The Terms of Trade and Economic Fluctuations
Author:
Mr. Enrique G. Mendoza https://isni.org/isni/0000000404811396 International Monetary Fund

Search for other papers by Mr. Enrique G. Mendoza in
Current site
Google Scholar Close
Publication Date:
01 Nov 1992
eISBN:
9781451852066
Language:
English
Keywords:
WP; standard deviation; real GDP; U.S. dollar; cross-expenditure effect; terms-of-trade fluctuation; variability of TOT; consumption basket; shocks in the developing country benchmark
Download PDF (3 MB)

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

article image
article image

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

article image
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

article image
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

article image
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/

article image
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

article image
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 [ Σ t = 0 ∞ ⁢ { u ⁢ ( x t ⁢ , f t , ⁢ n t ) ⁢ exp ⁡ ( − Σ τ = 0 t − 1 ⁢  v( x τ , ⁢ f τ , ⁢ n τ ) ) } ] ⁢ . ( 1 )

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

u ⁢ ( x , f , n ) ⁢  =   ( [ ( x α ⁢ f 1 − α ) − μ ⁢  +   n − μ ] − 1 μ ) 1 − γ 1 − γ , ( 2 )

and

v ⁢ ( x , f , n ) ⁢  =   β ⁢ ln ⁡ ( 1 ⁢  +   [ ( x α ⁢ f 1 − α ) − μ ⁢  +   n − μ ] − 1 μ ) , ( 3 ) 0 ≤ α ≤ 1 ,   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:

f t ⁢  +   e t p ⁢ p x ⁢ x t ⁢  +   p t n ⁢ n t ⁢  =  Q e t y ⁢ ( e t p ⁢ p x ⁢ ( K t x ) x ⁢  +  ( K t f ) t ⁢  +   p t n ⁢ N ) ( 4 ) −   K t + 1 ⁢  +   K t ⁢ ( 1 − δ ) ⁢  -   φ 2 ⁢ ( K t + 1 ⁢ - K t ) 2 ⁢  -   A t + 1 ⁢  +   A t ⁢ ( 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:

U f ⁡ ( t ) exp ⁡ ( − v ⁡ ( t ) ) ⁢ E t ⁢ [ U f ⁢ ( t + 1 ) ] ⁢  =  (1+ r * ), ( 5 )
U x ⁡ ( t ) U f ⁡ ( t ) ⁢  =   e t p ⁢ p x , ( 6 )
U n ⁡ ( t ) U f ⁡ ( t ) ⁢  =   p t x ⁢ . ( 7 )
( e t y ⁢ e t p ⁢ p x ) ⁢ X ⁢ ( K t x ) x − 1 ⁢  =   e t y ⁢   ι ⁢ ( K t f ) t − 1 , ( 8 )
exp ⁡ ( v ( t ) ) U f ( t ) [ 1  + φ ( K t + 1 - K t ) ]  = ( 9 ) E t U f ( t + 1 ) ( ( Q e t + 1 y e t + 1 p p x ) X ( K t + 1 - K t + 1 f ) x − 1  +  (1- δ )  +   φ ( K t + 2 − K t + 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 ⁢  =   ( α 1 − α ) ⁢ ( f t e t p ⁢ p x ) ⁢ . ( 10 )

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

p t x ⁢  =   ( Q ⁢ e t y ⁢ N ) − μ − 1 ( x t α ⁢ f t 1 − α ) − μ − 1 ⁢ ( 1 − α ) ⁢ x t α ⁢ f t − α ⁢ . ( 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 ^ t x ⁢  =   k x ⁢ ( K t , ⁢ e t p , e t y ), ( 12 )
K ^ t f ⁢  =   k f ⁢ ( K t , ⁢ e t p , e t y ), ( 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 ( K t . A t , λ t s )  = max { [ ( x ∧ t α f t 1 − α ) − μ + ( Q e t y N ) − μ ] − ( 1 − γ ) μ 1 − γ + ( 1 + [ ( x ∧ t α f t 1 − α ) − μ +  (Q e t y N ) − μ ] − 1 μ ) − β [ Σ x = 1 4 π s , x   V ( K t + 1 , A t + 1 , λ t + 1 x ) ] } , ( 14 )

subject to, 17/

f t  =  (1- α ) [ Q e t y ( e t p p x ( K ∧ t x ) x  +   ( K ∧ t f ) ι )  -   K t + 1  +   K t ( 1 − δ )  -   Φ 2 ( K t + 1 − K t ) 2  +  (1+ r * ) A t  -   A t + 1 ] , ( 15 ) A t ,   A t + 1   ≥   ▵  and    K t ,   K t + 1 , f t   ≥  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,

λ t s , λ t + 1 u   ∈ [ ( e − y , e − p ) , ( e − y , e p ) , ( e y , e ¯ p ) , ( e y , e p ) ] . ( 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,

π s , x ⁢  =  (1- θ ⁢ ) Π x ⁢  +   θ ⁢ Z s , 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 ⁢  =- e y ⁢ = e y , e ¯ p ⁢ = - e p ⁢ = e p , ( 18 )

and

Π ( e ¯ y , e ¯ p ) = ⁢ Π ( e y , e p )  = ⁢ Π ,   Π ( e ¯ y , e p ) ⁢ = Π ( e y , e ¯ p ) ⁢ = 1 2 − Π ⁢ . ( 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,

σ e y ⁢ = e y ,   σ e p ⁢ = e p ,   ρ e y ⁢ = ρ e p ⁢ = θ ⁢  ,   ρ e y , e p = 4 Π -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:

P t  =   [ ( α − α ( 1 − α ) − ( 1 − α ) ( e t p p x ) α ) μ 1 + μ  +  ( p t n ) μ 1 + μ ] 1 + μ μ . ( 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 ⁢  = { e y ⁢ =8.5,   e p ⁢ =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 =  { e y ⁢ =12.25,   e p ⁢ =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/

article image

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/

article image

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.

