advanced macroeconomics module 3: empirical models ...amoneta/m2019_2.pdfokun’s lawphillips curve...

Okun’s law Phillips curve

Advanced MacroeconomicsModule 3: Empirical models & methods

2. Crucial empirical relationships in macroeconomics

Alessio Moneta

Institute of EconomicsScuola Superiore Sant’Anna, Pisa

[email protected]

February-March 2019

LM in EconomicsScuola Superiore Sant’Anna - Universita di Pisa

Macroeconomic fluctuations 1/74


Introduction

In this series of lectures we deal with crucial relationships such as:• Output/Unemployment and Inflation;• Money and Output.• Fiscal policy (gov. exp.) and output

Several controversies emerged because of different interpretations ofthe empirical evidence which correspond to different schools ofthought.

We focus in particular on the:• Keynesian School;• New Classical School.



Introduction

Query: how is possible to have different interpretation of the sameempirical evidence? Two issues:

• Evidence may change over time;• Evidence is interpreted through the lens of econometrics, which

may encompass different approaches.



Output and Unemployment

(Okun’s law)



Output-Unemployment

The relationship between Output and Unemployment is not ascontroversial as the relationship between Unemployment (or Output)and Inflation:

When output falls unemployment raises.

But: when output raises unemployment does not alwaysdeclines (cfr. jobless recovery).

In sum: the relationship between unemployment and outputchanges during recoveries/recessions.



Output-Unemployment: Okun’s law

Okun, A. (1962): “Potential GNP: Its Measurement and Significance”(Proceedings of the ASA).

Okus’s “law” (gap version):

shortfall in GDP growth of x% relative to normal growth isassociated with a rise of y% in the unemployment rate

original formulation: x = 3; y = 1 (more recently: x = 2; y = 1)



Okun’s Law (difference version)

Suppose to estimate through a OLS regression the following empiricalrelationship:

∆Ut = a + bYt + εt (1)

where ∆Ut : change in the unemployment rate, Yt : growth rate of GDP, εt :error term.

Equation (1) can be re-written as

∆Ut = b(Yt +ab) + εt (2)

or (γ = −b, Y∗t = − ab )

∆Ut = −γ(Yt − Y∗t ) + εt (3)

Y∗t is a critical growth rate of GDP: below this rate unemployment rises,above this rate unemployment falls. It is called modified balanced rate ofgrowth.



Digression on the modified balanced rate of growth:

Let’s call LF: labour force, L: number of workers employed; POP:working-age population; θ := Y

L labour productivity; PR:= LFPOP , participation

rate; X:= growth rate of X (for any variable X).

Ut =LFt − Lt

LFt⇒ 1−Ut =

LtLFt

(1−Ut) ≈ L− LF ≈ ∆(1−Ut)

1−Ut

∆Ut ≈ (1−Ut)(LF− L) = (Ut− 1)(Yt− PR− POP− θ) = (Ut− 1)(Yt− Y∗)

where Y∗ := PR + POP + θ.

Cfr. Hoover (2012: pp. 590-592.)



Okun’s Law

Plot from Hoover (2012) Intermediate Macroeconomics, Cambridge University Press, Figure 15.4, p.

593. Okun’s Law for U.S., 1974-2009. Source data: Bureau of Labor Statistics (unemployment);

Bureau of Economic Analysis (GDP); calculations: Hoover (2012).



Okun’s Law (potential output)

Plot from Hoover (2012) Intermediate Macroeconomics, Cambridge University Press, Figure 15.5, p.

594. Okun’s Law for U.S., 1974-2009. Source data: Bureau of Economic Analysis (GDP); Board of

Governors of the Federal Reserve System and Bureau of Labor Statistics (scaled output),

calculations: Hoover (2012).Macroeconomic fluctuations 10/74


Unemployment (Output) and Inflation (Wages)

(Phillips curve and its interpretation)



Main features:

B Main features of the Keynesian approach:

• peculiarity of the propagation mechanism: nominal stickiness

prices and wages do not adjust instantaneously

• impulse mechanism:

monetary shocks

real shocks (e.g. changes in government purchases, investmentdemand, technology)

• emphasis to demand-side factors

• involuntary unemployment (some degrees of market failure)

• need of interventionist policy (fiscal and not only monetary policy)



Contributors

B Protagonists of the Keynesian approach:

B Keynes (1936)

B Neoclassical synthesis (1950s - 1960s) and the orthodox Keynesianschool: Tobin, Klein, Solow, Modigliani, Hicks, Samuelson

B New Keynesians: Blanchard, Mankiw, Phelps, D. Romer, Stiglitz,Bernanke, Krugman (1980s-)

B Post-Keynesians: Robinson, Kaldor, Minsky, Davidson.

