International recessions∗
Fabrizio Perri
University of Minnesota and Federal Reserve Bank of Minneapolis
Vincenzo Quadrini
University of Southern California
February 2011

Abstract
The 2008-2009 US crisis is characterized by an unprecedented degree of international
synchronization, as all other G7 countries experienced large contractions at the same time
the US did. Another feature of the crisis is the sharp fall in US employment but actual increase in productivity. These two features—international synchronization and productivity
increase—are not present in many of the previous US contractions. We study a two-country
model with financial markets frictions and show that the features of the recent recession
are consistent with ‘credit shocks’ playing a more prominent role as a source of businesscycle fluctuations, in an environment with international mobility of capital.

1

Introduction

This paper is motivated by two observations about the US 2008-2009 crisis. The first is thatthe crisis has been characterized by a high degree of international synchronization as mostdeveloped countries have experienced large macroeconomic contractions at around the sametime. The second observation is that, although employment in US has fallen dramatically,
productivity in US has actually increased. As we will document below, these two featuresof the recent crisis differentiate the recent recession from many of the previous recessions
experienced by the US economy.
∗
We thank seminar participants at Boston University, Columbia University, Harvard University, San Francisco FED, UC Berkeley, UCLA, University of Colorado, University of Notre Dame and attendees at the Advances in International Macroeconomics conference in Brussels, NBER IFM meeting, Stanford SITE conference.
We also thank Fabio Ghironi and Raf Wouters for excellent discussions.

1.1International co-movement

Figure 1 plots the US GDP against the GDP of the other G7 countries during the recent
recession, up to the second quarter of 2009. The numbers are percent deviations from the levelof GDP in the quarter preceding the beginning of the recession identified by the NBER Business
Cycle Dating Committee (fourth quarter of 2007). Four quarters before the official recession
are also plotted. The figure reveals the strong co-movement in macroeconomic activity among
the G7 countries.
Figure 1: The dynamics of GDP during the 2008 recession: US vs. other G7 countries.

To examine whether the international synchronization of the recent recession differs fromprevious contractions, Figure 2 plots the GDP dynamics for the G7 countries in six of the mostrecent US recessionary episodes: one recession experienced in the first half of the 1970s, twoin the first half of 1980s, one in the early 1990s and two in the 2000s. A quick glance at thefigure shows that the macroeconomic synchronization of the US with other G7 countries has
been significantly stronger in the recent recession. While the G7 countries experienced very
different GDP dynamics during the previous US recessions, in the most recent contraction all
countries have moved in the same direction.
The higher cross-country synchronization of the recent recession can also be seen in Figure 3
2

Figure 2: The dynamics of GDP during the six most recent recessions in the G7 countries.

which plots the average correlation of US GDP with the GDP of each of the other G7 countries.
The correlations are computed on rolling windows of 10 and 20 years. The dates in the graphcorrespond to the end points of the window used to compute the correlation. Although thefigure shows that the increase in correlation can also be seen in previous recessions, the current
contraction stands out as the one that marks an increase in correlation larger than in earlier
periods. For a similar point see also Imbs (2010).

3

Figure 3: Average rolling correlations of US GDP with other G7 countries.
.7
10 yrs window
.6
.5
.4
.3
.2
.1
.0
-.1
1970

1975

1980

1985

1990

1995

2000

2005

.50
20 years window
.45
.40
.35
.30
.25
.20
.15
1970

1975

1980

1985

1990

1995

2000

2005

The dramatic increase in co-movement is also observed in other variables, in particularasset prices and employment. The top two panels os figure 4 plot the growth rate of stock
prices 1 in the 1990s and in the 2000s. The bottom two panels of the figure plot the growthrate of employment in US and in the G6 in the same two subperiods. The figure shows quite
clearly how the last recession (and more in general the entire last decade) represent a periodof high international synchronization between US and the rest of the developed world.

1

The stock prices in US are the MSCI BARRA US stock market index, while stock prices in the G6 arecomputed using the MSCI BARRA EAFE + Canada index which is an average of stock prices in advanced
economies except US

4

Figure 4: International co-movement in stock prices and employment
Stock prices growth
.2

.2

.1

.1

.0

.0

-.1

-.1

-.2

-.2

-.3

-.3
USA
G6

Correlation = 0.95

Correlation = 0.6
-.4

-.4
90

91

92

93

94

95

96

97

98

99

2001

00

2002

2003

2004

2005

2006

2007

2008

2009

2010

2004

2005

2006

2007

2008

2009

2010

Employment growth
.010

.010

.005

.005

.000

.000

-.005

-.005

-.010

-.010
USA
G6

Correlation = 0.74

Correlation = -0.20

-.015

-.015
90

1.2

91

92

93

94

95

96

97

98

99

2001

00

2002

2003

Labor input and labor productivity

Figure 5 plots working hours and labor productivity (output per hour) in the private non farm
sector of the US economy for the six most recent recessions. The last panel shows that in
the recent recession labor productivity has actually increased for most of the period. Thispattern can also be seen in the 2001 recession. By contrast, in the first four recessions, laborproductivity has slowed down markedly during the recession and its level at the end of therecession was not higher than before the recession.
The different behavior of productivity and labor during the two most recent recessions
reflects a more general pattern for which the association between productivity and labor input
has declined sharply in the US economy. As a first visual measure of this decline figure 6
reports the Hodrick-Prescott filtered series of output per hour and hours in the private nonfarm business sector in the period 1947-1989 (the left panel) and the same two series in the
period 1990-2010 (the right panel). Notice that in the first panel the two series exhibit positive
co-movement, with productivity generally leading employment, while in the second the co-5

Figure 5: Labor productivity (output per hour) and hours in recessions

movement is sharply negative and no clear leading pattern is discernible.
Figure 7 plots rolling correlations of productivity growth (growth in output per hour or
output per employees in the private non-farm business sector) and labor growth (growth inhours worked or number of employees in the private nonfarm business sector) computed on 10
years rolling windows. The figure shows a drastic drop in the correlation between productivity
and labor starting in the 1990s and most importantly shows that for the most recent decade
the correlation between labor input and labor productivity is negative. This pattern is also
documented in Gali and Gambetti (2009).
Is the negative correlation between labor productivity and labor input also a feature ofother countries? Since comparable data on hours are not available for all G6 countries we use
simply GDP per worker as a measure of productivity and employment as a measure of labor.
Figure 8 plots the 10 years rolling correlation of growth in GDP per worker and growth in
employment for US and for the remaining G6 countries. Notice that even for G6 countries thecorrelation between labor input and labor productivity in recent years is negative.

6

Figure 6: Hp filtered labor productivity and hours

.04

.04

.02

.02

.00

.00

-.02

-.02

-.04

-.04
Output per hour
Hours

-.06

-.06
1950

1955

1960

1965

1970

1975

1980

1985

90

92

94

96

98

00

02

04

06

08

10

Figure 7: US: Rolling correlations of productivity and labor input
Rolling correlation between growth of labor productivity and labor input
.6

.4

.2

.0

-.2

-.4

-.6
60

65

70

75

80

85

Output per hour

1.3

90

95

00

05

10

Output per worker

Hints from the data

The evidence discussed above point to two distinguishing features of US business cycle overthe last decade and in particular during the recent crisis:7

Figure 8: US and G6: Rolling correlations of GDP per worker and employment growth

Average of G6 countries

United States
.4

.4

.3

.3

.2

.2

.1

.1

.0

.0

-.1

-.1

-.2

-.2

-.3

-.3

-.4

-.4

-.5

-.5
1975

1980

1985

1990

1995

2000

2005

2010

1975

1980

1985

1990

1995

2000

2005

2010

1. Historically high international synchronization with other developed economies
2. Historically low association between labor productivity and labor
Both findings suggest that in the recent decade shocks different from technological disturbances may have played a more prominent role in generating business cycle fluctuations. In
particular, the observation that labor productivity is negatively associated with labor input
casts doubts on the relevance of productivity shocks in a RBC type model as the major sourceof macroeconomic fluctuations. The higher cross-country synchronization in a period of highcapital market integration also is hard to reconcile with technology shocks. When countries
are financially integrated, the standard international RBC model, such as the one studied by
Backus, Kehoe and Kydland (1992), predicts that country-specific technology shocks generate
divergent macroeconomic responses, unless the productivity shocks are internationally correlated. See, for example, Heathcote and Perri (2004). However, if productivity shocks thatare internationally correlated were the main source of business cycle fluctuations, we shouldobserve a higher correlation between productivity and labor. It is then difficult to reconcile
the hypothesis of productivity driven recessions with the fact that productivity kept growing
during the most recent contractions.

