external shocks and debt accumulation in a small open economy

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Review of Economic Dynamics 6 (2003) 207–239 www.elsevier.com/locate/red External shocks and debt accumulation in a small open economy Abdelhak S. Senhadji International Monetary Fund, 700 19th Street, N.W., Room IS3-1220, Washington, DC 20431, USA Received 19 April 2000 Abstract This paper analyzes the borrowing behavior of a small open economy of a Less Developed Coun- try (LDC) that relies heavily on imports for its capital formation and faces an upward sloping sup- ply function of foreign loans, in an environment where decision makers face uncertainty about the longevity of external shocks. First, a dynamic general equilibrium model is developed which repli- cates fairly well the business cycle properties of the LDC data. Second, it is shown that uncertainty concerning the longevity of shocks (a relevant type of uncertainty, especially for LDCs) generates forecast errors that are autocorrelated in a way that is similar to Bayesian learning in the “peso problem.” This autocorrelated forecast errors can generate substantial debt accumulation. Third, it is shown that the assumption of an upward sloping supply function of foreign loans, which is a more realistic assumption for LDCs than the usual perfectly elastic one, offers an alternative to the Uzawa- type utility function for the analysis of asset accumulation in the small open economy framework. 2002 Elsevier Science (USA). All rights reserved. JEL classification: F41; O16; D58; G15 Keywords: Debt accumulation; Stochastic dynamic general equilibrium model; External shocks; Incomplete information; Less Developed Economies E-mail address: [email protected]. 1094-2025/02/$ – see front matter 2002 Elsevier Science (USA). All rights reserved. doi:10.1016/S1094-2025(02)00015-7

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Page 1: External shocks and debt accumulation in a small open economy

Review of Economic Dynamics 6 (2003) 207–239

www.elsevier.com/locate/red

External shocks and debt accumulationin a small open economy

Abdelhak S. Senhadji

International Monetary Fund, 700 19th Street, N.W., Room IS3-1220, Washington, DC 20431, USA

Received 19 April 2000

Abstract

This paper analyzes the borrowing behavior of a small open economy of a Less Developed Coun-try (LDC) that relies heavily on imports for its capital formation and faces an upward sloping sup-ply function of foreign loans, in an environment where decision makers face uncertainty about thelongevity of external shocks. First, a dynamic general equilibrium model is developed which repli-cates fairly well the business cycle properties of the LDC data. Second, it is shown that uncertaintyconcerning the longevity of shocks (a relevant type of uncertainty, especially for LDCs) generatesforecast errors that are autocorrelated in a way that is similar to Bayesian learning in the “pesoproblem.” This autocorrelated forecast errors can generate substantial debt accumulation. Third, it isshown that the assumption of an upward sloping supply function of foreign loans, which is a morerealistic assumption for LDCs than the usual perfectly elastic one, offers an alternative to the Uzawa-type utility function for the analysis of asset accumulation in the small open economy framework. 2002 Elsevier Science (USA). All rights reserved.

JEL classification: F41; O16; D58; G15

Keywords: Debt accumulation; Stochastic dynamic general equilibrium model; External shocks; Incompleteinformation; Less Developed Economies

E-mail address: [email protected].

1094-2025/02/$ – see front matter 2002 Elsevier Science (USA). All rights reserved.doi:10.1016/S1094-2025(02)00015-7

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208 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

Nomenclature

W Expected lifetime utility.U ′t Marginal utility of the composite good at timet .

β Discounting factor, 0< β < 1.cmt Consumption of the imported good.cht Consumption of the domestic good.imt Import content of investment.iht Domestic content of investment.1/φ Share of domestic investment inputs in gross national investment.1/η Share of foreign investment inputs in gross national investment.it Gross national investment.δ Capital depreciation rate.lt Labor input in the production of the domestic good.yt Output of the domestic good.ξt Productivity shock.ρ Persistence parameter of the AR(1) process forξt .yxt Export quantity.kt+1 Stock of capital next period.bt+1 Stock of foreign debt next period.rt Domestic real interest.pxt Terms of trade (import good is the numeraire).rwt World real interest rate.pxpt ,pxtt Permanent and transitory components of terms of trade.rwpt , rwtt Permanent and transitory components of the world interest rate.px, rw Unconditional means of terms of trade and world interest rate.st Spread over the world interest rate which is a function of the debt level.π Determines the slope of the spread.θ Adjustment cost parameter.zt 4 × 1 vector containing the permanent and transitory components of terms

of trade and world interest rate.Σ 4× 4 conditional variance-covariance matrix ofzt .A 4 × 4 coefficient matrix of the AR(1) process describing the permanent and

transitory components of terms of trade and world interest rate.εt 4 × 1 vector of innovations to the permanent and transitory components of

terms of trade and world interest rate.Vε Variance–covariance matrix ofεt .σpxp, σpxt Standard deviation of the permanent and transitory components ofpxt .σrwp, σrwt Standard deviation of the permanent and transitory components ofrwt .σe Standard deviation of the productivity shock.

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A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239 209

1. Introduction

In policy debates it is often argued that the foreign debt build-up by developing countrieswas essentially the result of their overborrowing and private banks over lending.1 If thisargument is true, it remains to be shown why developing countries and private banksexhibited this excessive behavior. The usual supply-side explanation is that overborrowingduring the 1970s was the result of very large OPEC surpluses searching for investmentopportunities. The usual demand-side explanation is that overborrowing resulted fromdeveloping countries’ high growth, improving terms of trade, and low world interest rates.It is also widely believed that developing countries borrowed heavily on internationalfinancial markets based on the perception that this favorable external environment wouldlast.2 But, the commodity price booms of the mid- and late 1970s were short-lived and theperiod of low interest rates ended by the early 1980s.

To what extent did uncertainty about the external environment contribute to developingcountries’ debt accumulation? It is reasonable to believe that their borrowing behavior willdepend crucially on the perceived longevity of shocks. This paper analyzes the borrowingbehavior of a small open economy that is subject to terms of trade and world interestrate shocks in an environment where policy makers face uncertainty about the longevity ofshocks. In particular, the analysis focuses on the conditions under which an optimistic view(that is alleged to have prevailed among developing countries during the debt accumulationperiod) about the longevity of external shocks, leading to overestimating the longevity ofpositive external shocks or underestimating the longevity of negative external shocks, canlead to significant debt accumulation.

It is found that this optimistic view is compatible with rational behavior and cangenerate persistent overborrowing, making debt accumulation likely. The paper does notargue that debt accumulation is non-optimal. In fact, it is shown that debt accumulationmay arise as a rational response to uncertainty in international markets. However, debtaccumulation increases the vulnerability of the debtor to interest rate fluctuations, aswas documented dramatically during the debt crisis. The paper also does not argue thatuncertainty was the main cause of debt accumulation in developing countries. Rather, itmay have been simply a contributing factor. The justification for focusing on terms oftrade and world interest rate shocks is twofold. First, the terms of trade determine thepurchasing power of developing countries’ exports. Scarce foreign exchange is essential fordevelopment because developing countries rely on imports of investment goods for theircapital formation. Second, world interest rates determine both the cost of new borrowingand the cost of servicing the debt outstanding.

The framework used is a stochastic dynamic general equilibrium model that capturessome important characteristics of developing economies. The stylized developing economy

1 “Overborrowing” refers to levels of borrowing higher than theoptimal level, which will be defined preciselylater in the paper.

2 The external environment of a small open economy, which will be modeled below, is fully characterized bythe evolution of terms of trade and the world interest rate. Henceforth, external shocks will refer to terms of tradeand world interest rate shocks.

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210 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

relies heavily on imports for capital formation and has imperfect access to internationalfinancial markets in the sense that the economy faces an upward-sloping supply functionof foreign loans. This assumption has strong empirical support. It also offers an interestingalternative to the Uzawa-type utility function for analyzing asset accumulation in asmall open economy. Finally, the model economy is characterized by an imperfectinformation structure where decision makers are uncertain about the longevity of externalshocks.

The contribution of this paper is threefold. First, a dynamic general equilibrium modelis developed that replicates fairly well the business cycle properties of the developingcountries’ data. Second, it is shown that uncertainty concerning the longevity of shocks(which is a very relevant type of uncertainty, especially for developing countries) generatesforecast errors that are autocorrelated in a way that is similar to Bayesian learning inthe “peso problem” (Lewis, 1989). These autocorrelated errors can generate substantialdebt accumulation. Third, it is not possible to analyze foreign asset accumulation with avariable interest rate within the standard small open economy framework. Under the usualassumption of a fixed discount factor, and given that the world interest rate is exogenous tothe small open economy, the rate of time preference must equal the world interest rate toensure the existence of a stationary equilibrium.3

Obstfeld (1982), following Uzawa (1968), solved this problem by endogenizing the timepreference parameter, making it a function of the utility level. More recently, Mendoza(1995) used this approach in the context of a real business cycle model of a smallopen economy. The approach implies that the steady-state utility level is exogenouslydetermined, leading to a saving target, that is, regardless of the nature and size of theexogenous shock, the economy will save enough to achieve the fixed steady-state utilitylevel. Another approach, attributed to Blanchard (1985) and applied in the context of asmall open economy by Cardia (1991), is to assume a finite probability of death. Then, theworld interest rate and the subjective discount rate do not necessarily have to be equal, andthe difference between them becomes a function of financial wealth.