Cfr. Snowdon and Vane 2005, pp. 24-29



Theoretical background

B Two pillars of the standard Keynesianism:

• IS/LM model (Hicks 1937, Modigliani 1944, Hansen 1949, 1953)

aim: explanation of the forces determining output andemployment

• Phillips curve (Phillips 1958)

aim: prediction of the rate of inflation which would result fromdifferent target levels of unemployment



AS-AD scheme (Keynesians)

P

Y

AD

AS

Keynesian scheme



AS-AD scheme (New Classicals)

P

Y

AD

AS

Classical model



IS-LM scheme

i

Y

IS

LM

IS−LM model

Note: this figure is drawn for a given price level and government expenditure



IS-LM-AD: fiscal policy effect

i

Y

IS0 IS1

LM

The effects of an increase in government purchases

P

Y

AD0 AD1

NB: The amount that Y increases in the IS-LM chart is the same as the amount that ADcurve shifts to the right at the value of P assumed in the IS-LM chart



IS-LM-AD: fiscal policy effect

B What is the final effect on output and prices?

this depends on the slope of the AS curve

vertical AS: no effect for Y (only P increases)

horizontal AS: viceversa

“Thus, incomplete adjustment of nominal prices introduces a new channel throughwhich shocks affect output...[If] nominal prices do not adjust fully in the shortrun...any change in the demand for goods at a given price level affects output. ”(Romer 2001: 224)



AS behaviour: an idealized Keynesian modelwith sticky wages, flexible prices and competitive product market

B Cfr. Keynes (1936)

B Nominal wage is rigid:

W = W

B Aggregate supply with labour L as the only factor of production(decreasing returns):

Y = F(L) F′(·) > 0 F′′(·) < 0

B Perfect competition + profit maximization implies that marginalrevenue = marginal cost1, i.e.

F′(L) =WP

=WP

1Cfr. e.g. Hoover (2012, section 9.1.2)




B What is the slope of the AS curve?

we have to find the sign of dYdP in the supply model

B Differentiating Y = F(L) (cfr. chain rule):

dYdP

=dF(L)

dLdLdP

N.B. F′(L) = dF(L)dL > 0 and F′′(L) = dF′(L)

dL =d(

WP

)dL < 0. Then

d(

WP

)dL

= −WP−2 dPdL

< 0 which impliesdPdL

> 0

B We have found that dYdP is the product of two positive quantities, then is

positive and therefore the AS curve is upward sloping




B Increases in aggregate demand lead to increases in prices, output andlabour demand and reduces real wages and unemployment

Source: Romer D. (4ed 2012) Advanced Macroeconomics, Mc Graw Hill, Figure 6.3.

Possible disequilibrium in the labour market and involuntary unemployment(cfr. distance EA)



Output-Inflation tradeoff

B Consider again the idealized Keynesian model (fixed W, flexible P andcompetitive goods market).

B Suppose that:

Wt = APt−1 A is a constant > 0

recall: Yt = F(Lt), F′(·) > 0, F′′(·) < 0, F′(Lt) =WtPt

B Suppose AD increases at time t = 1 (fiscal or monetary policy) such thatY1 > Y0

then L1 > L0 and P1 > P0

we have:

W2W1

=AP1AP0

=P1P0

B If P2 = P1 then W2P2

= A (since W2 = AP1)



Output-Inflation tradeoff

B Period 0: W0P0

= A

Period 1: W1P1

= AP0/P1

Period 2 (if price does not change): W2P2

= A⇒ employment and outputthe same as in period 0.

B Shifts in AD can keep output at the same level of period 1 or evenincrease it if inflation increases

Expansionary policies are possible at cost of inflation

B Phillips (1958): empirical study of wage inflation to the unemploymentrate in UK (1861-1957)

Phillips curve: relationship between unemployment and price inflation



Phillips curve

The Phillips curve in US 1960-1969. Source: Hoover, K.D: (2008) ”Phillips Curve.” The Concise

Encyclopedia of Economics. Library of Economics and Liberty.

