Global Imbalances and Lending Constraints in aStandard Real Business Cycle Model

Suparna Chakraborty�and Robert Dekley

February 16, 2007

AbstractDoes increased international liquidity, the "savings glut" explain the

recent deterioration of US current account balances? In this paper, wedevelop a simple, two country real business cycle model to answer thisquestion. The salient feature of our model is that lending by one countryis constrained by it�s wealth by a regulatory or institutional lending con-straint. We allow shocks to this lending constraint to capture a country�sability to lend as �nancial regulations evolve and the country�s �nancialmarkets develop. Applying our model to the test case of Japan (lender)and the US, we �nd that our general equilibrium model captures well, howdi¤erential productivity growth a¤ects the �ow of capital from the lend-ing country (Japan) to the U.S., and how the lending constraint interactswith productivity growth, to impact the borrowing country, or the U.S.current account.

1 Introduction

International liquidity and global current account imbalances are major topics ofconcern. According to the so-called "savings glut" view of Chairman Bernankeof the Federal Reserve Board, a combination of forces created a signi�cant in-crease in the global supply of saving, explaining both the relatively low level ofinternational interest rates and the increase in the U.S. current account de�cit(Bernanke, 2005). The U.S. current account de�cit has risen from a modest$120 billion in 1996 to $666 billion in 2005, and correspondingly the U.S. realinterest has fallen from about 4.3 percent in 2000 to about 1.8 percent in 2005.Bernanke attributes this expansion of the U.S. current account de�cit and fall inreal yields to an expansion of saving in Japan, Europe, and especially in emerg-ing Asia1 . In Japan and Europe, lower productivity growth relative to that in

�Dept. of Economics and Finance, Baruch College, CUNY. Please send correspondencesto suparna_chakraborty@baruch.cuny.edu

yDept. of Economics, University of South California and NY Fed1See Dekle, Eaton, and Kortum (2007) for how much exchange rates need to adjust in

the United States, Japan, China, and Germany to equilibrate the global current accountimbalances. See Chinn and Ito (2006) for a critical analysis of the "saving glut" view.

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the U.S. stimulated the out�ow of capital to the U.S. Although in emergingAsia, productivity growth is higher than in the U.S., in emerging markets, local�nancial markets are much shallower than U.S. �nancial markets, leading tocapital out�ows to the U.S., and the deterioration of the U.S. current account.In this paper, we develop a simple model of international liquidity and cur-

rent account imbalances. We develop a two country real business cycle model,in which lending by one country is constrained by that country�s wealth by aregulatory or institutional lending constraint. We de�ne wealth as the sum ofthe lending country�s capital stock and land. With this lending constraint, wetry to capture the role of �nancial market imperfections in the lending country.We allow shocks to this lending constraint, to capture a country�s ability to lend,as �nancial regulations evolve, and the country�s �nancial markets develop. We�nd that our general equilibrium model captures well, how di¤erential produc-tivity growth a¤ects the �ow of capital from the lending country to the U.S.,and how this lending constraint interacts with productivity growth, to impactthe borrowing country, or the U.S. current account.In our model, because of this lending constraint, shocks to a country�s wealth

impact net lending, and the current account in the borrowing country. This ad-ditional transmission mechanism through the lending channel o¤sets the initialimpact of the productivity shock on the current account in the borrowing coun-try. For example, suppose that a negative productivity shock hits the lendingcountry. This shock lowers investment opportunities in the lending country,and raises capital out�ows to the borrowing country, lowering global real inter-est rates, and increasing the current account de�cit in the borrowing country.However, with binding lending constraints, there is an o¤setting wealth e¤ect.The decline in wealth in the lending country lowers capital out�ows, and re-duces the current account de�cit in the borrowing country. Thus, whether thedecline in productivity of the lender results in an expansion of the current ac-count de�cit of the borrower, depends on the parameter values. For our chosenparameter values, we �nd that the �rst e¤ect dominates, a negative productiv-ity shock to the lender results in a deterioration of the current account in theborrowing country.In contrast to the e¤ects of productivity shocks� which tend to be small

because of the o¤setting e¤ects�we �nd large e¤ects on the borrower countrycurrent account, when shocks emanate from the lending constraints. One in-terpretation of say, a relaxation of the lending constraint is an increase in therelative attractiveness of borrowing country �nancial markets. For example,with a relaxation of capital out�ow restrictions, the �nancial markets of theU.S. will become more open to China and other emerging markets. We �ndthat a relaxation of the lending constraint will lead to a sharp increase in netlending, and a widening of the current account de�cit in the borrowing country.Thus, our model can explain how a widening of the U.S. current account canresult from the entry of large countries into the international lending market 2 .

2Another interpretation of the relaxation of the lending constraint is a change in regulatorycapital adequacy ratios, from a higher to a lower regulatory capital adequacy ratio. For

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The base model in this paper is a standard two country real business cyclemodel (Backus, Kehoe and Kydland (BKK, 1993)). The world comprises of twocountries denoted by superscript i 2 f1; 2g; the domestic country, country 1, andthe borrower country, country 2. Each country is composed of Nit i 2 f1; 2gin�nitely lived consumers, and an in�nite number of �rms. Firms are classi�edaccording to their types: the intermediate goods producing �rms and the �nalgood producing �rms. The countries trade in intermediate goods yji , j 2 f1; 2gwhere country i produces the intermediate good yii : The �nal good producing�rms use the intermediate goods to produce the �nal good yit; i 2 f1; 2g thatis used for domestic consumption, and investment in capital goods by the con-sumers. We assume that factors of production are immobile across geographicalborders. In addition to trading in intermediate goods, the countries can tradein one period international bonds. In terms of theory, our main contributionis that the amount of capital �ows to the borrower country is constrained by a"capital adequacy" requirement. As mentioned, this "capital adequacy" require-ment introduces another channel in which international productivity shocks arepropagated.

