A three-good, stochastic intertemporal equilibrium model of a small open economy is used to examine the link between terms of trade and business cycles. Equilibrium co-movements of model economies representing industrial and developing countries are computed and compared with the stylized facts of 30 countries. The results show that terms-of-trade shocks account for half of observed output variability and that the model mimics the Harberger-Laursen-Metzler effect and produces large deviations from purchasing power parity. The elasticity of substitution between tradable and nontradable goods and the persistence of the shocks play a key role in producing these results.

Abstract

A three-good, stochastic intertemporal equilibrium model of a small open economy is used to examine the link between terms of trade and business cycles. Equilibrium co-movements of model economies representing industrial and developing countries are computed and compared with the stylized facts of 30 countries. The results show that terms-of-trade shocks account for half of observed output variability and that the model mimics the Harberger-Laursen-Metzler effect and produces large deviations from purchasing power parity. The elasticity of substitution between tradable and nontradable goods and the persistence of the shocks play a key role in producing these results.

I. Introduction

Recurrent fluctuations in the terms of trade are commonly viewed as an important factor behind the generation and transmission of business cycles. Past issues of the International Monetary Fund’s bi-annual review of the world economy, the World Economic Outlook (WEO), have documented sharp fluctuations in economic activity that affected many countries after the large terms-of-trade disturbances caused by the increases in the price of oil in 1973-74 and 1979-80, and the subsequent declines in 1982-83 and 1985-86. The WEO has also documented marked fluctuations in non-oil commodity prices that induced large variations in the terms of trade of developing countries and played a key role in the business cycle of these economies—the terms of trade increased by 7 percent during 1983-84 for exporters of non-oil primary commodities, and then declined by more than 18 percent from 1985 to 1990 (see International Monetary Fund (1991a)).

Because of its empirical relevance, the link between terms of trade and economic fluctuations has been subject of intense theoretical debate. The well-known Keynesian analysis of Harberger (1950) and Laursen and Metzler (1950) argued that, when the terms of trade worsen, the trade balance worsens and savings decline because a fall in the purchasing power of exports is in fact a reduction in income, and the marginal propensities to consume and save are less than unit—the Harberger-Laursen-Metzler (HLM) effect. 2/ When introduced into the IS-LM apparatus under conditions of perfect capital mobility, this widening of the trade deficit produces a decline in output that is transitory or permanent depending on the exchange-rate regime. 3/ Central to this argument was the conjecture that, because prices and wages adjust slowly, the response of the real exchange rate to a terms-of-trade shock is not determined by domestic relative price movements and depends on the behavior of the nominal exchange rate—i.e. the property of nominal-exchange-regime neutrality, as described in Mussa (1990), breaksdown.

In the early 1980s some doubts were cast on the analysis of Harberger and Laursen and Metzler. Obstfeld (1982), Svensson and Razin (1983), and Persson and Svensson (1985) showed that, when savings in a small open economy are modeled as the outcome of optimal intertemporal plans, the effect of a change in the terms of trade on savings and the trade balance depends on the perceived duration of terms-of-trade shocks. In general, with a fixed rate of time preference, transitory changes in the terms of trade result in the HLM effect, but permanent changes tend to leave savings and net exports unaffected. Further work argued also that the response of the real exchange rate to a terms-of-trade shock is determined by the effect of the latter on the relative price of nontraded goods, as in Greenwood (1984), and hence that there is nominal-exchange-regime neutrality.

While early work on intertemporal equilibrium models questioned the savings behavior implicit in the HLM effect, it did not provide an interpretation of the link between terms of trade and business cycles because it focused mostly on deterministic models of endowment economies. Engel and Kletzer (1989) and Macklem (1991) showed both the complications that emerge with formal analysis when investment decisions are incorporated into these models, and the relevance of such decisions for predictions regarding the co-movement among macroeconomic aggregates. Moreover, the question of whether observed real-exchange-rate variability can be explained exclusively by adjustments in the relative price of nontraded goods stemming from real shocks was left unanswered and open to criticism. Mussa (1990) argued, for instance, that the variability of real exchange rates under floating nominal exchange rates has been too large to be accounted for by real disturbances.

Following the tradition of Obstfeld and Svensson and Razin, this paper examines the relationship between terms of trade and business cycles in a small open economy from a perspective of intertemporal equilibrium. The contribution is that this study derives the quantitative implications of a three-sector dynamic stochastic model and examines whether these implications are consistent with actual business cycles. Despite extensive theoretical work on the subject (see Frenkel and Razin (1987)), the actual co-movement between fluctuations in the terms of trade and other macroeconomic aggregates has not been documented in detail, nor has it been compared with the predictions obtained from theory. 4/ In this regard, the multi-country data base analyzed here highlights four stylized facts: (1) fluctuations in the terms of trade are large, not as persistent as productivity disturbances, and procyclical; (2) there is a Harberger-Laursen-Metzler effect and this effect is stronger in countries where terms-of-trade shocks are more persistent; (3) business cycles across countries exhibit similar characteristics; and (4) deviations from purchasing power parity are significant. The paper shows that business cycles in model economies driven by terms-of-trade shocks like those observed in the data, together with productivity shocks, are roughly consistent with these stylized facts.

