response of real money is hump-shaped in the habit model. However, the initial real money

in rease is lower in the habit model than in the baseline model. Furthermore, real money ontinues

to in rease after the impa t in the habit model as in the baseline model. Nonetheless, the in rease

of real money lasts one period more in the habit model than in the baseline model.

The in rease of the produ tivity sho k is transmitted to the gold se tor of the e onomy through

the optimal ondition on the non-monetary gold sto k. Spe i ally, the optimal ondition on the

marginal rate of substitution of onsumption for non-monetary gold, (54), also denes an optimal

demand fun tion for non-monetary gold63. The demand fun tion for non-monetary gold sto k is

impli itely given by equation (54). In the habit model, this demand fun tion for non-monetary gold

63The demand fun tion for non-monetary gold in the baseline model has been impli itely dened when the optimal

ondition on the marginal rate of substitution of onsumption for non-monetary gold is dis ussed. This demand

fun tion, in its log-linearized form, is given by equation (56), that is

Gc,t = Ct − pg,t + ϕqt

67

takes the following form

Gc,t =φ3

φ1

κt

pg,t

(

1 − 1 − δg

qt

)−1 [

1

Ct − bCt−1

− bβEt

(1

Ct+1 − bCt

)]−1

This equation states that given the real pri e of gold, the gross nominal interest rate and the trans-

a tion ost wedge, the demand for non-monetary gold in reases if the urrent hange in onsumption

is higher than the (dis ounted) future hange in onsumption. The non-monetary gold sto k is also

in reasing with the gross nominal interest rate. However, it is de reasing with the real pri e of gold

and the transa tion ost wedge. Sin e the impulse response of onsumption is hump-shaped, the

in rease of onsumption would lead the non-monetary gold sto k. The de line of the transa tion ost

wedge would raise the demand for non-monetary gold. Instead, the in rease of the real pri e of gold

and the de rease of the gross nominal interest rate would push down the demand for non-monetary

gold sto k. A ording to Figure 20, the net result is an in rease of the non-monetary gold sto k.

Sin e no additional gold is shipped in the e onomy, the household has to buy gold for non-monetary

use to the entral bank. Consequently, monetary gold and nominal money de line, as shown in Figure

20. After the impa t, the gold sto ks and nominal money go ba k toward their respe tive steady

state level. Note that later in the impulse responses, non-monetary gold sto k moves below its steady

state level while monetary gold moves above its steady state level.

The IRFs of the gold standard model's variables to the innovation to the produ tivity sho k are

also omputed in the ase where the model features non-separable preferen es and habit formation

in onsumption. Those IRFs are displayed in Figures 22 and 23.

0 20 400

0.5

1

1.5

Year

perc

ent d

evia

tion

Output

0 20 400

0.1

0.2

0.3

0.4

Year

perc

ent d

evia

tion

Consumption

0 20 40−2

0

2

4

6

Year

perc

ent d

evia

tion

Investment

0 20 40−0.5

0

0.5

1

Year

perc

ent d

evia

tion

Labor

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Capital

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real wage

0 20 40−0.5

0

0.5

1

1.5

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−0.1

−0.05

0

0.05

0.1

Year

perc

ent d

evia

tion

Velocity

0 20 40−6

−4

−2

0

2x 10

−3

Year

perc

ent d

evia

tion

Wedge

Figure 22: Sele ted impulse response fun tions to a 1 per ent innovation to the produ tivity sho k:

Complete model (a).

Output, onsumption, investment, labor and real wage follow similar patterns a ross the three

versions of the gold standard model. Nonetheless, the initial in reases of output and labor are lower

in the omplete model than in the two other models. After the impa t, the IRFs of output and labor

in the omplete model be ome lose to the IRFs of those same variables in the baseline and habit

models. On impa t, investment in reases slightly lower in the omplete model than in the habit

model. However, on impa t, it in reases in the omplete model almost as mu h as it does in the

baseline model. In the subsequent periods, investment behaves similarly a ross the three models.

The initial in rease of onsumption is lower in the omplete model than in the baseline model. The

initial (log-)deviation of onsumption from its steady state level is almost of the same size in the

68

0 20 40−8

−6

−4

−2

0x 10

−3

Year

perc

ent d

evia

tion

Gold demand

0 20 40−0.1

0

0.1

0.2

0.3

Year

perc

ent d

evia

tion

Non−monetary gold

0 20 40−0.2

−0.15

−0.1

−0.05

0

Year

perc

ent d

evia

tion

Monetary gold

0 20 40−10

−5

0

5x 10

−3

Year

perc

ent d

evia

tion

Nominal interest rate

0 20 40−0.05

0

0.05

0.1

0.15

Year

perc

ent d

evia

tion

Real interest rate

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real gold price

0 20 40−0.2

−0.15

−0.1

−0.05

0

Year

perc

ent d

evia

tion

Nominal money stock

0 20 400

0.2

0.4

0.6

0.8

Year

perc

ent d

evia

tion

Real money

baselinewith habit

0 50 1000

0.5

1

Year

perc

ent d

evia

tion

Productivity

Figure 23: Sele ted impulse response fun tions to a 1 per ent innovation to the produ tivity sho k:

Complete model (b).

omplete model as in the habit model. Though, interval of time in whi h onsumption ontinues to

in rease after the impa t is one period shorter in the omplete model than in the habit model. In

other words, onsumption ontinues to in rease after the impa t in the omplete model for as long

as it does in the baseline model. The pi k response of onsumption is slightly lower in the omplete

model than in the habit model. Therefore, the largest (log-)deviation onsumption from its steady

state level is signi antly smaller in the omplete model than in the baseline model. The highest

initial response of the real wage to the in rease of the produ tivity sho k is generated in the omplete

model. Nevertheless, after the impa t, the real wage behaves similarly in all three models. From

Figures 20 and 23 shows that the impulse response of the gross real interest rate in the omplete

model is similar to the impulse response of that variable in the habit model. Thus, introdu ing the

habit formation in onsumption and the non-separability of preferen es in the baseline model does

not lead the produ tivity sho k to have more persistent ee t on the real part of the e onomy.

The omparison of Figure 20 with Figure 23 shows that the real pri e of gold displays a hump-

shaped impulse response to the innovation to the produ tivity sho k in the omplete model as in the

habit and baseline models. The expansion part of the IRF of the real pri e of gold in the omplete

model is almost identi al to the one in the habit model. However, after its pi k response, the real

pri e of gold de lines ba k towards its steady state level more slowly in the omplete model than in

the two other models. Real money also displays a hump-shaped impulse response to the in rease of

the produ tivity sho k in the omplete model as in the habit and baseline models. The initial in rease

of real money is as large in the omplete model as in the habit model. The pi k response of real

money happens to be slightly higher in the omplete model than in the habit model. Nonetheless,

the period at whi h real money rea hes its highest response is the same in both omplete and habit

models. Thus, the initial in rease of real money is lower in the omplete model than in the baseline

model. The pi k response of real money takes pla e one period later in the omplete model than in

the baseline model. However, it is lower in the omplete model than in the baseline model. After

the pi k response, the de rease of real money towards its steady state level is slightly less steeper in

the omplete model than in the baseline and habit models. The gross nominal interest rate responds

negatively to the in rease of the produ tivity sho k in the omplete model as in the habit model.

However, there are some notable dieren es between the IRF of gross nominal interest rate generated

by the omplete model and the one generated by the habit model. The initial de rease of the gross

nominal interest rate is deeper in the habit model than in the omplete model. Besides, while the

gross nominal interest rate ontinues to de rease for one period after the impa t in the omplete

69

model, it is already in reasing ba k towards its steady state level. Hen e, the gross nominal interest

rate moves ba k to its steady state level more gradually in the omplete model than in the habit

model. As shown in Figures 20 and 23, when the innovation the produ tivity sho k is realized, the

non-monetary gold sto k in reases slightly more in the omplete model than in the habit model. In

both omplete and habit models, the non-monetary gold sto k de lines ba k towards its steady state

level one period after the impa t. However, it takes 11 periods after the impa t to the non-monetary

gold sto k for getting ba k to its steady state level in the omplete model whereas the non-monetary

gold sto k returns to its steady state level only 6 periods after the impa t in the habit model. As in

the habit model, monetary gold and hen efore nominal money fall in the omplete model following

an in rease of the produ tvity sho k. Then, they in rease ba k towards their respe tive steady state

level. However, on impa t, monetary gold sto k and nominal money de line slightly deeper in the

omplete model than in the habit model. Furthermore, the produ tivity sho k has a more persistent

ee t on monetary gold and nominal money in the omplete model than it has in the habit model.

Indeed, those two variables rea h ba k their respe tive steady state level later in the omplete model

than in the habit model.

5.1.4 Theoreti al moments of the gold standard model

To lose the dis ussion of the dynami properties of the gold standard model, Table 6 reports

sele ted se ond moments for the 3 versions of that model baseline, habit and omplete models. In

parti ular, Table 6 displays the standard deviations (s.d.)of several key variables and the orrelations

of output with the other key variables. As it an observed from Table 6, I onsider two ases. In the

rst ase (top part of Table 6), the u tuations in the model's variables are driven by all the sho ks

produ tivity, gold ow, gold ba king, and inverse of money multiplier sho ks. In the se ond ase

(bottom part of Table 6), the u tuations in the model's variables are driven by only the nominal

sho ks gold ow, gold ba king and inverse of money multiplier sho ks.

Above, I have shown that output and investment have ollapsed strongly during the 1929-1936

period in Fran e, meaning that investment has behaved pro y li ally (with output) over that period.

The gold standard model is intended to be used for an evaluation of the gold standard-based expla-

nation of the Fren h Great Depression. Hen e, the model, through all the nominal sho ks, should

be able to generate pro y li al investment. Thus, if one fo uses only on the ee ts of the nomi-

nal sho ks on the gold standard arti ial e onomy, one would onsider the omplete model rather

than the baseline and habit models. Indeed, the baseline model displays a weak orrelation between

output and investment. Though introdu ing habit formation in onsumption in the baseline model

in reases the orrelation between output and investment, the value of this orrelation generated from

the habit model is still low. One has to introdu e habit formation in onsumption and non-separable

preferen es in the baseline model to get the nominal sho ks generate pro y li al investment in the

gold standard arti ial e onomy. Indeed, the nominal sho ks driven omplete model displays a high

orrelation between output and investment. This onrms what have been said on the subje t when

the analysis of the IRFs has been ondu ted.

5.2 The gold standard and the Fren h Great Depression

Before analyzing the Fren h Great Depression through the gold standard model, it is worth to

have again in mind some fa ts about that histori al event. As soon as Fran e returned to the gold

standard, that is in 1928, an important ow of gold moved towards that ountry. Spe i ally, the

Fren h net import of gold in reased signi antly between 1928 and 1932. In the meantime, the Bank

of Fran e raised substantially its gold reserves. Despite of the large a umulation of monetary gold,

the nominal sto k of money in reased only mildly between 1928 and 1932. Indeed, the Bank of Fran e

raised its gold ba king ratio well above the 35 per ent legal minimum during that period. As well, the

money multiplier (inverse of money multiplier sho k) was de reasing (in reasing) between 1929 and

1932, meaning that the Fren h ommer ial banks were experien ing some di ulties. Nonetheless,

the in rease of the gold ba king ratio a ounts more than the de rease of the money multiplier does

for the gap between between nominal money and monetary gold. As the nominal sto k of money

was in reasing, the real pri e of gold that is the inverse of the pri e level dropped between

1928 and 1930. Besides, the Bank of Fran e lowered its gross nominal interest rate in the beginning

of the 1930s. From 1932 until Fran e left the gold standard, gold moved away from the ountry.

70

Table 6: Theoreti al moments of the gold standard model

Real + nominal sho ks driven e onomy

Models

Baseline Habit Complete

Variables ut s.d. corr (ut, yt) s.d. corr (ut, yt) s.d. corr (ut, yt)yt 0.1017 1.0000 0.0973 1.0000 0.0962 1.0000ct 0.0602 0.8023 0.0537 0.6715 0.0532 0.7243xt 0.3036 0.9194 0.3285 0.9154 0.3125 0.9210ht 0.0501 0.8343 0.0426 0.7483 0.0385 0.7654mt 0.3379 0.2127 0.3344 0.1985 0.3358 0.2166qt 0.0338 −0.0732 0.0337 −0.0944 0.0338 −0.1064wt 0.0660 0.9082 0.0713 0.9179 0.0712 0.9376pg,t 2.7780 −0.0528 2.7705 −0.0509 2.7705 −0.0498Gm,t 2.9398 0.0716 29299 0.0680 2.9298 0.0688Gc,t 3.0784 0.0772 3.0671 0.0825 3.0672 0.0846kt 0.0891 0.7291 0.0986 0.7416 0.1009 0.7432rt 0.0063 0.1272 0.0068 −0.0463 0.0069 −0.0580

Nominal sho ks driven e onomy

Models

Baseline Habit Complete

Variables ut s.d. corr (ut, yt) s.d. corr (ut, yt) s.d. corr (ut, yt)yt 0.0086 1.0000 0.0083 1.0000 0.0087 1.0000ct 0.0113 0.9228 0.0094 0.9579 0.0093 0.9699xt 0.0147 0.1786 0.0107 0.5563 0.0109 0.7276ht 0.0095 0.9472 0.0087 0.9763 0.0092 0.9849mt 0.3327 0.8642 0.3295 0.8493 0.3302 0.8924qt 0.0338 −0.8617 0.0337 −0.8441 0.0338 −0.8878wt 0.0031 −0.1246 0.0019 −0.1177 0.0016 −0.1992pg,t 2.7773 −0.8225 2.7697 −0.8317 2.7696 −0.7800Gm,t 2.9398 0.8428 2.9299 0.8492 2.9298 0.8040Gc,t 3.0784 0.9085 3.0670 0.9144 3.0671 0.8766kt 0.0099 0.7595 0.0086 0.08899 0.0087 0.9329rt 0.0006 0.1414 0.0003 0.1265 0.0002 0.1597

71

Indeed, after 1932, the Fren h net import of gold de reased substantially. After 1934, Fran e even

be ame a net exporter of gold. Hen e, the gold reserves of the Bank of Fran e de lined during that

period, though the monetary gold sto k was by 1936 still higher than its 1929 level. The nominal

sto k of money also ollapsed between 1932 and 1936. In 1935, it slightly dropped below its 1929

level, though the Bank of Fran e lowered the gold ba king ratio between 1934 and 1936. The de line

of the gold ba king was not large enough to oset the ee t of the monetary gold de rease on the

nominal money sin e the gold ba king ratio was still above the 35 per ent legal minimum in 1936.