Since our results, particularly on the e¤ects of productivity shocks, is sen-sitive to parameter values, we calibrate our model to U.S. and Japanese databetween 1980 and 2004. We chose Japan as the "lender" country, since amongall countries, Japan had the largest cumulative current account balances be-tween the early 1980s and early 2000, and thus was the largest lender to theglobal economy during this period. In addition, Japan was marred by highly�uctuating land values during this period, which, it is alleged, a¤ected Japanesenet lending (Klein, Peek and Rosengren, 2000) Japan�s story of �uctuating assetvalues impacting international net lending �ts well the setup of our model.

In related work, Callesari (2007), Mendoza, Quadrini, and Rios-Rull (MQR,2006), Cavallo and Tille (2006), Faruquee, Laxton, Muir and Pesenti (2005), andCaballero, Farhi, and Gourinchas (CFG, 2006) are among the few that examinecurrent account imbalances in dynamic optimizing models. Of these papers,

example, the 2006 implementation of the Basel II accord in many countries is expected tolower on average, regulatory capital adequacy ratios for major international banks from 8 to6 percent.For our purposes, the main di¤erence between Basel II and Basel I (implemented in 1988)

is that in Basel II, banks will be able to set their own capital adequacy standards, based ontheir own assessement of credit risk. It was deemed recently by the Basel Committee that arigid application of Basel I risk weightings to bank assets is no longer necessary, as banks havedeveloped their own risk assessment models. For example, rather than force banks to weightindustrial loans as 0.70, and uncollateralized real estate loans as 1.0 as in Basel I, Basel IIwould let banks use their own risk assessment models to determine the relative weightings.Because the bank-speci�c internal risk assessment models tend to assign lower risk weights

to some assets heavy in bank portfolios such as mortgage lending, it is believed that theimplementation of Basel II will result in a lowering of the level of overall capital adequacystandards. For example, the Bank of International Settlements (BIS) estimates that afterBasel II, bank capital will on average decline by between 16 and 20 percent (BIS, 2006).

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only MQR (2006) and CFG (2006) emphasize the importance of �nancial struc-ture for global imbalances; and embed this structure in a general equilibrium,optimizing framework. Our paper is closest to CFG (2006), in that we empha-size �nancial imperfections in the lending country, while MQR (2006) emphasize�nancial imperfections in the borrowing country.3

This paper is organized as follows. In Section 2, we present our basic realbusiness cycle model with "capital adequacy" constraints. In Section 3, wecalibrate our model to the U.S. and Japanese economies, and present impulseresponses. We �nd that a negative productivity shock in Japan increases U.S.borrowing as does a positive productivity shock in the US. This in turn adverselya¤ects the U.S. current account, worsening the de�cits. In a similar manner,a positive shock to the capital adequacy constraint, say due to a relaxationof access to international capital markets has a very large positive impact onlending from Japan that in turn worsens the US current account. In Section 4,we perform quantitative experiments, to see how well our model matches theout�ow of capital from Japan, and the evolution of the U.S. current account inrecent years.

2 Theoretical Model

We describe below the economic problem facing agents in country 1 (country2 is analogous). The economic problem of both countries is similar exceptfor one di¤erence�land enters only in the economic problem of country 1. Weassume that land is used for consumption as well production, and the aggregateamount of land in the economy is normalized to one. Also, we abstract fromany government sector, so we do not have government expenditure or taxationin our model.

2.1 Consumer�s problem

The economic problem of the representative consumer in country 1; the "lendingcountry" can be summarized by:

E0

1Xt=0

�t1u1(c1t; l1t; h1t)

where �1 denotes the rate of time preference, consumption is given by c1t andleisure is denoted by 1�h1t. In addition to consumption and leisure, residentialland l1t also adds to a consumer�s utility.

3There are many two country general equilibrium papers that impose credit constraintsin a two country general equilibrium setting, but relatively few papers that impose creditconstraints on agents in the lending country, as we do here.

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Utility is maximized subject to the budget constraint:

c1t + k1t+1 � (1� �1)k1t + qt(lt+1 � lt) + st+1 � w1th1t + rk1tk1t + rl1tl2t +Rtst

Note that there are four sources of income for the consumer: wage incomew1th1t, returns to capital rk1tk1t, returns to land used for production r

l1tl2t and

�nally the interest earnings from international bonds Rtst. The wage rate w1t;the rental rates on capital and land, rk1t and r

l1t and the interest on lending Rt

are in terms of the �nal consumption good y1t that is used as the numeraire.After spending on consumption, the remainder of the income is spent on

investment in domestic physical assets (comprising of domestic capital and land)and in savings (or equivalently purchase of international bonds). Investment incapital is denoted by k1t+1� (1� �1)k1t where �1 is the rate of depreciation andthe investment in land is denoted by qt(lt+1 � lt) where qt is the price of landin terms of the numeraire. Every period, the consumer splits aggregate land ltinto its two alternative uses: l1t is the amount of land allocated for consumptionpurposes, and l2t is the amount of land that is allocated for production of theintermediate good.

In our formulation, savings are lent in the international market but aresubject to some restrictions such that:

st+1 � �t(kt+1 + qtlt+1)

where �t determines the fraction of wealth of the consumer that is investedin the international market. One interpretation of �t is that it embodies invest-ment opportunities in the international market. For example, in our model, anincrease in � implies an increase in the relative pro�tability of investment inthe international market, such that consumers channel an increased fraction oftheir wealth abroad. A possible reason for the increase in �t is that �nancialliberalization opens up new investment opportunities outside of the domesticeconomy.

