real estate dynamics and international business cycle...
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Real Estate Dynamics and International
Business Cycle Synchronization
Jean-Francois Rouillard†
Queen’s University
JOB MARKET PAPER‡
January 25, 2012
Abstract
While business cycles of industrialized countries have become more synchronized in the pastdecade, the gap between cross-country correlation in output and in consumption has widened.Hence, the inconsistency between data and the standard international real business cycle model,known as the quantity anomaly, appears to have worsened. I examine the role of real estatedynamics in explaining these two stylized facts. I introduce a non-tradable and fixed-quantitygood, real estate, into a two-good, two-country real business cycle model with incomplete mar-kets and endogenous borrowing constraints. First, from calibrated shock processes’ persistenceand volatility, I show that the introduction of real estate, combined with terms of trade effectsis important in generating positive international co-movements. However, the quantity anomalycan only be replicated if country-specific financial shocks to borrowing capacity are added tothe business-cycle model. Second, I feed the model with shock processes constructed from U.S.and U.K. data. In this case, the model succeeds in matching output synchronization, but failsto explain the worsening of the quantity anomaly.
JEL identification: E44, F34, F44Keywords: business cycle synchronization, real estate dynamics, borrowing constraints, finan-cial shocks, correlation (quantity) puzzle
†Contact information: Ph.D. Candidate - Department of Economics - Queen’s University - 94 University Avenue,Kingston, Ontario, K7L 3N6, Canada; e-mail: [email protected]. I am grateful to Gregor W. Smith andparticipants at the Queen’s Macroeconomics Workshop, the Canadian Economics Association Conference 2011, theCIREQ Ph.D. Students’ Conference 2011, the Congres annuel de la societe canadienne de science econonomique 2011,and the Eastern Economics Annual Conference 2011 for excellent comments. I express my sincere gratitude to myadvisor, Huw Lloyd-Ellis, for his valuable support and supervision. I also thank Zheng Liu for providing me with dataon liquidity-adjusted land prices for the United States, the Bank for International Settlements for series on housingprices for the United Kingdom and Andrea Raffo for series on OECD countries’ aggregate variables. I acknowledgefinancial support from FQRSC (Fonds quebecois de la recherche sur la societe et la culture).
‡The most recent version of this paper can be found at: http://qed.econ.queensu.ca/pub/students/phds/rouillard
1
1 Introduction
Synchronization of business cycles across industrialized countries has magnified over the past decade
to levels that have culminated with the Great Recession.1 Additionally, during this period of en-
hanced financial globalization and sophistication, empirical evidence points to a widening gap be-
tween international co-movements of output and consumption, also known as the quantity anomaly.
This finding is important in assessing the degree of international risk-sharing. In order to repli-
cate these two phenomena, I introduce real estate into an international real business cycle (IRBC)
model, augmented with endogenous borrowing constraints. I show that I can match international
co-movements and moments of output, consumption, investment and hours worked. Moreover, the
inclusion of financial shocks to borrowing capacity appears to be crucial in explaining the gap be-
tween consumption and output cross-country correlations. Another result is that the inclusion of
financial shocks to borrowing capacity has some success in explaining the decline in international
risk-sharing of the past decade. One of real estate’s key feature, that is not shared with physical
capital, is its non-tradability. Real estate also fulfills multiple functions; it is (i) an input in the
production of an expenditure good, (ii) a consumption good, and (iii) a collateral asset.2 Moreover,
the reallocation of real estate from the residential to the commercial (productive) sector plays a key
role. Following a shock, firms can rapidly adjust their collateral by purchasing or selling real estate
in order to affect their borrowing level. As a result, there are important interest rate dynamics
created by the collateralization of the firm that are propagated internationally through a financial
channel.
In this paper, I consider international business cycles during a period of stronger financial
linkages internationally (1988-2007) that also coincides with a period of low aggregate volatility.
Since real estate markets are idiosyncratic, the calibration of my model is not based on a group of
countries, but on two of the world’s largest financial hubs: the United States and the United King-
dom. A contribution of the paper is to shed light on some long-standing puzzles from international
macroeconomics. Standing as a benchmark in the IRBC literature, Backus, Kehoe and Kydland’s
(1992) (hereafter BKK) model is not able to generate sufficiently high positive co-movements in
output, investment and employment. The reverse is true for consumption: it predicts too much
cross-country correlation. The quantity anomaly is defined by the authors as implying greater cross-
country correlation in output than in consumption. In fact, the gap between those two correlations
can also be interpreted as the degree of deficiency of international risk-sharing across countries.
The international co-movement puzzle pertains to the low, but positive, levels of cross-country
correlation for investment and hours worked in the data. I show that my model with technology
1See Imbs (2010) for an empirical analysis of the international dimensions of the crisis.2The reader should note that throughout the paper, I use real estate and land, but since there is not a housing
nor commercial construction sector in my model, these two variables are interchangeable.
2
shocks can help to resolve the international co-movement puzzle. However, in order to explain the
quantity anomaly, financial shocks must be added to the baseline model.
The inconsistency of the results generated by BKK’s model and data can be decomposed into
two parts: cross-country correlations in consumption are much lower in data, whereas for cross-
country correlations in output, they are much higher in data. In the case of technology shocks,
the underlying mechanism of my model emphasizes the latter correlation and the introduction of
financial shocks works to explain the gap between the two cross-country correlations. In my baseline
model, the two countries are linked internationally on two markets: the goods and assets markets.
I follow Backus, Kehoe and Kydland’s (1994) approach, so that each country specializes in the
production of one intermediate good but the final consumption good is an aggregate of these two
goods. This structure creates important terms of trade effects. I also assume that the only asset
countries can trade is a risk-less, non-contingent international bond, or that financial markets are
incomplete.
These two international market linkages have been examined in the literature. For example,
on the international linkages of the goods market, Ambler et al. (2002) build a model in which
countries have multiple sectors and sector-specific shocks in order to generate greater positive
co-movement in output. The two-good market structure embedded in my model also increases
output co-movement across countries, but there are some additional effects when it is combined to
a model with real estate and endogenous borrowing constraints, the level of this co-movement is
amplified. There has been much work in order to explain the low level of cross-country correlations
in consumption. One approach has been to rely on incomplete asset markets as shown by Kollmann
(1996). Baxter and Crucini (1995) obtain similar results with incomplete asset markets, but show
that technology shocks have to be either highly persistent or not transmittable internationally
in order for co-movements to be greater than a complete asset market structure. In contrast to
other work, Kehoe and Perri (2002) and Bai and Zhang (2011) have an endogenously determined
incomplete asset market structure that they introduce through a limited enforcement problem so
that countries can default on their loans. Financial frictions in my model take place within the
country rather than at the international level. Moreover, the asset market structure is not the main
factor that contributes in driving down the cross-country correlation in consumption. In fact, non-
separable preferences in consumption and leisure, introduced in the literature by Devereux et al.
(1992), play a much more important role.
With this type of preferences, the inter-temporal marginal rate of substitution depends not
only on consumption levels as it is the case for separable preferences, but additionally on leisure
decisions. Since agents across countries are trading a risk-free international bond, these marginal
rates of substitution are equalized and therefore there is less risk-sharing measured as cross-country
3
correlations in consumption. Another approach in the literature has been to introduce non-tradable
goods. Stockman and Tesar (1995) show that they can lower cross-country correlation in consump-
tion for non-tradable goods with the addition of taste shocks, but the puzzle still persists for
tradable goods. In my model, real estate is also non-tradable and housing services are included in
the measurement of consumption expenditures. However, the non-tradable composition effect of
the final good is marginal and all results remain the same if housing services are excluded from the
measurement of private consumption expenditures.
Similar to my work, Iacoviello and Minetti (2006) embed real estate in a two-country framework
in which a fraction of agents are borrowing-constrained. They show that they can raise the co-
movement of output by introducing different liquidation costs that depend on the lender’s origin. In
contrast, I do not allow for any international borrowing besides the international bond, so that this
channel is non-existent in my framework. Re-allocation of land from one sector to another within the
same country seems to matter most for my results. As stated above, the two-good structure in my
model allows for terms of trade dynamics that amplify output co-movements. Terms of trade effects
are also amplified by credit constraints in the model of Paasche (2001), but his framework differs
from mine, since it features two small open economies that export to a large country. Moreover,
he examines the effects of terms of trade shocks, that are, in contrast, endogenously determined in
my model.
My paper is also related to the literature that examines financial frictions in a two-country
environment. Most work has focused on balance-sheet effects and international portfolio reallo-
cations to explain the greater synchronization of business cycles. Hence, financial globalization
plays a central role in their analysis. That is the case for Faia (2007) and Dedola and Lombardo
(2009) who have models based on Bernanke, Gertler and Gilchrist’s (1999) financial accelerator
and endogenous portfolio choice. Examining the same effects but using a leverage constraint a
la Kiyotaki and Moore (1997) with two agents, Devereux and Yetman (2010) find that integrated
equity markets, but not bonds markets, can propagate a technology shock internationally. Even
though my framework integrates elements of the financial accelerator literature, the mechanism
that leads to my results does not hinge on amplification effects.
Perri and Quadrini (2011) also focus on international financial integration and introduce an en-
dogenous borrowing constraint derived from a debt renegotiation problem similar to Hart and Moore
(1994). Each country is populated by workers and investors: the shareholders of the firms. Since
investors are assumed to have a lower discount factor than workers, investors will borrow from
workers in equilibrium. The borrowing constraints in my model shares similar features, but I
depart from Perri and Quadrini (2011) on many dimensions. In their framework, investors are
shareholders of both domestic and foreign firms, and since liquidation costs are the same across
4
countries this is equivalent to have one international investor. Hence, the transmission of shocks
across countries takes place through this mechanism. In contrast, I do not allow for cross-border
dividend streams, so that the international portfolio optimization problem is not considered in my
analysis. The idea is that I hypothesize that shocks could be transmitted from other channels and
that real estate as collateral, a type of good absent from Perri and Quadrini’s (2011) framework,
can be important in explaining business cycle synchronization. Furthermore, my model differs on
the borrowing constraint that is not always binding in their model, while it always is in mine.
Terms of trade and exchange rate effects are also non-existent, since only one good is included.
Finally, the structure of their production function is AK, while it is Cobb-Douglas in my model.
In the next paragraphs, I will show, in the context of technology and financial shocks, why the
combination of endogenous borrowing constraints, real estate, and terms of trade dynamics leads
to greater international co-movements than a representative agent or one-good model.