Given χ, ι, δ, Q, r*, γ, and μ, a system of eight equations determines α, β, N, and the deterministic steady state of pn, K, Kf, Kh and A. The equations are: (1) the stationary equilibrium condition that equates the rate of time preference with r*; (2) the marginal rate of substitution between nontradables and importables; (3) the ratio of net foreign interest payments to output ω; (4) the ratio of expenditure on nontradables to expenditure on tradables Ω; (5) the ratio of total trade to output T; (6) the equilibrium condition that equates the net marginal productivity of Kf with r*; (7) a similar condition that equates the net marginal productivity of Kh with r*; and (8) the definition of aggregate capital K=Kf+Kh. To solve these equations, px is assumed to be equal to 1 in the steady state, and ω, Ω, and T are set using cross-country and time-series averages of actual data from Tables 6 and 7. Column (1) in Table 7 shows that the average Ω for industrialized and developing countries is similar, 0.87 and 0.86 respectively. The last column of the table shows that the mean T for industrialized countries is 0.62 and for developing countries is 0.51. The sixth column of Table 6 shows that the cross-section mean of ω for time-series averages of the G-7 and 23 DCs are -0.2 and -2.8 percent respectively. 25/

V. Simulation of the Benchmark Models

Tables 9 and 10 list the properties of the equilibrium stochastic processes that characterize macroeconomic variables in the benchmark models. Statistical moments for variables deflated using both import prices and the consumption-based price index are reported. The former can be compared with moments computed from actual data at constant import prices in Tables 1-6, and consumption deflated with the CPI can be compared with consumption at constant domestic prices in Table 3. The industrial country benchmark is calibrated by setting σey=8.5 percent, ρey eP=0.575, and Φ=0.1, while in the developing country benchmark these parameters are σey=12.25 percent, ρey eP=-0.18, and Φ=0.3. Thus, in order to rationalize observed differences in output variability and in the co-movement between GDP and TOT across the G-7 and the DCs, given the larger terms-of-trade shocks affecting the latter, the model requires that developing countries also experience larger productivity disturbances and that these disturbances be negatively correlated with terms-of-trade shocks.

Table 9.

Properties of Business Cycles in the Model of Industrial Countries 1/

article image

The statistical moments reported are the percentage standard deviation relative to the percentage standard deviation of the terms of trade, σx/σtot, the first order serial auto correlation, ρx, the correlation with GDP, ρx, y, and the correlation with the terms of trade, σx, tot. The numbers in brackets are the ratios of moments in the model to moments in actual data measured as averages for the G-7—the asterisks denote calibrated and exogenous parameters.

Except for the components of the consumption basket.

Variability ratio computed using standard deviations, not percentage standard deviations.

Each component measured in units of the corresponding consumption good.

Table 10.

Properties of Business Cycles in the Model of Developing Countries 1/

article image

The statistical moments reported are the percentage standard deviation relative to the percentage standard deviation of the terms of trade, σx/σtot, the first order serial auto correlation, ρx, the correlation with GDP, ρx, y and the correlation with the terms of trade, ρx, tot. The numbers in brackets are the ratios of moments in the model to moments in actual data measured as averages for the 23 developing countries in Table 1—the asterisks denote calibrated and exogenous parameters.

Except for the components of the consumption basket.

Variability ratio computed using standard deviations, not percentage standard deviations.

Absolute value of the difference between actual and estimated moments.

Each component measured in units of the corresponding consumption good.

In general, Tables 9-10 show that the models’ equilibrium co-movements are consistent with many qualitative features of the business cycle, although from a quantitative perspective the model fails to mimic some stylized facts. Consider the four empirical regularities mentioned in Section II with regard to the terms of trade and the trade balance. First, the model is consistent with the data in showing that TB and TOT are positively correlated, albeit weakly, and that this correlation is higher in industrial countries—although HLM effects in the data are somewhat higher than in the model. Second, given the differences in parameter values, the economy with more persistent terms-of-trade disturbances does exhibit a stronger HLM effect, as observed in the data. Moreover, the positive cross-country relationship observed in Figure 1 between coefficients of first-order serial autocorrelation of TOT and correlations between TB and TOT is also closely approximated by the model—the figure plots a predicted cross-country linear relationship between the two variables with a slope coefficient of 0.24 and t-statistic of 12, which compares to 0.44 with a t-statistic of 5.65 obtained using actual data. Hence, the fact that countries with more serially correlated disturbances in the terms of trade tend to have a stronger HLM effect cannot be viewed as evidence against intertemporal equilibrium models. Third, despite larger terms-of-trade shocks in the developing country benchmark, the model predicts a smaller standard deviation in the trade balance of DCs than in the G-7, contrary to what the data show. Fourth, the model cannot mimic the uniformity that characterizes the variability of TB relative to the variability of TOT because trade-balance fluctuations in industrial countries are significantly overestimated. In the industrial country benchmark the variability ratio is about 5.2, while in the developing country benchmark it is approximately 1. In the data the ratio is about 1.1 for both the average of the G-7 and the average of 23 developing countries.

The data of the G-7 and the DCs indicated that economic fluctuations in GDP, consumption, and investment across countries display similar characteristics. This is well duplicated by the model, except for the correlation between the terms of trade and aggregate consumption and its components deflated with the CPI, which differ significantly between the two benchmark economies. Quantitatively, the model fails to mimic some stylized facts by large margins. In particular, both benchmark models exaggerate the actual variability of consumption at consumer prices, and for developing countries the model underestimates the correlation between C and TOT regardless of the price index used to deflate consumption. Nevertheless, most stylized facts of consumption and investment measured at import prices are fairly well duplicated by the two benchmark economies.

The separation of the consumption basket into exportable, importable, and nontradable components allows the model to capture intratemporal and intertemporal substitution effects that are helpful for explaining some features of consumption behavior. In particular, and in contrast with one-good models of the small open economy, the correlation between C and GDP is positive but not perfect. This is because the response of consumption to output fluctuations resulting form terms-of-trade and productivity shocks reflects not only wealth effects, which affect the demand functions for x, f, and n positively, but also substitution effects between these three goods induced by changes in current and expected relative prices. These substitution effects also play a critical role in the dynamics of other components of the model, particularly the trade balance and the real exchange rate.