Other recent research, related to the development of open-economy real business cycle models, focuses on issues similar to those examined here. A number of researchers have examined a two-country framework with complete markets following Backus, Kehoe, and Kydland (1992a) and Baxter and Crucini (1992). This framework explains some international business cycle facts, although complete markets lead to excessive risk sharing and excessive correlation of consumption across countries. Backus, Kehoe, and Kydland (1992b) and Stockman and Tesar (1990) examined three-good variants of this approach with specialized trade and found that, although some key empirical regularities are well reproduced by the models, actual terms-of-trade fluctuations are significantly underestimated—the terms of trade in industrial countries fluctuate 2 to 6 1/2 times more than in the models.

In two-country real business cycle models, the terms of trade are endogenous and their stochastic properties reflect the influence of exogenous shocks. Hence, the fact that the variability of the terms of trade is underestimated suggests that the effects of changes in the relative price of exports in terms of imports may not be fully captured. In contrast, this paper introduces shocks to the terms of trade of the magnitude observed in the data directly as an input for model simulations. This approach follows McCallum’s (1989) view that real business cycle models should incorporate terms-of-trade effects explicitly to reduce their reliance on unobserved productivity disturbances, and to separate the effects of changes in imported input prices from the effects of technological change. As Finn (1991) showed, exogenous energy price shocks account for as much as one third of actual output variability in a closed-economy real business cycle model and, when these shocks are present, the conventional measure of Solow residuals is a misleading proxy for true productivity disturbances. 5/ This paper shows that terms-of-trade shocks account for more than half of actual output variability, although productivity disturbances continue to play an important role. 6/

The model examined here also departs from the three-good, two-country real business cycle framework in two important aspects. First, foreign assets in the form of one-period, risk-free bonds are the only claim exchanged internationally, and hence world markets of contingent claims are incomplete. 7/ Second, agents are allowed to trade internationally capital and consumption goods to be consistent with the fact that two thirds of a typical country’s imports are capital and intermediate goods and one third are consumption goods (see Section IV for details). Thus, the model combines the production and investment framework of a real business cycle model with the Obstfeld-Svensson-Razin intertemporal equilibrium approach to the analysis of the current account in a small open economy—particularly the extensions that introduced nontraded goods (Greenwood (1984) and Ostry (1988)). Previous work on real business cycle theory for small open economies has examined a variety of models in which all goods are tradable—as in Cardia (1991), Lundvik (1991), Mendoza (1991), and Correia, Neves, and Rebelo (1991). These models mimic many of the stylized facts, with the exception that savings and consumption are almost perfectly correlated with output due to weak intertemporal substitution in a setup where the intertemporal relative price of consumption (i.e. the world’s real interest rate) is independent of domestic saving decisions. Mendoza (1992a) examined an endowment model with nontraded goods and showed that, because the intertemporal relative price of consumption is affected by changes in the terms of trade and in the relative price of nontradables, consumption behavior is more realistic. However, the absence of investment produced unrealistic dynamics for the trade balance, foreign assets, and the real exchange rate.

A model in which changes in the terms of trade induce economic fluctuations may also be helpful for studying business cycles in developing countries. Since these countries typically import large amounts of capital goods and export primary commodities, terms-of-trade shocks affect significantly the productivity of investment and domestic relative prices. The mechanism by which changes in these variables cause economic fluctuations is well captured in real business cycle models, but until now research in this area has not focused much on developing countries. This paper documents stylized facts for 23 developing countries, and produces simulations for a version of the model parameterized and calibrated to represent a typical developing country.

The rest of the paper is organized as follows. Section II reviews the stylized facts that the model attempts to mimic, with emphasis on the Harberger-Laursen-Metzler effect and other properties of the terms of trade. Section III presents the model and discusses optimal intertemporal planning. Section IV discusses the determination of relevant parameter values and the simulation technique. Section V presents the results of numerical simulations for benchmark models of industrial and developing countries. Section VI discusses the robustness of the results to changes in preference parameters and in the stochastic processes of exogenous shocks. Some concluding remarks are included in the last section.

II. The Stylized Facts

This section documents some of the characteristics of recent business cycles in the seven largest industrialized countries (G-7) and 23 developing countries (DCs). Business cycle properties among industrialized countries have received much attention recently, 8/ but less work has been devoted to documenting stylized facts for developing countries. 9/ The section emphasizes the co-movement of macroeconomic aggregates with the terms of trade, particularly the correlation between the trade balance and the terms of trade as a measure of the HLM effect.