This paper explores an alternative approach. Instead of making the time preferencevary in order to generate well-defined dynamics around a stationary equilibrium, it is thedomestic interest rate that adjusts so as to equalize the time preference and the marginalcost of borrowing in equilibrium. This adjustment will be achieved by assuming anupward-sloping supply function of foreign loans, which is a more realistic assumptionfor developing countries than the usual perfectly elastic alternative. “. . . developingcountries typically face an upward-rising supply curve of capital funds.” Harberger (1985,p. 236).

The remainder of the paper is organized as follows. Section 2 develops the model.Section 3 describes briefly the solution procedure and the model calibration, and Section 4presents the results. Some concluding observations are contained in the final sections.

3 See (Sen, 1994) and (Turnovsky, 1995, Chapter 9) for good discussions of this problem in the deterministiccase.

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A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239 211

2. The model

The model outlined below is a stochastic growth model of a small open economy.There are two goods, a domestic and a foreign good. The foreign good is taken to bethe numeraire.

2.1. Preferences

Consumer preferences are represented by a utility function of the constant-relative-risk-aversion type. The representative consumer draws utility from the domestic and foreigngoods, earns income from labor services (supplied inelastically) and from renting capitalto the firms producing the domestic good. Consumers maximize the expected value of theirlifetime utility:4

W =E0

∞∑t=0

βt[chµt cm1−µ

t

]γ/γ, γ < 1, (1)

whereW is the expected lifetime utility,cht is consumption of the domestic good,cmt

is consumption of the imported good,β is the discounting factor,µ is the share of thedomestic good in consumption, and 1− γ is the level of relative risk aversion. Theconsumer is subject to the following budget constraint:

bt+1 = (1+ rt )bt + cmt + imt − pxtyxt , (2)

wherebt is the debt level,rt is the real interest rate (in terms of imports),imt is importsfor investment,pxt is the terms of trade (i.e., the relative price of the home good), andyxtis exports.

2.2. Technology

The technology for the production of the domestic good is represented by a constant-elasticity-of-substitution production function. The domestic good is produced underconstant returns to scale:

yt = Beξt kλt + l1−λt , λ � 1, (3)

whereyt is the production of the domestic good,kt is the capital stock,lt is total laborservices, andλ and(1− λ) are the shares of capital and labor in output, respectively. Theproductivity shockξt follows an AR(1) process:

ξt = ρξt−1 + et , et ∼WN(0, σ 2

e

). (4)

The home good can be consumed, invested, or exported:

cht + iht + yxt � yt , (5)

4 This formulation assumes implicitly that individuals do not value leisure. This assumption is used widely inthe development economics literature to capture the view that leisure is a luxury good for developing countrieshouseholds and thus is much less valued than consumption.

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212 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

wherecht , iht , andyxt are the quantities of the home good going to domestic consumption,to investment and to exports, respectively.

The investment good is a composite of the domestic and foreign goods. In order tocapture developing countries’ heavy dependence on imports of investment goods, zerosubstitutability between domestic and foreign investment goods is imposed:

it = min[φ iht , η imt ], (6)

whereit is gross national investment,iht andimt are the domestic and foreign content ofgross national investment, and 1/φ and 1/η are the shares of the domestic and importedinvestment inputs. The price of the investment good in terms of the numeraire can beobtained by computing its unit cost. This yields:pit = pxt /φ+1/η. Following the commonpractice in the real business cycle literature, quadratic adjustment costs on investment areimposed in order to keep the relative volatility of investment at a realistic level:

θ

2(kt+1 − kt)

2. (7)

2.3. International financial markets

The aim is to capture, in a simple way, the existence of an upward-sloping supplyfunction of foreign loans. This would arise, for example, in the imperfect informationframework of Stiglitz and Weiss (1981), in which the interest rate increases with the debtlevel until the latter reaches a threshold beyond which the debtor will be denied credit (inthe case with no uncertainty).

The domestic real interest rate on foreign debt, in terms of imports, is assumed to bethe sum of two components, the world interest rate and a spread that is increasing in asolvability indicator defined as the exponential of minus the debt–exports ratio:

rt = rwt + exp(−πpxtyxt /bt ), π > 0, (8)

wherert is the domestic real interest rate in terms of imports,rwt is the world risk free realinterest rate,bt is the debt level,pxt is the terms of trade, andyxt is the quantity exported.The coefficientπ determines the slope of the supply function of foreign funds.5 The supplycan be made arbitrarily close to the usual perfectly elastic formulation by choosingπ

that is very small. Interestingly, it can be shown that this upward-sloping supply functionguarantees the existence of a stationary equilibrium by allowing the domestic interest rateto adjust so that in equilibrium the marginal cost of borrowing equals the rate of timepreference.6 In the pure small open economy case, that is if the spread is put equal to zeroin Eq. (8), the decision rule for foreign debt in the linearized version of the model will havea unit-root which implies that shocks will have permanent effects. In contrast, the modelwith the spread yields a decision rule for foreign debt that is stationary.

5 This specification yields a positive spread for positive debt levels, which increases as the solvability ratio,measured bybt /pxt yxt worsens (decreases). Note that this specification is inappropriate for the creditor case.However, this paper is concerned only with the debtor case (the case in which the time preference of thedeveloping country is greater than the world interest rate).

6 See Senhadji (1994). Murphy (1991) and Lundvik (1993) used a similar assumption, the former in a perfectforesight model and the latter in a real business cycle model of a small open economy.

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A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239 213

2.4. Information structure

In addition to uncertainty about the future terms of trade and world interest rate, decisionmakers also face uncertainty about the longevity of external shocks. This uncertainty ismodeled as follows: external shocks are assumed to be the sum of two components, onepermanent, the other transitory. Decision makers observe the sum but not the individualcomponents. Thus they need to solve a signal extraction problem, that is they need to inferthe permanent and transitory components from their sum.7 Formally,

pxt = pxpt + pxtt + px and rwt = rwpt + rwtt + rw, (9)

where pxpt and rwpt are the permanent components,pxtt and rwtt are the transitorycomponents, andpx andrw are the unconditional means of the terms of trade and the worldinterest rate, respectively. The permanent components are assumed to follow a randomwalk and the transitory components a white noise process:

pxpt = pxpt−1 + εpxpt , E

pxpt

)2 = σ 2pxp, pxtt ∼WN

(0, σ 2

pxt

), (10)

rwpt = rwpt−1 + εrwpt , E

rwpt

)2 = σ 2rwp, rwtt ∼WN

(0, σ 2

rwt

). (11)

In vector notation:(pxtrwt

)=

(pxptrwpt

)+

(pxttrwtt

)+

(px

rw

). (12)

Decision makers observeχt = (pxt rwt )′, from which they extract an estimate of

pxpt , pxtt , rwpt , andrwtt . Their information structure is recursive and can therefore berepresented in a convenient way employing the state space form. This form allows theuse of Kalman filtering techniques. The certainty equivalence property of the quadraticapproximation solution method, used to solve the model, implies separation of estimationand control. Consequently, the estimation and control problems can be solved se-quentially.

As mentioned earlier, the solution to the estimation problem is easily derived by usingthe state space form. Let us definezt , a 4× 1 vector, aszt = (pxpt pxtt rwpt rwtt )′. Notethatzt is a Markov process:

zt =Azt−1 + εt , (13)

where:

A =

1 0 0 00 0 0 00 0 1 00 0 0 0

, εt =

ε

pxpt

pxttε

rwpt

rwtt

∼N(0,Vε), (14)

7 This problem is the same as the one analyzed in (Kydland and Prescott, 1982) except that this is a one-stageextraction problem while theirs is a two-stage. A similar information structure has also been used in (Christiano,1988).

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214 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

Vε =

σ 2

pxp 0 0 00 σ 2

pxt 0 00 0 σ 2

rwp 00 0 0 σ 2

rwt

. (15)

Decision makers do not observezt , the individual permanent and transitory components,butχt , the aggregate shock. To complete the state space representation, we need to expressχt as a function ofzt :

χt − χ = czt , whereχ = (px rw

)′andc =

(1 1 0 00 0 1 1

). (16)

In the Kalman filtering literature, Eqs. (13) and (16) are known as the transitionand measurement equation. Letzt be the expected value andΣt the covariance of thedistribution ofzt conditional onχk for k � t . The Kalman filter yields an updating equationfor the conditional mean of the permanent and transitory components of the terms of tradeand world interest rate (zt ) and the Ricatti equation for the conditional variance of theforecast error (Σt ). These two equations are:

zt =Azt−1 + [c(AΣtA

′ + Vε)]′[

c(AΣtA′ + Vε)c

′]−1[(χt − χ

) − cAzt−1], (17)

Σt =AΣt−1A′ + Vε

− [c(AΣt−1A

′ + Vε)]′[

c(AΣt−1A′ + Vε)c

′]−1[c(AΣt−1A

′ + Vε)]. (18)

Only stationary equilibria will be considered, that is equilibria for whichΣt =Σ for all t .Note that the presence of unit eigenvalues inA implies that there may be multiple stationaryequilibria which would depend on the initial values ofzt andΣt . The initial values chosenare the unconditional mean ofzt , that is the 4× 1 null vector, and the 4× 4 null matrix.