The model accounts for large deviations from purchasing power parity. The real exchange rate has been given different interpretations in the intertemporal equilibrium literature. Some of the literature treats the relative price of nontradables as equivalent to the real exchange rate (Ostry (1988)). An extension of the first definition views the real exchange rate as the relative price of nontradables weighted by the share of nontradables in total expenditure, which is the concept used to construct real-exchange-rate moments in Tables 9-10. A third definition assumes that the law of one price for all tradables holds, as in Greenwood (1984), and hence interprets the real exchange rate as equivalent to the domestic CPI—which is a function of both the relative price of nontradables and the terms of trade. According to these three measures, real-exchange-rate fluctuations range between 5.1 percent and 10.9 percent in the industrial country benchmark and between 8.5 percent and 20.8 percent in the developing country benchmark. These ranges are consistent with the evidence reported in Table 5 and in the work of Schlagenhauf and Wrase (1991).

The J-curve dynamics of the cross-correlations between the trade balance and the terms of trade, as identified in the data of the G-7 by Backus, Kehoe, and Kydland (1992b), can only be partially explained by the model. The first-order autoregressive structure of the shocks implies that the correlation between the trade balance at t and the terms of trade at lag k is simply θkρtot, tb. The evidence documented by Backus, Kehoe, and Kydland shows that this is a good proxy for some G-7 countries, but is not for Canada and the United States. 26/

The results of the simulations undertaken here are also indicative of the importance of modelling investment decisions in empirical research involving intertemporal equilibrium models. For instance, the endowment economy analyzed in Mendoza (1992a) mimics the positive but less-than-perfect correlation between consumption and GDP observed in the data, but fails to duplicate the countercyclical or acyclical behavior of the trade balance and the variability of the real exchange rate. In the model examined here, investment goods are part of the importables, and hence the dynamics of investment reflect the optimal portfolio allocation of savings across K and A, and the intertemporal and intratemporal substitution effects unchained by the effect of terms-of-trade disturbances on the relative productivity of capital in the industries producing exportables and importables. Depending on the persistence and co-movement of the disturbances affecting productivity and the terms of trade, the pro-borrowing effect that a positive productivity shock with some persistence induces, as agents plan to increase investment and take advantage of higher expected returns on domestic capital, may be offset or amplified by expectations regarding the future path of the terms of trade. This pro-borrowing effect is strong enough to weaken the correlation between TB and GDP significantly, relative to results obtained with the endowment economy. In the latter, the industrial country benchmark produced a coefficient of correlation between TB and GDP at import prices of 0.48, while in Table 9 this correlation is only 0.02.

The benchmark simulations consider both terms-of-trade and productivity disturbances as driving forces of the business cycle. However, it is important to measure the contribution of shocks to the terms of trade independently from productivity shocks in order to assess their empirical relevance. If the industrial country benchmark is simulated setting σey=0 and ρey eP=0, the standard deviation of GDP at import prices is 6.98 percent. Thus, terms-of-trade disturbances account for more than 1/2 of the observed variability of output (the G-7 average is 12.43 percent, 10.25 percent excluding Japan). Nevertheless, there is evidence indicating that productivity disturbances play an important role not only in accounting for the other 1/2 of output variability, but also for producing realistic co-movements among several macroeconomic aggregates—particularly consumption, investment and net exports. Moreover, the model is significantly more sensitive to changes in the magnitude of productivity shocks than in that of terms-of-trade disturbances. Around the stochastic steady state of the industrial country benchmark, a 1 percent increase in the variability of productivity increases the variability of output by 0.55, whereas a 1-percent increase in the variability of the terms of trade increases output variability by only 0.18.

VI. Sensitivity Analysis

The benchmark simulations provide a summary view of how intertemporal and intratemporal income and substitution effects, resulting from the specific parameter values assigned to each benchmark model, interact to produce different equilibrium co-movements. It is important to try to analyze these effects separately to provide a theoretical interpretation of the quantitative results. However, this analysis is complicated by two factors. First, as Frenkel and Razin (1987) noted, the definition of the ‘numeraire’ in multiple-good models is not innocuous, and hence changes in the units in which goods are measured affect equilibrium co-movements through relative price movements even when preferences and technology are unchanged. The differences in some statistical moments between variables at import prices and variables at consumer prices in Tables 9-10 illustrate this problem. Second, in a simple multiple-good framework similar to the one studied here, Greenwood (1984) and Ostry (1988) showed that comparative statics analysis aimed at determining analytically the direction and magnitude of income and substitution effects produces generally ambiguous results that depend on the relative values of a number of parameters. These theoretical exercises suggest that four key parameters determining equilibrium co-movements are the intertemporal elasticity of substitution in aggregate consumption, the intratemporal elasticity of substitution between tradable and nontradable goods, and the persistence and contemporaneous correlation of shocks to output and the terms of trade. 27/ The role that these parameters play in the benchmark simulations is examined next.

Consider first the adjustment of the industrial country benchmark in response to a 1-percent positive shock to the terms of trade. Figures 1A-1D in the appendix depict the impulse responses of the various macroeconomic aggregates. Figure 1A illustrates the procyclical behavior of consumption and investment at import prices, as well as the acyclical pattern of net exports. The impact effect of the terms-of-trade shock in all four variables is positive, but afterwards their behavior is quite different. After the initial boom, GDP adjusts monotonically and gradually back to the original steady state. Investment adjusts more rapidly reflecting the perfect international mobility of capital. Given that around the steady state adjustment costs are minimal, investors aim to equalize the marginal productivity of capital in the industries of exportables and importables with the world’s real interest rate. Figure 1B depicts the impulse responses of the aggregate capital and capital in the two industries; the impact effect is purely a redistribution of existing capital in favor of the exportables industry, favored by the increase in the terms of trade, but afterwards the perceived duration and co-movement of the shocks is such that aggregate capital expands and then returns monotonically to the initial equilibrium.