Note that the money multiplier ontinued to rise after 1932, though the in rease was still relatively

weak. Between 1931 and 1936 the Fren h e onomy was in deation as the real pri e of gold in reased

above its 1929 level. In the meanwhile, the Fren h entral bank raised its gross nominal interest rate

so that it was slightly above its 1929 level in 1936. The u tuations of the real pri e of gold and

nominal money in the 1930s lead real money to in rease between 1929 and 1932, then to stabilize

around its 1932 level until 1936. During all those years, the real part of the Fren h e onomy was

experien ing a depression as output, onsumption, investment, labor and gross real interest rate were

strongly de lining. The de line of the hours worked was followed by an in rease of the real wage.

5.2.1 Methodology

This subse tion aims at to answer to the question whether the perturbations that have hit the

nominal part of the Fren h e onomy in the 1930s also a ount for the depression that the real

part of the Fren h e onomy has undergone. Put it simply, this subse tion aims at to answer to

the question whether the ommitment of Fran e to the gold standard has put the ountry into a

depression. The gold standard related perturbations are the gold ow sho k, the gold ba king sho k

and the inverse of money multiplier sho k. In order to ontrol the role of the nominal sho ks in the

Fren h Great Depression, I also onsider a real sho k, that is the produ tivity sho k, in this study.

Basi ally, the produ tivity sho k is an alternative to the nominal sho ks for the understanding of

the Fren h Great Depression. The omplete (gold standard) model, whi h dynami properties has

been dis ussed above, is put to use to evaluate the roles of the nominal and real sho ks in the Fren h

Great Depression.

This analysis is performed in four steps. First, I use the onstru ted sequen es of innovations

to the gold ow sho k, gold ba king sho k and inverse of money multiplier sho k one at a time as

period-by-period impulses to the gold standard model omplete model to generate arti ial

time series for the key variables output, onsumption, investment, labor, gross real interest rate,

real wage, nominal money, real money, monetary gold, real pri e of gold and gross nominal interest

rate. Hen e, for ea h variable, st, 3 arti ial time series are reated, sj,t, j = gs, µ1, µ2. sj,t measures

the ee ts of the histori al sho k j on variable s. By doing so, I an isolate the ee ts of ea h

histori al nominal sho k on the Fren h e onomy during the 1930s. I assess the ee ts of ea h of

the histori al nominal sho k on the Fren h e onomy by omparing the model's realizations of the

key variables with the histori al data64. Se ond, I feed all the onstru ted sequen es of innovations

to the gold ow sho k, gold ba king sho k and inverse of money multiplier sho k into the omplete

model (hereafter the gold standard model) in order to generate arti ial time series for the key

variables. In this se ond step only one arti ial time series is generated for ea h variable. The

generated arti ial time series sns,t measures the ee ts of all the histori al nominal sho ks, taken

together, on variable st. This exer ise aims at to assess whether the gold standard is the main ause

of the Fren h Great Depression. Spe i ally, if the gold standard model's predi tions are lose to the

histori al data, then one an on lude that the ommitment to the gold standard is a good avenue

for understanding the Fren h Great Depression. Third, I analyze the ee ts of the alternative sho k,

that is the produ tivity sho k, on the Fren h e onomy. Thus, I feed the onstru ted sequen e of

innovations to the produ tivity sho k into the gold standard model in order to generate arti ial

time series for the key variables. The generated arti ial time series sz,t measures the ee ts of

the histori al produ tivity sho k on variable st. As in the rst step, I evaluate the ee ts of the

histori al produ tivity sho k on the Fren h e onomy by omparing the arti ial time series of the

key variables with the histori al data. Note that those exer ises steps 1 to 3 are performed

under the impli it assumption that the gold standard model oers a reasonable representation of

how the Fren h e onomy has worked in the 1930s. However, this assumption has not been veried

64Several resear hers have followed this methodology in their investigations into histori al events su h as the Great

Depression: Bordo et al. (2000), Cole and Ohanian (1999) and Weder (2006) among others.

72

yet. I do this in the fourth step. Spe i ally, I feed all the histori al sequen es of innovations to the

gold ow sho k, gold ba king sho k, inverse of money multiplier sho k and produ titivity into the

gold standard model in order to generate arti ial time series for the key variables. Then, I ompare

the simulated series of the key variables to their empiri al ounterparts. If the simulated time series

do mat h with the histori al data, one an on lude that the gold standard model is an a eptable

representation of how the Fren h e onomy has worked during the interwar gold standard period. If

it is not the ase, this would not mean that the simulation exer ises, performed in steps 1 to 3, areuseless. They might help the resear her to nd in whi h dimensions the gold standard model needs

to be improved.

5.2.2 Empiri al results

This subsubse tion presents and dis usses the results of the appli ation of the gold standard

model to the Fren h Great Depression.

5.2.2.1 The Ee ts of the gold ow sho k

Assuming that the gold standard model oers a reasonable representation of how the Fren h

e onomy has worked in the 1930s, I use that model and the onstru ted sequen e of innovations to

the gold ow sho k in order to evaluate the role of that sho k in the observed u tuations of key

ma roe onomi variables over the 1929-1936 period.

1930 1932 1934 1936−80

−60

−40

−20

0

20

40Nominal money

Year

perc

ent

ModelData

1930 1932 1934 1936−100

−50

0

50

100Monetary gold

Year

perc

ent

1930 1932 1934 1936−50

0

50

100

150Real price of gold

Year

perc

ent

1930 1932 1934 1936−6

−4

−2

0

2Nominal interest rate

Year

perc

ent

1930 1932 1934 1936−20

0

20

40

60Real money

Year

perc

ent

1930 1932 1934 1936−8

−6

−4

−2

0

2

4Gold flow shock

Year

perc

ent

Figure 24: Simulated data vs Fren h histori al data: Gold ow sho k ee ts, 1929 = 0 (a).

Figure 24 displays the ee ts of the histori al gold ow sho k on the nominal part of the gold

standard arti ial e onomy. As shown in Figure 24, the simulated variables represented in starred

lines are also onfronted to their respe tive histori al measure represented in solid line. The

gold standard model predi ts that the 1929-1932 in rease of the gold ow sho k leads the monetary

gold sto k to move above its steady state level. However, the simulated monetary gold sto k does

not in rease as mu h as the a tual monetary gold sto k does between 1929 and 1932. In parti ular,

in 1932, the gold standard, through the gold ow sho k, explains almost 40 per ent of the monetary

gold sto k in rease. Note that the Bank of Fran e has also in reased its gold reserves during that

period by onverting a large fra tion of its foreign ex hanges in gold. In the gold standard model,

additional monetary gold an ome from the new gold inow and/or the gold sto k held by the

household. Thus, the additional monetary gold oming from the onversion of the Bank of Fran e's

73

foreign ex hanges are not aptured by the model. This might explain, at least partly, why the gold

standard model generates a monetary gold sto k in rease that is milder than what is observed in

the histori al data. Indeed, the amount of foreign ex hange a umulated by the Bank of Fran e

between 1926 and 1928 is large. A ording to Nurkse (1944), the Bank of Fran e holds more than

half of the total world's sto k of foreign ex hanges by the end of 192865. The Bank of Fran e starts

to liquidate its foreign ex hanges for the bebet of its gold reserves when England leaves the gold

standard, that is in September 1931. The amounts of foreign ex hanges onverted into gold in reases

dramati ally during 1932. By 1933, the sto k foreign ex hange held by the Bank of Fran e is almost

fully liquidated66 (see Mouré, 1991, 2002, and Nurkse, 1944). From 1932 to 1936, the simulated

monetary gold sto k drops strongly. By 1936, the model's monetary gold sto k is 65.5 per ent below

its steady state level. However, as said above, the observed de line of the monetary gold sto k is

not su h large sin e the histori al monetary gold sto k is still above its 1929 level in 1936. The gold

standard model predi ts that the outow of gold leads the monetary gold sto k to de line more than

the non-monetary gold sto k does, as shown in Figure 25. The household is less willing to let its

non-monetary gold sto k de rease than to let the gold reserve of the entral bank de line. This might

explain why the monetary gold sto k falls so mu h in the arti ial e onomy following an outow of

gold.

1929 1930 1931 1932 1933 1934 1935 1936−70

−60

−50

−40

−30

−20

−10

0

10

20

30

Year

perc

ent

Monetary goldNon−monetary gold

Figure 25: Simulated monetary gold vs simulated non-monetary gold: Gold ow sho k ee ts, 1929 =0.

Sin e the produ tivity sho k and the money supply sho k are set to their respe tive steady state,

the gold standard model predi ts that the histori al sequen e of innovations to the gold ow sho k

65In August 1926 so before the ountry returned o ially to the gold standard Poin aré passed a law the

law of 7 August 1926 whi h allowed the Bank of Fran e to buy foreign ex hange and gold at market pri e. Between

1926 and 1928, the bank of Fran e bought a large amount of foreign ex hange and gold in the market in order to

ensure that the value of the Fren h urren y would not apre iate above its 1926 value. The volume of foreign ex hange

pur hased was signi antly greater than the a quired sto k of gold. With the monetary law of June 1928, the Bank of

Fran e was forbidden to buy further foreign ex hange after 1928. See Nurkse (1944) and Mouré (1991, 2002) for more

details.66A ording to Mouré (1991, 2002), the Fren h authorities are not keen to let the Bank of Fran e holding foreign

assets. They believe that the vertue of the pre-war gold standard annot be found into the gold-ex hange standard.

They laim that Fran e annot return to the pre-war gold standard system as long as the Bank of Fran e ontinues

to hold foreign assets. The Bank of Fran e suers important losses from its foreign ex hange held in pounds when

England devalues its urren y in September 1931. Thus, the Fren h authorities fear to get further losses from holding

foreign ex hanges. This leads the Bank of Fran e to liquidate its foreigh assets.

74

leads nominal money to behaves as the monetary gold sto k does over the 1929-1936 period. Figure

24 shows that the simulated nominal money u tuates relatively losely to the histori al measure of

nominal money between 1929 and 1933. Afterwhat, the simulated nominal money ollapses strongly

below its steady state while the a tual nominal money u tuates losely to its 1929 level. In the

urrent simulation exer ise the observed gap between nominal money and monetary gold is not

aptured by the gold standard model be ause both nominal supply sho ks are shut down.

As reported in Figure 24, the gold standard model predi ts that the observed movements in the

gold ow sho k ause large u tuations in the real pri e of gold. Spe i ally, the simulated real pri e

of gold drops by 40.6 per ent below its steady state level between 1929 and 1932. Then, the real

pri e of gold rises substantially until 1936, where it is 121 per ent above its steady state level. Even

though the simulated real pri e of gold and the a tual real pri e of gold follow qualitatively similar

patterns, the volatilities of both series have to be ontrasted. The model predi ts that if the Fren h

e onomy is perturbated only by the gold ow sho k, it would experien e a severer ination between

1929 and 1932 than what is observed in the histori al data. Afterwhat, the gold standard model

predi ts that the Fren h e onomy would undergo a stronger deation until 1936 omparatively to

what it is reported by the histori al data.

As one an note from Figure 24, the gold standard model, through the histori al gold ow sho k,

fails to repli ate the observed u tuations in the gross nominal interest rate over the 1929-1936

period. The simulated gross nominal interest rate and histori al gross nominal interest rate move in

opposite dire tions during the 1930s. Besides, the model's gross nominal interest rate is signi antly

more volatile than the a tual gross nominal interest rate. This result is not surprising. The histori al

data report that in the begining of the de ade, the in rease of the nominal money is followed by a

de line of the gross nominal interest. However, I have shown above that the gold ow sho k does

not generate a liquidity ee t in the gold standard model. Note that the apparent liquidity ee t

is most probably due to international fa tors rather than to domesti fa tors. A ording to Mouré

(1991), the Bank of Fran e lowers its nominal interest rate in mid-1930 then in early 1931 in response

to the drops of the Bank of England's nominal interest rate. By doing so, the Fren h entral bank

prevents the dierential between the Fren h nominal interest rate and the English nominal interest

rate from being exa erbated. The Bank of Fran e believes that an in rease of the interest rate gap

would en ourage gold ows towards Fran e, whi h in turn would ause an in rease of money supply

and henfore an in rease of the pri e level.

Figure 24 also ompares the gold standard model's real money to the histori al measure of real

money over the 1929-1936 period. A ording to the histori al data, real money in reases until 1932

where it is 21 per ent above its 1929 level. Then, it remains lose to its 1932 level until 1936.

The simulated real money follows a dierent pattern. In the gold standard arti ial e onomy, the

volatility of the real pri e of gold is larger than the volatility of nominal money. Consequently, the

simulated real money follows the same pattern as the simulated real pri e of gold. The simulated real

money drops below its steady state level by 19 per ent between 1929 and 1931. Then, real money

rises dramati ally until 1936, where it is 55.5 per ent above its steady state level.