8Since productivity shocks cannot be the major force underlying macroeconomic development in the recent decade, what other shocks can reconcile the two facts outlined above? In
this paper we argue that ‘credit shocks’ are a plausible candidate. In particular, we show thatcredit shocks can generate greater international synchronization and lower correlation between
productivity and labor in an environment with international mobility of capital. The empirical relevance of credit shocks has also been explored in Jermann and Quadrini (2009) but inclosed economies. In this paper we show that these shocks are also important for understanding
the macroeconomic dynamics of economies that are financially integrated as these shocks cangenerate significant cross-country co-movements in macroeconomic variables and asset prices.

1.4

The theoretical framework

We consider a model in which firms have an incentive to borrow but the debt is constrained bycredit frictions resulting from the limited enforcement of debt contracts. The ability to borrowis subject to random disturbances that we call ‘credit shocks’. Good (credit) times are periods
in which borrowers have lower incentives to default and, as a result, lenders are willing toprovide more credit. In bad (credit) times the incentive to default is higher and lenders cut on
lending. Following a credit cut, borrowers are forced to restructure their financial position byincreasing equity. Because raising equity quickly is costly, the equity holders ask for a higher
return which increases the financial cost for the firm. Since the financial cost contributes tothe cost of hiring workers and acquiring investments, the demands for labor and investment
decline.
In this environment a credit contraction in one country spills over other countries even if
foreign borrowers are not forced to cut their borrowing. To better illustrate the mechanism,
consider a world composed of two countries: country A and country B. A credit contraction incountry A requires a substitution between debt and equity for firms operating in this country.
In a closed economy, the increase in equity must be provided by investors of country A. At
the same time, the market for loans clears locally without any spillover to country B. Thus,
when economies are not financially integrated, a credit contraction in country A does not affectcountry B.
Let’s now consider the case in which the two countries are financially integrated. In thiscase firms located in country A can raise equity not only from investors in country A but
also from investors in country B. Having access to a larger pool of suppliers, the cost ofraising funds increases less, and therefore, the macroeconomic impact on country A is smaller.
9Essentially, financial integration makes the supply of funds to the producers of one country
more elastic. Although the increase in the cost of equity in country A is smaller, the financing
cost increases also for firms located in country B since now there is a single worldwide market(law of one price). Through the higher worldwide cost of financing, the credit contraction incountry A affects also country B.
The above description clarifies why a credit shock in country A spills to country B, generating a recession in both countries. What happens to the productivity of labor? Because TFP
does not change and the share of labor in production is smaller than one, a reduction in employment increases the productivity of labor. Thus, the model generates a negative correlation
between productivity and hours.
Our paper is related to two recent contributions: Dedola & Lombardo (2010) and Devereux & Yetman (2010). Both studies investigate the international transmission of shocks inmodels with financial market frictions. They also show that shocks to the financial system
can generate cross-country spillovers in macroeconomic variables. Also related is the study ofEnders, Kollmann & Muller (2010). This paper introduces a banking sector in an internationalmodel and shows that shocks to this sector could have important effects on the global economy.
The theoretical findings of these papers are consistent with the empirical results of Helbling,
Huidrom, Kose & Otrok (2010) according to which credit market shocks matter in explaining
global business cycles, especially during the 2009 global recession.

1.5

Outline of the paper

The remaining of this paper is organized in three main sections. In Section 2 we present firsta simpler version of the model without capital accumulation. This allows us to derive someresults analytically, providing simple intuitions for the quantitative results obtained with themore general model. Section 3 extends the model by adding capital accumulation and Section
4 presents the quantitative exercise.

2

The model without capital accumulation

There are two sectors populated by agents with different investment opportunities. In thefirst sector there is a continuum of risk-averse investors who are the shareholders of firms anddiscount the future at rate β. In the second sector there is a continuum of risk-averse workers
with discount factor δ > β. The different discounting between the owners of firms (investors)
10and workers implies that firms borrow from workers subject to the enforcement constraints wewill describe below. This result is based on the assumption that the market for the ownershipof firms is segmented, that is, only investors have access to this market while workers can only
save in the form of bonds.
The assumption that agents are risk-averse implies that the effective discount rates forinvestors and workers are not constant in equilibrium but fluctuate in response to aggregate
shocks. As we will see, fluctuations in the effective discount rates play a central role in theanalysis of this paper. To facilitate the presentation, we first describe the closed-economy
version of the model. Once we have characterized the key properties of the autarkic equilibrium,
it will be trivial to extend it to the environment with international mobility of capital.

2.1

Investors and firms

Investors have lifetime utility E0P∞tt=0 β u(ct ). They are the owners of firms and derive income

only from dividends. Denoting by dt the dividends paid by firms, the effective discount factor
for investors is mt+1 = βuc (dt+1 )/uc (dt ). This is also the discount factor used by firms since
they maximize shareholders’ wealth.
Firms operate the production function F (zt , ht ) = zt k̄hνt , where k̄ is a fixed input of capital,
ht is the variable input of labor, and zt is a stochastic variable affecting the technology of all
firms (total factor productivity). The parameter ν is smaller than 1 implying decreasing returns
to scale in the variable input. The input of capital is fixed and does not depreciate. We will
make the accumulation of capital endogenous in the next section when we present the generalmodel. For the moment, however, there is not capital accumulation.
Firms start the period with intertemporal debt bt . Before producing they choose the labor
input ht , the dividends dt , and the next period debt bt+1 . The budget constraint is:
bt + wt ht + dt = F (zt , ht ) +

bt+1
Rt

where Rt is the gross interest rate.
The payments of wages, wt ht , dividends, dt , and current debt net of the new issue, bt −bt+1 /Rt , are made before the realization of revenues. This implies that the firm faces a cash
flow mismatch during the period. The cash needed at the beginning of the period is wt ht + dt +bt − bt+1 /Rt . From the budget constraint we can verify that this is equal to the cash revenue
F (zt , ht ). To cover the cash flow mismatch, the firm contracts an intra-period loan which is11equal to the liquidity need lt = wt ht + dt + bt − bt+1 /Rt . This loan is repaid at the end of theperiod, after the realization of revenues.
Debt contracts are not perfectly enforceable. At the end of the period the firm can divert
the liquidity lt and default. Default gives the lender the right to liquidate the firm’s capital.
Suppose that the liquidation value is ξt k̄, where ξt is a stochastic variable that depends onmarket conditions. This is the value that guarantees the firm’s liabilities. Since default arises
at the end of the period, the total liabilities of the firm are lt + bt+1 /Rt . To ensure that thefirm does not default, the total debt is subject to the following enforcement constraint:ξt k̄ ≥ lt +