Documenting stylized facts for several countries is difficult because it involves dealing with international databases created with country data of uneven quality. The data used here were obtained from the IMF’s WEO Database and the International Financial Statistics Yearbook 1991 and from the World Bank’s World Tables as contained in the Socio-economic Time-series Access and Retrieval System (STARS) version 1.0 from March 1990. The data are annual observations of the U.S. dollar import and export unit values; the U.S. dollar value of credits and debits in the trade balance and factor payments accounts of the balance of payments; GDP, consumption, and investment at constant and current prices from national accounts; the average U.S. dollar exchange rate; and total population. Imports are selected as the ‘numeraire’, following Svensson and Razin (1983) and Greenwood (1984), and hence the terms of trade are the ratio of export to import unit values and all real variables are measured at constant import prices. Stylized facts for standard measures of real variables at constant prices have also been computed, and for simplicity these are referred to as variables at constant domestic prices. The sample period varies with country and variable, but in general it covers from 1960 or 1965 to 1988 or 1989. Details on this and other data-related issues are described in the notes to Tables 1-6. These tables list the statistical moments that characterize fluctuations in the terms of trade (TOT), the trade balance (TB), gross domestic product (GDP), private consumption (C), fixed investment (I), the real exchange rate (RER), and net foreign factor payments (NFFP).

Table 1.

The Terms of Trade and the Real Trade Balance: Summary Statisticsa

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Data from the IMF WEO Database for the period 1960-89 for the G7 and 1961-89 for developing countries. Terms of trade are the ratio of export to import unit values with 1985=100. Trade data are current exports and imports in US dollars, deflated by import unit values and divided by total population. Real exports, real imports and the terms of trade are logged and detrended with a quadratic time trend. The real trade balance corresponds to detrended exports minus detrended imports. σ is the percentage standard deviation, ρ(1) is the first-order serial autocorrelation (Bartlett standard error in parentheses) and ρtb, tot is the correlation between terms of trade and the real trade balance (least squares standard error in parentheses). An asterisk denotes statistical significance at the 5 percent level. A “+” sign identifies countries that are major fuel exporters according to WEO standard.

Table 2.

Real GDP at Domestic Prices and Import Prices: Summary Statistics

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Note: Real GDP at domestic prices is the standard measure, and real GDP at import prices is the U.S. dollar value of GDP deflated using U.S. dollar import unit values. The data are expressed in per capita terms, logged, and detrended with a quadratic time trend. The first number in brackets indicates the year of the first observation in the sample of real GDP at domestic prices, and the second indicates the year of the first observation in the sample of real GDP at import prices. The last observation for all data is 1989. The moments listed are the percentage standard deviation (Sd.), the percentage standard deviation of the terms of trade in the corresponding sample of real GDP (Sd. Tot), the standard deviation relative to the standard deviation of the terms of trade (Rsd.), the first-order serial autocorrelation (Ac.(1)), and the correlation with the terms of trade (Corr.Tot.). The source of the data is the IMF WEO Database.
Table 3.

Real Consumption at Domestic Prices and Import Prices: Summary Statistics

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Note: Consumption at constant domestic prices is the standard measure of real private consumption, and consumption at constant import prices is the U.S. dollar value of private consumption deflated using U.S. dollar import unit values. The data are expressed in per capita terms, logged and detrended with a quadratic time trend. The sample period is 1968–1988 and the source is the STARS database in World Bank (1990). The moments listed are the percentage standard deviation (Sd.), the percentage standard deviation of the terms of trade (Sd.Tot), the standard deviation relative to the standard deviation of the terms of trade (Rsd.), the first–order serial autocorrelation (Ac.(1)). the correlation with GDP (Corr.GDP). and the correlation with the terms of trade (Corr.Tot).
Table 4.

Real Investment at Domestic Prices and Import Prices: Summary Statistics

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Note: Investment at constant domestic prices is the standard measure of real fixed investment, and investment at constant import prices is the U.S. dollar value of fixed investment deflated using U.S. dollar import unit values. The data are expressed in per capita terms, logged, and detrended with a quadratic time trend. The sample period is 1968–1988 and the source is the STARS database in World Bank (1990). The moments listed are the percentage standard deviation (Sd.), the percentage standard deviation of the terms of trade (Sd.tot), the standard deviation relative to the standard deviation of the terms of trade (Rsd.), the first–order serial autocorrelation (Ac. (1)), the correlation with GDP (Corr.GDP), and the correlation with the terms of trade (Corr.Tot). For Mexico, Peru, Israel, Saudi Arabia, Egypt, Indonesia, Algeria, Cameroon, Kenya, and Nigeria the moments correspond to total real investment including inventories.
Table 5.