Figures 26 and 27 display the ee ts of the histori al gold ow sho k on the real part of the gold

standard arti ial e onomy. As shown in Figures 26 and 27, the simulated variables represented

in the left windows and in starred lines are also onfronted to their respe tive histori al measure

represented in the right windows and in solid line. Clearly, the hannels through whi h the gold

ow sho k is transmitted to the real part of the gold standard arti ial e onomy do not have a stong

ampli ation me hanism. The ee ts of the histori al measure of the gold ow sho k on output,

onsumption, investment, labor, real wage and gross real interest rate are very weak in the gold

standard model. Spe i ally, the u tuations of the simulated output, onsumption, investment,

labor, real wage and gross real interest rate are quantitatively insigni ant omparatively to what it

is observed in the histori al data. Nonetheless, it is worth to omment the qualitative ee ts of the

histori al gold ow sho k on those real variables. The gold standard model predi ts the histori al

sequen e of innovations to the gold ow sho ks leads output, onsumption, labor and gross real

interest rate to de line slightly between 1929 and 1932. Then, they in rease and move above their

respe tive steady state level. The simulated investment also de reases in the begining of the de ade.

However, the predi ted investment de line lasts one year less than the predi ted output de rease

does. The simulated investment in reases from 1931 to 1936 where it is 0.5 per ent above its steady

state level. The simulated real wage moves above its steady state level between 1929 and 1932.

Afterwhat, it de reases and drops below its steady state level. Those results are not surprising.

Indeed, the analysis of the impulse response fun tions of the gold standard model has shown that an

75

1930 1932 1934 1936−0.5

0

0.5

1Model

Year

perc

ent

Output

1930 1932 1934 1936−20

−10

0

10Data

Year

perc

ent

Output

1930 1932 1934 1936−0.5

0

0.5

1

Year

perc

ent

Consumption

1930 1932 1934 1936−8

−6

−4

−2

0

Year

perc

ent

Consumption

1930 1932 1934 1936−0.5

0

0.5

1

Year

perc

ent

Investment

1930 1932 1934 1936−100

−50

0

50

Year

perc

ent

Investment

Figure 26: Simulated data vs Fren h histori al data: Gold ow sho k ee ts, 1929 = 0 (b).

1930 1932 1934 1936−0.5

0

0.5

1

1.5Model

Year

perc

ent

Labor

1930 1932 1934 1936−20

−15

−10

−5

0Data

Year

perc

ent

Labor

1930 1932 1934 1936−0.4

−0.2

0

0.2

0.4

Year

perc

ent

Real wage

1930 1932 1934 19360

10

20

30

40

Year

perc

ent

Real wage

1930 1932 1934 1936−0.02

0

0.02

0.04

0.06

Year

perc

ent

Real interest rate

1930 1932 1934 19360

2

4

6

8

Year

perc

ent

Real interest rate

Figure 27: Simulated data vs Fren h histori al data: Gold ow sho k ee ts, 1929 = 0 ( ).

76

in rease of the gold ow sho k has a weak and negative ee t on output, onsumption, investment,

labor and gross real interest rate. This analysis also has demonstrated that an in rease of the gold

ow sho k leads the real wage to shift upwards. Thus, the predi tions of the gold standard model,

through the histori al gold ow sho k, in terms of output, onsumption, investment, labor, real

wage and gross real interest rate, have to be onstrasted with what the histori al data tell also from

a qualitative point of view. The histori al gold ow sho k auses the real arti ial gold standard

e onomy to enter into a (mild) re ession in the beginning of the de ade as it is observed in the

histori al data . However, through the histori al gold ow sho k, the real gold standard arti ial

e onomy ounterfa tually re overs qui kly afterwards. Indeed, the simulated output, onsumption,

investment and labor are above their respe tive steady state level after 1932 whereas the histori al

output, onsumption, investment and labor ontinue to de line until 1936. Besides, the histori al

gold ow sho k does not lead the real wage to in rease over all the 1929-1936 period in the arti ial

gold standard model as it is observed in the histori al data. As well, the simulated gross real interest

rate and the a tual gross real interest rate follow dierent patterns between 1929 and 1936.

Thus, the gold standard model, through the histori al gold ow sho k, annot fully explain the

observed u tuations in the nominal part of the Fren h e onomy during the 1930s. Besides, the gold

standard model does not in lude an ampli ation me hanism whi h would in rease the magnitude of

the ee t of the gold ow sho k on the real part of the e onomy. This leads me to wonder whether

the histori al measures of the two money supply sho ks together with the histori al measure of the

gold ow sho k an improve the predi tion power of the gold standard model, at least with respe t

to the nominal part of the Fren h e onomy. However, it is worth to study ee ts of the histori al

measures of the money supply sho ks on the arti ial gold standard model before answering to this

question.

5.2.2.2 The Ee ts of the money supply sho ks

Assuming that the gold standard model oers an a eptable representation of how the Fren h

e onomy has worked during the inter-war gold standard period, I use that model and the onstru ted

data on the nominal sho ks in order to evaluate separately the role of the gold ba king sho k and

the role of the inverse of money multiplier sho k in the observed u tuations of key ma roe onomi

variables over the 1929-1936 period.

1930 1932 1934 1936−30

−20

−10

0

10

20

30

40

Nominal money

Year

perc

ent

Model−mu1Model−mu2Data

1930 1932 1934 19360

10

20

30

40

50

60

70Monetary gold

Year

perc

ent

1930 1932 1934 1936−5

0

5

10

15

20

25Real price of gold

Year

perc

ent

1930 1932 1934 1936−1.5

−1

−0.5

0

0.5

1

1.5Nominal interest rate

Year

perc

ent

1930 1932 1934 1936−20

−10

0

10

20

30Real money

Year

perc

ent

1930 1932 1934 19360

10

20

30

40

50

60

70Money supply shocks

Year

perc

ent

mu1mu2

Figure 28: Simulated data vs Fren h histori al data: Money supply sho k ee ts, 1929 = 0 (a).

Figure 28 displays the ee ts of the histori al gold ba king sho k and the ee ts of the histori al

inverse of money multiplier sho k on the nominal part of the gold standard arti ial e onomy. As

77

shown in Figure 28, the simulated variables the ee ts of the gold ba king sho k are represented

in ir le lines while the ee ts of the inverse of money multiplier sho k are represented in starred

lines are also onfronted to their respe tive histori al measure represented in solid line. The

gold standard model predi ts that the in rease of the histori al gold ba king sho k that takes pla e

between 1929 and 1934 leads the nominal sto k of money to drop deeply below its steady state level

over that period. The simulated nominal money is 23.7 per ent below its steady state in 1934. From

1934 onwards, as the gold ba king sho k is de reasing, the predi ted nominal money in reases ba k

towards its steady state level. However, in 1936 the simulated nominal money is still below its steady

state level. As well, the gold standard model predi ts that the in rease of the inverse of money

multiplier sho k that takes pla e between 1929 and 1936 auses nominal money to de rease over all

that period. Nonetheless, the ee ts of the gold ba king sho k on nominal money are larger than

the ee ts of the inverse of money multiplier sho k on nominal money. This is not surprising sin e

the histori al measure of the gold ba king sho k is more volatile than the inverse of money multiplier

sho k. Thus, the two money supply sho ks annot explain the movements of the nominal sto k

of money that are observed in the histori al data. However, they might explain why the histori al

nominal money does not in rease as mu h as the histori al monetary gold sto k does in the beginning

of the 1930s.

The gold standard model, through the histori al gold ba king sho k, predi ts that the monetary

gold sto k in reases between 1929 and 1934, then de lines until 1936. Thus, the simulated monetary

gold sto k follows a pattern similar to the one followed the a tual monetary gold sto k over the 1929-

1936 period. However, the movements of the histori al monetary gold sto k are signi antly larger

than the movements of the simulated monetary gold sto k. The in rease of the histori al inverse

of money multiplier sho k leads the gold standard model to generate an in reasing monetary gold

sto k over the 1929-1936 period. The in rease of the simulated monetary gold sto k, driven by the

inverse of money multiplier sho k, is however weak. The simulated monetary gold sto k in reases

above its steady state level be ause the household hooses to redu e its non-monetary gold sto k by

selling gold to the entral bank following the in rease of either the gold ba king sho k or the inverse

of money multiplier sho k as shown in Figure 29.

1930 1932 1934 1936−8

−6

−4

−2

0

2

4

6

8

Year

perc

ent

Model−mu1

non−monetary goldmonetary gold

1930 1932 1934 1936−40

−30

−20

−10

0

10

20

30

Year

perc

ent

Model−mu2

Figure 29: Simulated monetary gold vs simulated non-monetary gold: Money supply sho k ee ts,

1929 = 0.

The gold standard model predi ts that the observed u tuations of the gold ba king sho k ause

the real pri e of gold to rise between 1929 and 1934, then to de line until 1936. Nonetheless, the

simulated real pri e of gold, driven by the gold ba king sho k, is still above its steady state level

in 1936. In the gold standard arti ial e onomy, the histori al inverse of money mutliplier sho k

78

leads the real pri e of gold to in rease over the 1929-1936 period. The ee ts of the histori al gold

ba king sho k on the real pri e of gold are signi antly larger than the ee ts of the inverse of

money multiplier sho k on the real pri e of gold. Thus, the money supply sho ks annot explain the

de line of the histori al real pri e of gold that takes pla e between 1929 and 1930. However, they

parti ularly the gold ba king sho k might a ount for a non-negligeable fra tion of the in rease

of the histori al real pri e of gold that starts after 1930.

As shown in Figure 28, in the gold standard arti ial e onomy, the histori al gold ba king sho k

leads the gross nominal interest rate to rise between 1929 and 1934 then to de line. The de rease

of the a tual gold ba king sho k is not su iently to push the gross nominal interest rate to its

steady state level in 1936. In the model, the gross nominal interest rate is predi ted to be still above

its steady state level by the time Fran e leaves the gold standard. Hen e, the gold ba king sho k

driven gross nominal interest rate and the histori al gross nominal interest rate move in opposite

dire tions over the 1929-1936 period. The gold standard model, through the histori al inverse of

money multiplier sho k, predi ts that the gross nominal interest mildly in reases between 1929 and

1936. Thus, the gold standard model through the two money supply sho ks annot explain the

observed movement in the gross nominal interest rate. Indeed, as said above, the u tuations of the

histori al gross nominal interest rate are most probably driven by international fa tors whi h are are

aptured by the model.

Figure 28 reports that in the gold standard arti ial e onomy, the histori al gold ba king sho k

auses real money to drop between 1929 and 1934 by 13.33 per ent. Then, the gold ba king sho k

driven real money in reases weakly until 1936. At this date the simulated real money is still below

its steady state level by 5 per ent. As well, the gold standard model, through the histori al inverse

of money multiplier sho k, generates a de reasing real money over the 1929-1936 period. However,

the de line of the inverse money multiplier sho k driven real money is milder than the gold ba king

sho k driven real money. Hen e, the two money supply sho k annot a ount for the in rease of the

a tual real money over the 1929-1936 period.

1930 1932 1934 1936−0.5

−0.4

−0.3

−0.2

−0.1

Model

Year

perc

ent

Output−mu1Output−mu2

1930 1932 1934 1936−20

−10

0

10Data

Year

perc

ent

Output

1930 1932 1934 1936

−0.4

−0.3

−0.2

−0.1

0

Year

perc

ent

Consumption−mu1Consumption−mu2

1930 1932 1934 1936−8

−6

−4

−2

0

Year

perc

ent

Consumption

1930 1932 1934 1936

−0.8

−0.6

−0.4

−0.2

0

0.2

Year

perc

ent

Investment−mu1Investment−mu2

1930 1932 1934 1936−100

−50

0

50

Year

perc

ent

Investment

Figure 30: Simulated data vs Fren h histori al data: Money supply sho k ee ts, 1929 = 0 (b).

Figures 30 and 31 display the ee ts of the histori al gold ba king sho k and the ee ts of the

histori al inverse of money multiplier sho k on the real part of the gold standard arti ial e onomy.

As one an note from Figures 26 and 27, the simulated variables represented in the left windows

are also onfronted to their respe tive histori al measure represented in the right windows.

As for the gold ow sho k, the hannels through whi h the money supply sho ks are transmitted to

the real part of the gold standard arti ial e onomy do not have a stong ampli ation me hanism.

Indeed, the ee ts of the histori al gold ba king sho k as well as those of the histori al inverse of

79

1930 1932 1934 1936

−0.6

−0.4

−0.2

0Model

Yearpe

rcen

t

Labor−mu1Labor−mu2

1930 1932 1934 1936−20

−15

−10

−5

0Data

Year

perc

ent

Labor

1930 1932 1934 19360

0.05

0.1

0.15

0.2

Year

perc

ent

Real wage−mu1Real wage−mu2

1930 1932 1934 19360

10

20

30

40

Year

perc

ent

Real wage

1930 1932 1934 1936−0.03

−0.02

−0.01

0

Year

perc

ent

Real interest rate−mu1Real interest rate−mu2

1930 1932 1934 19360

2

4

6

8

Year

perc

ent

Real interest rate

Figure 31: Simulated data vs Fren h histori al data: Money supply sho k ee ts, 1929 = 0 ( ).

money multiplier sho k on output, onsumption, investment, labor, real wage and gross real interest

rate are very small in the gold standard model. Pre isely, the movements of the simulated output,

onsumption, investment, labor, real wage and gross real interest rate are quantitatively insigni ant

omparatively to what it is observed in the histori al data. Nevertheless, it is worth to dis uss the

qualitative ee ts of the histori al gold ba king sho k and those of the histori al inverse of money

multiplier sho k on those real variables. The gold standard model predi ts that the histori al gold

ba king sho k leads ouput and labor to de line from 1929 until 1934. Then, the gold ba king sho k

driven output and labor weakly in rease ba k towards their respe tive steady state level. By 1936,

those simulated variables are not returned into their respe tive steady state level. In the gold standard

arti ial e onomy, the histori al gold ba king sho k auses onsumption to ollapse from 1929 to 1935.