bt+1
.
Rt

Since fluctuations in ξt affect the ability to borrow, we will call it ‘credit shock’. It can also
be interpreted as an asset price shock because it affects the value of selling the firm’s assets.
The asset price shock, however, is purely exogenous in this framework.2
To illustrate the role played by the stochastic liquidation value ξt , consider a pre-shockequilibrium in which the enforcement constraint is binding. Starting from this equilibrium,
suppose that ξt decreases. We will show that in response to the decline in ξt , the firm is forced
to reduce either the dividends and/or the input of labor.
Let’s start considering the case in which the firm is unwilling to change the input of labor.
This implies that the intra-period loan lt = F (zt , ht ) also does not change. Thus, the only way
to satisfy the enforcement constraint is by reducing the intertemporal debt bt+1 . We can thensee from the budget constraint, wt ht + dt + bt = bt+1 /Rt + F (zt , ht ), that the reduction in bt+1
requires an equivalent reduction in dividend payments. The firm is forced to substitute debt
with equities.
Alternatively the firm could keep the dividend payments unchanged but reduce the inputof labor. Since the reduction in ht reduces the intra-period loan, lt = F (zt , ht ), this will also
ensure that the enforcement constraint is satisfied. Therefore, after a negative shock to ξt ,the firm faces a trade-off: paying lower dividends or cutting employment. As we will see, theoptimal choice will depend on the relative cost of changing these two variables which depends
on the stochastic discount factor of the entrepeneurs mt+1 = βuc (dt+1 )/uc (dt ).
2

We can also think of ξt as a liquidity shock along the lines of Kiyotaki and Moore (2008).

12

Firm’s problem: The optimization problem of the firm can be written recursively as follows:()

V (s; b) = max0 d + Em0 V (s0 ; b0 )

(1)

d,h,b

subject to:b + d = F (z, h) − wh +ξ k̄ ≥ F (z, h) +

b0
R

bt+1
Rt

(2)

(3)

where s are the aggregate states, including the shocks z and ξ, and the prime denotes the next
period variable. The enforcement constraint takes into account that the intra-period loan isequal to the firm’s output, that is, lt = wt ht + dt + bt − bt+1 /Rt = F (zt , ht ).
In solving this problem the firm takes as given all prices and the first order conditions are:
w
1−µ

(4)

REm0 = 1 − µ,(5)

Fl (z, h) =where µ is the Lagrange multiplier for the enforcement constraint. These conditions are derived
under the assumption that dividends are always positive, which will be the case if the investors’
utility satisfies uc (0) = ∞. The detailed derivation is in Appendix A.
We can see from condition (4) that limited enforcement imposes a wedge in the demand
for labor. This derives from the fact that the labor input needs to be financed and, becauseof the agency problem, part of the financing has to come from equity (through lower payment
of dividends). As long as the cost of equity (1/Em0 ) is greater than the cost of debt (theinterest rate R), expanding the input of labor is costly in the margin because the firm needs
to substitute debt with equity. It is then the equity premium 1/Em0 − R that determines thelabor wedge as can be seen from condition (5).3 This wedge is strictly increasing in µ anddisappears when µ = 0, that is, when the enforcement constraint is not binding. In this case3

Notice that we are using the term ‘equity premium’ to denote the differential between the expected shareholders’ return and the interest rate on bonds. Since shareholders and bondholders are different agents, theequity premium is not only determined by the cost of risk (risk premium).

13the equity premium becomes zero.
Some (partial equilibrium) properties

The characterization of the firm’s problem inpartial equilibrium provides helpful insights about the property of the model once extended toa general equilibrium set-up. For partial equilibrium we mean the allocation achieved when
the interest rate and the wage rate are both exogenously given and constant.
Under these conditions, equation (5) shows that µ decreases with the expected discountfactor, Em0 . A decrease in ξ, that is, a negative credit shock, makes the enforcement constraint
tighter. Because firms reduce the payment of dividends, the investors’s consumption has todecrease. This induces a decline in the discount factor m0 = βuc (d0 )/uc (d) and an increase in
the multiplier µ (condition (5)). Condition (4) then shows that the demand for labor declines.
Intuitively, when the credit conditions become tighter, firms need to rely more on equity
financing and less on debt. However, it is costly to increase equity in the short-term sinceinvestors must cut consumption and their utility is concave. Because of this, the firm does notfind optimal in the short-term to raise enough equity to keep the pre-shock production scale andit cuts employment. If investors’ utility were linear (risk-neutrality), the discount factor would
be equal to Em0 = β and the credit shock would not affect employment. This also requiresthat the interest rate does not change, which is the case in the partial equilibrium consideredhere. In the general equilibrium, of course, prices also change. In particular, movements inthe demand of credit and labor affect the interest rate R and the wage rate w. To derive theaggregate effects we need to close the model and characterize the general equilibrium.

2.2

Closing the model and general equilibrium

There is a representative households/worker with lifetime utility E0P∞

tt=0 δ U (ct , ht ), where ct

is consumption, ht is labor and δ is the intertemporal discount factor. For the later analysisof the general model, it will be convenient to assume that the period-utility takes the form:
U (ct , ht ) = log(ct ) − α

h1+γ
t
.
1+γ

Workers have a higher discount factor than entrepreneurs, that is, δ > β. This condition
ensures that the enforcement constraint is binding, at least occasionally. Another key assumption is that there is market segmentation, that is, workers hold bonds issued by firms but they14

cannot buy shares of firms. The budget constraint is
wt ht + bt = ct +

bt+1
,
Rt

and the first order conditions for labor, ht , and next period bonds, bt+1 , areUh (ct , ht ) + wt Uc (ct , ht ) = 0,
δRt EtGeneral equilibrium:

Uc (ct+1 , ht+1 )Uc (ct , ht )

(6)


= 1.

(7)

We can now define a competitive equilibrium. The sufficient set ofaggregate states, s, are given by the level of productivity, z, the credit conditions, ξ, and theaggregate stock of bonds, B.
Definition 2.1 (Recursive equilibrium) A recursive competitive equilibrium is defined bya set of functions for (i) workers’ policies h(s), c(s), b(s); (ii) firms’ policies h(s; b), d(s; b) andb(s; b); (iii) firms’ value V (s; b); (iv) aggregate prices w(s), R(s) and m(s0 ); (v) law of motion
for the aggregate states s0 = Ψ(s). Such that: (i) household’s policies satisfy the optimality
conditions (6)-(7); (ii) firms’ policies are optimal and V (s; b) satisfies the Bellman’s equation(1); (iii) the wage and the interest rate are the equilibrium clearing prices in the markets forlabor and bonds, and the discount factor for firms is m(s0 ) = βuc (dt+1 )/uc (dt ); (iv) the lawof motion Ψ(s) is consistent with the aggregation of individual decisions and the stochastic
processes for z and ξ.
To illustrate the main properties of the model, we look at some special cases. Consider
first the economy without shocks. In this economy the enforcement constraint binds in thesteady state equilibrium. To see this, consider the first order condition for the bond, equation(7), which in a steady state becomes δR = 1. Using this condition to eliminate R in (5) andtaking into account that in a steady state Em0 = β, we get β/δ = 1 − µ. Because δ > β byassumption, the lagrange multiplier µ is greater than zero. Firms want to borrow as much as
possible because the cost of borrowing—the interest rate—is smaller than their discount rate.
In a model with uncertainty, however, the constraint may not be always binding. However,they will become binding after a sufficiently large and unexpected decline in ξ. In this casefirms will be forced to cut dividends and this affects the discount factor Em0 . Furthermore,

15

the change in the demand for credit impacts on the equilibrium interest rate. Using condition(5) we can see that these changes affect the multiplier µ, which in turn impacts on the demand
for labor (see equation (4)). On the other hand, a sufficiently large increase in ξ may make theenforcement constraint non-binding. This implies that the response to a positive credit shock
is bounded since the multiplier µ cannot be negative. Therefore, the responses of the economy
to credit shocks could be asymmetric: negative shocks induce large falls in employment andoutput while the impacts of positive shocks is moderate.
The asymmetric responses caused by occasionally binding constraints is also a feature of
the models studied in Mendoza (2010). These papers, however, abstract from credit shocks,
which is the main focus of the current paper. Furthermore, they consider only small open
economies, and therefore, they cannot address one of the key issues studied in the current
paper, that is, international comovement.