Variability and Persistence of Real Effective Exchange Rate Fluctuations 1/

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Source: International Monetary Fund, International Financial Statistics, and Information Notice System.

The data are for the period 1979.1-1992.2 quarterly and 1979-1991 annually. Real effective exchange rates are equal to nominal, trade-weighted effective exchange rates adjusted for relative changes in consumer prices. The data have been lagged and detrended using a quadratic time trend, σ is the standard deviation in percent and ρ(1) is the first-order serial autocorrelation. A “+” sign identifies countries that are major fuel exporters according to WEO standard.

Table 6.

Real Net Foreign Factor Payments (NFFP): Summary Statistics

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Note: The data are the net of credits and debits in the tactor payments accounts of the balance of payments in U.S. dollars, delated using U.S. dollar import unit values. The data are expressed in per capita terms, logged, and detrended with a quadratic time trend. The number in brackets indicates the year of the first observation in the sample of factor payments data; when necessary, a second number appears in brackets to indicate the year of the first observation in the sample of GDP in U.S. dollars used to compute the ratio NFPP/GDP. The moments are the standard deviation (Sd.), the standard deviation of the terms of trade in the sample of NFPP (Sd.Tot), the standard deviation relative to the standard deviation of the terms of trade (Rsd), the first–order serial autocorrelation (Ac(1)), and the correlation with the terms of trade (Corr.Tot). The source of the data is the IMPs WEO Database.

The moments reported in Tables 1-6 correspond to cyclical components of filtered data. The Hodrick-Prescott (HP) filter is the one most commonly used in the real business cycle literature to separate trend and cyclical components of macroeconomic time series, although a quadratic time trend and a first difference filter have also been used occasionally. Despite the controversy surrounding filtering procedures (see Canova (1991)), there is evidence suggesting that these filters produce similar results for the relevant statistics used in this study. 10/ The data are filtered here using the quadratic time trend for simplicity, given the short sample of the crosscountry data bases and the stagnating pattern of GDP per capita in many developing countries over the last two decades. For G-7 countries, Mendoza (1992a) reports the stylized facts for the same set of data examined here using the HP filter; the results show that although HP standard deviations are smaller, ratios of standard deviations as well as coefficients of correlation and persistence do not differ significantly.

Table 1 reports the standard deviation, contemporaneous correlation, and first-order serial autocorrelation of the terms of trade and the trade balance. Because the last two moments are critical for the analysis that follows, standard errors assessing their statistical significance are also reported. This table illustrates some interesting regularities. First, in every case in which the co-movement between TOT and TB is statistically significant, the correlation is positive. Thus, there is an HLM effect in the sense that positive deviations from trend of the terms of trade are associated with cyclical improvements in the trade balance. This observation is consistent with the Obstfeld-Svensson-Razin framework because fluctuations in TOT are not highly persistent—the average first-order autocorrelation is 0.62. However, that framework also predicts that the co-movement between TB and TOT should be positively related to the persistence of the latter, contrary to what the table shows. As illustrated in Figure 1, countries with higher autocorrelation in the terms of trade exhibit higher correlation between the trade balance and the terms of trade—a linear regression between the two produces a coefficient of 0.44 with a t-statistic of 5.65. The theoretical result follows from pro-saving and pro-borrowing wealth effects that tend to cancel out as income shocks become more persistent, 11/ given a fixed structure of preferences and technology. In contrast, the numerical analysis of the following sections explores to which extent international differences in tastes and technology could account for this puzzle.

Figure 1
Figure 1

The Harberger–Laursen–Metzler Effect

Citation: IMF Working Papers 1992, 098; 10.5089/9781451852066.001.A001

Another interesting regularity emerges from Table 1 by comparing the statistics reported for the G-7 and the DCs. The terms of trade for the G-7 exhibit on average a 7.4 percent standard deviation, which is about 2 to 3 times less than the average variability of the terms of trade for developing countries. Similarly, trade balances in DCs are 2 to 3 times more variable than in the G-7. This reflects the fact that the export base of developing countries is less diversified and that they specialize in exporting commodities that experience sharp price changes. Surprisingly, however, net exports are slightly more variable than the terms of trade in most countries, by a factor of 1.1 on average, regardless of differences in the export base. 12/ Thus, the data show that the trade balance fluctuates more in countries in which the terms of trade are more volatile, but with a uniform proportionality factor.

To summarize, Table 1 illustrates four facts: (1) there is a Harberger-Laursen-Metzler effect, albeit not a very strong one; (2) countries with more persistent terms-of-trade shocks are not the ones that exhibit less correlation between the trade balance and the terms of trade; (3) the ratio of variability of the real trade balance to variability in the terms of trade is similar for all countries; and (4) the trade balance fluctuates more in developing countries, which also experience larger fluctuations in the terms of trade.