Then, the gold ba king sho k driven onsumption initiates a mild in rease. The gold standard model,

through the histori al gold ba king sho k, predi ts that investment de lines between 1929 and 1932,

then in reases ba k toward its steady state level. The gold ba king sho k driven investment move

eventually above its steady state level. In the gold standard arti ial e onomy, the real wage is driven

upwards by the histori al gold ba king sho k over the 1929-1932 period. Afterward, the gold ba king

sho k driven real wage de lines slowly. This simulated variable is still above its steady state level by

1936. The model predi ts that the histori al gold ba king sho k leads the gross real interest rate to

drop between 1929 and 1932. The gold ba king sho k driven gross real interest rate remains at a

low level during the next two years, then it in reases ba k towards its steady state level. However,

in 1936 the simulated gross real wage is still lower than its steady state level. The histori al inverse

of money multiplier sho k also auses output, onsumption, investment, labor and gross real interest

rate to de rease over the 1929-1936 period in the gold standard arti ial e onomy. In addition, the

gold standard model, through the histori al inverse of money multiplier sho k, predi ts that the

real wage u tuates above its steady state level between 1929 and 1936. However, the ee ts of the

histori al inverse of money multiplier sho k on toutput, onsumption, investment, labor, real wage

and gross real interest rate are signi antly smaller than the ee ts of the histori al gold ba king

sho k on those real variables.

Thus, the predi tions of the gold standard model, through the histori al gold ba king sho k, in

terms of output, onsumption, investment, labor, real wage and gross real interest rate, have to be

onstrasted with what the histori al data tell also from a qualitative point of view. The histori al gold

ba king sho k auses ouput, onsumption and labor to de line in the arti ial gold standard e onomy

during the rst half of the 1930s, as it is observed in the histori al data. However, the (weak) re overy

those simulated variables initiate in 1934 is not observable in the histori al data. Indeed, the a tual

80

output, onsumption ontinue to de rease after 1934. The gold ba king sho k driven investment

starts to de line one year before than the a tual investment. Besides, the histori al investment is not

returned to its 1929 level by 1936 as the simulated investment is. The histori al investment ollapses

between 1930 and 1936. The histori al gold ba king sho k leads the real wage to u tuate above its

steady state level over all the 1929-1936 period in the arti ial gold standard model as it is observed

in the histori al data. Nonetheless, the a tual real wage in reases during all the 1929-1936 period

whi h is not the ase of the simulated real wage as shown above. Moreover, the gold ba king driven

gross real interest rate and the a tual gross real interest rate move in opposite dire tions between

1929 and 1936.

From a qualitative point of view, the predi tions of the gold standard model, through the histori al

inverse of money mutiplier sho k, in terms of output, onsumption, investment, labor and real wage,

are globally onsistent with what the histori al data tell. However, the inverse of money multiplier

gross real interest rate and the a tual gross real interest rate follows dierent patterns over the

1929-1936 period.

5.2.2.3 The nominal sho ks and the Fren h Great Depression

The analysis of the ee ts of ea h of the histori al nominal sho ks gold ow sho k, gold

ba king sho k and inverse of money multiplier sho k on the key variables of the gold standard

model, suggests that taken together those nominal sho ks might explain, within the framework of

the gold standard model, the observed u tuations in the nominal part of the Fren h e onomy over

the 1929-1936 period, at least partially. Pre isely, the histori al gold ow, gold ba king and inverse

of money multiplier sho ks are likely to ause the observed u tuations in monetary gold, real pri e

of gold, nominal money and real money over the period 1929-1936 in the gold standard arti ial

e onomy. However, it seems that the gold standard model, through the histori al nominal sho ks,

annot generate a series for the gross nominal interest whi h would resemble to a tual series for the

gross nominal interest rate. Besides, the study of the ee ts of ea h of the histori al nominal sho k

on the key variables of the gold standard model suggests that, within the framework of the gold

standard model, none of the histori al nominal sho ks virtually an ae t the real part of the Fren h

e onomy over the 1929-1936 period. Below, I simulate the gold standard model by feeding all the

nominal sho ks into it in order to assess whether those intuitions are veried or not.

1930 1932 1934 1936−80

−60

−40

−20

0

20Nominal money

Year

perc

ent

ModelData

1930 1932 1934 1936−60

−40

−20

0

20

40

60

80Monetary gold

Year

perc

ent

1930 1932 1934 1936−50

0

50

100

150Real price of gold

Year

perc

ent

1930 1932 1934 1936−6

−4

−2

0

2

4Nominal interest rate

Year

perc

ent

1930 1932 1934 1936−40

−20

0

20

40

60Real money

Year

perc

ent

1930 1932 1934 1936

0

20

40

60

80

Year

perc

ent

Nominal shocks

gsmu1mu2

Figure 32: Simulated data vs Fren h histori al data: Nominal sho k ee ts, 1929 = 0 (a).

First, I evaluate whether the gold standard model, through all the histori al nominal sho ks, an

repli ate the observed u tuations in monetary gold, nominal money, real money, real pri e of gold

81

and gross nominal interest rate over the 1929-1936 period. The results of the simulation are reported

in Figure 32, where the simulated series are represented in starred line and the histori al series are

represented in solid line. The gold standard model predi ts that the histori al nominal sho ks lead the

monetary gold sto k to rise between 1929 and 1932. The gold standard model, through the histori al

nominal sho k, an explain 77.6 per ent of the a tual in rease of the monetary gold sto k over the

1929-1932 period. As said above, the Fren h entral bank has also raised its gold reserves between

1929 and 1932 by onverting its foreign ex hange. This might explain why the simulated monetary

gold sto k does not in rease as mu h as the histori al monetary gold sto k over that period sin e the

model does not in lude foreign assets nor in lude the possibility to turn them into gold. From 1932

onwards, the gap between the histori al monetary gold and the simulated monetary gold in reases.

Indeed, the nominal sho ks driven monetary gold sto k drops deeply than the a tual monetary gold

sto k as the former moves below its steady state level eventually. By 1936, the simulated monetary

gold sto k is 48.1 per ent below its steady state level while the histori al monetary gold sto k is 35.4above its 1929 level.

In the gold standard arti ial e onomy, the histori al nominal money sho ks ause nominal money

to u tuate losely to its steady state level between 1929 and 1932. Then, the nominal sho ks driven

nominal money ollapses strongly below its steady state level. The histori al nominal money in reases

between 1929 and 1931. Afterward, the a tual nominal money de lines. It slightly drops below its

1929 level by 1935. Thus, the behavior of the simulated nominal money onstrasts with the one of

the a tual nominal money over the 1929-1936 period. This ontrast mirrors the one of the simulated

monetary gold sto k with the histori al monetary gold sto k. Indeed, the observed gap between

monetary gold and nominal money is repli ated in the gold standard arti ial e onomy sin e the two

histori al money supply sho ks are fed into the model.

As shown in Figure 32, the gold standard model, through the histori al money supply sho ks,

generates a highly volatile real pri e of gold. In parti ular, the pattern followed by the nominal

sho ks driven real pri e of gold is very similar qualitatively as mu h as quantitatively to the

one followed by the gold ow sho k driven real pri e of gold over the 1929-1936 period. Hen e,

the ee ts of the histori al gold ow sho ks on the real pri e of gold highly dominate those of the

histori al money supply sho ks on the real pri e of gold. Even though globally the nominal sho ks

driven real pri e of gold behaves qualitatively as the a tual real pri e of gold does over the 1929-1936

period, the former deviates from its 1929 level substantially more than the latter does.

As expe ted, the gold standard model, through the histori al nominal sho ks, fails to repli ate

the observed u tuations of the gross nominal interest rate between 1929 and 1936. In parti ular,

the simulated gross nominal interest rate and the a tual gross nominal interest rate move in opposite

dire tions during that period. Besides, the simulated gross nominal interest rate is more volatile than

the histori al gross nominal interest rate. Figure 32 shows also the ee ts of the histori al nominal

sho ks on real money in the 1930s. Hen e, the gold standard model, through the histori al nominal

sho ks, fails to predi t the observed movements in real money. While the histori al real money

in reases between 1929 and 1932, the simulated real money drops below its steady state level. After

1932, the a tual real money u tuates losely to its 1932 level. The simulated real money moves

above its steady state level only after 1933. However, the simulated real money be omes higher than

the a tual real money by 1936.

Se ond, I evaluate whether the gold standard model, through all the histori al nominal sho ks, an

repli ate the observed u tuations in output, onsumption, investment, labor, real wage and gross

real interest rate over the 1929-1936 period. The results of the simulation are reported in Figures

33 and 34, where the simulated series are represented in the left windows and the histori al series

are represented in the right windows. As expe ted, the histori al nominal sho ks have quantitatively

almost no ee ts on the real part of the e onomy. Nonetheless, it is worth to omment briey the

qualitative ee ts of the nominal sho ks on output, onsumption, investment, labor, real wage and

gross real interest rate. The gold standard model predi ts the histori al nominal sho ks ause output,

onsumption, labor and gross real interest rate to de line slightly between 1929 and 1932. Then, they

in rease ba k towards their respe tive steady state level. They move above their respe tive steady

state level by 1935. The nominal sho ks driven investment also de lines in the begining of the 1930s.

However, the predi ted investment de rease lasts one year less than the predi ted output de rease

does. The simulated investment in reases from 1931 to 1936. It moves above its steady state level

by 1933. The simulated real wage u tuates above its steady state level between 1929 and 1934.

Afterwhat, it drops below its steady state level. Thus, from 1932 onwards, the gold standard model,

through the histori al nominal sho ks, predi ts ounterfa tually a re overy period for the Fren h

82

1930 1932 1934 1936−0.5

0

0.5

1Model

Year

perc

ent

Output

1930 1932 1934 1936−20

−10

0

10Data

Year

perc

ent

Output

1930 1932 1934 1936−0.5

0

0.5

1

Year

perc

ent

Consumption

1930 1932 1934 1936−8

−6

−4

−2

0

Year

perc

ent

Consumption

1930 1932 1934 1936−1

−0.5

0

0.5

1

Year

perc

ent

Investment

1930 1932 1934 1936−100

−50

0

50

Year

perc

ent

Investment

Figure 33: Simulated data vs Fren h histori al data: Nominal sho ks ee ts, 1929 = 0 (b).

1930 1932 1934 1936−1

−0.5

0

0.5

1Model

Year

perc

ent

Labor

1930 1932 1934 1936−20

−15

−10

−5

0Data

Year

perc

ent

Labor

1930 1932 1934 1936−0.4

−0.2

0

0.2

0.4

Year

perc

ent

Real wage

1930 1932 1934 19360

10

20

30

40

Year

perc

ent

Real wage

1930 1932 1934 1936−0.05

0

0.05

Year

perc

ent

Real interest rate

1930 1932 1934 19360

2

4

6

8

Year

perc

ent

Real interest rate

Figure 34: Simulated data vs Fren h histori al data: Nominal sho ks ee ts, 1929 = 0 ( ).

83

e onomy. Indeed, the histori al data tell that the Fren h e onomy undergoes a depression until 1936:

The a tual output, onsumption, investment and labor de line during the 1930s. Besides, in the

gold standard arti ial e onomy, the histori al nominal sho ks do not ause the real wage to in rease

above its steady state level during all the 1929-1936 period as it is observed in the histori al data.

The nominal sho k driven gross nominal interest rate and the histori al gross nominal interest rate

follow dierent patterns between 1929 and 1936.

Thus, the gold standard model, through the nominal sho ks, fails the repli ate the Fren h Great

Depression. This is mainly due to the fa t that the hannels through whi h the nominal sho ks are

transmitted to the real e onomy have virtually no ampli ation me hanism. Furthermore, in the gold

standard arti ial e onomy, when a large quantity of gold is moving away, the household behaves

so that the non-monetary gold sto k is less redu ed than the monetary gold sto k. Consequently,

the gold standard model predi ts that after 1932 the histori al nominal sho ks ause the monetary

gold sto k to ollapse more deeply than what it is observed in the histori al data. This leads to

ounterfa tual predi tions of nominal money after 1932. The gold standard model, through the

histori al nominal sho ks, fails to tra k the observed movements in the gross nominal interest rate

be ause the u tuations of the a tual gross nominal interest rate are more likely due to international

fa tors than to domesti fa tors.

5.2.2.4 The ee ts of the produ tivity sho k

Assuming that the gold standard model oers an a eptable representation of how the Fren h

e onomy has worked during the inter-war gold standard period, I use that model and the onstru ted

data on the produ tivity sho ks in order to assess whether the produ tivity sho k is a better alter-

native to the nominal sho ks for explaining the Fren h Great Depression.

1930 1932 1934 1936−20

−15

−10

−5

0

5output

Year

perc

ent

ModelData

1930 1932 1934 1936−8

−6

−4

−2

0

2consumption

Year

perc

ent

1930 1932 1934 1936−80

−60

−40

−20

0

20investment

Year

perc

ent

1930 1932 1934 1936−20

−15

−10

−5

0

5labor

Year

perc

ent

1930 1932 1934 1936−10

0

10

20

30

40Real wage

Year

perc

ent

1930 1932 1934 1936−2

0

2

4

6

8Real interest rate

Year

perc

ent

Figure 35: Simulated data vs Fren h histori al data: Produ tivity sho k ee ts, 1929 = 0 (a).