2.3

Capital mobility

Let’s consider now two countries with the same size, preferences and technology as describedin the previous section. Although we characterize here only the case with two symmetriccountries, the model can be easily extended to any number of countries and with different
degrees of heterogeneity. The shocks z and ξ are country-specific and they follow a joint
Markov process.
Investors/firms:

We have to specify what agents can do in a financial market that is in-ternationally integrated. For investors, the opening of the international market allows themto hold shares of foreign firms, in addition to their domestic holdings. Because firms are
subject to country specific shocks, investors would gain from diversifying the cross-country
ownership. Therefore, in a financially integrated economy, investors choose to own the worldwide portfolio of shares and we have a representative ‘worldwide’ investor. Having a common representative shareholder, firms in different countries will use the same discount factor
mt+1 = βuc (dt+1 + d∗t+1 )/uc (dt + d∗t ), where investors’ consumption is the sum of dividends
paid by domestic firms, dt , plus the dividends paid by foreign firms, d∗t .4 From now on we will
use the star superscript to denote variables pertaining to the foreign country.
Besides the common discount factor, firms continue to solve problem (1) and the first order
4

Notice that this follows from the assumption that investors’ utility depends only on consumption. If investors
derived utility also from leisure, a perfect diversification of portfolio will not be necessarily optimal.

16

conditions are given by equations (4) and (5). Let’s focus on condition (5), which we rewrite
here for both countries:
Rt Emt+1 = 1 − µt

Rt∗ Em∗t+1 = 1 − µ∗t .
The first condition is for firms located in the domestic country and the second if for firms
located in the foreign countries. Since the discount factor is common to domestic and foreign
firms, that is, Emt+1 = Em∗t+1 , and the interest rate is equalized across countries, Rt = Rt∗ ,the above conditions imply that the lagrange multiplier will also be equalized, that is, µt = µ∗t .
Therefore, independently of which country is hit by a shock, if the enforcement constraint isbinding in one country, it will also be binding in the other. This also implies that the domestic
and foreign labor wedges 1/(1 − µt ) and 1/(1 − µ∗t ) (see condition (4)) are equalized acrosscountries. This property is crucial for understanding the cross-country impact of credit shocks.
Households/workers:

We keep the assumption that financial markets are segmented andhouseholds/workers cannot hold shares of firms. With capital mobility, however, they can
engage in international financial transactions with foreign workers. More precisely, in addition
to holding bonds issued by domestic firms, domestic workers can buy state contingent claims
from foreign workers. We still assume that firms borrow from domestic workers but they cannot
sign state contingent contracts with workers. The assumption that firms borrow only fromdomestic workers is without loss of generality: whether firms borrow from domestic or foreign
workers is irrelevant in an integrated capital market. The unavailability of state-contingent
claims between firms and the workers is essential to retain market incompleteness.
Denote by nt+1 (st+1 ) the units of consumption goods received at time t + 1 by domestic
workers if the aggregate states are st+1 . These are worldwide states, and therefore, they include
aggregates states of both countries, as will be made precise below. Of course, in equilibrium,
the consumption units received by workers in the domestic country must be equal to theconsumption units paid by workers in the foreign country, that is, nt+1 (st+1 ) + n∗t+1 (st+1 ) = 0.
This must be satisfied for any possible realization of the states st+1 .

17

The budget constraint of a worker in the domestic country is
bt+1
wt ht + bt + nt = ct ++RtZ
nt+1 (st+1 )q(st+1 )/Rt ,st+1

where qt (st+1 )/Rt is the unit price of the contingent claims.
Given the specification of the utility function, the first order conditions for the choice oflabor, ht , next period bonds, bt+1 , and foreign claims, nt+1 (st+1 ), are
αhγt ct = wt ,
δRt Et

δRt

ct
ct+1

(8)

=1

ct
ct+1 (st+1 )(9)p(st+1 ) = q(st+1 ),for all st+1 ,(10)

where p(st+1 ) is the probability (or probability density) of the aggregate states in the next
period for the world economy.
Since in equilibrium the prices and probabilities of the contingencies are the same fordomestic and foreign agents, condition (10) implies thatct
ct+1 (s̄t+1 )
= χ,
= ∗
∗
ct
ct+1 (s̄t+1 )(11)that is, the ratio of consumption of workers in the two countries remains constant over time.
This is a well known property of environments with a full set of state-contingent claims. In ourenvironment the constancy of the consumption ratio is among workers (and among investors)
but not between workers and investors because of the assumption of market segmentation.
Before continuing we would like to clarify that the assumption of contingent claims among
workers is not essential for the results of this paper. We could simply assume that workers
can engage in international non-contingent lending and borrowing. Or equivalently, that firms
can engage in international borrowing. However, the availability of contingent claims greatly
simplifies the characterization of the equilibrium because it allows us to reduce the number ofendogenous state variables. This will be especially convenient once we extend the model tocapital accumulation.

18

Aggregate states and equilibrium:

We can now define the equilibrium for the open-

economy version of the economy. The aggregate states s are given by the exogenous variablesz, ξ, z ∗ , ξ ∗ , the financial liabilities of firms, Bt and Bt∗ , and the net foreign asset position ofdomestic firms, Nt . Since in equilibrium the net foreign asset position of domestic firms is thenegative of the foreign position, once we know Bt , Bt∗ and Nt we also know the total wealthof domestic (Bt + Nt ) and foreign households (Bt∗ − Nt ). Therefore, the claims purchased byhouseholds are contingent on st = (z, ξ, z ∗ , ξ ∗ , Bt , Bt∗ , Nt ).
Definition 2.2 (Recursive equilibrium) A recursive competitive equilibrium is defined bya set of functions for: (i) households’ policies h(s), c(s), b(s), n(s; s0 ), h∗ (s), c∗ (s), b∗ (s),n∗ (s; s0 ); (ii) firms’ policies h(s; b), d(s; b), b(s; b), h∗ (s; b), d∗ (s; b), b∗ (s; b); (iii) firms’ values
V (s; b) and V ∗ (s; b); (iv) aggregate prices w(s), w∗ (s), R(s), m(s, s0 ), q(s; s0 ); (v) law of motion
for the aggregate states s0 = Ψ(s̄). Such that: (i) household’s policies satisfy the optimality
conditions (6)-(10); (ii) firms’ policies are optimal and satisfy the Bellman’s equation (1)for both countries; (iii) the wages clear the labor markets; the interest rates and the pricefor contingent claims clear the financial markets; the discount rate used by firms satisfiesm̄(s, s0 ) = βuc (dt+1 + d∗t+1 )/uc (dt + d∗t ); (iv) the law of motion Ψ(s) is consistent with theaggregation of individual decisions and the stochastic process for z, ξ, z ∗ , ξ ∗ .
The only difference with respect to the equilibrium in the closed economy is that thereis the additional market for foreign claims and the discount factor for firms is given by theworldwide representative investor. The market clearing condition for the foreign claims is
N (s0 ) + N ∗ (s0 ) = 0. This is in addition to the clearing conditions for the domestic bondmarkets (lending to firms).
Although the general definition of the recursive equilibrium is based on the set of statevariables st = (z, ξ, z ∗ , ξ ∗ , Bt , Bt∗ , Nt ), we can use some of the properties derived above andcharacterize the equilibrium using a smaller set of states. Let Wt = Bt + Bt∗ be the worldwide
wealth of households/workers. This is the sum of bonds issued by domestic firms, Bt , andforeign firms, Bt∗ . Then using the fact that the consumption ratio of domestic and foreign
households is constant at χ and the employment policy of firms does not depend on theindividual debt, the recursive equilibrium can be characterized using the state variables st =(z, ξ, z ∗ , ξ ∗ , Wt ). Essentially, the assumption of cross-country risk-sharing among workers andamong investors (but not between workers and investors) allows us to reduce the number of‘endogenous’ states to only one variable.
19Intuitively, by knowing Wt , we know the worldwide liability of firms, but not the distribution between domestic and foreign firms. However, to characterize the firms’ policies, we only
need to know the worldwide debt, which is equal to Wt . Since investors own an internationallydiversified portfolio of shares, effectively there is only one representative global investor. It is
as if there is a representative firm with two units: one unit located in the domestic country andthe other in the foreign country. Since both units have a common owner, it does not matter
how the debt is distributed between the two units. What matters, from the perspective of theinvestor, is the total debt and the total payment of dividends. Total households’ wealth is alsoa sufficient statistics for the characterization of the households’ policies since the consumption
ratio between domestic and foreign households remains constant at χ. Therefore, once we solve
for the aggregate worldwide consumption, country-specific consumption can be determined byχ. This property limits the computational complexity of the model, making feasible the use
non-linear approximation methods. We will come back to this point after the description of
the general model with capital accumulation.
We are not ready to prove the following proposition about the impact of a financial shock.
Proposition 2.1 A credit shock to the domestic country (change in ξt ) has the same impact
on employment and output of domestic and foreign countries.
We have already shown that the Lagrange multiplier µt is common for the firms of bothcountries. If the two firms have the same productivity and the wage ratio in the two countries
does not change, the first order conditions for the firms imply that they all choose the same
employment and investment. To complete the proof we have to show that the ratio of wagesof the two countries stays constant. Because firms in both countries have the same demand
for labor and the ratio of workers’ consumption remains constant, the first order condition forthe supply of labor implies that the wage ratio between the two countries does not change.
Before turning to capital accumulation, we would like to emphasize another feature of themodel. As we have seen, the credit shock of one country spills over other countries if the two
economies are financially integrated. However, the impact on the originating country is smallerwhen capital markets are integrated.
To see this, consider the channel through which a credit shock affects employment. Aftera credit contraction the firm is forced to reduce the payment of dividends and this decreases0

the discount factor m̄0 = βuc (d0 + d∗ )/uc (d + d∗ ). From condition (5) we can see that this20

increases µ which in turn decreases the demand for labor (see condition (4)). The bigger
the reduction in dividends, relatively to investors’ consumption, the larger the impact on the
discount factor, and therefore, on the demand of labor. In an economy that is financiallyintegrated, the change in dividends induced by the credit contraction in one country leads toa lower reduction in the consumption of investors since they are diversified. As a result, thedecrease in the discount factor is smaller and the impact on the demand of labor is smaller.
This can be proved analytically for the limiting case of a small open economy.
Proposition 2.2 Consider a credit shock only to the domestic country. If the country is asmall open economy and ψ = 0, the credit shock has not effect on domestic (and foreign)
employment.
In the case of a small open economy, investors are perfectly diversified internationally andthe reduction in the dividends paid in country 1 is negligible relatively to investors’ consumption. Therefore, the discount factor does not change, which implies that the demand for laborin country 1 and elsewhere remains unchanged. At the same time, the reduction in the demandfor debt is also negligible relative to the size of the international market. This implies thatthe interest rate does not change. Furthermore, the wealth effects on the supply of labor are
negligible, leaving the wage rate unaltered.

3

Model with capital accumulation

We now relax the assumption that the input of capital is fixed. This introduces additional
state variables that makes the model difficult to solve unless we use local approximation techniques. However, when the enforcement constraint is only occasionally binding, we need tosolve the model using global approximation techniques. Unfortunately, these techniques arecomputationally intensive and become quickly impractical when we have a large numbers ofstate variables. Therefore, in order to limit the number of state variables, we will make somespecial assumptions about the functional form for the production function.
Investors-firms

The production function takes the form:
yt = zt (Kt + Kt∗ )1−θ ktθ hνt ≡ F (zt , Kt + Kt∗ , kt , ht ),21

where Kt is the aggregate capital in the domestic country and Kt∗ in the foreign country, kt is
the individual input of capital and ht is the input of labor. The dependence of the production
function from the worldwide stock of capital, Kt + Kt∗ , captures positive externalities. We
assume that θ + ν < 1.
The production function is characterized by constant returns in the reproducible factor,
capital, and the model has the typical features of an AK model. The externality ensures that
there are not increasing returns at an individual level, and therefore, the economic environment
remains competitive. As we will see, the AK structure facilitates the analytical characterization of the equilibrium, and makes the numerical solution more tractable. This is the only
motivation for using this particular structure of the production function.
Given it the flow of investment, the stock of capital evolves according to
kt+1 = (1 − τ )kt + Υ

it
kt


kt ,

where τ is the depreciation rate and the function Υ(.) is strictly decreasing and concave,
capturing adjustment costs in investment. The adjustment cost prevents an excessive volatility of investment when the economy is financially integrated. This is a common element ofinternational macro models.
With capital accumulation the budget constraint of the firm becomes
bt + dt + it = F (zt , Kt , kt , ht ) − wt ht +

bt+1
,
Rt

and the enforcement constraint
ξt kt+1 ≥ F (zt , kt , ht ) +

bt+1
.
Rt

Thanks to the AK structure of the production function, the model can be normalized by
the worldwide stock of capital Kt + Kt∗ . Using the tilde sign to denote normalized variables,

22the budget constraint, law of motion for capital and enforcement constraint can be written as:
gt b̃t+1b̃t + d˜t + ĩt = F (zt , k̃t , ht ) − w̃t ht +
,
Rt


(12)



gt k̃t+1 = (1 − τ )k̃t + Υ

ĩt
k̃t

k̃t ,

(13)

ξt gt k̃t+1 ≥ F (zt , k̃t , ht ) +gt b̃t+1
.
Rt

(14)

∗ )/(K + K ∗ ) is the gross growth rate of worldwide capital
The variable gt = (Kt+1 + Kt+1
tt

and k̃t = kt /(Kt + Kt∗ ) is the normalized individual capital. Denote by st = Kt /(Kt + Kt∗ )the aggregate share of capital owned by domestic firms (and s∗t = 1 − st the share of foreign
firms). Since in equilibrium kt = Kt , we also have that k̃t = st .
As in the simpler model without capital accumulation, investors hold an internationallydiversified portfolio of shares and firms use the common discount factor mt+1 = β[(dt+1 +d∗t+1 )/(dt + d∗t )]−σ . In terms of variables normalized by the worldwide capital, the discountfactor can be rewritten as:
mt+1 = gt−σ βd˜t+1 + d˜∗t+1
d˜t + d˜∗!−σ= gt−σ m̃t+1

tUsing normalized variables, the optimization problem solved by a firm is)(Ṽ (s̃; k̃, b̃) =max

˜ h̃,ĩ,b̃0d,d˜ + g 1−σ E m̃0 Ṽ (s̃0 ; k̃ 0 , b̃0 )(15)

subject to (12), (13), (14)where Ṽ is the firm’s value normalized by aggregate worldwide capital K + K ∗ , and s̃ denotes
the normalized aggregate states as specified below.
We can now see the analytical convenience of having the capital externality. Thanks tothis assumption, we can write the firm’s value function as Vt = (Kt + Kt∗ ) · Ṽt and rescale theproblem of the firm by worldwide capital. By doing so, we do not need to keep track of theaggregate stock of capital as a state variable. Of course, because we are looking at a generalequilibrium, we also need to make sure that the supply of labor does not growth over time.