Since firms need to pay their factors of production and dividends to shareholders before receiv-
ing their revenues, they contract an intra-period loan from the workers. The debt renegotiation
problem comes about because firms can default on their obligations of that loan, although in equi-
librium it will not be optimal to do so. In the event of a default, workers would be able to repossess
a fraction of the firm’s collateral composed of real estate and physical capital. Moreover, since
investors have a lower discount factor than workers, firms also have some inter-period debt. Hence,
their total liabilities consist of both the intra-period loan and inter-period debt that cannot be
greater than the next period’s collateral values times an exogenous parameter. In fact, the credit
shock is just a stochastic shock to that parameter.
I describe the transmission mechanism of a temporary positive technology shock, first, in a
closed-economy environment and in an open-economy environment. From my derivations of the
enforcement problem, a positive shock tightens the borrowing constraint, so that the level of inter-
period debt is reduced. There are many effects that I will decompose. First, output is raised, directly
from a greater Solow residual and indirectly from greater marginal productivities of the production
factors, so that the intra-period loan will increase. Since total liabilities cannot be greater than
a fraction of the collateral’s value, it implies that there would be proportionally less inter-period
borrowing relative to intra-period borrowing. Second, the value of the collateral increases following
the shock. However, real estate plays a role to dampen this rise, more precisely through its feature of
a consumption good for workers. From a wealth effect, workers substitute consumption of the final-
good for land, so that land for productive uses drops. On the firms’ side, firms use the cash flows
generated by that sale to increase their investment. However, there are some costs associated to
increase physical capital, since its rapid adjustment would lead to important variations in dividends
that would be inconsistent with the investors’ problem. At last the variation in the intra-period
loan is greater than the variation of the collateral’s value and that implies lower inter-period debt
5
and consequently that would mean that the firms ask for a lower interest rate.
Since financial markets are partially integrated, the interest rate is unique across the two
economies and home workers lend to foreign workers. Moreover, the home economy increases its
imports from the foreign economy and consequently, foreign firms invest and produce more leading
to greater positive co-movements with the home economy’s same variables. Thus, the behavior of
the interest rate is key to the international transmission mechanism of technology shocks. Greater
foreign expenditures also lead to favorable terms of trade as the price of the imported intermediate
good drops.
Certain features of the Great Recession have led some authors to reject the notion that the
downturn was caused by a negative technology shock and instead had more to do with credit
conditions.3 Much progress has recently been made towards identifying financial shocks and their
role in international transmission.4 Moreover, technology shocks imply that the share of land used
for production is negatively correlated with output, an implication that is at odds with data. A
temporary positive financial shock in the home economy implies a relaxed borrowing constraint
and a greater interest rate, so that home workers lend to home firms. The latter increase their
investment and purchase a greater share of land from home workers. In this case, foreign workers
lend to home workers since the interest rate is greater in the home economy. Therefore, negative
co-movements in investment and output emerge, but they are reversed in the subsequent periods.
Since real estate can be rapidly reallocated from the worker to the firm, all the adjustment takes
place in the first period. In future periods, however, the interest rate reverts to its steady state
level.
As the principal and the interest on the first period’s international bond are repaid in the second
period and foreign workers reduce their lending internationally, they direct it towards foreign firms.
Hence, the same effects operate subsequently in the foreign economy as the firms acquire physical
capital and land for productive uses. In a similar fashion to technology shocks, favorable terms-of-
trade effects for the foreign economy result in greater international co-movements.
In the case for which the two-country model is symmetric and the persistence of the shocks
and the volatility of their innovations is calibrated from U.S. and U.K. data, the model is able to
generate levels of cross-country correlations that match the data. Moreover, the quantity anomaly
can be replicated if country-specific financial shocks to borrowing capacity are added. In light of
theses successes, I also assess the model’s performance in matching dynamics of rolling cross-country
correlations in output and in consumption. Sample paths are computed from estimated technology
and financial shocks. One finding is that greater output synchronization can be replicated, but the
3For instance, Mulligan (2011) shows that labor productivity has, in fact, increased during this period.4See, e.g., Bui and Bayoumi (2010); Helbling et al. (2011); Eickmeier et al. (2011)
6
ρ(GDP,GDP*)
ρ(PCE,PCE*)0
.2.4
.6.8
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Series are HP−filtered with λ=1,600. The description can be found in the appendix.
Figure 1: Cross-country correlations in output and consumption between the US and an averageof 12 OECD countries (rolling 40 quarter window estimates, 1987Q4-2007Q4)
model fails to explain the worsening of the quantity anomaly.
The rest of the paper is organized as follows. In section 2, I discuss some international business
cycle stylized facts with regards to synchronization and risk-sharing for the United States and the
United Kingdom. In section 3, I present my model in two distinct parts in order to show the effects
of collateral constraints. In section 4, I characterize the persistence and volatility of the technology
and financial shocks and calibrate the rest of the parameters. In section 5, I evaluate the effects of
those shocks and display my results. Section 6 concludes and offers some new potential paths for
further research on financial shocks in an international context.
2 Business Cycle Synchronization Stylized Facts
BKK identify many properties of international business cycle co-movements between the United
States and other industrialized countries and find some interesting anomalies. In this section, I
assess whether the evidence still persists for a more recent period of time. I compute rolling cross-
country correlations of the United States and twelve other OECD countries and present the results
for the average of these correlations in Figure 1.5 Moreover, since I evaluate the importance of
real estate markets in the international synchronization and those markets are rather idiosyncratic,
5These twelve OECD countries consist of Australia, Austria, Canada, Finland, France, Germany, Ireland, Italy,Japan, Norway, Spain and Sweden.
7
ρ(GDP,GDP*)
ρ(PCE,PCE*)
.5.6
.7.8
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Series are HP−filtered with λ=1,600. The description can be found in the appendix.
Figure 2: Cross-country correlations in output and consumption between the US and the UK(rolling 40 quarter window estimates, 1987Q4-2007Q4)
US−12 OECD countries average
US−UK
−.1
0.1
.2.3
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Series are HP−filtered with λ=1,600. The description can be found in the appendix.
Figure 3: Differences in cross-country correlations in output and consumption (rolling 40 quarterwindow estimates, 1987Q4-2007Q4)
8
I study co-movements between the United States and the United Kingdom. I choose the U.K.
because it is large on both economic and financial dimensions and because the gap between the
rolling correlations in output and in consumption exhibit a similar pattern than the average of the
OECD countries as shown by Figure 3. Although, its business cycle is more synchronized with the
U.S. one than the average OECD country, there is a clear upward trend for the co-movement of
output in the past decade that is shown in 2. However, in contrast to the group of countries, the
rolling cross-country correlation in consumption between the U.S. and the U.K. is decreasing for
the sample examined.
From Figure 1, the importance of business cycle synchronization across industrialized countries
can be appreciated as cross-country correlation in output has jumped from 0.2 for the window span-
ning from 1987Q4 to 1997Q3 to 0.68 for the window spanning from 1998Q1 to 2007Q4. Similarly
for the cross-country correlations in consumption for the same windows it has increased from 0.06
to 0.57. Another finding is that the gap between these two correlations has widened in recent years,
more precisely starting in 2003, as it is illustrated in Figure 3. One thing that really stands out
form that figure is that what BKK have called the quantity anomaly has still persisted in the past
two decades and it has some implications on the level of international risk-sharing.
However, it has to be clear that there is no consensus in empirical work to whether or not
industrialized countries have experienced more or less international risk-sharing. Kose et al. (2009)
discuss the results of different studies. For example, Bai and Zhang (2011) also observe that finan-
cial globalization has not led to better international risk-sharing. From a sample of 21 industrialized
countries, they regress consumption growth on output growth for each country, controlling for world
consumption and output growth. Their main finding is that they cannot reject the hypothesis in-
dicating that the coefficient of that regression is equal to zero and is the same for the following
time periods: 1970-1986 and 1987-2004. If perfect risk-sharing would prevail, consumption growth
would not be expected to depend on output growth.
3 The business-cycle model
In order to identify the sources of my findings, I first present a representative agent version of the
model. My benchmark model augments the incomplete financial markets version of Backus et al.
(1994) and the bond economy of Heathcote and Perri’s (2002) work on several dimensions. It
differs from previous work in two ways. First, the class of preferences over consumption and leisure
are similar to those proposed by Greenwood et al. (1988) (hereafter GHH), and the fact that real
estate is embedded in the model both in production and household preferences. This first version
is stripped of borrowing constraints and loan-to-value shocks that I introduce subsequently.
9
The structure of the model is a two-country one in which the world is populated by workers
that live either in the Home (H) country or in the Foreign (F ) country. Those workers consume two
types of goods: a final consumption good and housing services. The final good is a composite of the
differentiated intermediate goods produced locally and abroad and can also be used for investment
purposes. The factors of production for the intermediate good consist of labor provided by the
workers, capital and holdings of commercial real estate. I refer to real estate as land, a fixed asset
that can have productive uses but from which workers also derive utility that can be analogous to
housing services. The production of residential and commercial structures is ignored, since most
housing price fluctuations stem from changes in land prices. Davis and Palumbo (2008) document
that, from 1984 to 2004, land prices have increased eleven times more than residential structure
prices.
Agents of the two countries are linked in two ways: trade and finance. First, the intermediate
good can be traded abroad in order to form the final good. Second, I adopt an incomplete financial
market structure, such that workers trade an international non-contingent bond. I opt for non-
separable preferences in order to exploit the fact that there are no wealth effects on labor supply
and this will turn out to be important when considering financial shocks. GHH preferences are
derived from the reduced-form of a model that would comprise home production. This category
of preferences is widely used in the international real business cycle literature to explain different
cyclical properties. For example, Raffo (2008) shows that it can explain the negative correlation
between output and net exports. Devereux et al. (1992) also find that those preferences in a one-
good model can generate cross-country correlations of consumption that are much closer to data.
I will show that this basic model cannot match key moments of the data.
3.1 Representative agent model without borrowing constraints
3.1.1 Preferences
I have motivated above the choice of GHH preferences, but they are not standard in this model,
since housing services are included. I assume that the elasticity of substitution between the standard
non-separable preferences and housing services is equal to one in each country, i where i = {H,F}.