The interpretation of Eqs. (17) and (18) is intuitive. The estimated conditional meanof zt is updated, as new information becomes available by adding to the previousestimate,zt−1, the forecast error,((χt − χ)− cAzt−1, weighted by[c(AΣt−1A

′ + Vε)]′ ×[c(AΣt−1A

′ + Vε)c′]−1, which is thegain matrix. The vectorzt is a sufficient statistic for

estimatingzt , τ � t .The next step is to solve the control problem conditional on the transition and

measurement equations, and on the law of motion of the state vector estimate,zt , alongwith its conditional variance. Assuming that the central bank charges individual borrowersthe marginal cost of borrowing. The second welfare theorem applies, and the competitiveequilibrium can be obtained by solving the following social planning problem:8

Equilibrium

MAX{y}t=∞

t=0

W =E0

∞∑t=0

βt(chµt cm1−µ

t

)γ/γ whereyt = (cht cmt iht imt yxt kt+1 bt+1) (19)

8 The equivalent decentralized economy, giving households and firms individual optimization problems, isrelatively straightforward and therefore has been omitted.

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A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239 215

s.t.

bt+1 = (1+ rt )bt + cmt + imt − pxtyxt (current account), (20)

cht + iht + yxt � eξt B[λkαt + (1− λ)lαt

]1/α (resource constraint), (21)

ξt = ρξt−1 + et , et ∼WN(0, σ 2

e

)(law of motion for productivity shock), (22)

kt+1 = (1− δ)kt + it − θ

2(kt+1 − kt )

2 (law of motion for capital), (23)

it = min(φ iht , η imt ) (investment), (24)

lt � l (labor constraint), (25)

rt = rwt + exp(−πpxtyxt /bt ) (domestic real interest rate), (26)

limE0

t∏(1/(1+ rj )

)bt+1 = 0 (tranversality condition forbt+1), (27)

limE0

t∏(1/(1+ rj )

)U ′t kt+1 = 0 (tranversality condition forkt+1), (28)

zt =Azt−1 + εt (AR(1) for external shocks), (29)

χt − χ = czt (signal definition), (30)

zt =Azt−1 + (c(AΣt−1A+ Vε)

)′(c(AΣt−1A+ Vε)c

′)−1((χt − χ

) − cAzt−1)

(conditional mean updating equation), (31)

Σt =AΣt−1A′ + Vε

(c(AΣt−1A

′ + Vε))′(

c(AΣt−1A′ + Vε)c

′)−1(c(AΣA′ + V )

)(Ricatti equation for conditional variance); (32)

z0, k0, andb0 are given.

3. Solution method and calibration

This model cannot be solved analytically. Therefore, the solution will be obtainednumerically, using the linear–quadratic method. Kydland and Prescott (1982) firstintroduced this method for approximating the solution of stochastic nonlinear optimizationproblems. This method and an equivalent one, introduced by King et al. (1988), whichconsists of linearizing the decision rules, have been applied in numerous studies.9 Thelinear–quadratic method is described in detail in (Hansen and Prescott, 1995). It has beenshown to be quite accurate for the neoclassical stochastic growth model (Christiano, 1990)when shocks have a small variance. Since the approximated value function is quadratic andthe constraints (not substituted in the value function) are linear, the decision rules are linear.Note that the concavity of both the utility function and the production function ensures thatthe second-order conditions of the maximization problem are satisfied.

Before simulating the model, it is necessary to calibrate its parameters. The data setcontains thirty-five developing countries. Instead of choosing a particular country, themodel is calibrated for a “representative” economy, which is the median of the thirty-five. Sensitivity analysis is conducted for some key parameters. In (Taylor, 1990) the share

9 For a recent application of the linearization method, see (Kollmann, 1996).

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216 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

of capital goods and intermediate inputs in total imports is approximately 75 percent for asample of eleven developing countries. Therefore, the domestic content share, 1/φ, and theforeign content share, 1/η, of investment are set equal to 0.25 and 0.75, respectively. Theseshares reflect the heavy dependence of developing countries on foreign investment goods.Given the large share of imports used for investment, the share of imports for consumption,µ, is set at approximately 10 percent. A capital depreciation rate of 10 percent and acapital share of 30 percent are standard values, which yield a reasonable capital–outputratio of 2.1.

The adjustment cost parameter,θ , is equal to 0.5. This parameter value implies anadjustment cost expressed in terms of investment equal to 0.015 percent. Rossi’s (1988)detailed empirical study on the behavior of liquidity-constrained consumers in developingcountries reports estimates of the risk aversion parameter,γ . Unfortunately, the estimatesare imprecise, especially for Latin America. They range from−0.02 to−10.23, with amean of approximately−3, which is the value used in calibrating the model.10 Sensitivityanalysis shows that the qualitative results of the model are not very sensitive to thisparameter. The discounting factor,β , and the spread parameter,π , are used to replicatethe level of the spread and the debt–GDP ratio in the data. The spread is 1.5 percent(which is the difference between the median real interest rate on the foreign debt of5.5 percent, reported in the last column of Table 3, and the historical real interest rateof 4 percent for the US). The debt–GDP ratio is approximately 50 percent (which is themean during the sample period). This implies a value forβ and π of 0.90 and 9.20,respectively.

There are five standard deviations to calibrate:σpxp, σpxt, σrwp, σrwt, andσe whichcorrespond to the standard deviation of the innovations to the permanent and transitorycomponents of terms of trade (pxp and pxt) and the world real interest rate (rwp andrwt), and the innovation to the AR(1) productivity shocks (ξt ), respectively. These fiveshocks are calibrated using estimated values for the following parameters:σpxp/σpxt,σrwp/σrwt, σpx, σrw, and σe . The value assigned to the first two ratios are (average)estimates from an unobserved component model for terms of trade and the real worldinterest rate (see Table 1). These averages are 0.33 and 0.23, respectively. The values forσpx andσrw are also averages from country data estimates. These are 0.061 and 0.127,respectively.

The calibration of the productivity shocks was obtained directly from estimates ofSolow residuals for 66 developing countries for the period 1960–1994. Country time seriesof total factor productivity were calculated using a Cobb–Douglas production function:

ξit = yit

kαit (hit lit )1−α

, (33)

whereξit is total factor productivity,yit is real output,kit is the capital stock,lit is totalemployment,hit is an index of human capital, and thushit lit is skill-augmented labor, andthe parameterα is the share of physical capital in real output. The indicesi and t referto the country and time, respectively. The parameterα is set to 0.4 for all countries (as

10 Rossi (1988), Tables 1–6, column 2.

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A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239 217

Table 1Relative size of the permanent and transitory components of the terms oftrade and the world interest rate

px rw

1 Bangladesh 0.1968 –2 Brazil 0.3733 –3 Cote d’Ivoire 0.4466 –4 Dominican Republic 0.2312 0.19545 Ecuador 0.12846 Guyana 0.4581 0.10287 Hong Kong 0.7096 –8 India 0.4769 0.54869 Israel 0.4204 –

10 Jamaica 0.4550 0.257711 Korea, Republic of 0.2750 0.299112 Malawi 0.1381 0.134813 Malta 0.1342 –14 Mauritius – 0.116715 Niger 0.0404 –16 Peru 0.0618 –17 Portugal – 0.237518 Senegal 0.2637 0.302819 Sri Lanka 0.3244 –20 Togo 0.5051 –21 Tunisia – 0.231922 Turkey 0.4220 –

Mean 0.3296 0.2323Median 0.3489 0.2319Std 0.1710 0.1213Min 0.0404 0.1028Max 0.7096 0.5486

Note. The following unobserved-components model has been estimated forboth terms of trade (px defined as the ratio export price to the import priceof goods and nonfactor services) and the world real interest rate (rw definedas the LIBOR minus the growth rate of the import price of goods andnonfactor services):yt = xt + εT

t andxt = xt−1 + εPt ; E(εT

s .εPt ) = 0 for

all s, t ; xt andεTt are respectively the permanent and trasitory components;

E(εTt )

2 = σ2T and E(εP

t )2 = σ2

P. The relative size of the permanent andtransitory components is given byq = σP/σT. The samples are 1960–1993for px and 1970–1993 forrw.

is usually done in the growth accounting exercises). An estimate of the parameterρ isobtained for each country by estimating the following AR(1) process:

ξit = ρi ξit + eit (34)

for i = 1, . . . ,66. The estimate forρ retained for the simulations is the average of the 66ρiand the standard deviation of productivity shocks was computed as the average (over the66 LDC countries) of the standard deviation of theeit . These values are 0.92 forρ and0.046 forσe. For data sources and further details, see Senhadji (1999). Finally, Senhadji

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218 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

Table 2

Parameters Definition Value

1/η Share of imported investment good 0.75µ Share of domestic good in consumption 0.90γ Relative-risk-aversion parameter −3.00δ Depreciation of capital 0.10λ Share of capital 0.30θ Adjustment cost parameter for investment 0.50β Discount factor 0.90π Determines slope of supply function of foreign loans 9.20ρ Autocorrelation coefficient of total factor productivity 0.92σpxp/σpxt Relative size ofpxp with respect topxt 0.330σrwp/σrwt Relative size ofrwp with respect torwt 0.230σe Standard deviation of productivity shocks 0.046σpx Standard deviation of terms of trade 0.061σrw Standard deviation of real world interest rate 0.127

(1999) shows that total factor productivity is quite robust to reasonable variations in theshare of physical capital (α).