Another possible interpretation of the lending constraint comes from inter-national banking regulations. One way of interpreting the lending constraint isto say that every period the lender has to keep in reserve or maintain a capitalreserve equal to 1 � �t fraction of its assets which implies that lending cannotexceed �t fraction of its assets. In our model the asset holding of the lender isequal to the total amount of capital and land held. Hence the maximum amountthat the lender can lend any period is bound by the upper limit �t(kt+1+qtlt+1):Here, �t is determined by international laws (for example those mandated byBasel accords) as well as domestic government policies. An increase in � denotesa relaxation of the capital adequacy requirement, thus allowing agents to lendmore in the international market.

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2.2 Representative intermediate good producing �rm�s prob-lem

The representative �rm that produces the intermediate good y11 owns a Cobb-Douglas production technology. Every period the �rm hires labor, land andcapital to produce the intermediate good that is then sold domestically andinternationally to the �nal good producing �rms.

Every period the representative �rm maximizes pro�t:

�11t = p11ty

11t � w1th1t � rk1tk1t � rl1tl2t

subject to the production constraint:

y11t � A1tF1(k1t; l2t; h1t)

where �11t denotes the period t pro�ts of the representative intermediategoods producing �rm and p11t is the period t price of the intermediate good y

11t

in terms of the numeraire. A1t denotes the time varying productivity in country1:

In addition to the intermediate goods producing �rms, the country is alsopopulated by an in�nite number of �nal good producing �rms.

2.3 Representative �nal good producing �rm�s problem

A �nal goods producing �rm uses domestic and foreign intermediate goods toproduce the �nal good y1 using an aggregation technology.The representative �rm maximizes pro�ts:

�1t = y1t � p11tc11t � p12tc12tsubject to the production constraint.

y11t � G(c11t; c12t)

where �1t denotes the period t pro�ts of the representative �nal goods pro-ducing �rm, c11t is the amount of domestically produced intermediate good usedto produce the �nal good and c12t is the amount of the intermediate good pro-duced in country 2 that is used in the production of the �nal good. p11t andp12t is the period t price in country 1 of the intermediate goods in terms of thenumeraire.G(:) denotes the aggregation technology.

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2.4 Resource Constraints and Equilibrium

The resource constraints on �nal goods in country i; i 2 f1; 2g is given by:

yit = cit + kit+1 � (1� �i)kit

The current account of country i is the sum of net exports and the interestearnings on international bonds, or (pjitc

jit � pijtcijt) + rtsit:

Note that in equilibrium:

sit+1 � sit = pjitcjit � pijtcijt + rtsit

or that net lending is equal to the current account. One way to interpret thisresult is that if the current account exhibits a surplus, then the income receivedby a country in exports and interest on bonds purchased last period exceedsthe income spent by the country on its imports. One way to use the surplusmoney is to buy more international bonds. Equivalently, for the borrower, ifthe expenditure on imports and interest on borrowings exceed the income fromexports, a country will have an incentive to borrow to meet its current oblig-ations. Thus for the lender, an increase in out�ow of funds is associated withan improvement of the current account. Analogously, an increase in borrowingdeteriorates the current account balance of the borrowing nation.

We denote the terms of trade as the ratio of the price of intermediate goodsin the two countries, or p11t

etp22twhere et is the real exchange rate.

In equilibrium, the law of one price holds such that:

et =p11tp21t

=p12tp22t

In addition, the resource constraint on land in country 1 is denoted by :

N1t(l1t + l2t) = 1

which indicates that the aggregate amount of land in the economy is �xedand is normalized to one.

The world resource constraint on traded intermediate goods are denoted by:

N1ty11t = N1tc

11t +N2tc

21t

N2ty22t = N1tc

12t +N2tc

22t

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Finally the constraint on international borrowing and lending is denoted by:

N1tst = N2tbt

An equilibrium in this economy is given by a set of allocations:fc1t; c2t; y1t; y2t; k1t+1; k2t+1; l1t+1; l2t+1; h1t; h2t; st+1; bt+1; y11t; c11t;c21t; y

22t; c

12t; c

22tg and a set of prices fet; p11t; p21t; p12t; p22t; w1t; w2t; rk1t; rk2t;

rl1t; Rt; qtg such that given the set of prices, the equilibrium set of allocationssolve representative consumers and the �rms problem in each country and theresource constraints are satis�ed.

A balanced growth for this economy occurs when all allocation variablesin country i except for the variables fhit; ltg grow at the rate of long termtechnical progress denoted by i. The per capita labor supply hit is constant inthe steady state while the variable lt or per capita land holdings in country 1decreases at the rate �1 where �1 is the population growth rate that is assumedto be constant. As for the price variables along the balanced growth path allthe price variables except for fw1t; w2t; qtg remain constant. The wage rateswit increase at the rate i and the land price qt increases at the rate 1�1:

3 Quantitative Results

To derive the quantitative implications of our model, we use the technique of loglinearization by King, Plosser and Rebelo(1988). To apply the log-linearizationtechnique we �rst prove the su¢ cient condition for the lending constraint to holdwith equality, which is summarized in the Proposition below. The condition forthe lending constraint to bind can only be analytically established for the steadystate

Proposition 1 The lending constraint will bind in the steady state when �1 >�2

Proof. The formal proof is in Appendix One. The logic is as follows: �1 > �2implies that country 2 is more impatient than country 1. This creates an incen-tive for country 2 to borrow from country 1. In the absence of any borrowingconstraint, country 2 will ideally want to borrow as much as possible. However,country 1 will face an upper limit on the amount that it can lend to country 2and the lending constraint will bind.