Ei0
∞∑
t=0
βtitU(cit, h
Wit , nit)
where
U(cit, hWit , nit) = ln
(cit −
ζ
ηnη
it
)+ j ln hW
it . (1)
10
such that cit corresponds to the consumption of the final good, nit to the hours worked and hWit to
the fraction of land owned by the household for residential purposes. In the utility function, the
parameter j corresponds to the weight of housing in the household’s utility, such that jj+1 × 100 is
the percentage of that share. In order to ensure stationarity in an incomplete financial market, I
adopt Mendoza’s (1991) approach and render the discount factor endogenous6 as follows
βit =(1 + exp(U(cit, h
Wit , nit))
)−ςW.
3.1.2 Budget constraint
The representative agent’s budget constraint is expressed in terms of her own final good price.
Hence, output needs to be multiplied by the appropriate intermediate good price. Capital accu-
mulation is subject to depreciation and an adjustment cost similar to that described in Jermann
(1998) that serves the purpose of reducing the volatility of investment.
kit = (1 − δ)kit−1 +
((g1
1 − φk
)(xit
kit−1
)1−φk
+ g2
)kit−1 (2)
where 1/φk corresponds to the elasticity of investment with respect to Tobin’s q and δ corresponds
to the depreciation rate. The other parameters g1 and g2 are set to steady-state targets so that
∂kit/∂xit = 1 and so that Tobin’s q is equal to 1. Moreover, since agents possess both residential
and commercial land, only the quadratic reallocation adjustment costs for both sectors, similar to
Iacoviello (2005), appear in their budget constraint ΨhWit
(hWit , qit, h
Wit−1) and ΨhP
it(hP
it , qit, hPit−1).
7
ΨhWit
(hWit , qit, h
Wit−1) =
φh
2
(hW
it − hWit−1
hWit−1
)2
hWit−1qit (3)
ΨhPit(hP
it , qit, hPit−1) =
φh
2
(hP
it − hPit−1
hPit−1
)2
hPit−1qit (4)
At the international level, agents trade a risk-free bond fit, such that their budget constant is
as follows
6Bodenstein (2011) shows that an endogenous discount factor of this type always implies a unique steady state intwo-country models.
7These costs proxy a transaction cost that can arise when changes in land zoning occur or simply the costs of landrestructuring.
11
cit + xit + fit + ΨhWit
+ ΨhPit
= Rt−1fit−1 + witnit + Rkit−1kit−1 + fit. (5)
In equation (5), wit corresponds to the wage, xit to physical capital investment, Rkit corresponds to
the capital rental rate and Rt to the interest rate on the international bond. Since representative
agents are the owners of the firm the land transactions do not show up in their budget constraints.
3.1.3 Firms and Technology
In this version of the model, workers are the owners of the zero-profit intermediate-good and final-
good firms. Intermediate goods are produced from local input factors according to the following
Cobb-Douglas function, so that physical capital inputs and land have a unitary elasticity of substi-
tution in production.8 Intermediate goods firms solve the following problem in each country (where
i = {H,F}):
maxhP
it−1,kit−1,nit
piityit − witnit − Rkitkit (6)
subject to:
yit = AithP ν
it−1kµit−1n
1−ν−µit (7)
where hPit corresponds to the land holdings used for productive uses, kit to capital, nit to labor
supply and Ait to an exogenous technology shock. Land holdings and capital are purchased from
the workers themselves. In order to simplify the problem, I assume that land does not depreciate.
The exogenous technology shocks follow a bivariate autoregressive process as follows
Zt = ΓZt−1 + εt, εt ∼ N(0,Σ) (8)
where Zt = [AHt, AFt]′ and εt = [εAHt
, εAF t]′. Elements off the diagonal in matrix Γ are defined as
spill-overs. The variance-covariance matrix is given by: E(εtε′t) = Σ.
I assume that Home(Foreign) intermediate goods firms produce good a(b), such that the final
good is a composite of those two intermediate goods and are aggregated a la Armington.
8Sakuragawa and Sakuragawa (2011) show that the amplification effects of the financial accelerator are sensitiveto the elasticity of substitution in production.
12
G(aHt, bHt) =[ωǫ+1a−ǫ
Ht + (1 − ω)ǫ+1b−ǫHt
]− 1
ǫ (9)
G(aFt, bFt) =[(1 − ω)ǫ+1a−ǫ
F t + ωǫ+1b−ǫF t
]− 1
ǫ (10)
where ω > 0.5 represents home bias in the production intensity of the local intermediate good. The
elasticity of substitution between foreign and domestic intermediate goods is given by σ = 1/(1+ǫ).
3.1.4 Market Clearing
For the final goods’ market, the production of the goods is equal to the domestic absorption:
cit + xit = G(ait, bit) where i = {H,F}. (11)
As for the intermediate good, since firms from each country only produce one type of good,
markets clearing implies :
aHt + aFt = yHt, (12)
bHt + bFt = yFt. (13)
The bonds market clearing condition is:
fHt + fFt = 0, (14)
Moreover, since land is a fixed asset, its supply is normalized to one, such that:
hPit + hW
it = 1. (15)
3.1.5 Equilibrium
Definition 1. In each country (for which i = {H,F}), an equilibrium is defined as a set of functionsfor
13
(i) workers’ policies cWi (s), ni(s), hW
i (s), fi(s),(ii) firms’ allocations aHt, aFt, bHt and bFt for the production of the final good,(iii) intermediate goods prices pHHt, pHFt, pFHt and pHFt,(iv) prices of labor and capital wit and Rk
it
(v) the shock process described in (8),
such that
(i) household’s allocations maximize the household’s problem,(ii) firms’ policies are optimal,(iii) the wage, interest rates and prices clear the labor market, the bond market, the real estate
market and the goods markets and(iv) the resource constraint (11) is satisfied.
3.1.6 Equilibrium Prices
Under the assumption of perfect competition for firms, the equilibrium prices of goods a and b in
terms of the home final good correspond to the marginal products of these two goods. For prices
the first position of the subscript determines the production location of the intermediate good and
the second position of the subscript where it is used for the production of the final good. Hence,
pHHt corresponds to the price of good a in the Home country with i = {H,F}
pHit =∂G(ait, bit)
∂ait, pF it =
∂G(ait, bit)∂bit
. (16)
3.1.7 Terms of trade and real exchange rate
Terms of trade are defined as the price of good b in terms of the price of good a and also correspond
to the marginal rate of substitution:
TOTt =pFHt
pHHt=
1 − ω
ω
(aHt
bHt
)1+ǫ
(17)
=pFFt
pHFt=
ω
1 − ω
(aFt
bFt
)1+ǫ
The real exchange rate is defined as the ratio of the price of an intermediate good in the foreign
country over the price of the same good in the home country, RERt =pHFt
pHHtand from (17) is also
14
equal topFFt
pFHt.9
3.1.8 First order conditions
From the equilibrium conditions and the representative agent’s optimization problem, the first order
conditions are:
1
cit −ζηnη
it
= Eit
(βitRit
cit+1 −ζηnη
it+1
), (18)
ζnη−1it = wit, (19)
hPit
(1 − hPit)
=βitνYit
j(cit −ζηnη
it). (20)
Equation (18) corresponds to the standard Euler equation with portfolio adjustment costs.
Equation (19) refers to the labor market and, in contrast to Cobb-Douglas preferences, consumption
does not show up with GHH preferences. Rearranging this equation such that the wage bill is a
fraction of output: witnit = (1− µ− ν)Yit, which implies a positive relationship between labor and
output: ζnηit = (1−µ− ν)Yit. The third condition (20) can be expressed as a ratio of land used for
the production of the consumption good to land for residential uses.
3.2 Baseline model with borrowing constraints
The baseline model combines the two-country and two-good framework of the previous section with
borrowing constraints based on Hart and Moore (1994) and Perri and Quadrini (2011). There are
now two types of agents that differ in their discount factor and on other characteristics: the investors
have a lower discount factor and are the ones that borrow from the workers.
3.2.1 Investors
First, I describe the firms’ optimization problem and I follow by describing their shareholders’
problem (investors). Intermediate good firms have a Cobb-Douglas production function given by
(7). At the beginning of each period, the firm has inter-temporal debt Rit−1eit−1 contracted from
the household, capital kit−1 and real estate hPit−1. The choice of labor input nit, investment xit,
9This definition of the exchange rate is specific to the intermediate good sector. A more general definition wouldbe a composite of the prices of these tradable goods and the prices of a non-tradable component that would be realestate.
15
new real estate qit∆hPit , dividends dit, and the next period debt eit are made before production. Its
budget constraint is as follows :
piityit + eit = dit + xit + qit(hPit − hP
it−1) + ΨhPit
+ Rit−1eit−1 + witnit (21)
Since the payments of the wage bill witnit to the workers, of dividends dit to the investors,
investment expenses xit, land acquisitions qit∆hPit and adjustment costs ΨhP
itare all made before
the revenues are realized, the firm contracts an intra-period loan lit:
lit = Rit−1eit−1 − eit + dit + xit + qit(hPit − hP
it−1) + ΨhPit
+ witnit. (22)
From the budget constraint this loan must be equal to output. However, the contract is not
perfectly enforceable, and defaulting can occur with some positive probability. In the case of a
default, the lender can liquidate the firm’s capital and commercial real estate for a stochastic
fraction λitιk of the value of its capital holdings and λit of its real estate, where ιk ∈ [0, 1] allows
for a smaller fraction of physical capital to be collateralized, since it can be harder to liquidate
machinery and equipment than real estate.10 Hence, the recovery value if a default occurs is
λitEit(ιkkit + qit+1hPit). Since the total liabilities of the firm are lit + eit, in order to prevent any
defaults the borrowing constraint is as follows:11
λitEit(ιkkit + qit+1hPit) ≥ lit + eit (23)
Equation (23) can also be expressed as:
λit ≥eit
Eit
(ιkkit + qith
Pit
) +lit
Eit
(ιkkit + qith
Pit
)
The first term corresponds to a loan-to-value ratio for which capital and real estate play the roles
of collateral.
The equity value of the firm, defined as Vit(sit+1; kit+1, hPit+1, eit+1), is measured at the end
of the period after paying dividends to its shareholders, investing in physical capital and choosing
10Liu et al. (2011) argue that real estate is an important collateral asset, since for non-financial corporate firms itcorresponds, on average from 1952 to 2010, to 58% of total tangible assets.
11This problem is based on Hart and Moore (1994) and I assume that the borrower has all the bargaining power.I refer the reader to Appendix A of Perri and Quadrini (2011) for a complete derivation of the debt renegotiationproblem.