The off-diagonal elements of the variance–covariance matrix of the five shocks(εpxp, εpxt, εrwp, εrwt,e)′ are set equal to zero since the cross-correlation between thedifferent shocks are in general relatively weak in the data. As mentioned earlier, thepresence of unit eigenvalues inA implies that there may be multiple stationary equilibriawhich would depend on the initial values ofzt andΣt . The initial values chosen arethe unconditional mean ofzt , that is the 4× 1 null vector, and the 4× 4 null matrix,respectively. The unconditional meanspx andrw are 1 and 0.04, respectively. Note that thetime preference implied by the discount factor(1/β − 1) is greater than the unconditionalmean of the world interest rate. This implies that the small country tends to be a netborrower.11 Table 2 summarizes the calibration of the model.

4. Results

4.1. Business cycle properties of the data and model

The variables analyzed are GDP; private consumption (c), gross domestic investment(i), exports and imports of goods and non-factor services (x andm), net export (nx) definedas exports minus imports divided by exports with all three variables in current prices; thecurrent account divided by exports (ca); the current stock of foreign debt (b), terms of trade( px) defined as the implicit exports deflator divided by the imports deflator; and the realinterest rate on total debt (r), defined as the average interest rate on total debt minus thegrowth rate of the imports price.12 The variables GDP,c, i, x, m, b, andr are expressedin terms of importables by deflating them by the imports price (which is the numeraire in

11 Deaton (1991) argues that this assumption is more appropriate than the alternatives for developing countries.12 A more appropriate measure of the cost of foreign debt would be the real interest rate on foreign debt, which

is not available.

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the model). The source is World Data 1995 from the World Bank. All series are annual.The sample range is 1970–1993 forca,13 1971–1993 forb and r,14 and 1960–1993 forthe other series.15 The data have been detrended using the H–P filter with the smoothingparameterλ = 100.16

The business cycle properties of a variable are summarized by two statistics: its relativevolatility, which is the ratio of its standard deviation to the standard deviation of GDP,and its comovement with GDP which is its correlation with GDP (Table 3a). The tablegives also the persistence of output and the stock of foreign debt as measured by their firstautocorrelation coefficient.

The results in Table 3a can be summarized as follows: Unlike in developed countries,where consumption is smoother than income, in developing countries consumption ismore volatile than income. This may reflect both more noise in developing countries’consumption data and their less-developed financial markets, offering less opportunityfor consumption smoothing. The relative volatility of developing countries’ investmentis lower than that of developed countries. While exports, imports, net exports, and termsof trade are all less volatile than aggregate output, the current account is much morevolatile than GDP. Foreign debt and the real interest rate on total debt are as volatile asGDP. As expected, all four components of GDP (c, i, x, andm) are procyclical (theyhave a positive contemporaneous correlation with GDP). The variablesnx and ca areweakly countercyclical (they have a negative contemporaneous correlation with GDP).Foreign debt is procyclical. The variablepx is weakly procyclical, whiler is weaklycountercyclical. GDP and foreign debt have the same persistence on average.

The next step is to briefly compare the model’s business cycle properties to the data(Table 3b). The discussion will focus on comparing the business cycle statistics of thebenchmark models for the perfect and imperfect information economies to the mean ofthese statistics from the thirty-five country sample. It is worth noting that the focus of thispaper is not to replicate the business cycle properties of LDC data by including all relevantshocks for LDC economies (which would include government spending, civil wars, etc.),but by focusing on external shocks that are believed to have played an important role in theLDCs debt accumulation prior to the debt crisis.

The perfect information model replicates the relative volatility of imports, foreign debt,and real interest rate. It underestimates the relative volatility of consumption, investmentand current account, and overestimates the relative volatility of exports, imports, netexports, and terms of trade. The perfect information economy mimics theprocyclicalbehavior ofc, i, x, m, b, and px and thecountercyclical behavior ofnx, ca, and r.However, consumption, exports, net exports, the current account, and terms of trade aremore correlated with GDP while investment, imports, foreign debt, and real interest rateare less correlated with GDP in the model. The perfect information model replicates the

13 Except Hong Kong 1970–1991 and Zaïre 1971–1990.14 Except Venezuela and Bangladesh, for whichb has the sample range 1972–1993, and Zaire, for whichr has

the range 1971–1990.15 The exceptions are Brazil 1960–1992, Côte d’Ivoire 1965–1993, Ecuador 1965–1993, Singapore 1975–

1993, Sri Lanka 1970–1993, Sudan 1960–1990, Tunisia 1961–1993, Venezuela 1974–1993 and Zaire 1960–1989.16 The choice ofλ = 100 is consistent with previous work (see Correia et al., 1995 and Mendoza, 1995).

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Table 3(a) Business cycle properties of the data and model

Relative volatility Comovement AutocorrelationData c i x m nx ca b px rw c i x m nx ca b px rw GDP b rw

1 Bangladesh 3.91 1.47 0.97 0.96 1.87 3.85 1.55 1.01 – 0.18 0.66 0.60 0.72−0.12 0.15 0.29 0.60 – 0.08 0.33 –2 Brazil 8.84 1.39 0.74 1.01 1.07 7.18 1.13 0.63 0.70 0.42 0.90 0.15 0.48−0.31 0.07 0.55 0.45 0.50 0.26 0.22 7.543 Cote d’Ivoire 1.35 0.97 0.46 0.31 0.46 5.69 1.32 0.61 1.15 0.44 0.74 0.22 0.33−0.04 −0.64 0.91 0.19 0.69 0.57 0.69 6.544 Dominican Republic 1.07 1.07 0.53 0.51 0.33 2.56 1.11 0.49 0.69 0.32 0.82 0.59 0.47 0.32 −0.65 0.95 0.19 0.46 0.39 0.60 5.495 Ecuador 1.81 2.33 2.39 2.36 1.51 4.85 3.71 1.25 1.34 0.33 0.67 0.42 0.34 0.14 −0.08 0.39 0.48 −0.37 0.77 0.74 6.566 Guyana 4.77 4.10 1.73 1.60 0.81 6.10 2.41 0.72 0.54 0.26 0.34 0.24 0.23 0.08 −0.49 0.46 0.26 −0.85 0.29 0.53 1.537 Hong Kong 7.85 7.62 3.13 1.65 2.32 3.81 – 0.41 – 0.13 0.21 0.24 0.52−0.06 −0.40 – 0.10 – 0.43 – –8 India 4.87 3.36 1.85 1.63 0.62 2.86 1.11 1.51 – 0.73 0.81 0.88 0.90 0.34 −0.06 0.95 0.89 – 0.44 0.41 –9 Israel 1.28 0.81 0.75 0.80 0.18 1.61 – 0.18 – 0.54 0.87 0.88 0.90−0.48 0.17 – 0.77 – 0.61 – –

10 Jamaica 2.76 4.26 0.67 0.53 0.59 1.16 1.25 0.98 0.51 0.23 0.16 0.40 0.30 0.18 0.21 0.12 0.26 −0.80 0.43 0.66 8.6411 Korea, Republic of 1.79 0.75 0.73 0.73 0.14 8.23 0.54 0.15 0.68 0.47 0.83 0.83 0.84−0.10 0.26 0.58−0.40 0.08 0.58 0.45 5.6512 Malawi 1.14 0.69 0.98 0.86 0.33 2.99 0.61 0.34 1.84 0.07 0.26 0.88 0.87 0.42 −0.02 0.66−0.55 −0.50 0.63 0.52 2.5213 Malta 2.62 2.70 1.03 1.12 0.46 0.57 0.85 0.82 – 0.14 0.12 0.90 0.95−0.37 0.13 0.89−0.28 – 0.40 0.31 –14 Mauritania 0.78 0.88 0.18 0.19 0.24 0.37 0.67 0.20 0.93 0.49 0.46 0.31 0.08 0.21 0.02 0.32 0.06 −0.76 0.47 0.43 6.5815 Mauritius 1.35 0.89 0.62 0.62 0.09 2.74 0.57 0.15 0.99 0.42 0.72 0.80 0.80−0.01 −0.01 0.82 0.55 −0.22 0.64 0.58 1.5516 Mexico 1.37 0.98 0.52 0.57 0.16 – 0.52 0.16 1.04 0.51 0.85 0.75 0.72−0.14 – 0.24 0.69 −0.16 0.41 0.51 7.5217 Morocco 1.56 1.06 0.93 0.85 0.33 – 0.65 0.31 1.13 0.54 0.73 0.81 0.82 0.23 – 0.72 0.77 −0.28 0.41 0.18 5.5218 Niger 1.66 1.25 0.74 0.76 0.30 3.58 0.67 0.25 1.19 0.40 0.61 0.86 0.90−0.22 0.01 0.80 0.11 −0.72 0.58 0.44 5.5519 Pakistan 1.59 0.83 0.75 0.67 0.28 6.32 0.63 0.33 1.50 0.59 0.83 0.77 0.79 0.35 −0.17 0.69 0.69 0.27 0.34 0.25 3.5020 Peru 2.62 3.16 0.47 0.41 0.64 2.00 0.84 0.40 1.07 0.27 0.30 0.01 0.45−0.34 −0.16 0.67 0.21 −0.50 0.46 0.62 7.3921 Philippines 0.79 0.80 0.20 0.12 0.21 – 0.95 0.18 1.18 0.75 0.81 0.19 0.03 0.19 – 0.68 0.32 −0.57 0.54 0.48 6.5822 Portugal 1.40 0.90 0.96 0.96 0.13 7.04 0.71 0.14 1.03 0.73 0.99 0.94 0.95−0.17 0.07 0.96 0.04 −0.08 0.53 0.42 5.4523 Rwanda 1.91 2.20 1.43 1.26 0.74 3.94 1.31 0.49 – 0.77 0.77 0.32 0.40−0.05 −0.17 0.89−0.34 – 0.50 0.51 –24 Senegal 1.10 1.21 0.65 0.61 0.19 5.25 0.88 0.15 0.63 0.72 0.63 0.46 0.51−0.12 −0.31 0.86−0.23 0.68 0.37 0.41 4.2925 Singapore 1.56 0.98 0.99 0.99 0.01 1.70 – 0.07 – 0.94 1.00 1.00 1.00−0.05 −0.40 – −0.56 – 0.47 – –26 Sri Lanka 2.17 1.08 1.34 1.11 0.58 1.53 1.21 0.86 0.66 0.57 0.65 0.82 0.83 0.39 0.31 0.89 0.53 −0.71 0.44 0.59 2.6127 Sudan 0.81 0.79 0.72 0.68 0.30 2.74 0.68 0.20 1.11 0.84 0.79 0.61 0.64 0.06 −0.59 0.82−0.07 −0.31 0.51 0.50 4.4628 Thailand 1.18 0.93 0.93 0.93 0.06 2.35 0.70 0.17 0.29 0.79 0.74 0.81 0.80 0.18 −0.32 0.92 0.71 0.11 0.53 0.42 6.4829 Togo 1.63 1.24 0.91 0.81 0.46 1.80 1.30 0.83 0.35 0.61 0.42 0.61 0.65−0.02 0.64 0.72 0.34 −0.45 0.16 0.70 0.7230 Tunisia 1.18 0.87 0.54 0.63 0.18 2.16 0.66 0.33 0.72 0.39 0.25 0.62 0.58−0.12 −0.07 0.78 0.44 −0.13 0.51 0.43 4.5531 Turkey 1.24 1.25 0.80 0.87 0.26 1.50 0.93 0.30 0.48 0.79 0.83 0.73 0.78−0.37 −0.36 0.97 0.15 −0.18 0.51 0.54 4.54