The stylized facts of output, consumption, and investment reported in Tables 2-4 also support the view that there is some uniformity in business cycles across countries. Qualitatively, the properties of business cycles in DCs are the same as those reported in studies of Canada, the United States, and the G-7 (see, for example, Backus and Kehoe (1992), Backus, Kehoe, and Kydland (1992a), Cardia (1991), Stockman and Tesar (1990), and Mendoza (1991)). Considering variables measured at constant domestic prices, C is always less variable than the terms of trade and is less variable than GDP in 12 countries, 13/ while I varies about as much as TOT in many countries and significantly more than GDP in all countries. Using data measured at constant import prices, consumption and investment tend to fluctuate more than the terms of trade and GDP. Regardless of which deflator is used, C and I are procyclical and the fluctuations around trend of all three macroeconomic aggregates exhibit some persistence. The correlations with the terms of trade are less well defined, and although in general they are weakly positive, they range from large negative to large positive coefficients.

There are also interesting quantitative similarities. Although the G-7 exhibit less variability in GDP, C, and I than developing countries, the ratios of variability relative to the standard deviation of TOT do not differ significantly. Comparing averages of regional means for the G-7 and the four regions of DCs, the data shows that with respect to the standard deviation of TOT, the standard deviation of GDP at constant import prices (constant domestic prices) ranges from 0.87 to 1.71 (0.30 to 0.39), the standard deviation of C ranges from 0.78 to 1.56 (0.35 to 0.79), and the standard deviation of I is between 1.25 and 2.74 (0.9 and 1.3). The coefficients of first-order serial autocorrelation of TB, TOT, GDP, C, and I are also similar across countries. Cyclical components are stationary processes with positive roots well inside the unit circle. For all 30 countries, the cross-country average of the first-order autocorrelations range from 0.44 for consumption at domestic prices to 0.62 for the terms of trade, with standard deviations that are generally less than 1/3 of the corresponding average.

Table 5 reports the variability and persistence of fluctuations in the IMF’s measure of the real effective exchange rate. Correlations with annual national accounts aggregates are not reported because the sample period of these exchange rates covers only 10 years. Considering quarterly data, the table indicates that RER fluctuates between 2 and 9.5 percent in industrial countries and up to 38 percent in developing countries, with first-order serial autocorrelations for all countries generally in excess of 0.82 (0.45 annually). Moments reported by Schlagenhauf and Wrase (1991) for Hodrick-Prescott-filtered real exchange rates of four of the G-7, defined using bilateral U.S. dollar exchange rates and consumer price indexes, are roughly consistent with these results—the standard deviation of RER is between 2.9 and 9.7 percent and the first-order autocorrelation is about 0.8. Thus, as Mussa (1990) argued, the evidence shows that there have been large deviations from purchasing power parity in recent years.

III. The Model

This section describes the structure of preferences, technology, and financial markets that characterizes a three-good, stochastic intertemporal equilibrium model of a small open economy. The design of the model is based on the literature of the 1980s on the HLM effect, in particular Obstfeld (1982) and Greenwood (1984), and on open-economy real business cycle models by Mendoza (1991), Tesar (1990), and Stockman and Tesar (1990).

1. Preferences

The economy is inhabited by identical, infinitely-lived individuals that consume three goods; nontradables, n, and two tradables, exportable or home goods, x, and importable or foreign goods, f. 14/ Individuals maximize expected lifetime utility given by a stationary cardinal utility function:2/

U(x,f,n) = E[Σt=0{u(xt,ft,nt)exp(Στ=0t1 v(xτ,fτ,nτ))}].(1)

The functions u(.) and v(.) adopt the following form:

u(x,f,n) =([(xαf1α)μ +nμ]1μ)1γ1γ,(2)

and

v(x,f,n) =βln(1 +[(xαf1α)μ +nμ]1μ),(3)0α1,μ>1,γ>1,β>0.

Preferences over tradables and nontradables are described by a constant elasticity of substitution (CES) function, where 1/1+μ is the elasticity of substitution. The composite of tradables is a Cobb-Douglas function, where α is the share of home goods in total expenditure on tradables. The intertemporal elasticity of substitution in aggregate consumption is also constant and given by 15/γ. The elasticity of the rate of time preference with respect to the CES composite is approximated by β.