16
its land share. By definition, the equity value is just the sum of future discounted dividends dit,
starting to be payable in the next period such that:
Vit(sit+1; kit+1, hPit+1, eit+1) = Eit
∞∑
j=1
mit+jdit+j
where mit+j corresponds to the stochastic discount factor that will be derived from the en-
trepreneur’s problem. The firm’s problem can also be formulated recursively as follows:
V (si; ki, xi, hPi , ei) = max
di,ni,k′i,h
′Pi ,e′i
{di + Eim
′iV (s′
i; k′
i, h′Pi , e′i)
}(24)
subject to:
qihPi + Yi + e′i − wini = di + xi + qih
′Pi + ΨhP
i+ Riei,
λiEi(q′ih
′Pi + ιkk
′i) ≥ e′i + Yi,
k′i = (1 − δ)ki +
((g1
1 − φk
)(xi
ki
)1−φk
+ g2
)ki.
The recursive formulation is instructive because it shows the value of the firm as the sum of
the discounted stream of dividends. The first order conditions are with respect to ni, e′i, hPi and k′
i
and ϑi and Qi correspond respectively to Lagrange multipliers on the borrowing constraint and on
the capital accumulation equation.
Yni =wi
1 − ϑi, (25)
1 = Em′i(R
′i + ϑi), (26)
qi = Em′i
(q′i + Yh′P
i(1 − ϑ′
i))
+ λiϑiq′i, (27)
Qi = λiιkϑi + Em′
(Yk′i(1 − ϑ′
i) + Q′i
[1 − δ + g2 + g1
(φk
1 − φk
)(xi
ki
)1−φk
]). (28)
Equation (25) corresponds to the derivative with respect to labor. In the representative agent
model, labor productivity equals the wage, but in this case the borrowing constraint creates a
labor wedge. Jermann and Quadrini (2009) put much emphasis on this response mechanism of
hours worked in order to match business cycle moments. A relaxed borrowing constraint directly
affects labor demand as the wedge between wages and labor productivity increases. Equation
(26) refers to a standard Euler equation for a model in which there are borrowing constraints.
The Lagrange multiplier ϑi affects the intertemporal substitution of consumption as the marginal
utility of consumption decreases while the borrowing constraint is relaxed. Equation (27) shows
17
the dynamics of the real estate demand for production. The future price of land is important as
it enters the borrowing constraint. Finally, equation (28) corresponds to capital dynamics since a
fraction of capital can be used as collateral and there are some adjustment costs.
The description of the firm’s problem is not sufficient, because investors own the firms from
which they receive dividends dit and have the following utility function: E0∑∞
t=0 γt ln cPit . As
shareholders of the firms, their budget constraint is as follows:
sit(dit + pit) = cPit + sit+1 (29)
where sit corresponds to the equity shares and pit to their market price of those shares. As
investors maximize over their consumption level and shares’ quantity, the first order condition is
this following one:
pit
cPit
− γitEit(dit+1 + pit+1)
cPit+1
= 0 (30)
By forward substitution, it is possible to find a value for the market price of shares:
pit = Eit
∞∑
j=1
(γj
itcPit
cPit+j
)dt+j
Hence, similarly to the findings of Jermann and Quadrini (2009), the effective discount factor
that is consistent with the firms’ problem is: mit+1 = γituc(dit+1)/uc(dit).
3.2.2 Workers
As stated previously, the household’s discount factor βit is greater than the entrepreneur’s one and
their utility function has the same form as the representative agent model.
U(cWit , hW
it , nit) = ln
(cWit −
ζ
ηnη
it
)+ j lnhW
it (31)
At the beginning of each period, workers have a housing stock hWit and bond holdings coming
to maturity. After production occurs they get their loan and the interest on that loan back plus
a wage for the hours they work witnit. They allocate their revenues by either buying more bonds,
18
selling or buying some part of the real estate or they can modify their consumption. Their budget
constraint is as follows
Rit−1eit−1 + Rt−1fit−1 + witnit = cWit + qit∆hit + ΨhW
it+ eit + fit (32)
Since the workers optimize also with respect to loans to investors, in addition to the first
order conditions (18)-(20), there is an additional condition such that the interest rate on bonds are
equalized.
Rit = Rt (33)
3.2.3 Production
As was stated previously the production structure of the benchmark model is similar to the rep-
resentative agent one. However, four financial shocks supplement to the two technology shock and
jointly follow a multivariate autoregressive process as follows
Zt = ΓZt−1 + εt, εt ∼ N(0,Σ) (34)
where Zt = [AHt, AFt, λHt, λFt]′ and εt = [εAHt
, εAF t, ελHt
, ελF]′. Elements off the diagonal in
matrix Γ are defined as spill-overs. The variance-covariance matrix is given by: E(εtε′t) = Σ.
3.3 Recursive competitive equilibrium
Definition 2. In each country (where i = {H,F} and j = H,F , but i 6= j) a recursive competitiveequilibrium is defined as a set of functions for
(i) workers’ policies cWi (s), ni(s), hW
i (s), fi(s), ei(s);(ii) investors’ policies cP
i (s)(iii) firms’ policies d(s; k, hP , ei), l(s; k, hP , ei), k(s; k, hP , ei), hP (s; k, hP , ei) and ei(s; k, hP , ei);(iv) firms’ value V (s; k, hP , ei);(v) aggregate prices for each country w(s), R(s), Ri(s), pii(s), pij(s), q(s) and m(s, s’);(vi) law of motion for the aggregate state s′ = Ψ(s).
Such that:
(i) workers’ policies satisfy conditions (18-20 and 33);(ii) investors’ policies satisfy conditions 30;
19
(iii) firms’ policies are optimal and V (s; k, hP , ei) satisfies the Bellman’s equation (24);(iv) the wage, interest rates and prices clear the labor, bond markets, housing markets (hP +hW =
1), goods markets(12) and (13), and m(s, s’) = γUcP ′/UcP ;(v) the resource constraint (11) is satisfied;(vi) the law of motion in each country Ψ(s) is consistent with individual decisions and the stochas-
tic processes for Ai and λi.
3.4 Adjusting for housing services
The real estate market in my model is simplistic in the sense that there is no sector for the production
of housing nor commercial structures; land parcels are divided between investors and workers.
Moreover, rental and mortgage markets do not play a role. However, data on Personal Consumption
Expenditures and Gross Domestic Product compiled in the National Income and Product Accounts
comprises values for housing services. Therefore, in order for my statistics to be compared to data,
I follow Davis and Heathcote’s (2005) approach and assume that a household could well rent out
some parts of their own real estate. In fact, it would be indifferent to doing so if the lower marginal
utility caused by a smaller share of housing is counterbalanced by greater consumption, so that the
price is equal to ξit.
ξit =UhW it(c
Wit , lit, h
Wit )
Ucit(cWit , lit, hW
it )
The adjustment takes place both for PCE and GDP such that:
PCEit = cPit + cW
it + ξithWit ,
GDPit = Yit + ξithWit .
4 Calibration
4.1 Technology and financial shocks
Since the data analyzed is at a business cycle frequency, the first step is to de-trend it to retrieve
the shocks. I follow the approach of Jermann and Quadrini (2009) in log-linearizing the shocks and
work with deviations rather than levels, since that can matter greatly for the financial shocks. I
remove a quadratic trend from the logarithm of all series for which the deviation from the steady
state is required. All variables and their construction are described in the appendix at the end of
the paper.
20
The technology shock (or Solow residual) has the following form12:
Ait = Yit − νhPit−1 − µkit−1 − (1 − ν − µ)nit (35)
where Yit, hPit , kit and nit are log-deviations from a linear trend of their respective variables. For
example, Yit = log(Yit) − β0 − β1t where β0 and β1 are estimated from an OLS regression.
As for the financial shocks, I assume that the borrowing constraint (23) always binds, so that
in the steady state is described by:
λ(ιkk + qhP
)= e + Y
The log-linearization of this constraint results in:
λit = αkkit + αhqithPit + αeeit + αy yit (36)
where αk =−ιkk
ιkk + qhP, αhP =
−qh
ιkk + qhP, αY =
Y
Y + eand αe =
e
Y + e. I also make the as-
sumption that next period’s expected real estate price is equal to the current one: Eitqit+1 = qit.
Estimated technology and financial shocks for the United States and the United Kingdom are dis-
played in Figures 4-5 for ιk = 0.52 that is the calibrated value for the baseline model as described
in the next sub-section. Technology shocks experienced a severe downturn for both countries dur-
ing the 1990-91 recession, whereas the response of financial shocks has been delayed with troughs
occurring in 1993. Financial shocks also capture the economic boom that preceded the crisis and
in particular for the United States where financial conditions improved dramatically in 2007.
In Table 1, I report the results of the maximum likelihood estimation of equation (34) from
which shocks are derived from equations (35)-(36). Asymmetric and symmetric shock processes are
presented. In order to be consistent with the rest of the literature, symmetry is imposed to the shock
process matrix for business cycle statistics, whereas I construct sample paths from the asymmetric
shock process matrix. Compared to BKK’s estimated technology process for the United States and
Europe, the persistence and spill-overs are somewhat smaller and the correlation of innovations is
also lower. An interesting observation is that financial shocks are more persistent than technology
shocks.
21
−.0
4−
.02
0.0
2.0
4
1988q1 1993q1 1998q1 2003q1 2008q1Last quarter of window
US Solow Residual UK Solow Residual
Solow residuals are constructed by the author from series described in the appendix.
Figure 4: Technology shocks for the United States and the United Kingdom (1988Q1-2007IV)
−.0
6−
.04
−.0
20
.02
.04
1988q1 1993q1 1998q1 2003q1 2008q1Last quarter of window
US Financial Shock UK Financial Shock
Financial shocks are constructed by the author from series described in the appendix.
