bilateral trade elasticities

Bilateral Trade ElasticitiesAuthor(s): Jaime MarquezSource: The Review of Economics and Statistics, Vol. 72, No. 1 (Feb., 1990), pp. 70-77Published by: The MIT PressStable URL: http://www.jstor.org/stable/2109741 .

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BILATERAL TRADE ELASTICITIES

Jaime Marquez*

Abstract-This paper estimates income and price elasticities for bilateral world trade. In addition to testing the properties of the error terms, the dynamic specification, and the assumption of parameter constancy, the analysis presents the first application of the Band Spectrum estimator to bilateral trade flows for all countries. The paper finds that bilateral trade elasticities exhibit enough of a dispersion to suggest that the direction of trade is sensitive to changes in income and prices. Using the bilateral elasticities as raw data, the analysis obtains the associated multilateral estimates and finds that they are both consistent with the literature and suitable to addressing questions involving multilateral trade. But the evidence also reveals that sole reliance on multilateral elasticities conceals valuable information for both policy applications and empirical analyses of international trade.

I. Introduction

THIS paper estimates income and price elasticities for bilateral world trade. Although these

elasticities are relevant to designing commercial policies and studying international linkages, they have received very little attention in the empirical literature. In addition to being scant, the econometric evidence on bilateral elasticities rests on samples that exclude post-1973 developments, such as flexible exchange rates and commodity price shocks, and neglects the increasingly important role of developing countries.1

To fill these gaps, section II develops an econometric model to explain bilateral trade among Canada, Germany, Japan, the United Kingdom, the United States, other industrial countries, OPEC, and non-OPEC developing countries. For each country, the analysis estimates elasticities for seven bilateral trade flows for a total of 56 estimating equations. To assess the reliability of these estimates, the paper tests the properties of the error term, the choice of dynamic specification, and the assumption of parameter constancy. Fur- thermore, the analysis examines the robustness of the estimates using Engle's Band Spectrum estimator (Engle, 1974).2 Section III presents the empirical results and the associated test statistics.

Using the bilateral elasticities as raw data, section IV estimates the associated multilateral elasticities to address three questions: How do these multilateral estimates compare to those available in the literature? What are their implications for balance-of-payment forecasting? How serious is the loss of information involved in aggregation? Based on the evidence, the multilateral estimates are consistent with the existing literature and suitable to addressing questions involving multilateral trade. But the evidence also reveals a significant dispersion in bilateral trade elasticities. Thus sole reliance on multilateral elasticities conceals valuable information for both policy applications and empirical analyses of international trade. Finally, section V summarizes the paper.

II. The Behavior of Bilateral Trade Flows

The analysis assumes that bilateral imports of country k from country s behave according to the imperfect-substitute model (Goldstein and Khan,

Received for publication January 23, 1989. Revision accepted for publication July 12, 1989.

* Federal Reserve Board. Comments by two anonymous referees helped to clarify the

ideas and are greatly appreciated. I have also benefited from comments by F. Gerard Adams, Russell Cooper, Frank Diebold, Jonathan Eaton, Sebastian Edwards, Rob Engle, Neil Ericsson, William Helkie, Peter Hooper, David Howard, Joe Gagnon, Lawrence Klein, Edward Leamer, Nathaniel Leff, Ross Levine, Cathy Mann, Ann McGuirk, Marc Noland, Adrian Pagan, and Peter Tinsley. The empirical tests are performed with the GIVE computer software developed by David Hendry and installed into TROLL by Ralph Tryon. Earlier versions of this paper have been presented in seminars at the Federal Reserve Board, the U.S. Department of Agricul- ture, the 1987 and 1988 meetings of the Society for Economic Dynamics and Control, the Departments of Economics of University of Iowa and University of Illinois at Champaign, and the 1987 Summer School in Dynamic Optimization, Dublin, Ireland. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff.

1 Based on the surveys of Stem et al. (1975), Magee (1975), and Goldstein and Khan (1985), the evidence on bilateral trade elasticities for world trade consists of Armington (1970), Bran-

son (1972), Hickman and Lau (1973), Resnick and Truman (1973), and Marwah (1976). Armington and Branson do not rely on statistical methods for parameter estimation; Marwah allows for developing countries. For the United States, Houthakker and Magee (1969) are among the first to estimate bilateral elasticities. More recent work for the United States includes Haynes et al. (1986) and Cushman (1987, 1988a, 1988b).