2. Production technology and financial markets

Firms produce exportable and importable goods using capital, which is an homogeneous, importable good, as the only variable input. 16/ The supply of nontradables is assumed to be given by an endowment to keep the number of state variables at a minimum. Firms maximize the present value of profits facing convex, quadratic adjustment costs. Firms and households have access to an international financial market in which they trade non-contingent one-period real bonds paying a fixed real interest rate with the rest of the world. Stochastic disturbances affect productivity in the exportables and importables industries, the endowment of nontradables, and the terms of trade. The resource constraint of the economy is:

ft +etppxxt +ptnnt = Qety(etppx(Ktx)x + (Ktf)t +ptnN)(4)Kt+1 +Kt(1δ) -φ2(Kt+1-Kt)2 -At+1 +At(1+r*),

for t=0, . . ,∞. The price of foreign goods is the numeraire, so px is the exogenous, time-invariant mean of the relative price of exportables in terms of importables (i.e. the terms of trade), and ptn is the endogenous relative price of nontradables in terms of importables. The random variables ety and etP are the disturbances affecting domestic output and the terms of trade, and these follow stochastic processes as defined below. Q is a productivity scale factor that accounts for the different size of developing and industrialized economies, X and ι are the income shares of capital in the industries producing exportables and importables respectively, and Ktx and Ktf are the corresponding capital stocks. Since capital is homogenous the aggregate capital stock is Kt=Ktx+Ktf, and ϕ is the parameter governing the marginal adjustment cost of capital in terms of importables. N is the endowment of nontradables. The holdings of real foreign assets, denominated in units of importables, are given by At, and the world’s real interest rate is r*.

3. Equilibrium and dynamic programming formulation

The equilibrium of this economy is characterized by the stochastic processes {Kt+1}0, {At+1}0, {Ktx}0, {Ktf}0, {xt}0, {ft}0, and {nt}0 that maximize (1) subject to the resource constraint (4). Given (2) and (3), the optimality conditions of this problem can be expressed as follows:

Uf(t)exp(v(t))Et[Uf(t+1)] = (1+r*),(5)
Ux(t)Uf(t) =etppx,(6)
Un(t)Uf(t) =ptx.(7)
(etyetppx)X(Ktx)x1 =etyι(Ktf)t1,(8)
exp(v(t))Uf(t)[1 +φ(Kt+1-Kt)] =(9)EtUf(t+1)((Qet+1yet+1ppx)X(Kt+1-Kt+1f)x1 + (1-δ) +φ(Kt+2Kt+1))].

These conditions have straightforward interpretation, except that the lifetime marginal utilities of importables, Uf(t), exportables, Ux(t), and nontradables, Un(t), include a term that accounts for the impact of changes in current consumption on the rate of time preference. Condition (5) sets the intertemporal marginal rate of substitution in consumption of importables equal to their intertemporal relative price, (1+r*), while (6) and (7) set the intratemporal marginal rates of substitution between exportables and importables, and nontradables and importables equal to their corresponding relative prices. Equation (8) determines the optimal allocation of capital across firms producing exportables and importables, and (9) sets optimal investment by equating the marginal costs and benefits of sacrificing a unit of consumption of importables.

The equilibrium of this economy can be expressed as the solution to a dynamic programming problem with only three state variables. Using (2), (3) and (6), one can show that in equilibrium the ratio of x to f, using f as the numeraire, is given by α/(1-α). Hence optimal consumption of exportables as a function of importables is:

x^t =(α1α)(ftetppx).(10)

The market of nontradables must clear so nt=QetyN, and hence from (7) it follows that:

ptx =(QetyN)μ1(xtαft1α)μ1(1α)xtαftα.(11)

Given production parameters and the equality Kt=Ktx+Ktf, equation (8) determines optimal allocations of capital in the exportables and importables industries as functions of the aggregate capital stock and the shocks:

K^tx =kx(Kt,etp,ety),(12)
K^tf =kf(Kt,etp,ety),(13)

It follows from (10) - (13) that, if the stochastic structure of the model is simplified as explained below, the problem of maximizing (1) subject to (4) can be rewritten as:

V(Kt.At,λts) = max{[(xtαft1α)μ+(QetyN)μ](1γ)μ1γ+(1+[(xtαft1α)μ+ (QetyN)μ]1μ)β[Σx=14πs,xV(Kt+1,At+1,λt+1x)]},(14)

subject to, 17/

ft = (1-α)[Qety(etppx(Ktx)x +(Ktf)ι) -Kt+1 +Kt(1δ) -Φ2(Kt+1Kt)2 + (1+r*)At -At+1],(15)At,At+1 and Kt,Kt+1,ft 0.

At the beginning of date t, agents start with foreign assets or debt Atand aggregate capital Kt. They observe disturbances affecting the terms of trade and productivity—a state of nature λt that is given by the realizations etY and etP—and they know the stochastic process that governs the behavior of future realizations of these shocks. Agents formulate optimal decision rules regarding the accumulation of foreign assets and domestic capital. Given these, equilibrium stochastic processes for the allocation of capital between firms producing exportables and importables, the relative price of nontradables, and consumption of the three goods in the utility function are determined by equations (10)-(13) and (15). Once these processes are determined, equilibrium processes for other variables of interest follow from the appropriate definitions.