Figure 35 displays the ee ts of the histori al produ tivity sho k on the real part of the gold

standard arti ial e onomy. As shown in Figure 35, the simulated variables represented in starred

line are also onfronted to their respe tive histori al measure represented in solid line. The gold

standard model, through the histori al produ tivity sho k, performs well in tra king the observed

u tuations in output over the 1929-1936 period. Still, the predi ted ollapse of output is slightly

less deeper than the a tual de rease of output. Indeed, by 1936, the simulated output is 13.7 per ent

below its steady state level while the histori al output is 16.5 per ent below its 1929 level. The

gold standard model predi ts that the histori al produ tivity sho k leads onsumption to drop below

84

its steady state in 1932. This ontrasts with what the histori al data tell. Indeed, the histori al

onsumption falls below its 1929 level in 1930. Globally, during the 1930s the simulated onsumption

de lines almost as mu h as the a tual onsumption does. In 1936 the predi ted onsumption is

5.2 per ent below its steady state level while the histori al onsumption is 6.4 per ent below its

1929 level. However, the de rease of the histori al onsumption is errati whereas the de line of the

simulated onsumption is rather regular. Consistenly to the what it is observed in the data, the

histori al produ tivity sho k auses investment to in rease between 1929 and 1930 then to ollapse

dramati ally until 1936 in the gold standard arti ial e onomy. Note that between 1929 and 1931,

the predi ted investment and the a tual investment move very losely to ea h other. After 1931, the

de rease of the histori al investment be omes qui ker than the de line of the simulated investment.

Thus, in 1936, the predi ted investment is 41.8 per ent below its steady state level whereas the a tual

investment is 60.8 per ent below its 1929 level. In the gold standard arti ial e onomy, the histori al

produ tivity sho k leads labor to u tuate above its steady state level between 1929 and 1930, then

to de line below its steady state level until 1936. However the de rease of the predi ted labor happens

one year later than in the histori al data. Besides, the de line of the simulated labor is not as severe

as the the fall of the histori al labor is. Indeed, in 1936 the simulated labor is 4.2 per ent below its

steady state level whereas the a tual labor is 16.5 per ent below its 1929 level. The gold standard

model, through the histori al produ tivity sho k, fails to repli ate the observed movement in the real

wage and the gross real interest rate between 1929 and 1936. The histori al produ tivity sho k ause

ounterfa tually the real wage to de rease between 1930 and 1936. Indeed, the histori al wage rises

over the 1929-1936 period. In turn, the histori al produ tivity sho k has almost no ee ts on the

gross real interest rate in the gold standard arti ial e onomy between 1929 and 1936. This ontrasts

with what the data tell: The a tual gross real interest rate in reases between 1929 and 1935 then

de lines towards its 1929 level.

1930 1932 1934 1936−1

0

1

2Model

Year

perc

ent

Nominal money

1930 1932 1934 1936−10

0

10

20Data

Year

perc

ent

Nominal Money

1930 1932 1934 1936−1

0

1

2

Year

perc

ent

Monetary gold

1930 1932 1934 19360

20

40

60

80

Year

perc

ent

Monetary gold

1930 1932 1934 1936−10

−5

0

5

Year

perc

ent

Real price of gold

1930 1932 1934 1936−10

0

10

20

30

Year

perc

ent

Real price of gold

Figure 36: Simulated data vs Fren h histori al data: Produ tivity sho k ee ts, 1929 = 0 (b).

Figures 36 and 37 show the ee ts of the histori al produ tivity sho k on the nominal part of the

gold standard arti ial e onomy. As one an note from Figures 36 and 37, the simulated variables

represented in the left windows are also onfronted to their respe tive histori al measure

represented in the right windows. The results of the simulation show that the hannels through whi h

the produ tivity sho ks are transmitted to the nominal part of the gold standard arti ial e onomy do

not in lude a stong ampli ation me hanism. Indeed, the ee ts of the histori al produ tivity sho k

on monetary gold, nominal money and gross nominal interest rate are small in the gold standard

arti ial e onomy. However, the ee ts of the histori al produ tivity sho k on the real pri e of gold

and real money are quantitatively signi ant for the histori al event under study.

85

1930 1932 1934 1936−10

−5

0

5Model

Yearpe

rcen

t

Real money

1930 1932 1934 19360

10

20

30Data

Year

perc

ent

Real Money

1930 1932 1934 1936−0.05

0

0.05

0.1

0.15

Year

perc

ent

Nominal interest rate

1930 1932 1934 1936−1.5

−1

−0.5

0

0.5

Year

perc

ent

Nominal interest rate

1930 1932 1934 1936−0.1

−0.05

0

0.05

0.1

Year

perc

ent

Productivity shock

Figure 37: Simulated data vs Fren h histori al data: Produ tivity sho k ee ts, 1929 = 0 ( ).

As shown in Figure 36, in the gold standard arti ial e onomy, the histori al produ tivity sho k

auses the real pri e of gold to move above its steady state in 1930 then to de line below its steady

state level until 1936. The simulated real pri e of gold is 8.2 per ent below its steady state level

by 1936. Hen e, the simulated real pri e of gold and the a tual real pri e of gold move in opposite

dire tions during the 1929-1936 period. The gold standard model, through the histori al produ tivity

sho k, predi ts that the real money u tuates above its steady state level between 1929 and 1931,

then drops below its steady state level until 1936. The behavior of the produ tivity sho k driven

real money ontrasts with the the behavior of the histori al real money. Indeed, the latter in reases

above its 1929 level between 1929 and 1936.

Even though the histori al produ tivity sho k ae ts only a little the monetary gold sto k, the

nominal money and the gross nominal interest rate over the 1929-1936 period in the arti ial gold

standard e onomy, it is worth to examine the qualitative ee ts of that sho k on those variables.

The gold standard model, through the histori al produ tivity sho k, predi ts that monetary gold,

nominal money and gross nominal interest rate drop below their respe tive steady state level between

1929 and 1930, then in rease above their respe tive steady state level until 1936. Thus, the histori al

produ tivity sho k does not lead nominal money, monetary gold and gross nominal interest rate

to u tuate onsistently to what it is observed in the histori al data neither quantitatively nor

qualitatively.

Thus, within the gold standard arti ial e onomy framework, the histori al produ tivity sho k

appears as an a eptable alternative to the histori al nominal sho ks for the understanding of what

happens in the real part of the Fren h e onomy in the 1930s. However, the histori al produ tivity

sho k seems not appropriate to explain the u tuations that takes pla e in the nominal part of the

Fren h e onomy during that period.

5.2.2.5 Evaluation of the gold standard model

The evaluation of the ee ts of ea h of the nominal sho ks and of the produ tivity sho k on the

key variables of the gold standard model has been performed under the assumption that the model

provides a reasonable representation of how the Fren h e onomy has worked during the interwar gold

standard period. Here, I assess whether this assumption is relevant or not.

The analysis of the ee ts of ea h of the nominal sho ks and of the produ tivity sho k on the

key ma roe onomi variables suggests that the nominal part of the arti ial gold standard e onomy

is mainly ae ted by the histori al nominal sho ks while the real part of that arti ial e onomy is

86

mainly ae ted by the histori al produ tivity sho k. Thus, onsidering the results of the simulations

performed above, it seems that the gold standard model, through the histori al gold ow, gold ba k-

ing, inverse of money multiplier and produ tivity sho ks, taken together, is not a good representation

of how the Fren h e onomy has worked during the Great Depression. This suggestion is onrmed by

Figures 38 and 39 where I report the ombined ee ts of all the nominal sho ks and the produ tivity

sho ks on the key variables of the gold standard model.

1930 1932 1934 1936−80

−60

−40

−20

0

20Nominal money

Year

perc

ent

ModelData

1930 1932 1934 1936−60

−40

−20

0

20

40

60

80Monetary gold

Year

perc

ent

1930 1932 1934 1936−50

0

50

100

150Real price of gold

Year

perc

ent

1930 1932 1934 1936−6

−4

−2

0

2

4Nominal interest rate

Year

perc

ent

1930 1932 1934 1936−40

−20

0

20

40

60Real money

Year

perc

ent

1930 1932 1934 1936

0

20

40

60

80

100

Year

perc

ent

All shocks

gsmu1mu2z

Figure 38: Simulated data vs Fren h histori al data: Eets of all the sho ks, 1929 = 0 (a).

Even though the gold standard model does not oer a good des ription of how the Fren h e onomy

has worked in the interwar gold standard period, the analysis of the ee ts of ea h of the histori al

sho ks on the arti ial gold standard e onomy provides some indi ations on how to improve the

model's predi tions. Below, I dis uss briey two possible avenues to improve the gold standard

model'a ability to repli ate the Fren h Great Depression.

The two hannels of transmission of the nominal sho ks to the real part of an e onomy the

transa tion ost wedge and the optimal ondition on non-monetary gold are not su ient to

lead those sho ks to a ount for the Fren h Great Depression. Most of the proponents of the gold

standard explanation of the worldwide Great Depression Ei hengreen and Sa hs (1985) Bernanke

(1995) and, Bernanke and Carey (1996) among others laim that the non-neutrality of the fall

in the global money supply is more likely due to nominal wage sti kiness. The role of the nominal

wage sti kiness in the transmission of the money supply ollapses to real e onomies an be stated

as follows: Following a monetary ontra tion, pri es go down. Produ tion osts should de rease in

order to maintain the level of produ tion. Thus, when nominal wages do not respond qui kly to the

de rease in pri es (due to labor market imperfe tions), rms lay o and produ e less. This results in

an in rease of unemployment and a drop in output. As shown in the Fren h histori al data, nominal

money and the pri e level (inverse of the real pri e of gold) de line from 1931. In the meanwhile,

the Fren h real wage rises. This means that if the nominal wage de reases in the 1930s, its drop

is less sever than the pri e level's one. In other words, the adjustment of the nominal wage to the

money supply de line happens to be slow in Fran e during the 1930s. Hen e, the sti ky nominal

wage hypothesis seems to be an interesting avenue for the understanding of the transmission of the

nominal sho ks to the real part of the Fren h e onomy.

In the gold standard arti ial e onomy, neither of the histori al nominal sho ks is not able to

lead the gross nominal interest rate follows a pattern similar to the one followed by the histori al

gross nominal interest rate. As said above, the u tuations of the gross nominal interest rate are

more likely driven by non-domesti fa tors. Thus, the gold standard model should be extended to

a small open e onomy in order to better apture the observed u tuations of the gross nominal

87

1930 1932 1934 1936−20

−15

−10

−5

0

5output

Year

perc

ent

ModelData

1930 1932 1934 1936−8

−6

−4

−2

0

2consumption

Year

perc

ent

1930 1932 1934 1936−80

−60

−40

−20

0

20investment

Year

perc

ent

1930 1932 1934 1936−20

−15

−10

−5

0

5labor

Year

perc

ent

1930 1932 1934 1936−10

0

10

20

30

40Real wage

Year

perc

ent

1930 1932 1934 1936−2

0

2

4

6

8Real interest rate

Year

perc

ent

Figure 39: Simulated data vs Fren h histori al data: Eets of all the sho ks, 1929 = 0 (b).

interest rate. Indeed, Fran e an be onsidered as a small open e onomy during that time. This

ould be done by following the standard literature on small open real business y le models su h

that S hmitt-Grohé and Uribe (2003). An other way to deal with that problem might be to add a

me hanism in the model so that the gold ow sho k indu es a liquidity ee t. Indeed, the histori al

data show that the nominal money and the gross nominal interest rate u tuate in opposite dire tions

between 1929 and 1936. In parti ular, the nominal in reases in the beginning of the de ade while the

gross nominal interest rate drops. Agreed, the two money supply sho ks generate a liquidity ee t.

However, only the histori al gold ow sho k pushes the nominal money upwards in the beginning of

the 1930s. Introdu ing pri e sti kiness in the good market might lead the gold ow sho k to generate

a liquidity ee t. Nonetheless, the pri e sti kiness hypothesis would bring a new di ulty in the

onstru tion of the model as in the gold standard literature the pri e level is determined in the gold

market whi h is assumed ompetitive. In order to ensure that the determination of the pri e level in

the good market oin ides with the determination of the pri e level in the gold market, one should

dierentiate the denition of the pri e level from the one of the real (relative) pri e of gold in the

model as in Goodfriend (1988). In the urrent state of the gold standard model, this dieren iation

is not expli itly done sin e the only pri e variable that is onsidered in the model is the real pri e of

gold.

6 Con lusion

The analysis of the Great Depression through the lens of the gold standard theory has been mainly

ondu ted from an international omparative perspe tive. As far as I know there is no stru tural

model-based studies of the link between the malfun tioning of the gold standard and the Great

Depression. A su h analysis would be helpful to assess the role of gold standard in the worldwide

depression. In this work, I have intended to take step into this dire tion. In parti ular, I have

developed a gold standard DSGE model whi h aims to emphasize the working of the gold standard

and the link of the latter with the real part of an e onomy. The u tuations of the aggregate variables

of the arti ial e onomy are driven by one real and three nominal sho ks. The real sho k is assumed

to be a produ tivity sho k in the nal good se tor. The nominal sho ks are all related to the working

of the gold standard: a gold ow sho k, a gold ba king sho k, and a money multiplier sho k. The two

lastest nominal sho ks alter the ratio of the urren y value of the monetary gold sto k to the nominal

money sto k. The gold standard model is then put to use to study, through simulation exer ises,

88

the Fren h Great Depression over the 1929-1936 period. The results of the simulation exer ises

an be summarized as follows. The histori al measures of the nominal sho ks ae t signi antly the

nominal part of the arti ial gold standard e onomy and very little the real part of that e onomy. The

histori al produ tivity sho k ae ts signi antly the real part of the arti ial e onomy and weakly

the nominal part of that e onomy. Nonetheless, with all the histori al sho ks taken together, the gold

standard model is not able to repli ate the Fren h Great Depression. Thus, the gold standard model,

in its state, suers from two de ien ies. First, the hannels of transmission of the nominal sho ks

to the real part of the e onomy are strong enough to allow the model to repli ate an histori al event

su h as the Great Depression. Se ond, the fun tioning of the gold standard in Fran e during the

1930s seems not to be fully aptured by the model. Even though this work lets the question of the

stru tural model-based evaluation of the gold standard-based explanation of the Great Depression

still fully open, it an be seen as a starting point for futur resear hs.