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3.1 Calibration

For our quantitative analysis, we use the following speci�c utility and productionfunctions:

u1(c1t; l1t;h1t) =

�c�11t l

�31t (1� h1t)1��1��3

�1��1� � ; � > 1

= �1 log c1t + �3 log l1t + (1� �1 � �3) log(1� h1t); � = 1

u2(c2t; h2t) =

�c�22t (1� h2t)1��2

�1��1� � ; � > 1

= �2 log c2t + (1� �2) log(1� h2t); � = 1

F1(k1t; l1t; h1t) = k�1k1t l�1l2t h

1��1k��1l1t

F2(k2t; h12t) = k�2k2t h1��2k2t

G(c11t; c12t) =

h!�c11t��+ (1� !)(c12t)�

i 1�

G(c21t; c22t) =

h!�c22t��+ (1� !)(c21t)�

i 1�

We calibrate our model parameters such that the steady state moments fromthe model match the moments of the data. We take country 1 to be Japan andcountry 2 to be US.4 The steady state period is assumed to be 1980 to 1984.For our analysis, we assume no population growth and the long term averagegrowth rate of U.S. and Japan is 2%5 . Further, the per capita GDP in Japanis 70% of the per capita GDP of the U.S.For our baseline, we begin by assuming � = 2 and � = �:5 which is taken

from BKK(1993). The average interest rate R = 1:06 which yields �2 = :9815:Given Proposition 1, we assume the rate of time preference in country 1 �1 = :99such that �1 > �2. The average capital to output ratio in Japan is 1.8 and the

4All data for Japan are from the Japan Statistical Yearbook; and all data for the U.S. arefrom the Bureau of Economic Analysis.

5Business cycle literature commonly takes the long run growth rate on the balanced growthpath to be 2% that is the long run growth rate of per capita GDP in the US. As for Japan,Hayashi and Prescott (2002) assumes the long run growth rate to be the same as that of US,i.e. 2%.

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average investment to output ratio is .22 during the steady-state period. Thisyields a rate of depreciation �1 = :1022: The average share corporate land inoutput is .98; and the value of residential land in output 1.67. The net lendingby Japan to the rest of the world is 1.8% of its GDP. The U.S. has been oneof the major recipients of Japanese net lending, so we take the share of netlending to U.S. as a ratio of Japanese output to be 1.8% (or in our formulation,U.S. represents the rest of the world). Given the share of capital, land andnet lending in output, the steady state capital adequacy ratio or � = :0041: Inaddition , we estimate the share of capital in output of country 1, or �1k = :2756;and the share of land in output, or �1l = :0255: The share of labor in output,or �1h = :6989: Given that the share of residential land in Japan is 63% of totalland and workers in Japan spend 33% of their time working, the elasticity ofsubstitution between consumption and land, or �3 = :0225; and the elasticityof substitution between consumption and labor or �1 = :3469:

We further assume that import share of output is 12.8% in Japan and 8.6%in United States. The values are taken from the World Development Indicators.Given our assumption, ! = :9613; which indicates a strong home bias. As forthe remaining parameters �2k = :36, �2h = :64 and �2 = :1 as in BKK(1993).Furthermore, assuming that in United States, workers spend one-third of theirtime at work yields an elasticity of substitution of consumption and leisure of�2 = :3596: We summarize the calibrated parameters in Table 1.

Given Proposition 1, we assume that the capital adequacy constraint bindsin the neighborhood of the steady state which allows us to solve the model usinglog-linearization technique. For our analysis, we assume a vector autoregressiveprocess of order one for the log deviations of productivities A1t and A2t and thedeviation of capital adequacy ratio �t from their respective steady states.Summarizing the VAR processes:

ea1t+1 = �a1ea1t + �1t+1ea2t+1 = �a2ea2t + �2t+1e�t+1 = ��e�t + ��t+1

where we de�ne:

ea1t = logA1t � logA1ea2t = logA2t � logA2e�t = �t � �

The error terms are assumed to be i.i.d.

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3.2 Impulse Responses

To analyze the properties of the model, we examine impulse responses.

Given the theoretical model we expect the following to occur:(1) A decline in productivity in Japan or the lending nation would on the

one hand create an incentive for out�ow of funds to be invested in the interna-tional market which would lead to a deterioration of the current account of theborrower. At the same time, reduced productivity of the lender in the presenceof binding lending constraint, reduces lending (as wealth declines) that wouldlead to an improvement in the current account of the recipient country. The�nal e¤ect on the current account depends on which e¤ect dominates.(2) An increase in productivity of the borrower would increase the incentive

for the lender to lend more by making investment opportunities in the borrowingcountry more lucrative. The current account of the borrower is expected todeteriorate.(3) Finally, an increase in the "capital-adequacy" or "loan to value" ratio �

will relax international lending constraints encouraging an out�ow of funds anddeteriorating the current account of the borrower.

Does our impulse responses predict the same?

Given the time series on capital, labor and the land used by the corporatesector in Japan, we estimate the productivity of Japan as a Solow residual.In addition, given the amount of net lending by Japan, we can estimate thetime series of the loan to value ratio or �: The productivity series in U.S. isalso estimated as a Solow residual, but without land as a factor of production.Given the time series thus constructed, we estimate �a1 = :93; �a2 = :91 and�� = :67: Since we are working with annual data, and are interested in theperiod 1980 to 2004, we set the length of our simulation series to be 25. Weare primarily interested in the e¤ect of exogenous shocks on three variables, thecurrent account of country 2, (current2); the interest rate, (interest); and theamount of borrowing, or (borrow). The results are plotted in Figures 1 to 3.

In Figure 1 we plot the response to a 1% negative shock to A1. A declinein the productivity of country 1 has two opposing e¤ects: a decline in produc-tivity reduces the returns to domestic investment providing an incentive for anout�ow of funds from country 1 that causes the current account of country 2(the recipient country) to deteriorate. On the other hand, reduction in produc-tivity reduces the wealth of country 1 that in the presence of a binding lendingconstraint would reduce the out�ow of funds and improve the current accountof country 2 In this case, the �rst e¤ect dominates the second, there is a .3%increase in out�ow of funds on impact that continues for a couple of periodsbefore declining and the current account of country 2 further deteriorates. Theglobal real interest rate for its part reduces by 10%.