23This will be the case with the worker’s utility specified earlier.
Appendix B derives the first order conditions for the firm’s problem. After imposing theequilibrium conditions kt = Kt and k̃t = st , the first order conditions can be written as:w̃t,
1 − µt(16)ḡt−σ Rt E m̃t+1 = 1 − µt ,(17)Qt Υ0 ĩt = 1,

(18)

Fh (zt , st , ht ) =Qt = ξt µt + ḡt−σ E m̃t+1

(1 − µt+1 )Fk (zt+1 , st+1 , ht+1 ) − ĩt+1hi+ 1 − τ + Υ ĩt+1 Qt+1 .

(19)

Here µt is the Lagrange multiplier associated with the enforcement constraint and Qt is
the Lagrange multiplier associated with the law of motion for the stock of capital (Tobin’s q).
We can verify that there is no capital that enters these equations. This confirms that we canignore the stock of capital when we solve for the normalized equilibrium.
Notice that the property established in the simpler model for which the Lagrange multiplieris common across domestic and foreign firms, also applies to this extended model. In fact, fromcondition (17) we can see that the common discount factor and the equalization of the interest
rates across countries imply µt = µ∗t . Therefore, if the enforcement constraint is binding in
one country, it must also be binding in the other country. The labor wedge in the demand oflabor, 1/(1 − µt ), is also equalized across countries.
Aggregate states and equilibrium:

Denote by W̃t = B̃t st + B̃t∗ (1 − st ) the normalized

worldwide wealth of households. Thanks to the AK structure of the model and the normalization described above, we only need to keep track of two ‘endogenous’ state variables: W̃t andst . Therefore, compared to the simpler model considered earlier, the introduction of capital
accumulation adds only one state variable, that is, the share of worldwide capital owned bydomestic firms, st .
With only two ‘endogenous’ states it becomes manageable to solve the model numericallyusing global approximation methods. In addition to the two endogenous states, we also have the24four exogenous processes for zt , ξt , zt∗ , ξt∗ ). However, the processes for the exogenous states canbe approximated with parsimonious discrete Markov chains, which contains the dimensionalityof the computational problem. Appendix C reports for the full list of equilibrium conditions
and describes the computational procedure.
We are not ready to prove the following proposition about the impact of a credit shock.
Proposition 3.1 A credit shock to the domestic country (change in ξt ) has the same impact
on the employment and output of the foreign country in the current period. The impact on
investment, however, is not the same.
We have already shown that the Lagrange multiplier µt is common for firms of both countries. If firms have the same productivity, same capital and pay the same wage, the first ordercondition (16) implies that they all choose the same employment. This must be the case in
the current period since the stock of capital was chosen in the previous period before the observation of the shock and workers have the same consumption ratio. However, the choice ofinvestment differs as we can verify from equations (18) and (19). Thus, starting in the next
period, firms will have different stocks of capital, which in turn implies different employment
levels. In the current period, however, they experience the same response of employment andoutput. Furthermore, even if the responses are different starting in the next period, we will
see that the differences are quantitatively small.

4

Quantitative analysis

This section studies the properties of the model quantitatively using a calibrated version of
the model. We think of country 1 as the US and country 2 as the other countries in thegroup of the seven largest industrialized economies, that is, Canada, Japan, France, Germany,
Italy, UK. We refer to this group as G6 countries. The model is solved numerically using theprocedure described in Appendix C.
The discount factor of workers determines the average return on bonds. We set it to thequarterly value of δ = 0.9925 which implies a yearly return close to 3%. The discount factor
for investor is set to β = 0.99. This will affect the return on stocks.
The utility function takes the form U (c, h) = ln(c) − αh1+γ /(1 + γ). The parameter γ isset to 2 which implies a Frish elasticity of labor supply of 0.5. The parameter α is set so thatworkers spent about 1/3 of their time working.
25

Next we parameterize the production function. The parameter ν is chosen to have a labor
income share of 0.7. Without uncertainty, the labor income share, that is, the fraction of output
going to workers in the form of wages is equal to νβ/δ.5 Given δ and β, we determine ν. Of
course, in the stochastic economy the average labor share is not exactly 0.7 but the difference
is not small. Next we fix the return to scale at the level of an individual firm which is equalto θ + ν = 0.9. Given the value of ν chosen above, this pins down the value of θ = 0.9 − ν.
The stock of capital evolves according to k 0 = (1 − τ )k + Υ(i/k)k, with the function Υ
taking the functional form used in Jermann (1998), 1−ζ
 
φ1ii=+ φ2 .
Υk1−ζ k
The parameters φ1 and φ2 are chosen so that in the deterministic steady state the adjustment
cost does not play any role, that is, Q = 1 and I = τ K. This requires φ1 = τ ζ and φ2 =−ζτ /(1 − ζ). Under these conditions the average depreciation rate is close to τ , which we set
to 0.02. The parameter ζ determines the sensitivity of the cost to investment which we set to
0.5.
At this point we are left with the parameters that determine the stochastic properties ofthe shocks. The exogenous states follow independent the first order autoregressive processes,
log(zt+1 ) = (1 − ρz )z̄ + ρz log(zt ) + t+1 ,∗log(zt+1) = (1 − ρz )z̄ + ρz log(zt∗ ) + ∗t+1 ,log(ξt+1 ) = (1 − ρξ )ξ¯ + ρξ log(ξt ) + εt+1 ,∗log(ξt+1) = (1 − ρξ )ξ¯ + ρξ log(ξt∗ ) + ε∗t+1 ,Here t+1 and ∗t+1 are mean zero iid shocks with standard deviation σz . Similarly, εt+1 andε∗t+1 are mean zero shocks with standard deviation σξ .
We are assuming that the second country (G6 countries) has the same characteristicsof the first country (the US). Then we use data for the US to calibrate these parameters.
The parameters governing the productivity shocks are set to ρz = 0.95 and σz = 0.01 (z̄ is5
From the first order condition of labor, equation (4), we derive wh/F (z, k, h) = ν(1 − µ), which provides
an expression for the labor share. To derive an expression for µ we use condition (5) evaluated in the version of
the model without uncertainty. Taking into account that in a deterministic steady state m0 = β and R = 1/δ,
this condition becomes β/δ = 1 − µ. Substituting in the labor share ν(1 − µ), we get the expression reported in
the main text.

26

normalized to 1). These are typical calibration values in business cycle studies. The averagevalue of the enforcement parameter ξ¯ affects the average leverage. Higher is the value of ξ¯ andhigher is the average leverage. We set this parameter to 0.5, implying an average ratio of total
debt over physical capital, (bt+1 /Rt + yt )/kt+1 , slightly lower than 0.5.6 The remaining two
parameters ρξ and σξ are chosen to replicate the properties of the stock of debt in the US. In
particular we use data from the Flows of Funds for the nonfinancial business sector (financial
markets instruments). By setting ρξ = 0.95 and σξ = 0.015 the model generates a dynamics
of debt whose persistence and standard deviation is close to the data.