A Solving the Gold Standard Model

A.1 Calibration

Table 7 displays the values of the model parameters.

A.2 Log-linearization

In order to log-linearize the non-linear stationary dynami equations, we express all the variables

in logarithmi deviation (log-deviation hereafter) from their respe tive steady-state level. We denote

xt the log-deviation of variable xt. Formally,

xt = ln(xt

x

)

Thus, a ording to this denition,

xt = x exp (xt)

If xt is lose enough to zero, then

xt = x exp (xt) ≈ x (1 + xt)

In the system of the non-linear stationary dynami equations, there is a variable, namely the

gold ow sho k, gst , whi h an have negative realizations. Therefore, this exogenous variables annot

be expressed in log-deviation from its steady state level. Consequently, gst is expressed rather in

deviation from its steady state level, with the following notation gst = gs

t − gs.

The log-linearized expression of equation (45) is omputed as follows:

First, I restate equation (45)

φ2

φ1

[

(Ct − bCt−1)φ1 G

φ3c,t

]1−φ4

(1 − ht)1−φ2(1−φ4)

ζ−1t =

wt

κt

(45')

where

ζt =

[

(1 − ht)φ2 G

φ3c,t

]1−φ4

(Ct − bCt−1)1−φ1(1−φ4)

− bβEt

[

(1 − ht+1)φ2 G

φ3

c,t+1

]1−φ4

(Ct+1 − bCt)1−φ1(1−φ4)

(79)

Se ond, I log-linearize (45')

φ2

φ1

[

(C − bC)φ1 Gφ3c

]1−φ4

(1 − h)1−φ2(1−φ4)ζ−1

(

1 +(1 − φ4) φ1

1 − bCt −

(1 − φ4) φ1b

1 − bCt−1 + φ3 (1 − φ4) Gc,t+

+(1 − φ2 (1 − φ4)) h

1 − hht − ζt

)

=w

κ(1 + wt − κt)

89

Table 7: Calibration

Model with b = 0 Model with b = 0.65Dis ount fa tor β = 0.9659 β = 0.9659Capital share parameter θ = 0.34 θ = 0.34Degree of habit formation in onsumption parameter b = 0 b = 0.65Preferen e for onsumption parameter φ1 = 0.2661 φ1 = 0.2543Preferen e for leisure parameter φ2 = 0.7319 φ2 = 0.7437Preferen e for non-monetary gold parameter φ3 = 0.002 φ3 = 0.002Utility fun tion urvature parameter φ4 = 1 or = 2 φ4 = 1 or = 2Non-monetary gold depre iation rate parameter δg = 0.02 δg = 0.02Capital depre iation rate parameter δk = 0.0752 δk = 0.0752Transa tion ost parameter γ1 = 0.0124 γ1 = 0.0124Transa tion ost parameter γ2 = 0.0166 γ2 = 0.0166Produ tivity sho k sto hasti pro ess autoregressive pa-

rameter

ρz = 0.6557 ρz = 0.6557

Te hnology sho k sto hasti pro ess standard deviation

parameter

σz = 0.0443 σz = 0.0443

Inverse of money multiplier sho k sto hasti pro ess au-

toregressive parameter

ρµ1 = 0.7904 ρµ1 = 0.7904

Inverse of money multiplier sho k sto hasti pro ess

standard deviation parameter

σµ2 = 0.0601 σµ2 = 0.0601

Gold ba king sho k sto hasti pro ess autoregressive pa-

rameter

ρµ2 = 0.9065 ρµ2 = 0.9065

Gold ba king sho k sto hasti pro ess standard devia-

tion parameter

σµ2 = 0.1627 σµ2 = 0.1627

Gold ow sho k sto hasti pro ess autoregressive pa-

rameter

ρgs = 0.8225 ρgs = 0.8225

Gold ow sho k sto hasti pro ess standard deviation

parameter

σgs = 0.0177 σgs = 0.0177

90

⇔ (1 − φ4) φ1

1 − bCt −

(1 − φ4) φ1b

1 − bCt−1 + φ3 (1 − φ4) Gc,t +

(1 − φ2 (1 − φ4)) h

1 − hht − ζt = wt − κt (45)

and (79)

ζ(

1 + ζt

)

=

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

(

1 − (1 − φ4) φ2h

1 − hht + (1 − φ4) φ3Gc,t −

1 − (1 − φ4) φ1

1 − bCt+

+[1 − (1 − φ4) φ1] b

1 − bCt−1

)

− bβ

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)

Et

(

1 − (1 − φ4) φ2h

1 − hht+1 + (1 − φ4) φ3Gc,t+1−

−1 − (1 − φ4) φ1

1 − bCt+1 +

[1 − (1 − φ4) φ1] b

1 − bCt

)

⇔ ζt = −(1 − φ4) φ2

1 − bβ

h

1 − hht +

(1 − φ4) φ3

1 − bβGc,t −

[1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)

]

Ct+

+[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)Ct−1 +

(1 − φ4) φ2

1 − bβ

h

1 − hbβEt

(

ht+1

)

− (1 − φ4) φ3

1 − bβbβEt

(

Gc,t+1

)

+

+1 − (1 − φ4) φ1

(1 − bβ) (1 − b)bβEt

(

Ct+1

)

(80)

Then, ombining equations (45) and (80), I get the log-linearized expression of (45)

bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+1

)

− bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

+bβ [1 − (1 − φ4) φ1]

(1 − bβ) (1 − b)Et

(

Ct+1

)

=

=

[(1 − φ4) φ1

1 − b+

1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)

]

Ct −φ3 (1 − φ4) bβ

1 − bβGc,t+

+

[

1 − φ2 (1 − φ4) +(1 − φ4) φ2

1 − bβ

]h

1 − hht − wt + κt −

[(1 − φ4) φ1bβ

1 − bβ− 1

1 − bβ

]b

1 − bCt−1

(81)

The log-linearized expression of equation (44) is omputed as follows:

First, I restate equation (44)

pg,t

κt

ζt −φ3

φ1

[

(Ct − bCt−1)φ1 (1 − ht)

φ2

]1−φ4

G1−φ3(1−φ4)c,t

= (1 − δg) βEt

(pg,t+1

κt+1

ζt+1

)

(44')

Se ond, I log-linearize equation (44')

pg

κζ

(

1 + pg,t − κt + ζt

)

− φ3

φ1

[

(C − bC)φ1 (1 − h)φ2

]1−φ4

G1−φ3(1−φ4)c

(

1 + (1 − φ4) φ1

(1

1 − bCt −

b

1 − bCt−1

)

−

− (1 − φ4) φ2h

1 − hht − [1 − φ3 (1 − φ4)] Gc,t

)

= (1 − δg) βpg

κζEt

(

1 + pg,t+1 − κt+1 + ζt+1

)

⇔ pg,t − κt + ζt −κ

pgζ

φ3

φ1

[

(C − bC)φ1 (1 − h)φ2

]1−φ4

G1−φ3(1−φ4)c

((1 − φ4) φ1

1 − bCt −

[(1 − φ4) φ1] b

1 − bCt−1−

− (1 − φ4) φ2h

1 − hht − [1 − φ3 (1 − φ4)] Gc,t

)

= (1 − δg) βEt

(

pg,t+1 − κt+1 + ζt+1

)

91

⇔ pg,t − κt + ζt −[1 − (1 − δg) β] (1 − φ4) φ1

1 − bCt +

[1 − (1 − δg) β] [(1 − φ4) φ1] b

1 − bCt−1+

+ [1 − (1 − δg) β] (1 − φ4) φ2h

1 − hht + [1 − (1 − δg) β] [1 − φ3 (1 − φ4)] Gc,t =

= (1 − δg) βEt (pg,t+1) − (1 − δg) βEt (κt+1) + (1 − δg) βEt

(

ζt+1

)

(44)

noting that

ζ =

[

(1 − h)φ2 Gφ3c

]1−φ4

(C − bC)1−φ1(1−φ4)(1 − bβ)

κ

pgζ

φ3

φ1

[

(C − bC)φ1 (1 − h)φ2

]1−φ4

G1−φ3(1−φ4)c

= 1 − (1 − δg) β

Then, ombining equations (44) and (80), I get the log-linearized expression of (44)

(1 − δg) βEt (pg,t+1) − (1 − δg) βEt (κt+1) −[

φ2h

1 − h

(1 − φ4) (1 − δg) β

1 − bβ+

φ2h

1 − h

(1 − φ4) bβ

1 − bβ

]

Et

(

ht+1

)

+

+

[(1 − φ4) (1 − δg) βφ3

1 − bβ+

(1 − φ4) bβφ3

1 − bβ

]

Et

(

Gc,t+1

)

−[(1 − δg) β [1 − φ1 (1 − φ4)]

(1 − bβ) (1 − b)+

+(1 − δg) [1 − φ1 (1 − φ4)] b

2β2

(1 − bβ) (1 − b)+

[1 − φ1 (1 − φ4)] bβ

(1 − bβ) (1 − b)

]

Et

(

Ct+1

)

+[(1 − δg) bβ2 (1 − φ4) φ2] h

(1 − bβ) (1 − h)Et

(

ht+2

)

−

− φ3 (1 − φ4) bβ2 (1 − δg)

1 − bβEt

(

Gc,t+2

)

+[1 − φ1 (1 − φ4)] bβ

2 (1 − δg)

(1 − bβ) (1 − b)Et

(

Ct+2

)

= pg,t − κt−

−[(1 − φ4) φ1 [1 − (1 − δg) β]

1 − b+

1 − φ1 (1 − φ4)

(1 − bβ) (1 − b)+

[1 − φ1 (1 − φ4)] b2β

(1 − bβ) (1 − b)+

[1 − φ1 (1 − φ4)] (1 − δg) bβ

(1 − bβ) (1 − b)

]

Ct +

[(1 − φ4) φ2 [1 − (1 − δg) β] h

1 − h− (1 − φ4) φ2h

(1 − bβ) (1 − h)

]

ht+

+

[

[1 − (1 − δg) β] [1 − φ1 (1 − φ4)] +(1 − φ4) φ3

1 − bβ

]

Gc,t +

[φ1 (1 − φ4) b [1 − (1 − δg) β]

1 − b+

[1 − φ1 (1 − φ4)] b

(1 − bβ) (1 − b)

]

Ct−1

92

⇔ (1 − δg) βEt (pg,t+1) − (1 − δg) βEt (κt+1) −φ2h

1 − h

(1 − φ4) β [1 − δg + b]

1 − bβEt

(

ht+1

)

+

+(1 − φ4) β (1 − δg + b)

1 − bβEt

(

Gc,t+1

)

+1

1 − b

[(1 − φ4) (1 − δg + b) βφ1

1 − bβ+

bβ2 (1 − φ4) (1 − δg) φ1b

1 − bβ−

β [b + (1 + b2β) (1 − δg)]

1 − bβ

]

Et

(

Ct+1

)

+(1 − δg) bβ2 (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+2

)

−

− φ3 (1 − φ4) bβ2 (1 − δg)

1 − bβEt

(

Gc,t+2

)

+bβ2 (1 − δg) (1 − φ4)

(1 − bβ) (1 − b)

[1

(1 − φ4)− φ1

]

Et

(

Ct+2

)

=

= pg,t − κt −(1 − φ4) φ2h

1 − h

[bβ

1 − bβ+ (1 − δg) β

]

ht+

+

[

−1 + b2β + (1 − δg) bβ

(1 − bβ) (1 − b)+

β (1 − φ4) (1 − δg + b)

1 − bβ

bφ1

1 − b+

φ1 (1 − φ4)

1 − b

(bβ

1 − bβ+ (1 − δg) β

)]

Ct+

+

[

1 − (1 − δg) β + (1 − φ4)

(bβ

1 − bβ+ (1 − δg) β

)

φ3

]

Gc,t +

+

b[

11−bβ

− (1 − φ4)(

bβ

1−bβ+ (1 − δg) β

)

φ1

]

1 − b

Ct−1

(82)

The log-linearized expression of equation (46) is omputed as follows:

First, I restate equation (46)

γ1v2t − γ2 = 1 − βEt

(κt

κt+1

pg,t+1

pg,t

ζt+1

ζt

)

(46')

Se ond, I loglinearize equation (46')

γ1v2 (1 + 2vt) − γ2 = 1 − β

κ

κ

pg

pg

ζ

ζEt

(

1 + κt − κt+1 + pg,t+1 − pg,t − ζt + ζt+1

)

⇔ 2γ1v2

βvt + κt − pg,t − ζt = Et

(

κt+1 − pg,t+1 − ζt+1

)

(46)

Then, ombining equations (46) and (80), I get the log-linearized expression of (46)

Et (κt+1) − Et (pg,t+1) +

[(1 − φ4) φ2

1 − bβ

h

1 − h+

bβ (1 − φ4) φ2

1 − bβ

h

1 − h

]

Et

(

ht+1

)

−

−[(1 − φ4) φ3

1 − bβ+

(1 − φ4) φ3bβ

1 − bβ

]

Et

(

Gc,t+1

)

+

[1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)+

+[1 − (1 − φ4) φ1] bβ

(1 − bβ) (1 − b)

]

Et

(

Ct+1

)

− bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+2

)

+bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+2

)

−

− [1 − (1 − φ4) φ1] bβ

(1 − bβ) (1 − b)Et

(

Ct+2

)

=2γ1v

2

βvt + κt − pg,t +

(1 − φ4) φ2

1 − bβ

h

1 − hht −

(1 − φ4) φ3

1 − bβGc,t+

+

[1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)

]

Ct −[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)Ct−1

93

⇔ Et (κt+1) − Et (pg,t+1) +(1 + bβ) (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+1

)

− (1 + bβ) (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

+

+1

1 − b

[1 + b2β + bβ

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1 −

(1 − φ4) bβ

1 − bβφ1b

]

Et

(

Ct+1

)

+bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+2

)