Figure 5: Domestic financial shocks for the United States and the United Kingdom (1988Q1-2007IV)
22
Table 1: Parametrization of the shock processes
Asymmetric
shock process
Technologyshocks
(1) Γ =
0.84 −0.07 0 00.06 0.94 0 00 0 0 00 0 0 0
σAH= 0.0057
σAF= 0.0051
ρAH ,AF= 0.16
(2) Γ =
0.8 −0.06 0 00.13 0.91 0 00 0 0 00 0 0 0
σAH= 0.0058
σAF= 0.005
ρAH ,AF= 0.15
Financialshocks
(3) Γ =
0 0 0 00 0 0 00 0 0.94 0.030 0 0.05 0.84
σλH= 0.0071
σλF= 0.0043
ρλH ,λF= 0.27
Bothshocks
(4) Γ =
0.75 0.14 0.06 −0.16−0.01 0.8 0.1 −0.37−0.14 0.18 0.96 0.040.04 −0.03 0.07 0.72
σAH= 0.0057
σAF= 0.0046
σλH= 0.007
σλF= 0.0042
ρ =
1.000.17 1.000.42 0.29 1.000.004 0.26 0.3 1.00
Symmetric
shock process
Technologyshocks
(5) Γ =
0.89 0 0 00 0.89 0 00 0 0 00 0 0 0
σA = 0.0055 ρAH ,AF
= 0.18
(6) Γ =
0.82 0.05 0 00.05 0.82 0 00 0 0 00 0 0 0
σA = 0.0054 ρAH ,AF
= 0.19
Financialshocks
(7) Γ =
0 0 0 00 0 0 00 0 0.95 0.020 0 0.02 0.95
σλ = 0.0059 ρλH ,λF
= 0.19
Bothshocks
(8) Γ =
0.82 0.08 −0.12 0.070.08 0.82 0.07 −0.120.01 −0.04 0.96 0.02−0.04 0.01 0.02 0.96
σA = 0.0054
σλ = 0.0059ρ =
1.000.19 1.000.36 0.11 1.000.11 0.36 0.21 1.00
I perform a joint test for symmetry of the shocks processes parameters. For shock process (1) and (2), H0: γ1,1 = γ2,2,γ1,2 = γ2,1 and σAH
= σAF. For (1), I cannot reject the null hypothesis at 5% from a Lagrange multiplier test such that
χ2(3) = 4.88. For (2), I cannot reject the null hypothesis at 1% from a Lagrange multiplier test such that χ2(3) = 6.36. Forshock process (3), H0: γ3,3 = γ4,4, γ3,4 = γ4,3 and σλH
= σλF. For (3), I reject the null hypothesis at a 5% level from a
Lagrange multiplier test such that χ2(3) = 26.8. The symmetry joint tests for (4) have H0: γ1,1 = γ2,2, γ3,3 = γ4,4, γ1,2 = γ2,1,γ1,3 = γ2,4, γ1,4 = γ2,3, γ3,1 = γ4,2, γ3,2 = γ4,1, γ3,4 = γ4,3, σAH
= σAF, σλH
= σλF, ρ1,3 = ρ2,4 and ρ1,4 = ρ2,3. For (4) I
reject the null hypothesis with a p-value lower than 0.001, such that χ2(12) = 38.8.
23
Table 2: Parametrization
Symbol Value Definition(1) (2)
PreferencesςW 0.033 0.066 worker discount factorγ - 0.97 investor discount factorη 1.58 parameter controlling the labor wage elasticityj 1.56 0.07 h utility weightζ 4.55 2.99 n disutility weight
Technologyν 0.0035 0.031 h share1 − ν − µ 0.64 n shareδ 0.025 k depreciationω 0.85 weight on domestic goodσ=1/(1+ǫ) 0.85 elasticity of substitution between traded goods
Creditλ - 0.5 steady-state financial shock
Column (1) corresponds to the representative agent model and column (2) to the benchmark model with borrowing constraintswith capital and real estate as collateral.
4.2 Preferences, Production and Credit Parameters
In Table 2, I report the parametrization of preferences, technology and credit. I assume that they
are the same in the two countries and that steady state targets match US data. The calibration
of the housing parameters are based on Iacoviello (2005), but differs from it, since I consider the
value of commercial and residential land rather than on the value of real estate of these sectors. I
use Davis’s (2009) database to measure the value of real estate attributed to land and structures
on average between 1988 and 2007. Hence, by using land measures, double accounting of capital
is avoided when measures of land are used. I set ν so that commercial land corresponds to the
average of 8.7% of annual output (real estate corresponds to 62% of annual output). As or the
form of the household’s utility function, the housing services interact with the GHH component
in a Cobb-Douglas function and that is consistent with the findings of Davis and Ortalo-Magne
(2011), so that expenditure shares on housing are constant. The parameter that controls utility
from housing services is j and is set so that residential land corresponds to 41% of annual output
(real estate corresponds to 140% of annual output). As for the parameters that control labor, τ
is set so that working hours correspond to 30% of total time. For the parameter that controls the
elasticity of labor, η, I set it equal to 1.58, the value of Greenwood et al. (1988) since I have their
category of preferences. However, the Frisch elasticity of labor depends on steady state values and
12I follow the approach of Backus et al. (1994) in retrieving shocks from the final good’s output as intermediategood output is difficult to measure.
24
is as follows
ηn =1
n
((η − 1)n−1 + ζnη−1
(cW−ζηnη)( ¯hW j
)+ (cW − ζ
ηnη)( ¯hW
j)
) .
In my model the Frisch elasticity is equal to 0.34. The discount factor for workers is standard in
the literature and ςW is set so that β is equal to 0.99 in the steady state and that corresponds to
an annual real interest of 4%. As for the discount factor for investors γ, it is set to 0.97 so that
there is an interest premium of two percentage points, following the calibration of Bernanke et al.
(1999). Since I construct the shocks from quarterly data, I assume a depreciation rate δ of 2.5% that
corresponds to an annual depreciation rate of 10%. For the elasticity of the different input factors in
the Cobb-Douglas production function, the share of labor is 0.63 that is standard in the literature.
Finally, I follow the standard practice in the international real business cycle literature by setting
φk so that the relative standard deviation of investment over GDP generated by the model matches
the data’s ratio. In a similar fashion, there is no steady state target for φh, the parameter that
controls for the transaction costs from the productive sector to the residential sector, it is set to
match the ratio of volatility of productive real estate over output volatility.
International parameters are set in accordance to Heathcote and Perri (2002), since ω is greater
than 0.5 there is some home bias. In the sensitivity analysis, I test the model with different values
for that parameter. The elasticity of substitution between domestic and foreign goods seems to be
quite disputed in the literature. In fact, the range of values is quite large depending amongst other
things, on whether the model has non-traded goods, a distribution sector and price stickiness.13
For the benchmark calibration I use the value of 0.85, which seems to be an intermediate value and
is the one reported in Bodenstein (2011). The parameter that controls for home bias ω is set to
0.85, so that imports correspond to 15% of output, a value that also corresponds to the average for
the United States from 1988 to 2007.
The parameter that controls the loan-to-value in the steady state λ is set similarly to the low
leverage of Devereux and Yetman (2010). It corresponds to λ = 0.5. Moreover, ιk is set so that it
minimizes the sum-squared distance between the cross-country correlations in output, consumption,
investment and hours worked of the model and the ones of data as described in the next section. In
the baseline model, it is equal to 0.52, so that 26% of capital can be used as collateral. Resulting
from this parametrization, in the steady state of the benchmark model, consumption of workers is
63.3% of output, consumption of investors corresponds to 21.4% and investment to 15.3%.
13See Bodenstein (2011) for a discussion on the different values this parameter has taken in the literature.
25
5 Results of the business cycle simulation
5.1 Impulse responses
In this section, I examine the responses of key variables to temporary domestic technology and
financial shocks that are reported in Figures 9-10, for which the standard deviations of the shocks
correspond to the estimated ones for the United States. Since the international transmission effects
differ from one shock to another, I examine them separately. For technology shocks, my contribution
lies in building a model that can achieve greater cross-country correlation in output than a standard
international real business cycle model. However, the quantity anomaly can only be resolved when
financial shocks are added. The lower cross-country correlation in consumption is a result of the
combination of households’ non-separable preferences and the labor wedge that originates from the
borrowing constraint.14
5.1.1 Technology shocks
In order to have a better understanding of the borrowing mechanism, I will start by presenting
the effects in a closed-economy environment. It should be noted that the various effects described
below hinge on the parametrization. I assume, similarly to Figure 9, that the Home economy is
hit by a positive temporary shock. As a result, output grows: directly from the Solow residual
and indirectly because the marginal product of its inputs are increased. Since the firm must pay
its factors of production and dividends to its shareholders before receiving its revenues, it has to
contract a greater intra-period loan. From equation (23), liabilities on the right hand side cannot
exceed the value of real estate and capital that can be repossessed on the left hand side. For the
production of the intermediate good, firms will want to substitute real estate for capital. Moreover,
from a positive wealth effect, workers will want to acquire more real estate. Hence, a fraction
of real estate will switch from the commercial to the residential sector. As a result and for the
parametrization described in the previous section, the value of the collateralized assets will not be
sufficiently important for the inter-period debt to increase and that leads firms to ask for a lower
interest rate.
How do these effects matter in an open-economy? The answer is through the partially integrated
financial market structure that calls for a unique interest rate across countries. From the impulse
responses displayed in Figure 9, the interest rate decreases and stays below its steady state value.
Hence, in order to benefit from a higher interest rate, Home workers will lend to Foreign workers.
This result is in stark contrast with BKK who predict that Home workers would borrow from
14All simulations have been performed with DYNARE 4.1.1 and Figures are in Appendix C.
26
Foreign workers, because the marginal productivity would have increased in the Home economy.
On the production side, the Home economy exports more of good a, so that its price decreases in
the Foreign economy implying favorable terms of trade for the foreign economy. From a certain
form of complementarity that also leads to a greater production of good b.15 Therefore, interest rate
dynamics and terms of trade effects both contribute to the positive correlation of output. Another
characteristic of real estate that plays a role is its non-tradability, as home workers cannot purchase
it from the foreign country, it is reduced from the home firms’ holdings and that has an effect on
their borrowing constraint.
In the context of technology shocks, the cross-country correlation in consumption is still greater
than the cross-country correlation in output, but it is much lower than unity, suggesting that in-
ternational risk-sharing is imperfect. Most of the effects do not arise from the non-contingent
international bond, but rather from non-separable preferences. Moreover, investors’ consumption
across countries follow similar paths and their levels are much smaller compared to workers’ con-
sumption. Combining equation (18) for the Home and Foreign countries leads to the following
approximation:
cWHt −
ζnηHt
η≈ cW
Ft −ζnη
F t
η. (37)
Equation (37) is an approximation because bonds are not state-contingent and βit is endoge-
nous. However, as discussed above, these effects are marginal. The most that can be conveyed
from this equation is that cross-country correlation in consumption depends on the correlations
with hours worked that are also related to output from the optimization problems of the firms and
workers. Since the firms’ borrowing is constrained, wages are not equal to the marginal product
of labor. Hence, the labor wedge, that is the difference between the marginal rate of substitution
between consumption and leisure and the marginal product of labor, also plays a role in driving
cross-country correlation in consumption. Combining equation (25) for the firm and the marginal
rate of substitution for the worker and substituting it in equation (37) leads to the following equa-
tion:
cWHt −
(1 − ν − µ)YHt(1 − ϑHt)
η≈ cW
Ft −(1 − ν − µ)YFt(1 − ϑFt)
η. (38)
Therefore, non-separable preferences combined to the effects of a more relaxed or more binding
borrowing constraint, summarized by the Lagrange multiplier ϑ, are important in lowering interna-
tional co-movements in consumption. As it will be shown in the next sub-section, the latter effects
15Results for which countries do not specialize in the production of a good are presented in Appendix D.