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Table 3 (continued)

Relative volatility Comovement AutocorrelationData c i x m nx ca b px rw c i x m nx ca b px rw GDP b rw

32 Uruguay 1.09 1.11 0.71 0.67 0.20 4.14 0.90 0.35 0.23 0.52 0.74 0.61 0.66−0.02 −0.35 0.78 −0.20 0.17 0.39 0.35 7.2133 Venezuela 1.29 1.06 1.07 1.08 0.28 4.30 0.65 0.29 3.51 0.75 0.78 0.85 0.85−0.06 0.15 0.47 −0.15 −0.41 0.61 0.51 3.6534 Zaire 1.24 1.31 0.74 0.73 0.54 0.52 0.66 0.73 1.34 0.30 0.50 0.41 0.65−0.31 −0.53 0.65 −0.37 −0.72 0.34 0.14 5.8535 Zambia 1.07 0.92 0.60 0.44 0.30 0.66 0.69 0.42 0.51 0.47 0.18 0.28 0.36 0.04 −0.35 0.49 0.50 −0.17 0.37 0.29 6.97

Mean 2.13 1.63 0.94 0.86 0.49 3.32 1.01 0.47 0.98 0.50 0.63 0.59 0.63−0.01 −0.12 0.68 0.20 −0.21 0.46 0.46 5.19Median 1.40 1.07 0.75 0.80 0.30 2.80 0.85 0.34 0.96 0.49 0.73 0.61 0.66−0.04 −0.08 0.72 0.21 −0.25 0.46 0.47 5.54Std 1.82 1.39 0.58 0.44 0.50 2.09 0.62 0.34 0.62 0.22 0.25 0.27 0.25 0.23 0.30 0.23 0.40 0.44 0.13 0.15 2.01Min 0.78 0.69 0.18 0.12 0.01 0.37 0.52 0.07 0.23 0.07 0.12 0.01 0.03−0.48 −0.65 0.12 −0.56 −0.85 0.08 0.14 0.72Max 8.84 7.62 3.13 2.36 2.32 8.23 3.71 1.51 3.51 0.94 1.00 1.00 1.00 0.42 0.64 0.97 0.89 0.69 0.77 0.74 8.64

Note. Statistics are based on detrended (by H–P filter,λ = 100) series. Variables are private consumption (c), gross domestic investment(i), exports(x), imports(m),net exports (nx), current account (ca), external debt (b), terms of trade (px), and the real interest rate on total debt (rw). All variables are in logs exceptr , nx, andca. nxis defined as exports minus imports divided by exports with all three variables in nominal terms.ca is the World Bank’s official statistic divided by exports in nominalterms. All variables are expressed in terms of importables.Relative volatility is defined as the relative standard deviation of each variable of GDP.Comovement is definedas the correlation of each variable with GDP. In the model these statistics are the sample means of statistics computed for each of 100 simulations. Each simulationconsists of 35 observations, which is the sample size of the data. The numbers in parentheses are sample standard deviations of these statistics. The last column gives theaverage (over 1970–1993) real interest rate on total debt.

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Table 3(continued)(b) Business cycle properties of the model with one source of shock

Relative volatility Comovement Autocorrelationσγ c i x m nx ca b px rw c i x m nx ca b px rw GDP b

I. DataMean 13.07 2.13 1.63 0.94 0.86 0.49 3.32 1.01 0.47 0.98 0.500.63 0.59 0.63 −0.01 −0.12 0.68 0.20 −0.21 0.46 0.46Median 11.79 1.40 1.07 0.75 0.80 0.30 2.80 0.85 0.34 0.96 0.490.73 0.61 0.66 −0.04 −0.08 0.72 0.21 −0.25 0.46 0.47Std 8.63 1.82 1.39 0.58 0.44 0.50 2.09 0.62 0.34 0.62 0.220.25 0.27 0.25 0.23 0.30 0.23 0.40 0.44 0.13 0.15Min 2.49 0.78 0.69 0.18 0.12 0.01 0.37 0.52 0.07 0.23 0.070.12 0.01 0.03 −0.48 −0.65 0.12 −0.56 −0.85 0.08 0.14Max 30.14 8.84 7.62 3.13 2.36 2.32 8.23 3.71 1.51 3.51 0.941.00 1.00 1.00 0.42 0.64 0.97 0.89 0.69 0.77 0.74

II. Model1. Benchmark 7.83 1.07 1.66 1.54 1.29 1.43 0.76 0.73 0.95 0.94 0.930.40 0.54 0.41 −0.19 −0.33 0.02 0.94 0.01 0.16 0.50

(imperfect info) (0.07) (0.26) (0.22) (0.20) (0.24) (0.17) (0.20) (0.06) (0.16) (0.02)(0.15) (0.12) (0.14) (0.16) (0.16) (0.19) (0.03) (0.18) (0.18) (0.13)2. Benchmark 6.27 0.91 1.05 1.48 0.78 1.12 1.35 1.00 0.95 0.94 0.970.15 0.84 0.22 −0.64 −0.50 0.27 0.94 −0.01 0.09 0.33

(perfect info) (0.04) (0.19) (0.15) (0.14) (0.16) (0.22) (0.20) (0.05) (0.16) (0.01)(0.18) (0.06) (0.17) (0.12) (0.13) (0.17) (0.03) (0.18) (0.17) (0.15)3. σpxt = σrwp = 2.11 1.18 1.35 0.44 1.09 0.52 0.49 0.51 0.99 – 1.000.88 0.62 0.95 0.64 0.74 0.32 1.00 – 0.40 0.65

σrwt = σξ = 0 (0.01) (0.09) (0.05) (0.06) (0.04) (0.04) (0.04) (0.01) – (0.00)(0.02) (0.09) (0.01) (0.09) (0.06) (0.15) (0.00) – (0.15) (0.10)4. σpxp = σrwp = 6.23 0.84 0.33 1.41 0.17 0.96 0.89 0.62 1.00 – 1.00−0.37 0.97 −0.29 −0.95 −0.97 0.39 1.00 – −0.19 0.24

σrwt = σξ = 0 (0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.07) (0.00) – (0.00)(0.15) (0.01) (0.16) (0.02) (0.01) (0.13) (0.00) – (0.16) (0.17)5. σpxp = σpxt = 0.31 6.45 25.68 21.24 20.25 23.74 14.66 15.90 – 7.95 0.16−0.28 0.20 −0.07 −0.14 −0.29 0.98 – −0.31 0.66 0.68

σrwt = σξ = 0 (0.69) (3.97) (3.05) (2.87) (3.42) (2.21) (0.60) – (0.69) (0.15)(0.09) (0.10) (0.13) (0.11) (0.09) (0.01) – (0.16) (0.11) (0.10)6. σpxp = σpxt = 0.17 9.51 23.90 35.65 14.92 29.74 98.15 66.80 – 88.53 0.10−0.22 −0.01 −0.38 −0.08 0.38 −0.26 – 0.39 0.70 0.24

σrwp = σξ = 0 (0.97) (3.46) (4.20) (2.23) (3.71) (21.78) (8.86) – (18.85) (0.17)(0.10) (0.15) (0.12) (0.15) (0.11) (0.11) – (0.12) (0.08) (0.16)7. σpxp = σpxt = 2.31 0.99 1.93 0.87 1.37 0.41 0.39 0.42 – – 1.000.88 0.96 0.93 0.23 0.35 0.55 – – 0.44 0.68

σrwp = σrwt = 0 (0.01) (0.14) (0.05) (0.08) (0.03) (0.03) (0.05) – – (0.00)(0.02) (0.01) (0.01) (0.18) (0.15) (0.15) – – (0.14) (0.10)

Note. Simulation 3 to 7 are the imperfect information economy. Statistics are based on detrended (by H–P filter,λ = 100) series. The first column gives the standarddeviation of real output(σy). Variables are private consumption (c), gross domestic investment(i), exports(x), imports(m), net exports (nx), current account (ca),external debt (b), terms of trade (px), and the real interest rate on total debt (rw). All variables are in logs exceptr , nx, andca. nx andca are normalized by steady-stateexports.ca is the World Bank’s official statistic. All variables are expressed in terms of importables both in the data and in the model.Relative volatility is defined as therelative standard deviation of each variable of GDP.Comovement is defined as the correlation of each variable with GDP. In the model, these statistics are the samplemeans of statistics computed for each of 100 simulations. Each simulation consists of 35 observations, which is the sample size of the data. The numbers in parenthesesare sample standard deviations of these statistics.