4.1

Results

Appendix C describes the computational procedure. To implement this procedure we discretize
the space for the exogenous and endogenous states. Both zt and ξt are approximated with athree-state Markov chain (see Tauchen (1986)). The spaces for the endogenous states, b̃t and st
are each discretized on a grid containing eleven points. Values outside the grids are determinedthrough linear interpolation.
We present the results outlining five main properties. In particular, we emphasize (i) the
asymmetric response to shocks; (ii) the countercyclicality of labor productivity in response tocredit shocks; (iii) the international spillover of credit shocks; (iv) the severity of crisis after
long periods of credit and macroeconomic booms; (v) the importance of credit shocks for thevolatility of labor and asset prices.
Asymmetry:

Figure 9 plots the impulse responses to a credit shock. The responses are

generated starting from a limiting equilibrium the economy would converge after a long seriesof draws ξt = ξ2 . Starting from this equilibrium we consider two cases. In the first case, startingat time 1, the economy experiences a sequence of ξt = ξ3 leading to a credit expansion. In thesecond case the economy experiences a sequence of draws ξt = ξ1 leading to a credit contraction.
There is no uncertainty in productivity zt which is constant and equal to its mean.
In response to the credit expansion (left panels of Figure 9) we see a gradual increase in thestock of debt and a persistent expansion in labor, investment and Tobin’s q. The magnitudeof the macroeconomic expansion, however, is not large. In contrast, the responses to a credit
contraction (right panels of Figure 9) display a very different pattern. The stock of debt
declines much more drastically. Also, the responses of labor, investment and Tobin’s q are
6

The average ratio is smaller than 0.5 since the enforcement constraint is only occasionally binding.

27

Figure 9: Impulse responses to credit expansions and contractions.

28

much larger but not persistent. Therefore, there is a very strong asymmetry in the responses
to credit shocks.
Countercyclicality in labor productivity:

Figure 10 plots the impulse responses of laborproductivity generated using the approach described above. As in the previous figure, we seean asymmetry between credit expansions and credit contractions. More importantly, a credit
expansion generates a decline in labor productivity while a credit contraction generates anincrease. Therefore, the dynamics of labor productivity induced by credit shocks is countercyclical. This is important for capturing one of the facts we outlined in the first section of thepaper.
Figure 10: Impulse responses to credit expansions and contractions.

Macroeconomic comovement:

Figure 11 plots the impulse responses of labor, investment

and Tobin’s q to a credit contraction in country 1, differentiating the cases of financial autarky
and capital mobility. Since the shock is only to country 1, in the autarky regime country 2 is notaffected by the shock. In the regime with capital mobility, instead, the shock impacts country 2
in the same way it impacts country 1 (international spillover). It can be noticed, however, thatthe effect on country 1 is smaller when the economies are financially integrated. Therefore, froma macroeconomic perspective, capital markets integration allows for an international sharingof credit shocks. This helps us to understand the high international comovement observed in
the recent crisis.

29

Figure 11: Impulse responses to credit contractions in closed and open economies.

30

Credit booms and severity of recessions:Figure 12 plots the impulse responses to acredit expansion that later reverts back to the initial level. Starting from an equilibrium theeconomy would converge after a long series of ξt = ξ2 , at time 1 the economy experience a drawof ξt = ξ3 (credit expansion). This higher value of ξ is drawn for several period after which
it reverts back to ξt = ξ2 . We consider several durations for the credit expansions, before thereversal: 5 quarters, 20 quarters and 60 quarters.
The key finding is that the severity of the credit contraction increases with the duration of
the credit expansion. After a protracted credit boom, the economy accumulate large leverages.
Then, when the shock reversal arrives, the required de-leveraging is much bigger generating astronger macroeconomic contraction. In this way the model can explain why recessions thatarise after long periods of financial expansions tend to be more severe.
Volatility of labor and asset prices: Table 1 reports the standard deviations of various
variables. Three versions of the economy are considered: the economy with productivity shocks
only; the economy with credit shocks only; and the economy with both shocks. The statistics
are computed after detrending the simulated series with a band-pass filter that preserves cyclesof 1.5-8 years (Baxter and King (1999)).
Table 1: Standard deviations of key variables from detrended simulated series.
Productivity
shocks only

Creditshocks only

Bothshocks

OutputConsumption
Labor
Investment
Firms’ value
Tobin’s q
Liquidity

0.57
0.31
0.14
0.60
0.38
0.30
0.02

0.37
0.19
0.53
1.70
1.74
0.84
0.42

0.60
0.50
0.43
1.62
1.52
0.81
0.46

% Nonbinding

99.93

94.87

95.73

Two properties are especially noticeable. First, the model with credit shocks can generatemuch higher volatility of labor, bringing the model closer to the data. Second, credit shocks
also generate a high volatility of asset prices. In particular, in the version of the model with
only credit shocks, the value of the firm becomes more than four times as volatile as output.

31

Figure 12: Duration of credit expansions and severity of contractions.

32

In contrast, with only productivity shocks, the value of the firm is less volatile than output.
Therefore, credit shocks are important for understanding the high volatility of labor and asset
prices observed in the data.

5

Conclusion

The recent decade and in particular the 2008-2009 crisis has been characterized by an historically high degree of international synchronization. Furthermore, the internationalization of therecent crisis has taken place in an environment where the association between labor productivity and labor input is at historically low levels for US and, on average, for other industrializedcountries. Motivated by these observations we have considered a theoretical environment inwhich shocks to credit is one of the driving forces of the business cycle. These shocks affectthe real sector of the economy through a credit channel: booms enhance the borrowing capacity of firms and in the general equilibrium they lead to higher employment, production
but lower productivity of labor. The opposite arises after a credit contraction. Interestingly
credit shocks, relative to productivity shocks, tend to generate asymmetric business cycles (i.e.
contraction that are sharper than expansion) and more volatile asset prices, thus bridging the
gap between a standard model and the data.
Within this framework we have shown that, when countries are financially integrated, credit
shocks that are specific to one country affect the employment and production of other countries,
with significant macroeconomic spillovers. At the same time, these shocks generate a negative
correlation between labor productivity and working hours. On the contrary, country-specificproductivity shocks do not generate large cross-country co-movement in real macroeconomic
variables unless the shocks are internationally correlated. However, if productivity shocks arecorrelated across countries and they are the major source of business cycle fluctuations, it isdifficult to reconcile the fact that the correlation of labor productivity with hours is low andit has further declined in recent years.
Of course, other shocks besides the ones considered here that could also generate large
cross-country comovement and weak correlation between productivity and labor. However,
it is not obvious how the most common shocks that have been studied in the literature (forexample labor-wedge shocks like those considered by Smets and Wouters, 2007 or by Chari,Kehoe and McGrattan 2007) can generate international co-movement unless the shocks areinternationally correlated. We conclude by noting that our research points to disturbance in33

credit markets as potential drivers of economic fluctuations within and across countries, but
it does not attempt to explain the deep cause of these disturbances. In order to assess theappropriate policy responses to these disturbances future research should attempt to better
understand how and why these shocks arise.

34

Appendix
A

First order conditions

Consider the optimization problem (1) and let λ and µ be the Lagrange multipliers associate with thetwo constraints. Taking derivatives we get:
d:

1−λ=0

h:

λ[Fh (z, h) − w] − µFh (z, h) = 0
λ(1 + φµ)Em0 Vb0 (s0 ; b0 ) +
=0
R

b0 :
The envelope condition is:Vb (s; b)= −λThe above conditions can be re-arranged as in (4) and (5).

BFirst order conditions for the model with capital

Differentiating the firm’s problem (15) with respect to ht , b̃t+1 , ĩt , k̃t+1 , we get:Fh (zt , k̃t , ht ) =w̃t
1 − µt1 − µt+ gt−σ E m̃t+1 Ṽb (s̃t+1 ; k̃t+1 , b̃t+1 ) = 0
Rt
0

Qt Υ



ĩt
k̃t

(20)

(21)


=1

(22)

Qt = ξt µt + gt−σ E m̃t+1 Ṽk (s̃t+1 ; k̃t+1 , b̃t+1 )(23)

where µt is the lagrange multiplier associated with the enforcement constraint and Qt (Tobin’s q) is
the lagrange multiplier associated with the law of motion of capital. The multiplier associated with thebudget constraint is 1. For the foreign country we have the same conditions but with country specificvariables denoted with the start superscript.