<www.econlib.org/library/Enc/PhillipsCurve.html>



The Phillips curve and the new classical view



Phillips curve

B The close fit between the Phillips curve and data in the 1960sencouraged some economists (e.g. Samuelson and Solow AER 1960) toexploit the Phillips curve for policy interventions

B Criticisms:

• Edmund Phelps “Phillips curves, expectations of inflation andoptimal unemployment over time” Economica 1967; “Money-wagedynamics and labor-market equilibrium” JPE 1968

• Milton Friedman “The role of monetary policy” AER 1968

B Historical facts: stagflation in the 1970s (cfr. OPEC embargo 1973-75)



4 5 6 7 8 9

02

46

810

1214

Unemployment

Infla

tion

6162636465

6667

68

6970

71

72

73

74

75

7677

78

79

80

81

82

83

8485

86

878889

90

91

929394959697

9899

0001

0203

040506

07

08

09

10

11

121314

Inflation and Unemployment US 1961−2014

Source: FRED data (Inflation, consumer prices for the United States; Civilian Unemployment Rate).



3.5 4.0 4.5 5.0 5.5 6.0 6.5

12

34

5

Unemployment

Infla

tion

61626364

65

6667

68

69

Inflation and Unemployment US 1960s




5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5

46

810

Unemployment

Infla

tion

70

71

72

73

74

75

76

77

78

79





6 7 8 9

24

68

1012

Unemployment

Infla

tion

80

81

82

83

84

85

86

8788

89





4.5 5.0 5.5 6.0 6.5 7.0 7.5

23

45

Unemployment

Infla

tion

90

91

9293

9495

96

97

98

99





4 5 6 7 8 9

01

23

4

Unemployment

Infla

tion

00

01

02

03

04

0506

07

08

09

10

11

12

1314

Inflation and Unemployment US 2000−2014




The natural rate

B Friedman’s (1968) challenge to the interventionist interpretation of thePhillips curve: workers would be irrational, i.e. would suffer frommoney illusion, if they decided their labour supply looking at (nominal)wage only

N.B. if prices rise faster than wages, then hiring more workers becomesprofitable

B Rational agents understand that their wages can be eroded by inflation.If they expect inflation, they will demand higher wage settlements inadvance, so that nominal wages keep up with prices.

B If real wages adjust, the unemployment rate stand at a level uniquelyassociated with that real wage: the natural rate of unemployment.



The natural rate

B Friedman (1968) - Phelps (1967): nominal variables (e.g. inflation,nominal supply) cannot permanently affect real variables (e.g. output,unemployment).

B There is a normal or natural (cfr. Wicksell) rate of unemployment whichcannot be permanently affected by nominal forces and which isultimately determined by real forces only

“there is some level of unemployment which has the property that it is consistentwith equilibrium in the structure of real wage rates. At that level of unemployment,real wage rates are tending on the average to rise at a “normal” secular rate, i.e., at arate that can be indefinitely maintained so long as capital formation, technologicalimprovements, etc., remain on their long-run trends.” Friedman (1968: 8)



The natural rate

“ ‘The natural rate of unemployment’ ... is the level that would be ground out by theWalrasian system of general equilibrium equations, provided there is embedded inthem the actual structural characteristics of the labour and commodity markets,including market imperfections, stochastic variability in demands and supplies, thecosts of gathering information about job vacancies, and labor availabilities, the costsof mobility, and so on” Friedman (1968: 8)



The expectations-augmented Phillips curve

• Vertical long-run aggregate supply: prices and wages are fully flexiblein the long-run

• Formulation of the Phillips curve after Friedman (1968):

log Pt = log Pt−1 + π∗t + λ(log Yt − log Yt) + εSt λ > 0 (4)

or (πt = log Pt − log Pt−1)

πt = π∗t + λ(log Yt − log Yt) + εSt λ > 0 (5)

π∗t = core or underlying inflation

Yt is the natural rate of output or potential output

εSt : supply shocks




B Simple case: π∗t = πt−1 (cfr. adaptive expectations)

• no permanent tradeoff between output and inflation

• possible tradeoff with change in inflation

• importance of steady inflation

• better fit with the data



4 5 6 7 8 9

−4

−2

02

4

Unemployment

Del

ta In

flatio

n

62636465

66

67

6869

70

71

72

73

74

75

76

7778

79

80

81

82

83

84

85

86

87

8889

90

91 92

9394

9596

9798

9900

01

02

0304

05

0607

08

09

1011

1213

14

Inflation (first differences) and Unemployment US 1962−2014




AS-AD in the output-inflation space





B General case: π∗t = πet (cfr. rational expectations)

NB πet ≡ Et−1[πt]

• path followed by the new classical macroeconomics

• compromise with the new Keynesian view of sluggishness in nominalvariables:

πt = φπet + (1− φ)πt−1 + λ(log Yt − log Yt) + εS

t (6)

where φπet + (1− φ)πt−1 = π∗t .