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positive autocorrelation of both GDP and foreign debt but underestimates the persistenceof GDP.

The imperfect information economy performs better than the perfect informationeconomy in explaining the variability of output (60 percent against 48 percent), inreplicating the relative volatility of investment and consumption, and in replicating thecomovement of macroeconomic variables with GDP. Note, however, that the perfectinformation economy performs better with respect to the relative volatility of imports, netexports and current account, and with respect to the comovement of foreign debt with GDP.

Besides the two benchmark simulations (one for the imperfect information economyand the other for the perfect information economy), where all five shocks are included, thetable also reports simulations where only one of the five shocks is included (simulations 3to 7 which pertain to the imperfect information economy). It is clear from simulations 3 to7 that terms of trade have the highest contribution in the variability of output and are crucialin replicating the relative volatility and the comovement of macroeconomic variables.Furthermore, transitory terms of trade shocks have a significantly larger contributionto output variability than permanent shocks. Interestingly, interest shocks have only amarginal contribution to output variability and business cycle properties of the model.

Interest rate shocks alone in simulations 3 and 4 increase substantially the relativevolatility of investment (as imports of investment goods are essential for capital buildingin this model), leading to unrealistic relative volatility of imports, exports, trade balanceand current account. This simply reflects the fact that the real interest rate has littleeffect on output but a large effect on the marginal product of investment and thus on theinvestment level (see the impulse response functions in Fig. 1). Shocks that move bothoutput and investment are productivity shocks which yield a strong procyclical behavior forinvestment (see simulation 7 where only productivity shocks are included). This explainswhy investment becomes significantly more correlated with output, reinforcing also thecorrelation of imports with output (since most imports are investment goods). Simulations4 and 5 reveal that transitory terms of trade and permanent interest rate shocks are thedriving force behind the countercyclical behavior of net export (nx) and current account(ca).

4.2. Decision rules and impulse response analysis

The solution to the linear–quadratic dynamic programming problem of the perfectinformation economy yields a set of three linear decision rules forbt+1, kt+1, andyxt :

bt+1 = 1.08+ 0.71bt − 0.27kt + 0.38pxpt − 0.63pxt − 1.43rwpt + 0.79rwtt

+ 0.24ξt , (35)

kt+1 = 1.22− 0.12bt + 0.63kt + 0.34pxpt − 0.08pxt − 0.95rwpt − 0.03rwtt

+ 0.60ξt , (36)

yxt = −0.02+ 0.28bt + 0.07kt − 0.38pxpt + 0.11pxtt + 1.19rwpt + 0.11rwtt

+ 0.30ξt . (37)

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c consumptioni investmentx exportsxs steady-state exportsnx net exportsm importsca current account,b foreign debtEt(pxp) conditional mean ofpxpEt(pxt) conditional mean ofpxt

Fig. 1. Impulse response for the imperfect information economy. (a) Permanent increase of 1% in the terms oftrade.

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c consumptioni investmentx exportsxs steady-state exportsnx net exportsm importsca current account,b foreign debtEt (pxp) conditional mean ofpxpEt (pxt) conditional mean ofpxt

Fig. 1. (Continued). (b) Transitory increase of 1% in the terms of trade.

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c consumptioni investmentx exportsxs steady-state exportsnx net exportsm importsca current account,b foreign debtEt(rwp) conditional mean ofrwpEt(rwt) conditional mean ofrwt

Fig. 1. (Continued). (c) Permanent increase of 1% in the world interest rate.

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c consumptioni investmentx exportsxs steady-state exportsnx net exportsm importsca current account,b foreign debtEt(rwp) conditional mean ofrwpEt(rwt) conditional mean ofrwt

Fig. 1. (Continued). (d) Transitory increase of 1% in the world interest rate.

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Note that the certainty equivalence property of the linear–quadratic solution methodimplies that the coefficients of these decision rules are identical for both the perfectinformation economy (where decision makers observe the state vectorzt ) and the imperfectinformation economy (where decision makers do not observe the state vectorzt butcompute an estimatezt ). However, in the imperfect information economy,pxpt , pxtt , rwpt ,rwtt must be replaced by their estimate in Eqs. (35)–(37).

A few points about these decision rules are worth mentioning. First, note that thecoefficient onbt in Eq. (36) is different from zero, which implies that the usual separationbetween capital accumulation and foreign debt in the small open economy framework doesnot hold due to the upward-sloping supply function of foreign loans. Second, the negativecross effect of both assets (the negative coefficient onbt in kt+1 equation and the negativecoefficient onkt in bt+1 equation reflects the substitutability between physical capital andthe foreign bond).17

Third, a negative external shock (that is, a deterioration in the terms of trade or anincrease in the world interest rate) will trigger a different borrowing response dependingon whether the shock is perceived to be permanent or transitory. A permanent negativeshock will reduce foreign borrowing, while a transitory one will be smoothed out byadditional foreign borrowing. This effect reflects simply the consumption–smoothingmotive characteristic of these dynamic general equilibrium models.

Fourth, as far as the decision rule for the capital stock is concerned, an increase in theterms of trade affects the stock of capital through three channels. The first one is throughthe marginal product of capital. A transitory improvement in the terms of trade leaves nextperiod’s marginal product of capital intact (the only small effect is through the spread),while a permanent improvement increases the marginal product of capital and thereforestimulates investment. The second channel is through the price of investment, which isa weighted average of the price of the domestic and foreign good:pit = pxt /φ + 1/η.A permanent improvement in the terms of trade will increase the price of investment, thusdiscouraging investment. The third channel is through a pure wealth effect coming fromthe purchasing value (in terms of the imported good) of the foreign exchange generated bythe current trade balance.

Fifth, export volume( yxt ) increases to take advantage of a transitory improvement inthe terms of trade but declines if the improvement is permanent. An increase in the worldinterest rate, especially a permanent increase, triggers a rise in exports in order to meet thehigher servicing cost of the debt outstanding.

Once the decision rules are computed, one can compute the impulse response functions(IRF). The IRF of an endogenous variable traces out its dynamic response to exogenousshocks. Three exogenous shocks are examined: terms of trade, real interest rate, andproductivity shocks. Both temporary and a permanent version of the first two shocks areanalyzed. The IRF for the imperfect information economy are presented in Fig. 1. Thevariables GDP, consumption(c), investment(i), exports(x), imports (m), and foreigndebt are in logs so that the IRF can be interpreted as percentage deviation from steady-state

17 A positive value ofbt+1 means that the small open economy is a debtor on international financial markets.Therefore, a decrease inbt+1 means an increase in its portfolio of foreign bonds or, equivalently, a decrease inits short position in foreign bonds.

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value. Net exports (nx) and the current account (ca) have been normalized by steady-stateexports (xs).

A permanent increase in the terms of trade raises the marginal product of capital in termsof the numeraire, stimulating investment. There is overshooting of investment on impact.As expected, consumption also responds positively resulting in an increase in GDP. TheIRF for exports, imports, and thus the trade balance and the current account has threephases. First, exports increase more than imports, yielding a trade and a current accountsurplus on impact. Second, exports decline while imports increase reversing the trade andcurrent account surpluses to large deficits. Third, exports increase and imports decreasetoward their steady-state level leaving only a slight trade and current account surplus.Foreign borrowing declines before increasing progressively toward its new steady-statelevel. The spread, which is a function of the debt–export ratio, follows closely the patternof the debt level. Note that the effect on the spread is only transitory, even though theeffect on exports and foreign debt is permanent. This implies that the cumulative responseof debt–export ratio to a permanent terms of trade shock is zero. A temporary increase inthe terms of trade produces similar effects on these variables, except that all effects aretransitory.

A permanent increase in the world interest rate depresses consumption and investment.Aggregate output falls only slightly because of the large trade surplus destined to pay forthe higher servicing cost of the debt. The developing economy responds to the permanentincrease in this cost by reducing new borrowing, which lowers the spread. Note thatcontrary to the case of a permanent increase in the terms of trade, the spread decreasespermanently, implying that the cumulative response of the debt–export ratio to a permanentrise in the world interest rate is negative. A temporary increase in the world interestrate has similar but transitory effects. Finally, middle right panels depict the conditionalmean of the permanent and transitory components of terms of trade,Et(pxp) = pxpt andEt(pxt) = pxtt , and world interest rate,Et(rwp) = rwpt andEt(rwt) = rwtt . Note thatlearning is relatively quick in this model as the predicted components converge to theirtrue value after less than 10 periods. Note thatpxpt , pxtt , rwpt , rwtt yield identical valuesunder permanent and transitory shocks on impact.