−

− bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+2

)

+(1 − φ4) bβ

(1 − bβ) (1 − b)

(

φ1 −1

(1 − φ4)

)

Et

(

Ct+2

)

=2γ1v

2

βvt + κt − pg,t+

+(1 − φ4) φ2

1 − bβ

h

1 − hht −

(1 − φ4) φ3

1 − bβGc,t +

1

1 − b

[1 + b2β + b

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1b −

(1 − φ4)

1 − bβφ1

]

Ct−

− [1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)Ct−1

(83)

The log-linearized expression of equation (47) is omputed as follows:

First, I restate equation (47)

ζt

κt

= βEt

(

ζt+1

[rt+1 + 1 − δk

κt+1

])

(47')

Se ond, I loglinearize equation (47')

ζ

κ

(

1 + ζt − κt

)

= βζ (r + 1 − δk)

κEt

(

1 + ζt+1 − κt+1 +r

r + 1 − δk

rt+1

)

⇔ ζt − κt = Et

(

ζt+1 − κt+1 +r

r + 1 − δk

rt+1

)

(47)

Then, ombining equations (47) and (80), I get the log-linearized expression of (47)

r

r + 1 − δk

Et (rt+1) − Et (κt+1) −[(1 − φ4) φ2

1 − bβ

h

1 − h+

bβ (1 − φ4) φ2

1 − bβ

h

1 − h

]

Et

(

ht+1

)

+

+

[(1 − φ4) φ3

1 − bβ+

(1 − φ4) φ3bβ

1 − bβ

]

Et

(

Gc,t+1

)

−[

1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)+

+[1 − (1 − φ4) φ1] bβ

(1 − bβ) (1 − b)

]

Et

(

Ct+1

)

+bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+2

)

− bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+2

)

+

+[1 − (1 − φ4) φ1] bβ

(1 − bβ) (1 − b)Et

(

Ct+2

)

= −(1 − φ4) φ2

1 − bβ

h

1 − hht +

(1 − φ4) φ3

1 − bβGc,t − κt−

−[

1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)

]

Ct +[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)Ct−1

⇔ r

r + 1 − δk

Et (rt+1) − Et (κt+1) −[(1 + bβ) (1 − φ4) φ2] h

(1 − bβ) (1 − h)Et

(

ht+1

)

+(1 + bβ) (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

−

− 1

1 − b

[1 + b2β + bβ

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1 +

(1 − φ4) bβ

1 − bβφ1b

]

Et

(

Ct+1

)

− bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+2

)

+

+bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+2

)

− (1 − φ4) bβ

(1 − bβ) (1 − b)

(

φ1 −1

(1 − φ4)

)

Et

(

Ct+2

)

= −(1 − φ4) φ2

1 − bβ

h

1 − hht+

+(1 − φ4) φ3

1 − bβGc,t − κt −

1

1 − b

[1 + b2β + b

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1b −

(1 − φ4)

1 − bβφ1

]

Ct+

+[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)Ct−1

(84)

94

The loglinearized expression of equation (41) is

m (1 + mt) =1

µ1

1

µ2

pgGm

(

1 + pg,t + Gm,t − µ1,t − µ2,t

)

⇔ mt = pg,t + Gm,t − µ1,t − µ2,t (85)

The loglinearized expression of equation (42), is

v (1 + vt) =C

m

(

1 + Ct − mt

)

⇔ vt = Ct − mt (86)

The loglinearized expression of equation (6) is

K(

1 + Kt

)

= (1 − δk) K(

1 + Kt−1

)

+ I(

1 + It

)

⇔ Kt = (1 − δk) Kt−1 + δkIt (87)

The loglinearized expression of equation (10) is

Gd(

1 + Gdt

)

= Gc

(

1 + Gc,t

)

+ Gm

(

1 + Gm,t

)

⇔ GdGdt = GcGc,t + GmGm,t (88)

The loglinearized expression of equation (23) is

κ (1 + κt) = 1 + 2γ1v (1 + vt) − 2√

γ1γ2

⇔ κt =2γ1v

κvt (89)

The loglinearized expression of equation (48), is

γ1v2 (1 + 2vt) − γ2 = 1 − 1

q(1 − qt)

⇔ qt = 2γ1v2qvt (90)

The loglinearized expression of equation (49) is

w (1 + wt) = (1 − θ)Y

h

(

1 + Yt − ht

)

⇔ wt = Yt − ht (91)

The loglinearized expression of equation (50) is

r (1 + rt) = θY

K

(

1 + Yt − Kt−1

)

⇔ rt = Yt − Kt−1 (92)

The loglinearized expression of equation (51) is

Y(

1 + Yt

)

= zKθh1−θ(

1 + zt + θKt−1 + (1 − θ) ht

)

95

⇔ Yt = zt + θKt−1 + (1 − θ) ht (93)

The loglinearized expression of equation (36) is

Gd(

1 + Gdt

)

= Gd(

1 + Gdt−1

)

− δgGc

(

1 + Gc,t−1

)

+ gs (1 + gst )

⇔ GdGdt = GdGd

t−1 − gsGc,t−1 + gst (94)

The loglinearized expression of equation (39) is

Y(

1 + Yt

)

= C(

1 + Ct

)

+ I(

1 + It

)

⇔ Y Yt = CCt + IIt (95)

The loglinearized expression of equation (52) is

r(1 + ˆrt

)= q

pg

pg

(1 + qt + Et (pg,t+1) − pg,t)

⇔ Et (pg,t+1) = ˆrt − qt + pg,t (96)

Consistenly, the exogenous sto hasti pro esses are restated as follows

zt = ρz zt−1 + εz,t (97)

µ1,t = ρµ1µ1,t−1 + εµ1,t (98)

µ2,t = ρµ2µ2,t−1 + εµ2,t (99)

gst = ρgs gs

t−1 + εgs,t (100)

The system of log-linearized stationary equilibrium equations, (81)-(96), an be restated, in a

matrix form, as a linear sto hasti dieren e equation of order 3. Indeed, the dieren e between

the highest lead (2) and the highest lag (1) is of order 3. However, the method for solving rational

expe tation models onsidered in the urrent work Klein (2000) method is suitable for rst

order linear sto hasti dieren e equations. In order to obtain a system of rst order (log-)linear

sto hasti dieren e equations, it is onvenient to use auxiliary variables. Therefore, one needs to

dene the following auxiliary variables:

C+t+1 := FCt+1 = Ct+2

h+t+1 := Fht+1 = ht+2

G+c,t+1 := FGc,t+1 = Gc,t+2

K−

t := LKt = Kt−1

C−

t := LCt = Ct−1

Gd−t := LGd

t = Gdt−1

G−

c,t := LGc,t = Gc,t−1

where F and L are the lead and lag operator, respe tively.

96

By substituting C+t+1, h+

t+1, G+c,t+1, K−

t , C−

t , Gd−t and G−

c,t for Ct+2, ht+2, Gc,t+2, Kt−1, Ct−1, Gdt−1

and Gc,t−1, respe tively, in the system of log-linearized stationary equilibrium equations,

bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+1

)

− bβ (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

+bβ [1 − (1 − φ4) φ1]

(1 − bβ) (1 − b)Et

(

Ct+1

)

=

=

[(1 − φ4) φ1

1 − b+

1 − (1 − φ4) φ1

(1 − bβ) (1 − b)+

[1 − (1 − φ4) φ1] b2β

(1 − bβ) (1 − b)

]

Ct −φ3 (1 − φ4) bβ

1 − bβGc,t+

+

[

1 − φ2 (1 − φ4) +(1 − φ4) φ2

1 − bβ

]h

1 − hht + κt − wt −

[(1 − φ4) φ1bβ

1 − bβ− 1

1 − bβ

]b

1 − bC−

t

(101)

(1 − δg) βEt (pg,t+1) − (1 − δg) βEt (κt+1) −φ2h

1 − h

(1 − φ4) β [1 − δg + b]

1 − bβEt

(

ht+1

)

+

+(1 − φ4) β (1 − δg + b)

1 − bβφ3Et

(

Gc,t+1

)

+1

1 − b

[(1 − φ4) (1 − δg + b) βφ1

1 − bβ+

bβ2 (1 − φ4) (1 − δg) φ1b

1 − bβ−

β [b + (1 + b2β) (1 − δg)]

1 − bβ

]

Et

(

Ct+1

)

+(1 − δg) bβ2 (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

h+t+1

)

−

− φ3 (1 − φ4) bβ2 (1 − δg)

1 − bβEt

(

G+c,t+1

)

+bβ2 (1 − δg) (1 − φ4)

(1 − bβ) (1 − b)

[1

(1 − φ4)− φ1

]

Et

(

C+t+1

)

=

= pg,t − κt −(1 − φ4) φ2h

1 − h

[bβ

1 − bβ+ (1 − δg) β

]

ht+

+

[

−1 + b2β + (1 − δg) bβ

(1 − bβ) (1 − b)+

β (1 − φ4) (1 − δg + b)

1 − bβ

bφ1

1 − b+

φ1 (1 − φ4)

1 − b

(bβ

1 − bβ+ (1 − δg) β

)]

Ct+

+

[

1 − (1 − δg) β + (1 − φ4)

(bβ

1 − bβ+ (1 − δg) β

)

φ3

]

Gc,t+

+

b[

11−bβ

− (1 − φ4)(

bβ

1−bβ+ (1 − δg) β

)

φ1

]

1 − b

C−

t

(102)

Et (κt+1) − Et (pg,t+1) +(1 + bβ) (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+1

)

− (1 + bβ) (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

+

+1

1 − b

[1 + b2β + bβ

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1 −

(1 − φ4) bβ

1 − bβφ1b

]

Et

(

Ct+1

)

+bβ (1 − φ4) φ3

1 − bβEt

(

G+c,t+1

)

−

− bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

h+t+1

)

+(1 − φ4) bβ

(1 − bβ) (1 − b)

(

φ1 −1

(1 − φ4)

)

Et

(

C+t+1

)

=2γ1v

2

βvt + κt − pg,t+

+(1 − φ4) φ2

1 − bβ

h

1 − hht −

(1 − φ4) φ3

1 − bβGc,t +

1

1 − b

[1 + b2β + b

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1b −

(1 − φ4)

1 − bβφ1

]

Ct−

− [1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)C−

t

(103)

97

r

r + 1 − δk

Et (rt+1) − Et (κt+1) −(1 + bβ) (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

ht+1

)

+(1 + bβ) (1 − φ4) φ3

1 − bβEt

(

Gc,t+1

)

−

− 1

1 − b

[1 + b2β + bβ

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1 +

(1 − φ4) bβ

1 − bβφ1b

]

Et

(

Ct+1

)

− bβ (1 − φ4) φ3

1 − bβEt

(

G+c,t+1

)

+

+bβ (1 − φ4) φ2

1 − bβ

h

1 − hEt

(

h+t+1

)

− (1 − φ4) bβ

(1 − bβ) (1 − b)

(

φ1 −1

(1 − φ4)

)

Et

(

C+t+1

)

= −(1 − φ4) φ2

1 − bβ

h

1 − hht+

+(1 − φ4) φ3

1 − bβGc,t − κt −

1

1 − b

[1 + b2β + b

1 − bβ− (1 + bβ) (1 − φ4)

1 − bβφ1b −

(1 − φ4)

1 − bβφ1

]

Ct+

+[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)C−

t

(104)

Kt = (1 − δk) K−

t + δkIt (105)

rt = Yt − K−

t (106)

Yt = zt + θK−

t + (1 − θ) ht (107)

GdGdt = GdGd−

t − gsG−

c,t + gst (108)

and adding the following equations

EtK−

t+1 = Kt (109)

EtGd−t+1 = Gd

t (110)

EtG−

c,t+1 = Gc,t (111)

EtC−

t+1 = Ct (112)

Etht+1 = h+t (113)

EtGc,t+1 = G+c,t (114)

EtCt+1 = C+t (115)

one get the required system of rst order (log-)linear sto hasti dieren e equations.