B Expectations-augmented Phillips curve

πt = π∗t + λ(log Yt − log Yt) + εSt (7)

• general case: π∗t = πet = Et−1[πt]

• interpretation followed by the new classical macroeconomics: π∗t asrational expectation

• interpretation of core inflation as adaptive expectation: π∗t = πt−1

• compromise with the new keynesian view of sluggishness in nominalvariables: φπe

t + (1− φ)πt−1 = π∗t



The natural rate and the NAIRU

B Since output Yt is related to unemployment Ut via the Okun’s law (if Yt ↓by 3% – or 2% – then Ut ↑ by 1%) we can write the expectations-augmentedPC as

πt = π∗t − β(Ut −U∗t ) + εSt β > 0 (8)

where U∗t is the natural rate of unemployment.

B New Keynesians prefer the term NAIRU (instead of naturalunemployment) to discuss the long-run unemployment

NAIRU : non-accelerating inflation rate of unemployment

• Modigliani and Papademos (1975) introduced the term NIRU(non-inflationary rate of unemployment): “a rate such that, as long asunemployment is above it, inflation can be expected to decline”

• Tobin (1980) introduced the acronym NAIRU

• Query: is NAIRU a misnomer?



The natural rate and the NAIRU

B In much economic discussion “natural rate of unemployment” andNAIRU are used interchangeably. However, there are actually subtle butimportant differences.

• NAIRU (unlike n.r.) “does not suggest that an unemployment rateis socially optimal, unchanging, or impervious to policy” (Hoover2008)

• because it is defined as the Ut at which πt is stable, “it is a reducedform — not a structural — variable” (King 1999)

• while the n.r. is a general equilibrium concept, NAIRU ismicro-founded as a balance of power between workers and firm inan imperfect competition settings (Carlin and Soskice 1990)



Estimate of NAIRU

The Expectations-augmented Phillips curve, US 1981-2009 (expectations based on surveys of

expected inflation). Source: Hoover (2012) Intermediate Macroeconomics, Cambridge University Press,

Figure 15.6, p. 600. NB: in Hoover (2012) the inflation rate (π in our notation) is denoted by p.



Estimate of NAIRU

The Expectations-augmented Phillips curve, US 1981-2009 (expectations based on past inflation

rates) Source: Hoover (2012) Intermediate Macroeconomics, Cambridge University Press, Figure 15.7,

p. 602. NB: in Hoover (2012) the inflation rate (π in our notation) is denoted by p.



NAIRU as scaled output

A Phillips curve can be estimated with output as independent variable. If (πt − π∗t ) isregressed on scaled output (Yt/Yt), we get a NAIRU which is actually a rate ofpotential output (resource utilization) for which inflation is stable.

The Expectations-augmented Phillips curve, US 1981-2009 with scaled output as dependent

variable Source: Hoover (2012) Intermediate Macroeconomics, Cambridge University Press, Figure

15.9, p. 604. NB: in Hoover (2012) the inflation rate (π in our notation) is denoted by p.



Is the NAIRU constant?

B According to the classical view (cfr. Friedman 1968), the level of theNAIRU (or n.r.) is determined by real supply-side influences only

i.e. demographics, technology, union power, structure of taxation,relative prices (e.g. oil prices)

and the NAIRU should not vary with monetary and fiscal policy

short-lived fluctuations, steep Phillips curve

B NAIRU seems to have changed, by looking at empirical estimations fordifferent time windows

In Europe (cfr. Italy but also UK) seems to have been risen

B The tendency of U to return to NAIRU is weak.



Estimate of changing NAIRU

The NAIRU for the United States 1949-2010 Source: Hoover (2012) Intermediate Macroeconomics,

Cambridge University Press, Figure 15.8, p. 604.



Hysteresis

B Many new Keynesians argue that there is no tendency for the economyto return to a NAIRU

hysteresis hypothesis: NAIRU depends on actual unemployment andon its history (path dependent)

thus aggregate demand can influence the NAIRU

B The term was introduced by Phelps (1972) and is borrowed fromphysics (magnetism)



Hysteresis

B Different interpretation of hysteresis

• conservative view: blame on unionisation and labour laws (in Europe)

• under this view it is difficult to explain rising unemployment in UK inthe 1980s and 1980s after reduction of union power

• lost of skills of unemployed people during long periods ofunemployment



Money and output in empirical applications



The effect of monetary shocks

B An important test to assess real-business-cycle vs. Keynesiantheories of fluctuations is based on the empirical analysis of theeffects of monetary changes.