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When there is a 1% positive shock to A2 as Figure 2 outlines; investmentopportunities in country 2 become more attractive, resulting in the �ow ofcapital from country 1 to country 2. Consequently borrowing by country 2increases, resulting in a worsening of the current account by .004%. The realinterest rate increases by 25%.The external shock that we are most interested in is a change in the capital

adequacy ratio, or �:A 1% positive shock to � (that denotes a relaxation ofrestrictions on international lending) sharply increases the lending by country2, and worsens the current account by -3%. The interest rate sharply increaseson impact, before gradually declining (Figure 3).

4 Application: The case of United States andJapan

To evaluate the performance of our model quantitatively, we compare our modelpredictions with data. Our period of interest is 1980 to 2004. The stylized factsfrom Japan and the US that we try to match are summarized in Figures 4 to6. The exogenous shocks in our model as estimated from the data and the �rstorder conditions of our model are plotted in Figures 7 and 8.

4.1 Stylized facts

Figure 4 depicts the �uctuations in output per worker in Japan and the USwith respect to the long term trend. The long run growth rate is taken as 2%.The eighties was a period of boom both in Japan and in the U.S However,since 1991, the growth paths of Japan and the U.S. diverged, as U.S. outputrecovered and grew robustly, while Japanese output growth stagnated. As fornet lending by Japan to the rest of the world as a share of output (Figure 5),it is almost countercyclical to Japanese output growth and quite volatile. Since1996, the net lending almost monotonically increases except for a brief declineduring 1998. As for current account in US as a share of output (Figure 6), we�nd that in the early eighties, US current account de�cit increased but the trendreversed in late eighties. Since 1991, the current account de�cit has worsenedand the rate of increase in de�cit has picked up since 1996.

Comparing the trends in US current account with the net lending by Japan,we notice that the trend is almost countercyclical as expected (except for a briefperiod of 1992 to 1996). During the early eighties, Japanese net lending as ashare of GDP increased and so did the US current account de�cit. The lateeighties were a period of decline in Japanese net lending which also coincideswith an improvement in US current account. Since 1996, Japanese net lending

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has pretty much increased (though it is quite volatile), and the US current ac-count de�cit shows a monotonic increase. We suspect that the 1990s, especiallythe period after 1996 saw a lot of in�ow of funds in the US from the emergingAsian economies and later, China. Hence, even though the Japanese lendingshows �uctuations, US current account de�cit increased due to in�ux of the newsources of funds.

There are three possible sources of external shocks in our model: shocks toproductivities in U.S. and in Japan (measured as a Solow residual); and shocksto the loan-to-value ratio (measured as the ratio of net lending to aggregatewealth). We plot the U.S. and Japanese productivities, and the loan-to-valueratios in Figures 7 and 8. We �nd that productivities follow the same patternas the �uctuations in output. As for the loan-to-value ratio, it is quite volatile,and countercyclical to Japanese output growth. At the same time, loan to valueratio is also countercyclical to US current account (an increase in loan to valueratio corresponds to a deterioration of the US current account and vice-versa).

4.2 Results of the quantitative analysis

The model predictions resulting from feeding in the exogenous shocks bothindividually and in combination are plotted in Figures 9 to 12.In Table 2 we summarize the real business cycle properties of our model and

data. The standard deviations of output per capita in Japan and in the U.S.are 5.8 and 2.76, respectively. Feeding in productivity �uctuations in Japan asestimated from the data in our model, we get a standard deviation of outputper capita of 9.75 in Japan and 6.61 in U.S, and feeding in �uctuations in USproductivity, our model predicts a standard deviation of output of .1 in Japanand 1.74 in the US. If we feed in the time series of �t in our model, the standarddeviation of output in Japan reduces to .62, and that in the U.S. reduces to .18.Feeding in all three wedges jointly, the standard deviation of output in Japan is9.69 while it is 6.69 in US. A pictorial depiction is presented in Figures 9 and10. In international macro literature, the correlation of output across nationshas been another area of concern. According to data, the correlation of outputin Japan and US between 1980 and 2004 was .058. With productivity shocksfed individually, the model predicts a correlation of -.94 (with A1 alone) and-.96 (with A2 only). If we feed in � alone, we can bring down the correlation to-.28, a number much closer to the data. Feeding in the time series of all wedgesjointly, the correlation predicted by the model is -.91.We are mostly interested in the evolution of net lending by Japan and its

consequent impact on the U.S. current account. In Figures 11 and 12, wedepict how our model can explain Japanese net lending, or if we take the twocountry model literally, the U.S. current account. The standard deviation ofthe current account is .016 and that of net lending as a share of output is.0094. Productivity shocks individually are not very successful in generating

13

net lending or current account to match the data. Our model performanceimproves when we feed in the time series of �: Thus, when we feed in all threeshocks, we �nd that our model explains Japanese net lending or capital out�owsquite well. As Table 2 depicts, the standard deviation of current account asa share of output is .016. Feeding in all the frictions, or model predicts astandard deviation of .0042, with �uctuations in �t playing an important role.The model does not do a very good job explaining the actual U.S. currentaccount, especially since 1994 (as outlined in Figure 12). This is probablybecause the "rest-of-world" for Japan is actually not just the U.S., and thishas been especially true since the mid-1990s, with the emergence of China as aglobal lender as discussed in section 4.1.

5 Conclusion

The issue of global current account imbalances is a major cause of concern inthe academic and policy making circles today. One possible explanation for thisphenomenon might be international liquidity, or the "savings glut" as proposedby Chairman Bernanke. The intuition is that a combination of forces includinglack of domestic investment opportunities in Asia in the aftermath of the AsianCrisis and an easier access to international �nancial markets created a signi�cantincrease in the global supply of saving, explaining both the relatively low level ofinternational interest rates and the increase in the U.S. current account de�cit.