35

The envelope conditions are:Ṽb (s̃t ; k̃t , b̃t ) = −1

(24)


 
  
ĩt
ĩt ĩt0Ṽk = (1 − µt )Fk (zt , k̃t , ht ) + 1 − τ + Υ
−Υ
Qt
k̃t
k̃t k̃t(25)

Substituting the envelope conditions and imposing the equilibrium conditions kt = Kt and k̃t = st ,we obtain (16)-(19).

C

Dynamic system and solution approach

We will use the bar sign to denote aggregate worldwide variables normalized by the worldwide stock of
capital. For example, the d¯t is the normalized worldwide dividend, defined as:
dt + d∗t≡ d˜t + d˜∗t .
d¯t =Kt + Kt∗

36

The full list of equilibrium conditions are:
1 = δgt−1 Rt Et



c̄t+1
c̄t

−1
(26)

c̃∗t = χc̃t

(27)

w̃t ht + w̃t∗ h∗t + b̄t = c̄t +gt b̄t+1
Rt(28)

ḡt b̄t+1
b̄t + d¯t + īt = F (zt , st , ht ) + F (zt∗ , s∗t , h∗t ) − w̃t ht − w̃t∗ h∗t +Rtgt (ξt st+1 + ξt∗ s∗t+1 ) ≥gt b̄t+1+ F (zt , st , ht ) + F (zt∗ , s∗t , h∗t )Rt(1 − µt )d¯−σ= βgt−σ Rt E d¯−σtt+1αhγt =

(30)

(31)

w̃t
c̃t

α(h∗t )γ =

(29)

(32)
w̃t∗
c̃∗t

(33)


gt st+1 = (1 − τ )st + Υ

gt s∗t+1 = (1 − τ )s∗t + Υ

ĩt
st


st

(34)

 ∗
ĩt
s∗t
s∗t

(35)

Fh (zt , st , ht ) =w̃t
1 − µt(36)

Fh (zt∗ , s∗t , h∗t ) =w̃t∗
1 − µt

(37)

Qt Υ0

Q∗t Υ0



ĩt
st


=1

(38)

 ∗
ĩt
=1
s∗t

(39)

Qt = ξt µt + βgt−σ E ¯ −σ 




dt+1
ĩt+1
ĩt+1
(1
−
µ
+
1
−
τ
+
Υ
Q
t+1 )Fk (zt+1 , st+1 , ht+1 ) −t+1 (40)
st+1
st+1
d¯t

Q∗t = ξt∗ µt + βgt−σ E ∗  ¯ −σ ĩ∗t+1
ĩt+1
dt+1
∗
∗
∗
∗
(1
−
µ
+
1
−
τ
+
Υ
Q
(41)
t+1 )Fk (zt+1 , st+1 , ht+1 ) − ∗
t+1
∗
st+1
st+1
d¯t

37

Equations (26)-(41) form a dynamic system composed of 16 equations. Given the states zt , ξt , zt∗ , ξt∗ , b̄t , st ,the unknown variables are ht , h∗ , ct , c∗ , wt , w∗ , it , i∗ , Qt , Q∗ , gt , µt , Rt , d¯t , b̄t+1 , st+1 . Therefore, we
t

t

t

t

t

have a dynamic system of 16 equations in 16 unknowns.
The computational procedure is based on the approximation of four functions:Γ1 (st+1 )= c̄−1t+1

Γ2 (st+1 )= d¯−σt+1

Γ3 (st+1 )






ĩt+1
ĩt+1
+
1
−
τ
+
Υ
Q
= d¯−σ
(1
−
µ
)F
(z
,
s
,
h
)
−
t+1
t+1
k t+1 t+1
t+1
t+1
st+1
st+1
(

Γ4 (st+1 )

=

d¯−σ
t+1

ĩ∗
∗
(1 − µt+1 )Fk (zt+1, s∗t+1 , h∗t+1 ) − t+1
+
s∗t+1

"
1−τ +Υ

ĩ∗t+1
s∗t+1

!#

)
Q∗t+1

The procedure starts with a guess for the values of the approximated functions Γ1 (st+1 ), Γ2 (st+1 ),Γ3 (st+1 ) and Γ4 (st+1 ). We first form a two dimensional grid for the endogenous states b̄ and s. Then foreach realization of the exogenous shocks—zt , ξt , zt∗ , ξt∗ —we guess the values taken by the above functions
over the grid points. Values outside the grid are obtained through bi-linear interpolation. Once we know
these functions, we can solve for the 18 unknowns of the system (26)-(41) at each grid point and foreach realization of the shocks. In finding the solutions we check whether the enforcement constraint isbinding (µt > 0) or not binding (µt = 0). We then use the solutions found at each grip point to update
the guess for the three functions. We keep iterating until the guesses for Γ1 (st+1 ), Γ2 (st+1 ), Γ3 (st+1 )and Γ4 (st+1 ) at each grid point are equal to the values obtained by solving the dynamic system.

38

References
Backus, D. K., Kehoe, P. J. and F. E. Kydland (1992). International Real Business Cycles.
Journal of Political Economy, 100(4), 74575.
Baxter, M. and R. G. King (1999). Measuring Business Cycles: Approximate Band-Pass
Filters for Macroeconomic Time Series. Review of Economics and Statistics, 81(4), 57593.
Chari, V. Kehoe P. and E. McGrattan (2007) Business Cycle Accounting, Econometrica,
75(3), 781-836
Dedola L. and G. Lombardo (2010). Financial frictions, Financial integration and the international propagation of shocks. Unpublished manuscript, European Central Bank.
Devereux, M. B. and J. Yetman (2010). Leverage Constraints and the International Transmission of Shocks. Unpublished manuscript, University of British Columbia and Bankof International Settlements.
Enders, Z., Kollmann, R. and G. J. Muller (2010). Global Banks and International Business
Cycle. Unpublished manuscript ECARES, Universite Libre de Bruxelles.
Gali, J. and L. Gambetti (2009) On the Sources of the Great Moderation. American Economic
Journal: Macroeconomics, 1(1), 26-57.
Heathcote, J. and F. Perri (2004), Financial Globalization and Real Regionalization. Journalof Economic Theory, 119(1), 207-43.
Helbling, T., Huidrom, R., Kose, M. A. and C. Otrok (2010). Do Credit Shocks Matter? A
Global Perspective. Unpublished manuscript, International Monetary Fund and University of Virginia.
Imbs, J. (2010). The First Global Recession in Decades. Unpublished manuscript, HEC
Lausanne.
Jermann, U. (1998). Asset Pricing in Production Economies. Journal of Monetary Economics, 41(2), 257-75.
Jermann, U. and V. Quadrini (2009). Macroeconomic Effects of Financial Shocks, NBER
Working Paper No. 15338.
39

Kiyotaki, N. and J. H. Moore (1997). Credit Cycles. Journal of Political Economy, 105(2),211-48.
Kiyotaki, N. and J. H. Moore (2008). Liquidity, Business Cycle, and Monetary Policy. Unpublished manuscript, Princeton University and Edinburgh University.
Mendoza, E. (2010). Sudden Stops, Financial Crises and Leverage. American Economic
Review, forthcoming.
Morgan, P., Rime, B. and P. Strahan, (2004), Integration and State Business Cycles. Quarterly Journal of Economics, 119(3), 1555-85.
Smets, F. R. and R. Wouters (2007). Shocks and Frictions in US Business Cycles: A Bayesian
DSGE Approach. American Economic Review, 97(3), 586-606.
Tauchen, G. (1986). Finite State Markov-Chain Approximations to Univariate and Vector
Autoregressions. Economic Letters 20(2), 177-81.

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