A variety of algorithms are available for solving stochastic dynamic programming problems like (14). Linear and log-linear approximation methods are widely used in the real business cycle literature, but they may not provide reliable results in this case because of the large magnitude of terms-of-trade shocks and their interaction with sizable productivity disturbances (for a discussion of how the accuracy of approximation methods deteriorates as the variance of the underlying disturbances increases see Christiano (1989) and Dotsey and Mao (1992)). Consequently, the method applied here is an exact-solution procedure based on iterations of the value function and the transition probability matrix using discrete grids to approximate the state space. This procedure is an extension of the method used by Mendoza (1991), following previous work by Greenwood, Hercowitz, and Huffman (1988) on the basis of algorithms designed by Bertsekas (1976). The drawback is that this method adopts simple representations for the stochastic shocks in order to minimize the dimension of the state space.

In this case the shocks are assumed to follow two-point symmetric Markov chains according to the simple persistence rule. There are four states of nature,

λts,λt+1u[(ey,ep),(ey,ep),(ey,e¯p),(ey,ep)].(16)

The transition probability of the current state s moving to state u in one period is πs, u for s, u=1, 4. Transition probabilities satisfy usual conditions—each one ranges between 0 and 1 and they add up to unity for each starting state s. These probabilities are given by the rule of simple persistence,

πs,x = (1-θ)Πx +θZs,x.(17)

Here, θ governs the persistence of the two shocks, Πu is the long-run probability of state u, and Zs, u=1 if s=u and 0 otherwise. The symmetry conditions are:

e¯y =-ey=ey,e¯p=-ep=ep,(18)

and

Π(e¯y,e¯p)=Π(ey,ep) =Π,Π(e¯y,ep)=Π(ey,e¯p)=12Π.(19)

This setup simplifies the analysis by minimizing the number of parameters that characterize the stochastic structure of the model. Once the values of ey, ep, θ, and Π are determined, the properties of the stochastic processes of the two disturbances are given by,

σey=ey,σep=ep,ρey=ρep=θ ,ρey,ep=4Π-1.(20)

The standard deviations of shocks to productivity and the terms of trade are σey and σep respectively, ρey and ρeP are their coefficients of first-order serial autocorrelation, and their contemporaneous correlation is ρey, eP.

Up to this point, macroeconomic aggregates have been measured in units of importables, and hence they are comparable with actual data expressed at constant import prices, as documented in Section II. It is also useful, as Frenkel and Razin (1987) argued, to express these aggregates in terms of a consumption-based price index (CPI) to produce equilibrium co-movements that can be compared with more familiar definitions of variables at constant prices—which involve price indices that consider traded and nontraded goods—and to obtain measures that can be used as basis for welfare comparisons in policy analysis. 18/ This is done by applying duality principles to create the CPI. Because the CES component of (2) is homogenous of degree one, there is an expenditure function at date t that embodies the following consumer price index:

Pt =[(αα(1α)(1α)(etppx)α)μ1+μ + (ptn)μ1+μ]1+μμ.(21)

IV. Selection of Parameters

Two sets of parameter values are defined to construct model economies that reproduce some essential characteristics of industrialized and developing countries. Unfortunately, the information available in international databases provides only a crude approximation for some of the variables defined in the model, particularly the breakdown of production and consumption into tradables and nontradables, and hence the parameterization proposed here is only a first approximation. The two sets of parameters are as follows:

Industrial country benchmark parameters:

I = {ey=8.5,ep=7.3,θ=0.668,Π=0.394,r*=0.04,(22)N=3.29, x=0.487,ι=0.404,δ=0.1,φ=0.1,Q=1.0,γ=1.5,μ=0.35,α=0.19,β=0.125 }.

Developing country benchmark parameters:

A = {ey=12.25,ep=18.0,θ=0.604,Π=0.205,r*=0.04,(23)N=0.702, x=0.661,ι=0.698,δ=0.1,φ=0.3,Q=1.3,γ=2.61,μ=-0.218,α=0.15,β=0.019 }.

The values of parameters describing stochastic disturbances are determined by combining information from actual data with a calibration strategy, taking into account the conditions 1 listed in (20). The variability and persistence of the terms of trade are determined by taking averages for the G-7 and the DCs from Table 1. The variability of productivity shocks and their contemporaneous correlation with terms-of-trade shocks are set to mimic the variability of real GDP at import prices and its correlation with TOT as given by averages for the G-7 and the DCs from Table 2. The parameter Φ is also set by calibration, so as to mimic the average standard deviation of investment at import prices for the G-7 and the DCs in Table 4.

