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: jf.rouillard@gmail.com. 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

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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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