• In the RBC approach purely monetary disturbances have no realeffects

• In Keynesian models monetary shocks have important effects onemployment and output

B Notice, however, that in Keynesian approach fiscal policy haspriority to monetary policy

B On the contrary Friedman: monetary policy is all that is needed



The St. Louis equation

B The relationship between money and output was empirically analysedmuch before the flourishing of the RBC approach

Cfr. Andersen and Jordan (1968) “Monetary and fiscal actions: a test oftheir relative importance in economic stabilization”, Federal Reserve Bankof St. Louis Review

straightforward idea: regress output on money



The St. Louis equation

B Example of St. Louis equation (from Romer 2012, p. 221)

US quarterly data 1960Q2-2008Q4

Yt real GDP, mt money stock as measured by M2

the estimated regression is

∆ log Yt = 0.0046 −0.09∆ log mt +0.18∆ log mt−1+(0.0024) (0.10) (0.12)

+0.16∆ log mt−2 +0.02∆ log mt−3 −0.02∆ log mt−4 +0.000010t(0.12) (0.12) (0.10) (0.000011)

R2= 0.056

sum of coefficients= 0.25 (s.e. 0.10)



Problems with the money-income correlation

B Causation may run Y −→ m instead of Y←− m (endogeneity problem)

cfr. King and Plosser (1984) “Money, credit, and prices in a RBC” AER

possible changes in the money stock (by firms and households) inadvance of output movements: the actual cause is output (changes inproduction or expenditures)

B Even if m −→ Y (money causes output) m can result to be uncorrelatedto Y if the central bank adjusts m to offset other factors influencing Y:we will observe fluctuations in m which are not associated withmovements in Y (cfr. Kareken and Solow 1963).



The narrative approach

B The narrative or natural experiments approach

• Friedman and Schwartz (1963) A Monetary History of the UnitedStates, 1867 - 1960, PUP

criticism by Tobin (1970), “Money and income: Post hoc ergo propterhoc?” QJE

• Romer C. and D. Romer (1989) “Does monetary policy matter? Anew test in the spirit of Friedman and Schwartz”, NBERMacroeconomics Annual

criticism by Hoover and Perez (1994), “Post Hoc Ergo Propter Hoc:An Evaluation of ’Does Monetary Policy Matter?’ in the Spirit ofJames Tobin” JME



The Structural VAR approach

B VAR approach pioneered by Sims (1980) “Macroeconomics and reality”Econometrica

VARs are Vector Autoregressions: a vector of variables is regressed onits lagged values (until a lag p)

all the variables are considered as endogenous

reduced form model



The Structural VAR approach

B SVAR: structural form underlying the VAR

orthogonalisation of the VAR residuals

identification of the SVAR imposing causality restrictions on theestimated VAR

identification of the structural shocks in particular the monetary shock

analysis of the effect of this shock on output

empirical evidence shows that actually shocks to nominal variable playan important role, contrary to what the RBC theory predict

cfr. e.g. King Plosser Stock Watson (1991), “Stochastic trends and economicfluctuations” AER



Structural equations and causality

B Cowles Commission Approach: dominant approach inmacro-econometrics 1940s-1960s

• Haavelmo’s “The Probability Approach in Econometrics” (1944)

• Economic theory dictates the causal structure

• If the structure is adequate: error terms conform to standardprobabilistic properties (independence and normality)

• Measuring the strengths of causal linkages.



Example of structural model

B Example: (borrowed from Hoover 2006: 8ff.)

m = αy + εm (9)

y = βm + εy, (10)

where m ≡money, y ≡ GDP (both in logs).

B Statistical properties of εm and εy tell whether the model is goodsspecified.

B can we get α, β, εm, εy from the data?

B No. Problem of identification

B m and y are both endogenous variables

εm −→m←→ y←− εy


http://econ.duke.edu/%7Ekdh9/Source%20Materials/Research/Economic%20Theory%20and%20Causal%20Inference.pdf


Example of structural model

B Problem of identification solved introducing two exogenousvariables:

m = αy + δr + εm (11)

y = βm + γp + εy, (12)

where r ≡ interest rate, p ≡ price level (both in logs).

B can we get α, β, δ, γ εm, εy from the data?