A.3 Setting up the system in a matrix form

The system of rst order (log-)linear sto hasti dieren e equations is given by

qt − 2γ1v2qvt = 0 (S1)

δkIt = Kt − (1 − δk) K−

t (S2)

vt + mt − Ct = 0 (S3)

98

Yt − ht = wt (S4)

Yt − rt = K−

t (S5)

Yt − (1 − θ) ht = θK−

t + zt (S6)

mt − Gm,t = pg,t − µ1,t − µ2,t (S7)

Y Yt − CCt − IIt = 0 (S8)

GdGdt − GmGm,t = GcGc,t (S9)

GdGdt = GdGd−

t − gsG−

c,t + gst (S10)

(1 − δg) βEt (pg,t+1) − (1 − δg) β2γ1v

κEt (vt+1) −

φ2h

1 − hχ1Et

(

ht+1

)

+ χ1φ3Et

(

Gc,t+1

)

+

+1

1 − b[χ1φ1 + χ2φ1b − χ3] Et

(

Ct+1

)

+ χ2φ2h

1 − hEt

(

h+t+1

)

− φ3χ2Et

(

G+c,t+1

)

+

+

[1

1 − φ4

− φ1

]χ2

1 − bEt

(

C+t+1

)

= pg,t −2γ1v

κvt − χ4

φ2h

1 − hht+

+

[

−χ5 + χ1bφ1

1 − b+ χ4

φ1

1 − b

]

Ct + [1 − (1 − δg) β + χ4φ3] Gc,t +b

1 − b

[1

1 − bβ− φ1χ4

]

C−

t

(D1)

Ψ1φ2h

1 − hEt

(

ht+1

)

− Ψ1φ3Et

(

Gc,t+1

)

+Ψ1

1 − b

[1

1 − φ4

− φ1

]

Et

(

Ct+1

)

=

=1

1 − b

[1 + b2β

1 − bβ− Ψ1φ1 (1 + b)

]

Ct − φ3Ψ1Gc,t + [1 + φ2Ψ1]h

1 − hht+

+2γ1v

κvt − wt +

[

Ψ1φ1 −1

1 − bβ

]b

1 − bC−

t

(D2)

2γ1v

κEt (vt+1) − Et (pg,t+1) + Ψ2φ2

h

1 − hEt

(

ht+1

)

− Ψ2φ3Et

(

Gc,t+1

)

+

+1

1 − b[Ψ3 − Ψ2φ1 − Ψ1φ1b] Et

(

Ct+1

)

+ Ψ1φ3Et

(

G+c,t+1

)

− Ψ1φ2h

1 − hEt

(

h+t+1

)

+

+Ψ1

1 − b

[

φ1 −1

1 − φ4

]

Et

(

C+t+1

)

= 2γ1v

(v

β+

1

κ

)

vt − pg,t +(1 − φ4) φ2

1 − bβ

h

1 − hht−

− (1 − φ4) φ3

1 − bβGc,t +

1

1 − b

[1 + b2β + b

1 − bβ− 1 − φ4

1 − bβφ1 − Ψ2φ1b

]

Ct +[(1 − φ4) φ1 − 1] b

(1 − b) (1 − bβ)C−

t

(D3)

99

r

r + 1 − δk

Et (rt+1) −2γ1v

κEt (vt+1) − Ψ2φ2

h

1 − hEt

(

ht+1

)

+ Ψ2φ3Et

(

Gc,t+1

)

+

+1

1 − b[Ψ2φ1 − Ψ3 + Ψ1φ1b] Et

(

Ct+1

)

− Ψ1φ3Et

(

G+c,t+1

)

+

+ Ψ1φ2h

1 − hEt

(

h+t+1

)

+Ψ1

1 − b

[1

1 − φ4

− φ1

]

Et

(

C+t+1

)

= −(1 − φ4) φ2

1 − bβ

h

1 − hht+

+(1 − φ4) φ3

1 − bβGc,t −

2γ1v

κvt +

1

1 − b

[

−1 + b2β + b

1 − bβ+ Ψ2φ1b +

(1 − φ4)

1 − bβφ1

]

Ct+

+[1 − (1 − φ4) φ1] b

(1 − bβ) (1 − b)C−

t

(D4)

Et (pg,t+1) = ˆrt − qt + pg,t (D5)

EtK−

t+1 = Kt (D6)

EtGd−t+1 = Gd

t (D7)

EtG−

c,t+1 = Gc,t (D8)

EtC−

t+1 = Ct (D9)

Etht+1 = h+t (D10)

EtGc,t+1 = G+c,t (D11)

EtCt+1 = C+t (D12)

where

χ1 = β(1 − φ4) (1 − δg + b)

1 − bβ

χ2 =bβ2 (1 − φ4) (1 − δg)

1 − bβ

χ3 =β [b + (1 + b2β) (1 − δg)]

1 − bβ

χ4 = (1 − φ4)

[bβ

1 − bβ+ (1 − δg) β

]

χ5 =1 + b2β + (1 − δg) bβ

(1 − bβ) (1 − b)

Ψ1 =(1 − φ4) bβ

1 − bβ

Ψ2 =(1 − φ4) (1 + bβ)

1 − bβ

Ψ3 =1 + b2β + bβ

1 − bβ

100

Note that I have eliminated variable κt and equation (89) from the system of log-linearized

equilibrium equations.

Besides, the sto hasti pro esses of the exogenous variables are given by

zt = ρz zt−1 + εz,t (E1)

µ1,t = ρµ1µ1,t−1 + εµ1,t (E2)

µ2,t = ρµ2µ2,t−1 + εµ2,t (E3)

gst = ρgs gs

t−1 + εgs,t (E4)

The systems of equilibrium equations and exogenous sto hasti pro esses an be set up in the

following matrix form:

NyYt = NxXt + NzZt (116)

MxpEtXt+1 + MypEtYt+1 + MzpEtZt+1 = MxXt + MyYt + MzZt (117)

Zt = PzZt−1 + ǫt ǫt ; i.i.d. (04, Ω) (118)

Matrix equation (116) gathers all the stati log-linear equilibrium equations. Matrix equation

(117) on erns all the dynami log-linear equilibrium equations. The sto hasti exogenous pro esses

are put in matrix equation (118). Hen e, matrix equation (116) is built a ording to the stati equa-

tions (S1)-(S10). Equations (D1)-(D12) form the matrix equation (117). The sto hasti exogenous

pro esses (E1)-(E4) dene the matrix equation (118).

Before giving expli it expressions to matri es Ny, Nx, Nz, Mxp, Myp, Mzp, Mx, My, Mz, Pz and

Ω I have to dene the ve tors of variables Yt, Xt, Zt and ǫt:

Yt =

Yt

Ct

It

ht

qt

mt

vt

Gm,t

Gdt

rt

Xt =

K−

t

Gd−t

G−

c,t

C−

t

Kt

wt

pg,t

ˆrt

Gc,t

h+t

G+c,t

C+t

Zt =

zt

µ1,t

µ2,t

gst

ǫt =

ǫz,t

ǫµ1,t

ǫµ2,t

ǫgs,t

Yt is a (10 × 1) ve tor whi h elements are the ontrol variables. Zt is a (4 × 1) ve tor whi h

elements are the exogenous variables. ǫt is a (4 × 1) ve tor whi h elements are the perturbations to

the exogenous variables. Xt is a (12 × 1) ve tor of state variables. The latter an be partitioned in

two ve tors as follows,

Xt =

(Xb

t

Xft

)

where ve tor Xbt ontains the predetermined state variables and ve tor X

ft ontains the jump state

variables. In the gold standard model, K−

t , Gd−t , G−

c,t and C−

t are onsidered as predetermined state

variables, and Kt, wt, pg,t, ˆrt, Gc,t, h+t , G+

c,t and C+t as jump state variables.

101

Thus, the matri es appearing in (116) are dened as follows:

Ny =

0 0 0 0 1 0 −2γ1v2

β0 0 0

0 0 δk 0 0 0 0 0 0 00 −1 0 0 0 1 1 0 0 01 0 0 −1 0 0 0 0 0 01 0 0 0 0 0 0 0 0 −11 0 0 θ − 1 0 0 0 0 0 00 0 0 0 0 1 0 −1 0 0Y −C −I 0 0 0 0 0 0 00 0 0 0 0 0 0 −Gm Gd 00 0 0 0 0 0 0 0 Gd 0

Nx =

0 0 0 0 0 0 0 0 0 0 0 0δk − 1 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0θ 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 Gc 0 0 00 Gd −gs 0 0 0 0 0 0 0 0 0

Nz =

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 −1 −1 00 0 0 00 0 0 00 0 0 1

Myp =

0 φ1χ1+φ1bχ2−χ3

1−b0 −χ1

φ2h

1−h0 0 − (1−δg)2γ1vβ

κ0 0 0

0Ψ1

“

11−φ4

−φ1

”

1−b0 Ψ1

φ2h

1−h0 0 0 0 0 0

0 Ψ3−Ψ2φ1−φ1bΨ1

1−b0 Ψ2

φ2h

1−h0 0 2γ1v

κ0 0 0

0 −Ψ3−Ψ2φ1−φ1bΨ1

1−b0 −Ψ2

φ2h

1−h0 0 −2γ1v

κ0 0 r

r+1−δk

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0

102

Mxp =

0 0 0 0 0 0 (1 − δg) β 0 χ1φ3 χ2φ2h

1−h−χ2φ3

χ2

“

11−φ4

−φ1

”

1−b

0 0 0 0 0 0 0 0 −Ψ1φ3 0 0 0

0 0 0 0 0 0 −1 0 −Ψ2φ3 −Ψ1φ2h

1−hΨ1φ3 −Ψ1

“

11−φ4

−φ1

”

1−b

0 0 0 0 0 0 −1 0 Ψ2φ3 Ψ1φ2h

1−h−Ψ1φ3

Ψ1

“

11−φ4

−φ1

”

1−b

0 0 0 0 0 0 1 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 0 0 0

Mzp =

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

Mzp =

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

My =

0 χ1φ1b

1−b+ χ4

φ1

1−b− χ5 0 −χ4

φ2h

1−h0 0 −2γ1v

κ0 0 0

01+b2β

1−bβ−Ψ1φ1(1+b)

1−b0 (1+Ψ1φ2)h

1−h0 0 2γ1v

κ0 0 0

01+b2β+b

1−bβ−

1−φ41−bβ

φ1−Ψ2φ1b

1−b0 (1−φ4)φ2h

(1−bβ)(1−h)0 0 2γ1v

(vβ

+ 1κ

)

0 0 0

0 −1+b2β+b

1−bβ−

1−φ41−bβ

φ1−Ψ2φ1b

1−b0 − (1−φ4)φ2h

(1−bβ)(1−h)0 0 −2γ1v

κ0 0 0

0 0 0 0 −1 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

103

Mx =

0 0 0b( 1

1−bβ−φ1χ4)

1−b0 0 1 0 1 − (1 − δg) β + χ4φ3 0 0 0

0 0 0 − b( 11−bβ

−φ1Ψ1)1−b

0 −1 0 0 −Ψ1φ3 0 0 0

0 0 0 b((1−φ4)φ1−1)(1−bβ)(1−b)

0 0 −1 0 −1−φ4

1−bβφ3 0 0 0

0 0 0 − b((1−φ4)φ1−1)(1−bβ)(1−b)

0 0 0 0 1−φ4

1−bβφ3 0 0 0

0 0 0 0 0 0 1 1 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 1

Pz =

ρz 0 0 00 ρµ1 0 00 0 ρµ2 00 0 0 ρgs

Ω =

σ2z 0 0 00 σ2

µ10 0

0 0 σ2µ2

00 0 0 σ2

gs

Noti e that matrix Ny should be square and invertible. Moreover, both Mxp and Mx should be

square matri es. The matrix governing the exogenous pro esses, Pz, should have its eigenvalues lying

inside the unit ir le.

Hen e, the method developed by Klein (2000) is used to solve the matrix form equations (116)-

(118).

B Additional Figures

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

45

50

Year

devi

atio

n

monetary goldnon−monetary gold

Figure 40: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Non-

monetary gold sto k vs monetary gold sto k with δg = 0.1.

104

0 10 20 30 40 50 60 70 80 90 100−2

0

2

4

6

8

10

12

14

16x 10

−7

Year

devi

atio

n

monetary goldnon−monetary gold

Figure 41: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Non-

monetary gold sto k vs monetary gold sto k with δg = 10−9.

0 20 40−5

0

5

10x 10

−5

Year

perc

ent d

evia

tion

Output

0 20 40−2

−1

0

1

2x 10

−4

Year

perc

ent d

evia

tion

Consumption

0 20 400

1

2

3

4x 10

−4

Year

perc

ent d

evia

tion

Investment

0 20 40−1

−0.5

0

0.5

1x 10

−4

Year

perc

ent d

evia

tion

Labor

0 20 400

0.5

1x 10

−4

Year

perc

ent d

evia

tion

Capital

0 20 40−1

0

1

2

3x 10

−5

Year

perc

ent d

evia

tion

Real wage

0 20 40−6

−4

−2

0

2x 10

−5

Year

perc

ent d

evia

tion

Capital rental rate

0 20 40−10

0

10

20

Year

perc

ent d

evia

tion

Velocity

0 20 40−2

0

2

4x 10

−4

Year

perc

ent d

evia

tion

Wedge

Figure 42: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Baseline

model with small transa tions osts (a).

105

0 50 1000

20

40

60

Year

perc

ent d

evia

tion

Gold demand

0 50 1000

20

40

60

Year

perc

ent d

evia

tion

Non−monetary gold

0 50 1000

10

20

30

40

Year

perc

ent d

evia

tion

Monetary gold

0 50 100−1

0

1

2

Year

perc

ent d

evia

tion

Nominal interest rate

0 50 100−6

−4

−2

0

2x 10

−6

Yearpe

rcen

t dev

iatio

n

Real interest rate

0 50 100−40

−30

−20

−10

0

Year

perc

ent d

evia

tion

Real gold price

0 50 1000

10

20

30

40

Year

perc

ent d

evia

tion

Nominal money stock

0 50 100−20

−10

0

10

Year

perc

ent d

evia

tion

Real money

0 50 1000

0.5

1

Year

devi

atio

n

Gold supply

Figure 43: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Baseline

model with small transa tions osts (b).

0 50 1000

20

40

60

Year

perc

ent d

evia

tion

Gold demand

0 50 100−20

0

20

40

60

Year

perc

ent d

evia

tion

Non−monetary gold

0 50 1000

20

40

60

Year

perc

ent d

evia

tion

Monetary gold

0 50 100−60

−40

−20

0

Year

perc

ent d

evia

tion

Real gold price

0 50 1000

20

40

60

Year

perc

ent d

evia

tion

Nominal money stock

0 50 100−30

−20

−10

0

10

Year

perc

ent d

evia

tion

Real money

baselinepersistence

0 50 100−0.1

0

0.1

0.2

0.3

Year

perc

ent d

evia

tion

Real wage

0 50 100−0.6

−0.4

−0.2

0

0.2

Year

perc

ent d

evia

tion

Capital rental rate

0 50 100−10

0

10

20

Year

perc

ent d

evia

tion

Velocity

Figure 44: Impulse response fun tions to a 1 per ent innovation to the gold ow sho ks: Baseline

model vs baseline model with highly persistent gold ow sho k (b).

106

Referen es

[1 Annuaire statistique (1966). Institut National de la Statistique et des Études É onomiques Im-

primerie Nationale, Paris.

[2 Barro R. (1979). Money and the pri e level under the gold standard. The E onomi Journal,

vol. 89, pp. 13-33.

[3 Barsky R. and L. Summers (1988). The Gibson's Paradox and the Gold Standard. The Journal

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