In contrast with the monotonic adjustment of GDP and investment after the initial boom, consumption and net exports exhibit non-monotonic adjustment patterns which reflect the impulse responses of the components of the consumption basket (Figure 1C) and foreign asset holdings, exports, and imports (Figure 1D). In Figure 1C only the consumption of nontradables is measured at import prices, whereas the other consumption measures are in units of the corresponding good (i.e. importables, exportables, or the CES composite good). When there is an increase in the relative price of exportables in terms of importables, the substitution effect dominates at first and consumption of exportables falls while consumption of importables increases. The supply of nontradables is fixed, and although tradables and nontradables are not good substitutes, the net income and substitution effect on the demand for these goods is positive and hence the relative price of nontradables, and consumption of nontradables valued at import prices, rise. The non-monotonic adjustment of consumption at import prices in Figure 1A follows from the nonmonotonic adjustment of the consumption of importables and exportables and the relative price of nontraded goods. This, in turn, results from the wealth effects induced by the terms-of-trade shock which dominate the dynamics of consumption after the relative price of exports in terms of imports has returned to its initial equilibrium.

The behavior of net exports is consistent with familiar theoretical results obtained using two-period models (see Greenwood (1984) and Svensson and Razin (1983)). A temporary improvement in the terms of trade in the first period induces agents to increase savings in order to increase consumption permanently, since consumption in the two periods is a normal good. The trade balance improves because agents increase their holdings of foreign assets. In the second period the trade balance deteriorates as agents reduce their holdings of foreign assets to finance additional imports of consumer goods. The budget constraint implies, however, that the present value of the trade balance must be zero. In Figure 1A the improvement in net exports follows the improvement in the terms of trade, then the trade balance starts to deteriorate, reaches a minimum, and improves gradually to return to the initial equilibrium. It is this eventual narrowing of the trade deficit that produces the countercyclical or acyclical behavior of net exports. In present value, the few surpluses at first require deficits for a long period afterwards to be canceled out. This is consistent with the slow adjustment of the current account depicted in Figure 1D.

Compared with the industrial country benchmark, the developing country benchmark displays lower intertemporal elasticity of substitution in consumption (0.38 v. 0.66), higher intratemporal elasticity of substitution between tradables and nontradables (1.28 v. 0.74), slightly less serially correlated income shocks (0.604 v. 0.668) and negative contemporaneous correlation between terms-of-trade and productivity disturbances (-0.18 v. 0.575). The effects of altering each of these parameters on the equilibrium co-movements of the industrial country benchmark are summarized in Table 11 and the impulse responses of macro-aggregates to a 1-percent terms-of-trade shock under all parameter specifications considered are illustrated in Figures 1A-6D in the Appendix.

Table 11.

Variability Ratios and Correlation Coefficients of Macroeconomic Variables for Alternative Industrial Country Model Economies 1/

article image

The variables listed are output (Y), consumption (C), investment (I), savings (S), the trade balance (TB) and the consumer price index (CPI). C is measured at consumer prices, Y, I, S and TB at import prices.

Standard deviation relative to the standard deviation of the terms of trade.

γ = 2.61.

μ = 0.218.

ρeY, eP = 0.

θ = 0.200.

Table 11 and the impulse response charts indicate that quantitatively, and in the neighborhood of the parameter specifications in question, the persistence of the disturbances and the intratemporal elasticity of substitution between tradable and nontradable goods are the main factors explaining differences in the behavior of the two benchmark models. The intertemporal elasticity of substitution in consumption is not critical as long as it represents a small degree of relative risk aversion—as in the case of the one good model examined in Mendoza (1991). Similarly, changes in the contemporaneous correlation between the two shocks affect investment and savings variability, but are not very important for the equilibrium co-movements of aggregate consumption.

The persistence of the shocks is important because it determines the magnitude of wealth effects, which are not neutral under the assumption of incomplete insurance markets, and because of the Fisherian separation that characterizes savings and investment decisions. 28/ The variability ratios of output, consumption, and investment decline when the shocks are transitory, while those of savings, the trade balance, and the real exchange rate increase. The Fisherian separation is reflected in the reduced investment variability and the decline in the correlations of investment with savings and output. As the shocks become less persistent, there is less of an incentive to adjust the capital stock in response to contemporaneous shocks to productivity or the terms of trade because their effect on the marginal productivity of future capital is expected to be small. In fact, the savings-investment correlation becomes negative even when the first-order autocorrelation of the shocks is still positive, at 0.2, because of the weakening of wealth effects and the positive correlation of shocks to output and the terms of trade under simple persistence. Previous theoretical results obtained in deterministic, endowment-economy models regarding the implications of the duration of shocks for the HLM effect and the correlation between output and net exports extend to the stochastic model with production. As the persistence of the shocks declines, both the correlation between net exports and the terms of trade and net exports and output increase reflecting the weaker pro-borrowing effect induced by expectations of a less persistent income gain.

The intratemporal elasticity of substitution between tradables and nontradables plays an important role because the values of μ specified for the two benchmark economies imply that the goods are gross complements in industrial countries and gross substitutes in developing countries. Table 11 shows that if one simulates the industrial country benchmark setting μ=1.28, the value in the developing country benchmark, savings, investment, and net exports become more variable, while the correlations of the trade balance with output and the terms of trade increase significantly. The last results suggest that, everything else constant, the pro-saving effects operating in the model are stronger the higher the elasticity of substitution between consumption of tradable and nontradable goods—a well-established result in deterministic two-period models (see Greenwood (1984) and Ostry (1988)). Moreover, the impulse response charts show that, from the set of parameter specifications considered, it is only when tradable and nontradable goods are made gross substitutes in the industrial country benchmark that this model can produce a pattern of adjustment of consumption of the CES composite good similar to that observed in the developing country benchmark (see Figures 1C, 2C and 4C).