Preference parameters are assigned values using information on consumption of nontradables and tradables, combined with evidence from econometric studies and the conditions imposed by the non-stochastic steady-state equilibrium of the model. The value of γ is in the range of estimates obtained in studies of industrial and developing countries. Point estimates of γ are controversial, but real business cycle models for industrial countries have shown that values between 1 and 2 are useful to mimic key stylized facts (see, for example, Prescott (1986), Greenwood, Hercowitz, and Huffman (1988) and Mendoza (1991)). For DCs, γ=2.6 corresponds to a GMM estimate of 1/γ produced by Ostry and Reinhart (1992) for a sample combining time series for 13 developing countries. 19/ μ for industrial countries is estimated using data on relative expenditures and relative prices for traded and nontraded goods listed in Table 7 and obtained from Kravis, Heston, and Summers (1982). As in Stockman and Tesar (1990), μ is obtained by regressing logged relative expenditures on logged relative prices and logged per capita GDP adjusted for purchasing power (also from Kravis, Heston and Summers). This gives an estimate of 1/(1+μ) of 0.74 with a standard error of 0.438. 20/ For developing countries, Ostry and Reinhart (1992) estimated 1/(1+μ) at 1.279 with a standard error of 0.154, and showed that in the more industrialized DCs the coefficient is lower. 21/ α is set to mimic the average ratios of total trade to output for the G-7 and the DCs in the deterministic steady state, 22/ and the value of β is also determined as part of the steady-state conditions described below.

Table 7.

Selected Data on the Composition of Consumption Expenditures and Imports, 1975 1/

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Columns (1) and (2) correspond to the ratios of column (8) to column (9) in Tables 6-10 and 6-12 of Kravis, Heston, and Summers (1982). Column (3) is the sum of the shares of imports of food and manufactures (excluding chemical products and machinery and equipment) in total imports obtained from UNCTAD (1987) pp. 158-179. Column (4) is generated by applying the shares from Column (3) to data on total imports (UNCTAD (1987)), and then using the resulting U.S. dollar amount of consumer good imports to produce the shares of imports in consumption of tradables using the data on private consumption, exchange rates, and share of tradables in total private consumption from Tables 1-2, 1-7, and 6-10 in Kravis, Heston, and Summers (1982). Column (5) is the ratio of the sum of exports and imports of goods and nonfactor services to total GDP at current prices computed with data from World Bank (1990).

For Columns (3) and (4) Belgium includes Luxembourg.

Excluding the United States which is the base for the purchasing power correction in Kravis, Heston, and Summers (1982).

Data on imports for the Philippines includes unallocated imports.

Production parameters are difficult to define because of limitations in the data on sectoral input earnings, capital stocks, and employment in many countries. Some of the information that is available on the STARS database and the OECD National Accounts (OECD (1988)) regarding these variables is summarized in Table 8. For the countries in the Kravis-Heston-Summers sample, the table reports GDP shares in agriculture, industry, manufacturing industry, non-manufacturing industry, and services; the percentage of manufacturing value added pertaining to labor earnings; total labor income as a percentage of total value added; and earnings in sectors other than manufacturing as a percentage of value added in those sectors. For the last two variables, the table reports actual data only for OECD countries and Mexico, 23/ while for the rest of the DCs it reports estimates constructed by assuming that unit labor costs in sectors other than manufacturing relative to Mexico are the same as those observed in the manufacturing sector. Given that industrialized countries are net exporters of manufactures, while most DCs are net importers, the average of earnings as a percent of value added in manufacturing determines 1-χ for industrial countries and 1-ι for developing countries. Similarly, the averages of labor earnings as a percent of value added in other sectors are used to set ι for industrial countries and X for developing countries. The efficiency parameter Q is a multiplicative constant that does not affect the statistics examined in the rest of the paper. However, to be consistent with observed differences in economy size between industrial countries and large developing countries, Q is set to unity for industrial countries and for DCs is set to make their mean output about 1/5 of the mean output of industrial countries. 24/ The depreciation rate δ is set to 10 percent and the real interest rate r* is set to 4 percent following the literature on real business cycles.

Table 8.

Sectoral Value Added and Labor Income, 1975. 1/

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GDP shares and manufacturing earnings are from STARS, World Bank, 1990. Total labor incomeshare for indestrial countries is from OECD, National Accounts.

For developing countries, except Mexico, it is estimated by assuming that the ratio of earnings relative to Mexico is the same as in manufacturing industries. For Mexico it is taken from Mendoza (1992b), where was claculated on the basis of date from Indicadores Economicos, Banco de Moxico.

Computed using the GDP shares of nonmanufacturing sertors and the total labor income share by assuming a constant labor income shere in those sectors.