In this paper, we develop a simple model of international liquidity and cur-rent account imbalances. We develop a two country real business cycle model,where lending by one country is constrained by it�s wealth by a regulatory orinstitutional lending constraint. We allow shocks to this lending constraint, tocapture a country�s ability to lend, as �nancial regulations evolve, and the coun-try�s �nancial markets develop. We �nd that our general equilibrium modelcaptures well, how di¤erential productivity growth a¤ects the �ow of capitalfrom the lending country to the U.S., and how this lending constraint interactswith productivity growth, to impact the borrowing country, or the U.S. currentaccount. In our model, because of this lending constraint, shocks to a country�swealth impact net lending, and the current account in the borrowing country.

We test the performance of our model by applying it to US and Japan duringthe period 1980 to 2004. Throughout this period, Japan has been a net lenderto United States. At the same time, this period marks upheavals in Japanesedomestic market which in turn a¤ected the amount of its lending to the US.Thus it provides us an ideal test case.

We �nd that productivity �uctuations by themselves in our model contexthave a small e¤ect on US current account. We suspect the e¤ect is small due to

14

o¤setting e¤ects: for example, a reduction in productivity in Japan creates anincentive for out�ow of funds which causes current account of US to deteriorate,but at the same time, a binding lending constraint implies that a reduction inwealth (as a result of reduced productivity) reduces the amount Japan canlend internationally thus improving the current account of US. The impact oncurrent account depends on which e¤ect dominates. In our case though theformer dominates but the magnitude is much smaller (due to the opposingwealth e¤ect on lending).In contrast to the e¤ects of productivity shocks, we �nd large e¤ects on

the borrower country current account, when shocks emanate from the lendingconstraints. One interpretation of say, a relaxation of the lending constraint isan increase in the relative attractiveness of borrowing country �nancial mar-kets. For example, with a relaxation of capital out�ow restrictions, the �nancialmarkets of the U.S. became more open to China and other emerging markets.We �nd that a relaxation of the lending constraint will lead to a sharp increasein net lending, and a widening of the current account de�cit in the borrowingcountry. Thus, our model can explain how a widening of the U.S. current ac-count can result from the entry of large countries into the international lendingmarket.

15

References

[1] Backus, David K & Kehoe, Patrick J & Kydland, Finn E, 1992, "Interna-tional Real Business Cycles," Journal of Political Economy, University ofChicago Press, vol. 100(4), pages 745-75

[2] Bernanke, Ben S, 2005, "The Global Saving Glut and the U.S. CurrentAccount De�cit", Sandridge Lecture, Virginia Association of Economists,Richmond, Virginia

[3] Caballero, Ricardo, Emmanuel Farhi and Pierre-Olivier Gourinchas, 2006,"An Equilibrium Model of �Global Imbalances�and Low Interest Rates,"NBER Working Paper 11996

[4] Cavallo, Michele and Cédric Tille, 2006, "Could capital gains smooth a cur-rent account rebalancing?," Federal Reserve Bank of San Francisco WorkingPaper 2006-03

[5] Chinn, Menzie and Eswar S. Prasad, 2000, "Medium-Term Determinantsof Current Accounts in Industrial and Developing Countries: An EmpiricalExploration," NBER working paper No. 7581

[6] Chinn, Menzie, 2005, "Getting Serious about the Twin De�cits," SpecialCouncil Report No. 10 (Council on Foreign Relations)

[7] Edwards, Sebastian, 2004, "Thirty Years of Current Account Imbalances,Current Account Reversals, and Sudden Stops," IMF Sta¤ Papers Vol. 51,Special Issue

[8] Edwards, Sebastian, 2005, "Is The U.S. Current Account De�cit Sustain-able? And If Not, How Costly Is Adjustment Likely To Be?," NBER Work-ing Paper 11541

[9] Engel, Charles and John H. Rogers, 2006, "The U.S. Current AccountDe�cit and the Expected Share of World Output," Federal Reserve BoardInternational Finance Discussion Paper 2006-856

[10] Faruqee, Hamid, Douglas Laxton, Dirk Muir, and Paolo Pesenti, 2005,"Smooth landing or crash? Model-based scenarios of global current ac-count rebalancing," Revised draft of the paper presented at the NBERconference on G-7 Current Account Imbalances: Sustainability and Ad-justment, Newport

[11] Frankel, Je¤rey A., 2006, "Global Imbalances and Low Interest Rates: AnEquilibrium Model vs. a Disequilibrium Reality"

[12] Goldberg, Linda S. and Cédric Tille, 2006, "The Internationalization of theDollar and Trade Balance Adjustment," Federal Reserve Bank of New YorkSta¤ Reports 255

16

[13] Gourinchas, Pierre-Olivier and Helene Rey, 2005, "International FinancialAdjustment," NBER Working Paper No. 11155

[14] Gourinchas, Pierre-Olivier and Helene Rey, 2005, "From World Banker toWorld Venture Capitalist: The US External Adjustment and the Exorbi-tant Privilege," Paper presented at the NBER conference on G-7 CurrentAccount Imbalances: Sustainability and Adjustment, Newport

[15] King, Robert, Charles Plosser, and Sergio Rebelo, 1988, �Production,Growth and Business Cycles: I. the Basic Neoclassical Model,� Journalof Monetary Economics, 21: 195-232

[16] Klein, Michael W., Peek, Joe and Rosengren, Eric S., 2002, "TroubledBanks, Impaired Foreign Direct Investment: The Role of Relative Accessto Credit," American Economic Review, American Economic Association,vol. 92(3), pages 664-682, June.