VII. Concluding Remarks

This paper examined a dynamic stochastic equilibrium model of a small open economy where agents consume three goods, importables, exportables, and nontradables, and firms produce importables and exportables using capital that is also an importable good. International trade of financial assets was assumed to be limited to one-period, risk free real bonds denominated in units of importables, and hence financial markets are incomplete but still “perfect”—in the sense that agents can borrow or lend any amount at a fixed real interest rate. Stochastic disturbances were modelled as affecting productivity and the terms of trade separately, and business cycles resulted as the outcome of optimal intertemporal decisions formulated by households and firms.

The stylized facts of the G-7 and 23 developing countries, in particular the statistical moments that characterize cyclical fluctuations in the trade balance and the terms of trade, were briefly reviewed to define the regularities that the model should explain. Other empirical evidence was used to parameterize the model, and an exact-solution method was used to compute equilibrium co-movements in two artificial economies that represent industrial and developing countries. The results of the numerical simulations showed that the model is consistent with most of the qualitative properties of actual business cycles, particularly with the positive correlation between the trade balance and the terms of trade (the Harberger-Laursen-Metzler effect), the positive but less-than-unitary correlation between consumption and output, and the large deviations from purchasing power parity. Nevertheless, from a quantitative standpoint the model fails to mimic some stylized facts. The sensitivity of the results to changes in preference parameters and in the properties of the stochastic processes of the exogenous shocks was also examined. The persistence of productivity and terms-of-trade shocks and the intratemporal elasticity of substitution between consumption of tradable and nontradable goods were found to play a key role. The former is important because, under incomplete markets, optimal savings behavior is affected by wealth effects resulting from country-specific shocks. The latter has significant implications because the parameters suggested by the data indicate that tradables and nontradables are gross complements in industrial countries and gross substitutes in developing countries. This implies differences for cross-price and cross-expenditure effects operating in the model economies.

Further work is necessary to examine the implications of relaxing the assumptions of perfect capital markets and perfect capital mobility adopted here. This would be particularly important in order to assess the effects of the borrowing constraints that affected developing countries during the debt crisis, as well as episodes of tight credit conditions in world capital markets for industrial countries. Given that the model is consistent with some basic features of the business cycle, additional work will extend the model to examine policy implications. The credibility effects widely discussed in the literature on stabilization and commercial policies are a prime candidate.

Appendix: Impulse Response Diagrams

This appendix contains the charts depicting impulse responses of macroeconomic aggregates to a 1-percent, positive terms of trade shock under six different sets of parameter values. Figures 1A-1D and 2A-2D are the impulse responses for the industrial and developing country benchmarks respectively. Figures 3A-6D present impulse responses for simulations in which one of the following parameters in the industrial country benchmark is modified; the intertemporal elasticity of substitution (γ=2.61), the intratemporal elasticity of substitution between consumption of tradables and consumption of nontradables (μ=-0.218), the correlation between productivity and terms-of-trade shocks (ρeP, eY=0), and the first-order autocorrelation of the two shocks (θ=0.2).

Figure 1A
Figure 1A

Impulse Responses in Industrial Countries Benchmark

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

Figure 1B
Figure 1B

Impulse Responses in Industrial Countries Benchmark

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

Figure 1C
Figure 1C

Impulse Responses in Industrial Countries Benchmark

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

Figure 1D
Figure 1D

Impulse Responses in Industrial Countries Benchmark

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

Figure 2A
Figure 2A

Impulse Responses in Developing Countries Benchmark

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

Figure 2B
Figure 2B

Impulse Responses in Developing Countries Benchmark

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

Figure 2C
Figure 2C

Impulse Responses in Developing Countries Benchmark

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

Figure 2D
Figure 2D

Impulse Responses in Developing Countries Benchmark

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

Figure 3A
Figure 3A

Impulse Responses: High Risk–Aversion Economy

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

Figure 3B
Figure 3B

Impulse Responses: High Risk–Aversion Economy

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

Figure 3D
Figure 3D

Impulse Responses: High Risk–Aversion Economy

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

Figure 4A
Figure 4A

Impulse Responses: High Substitution Economy

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

Figure 4B
Figure 4B

Impulse Responses: High Substitution Economy

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

Figure 4C
Figure 4C

Impulse Responses: High Substitution Economy

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

Figure 4D
Figure 4D

Impulse Responses: High Substitution Economy

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

Figure 5A
Figure 5A

Impulse Responses: Independent Shocks

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

Figure 5B
Figure 5B

Impulse Responses: Independent Shocks

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

Figure 5C
Figure 5C

Impulse Responses: Independent Shocks

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

Figure 5D
Figure 5D

Impulse Responses: Independent Shocks

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

Figure 6A
Figure 6A

Impulse Responses: Transitory Shocks

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

Figure 6B
Figure 6B

Impulse Responses: Transitory Shocks

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

Figure 6C
Figure 6C

Impulse Responses: Transitory Shocks

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

Figure 6D
Figure 6D

Impulse Responses: Transitory Shocks

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

The impulse response functions used to create the charts were determined by assuming that optimal decision rules around the model’s stochastic steady state are linear. Under this assumption, the model’s dynamics around the steady state are described by a reduced-form system of the form:

K t + 1  =   α 0  +   α 1 K t  +   α 2 A t  +   α 3 e t p  +   α 4 e t y  +   u t k K t + 1  =   β 0  +   β 1 K t  +   β 2 A t  +   β 3 e t p  +   β 4 e t y  +   u t k e t + 1 p  =   γ 0  +   γ 1 e t p  +   γ 2 e t y  +   u t p e t + 1 y  =   δ 0  +   δ 1 e t p  +   δ 2 e t y  +   u t y

The coefficients of this system were estimated by Ordinary Least Squares, using standard deviations and correlation coefficients computed with the model’s limiting probability distribution that results from the recursive solution method described in the paper.

References

  • Backus, David K., “Interpreting Comovements in the Trade Balance and the Terms of Trade,” Federal Reserve Bank of Minneapolis, Research Department, Working Paper No. 441, 1989.

    • Search Google Scholar
    • Export Citation

  • Backus, David K., and Kehoe, Patrick J., “International Evidence on the Historical Properties of Business Cycles,” American Economic Review, September 1992, 82, 864–888.