While the terms of trade and the world interest rate are modeled as two-componentstochastic processes (one permanent and the other transitory), total factor productivityis modeled as a one-component AR(1) process. Thus all productivity shocks have somepersistence but are not permanent. Figure 2 shows that a favorable productivity shock spursan increase in investment, consumption, and GDP. Imports increase more than exports onimpact, leading to a trade and current account deficits. The deficits revert to slight surplusesbefore dieing out. The stock of foreign debt follows the evolution of the current account.The spread declines on impact as the solvability ratiopxtyxt /bt improves.

4.3. Borrowing behavior under perfect and imperfect information

This subsection analyzes conditions under which imperfect information about thelongevity of terms of trade and world interest rate shocks lead to overborrowing. In theperfect information economy the decision-maker is assumed to observe the permanent andtransitory components of the terms of trade and world interest rate, while in the imperfect

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Fig. 2. Impulse response to an increase of 1% in productivity (in %):c consumption,i investment,x exports,xs steady-state exports,m imports,nx net exports,ca current account,b foreign debt.

information economy, the decision-maker observes their sum, from which she extracts anestimate of the individual components. Overborrowing is defined as the excess of foreigndebt in the imperfect information economy over the foreign debt in the perfect informationeconomy. Thus overborrowing may occur either because there is more borrowing inthe imperfect information economy than in the perfect information economy or becauseimperfect information prevents decision-makers from reducing the debt when it is optimalto do so. This definition of overborrowing isolates the excess debt due to imperfectinformation only.

The decision rule for foreign debt, Eq. (35), implies that overborrowing will occur if apermanent decline in the terms of trade is perceived to be transitory or if a transitoryimprovement in the terms of trade is believed to be permanent. Similarly, overborrowingwill occur if a permanent increase in the world interest rate is believed to be transitoryor if a transitory decline in the world interest rate is believed to be permanent.

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When agents face uncertainty about the longevity of a shock, overborrowing may resulteven if they are rational. It is shown below that this type of uncertainty generates forecasterrors that are autocorrelated. Therefore, when overborrowing occurs it can be persistent,permitting debt accumulation.

Note that the decision rules forbt+1 andkt+1 form a vector autoregression of order 2.It can be written as:

yt+1 =Φ0 +Φ1yt +Φ2zt , (38)

whereΦ0, Φ1, andΦ2 are a 2× 1 vector, a 2× 2 matrix, and a 1× 4 vector of coefficients,respectively;yt = (bt kt )

′; andzt = (pxpt pxtt rwpt rwtt )′. We are interested in comparingthe dynamics of the stock of foreign debt in the perfect and imperfect informationeconomies. Therefore, the central variable in this analysis is the difference between thedebt level in the imperfect and perfect information economies:bet+1 = biit+1 − b

pit+1. Thus

overborrowing corresponds to positive values ofbet+1. Because of the separation betweenestimation and control, the only difference between the perfect and imperfect informationeconomies is that the decision rules are based on the actual permanent and transitorycomponents of terms of trade and world interest rate(zt ) in the former and on their estimate(zt ) in the latter. Thus:

yet+1 =Φ1yet + φ2

(z− zt

) =Φ1yet +Φ2ut , (39)

whereyet+1 = (bet+1 ket+1)

′ andut is a 4×1 vector of forecast errors:(upxpt u

pxtt u

rwpt urwt

t )′.Uncouplingyet+1 requires diagonalizingΦ1. DefineT as the diagonalizing matrix (matrixcontaining the eigenvectors ofΦ1) andD the diagonal form ofΦ1. To uncoupleyet+1, wesimply premultiply Eq. (39) byT −1:

yet+1 =Dyet + Φ2ut ⇒ bet+1 = d1bet + Φ2(1, .)ut ,

ket+1 = d2ket + Φ2(2, .)ut , (40)

whereyet+1 = T −1yY et+1, Φ2 = T −1Φ2, andd1 andd2 are the diagonal elements ofD.

Thus, yet+1 is simply a linear transformation of the forecast errorut . Interestingly,Proposition 1 shows that the latter follows an AR(1) process:

Proposition 1. The forecast errors follow an AR(1) process:

upxpt = (

1− kpxpt−1

)u

pxpt−1 + (

1− kpxpt−1

pxpt − k

pxpt−1ε

pxtt , u

pxtt = −u

pxpt , (41)

urwpt = (

1− krwpt−1

)u

rwpt−1 + (

1− krwpt−1

rwpt − k

rwpt−1ε

rwtt , urwt

t = −urwpt , (42)

where ujt is the forecast error for j , j = pxp,pxt, rwp, rwt;

kpxpt−1 = s2

t−1,pxp

s2t−1,pxp + σ 2

pxt, k

rwpt−1 = s2

t−1,rwp

s2t−1,rwp + σ 2

rwt,

s2t,i is the conditional variance of i at time t (i.e., the diagonal element of Σt corresponding

to i), i = pxp, rwp.

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232 A.S. Senhadji / Review of Economic Dynamics 6 (2003) 207–239

Proof. After simplification, the updating equation (17) forpxpt andpxtt can be written as:

pxpt = pxpt−1 + kpxpt−1

((pxt − px)− pxpt−1

), pxtt = (pxt − px)− pxpt . (43)

The corresponding conditional variances are:

s2t,pxp = (

s2t−1,pxp + σ 2

pxp

)[1− s2

t−1,pxp + σ 2pxp

s2t−1,pxp + σ 2

pxp + σ 2pxt

], (44)

and a similar formula fors2t,rwp. Define the forecast errorsupxp

t = pxpt − pxpt . Using theupdating Eqs. (43), the forecast error can be rewritten as:

upxpt = pxpt−1 + k

pxpt−1

((pxt − px)− pxpt−1

) − pxpt . (45)

Using the fact thatpxt = pxpt + pxtt + px, Eq. (45) can be rewritten as:

upxpt = ( pxpt−1 − pxpt )+ k

pxpt−1

((pxpt − pxpt−1)+ pxtt

). (46)

And given the fact thatpxpt is a random walk:pxpt = pxpt−1 + εpxpt , Eq. (46) can be

simplified to:

upxpt = (

1− kpxpt−1

)u

pxpt−1 + k

pxpt−1pxtt − (

1− kpxpt−1

pxpt . (47)

A similar formula forrwpt holds. ✷From Eq. (47) and the definition of the gain factor,k

pxpt , the forecast errorupxp

t

converges to a random walk as the relative size of the transitory component (σpxt/σpxp)

converges to infinity. Intuitively, when the relative size of the transitory component is verylarge, a change in the terms of trade is interpreted as a change in the transitory componentpxtt , which leaves the estimate ofpxpt unchanged. In the extreme case ofσpxt/σpxp = ∞,the forecast error follows a random walk:u

pxpt = u

pxpt−1−εpxp. In other words, the permanent

component is entirely allocated to the forecast error as the decision maker interprets anychange in the terms of trade as a transitory movement. In the other extreme case, inwhich the relative size of the transitory component is zero, the gain factor is one andall changes in the terms of trade are attributed to the permanent componentpxpt . Then,the forecast error is:upxp

t = pxtt . Consequently, the forecast error is simply the transitorycomponentpxtt which is white noise. For the intermediate cases the forecast error followsa stationary AR(1) process. Sincebet+1 is simply a linear transformation ofut , it inheritsall the properties ofut .

Proposition 1 establishes that the forecast errorut is an AR(1) process and is thereforeautocorrelated. This implies that uncertainty concerning the longevity of a shock maylead to persistentoverborrowing and therefore contribute to debt accumulation. When thesize of the transitory component is relatively large, and consequently when shocks arehighly unpredictable, the forecast error becomes more persistent, resulting in persistentoverborrowing and making debt accumulation likely.

Table 4 gives a quantitative assessment of the deviations from the optimal borrowingbehavior, as measured bybet+1/GDPt .18 A permanent decline in the terms of trade of 10

18 The stock of foreign debt in the perfect information economy is referred to as the optimal debt level, eventhough the stock of foreign debt in the imperfect information economy is also optimal under that informationstructure.