[17] Mendoza, Enrique G., Vincenzo Quadrini and José-Víctor Ríos-Rull, 2006,"Financial Integration, Financial Deepness and Global Imbalances"

[18] Obstfeld Maurice and Kenneth Rogo¤, 2001, "Perspectives on OECD Cap-ital Market Integration: Implications for U.S. Current Account Adjust-ment," Federal Reserve Bank of Kansas City Global Economic Integration:Opportunities and Challenges, pp. 169-208. (Paper presented at a sympo-sium sponsored by the Federal Reserve Bank of Kansas City, at JacksonHole, Wyoming, August 24-26, 2000)

[19] Obstfeld Maurice and Kenneth Rogo¤, 2005, "Global Current Account Im-balances and Exchange Rate Adjustments," William Brainard and GeorgePerry (eds.) Brookings Papers on Economic Activity 1:67-146

[20] Obstfeld, Maurice and Kenneth Rogo¤, 2005, "The Unsustainable US Cur-rent Account Position Revisited," Paper prepared for NBER conference onG-7 Current Account Imbalances: Sustainability and Adjustment, Newport

17

Table 1: Model Parameters

Parameters Description ValuesCountry 1 Country2

�3 Elasticity of substitution .0225 -between consumption and land

�i; i 2 (1; 2) Elasticity of substitution .3483 .3596between consumption and leisure in country1

�i; i 2 (1; 2) Rate of time preference .99 .9815�i; i 2 (1; 2) Rate of depreciation .1022 .1�ik; i 2 (1; 2) Share of capital in output .2756 .36�1l Share of land in output in country 1 .0297 -�ih; i 2 (1; 2) Share of labor in output .6947 .64� Capital adequacy ratio .0052 -� Curvature of the utility function 2 2� Armington elasticity -.5 -.5! Home-bias .9613 .9613

Note: The parameters are calibrated such that the moments from the model matchthe moments from the data where the data is collected from the National IncomeAccounts of US and Japan.

Source of data: Japan Statistical Yearbooks and Economic Social Research Insti-tute(ESRI) for Japan and Bureau of Economic Analysis for US. In addition, to getdata on trade balances, we also look at World Development Indicators.

18

Table 2: Real business cycle properties of data and model

Standard deviation Correlationy11 y22

s1y11

current2 (y11 ; y22) (current2; s1)

(output ) (output ) (Net Japanese (Currentlending as a a/c of US)

of Japan of US share of GDP)Data 5.8 2.76 .0094 .016 .058 -.69Model (with A1 only) 9.64 6.55 .0012 .0001 -.94 -.09Model (with A2 only) .1 1.74 .00003 .00004 -.96 -.39Model (with � only) .4 .09 .008 .0044 -.28 -.58Model (all frictions) 9.61 6.62 .0076 .00416 -.91 -.577

Note: The data is taken from US and Japanese national accounts. We take thestandard deviation and correlation of the data over the period 1980 to 2004. We solveour model to get the decision rules. We feed in the exogenous shocks to productivitiesin Japan and the US and the time series of loan to value ratio or � individually andjointly in our model to get the model predictions

19

Figure 1: Impulse response to a 1% negative shock to A1

0 5 10 15 200

0.1

0.2

0.3

0.4

Response to tech1

Periods

% d

evia

tion 

from

 SS

borrowborrowborrow

0 5 10 15 20­10

­5

0

5

10

Response to tech1

Periods

% d

evia

tion 

from

 SS

interestinterestinterest

0 5 10 15 20­0.01

­0.005

0

0.005

0.01

0.015

0.02Response to tech1

Periods

% d

evia

tion 

from

 SS

current2current2current2

Note: This is the benchmark case when import share of United States in its GDPis 8.6% and that of Japan is 12.8% (the �gures are from World Development Indi-cators). The persistence parameter �a1 is .93 where we measure productivity as aSolow Residual (data collected from Japan Statistical Yearbooks and the Economicand Social Research Institute). We set the simulation period to 25 to match the dataand we run 1000 simulations .

20

Figure 2: Impulse response to a 1% positive shock to A2

0 5 10 15 200

0.02

0.04

0.06

0.08

0.1Response to tech2

Periods

% d

evia

tion 

from

 SS

borrowborrowborrow

0 5 10 15 20

­10

­5

0

5

10

15

20

25Response to tech2

Periods

% d

evia

tion 

from

 SS

interestinterestinterest

0 5 10 15 20­2

­1.5

­1

­0.5

0

0.5

1x 10

­3Response to tech2

Periods

% d

evia

tion 

from

 SS

current2current2current2

Note: This is the benchmark case when import share of United States in its GDP is8.6% and that of Japan is 12.8% (the �gures are from World Development Indicators).The persistence parameter �a2 is .91 where we measure productivity as a Solow Resid-ual (data collected from National Income and Product accounts of United States). Weset the simulation period to 25 to match the data and we run 1000 simulations .

21

Figure 3: Impulse response to a 1% positive shock to �

0 5 10 15 200

50

100

150

Response to phi

Periods

% d

evia

tion 

from

 SS

borrowborrowborrow

0 5 10 15 20

0

20

40

60

80

Response to phi

Periods

% d

evia

tion 

from

 SS

interestinterestinterest

0 5 10 15 20

­2

­1.5

­1

­0.5

0

0.5

Response to phi

Periods

% d

evia

tion 

from

 SS

current2current2current2

Note: This is the benchmark case when import share of United States in its GDP is8.6% and that of Japan is 12.8% (the �gures are from World Development Indicators).The persistence parameter �� is .67 as measured from data on net lending by Japan(collected from Japan Statistical Yearbooks and the Economic and Social ResearchInstitute). We set the simulation period to 25 to match the data and we run 1000simulations .

22

Figure 4: Output per working age population in United States andJapan detrended at 2%

Output in US & Japan

60

65

70

75

80

85

90

95

100

105

110

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Inde

x (U

S G

DP 

in 1

980=

100)

Output in USOutput in Japan

Note: We plot the deviations in output per working population from the long termgrowth rate (2%) where working population is taken as population aged 15 to 64.The data of US is from the NIPA accounts and that of Japan is from the nationalincome statistics of Japan Statistical Yearbook (also consistent with data from ESRI)converted to US dollars in chained 2000 prices. We take the output of US in 1980 andplot the index.