27
are more important in the case of financial shocks.
5.1.2 Financial shocks
Even though a model with only financial shocks is not able to match the positive co-movements of
output and inputs in the data, I show that the presence of real estate can generate moments that
are closer to the data. Additionally, combined with non-separable preferences, it can replicate the
quantity anomaly. Impulse responses to a temporary Home positive shock are plotted in Figure 10.
First, firms increase their level of investment and real estate in order to have a greater collateral
as their borrowing constraint is relaxed temporarily. In this case, my calibration suggests that the
effects of real estate as collateral and productive uses dominate the wealth effects that workers by
substituting real estate for consumption. Since acquiring real estate from workers does not involve
any reallocation costs and since there is not an accumulation process as there is for physical capital,
firms purchase a large share of real estate. From the impulse responses, it is also possible to assess
that the levels of productive real estate and borrowing reach their maxima in the first period. In
order to attract workers to lend more to them, they must initially raise their loan rate. However,
in the subsequent periods, firms do not need to borrow as much and workers are willing to accept
a lower loan rate. If capital was the only collateralized asset, the accumulation process would be
costly and lengthy so that borrowing would grow for many periods and that would imply that the
loan rate would not revert to its steady state level. Moreover, the non-tradable feature of real estate
results in less international lending.
In similar fashion to technology shocks, the international transmission of the financial shock
arises both from the interest rate parity and the terms of trade effects. Since, it is facing a greater
interest rate, foreign workers lend to home workers, so that the latter have more funds to lend to
the home firm. In the period following the shock, foreign workers receive their first period loan and
proceeds and consume some fraction of it. Hence, foreign expenditures grow after the first period
and foreign workers and investors import more of good a and combined to home demand for that
good it has the effect to reduce its import price. Consequently, terms of trade become favorable for
the foreign in subsequent periods and they can invest and produce more. In contrast to a technology
shock, foreign variables following a financial shock are subjected to a one-period lagged effect, so
that international co-movements are not as important. As for the lower cross-country correlation
in private consumption expenditures, two effects are concurring. First, since investors do not
share risk internationally, dividends that they consume are weakly positively correlated and since
investors’ consumption correspond to 17.3% of aggregate consumption this effect can be important.
Following a positive financial shock, home investors’ dividends increase whereas they decrease for
foreign investors. Second, from equation (38), the borrowing constraint is relaxed much more for
28
the Home worker than the Foreign worker and that leads also to reduce cross-country correlation
in consumption.
5.2 Quantitative analysis
Table 4 reports the moments of the simulated economies from the shock processes calibrated in
Table 1. Since there are no borrowing constraints in the representative agent model, financial
shocks are ruled out and therefore, statistics generated by that model appear in the first column
only. In the three other columns, I examine the case for which both capital and real estate are
collateralized. The fifth column stands for the moments computed from data series described in the
appendix (the volatility and domestic co-movement correspond to US data). In order to compare
all versions of the models, I set the capital adjustment cost parameter φk so that the ratio of the
standard deviation of investment to the standard deviation of GDP corresponds to the value in the
data for the United States from 1988Q1 to 2007Q4. As for the parameter controlling the volatility
of the re-allocation of land between the residential and productive sectors φh, it is set to zero for
all models except for the one with financial shocks, since hit is more volatile in data than from
the results of the model. Therefore, I set it to 0.056. Finally, the parameter that controls the
fraction of physical capital that is collateralized ιk is picked, so that it minimizes the squared sum
of distance between moments generated by the model(ρ) and data (ρ), as it is described by the
following function:
Λ = Φ′Φ where Φ =
ρ(GDPUS , GDPUK) − ρ(GDPUS , GDPUK)
ρ(PCEUS, PCEUK) − ρ(PCEUS, PCEUK)
ρ(XUS ,XUK) − ρ(XUS ,XUK)
ρ(NUS , NUK) − ρ(NUS , NUK)
(39)
For the baseline model, the value of ιk that minimizes equation 39 is 0.52. In the steady state,
land correspond to 9.92% of the collateralized assets. According to Davis’s (2009) estimates, land
corresponds to 14% of commercial real estate over the period studied. Hence, real estate stands for
71% of collateralized assets, a value that is not so far away from the average of 58% of real estate
in total tangible assets as reported by Liu et al. (2011).
The effects of borrowing constraints can be appreciated by comparing the first and second
columns, in particular, for international correlations. However, the model with collateral constraints
and technology shocks diverges from data on many accounts. First, net exports are much less
volatile than in the data and are positively correlated with output. It occurs in this model because
the use of the international bond is reduced by the addition of other lending linkages. Second,
29
Table 3: Business cycle statistics
Model: Representative-agent Baseline: Two-agent without real estate
Type of Shocks: Technology Tech. Fin. Both BothData
Capital adjustment cost (φk) 0.004 0 0.24 0.134 0.12
Volatility
% Standard deviations
GDP 1.01 0.83 0.61 1.04 2.24 1.15Net Exports/GDP 0.34 0.1 0.29 0.28 0.7 0.27
Standard deviationsrelative to GDP
PCE 0.6 0.61 1.05 0.7 0.77 0.65Investment 3.43 3.14 3.43 3.43 3.43 3.43Hours worked 0.72 0.59 1.35 0.7 1.12 0.95Prod. real estate (qth
Pt ) 0.86 0.75 4.86 3.49 - 4.86
Terms of trade 2.08 2.18 1.66 2.3 1.14 0.89
Domestic Co-movement
Correlations with GDP
PCE 0.99 0.99 0.99 0.99 0.995 0.72Investment 0.91 0.97 0.89 0.91 0.91 0.85Hours worked 1.00 0.999 0.97 0.99 0.97 0.77Net Exports/GDP -0.52 0.13 -0.76 -0.26 -0.53 -0.41
International Correlations
GDP, GDP ∗ 0.26 0.86 -0.18 0.62 0.39 0.69PCE, PCE∗ 0.36 0.9 -0.33 0.53 0.29 0.61X, X∗ -0.43 0.86 -0.82 0.08 -0.37 0.34N, N∗ 0.26 0.86 0.2 0.52 0.63 0.62
The statistics of the first column are generated from the representative agent model sketched in the first part of the modelsection, whereas the statistics of the second to fourth columns are from the model with collateral constraints and real estate.The statistics of the fifth column are generated from a model with both shocks but without real estate. The statistics of thelast column for the volatility and domestic co-movement sections are calculated from US time series described in the appendixfrom 1988Q1 to 2007Q4. The international correlations are calculated from US and UK time series. All series have been logged(except net exports) and Hodrick-Prescott filtered with a smoothing parameter of 1,600.
30
another drawback of the model is that international correlations are all much higher that what
they are in the data. The model is successful in solving the international co-movement puzzle,
but the quantity anomaly remains unsolved as the cross-country correlation in PCE is greater
than in GDP. Both cross-country correlations in investors’ and workers’ consumption are than the
cross-country correlation in output: they are respectively 0.2 and 0.58.
The introduction of financial shocks remedies this anomaly and the preceding drawbacks. The
presence of non-separable preferences combined with borrowing constraints for firms that create a
labor wedge are key to explain the anomaly. In fact, borrowing constraints have a greater impact
in the presence of financial shocks, so that wages deviate more from the marginal product of labor.
Hence, volatility of hours worked and consumption are enhanced. In response to financial shocks,
capital flows to the more productive country and that leads to much cross-country correlation in
investment. However, this seems to be the only drawback as many other statistics are closer to
data.
Finally, the value-added of real estate can be assessed by comparing the results generated by
the baseline model to a similar model that does not include any real estate assets. The results of the
latter model are reported in the fifth column of Table 4. In this case, the firm’s borrowing simply
consists of eit + Yit ≤ λitkit, where in the steady-state financial shock or the loan-to-value ratio
(λ = 0.16) is set so that it also minimizes equation (39). It appears that both the non-tradable
feature of real estate and its substitutability with capital are important to generate a positive cross-
country correlation in investment. For example, following a positive financial shock in the context
of the baseline model, some land would switch from the residential to the commercial sector in
order to increase the value of the collateral. Hence, there would be less capital required to flow
internationally.
5.3 Sample paths
In order to construct sample paths, the baseline model is feeded with technology and financial
innovations retrieved from data. In Figure 6, I present those sample paths for U.S. GDP and Hours
Worked and compare them to data for which series have been HP-filtered. Directly from the Solow
residuals, the model’s series for GDP can match a certain fraction of data more closely. However,
a model with endogenous borrowing constraints and financial shocks can generate propagation and
amplification effects that lead results to be more in line with data. As in Jermann and Quadrini’s
(2009) framework, the addition of financial shocks is crucial to render hours worked more volatile.
These amplification effects are the consequence of a borrowing constraint that creates a labor wedge.
Moreover, rolling cross-country correlations are computed for GDP and PCE and its difference
31
−.0
4−
.02
0.0
2.0
4
1988q1 1993q1 1998q1 2003q1 2008q1Quarters
U.S. GDP Sample Path
−.0
2−
.01
0.0
1.0
2
1988q1 1993q1 1998q1 2003q1 2008q1Quarters
U.S. Hours Worked Sample Path
Figure 6: In both panels, the blue solid line corresponds to the data that has been HP-filtered withλ = 1, 600 and the red dashed line to sample paths generated by the baseline model for the UnitedStates, (1987Q4-2007Q4).