    • Search Google Scholar
    • Export Citation

  • Backus, David K., Kehoe, Patrick J. and Kydland, Finn E. (1992a), “International Real Business Cycles,” Journal of Political Economy, August, 100, 745–775.

    • Search Google Scholar
    • Export Citation

  • Backus, David K., Kehoe, Patrick J. and Kydland, Finn. E. (1992b), “Relative Price Movements in Dynamic General Equilibrium Models of International Trade,” Working Paper No. EC-92-25, Department of Economics, New York University.

    • Search Google Scholar
    • Export Citation

  • Baxter, Marianne, and Crucini, Mario J., “Explaining Savings/Investment Correlations,” Rochester Center for Economic Research, University of Rochester, Working Paper No. 224, forthcoming American Economic Review, 1992.

    • Search Google Scholar
    • Export Citation

  • Bertsekas, Dimitri P., Dynamic Programming and Stochastic Control, New York, NY: Academic Press, 1976.

  • Canova, Fabio, “Detrending and Business Cycle Facts,” unpublished manuscript, Department of Economics, Brown University, Providence RI, 1991.

    • Search Google Scholar
    • Export Citation

  • Cardia, Emanuela, “The Dynamics of a Small Open Economy in Response to Monetary, Fiscal, and Productivity Shocks,” Journal of Monetary Economics, September 1991, 28, 411–434.

    • Search Google Scholar
    • Export Citation

  • Christiano, Lawrence J., “Solving a Particular Growth Model by Linear Quadratic Approximation and by Value Function Iteration,” Discussion Paper No. 9, Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis, 1989.

    • Search Google Scholar
    • Export Citation

  • Christiano, Lawrence J., and Eichembaum, Martin, “Current Real Business Cycle Theories and Aggregate Labor Fluctuations,” American Economic Review, June 1992, 82, 430–450.

    • Search Google Scholar
    • Export Citation

  • Cole, Harold L. and Obstfeld, Maurice, “Commodity Trade and International Risk Sharing: How Much Do Financial Markets Matter,” Journal of Monetary Economics, 27, 1991.

    • Search Google Scholar
    • Export Citation

  • Correia, Isabel H., Neves, Joao C. and Rebelo, Sergio, “Business Cycles in Portugal: Theory and Evidence,” working paper, Research Department, Bank of Portugal, 1991.

    • Search Google Scholar
    • Export Citation

  • Costello, Donna M., and Praschnik, J., “The Sources of Aggregate Fluctuations in Developing Countries: An Investigation of Latin American and Asian Economies,” unpublished manuscript, Department of Economics, University of Florida, June 1992.

    • Search Google Scholar
    • Export Citation

  • Dotsey, Michael, and Mao, Ching Sheng, “How Well do Linear Approximation Methods Work?,” Journal of Monetary Economics, 29, 25–58, 1992.

    • Search Google Scholar
    • Export Citation

  • Engel, Charles, and Kletzer, Kenneth, “Saving and Investment in an Open Economy with Non-traded Goods,” International Economic Review, November 1989, 30, 735–752.

    • Search Google Scholar
    • Export Citation

  • Epstein, Larry G., “Stationary Cardinal Utility and Optimal Growth under Uncertainty,” Journal of Economic Theory, June 1983, 31, 133–152.

    • Search Google Scholar
    • Export Citation

  • Finn, Mary G., “Energy Price Shocks, Capacity Utilization and Business Cycle Fluctuations,” Federal Reserve Bank of Minneapolis, Institute for Empirical Macroeconomics, Discussion Paper 50, 1991.

    • Search Google Scholar
    • Export Citation

  • Frenkel, Jacob A. and Razin, Assaf, Fiscal Policies and the World Economy, Cambridge, MA: MIT press, 1987.

  • Greenwood, Jeremy, “Non-traded Goods, the Trade Balance, and the Balance of Payments,” Canadian Journal of Economics, November 1984, XVII, 806–823.

    • Search Google Scholar
    • Export Citation

  • Greenwood, Jeremy, Hercowitz, Zvi and Huffman, Gregory W., “Investment, Capacity Utilization and the Real Business Cycle,” American Economic Review, June 1988, 78, 402–417.

    • Search Google Scholar
    • Export Citation

  • Harberger, Arnold C., “Currency Depreciation, Income, and the Balance of Trade,” Journal of Political Economy, February 1950, 58, 47–60.

    • Search Google Scholar
    • Export Citation

  • International Monetary Fund (1991a), World Economic Outlook, Washington: International Monetary Fund, October.

  • International Monetary Fund (1991b), International Financial Statistics, Yearbook 1991, Washington: International Monetary Fund.

  • Kravis, Irving B., Heston, Alan and Summers, Robert, World Product and Income: International Comparisons of Real Gross Product, United Nations International Comparison Project Phase III, published for the World Bank by the Johns Hopkins University Press (Baltimore: Maryland, 1982)

    • Search Google Scholar
    • Export Citation

  • Laursen, Svend and Metzler, Lloyd A., “Flexible Exchange Rates and the Theory of Employment,” Review of Economics and Statistics, November 1950, 32, 281–299.

    • Search Google Scholar
    • Export Citation

  • Lundvik, Petter, “Business Cycles in a Small Open Economy: Sweden 1871-1987,” unpublished manuscript, Institute for International Economic Studies,” Stockholm University, 1991.

    • Search Google Scholar
    • Export Citation

  • Macklem, R. Tiff, “Terms of Trade Disturbances and Fiscal Policy in a Small Open Economy,” unpublished manuscript, Research Department, Bank of Canada, 1991.

    • Search Google Scholar
    • Export Citation

  • McCallum, Bennett T., “Real Business Cycle Models,” in R. J. Barro, ed., Modern Business Cycle Theory, Cambridge, MA: Harvard University Press, 1989, 16–50.

    • Search Google Scholar
    • Export Citation

  • Mendoza, Enrique G. (1991), “Real Business Cycles in a Small Open Economy,” American Economic Review, September, 81, 797–818.