23

Figure 5: Net lending by Japan to the rest of the world as a shareof Japanese output

Share of net lending in gdp

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Shar

e

Share of net lending in gdp

Note: We get the net lending to rest of the world from �nancial accounts of Japanand express it as a share of GDP. United States is one of the largest recipients ofJapanese funds.

24

Figure 6: Current account of US as a share of US output

­0.06

­0.05

­0.04

­0.03

­0.02

­0.01

0

0.01

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Current a/c as a share of GDP

Note: The current account of US is expressed as a share of US GDP. A negativenumber denotes a current account de�cit.

25

Figure 7: Time series of productivity measured as a Solow residual

Index of Productivity

80

85

90

95

100

105

110

115

120

125

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Inde

x (1

980=

100)

Productivity in USProductivity in Japan

Note: There are three sources of exogenous shocks in our model: �uctuations inproductivities in United States and Japan are two of them We calculate productivityas the Solow residual assuming a Cobb-Douglas production function. We plot theindex of productivities in Japan and United States assuming that the productivitiesof the respective countries in 1980 are normalized to a 100.

26

Figure 8: Time series of �

Loan to value ratio

0

0.002

0.004

0.006

0.008

0.01

0.012

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Valu

e

Loan to value ratio

Note: Time series of loan to value ratios are calculated as the ratio of net lending byJapan to the aggregate wealth of the economy. The aggregate wealth is calculated asthe sum of the capital stock and the value of aggregate land (comprised of Residentialand Commercial land) in a given time period.

27

Figure 9: Output per working population in Japan - data andmodel predictions

80

85

90

95

100

105

110

115

120

125

130

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Inde

x (1

980=

100)

y1­data y1­model (A1 only) y1­model (A2 only)y1­model (phi only) y1­model (all frictions)

Note: We plot the performance of our model vis a vis the data on output perworking population in Japan. The time series is detrended at 2% (the long run growthrate). We set the output in 1980 to be 100. We feed in various combinations of theshocks and plot the model predictions. The di¤erent combinations are outlined in thelegend.

28

Figure 10: Output per working population in United States - dataand model predictions

75

80

85

90

95

100

105

110

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Inde

x (1

980=

100)

y2­data y2­model(A1 only) y2­model(A2 only) y2­model(phi only) y2­model(all frictions)

Note: We plot the performance of our model vis a vis the data on output perworking population in United States. The time series is detrended at 2% (the long rungrowth rate). We set the output in 1980 to be 100. We feed in various combinationsof the shocks and plot the model predictions. The di¤erent combinations are outlinedin the legend.

29

Figure 11: Net lending as a ratio of output - data and modelpredictions

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Shar

e of

 out

put

net borrow­data net­borrowing­model(A1only) net­borrowing­model(A2 only)net­borrowing­model(phi only) net­borrowing­model(all frictions)

Note: We plot the performance of our model vis a vis the data on net lending byJapan as a share of Japanese output. We feed in various combinations of the shocksand plot the model predictions. The di¤erent combinations are outlined in the legend.

30

Figure 12: Current a/c as a ratio of output (US)- data and modelpredictions

­0.07

­0.06

­0.05

­0.04

­0.03

­0.02

­0.01

0

0.01

0.02

0.03

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Shar

e of

 out

put

Current a/c­data Current a/c­ model(A1only) Current a/c­ model(A2 only)Current a/c­ model(phi only) Current a/c­ model(all frictions)

Note: We plot the performance of our model vis a vis the data on Current Accountof United States as a share of US output. We feed in various combinations of the shocksand plot the model predictions. The di¤erent combinations are outlined in the legend.

31

APPENDIX A

To prove proposition one, we need to solve the consumer�s problem in countryone and twoLagrangian for the consumer�s problem in country 1:

$1 =

2664 E01Pt=0�t1u(c1t; l1t; h1t)

+�1t�t1(w1th1t + r

k1tk1t + r

l1tl2t +Rtst � c1t � k1t+1 + (1� �1)k1t � qt(l1t+1 � l1t)� st+1

+�1t�t1(S(t+ 1)� s(t+ 1))

3775where �t1�1t is the lagrange multiplier on budget constraint and �1t�

t1 is the

lagrange multiplier on the capital adequacy requirement.To prove proposition one, we need the �rst order condition with respect to

savings: �Rt+1�

t+11 �1t+1 � �t1�1t � �1t�t1

��1t�

t1 = 0

Given � > 0; the above equation reduces to�Rt+1�

t+11 �1t+1 � �t1�1t � �1t�t1

��1t = 0

which in the steady-state reduces to:

(R�1 � (1 + gz)� � �1)�1 = 0where the average long term growth rate of the economy is gz and � is the

curvature of the utility function.Borrowing constraint binds in the steady state if � > 0:

Lagrangian for the consumer�s problem in country 2:

$2 =

24 E01Pt=0�t2u(c2t; h2t)

+�2t�t2(w2th2t + r

k2tk2t �Rtbt � c2t � k2t+1 + (1� �2)k2t + bt+1

35The �rst order condition with respect to borrowing reduces to:�

�t2�2t �Rt+1�t+12 �1t+1�= 0

In the steady-state,

R =(1 + gz)

�

�2

Then

32

� > 0) (R�1 � (1 + gz)� � �1) = 0) �1 = R�1 � (1 + gz)�Substituting for R;

�1 =(1+gz)

�

�2�1 � (1 + gz)�

�1 = (1 + gz)���1�2� 1�

Then �1 > 0

) (1 + gz)���1�2� 1�> 0

)��1�2� 1�> 0 or

�1 > �2

33