Data
Both shocks
.6.6
5.7
.75
.8
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Data
Both shocks
.5.5
5.6
.65
.7
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Figure 7: Rolling cross-country correlations in output (left panel) and in consumption (right panel)generated by the model and data (rolling 40 quarter window estimates, 1987Q4-2007Q4)
32
−.1
0.1
.2.3
1997q3 2000q1 2002q3 2005q1 2007q3Last quarter of window
Data Technology shockFinancial shock Both shocks
Figure 8: Differences between the rolling cross-country correlations in output and in consumptiongenerated by the model and data (rolling 40 quarter window estimates, 1987Q4-2007Q4)
in each quarter can be compared to data from Figure 3. The only asymmetry between the two
countries are the shock processes that correspond to matrices 6 to 8 of Table 1. The success of
the baseline model in matching business cycle synchronization can be assessed in Figure 7. While
it predicts cross-country correlations in output that are much higher than data in the first part
of the sample, it can capture the greater synchronization that took place initially around 2002.
However, the downward trend in the rolling cross-country in consumption cannot be replicated
by the baseline model. The differences in correlations generated by various shock processes, the
quantity anomaly are plotted in Figure 8. Technology shocks do not seem to capture at all the gap
between the two cross-country correlations as it is negative throughout all the sample periods. In
contrast, when the model is feeded with financial shocks, the gap is positive but it does not generate
sample paths that lead to an increasing gap. The baseline model with the two shocks generates a
gap that corresponds to intermediate values.
The failure to account for the dynamics of consumption correlations and the quantity anomaly
may partly be due to the structure of the shocks. The persistence and spill-overs of both technology
and credit shocks across countries and the correlation of innovations can create different degrees of
business cycle synchronization. Therefore, it is possible that the estimation of a VAR(1) process
may not be the appropriate one to consider. Moreover, the parametrization has been based on
United States steady state targets. An asymmetric calibration would lead to different sample paths
that may help to account for the increasing gap.
33
6 Conclusion and extensions
To conclude, I have built a two-country two-good model with endogenous borrowing constraints
and real estate in order to have a better understanding of two phenomena that took place in
the past decade across industrialized countries: (i) the accrued business synchronization and (ii)
the widening gap between cross-country correlations in output and in consumption: the quantity
anomaly. My main contribution is to show that the inclusion of real estate is important for the
baseline model to generate greater cross-country correlation in output. The interaction of interest
rate dynamics and terms of trade effects are key for the propagation of shocks from one country to
another in the baseline model with endogenous borrowing constraints. When the baseline model is
feeded with the technology and financial shocks, it can account for the dynamics of greater output
synchronization. Additionally, firms’ borrowing constraints create a labor wedge that is important
to explain the quantity anomaly when financial shocks are added to the model. However, the model
fails to explain the dynamics of that anomaly.
While I have adopted an agnostic approach in assuming that financial shocks are exogenous,
in contrast, Perri and Quadrini (2011) hypothesize that self-fulfilling expectations might play an
important role in the shocks’ propagation, in particular, when financial markets are internationally
integrated. Hence, it may not be clear in my framework why negative shocks have affected simulta-
neously the United States and the United Kingdom during the Great Recession. Are more correlated
financial shocks driven by the phenomenon of financial globalization? Moreover, the structure of
these shocks is such that they are transitory in my model. It would be interesting to see what
could be the effects of a permanent shock and similarly to the approach of Mandelman et al. (2011)
that examine investment-specific technology shocks, to investigate issues of co-integration. Another
extension could be to introduce a labor-intensive construction sector for commercial and residential
structures, so that firms would have real estate as collateral rather than land.
34
References
Ambler, S., E. Cardia, and C. Zimmermann (2002): “International transmission of the busi-
ness cycle in a multi-sector model,” European Economic Review, 46, 273–300.
Backus, D. K., P. J. Kehoe, and F. E. Kydland (1992): “International Real Business Cycles,”
Journal of Political Economy, 100, 745–775.
——— (1994): “Dynamics of the Trade Balance and the Terms of Trade: The J-Curve?” The
American Economic Review, 84, 84–103.
Bai, Y. and J. Zhang (2011): “Financial Integration and International Risk Sharing,” Tech. rep.,
University of Michigan.
Baxter, M. and M. J. Crucini (1995): “Business Cycles and the Asset Structure of Foreign
Trade,” International Economic Review, 36, 821–54.
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999): “The financial accelerator in a
quantitative business cycle framework,” in Handbook of Macroeconomics, ed. by J. B. Taylor and
M. Woodford, vol. 1 of Handbook of Macroeconomics, chap. 21, 1341–1393.
Bodenstein, M. (2011): “Closing large open economy models,” Journal of International Eco-
nomics, 84, 160–177.
Bui, T. T. and T. Bayoumi (2010): “Deconstructing The International Business Cycle: Why
Does A U.S. Sneeze Give The Rest Of The World A Cold?” IMF Working Papers 10/239,
International Monetary Fund.
Davis, M. A. (2009): “The price and quantity of land by legal form of organization in the United
States,” Regional Science and Urban Economics, 39, 350–359.
Davis, M. A. and J. Heathcote (2005): “Housing and the Business Cycle,” International Eco-
nomic Review, 46, 751–784.
Davis, M. A. and F. Ortalo-Magne (2011): “Household Expenditures, Wages, Rents,” Review
of Economic Dynamics, 14, 248–261.
Davis, M. A. and M. G. Palumbo (2008): “The price of residential land in large US cities,”
Journal of Urban Economics, 63, 352–384.
Dedola, L. and G. Lombardo (2009): “Financial frictions, financial integration and the inter-
national propagation of shocks,” .
35
Devereux, M. B., A. W. Gregory, and G. W. Smith (1992): “Realistic cross-country con-
sumption correlations in a two-country, equilibrium, business cycle model,” Journal of Interna-
tional Money and Finance, 11, 3–16.
Devereux, M. B. and J. Yetman (2010): “Leverage Constraints and the International Trans-
mission of Shocks,” Journal of Money, Credit and Banking, 42, 71–105.
Eickmeier, S., W. Lemke, and M. Marcellino (2011): “The Changing International Trans-
mission of Financial Shocks: Evidence from a Classical Time-Varying FAVAR,”CEPR Discussion
Papers 8341, C.E.P.R. Discussion Papers.
Faia, E. (2007): “Finance and international business cycles,” Journal of Monetary Economics, 54,
1018 – 1034.
Greenwood, J., Z. Hercowitz, and G. W. Huffman (1988): “Investment, Capacity Utiliza-
tion, and the Real Business Cycle,” The American Economic Review, 78, 402–417.
Hart, O. and J. Moore (1994): “A Theory of Debt Based on the Inalienability of Human
Capital,” The Quarterly Journal of Economics, 109, pp. 841–879.
Heathcote, J. and F. Perri (2002): “Financial autarky and international business cycles,”
Journal of Monetary Economics, 49, 601 – 627.
Helbling, T., R. Huidrom, M. A. Kose, and C. Otrok (2011): “Do credit shocks matter?
A global perspective,” European Economic Review, 55, 340 – 353, special Issue: Advances in
International Macroeconomics: Lessons from the Crisis.
Iacoviello, M. (2005): “House Prices, Borrowing Constraints, and Monetary Policy in the Busi-
ness Cycle,” American Economic Review, 95, 739–764.
Iacoviello, M. and R. Minetti (2006): “International business cycles with domestic and foreign
lenders,” Journal of Monetary Economics, 53, 2267–2282.
Imbs, J. (2010): “The First Global Recession in Decades,” IMF Economic Review, 58, 327–354.
Jermann, U. (1998): “Asset pricing in production economies,” Journal of Monetary Economics,
41, 257 – 275.
Jermann, U. and V. Quadrini (2009): “Macroeconomic Effects of Financial Shocks,” NBER
Working Papers 15338, National Bureau of Economic Research.
Kehoe, P. J. and F. Perri (2002): “International Business Cycles with Endogenous Incomplete
Markets,” Econometrica, 70, 907–928.
36
Kiyotaki, N. and J. Moore (1997): “Credit Cycles,” Journal of Political Economy, 105, 211–48.
Kollmann, R. (1996): “Incomplete asset markets and the cross-country consumption correlation
puzzle,” Journal of Economic Dynamics and Control, 20, 945–961.
Kose, M. A., E. S. Prasad, and M. E. Terrones (2009): “Does financial globalization promote
risk sharing?” Journal of Development Economics, 89, 258–270.
Liu, Z., P. Wang, and T. Zha (2011): “Land-price dynamics and macroeconomic fluctuations,”
NBER Working Papers 17045, National Bureau of Economic Research.
Mandelman, F., P. Rabanal, J. F. Rubio-Ramirez, and D. Vilan (2011): “Investment
Specific Technology Shocks and International Business Cycles: An Empirical Assessment,”Review
of Economic Dynamics, 14, 136–155.
Mendoza, E. G. (1991): “Real Business Cycles in a Small Open Economy,” The American Eco-
nomic Review, 81, 797–818.
Mulligan, C. (2011): “Rising Labor Productivity during the 2008-9 Recession,” NBER Working
Papers 17584, National Bureau of Economic Research.
Ohanian, L. E. and A. Raffo (2011): “Aggregate Hours Worked in OECD Countries: New
Measurement and Implications for Business Cycles,” NBER Working Papers 17420, National
Bureau of Economic Research.
Paasche, B. (2001): “Credit constraints and international financial crises,” Journal of Monetary
Economics, 48, 623 – 650.
Perri, F. and V. Quadrini (2011): “International Recessions,” Working Paper 17201, National
Bureau of Economic Research.
Quan, D. C. and J. M. Quigley (1991): “Price Formation and the Appraisal Function in Real
Estate Markets,” The Journal of Real Estate Finance and Economics, 4, 127–46.
Raffo, A. (2008): “Net exports, consumption volatility and international business cycle models,”
Journal of International Economics, 75, 14 – 29.
Sakuragawa, M. and L. Sakuragawa (2011): “Quantitative Impacts of the Asset Price Channel
in the Credit-Constrained Economy,” .
Stockman, A. C. and L. L. Tesar (1995): “Tastes and Technology in a Two-Country Model of
the Business Cycle: Explaining International Comovements,” The American Economic Review,
85, 168–185.
37
A The model
A.1 The steady state
qhP
Y=
γνβ
(2β − γ)
1 − γ − (1 − γβ)λ
k
Y=
γµβ
(2β − γ)
1 − γ(1 − δ) − (1 − γβ)λ
e
Y= α
(λ
(qhP
Y+
k
Y
)− 1
)
cW
Y= (1 − β)
(Re
Y
)+ (1 − ν − µ) (γ − β)
cP
Y= (ν + µ) (γ − β) + 1 − (γ − β) − δ
k
Y+ (1 − R)
( e
Y
)
Y = hP ν
kµl1−ν−µ
nx = Y − (cP + cW ) − δk
Since all variables are in real terms, finding prices pHHt, pHFt, pFFt, pFHt is done by nonlinear
methods with four equations two from the production approach and two from the expenditure
approach to output.