  • Mendoza, Enrique G. (1992a), “Macroeconomic Effects of Income Shocks in an Intertemporal Equilibrium Model of a Small Open, Endowment Economy,” IMF Staff Papers, forthcoming.

    • Search Google Scholar
    • Export Citation

  • Mendoza, Enrique G. (1992b), “Dynamic Gains from North American Free Trade in an Equilibrium Model of the Current Account,” North American Journal of Economics and Finance, forthcoming.

    • Search Google Scholar
    • Export Citation

  • Mussa, Michael L., “Exchange Rates in Theory and in Reality,” Department of Economics, Princeton University, Essays in International Finance No. 179, December 1990.

    • Search Google Scholar
    • Export Citation

  • Obstfeld, Maurice, “Macroeconomic Policy, Exchange Rate Dynamics and Optimal Asset Accumulation,” Journal of Political Economy, December 1981, 89, 1142–1161.

    • Search Google Scholar
    • Export Citation

  • Obstfeld, Maurice, “Aggregate Spending and the Terms of Trade: Is there a Laursen-Metzler Effect,” Quarterly Journal of Economics, May 1982, 97, 251–270

    • Search Google Scholar
    • Export Citation

  • OECD, National Accounts, Organization for Economic Co-Operation and Development, Paris, 1988.

  • Ostry, Jonathan D., “The Balance of Trade, Terms of Trade, and Real Exchange Rate,” IMF Staff Papers, December 1988, 35, 541–573.

  • Ostry, Jonathan D., and Reinhart, Carmen M., “Private Saving and Terms of Trade Shocks,” IMF Staff Papers, September 1992, 39, 495–517.

    • Search Google Scholar
    • Export Citation

  • Praschnik, J., and Costello, Donna M., “The Role of Oil Price Shocks in a Two-Sector, Two-Country Model of the Business Cycle,” unpublished manuscript, Department of Economics, University of Western Ontario, 1992.

    • Search Google Scholar
    • Export Citation

  • Persson, Torsten, and Svensson, Lars E. O., “Current Account Dynamics and the Terms of Trade: Harberger-Laursen-Metzler Two Generations Later,” Journal of Political Economy, February 1985, 93, 43–65.

    • Search Google Scholar
    • Export Citation

  • Prescott, Edward C., “Theory Ahead of Business Cycle Measurement,” Carnegie-Rochester Conference Series on Public Policy, Autumn 1986, 25, 11–44.

    • Search Google Scholar
    • Export Citation

  • Schlagenhauf, Don E. and Wrase, Jeffrey M., “Liquidity and Real Activity in a Simple Open Economy Model,” unpublished manuscript, Arizona State University.

    • Search Google Scholar
    • Export Citation

  • Stockman, Alan C. and Tesar, Linda L., “Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements,” unpublished manuscript, Department of Economics, University of California-Santa Barbara, Santa Barbara: California, October 1990.

    • Search Google Scholar
    • Export Citation

  • Svensson, Lars E.O. and Razin, Assaf, “The Terms of Trade and the Current Account: The Harberger-Laursen-Metzler Effect,” Journal of Political Economy, February 1983, 91, 97–125.

    • Search Google Scholar
    • Export Citation

  • Tesar, Linda L., “Nontraded Goods, Risk Sharing and Trade in Capital,” unpublished manuscript, Department of Economics, University of Rochester, Rochester: NY, 1990.

    • Search Google Scholar
    • Export Citation

  • World Bank, World Tables, 1989-90, Socio-economic Time-series Access and Retrieval System, version 1.0, The World Bank/IFC, Washington D.C., March 1990.

    • Search Google Scholar
    • Export Citation

  • UNCTAD, Handbook of International Trade and Development Statistics, United Nations, New York: NY, 1987.

1/

Helpful comments by Dave Backus, Guillermo Calvo, Mary Finn, Jeremy Greenwood, Jonathan Ostry, Assaf Razin, Carmen Reinhart, Lars Svensson, Linda Tesar and Peter Wickham are gratefully acknowledged. Suggestions by seminar participants at the International Monetary Fund, and the 1992 North American Summer Meeting and Latin American Meeting of the Econometric Society are also acknowledged.

2/

Harberger and Laursen and Metzler aimed to show that even under a flexible exchange rate the economy could not be protected from business cycles abroad. For a review of this issue see Svensson and Razin (1983).

3/

A widening of the trade deficit shifts the IS curve to the left, and with a flexible exchange rate it produces a temporary fall in output and the nominal interest rate. With a fixed exchange rate the supply of money falls and the decline in output is permanent. These arguments ignore the direct relative price effect of a decline in the price of exports in terms of imports, which reduces the trade deficit and shifts the IS to the right.

4/

Recently, Backus, Kehoe, and Kydland (1992b) have examined the stylized facts of the terms of trade in industrial countries using a two-country real business cycle model.

5/

Praschnik and Costello (1992) obtained similar results in a study that examines technology and oil-price shocks as sources of business cycles in a two-country real business cycle model.

6/

Lundvik (1991) arrives to a similar conclusion using Swedish data and an overlapping generations model in which all goods are tradable.

7/

Market incompleteness limits the agents’ ability to completely insure away country-specific shocks and strengthens the wealth effects resulting from these disturbances. Although it potentially could induce excessive consumption variability, Mendoza (1991a) showed that this is not the case. Moreover, Cole and Obstfeld (1991), showed that market incompleteness per se does not affect competitive allocations significantly under some specifications of preferences and technology.

8/

Backus and Kehoe (1992) documented historical evidence on the international properties of business cycles, and some international stylized facts were also reported in Backus, Kehoe, and Kydland (1992a) and Baxter and Crucini (1992). The stylized facts of the terms of trade, including their correlation with net exports, were examined by Backus, Kehoe, and Kydland (1992b).

9/

Costello and Praschnik (1992) and Mendoza (1992b) report some stylized facts for developing economies.

10/

The statistical moments that Stockman and Tesar (1990) and Backus, Kehoe, and Kydland (1992b) calculated for the U.S., the U.K., Italy, Canada and France using the Hodrick-Prescott filter and the first-difference filter are roughly consistent with the corresponding moments reported in Table 1—taking into account that these authors define the terms of trade as the ratio of import to export prices.