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Table 4The difference between debt/GDP in imperfect and perfect information economies (%)

k 2 5 10 20 inf

Steady-state debt/GDP Decrease of 10% inpxp

0.01 0.15 0.35 0.44 0.47 0.470.25 3.39 8.68 11.43 12.64 12.850.50 3.97 12.19 19.19 23.04 24.041.00 3.85 15.92 28.91 41.09 47.94

Increase of 10% inpxt

0.01 0.12 0.27 0.33 0.36 0.360.25 2.58 6.62 8.71 9.64 9.800.50 3.03 9.80 14.64 17.57 18.331.00 2.93 12.14 22.05 31.33 36.56

Increase of 10% inrwp

0.01 0.23 0.50 0.59 0.60 0.600.25 5.93 16.16 21.95 24.47 24.890.50 9.12 32.14 50.91 62.68 65.741.00 12.84 57.51 110.40 161.35 190.08

Decrease of 10% inrwt

0.01 0.14 0.31 0.36 0.37 0.370.25 3.63 9.88 13.42 14.96 15.220.50 5.58 19.65 31.13 38.33 40.201.00 7.85 35.17 67.51 98.67 116.24

Note. The figures are cumulative effects overk periods after the shock. The variation in the terms of trade andworld interest rate components arepercentage point variations. The table is divided into 4 panels correspondingto a 10% increase in the permanent component of terms of trade (pxp), a 10% decline in the transitory componentof terms of trade(pxt), a decrease of 10% in the permanent component of the world interest rate(rwp), a 10%increase in the transitory component of the world interest rate (rwt).

percent will generate an overborrowing effect between 0.15 percent and 3.85 percent ofGDP (for initial debt–GDP ratios varying from 1 to 100 percent) during the first two periodsafter the shock. The total cumulative effect varies from 0.47 percent of GDP (for an initialdebt–GDP ratio of 1 percent) to 47.94 percent (for a debt–GDP ratio of 100 percent). Theseeffects are smaller for temporary terms of trade shocks but the cumulative effects remainsignificant for high debt–GDP ratios (36.56 percent for a debt–GDP ratio of 100 percent).

A permanent decline of 10 percent in the world interest rate generates cumulativeoverborrowing effects ranging from 0.60 percent to 190.08 percent of GDP correspondingto initial debt–GDP ratios of 1 and 100 percent, respectively. The overborrowing effectsfrom transitory declines in real interest rate shocks, while weaker than the correspondingones from permanent increases in the real interest rate, remain substantial.

To sum up, overborrowing is substantial for high initial debt–GDP ratios and are moreimportant for permanent than for transitory shocks, and is more important for interest ratethan for terms of trade shocks.

Having shown that overborrowing can be substantial under four possible scenarios, thenext step is to narrow down these scenarios for LDCs debt accumulation by identifying themajor shocks faced by LDCs prior to the early-eighties debt crisis and by using the size

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Fig. 3. Terms of trade, world interest rate, and debt–GDP ratio.

of those shocks to calibrate the model. It is argued that the large run up in debt started inthe mid seventies with large terms of trade improvements in 1974 and 1977 (first panel ofFig. 3). Developing countries, believing that these favorable shocks would be long lasting,started borrowing heavily as the improved terms of trade would increase their capacity toservice higher levels of debt (third panel of Fig. 3). However, the commodity price boomsof 1974 and 1977 which were the source of the improvement in LDCs terms of trade,were followed by a persistent bust by early 1980s (first panel of Fig. 3). Compoundingthe problem was the skyrocketing world interest rate in early 1980s which significantlyincreased the servicing cost of the accumulated debt and precipitated the debt crisis of theearly eighties.

Thus, the accumulation of foreign debt can be decomposed into two phases. The firstphase started around the first commodity boom and ended by end 1970s. The source ofthis first build up is due, to a large extent, to the uncertainty about the longevity of theimprovement in terms of trade in 1974 and 1977. The second phase, starting early 1980s

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and ending late 1990s, was mainly due to the increase in the servicing cost of the debtbrought about by the significant hike in world interest rate and declining terms of tradewhich led many countries to heavy new borrowing in order to service their debt. Thus,overborrowing due to uncertainty about the longevity of shocks played a major role in thefirst phase but not in the second.

The overborrowing effect, due to the two commodity boom prices, has been computedusing the actual size of the terms of trade shocks (that is, 18 percent in 1974 and 10percent in 1977). In addition, the overborrowing effect is computed under different degreeof misperception of the longevity of the terms of trade shocks. Note that the degree ofmisperception of the longevity of the shocks depends on the relative size of the transitoryand permanent components (σpxt/σpxp). In the model, if agents believe that this ratio ishigh (low), a large component of a terms of trade shock will be assumed to be transitory(permanent) on impact. As learning progresses, the transitory and permanent componentswill converge to their true value. Thus, in the case of a transitory terms of trade shock,a high (low) relative size of the transitory components will lead initially (that is, on impact)to a small (large) errors in the forecast of the transitory and permanent components.

Figure 4 shows the overborrowing effects for the transitory terms of trade shocks of1974 (18 percent increase in terms of trade index) and 1977 (a 10 percent increase inthe terms of trade index) for three different relative sizes of the transitory components.The benchmark value forσpxt/σpxp is 3, that is, the standard deviation of the transitorycomponent is three time larger than the standard deviation of the innovation to thepermanent component. This value corresponds to the average econometric estimate usingan unobserved component model (see Section 3). To check robustness, the overborrowingeffects have also been computed for two additional values ofσpxt/σpxp, namely 100and 0.01. Since the overborrowing effects tend to be very sensitive to the initial levelof debt, the computations are shown for four different levels of initial debt–GDP ratios(1 percent, 25 percent, 39 percent, and 100 percent). The benchmark values for the initialdebt–GDP ratio are 25 percent for the 1974 terms of trade shock (corresponding to theaverage debt–GDP ratio in 1974 for the sample countries) and 39 percent for the 1977terms of trade shock (corresponding to the average debt–GDP ratio in 1977).

Note that the steady-state overborrowing effect is invariant to the relative size of thetransitory component (σpxt/σpxp) as in all cases (but extreme values of 0 and∞), theKalman filter estimates of the transitory and permanent components converge to their truevalue. However,σpxt/σpxp determines the speed of convergence. Because both shocks aretransitory, a higherσpxt/σpxp leads to slower convergence shown in Fig. 4. This seeminglycounterintuitive result hinges on two facts:

(i) in the case of a transitory terms of trade shock, a highσpxt/σpxp imply fast convergenceof pxtt to pxtt and ofpxpt to pxpt ,

(ii) the rate of convergence of the overborrowing effect is inversely related to the speedof convergence ofpxtt andpxpt because at each point in time, the larger the forecasterror the larger the overborrowing effect.

For the benchmark value of initial debt–GDP ratio of 25 percent (the average debt–GDPratio in 1974), the steady-state overborrowing effect for the first terms of trade shock of

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Fig. 4. Estimated overborrowing effect of transitory terms of trade shocks in 1974 and 1977. (a) Transitoryincrease of 18% in the terms of trade (1974). Solid line:σpxt/σpxp = 3, dotted line:σpxt/σpxp = 100, dots anddashes:σpxt/σpxp = 0.01.

18 percent is 17.6 percent of GDP. For the benchmark value of initial debt–GDP ratio of39 percent (the average debt–GDP ratio in 1979), the steady-state overborrowing effectfor the second terms of trade shock of 10 percent is 14.7 percent of GDP. The totaloverborrowing effect due to the two transitory improvements in terms of trade during theseventies amounted to 32.3 percent of GDP. The large accumulated debt increased thevulnerability of LDCs to the high interest rates in the early eighties. Thus, uncertaintyabout the longevity of the two transitory terms of trade improvements during the seventiesmay have contributed significantly to LDCs foreign debt build-up and the debt crisis.

To sum up, when all parameters of the model are calibrated on data estimates (includingthe relative size of the transitory component), the total overborrowing effect generated bythe model for the two transitory improvements in terms of trade during the seventies is

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Fig. 4. (Continued). (b) Transitory increase of 10% in the terms of trade (1977). Solid line:σpxt/σpxp = 3, dottedline: σpxt/σpxp = 100, dots and dashes:σpxt/σpxp = 0.01.

substantial. Thus, uncertainty about the longevity of external shocks may have played animportant role in the debt accumulation leading to the debt crisis of the early 1980s.

5. Conclusions

This paper analyzes the borrowing behavior of a small open economy that reliesheavily on imports for its capital formation and faces an upward-sloping supply functionof foreign loans, in an environment where decision-makers face uncertainty about thelongevity of external shocks. The model replicates fairly well the business cycle propertiesof developing countries’ data.

It is shown that uncertainty concerning the longevity of shocks generates forecasterrors that are autocorrelated even when decision makers use rationally all the information

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available. These autocorrelated forecast errors can generate substantial debt accumulation.In particular, decision makers tend to overborrow during periods of negative, permanentexternal shocks (permanent declines in the terms of trade and permanent increases inthe world interest rate) and during periods of positive transitory external shocks, evenunder therationality paradigm. Furthermore, this overborrowing behavior can be relativelypersistent, generating debt accumulation especially if shocks are highly unpredictable. Thisfinding supports the view that the short-lived commodity booms of the 1970s may havedone more harm than good by encouraging some developing countries to overborrow,contributing to their debt accumulation and, hence, increased their vulnerability to theexceptionally high interest rates of the early 1980s. Using estimates of the transitory termsof trade shocks in 1974 and 1977, the model yields an overborrowing effect of 32 percentof GDP.

Finally, it is worth stressing that other mechanisms can lead to overborrowing,uncertainty about the longevity of external shocks is only one of them. This is especiallytrue if one is ready to depart from the full rationality of all agents. For example, theexplicit or implicit government guarantee of foreign debt has certainly contributed to debtaccumulation in many countries.

Acknowledgments

I am grateful to Frank Diebold, Bill Ethier, Jere Behrman, Lee Ohanian, AndrewAtkinson, Gary Hansen, Fumio Hayashi, Patrick Kehoe, Akihiko Matsui, and a referee forvery helpful comments. Thanks also to Alan Heston and Robert Summers for providingthe data. I am of course solely responsible for any errors.

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