B Data sources and construction of variables
B.1 Data used for Figures 1 and 3
Real GDP and Real Private Consumption from the OECD, as compiled by Ohanian and Raffo (2011)
B.2 United States
Variable name: CPISource: BLSDefinition: U.S. City Average (Quarter Average, Seasonally Adjusted)
Variable name: GDP deflator
38
Source: BEA, NIPA, Table 1.1.9Definition: Index 2005=100 (Seasonally Adjusted)
Variable name: Price Index for Business Value AddedSource: BEA, NIPA, Table 1.3.4Definition: Index 2005=100 (Seasonally Adjusted)
Variable name: Net New BorrowingSource: Federal Reserve Board, Table F.101Definition: Net increase in credit markets instruments of non-financial business (Quarter Average, SeasonallyAdjusted)Deflator used: Price Index for Business Value Added
Variable name: Land Price Index (QUS)Source: Constructed by Liu et al. (2011)16
Definition: Liquidity-adjusted price index for residential land (Quarterly)Deflator used: Consumption deflator
Variable name: Business Value Added (YUS)Source: NIPA 1.3.5Deflator: Index for business value added (NIPA 1.3.4) (seasonally adjusted)
Variables names: Real Consumption (CUS)Real Net Exports of Goods and Services (NXUS)Source: BEA, NIPA, Table 1.1.6Definition: Billions of chained (2005) dollars (Seasonally adjusted)
Variable name: Nominal Market Value and Price Index of LandSource: Davis’ (2009) databaseDefinition: 2 different categories: households and non-profits and corporate non-financial (Quarterly)
Variables names: Total EmploymentHours worked per workerThe product of those two variables is equal to NUS
Source: Ohanian and Raffo (2011)
Variables names: Consumption of Fixed Capital in Non-Financial Corporate BusinessConsumption of Fixed Capital in Non-Financial Non-Corporate BusinessSource: Federal Reserve Statistical Release, Flow of Funds, Table F.8Definition: Millions of US Dollars (Quarterly)Deflator used: Business Value Added
B.3 United Kingdom
Variable name: CPISource: IFS (International Financial Statistics)Definition: All items (seasonally adjusted with X12-ARIMA)
16I refer the reader to Appendix A of their paper for a thorough description of that variable.
39
Variable name: GDP deflatorSource: ONS, YBGBDefinition: GDP (Expenditure) at market prices deflator (Seasonally Adjusted)
Variable name: Domestic Loans (eUK)Source: Bank of England, LPQVQJMDefinition: Quarterly amounts outstanding of monetary financial institutions’ sterling net lending to privatenon-financial corporations (Seasonally Adjusted)Deflator used: CPI
Variable name: Residential property prices, all dwellings (QUK)Source: Halifax Building Society, Press Release17
Definition: Index 1983=100 (seasonally adjusted with X12-ARIMA and liquidity-adjusted for time-on-marketuncertainty following the methods of Quan and Quigley (1991).)Deflator used: GDP deflator
Variable name: Consumption (CUK)Source: OECD, Quarterly National AccountsDefinition: Chained-volume estimates (2005 in pounds) (seasonally adjusted)
Variables names: Gross value added at basic prices (seasonally adjusted) (YUK)Gross Fixed Capital Formation: Total GFCF (seasonally adjusted)Total capital consumption (seasonally adjusted)
Source: ONS (CGCE, NPQT, CIHA)Definition: Millions of pounds
Variables names: Gross Fixed Capital Formation non-residential and residential construction (seasonally adjusted)Source: OECDDefinition: Millions of pounds
Variables names: Tangible Assets: Residential Buildings & Commercial, Industrial and Other BuildingsSource: ONS(CGLK,CGMU)Definition: Millions of pounds
Variables names: Total EmploymentHours worked per workerThe product of those two variables is equal to NUK
Source: Ohanian and Raffo (2011)
B.4 Construction of variables
HP
USis constructed from the market land value series of each sector divided by the liquidity-adjusted price
index from the methods of Quan and Quigley (1991). Finally, the productive land index corresponds to thevalue of the created variable for the corporate non-financial over the sum of the two sectors:
HP
US =Corporate Non-Financial
Households and Non-Profits + Corporate Non-Financial
17I am thankful to the BIS for providing me this series.
40
Similarly to HP
US, HP
UKalso corresponds to the ratio of land of the corporate non-financial over total land.
I construct land series for each sector by following Davis (2009), so that the value of land is equal to thevalue of tangible assets minus the capital stock’ value. In order to have quarterly values, capital stocks areconstructed recursively as follows:
KNR;R
UKt+1 = 0.9961KNR;R
UKt+ GFCFNR;R
where the quarterly depreciation rate corresponds to 0.39%, a value consistent with the one found byDavis and Heathcote (2005) for residential structures. The initial quarter for the residential (non-residential)capital stock is 1955Q4 (1964Q4) and the corresponding value is 9,100 (9,300) and the corresponding seriesare Net Capital Stock: Dwellings: Households (CIWV) and Net Capital Stock: Other buildings and works:PNFCs (CIXB). As for tangible assets, since the frequency of series is yearly, I interpolate linearly for eachquarter.
KUS is constructed recursively in the same way as described in the appendix of Jermann and Quadrini (2011).I pick the initial value of KUS for the first quarter of 1952 such that the capital-output ratio does not exhibitany trend over the period 1952-2010. Depreciation corresponds to the sum of Non-Financial Corporate andNon-Corporate Business Consumption of Fixed Capital and Investment to Capital Expenditures in Non-Financial Business.
KUSt+1 = KUSt − Depreciation + Investment
For the United Kingdom, the recursion is similar to the one described for the United States and in this casethe period is a bit shorter: 1955-2010. Investment corresponds to Total Gross Fixed Capital Formation andDepreciation to Total Capital Consumption.
eUS is also constructed recursively in the same way as described in the appendix of Jermann and Quadrini(2009). The initial value for the (nominal) stock of debt is set to 94.12, which is the value reported in thebalance sheet data from the Flow of Funds in 1952I for the nonfarm non-financial business (Table B.102,line 22).
eUSt+1 = eUSt + NetNewBorrowing
The terms of trade series (TOT ) corresponds to the ratio of the implicit price deflator for imports to theimplicit price deflator for exports (NIPA 1.1.9).
C Figures: Impulse Responses
• Figure 9 : Impulse responses to a Home technology shock
• Figure 10 : Impulse responses to a Home financial shock
41
0 10 200
0.5
1
1.5
Quarters
GDP
0 10 200
0.2
0.4
0.6
Quarters
PCE
0 10 200
2
4
Quarters
Investment
0 10 200
0.2
0.4
0.6
Quarters
Hours worked
0 10 20−1.5
−1
−0.5
0
0.5
Quarters
Prod. Real Estate
0 10 20−1.5
−1
−0.5
0
0.5
Quarters
Lending to Firms
0 10 20−2
0
2
4
6
Quarters
Lagrange Multiplier
0 10 200
0.005
0.01
Quarters
International Bond
0 10 20−0.03
−0.02
−0.01
0
Quarters
Interest Rate
0 10 200
1
2
3
Quarters
Terms of trade
Figure 9: Impulse responses to a 1% temporary Home technology shock: Home (blue solid line) Foreign (dashed red line) generatedfrom the baseline model. Responses are all measured in percentage deviations from their steady state, except for the internationalbond that is scaled to match the deviation of the inter-period loan.
42
0 10 20−0.5
0
0.5
1
1.5
Quarters
GDP
0 10 20−0.5
0
0.5
1
1.5
Quarters
PCE
0 10 20−2
0
2
4
Quarters
Investment
0 10 20−0.5
0
0.5
1
1.5
Quarters
Hours worked
0 10 200
2
4
6
Quarters
Prod. Land
0 10 200
2
4
6
Quarters
Lending to Firms
0 10 20−100
−50
0
50
Quarters
Lagrange Multiplier
0 10 20−1.5
−1
−0.5
0
Quarters
International Bond
0 10 20−0.2
0
0.2
0.4
Quarters
Interest Rate
0 10 20−1
−0.5
0
0.5
Quarters
Terms of trade
Figure 10: Impulse responses to a 1% temporary Home financial shock: Home (blue solid line) Foreign (dashed red line) generatedfrom the baseline model. Responses are all measured in percentage deviations from their steady state, except for the internationalbond that is scaled to match the deviation of the inter-period loan.
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D Additional Results
Table 4: Business cycle statistics (one-good)
Model: Representative-agent Two-agent
Type of Shocks: Technology Technology Financial BothData
Capital adjustment cost (φk) 0.033 0.001 0.29 0.093
Volatility
% Standard deviations
GDP 1.06 1.01 0.57 1.18 1.15Net Exports/GDP 0.41 0.45 0.42 0.57 0.27
Standard deviationsrelative to GDP
PCE 0.64 0.59 1.23 0.63 0.65Investment 3.43 3.43 3.43 3.43 3.43Hours worked 0.72 0.6 1.61 0.67 0.95Prod. real estate (qth
Pt ) 1.05 1.01 4.86 3.00 4.86
Domestic Co-movement
Correlations with GDP
PCE 0.997 0.99 0.95 0.97 0.72Investment 0.9 0.68 0.74 0.71 0.85Hours worked 1.00 0.999 0.98 0.99 0.77Net Exports/GDP -0.49 0.33 -0.52 0.23 -0.41
International Correlations
GDP, GDP ∗ 0.13 0.26 0.34 0.26 0.69PCE, PCE∗ 0.14 0.42 -0.13 0.34 0.61X, X∗ -0.51 0.04 -0.82 -0.02 0.34N, N∗ 0.13 0.23 0.4 0.28 0.62
The statistics of the first column are generated from the representative agent model sketched in the first part of the modelsection, whereas the statistics of the three other columns are from the model with collateral constraints. The statistics of thelast column for the volatility and domestic co-movement sections are calculated from US time series described in the appendixfrom 1988Q1 to 2007Q4. The international correlations are calculated from US and UK time series. All series have been logged(except net exports) and Hodrick-Prescott filtered with a smoothing parameter of 1,600.
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