B Yes. Model identified under the assumption that p is not a directcause of m and r is not a direct cause of y

B Omitting the error terms:

r −→ m←→ y←− p



Reduced form model

B After substituting eq. (11) into eq. (12) and simplifying:

m =αγ

1− αβp +

δ

1− αβr +

α

1− αβεy +

11− αβ

εm (13)

y =γ

1− αβp +

βδ

1− αβr +

β

1− αβεm +

11− αβ

εy (14)

B This system of reduced-form equations can be now estimated,since on the r.h.s. there are only exogenous variables:

m = a p + b r + um (15)

y = c p + d r + uy (16)

B From the OLS estimates a, b, c, d, um, uy, using the respectivecorrespondences between eq. (13) (14) and (15) (16) it is possibleto recover α, β, γ, δ, εm, εy, i.e. parameter estimates of thestructural model.



Instrumental variables

B Notice that the structural-form coefficients (α, β in the ex.) couldbe equivalently obtained by instrumental variables estimation.

B Following the previous example:

• p: instrumental variable for eq. (9) (m = αy + εm)

• r: instrumental variable for eq. (10) (y = βm + εy)

B Two-stage least squares estimation for eq. (9):

1 OLS regression of y on p: obtain y

2 OLS regression of m on y: obtain αIV



Identification of SVAR

B Problem of identification: from the estimate of the VAR

yt = A1yt−1 + . . . + Apyt−p + ut (17)

B we want to recover the SVAR (where W = I− Γ0):

Wyt = Γ1yt−1 + . . . + Γpyt−p + εt, (18)

yt = Γ0yt + Γ1yt−1 + . . . + Γpyt−p + εt, (19)

B more parameters in SVAR than in VAR.

B Notice that:

ut = W−1εt = Bεt (20)

• Knowing B (and all the parameters in 17) one can recover:• Γ0 = I− B−1

• Γ1 = B−1A1• . . .• Γp = B−1Ap



MA representation

MA (moving average) representation of the VAR (understability):

yt = (I−A1L− . . .−ApLp)−1ut =∞

∑j=0

Φjut−j (21)

where Φ0 = I, Φi = ∑ij=1 AjΦi−j, for i = 1, 2, . . .

Since Γ0ut = εt

yt =∞

∑j=0

ΦjBB−1ut−j =∞

∑j=0

Ψjεt−j (22)

Ψj (k× k matrices): structural impulse response functions, theydescribe how structural shocks affect variables.



King et al. 1991

King Plosser Stock Watson (1991), “Stochastic trends and economicfluctuations” American Economic Review

Empirical analysis using US quarterly data 1949:Q1-1988:Q4(1954:Q1-1988:Q4):

• c: per capita real consumption expenditures (logs);

• i: per capita gross private domestic fixed investment (logs);

• y: per capita private gross national product (logs);

• m: M2 (currency, demand deposits, and savings deposits, per capita inlogs);

• p: GNP implicit price deflator (logs);

• R: interest rate (the three-month U.S. Treasury bill rate).



King et al. 1991

Three questions (King et al. 1991: p. 820):

• What are the cointegration properties of the data? Are these consistentwith the presence of a common stochastic (productivity) trend?

• How much variation of the main variables can be attributed to shocks tothe common stochastic trend?

• Do innovations associated with nominal variables explain importantvariation in the real variables?



King et al. 1991

Theoretical background

• Real Business Cycle literature: Kydland-Prescott (1982).Cobb-Douglas production function:

Yt = AtK1−αt Lα

t

Total factor productivity following a random walk:

log At = µ + log At−1 + εt

• Solow (1957) model: per capita consumption, investment and output allgrow at the same growth rate in the steady state.



King et al. 1991

Cointegration

• Two cointegrating relationships between (c, i, y):

the linear combination of c and y and the linear combination of iand y are I(0)

• Three cointegrating relationship between (c, i, y, m, p, R):

• one linking m− p, y and R (money demand)

• two linking the real ratios (c− y) and (i− y) with the real interestrates (R− ∆p)



King et al. 1991

Estimation and identification

• Vector error correction model:

∆yt = Πyt−1 + F1∆yt−1 + . . . + Fp−1∆yt−p+1 + ut

• Long-run restrictions



King et al. 1991

Results

• Balanced-growth shock explains great variation in output in the threevariables (c, i, y) model.

• Much less in the six variables model.

• Permanent productivity shock is not able to account most of thebusiness cycles fluctuations.


advanced macroeconomics module 3: empirical models ...amoneta/m2019_2.pdfokun’s lawphillips curve...

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