11/

The assumption of incomplete markets in the Obstfeld-Svensson-Razin models is also crucial for this result. As Backus (1989) proved, under complete markets the co-movement between TOT and TB is independent of country-specific shocks.

12/

In terms of individual countries, the ratio of the standard deviation of the trade balance to the standard deviation of the terms of trade can be as low as 0.4 for Indonesia and as high as 2.7 for Peru, but for most countries is between 0.8 and 1.6.

13/

Consumption data here includes durables. Usually, consumption becomes less variable than output once durables are taken out.

14/

Whether exportable and importable goods are actually exported or imported in this model is not arbitrary. It is an equilibrium outcome in which production of exportables exceeds consumption and consumption of importables exceeds production.

15/

The reader interested in the theoretical aspects of stationary cardinal utility is referred to Epstein (1983). Obstfeld (1981), Engel and Kletzer (1989), and Mendoza (1991a) discuss the role of the endogenous rate of time preference present in this utility function on the dynamics of models of small open economies.

16/

Labor is assumed to be supplied inelastically or available to firms as a fixed endowment, and to simplify notation it is dropped from the utility and production functions. Alternatively, it is possible to introduce labor as independent of the dynamics of consumption—as in Greenwood, Hercowitz, and Huffman (1988) or Mendoza (1991a). In either case, the model would not mimic the stylized facts of hours worked because of the reasons argued in McCallum (1989) and Christiano and Eichembaum (1992).

17/

Δ in the resource constraint (15) is a non-binding borrowing constraint that ensures intertemporal solvency (see Mendoza (1991) for details).

18/

Note, however, that as Frenkel and Razin (1987) acknowledge, the choice of units in which variables are to be expressed is not innocuous in circumstances where relative prices change.

19/

These authors estimate 1/γ at 0.383 with a standard error of 0.087 (they also provide an alternative estimate at 0.504 with a standard error of 0.228).

20/

Stockman and Tesar (1990) used a sample that includes 17 developing countries. Their point estimate of the elasticity of substitution is 0.44 with a standard error of 0.225.

21/

Using the same regression method applied to industrial countries with the data for DCs in Table 7 yields 1/(1+μ)=0.43. This estimate is incompatible with the GMM estimates of Ostry and Reinhart (1991), and it requires the use of GDP per capita as an explanatory variable in violation of the homotheticity assumption implicit in (2). The estimate for industrial countries also violates homotheticity, but is in line with the view that these countries exhibit lower intratemporal substitution, as implied by the GMM estimates of Ostry and Reinhart.

22/

Alternatively, α can be set by computing the share of consumer good imports in tradable expenditures. Column (3) of Table 7 lists consumer good imports as a percent of total imports obtained from UNCTAD (1987), and this combined with data from Kravis, Heston, and Summers (1982) would yield 1-α in Column (4)—resulting in averages of 0.28 (α=.72) and 0.18 (α=0.82) for industrial and developing countries respectively. This computation excludes consumption of importables produced in the domestic economy and the resulting high α values imply total trade ratios significantly below those observed in the data.

23/

The labor income share for Mexico is taken from Mendoza (1992b).

24/

This estimate is based on measures of GDP per capita adjusted for purchasing power provided by Kravis, Heston, and Summers (1982).

25/

Given that Canada’s relatively large ω dominates the average for the G-7, ω is set at zero for industrial countries to reflect more closely the typical ratio of net factor payments to output in these countries.

26/

Cross-correlations between TB and TOT for the G-7 computed with the data used in Table 1 also support this argument.

27/

The relative expenditure shares of the three goods in the consumption basket, as well as the ratios of consumption to production of the three goods, are also parameters that determine the signs of comparative statics derivatives.

28/

Investment is governed by the investors’ desire to equalize the expected value of the productivity of domestic capital and the return on foreign assets weighted by the marginal utility of consumption. Savings, on the other hand, are determined by equating the intertemporal marginal rate of substitution in consumption with its intertemporal relative price.

Same Series

Other IMF Content

Other Publishers

  • Collapse
  • Expand
Cover IMF Working Papers
The Terms of Trade and Economic Fluctuations
Author:
Mr. Enrique G. Mendoza
Volume/Issue:
Volume 1992: Issue 098
Publisher:
International Monetary Fund
ISBN:
9781451852066
ISSN:
1018-5941
Pages:
72
DOI:
https://doi.org/10.5089/9781451852066.001
Figure 1

The Harberger–Laursen–Metzler Effect
Figure 1A

Impulse Responses in Industrial Countries Benchmark
Figure 1B

Impulse Responses in Industrial Countries Benchmark
Figure 1C

Impulse Responses in Industrial Countries Benchmark
Figure 1D

Impulse Responses in Industrial Countries Benchmark
Figure 2A

Impulse Responses in Developing Countries Benchmark
Figure 2B

Impulse Responses in Developing Countries Benchmark
Figure 2C

Impulse Responses in Developing Countries Benchmark
Figure 2D

Impulse Responses in Developing Countries Benchmark
Figure 3A

Impulse Responses: High Risk–Aversion Economy
Figure 3B

Impulse Responses: High Risk–Aversion Economy
Figure 3D

Impulse Responses: High Risk–Aversion Economy
Figure 4A

Impulse Responses: High Substitution Economy
Figure 4B

Impulse Responses: High Substitution Economy
Figure 4C

Impulse Responses: High Substitution Economy
Figure 4D

Impulse Responses: High Substitution Economy
Figure 5A

Impulse Responses: Independent Shocks
Figure 5B

Impulse Responses: Independent Shocks
Figure 5C

Impulse Responses: Independent Shocks
Figure 5D

Impulse Responses: Independent Shocks
Figure 6A

Impulse Responses: Transitory Shocks
Figure 6B

Impulse Responses: Transitory Shocks
Figure 6C

Impulse Responses: Transitory Shocks
Figure 6D

Impulse Responses: Transitory Shocks