2 Previous applications of spectral methods to trade include Haynes and Stone (1983) and McPheters and Stronge (1979).

[ 70 ] Copyright ?D 1990



BILATERAL TRADE ELASTICITIES 71

1985): In Mkst = OOks + ?(lks In Y1,

+ ?2ks(ln Ykt ln Yft) +? Yja3ksjln Pks, t-j

+ Y:ja4ksj ln Pkqls, t-j

+ a5ks ln Mks, t1 + Ukst (1)

where Mks= volume of imports of country k from

country s, Yk= real income of country k, Y1 = potential real income of country k,

Pks = relative price for imports of country k from country s,

Pkqls = relative price for imports of country k from country q,

a3ks, = 4030ks + 4031ksi + '032ks ]' for i =

0 9... 9j39

a4ksj = 440ks + 4)41ks] + 042ks ] ' for j =

0 9... 9 j49

UkSt N(0, ak2); E(ukstuks,t-h) = 0 V h.

According to (1), the response of imports to income has two components: a secular effect, mea- sured by a1, and a cyclical effect captured by a2.

The own-price elasticity is a3 and the cross-price elasticity is a4. The choice of a logarithmic formulation is based on the Box-Cox tests reported in Marquez (1988). Finally, (1) assumes homogeneity of degree zero in prices.3

The reliability of (1) depends on three factors: the properties of the disturbance term, the choice of dynamic specification, and the constancy of the parameter estimates. The paper applies the Jarque-Bera statistic (Jarque and Bera, 1980) to test normality and the ARCH statistic (Engle, 1982) to test homoskedasticity. For serial independence, the analysis applies an F-test to the hypothesis that all the coefficients of an AR(4) for the residual are equal to zero.

To test the choice of dynamic specification, the paper performs two F-tests. The first test involves estimating (1) with and without the Almon restrictions. The second test involves estimating both (1) and an "unrestricted" dynamic specification that eliminates the Almon restrictions and includes all predetermined variables lagged one period. For

both F-tests, equation (1) is the null hypothesis.4 To test for parameter constancy, (1) is first estimated with a sample that excludes the last eight observations and then used to forecast imports over the omitted sample. Testing for parameter constancy amounts to applying an F-test to the hypothesis that the expected forecast error is zero (Chow, 1960).

The (long-run) income and own-price elasticity estimates associated with (1), 4ks and ,ks respec- tively, are

'1ks =lks/(1 - &5ks) (2)

4ks =- 3ksj/(1 -5ks)* (3)

Because (2) and (3) are ratios of normal random variables, their distributions are complicated and difficult to deal with (Marsaglia, 1965). As a result, this paper generates these distributions empirically using the Monte Carlo procedure developed by Krinsky and Robb (1986). To implement this procedure, the paper assumes that

( okS.&3ks(L) ...&sks )

- akS N(aks 9 ks) (4) and uses this assumption to generate a random sample of &kS, the ith drawing of which is denoted as &ak i = 1 ... 4000. Substitution of each &aks

into (2) and (3) generates the empirical distributions for the long-run income and price elasticities.5 The paper presents the median and the scaled median absolute deviation for each of the empirically-generated elasticity distributions.

Equation (1) assumes that the secular and cyclical responses of imports (a1 and a2) are invariant across business cycles. Haynes and Stone (1983) rely on spectral analysis to relax this assumption, a suggestion that this paper follows by applying Engle's Band Spectrum estimator (Engle, 1974) to

In Mkst = 1% + I8ks ln Ykt + 82ks In Pkst

+ 133ks ln Pkqlst + Ukst. (5)

3Warner and Kreinin (1983) and Wilson and Takacs (1979) relax the assumption of price homogeneity. Finally, equation (1) includes dummies for one-time events and seasonal factors but they are not shown for notational convenience (a data appendix available on request documents the dates for the dummy variables).

4 The paper relies on a 99% significance level for statistical inferences because j3 and j4 are empirically determined. Equa- tion (1) also assumes that the speed of adjustment, a5, is fixed once estimated; Husted and Kollintzas (1984) allow a variable speed of adjustment. For equation (1), however, Brown- Durbin-Evans tests for parameter stability suggest a fixed speed of adjustment (See Marquez (1988), appendix B).

5 The reliability of this procedure depends on the assumption that (2) and (3) are continuous functions, an assumption that is violated if a5 = 1. Marquez (1988, table 6) reports results suggesting that the continuity assumption is not violated by the data.



72 THE REVIEW OF ECONOMICS AND STATISTICS

Greatly simplified, the Band Spectrum estimator applies least squares to (5) using data for all the frequencies enclosed by a given spectral band. To facilitate comparisons with 71ks and ksI the paper uses the low-frequency data associated with a spectral band of (0, 0.125], which encloses frequency components requiring at least two years to complete a cycle.6

As it stands, (1) has two potentially important limitations: the lack of system estimation and the exclusion of uncertainty in exchange rates as a separate variable. However, treating (1) as a demand system involves estimating simultaneously more than 1900 parameters, a task that proved to be beyond the capacity of available computer fa- cilities. Furthermore, whether prices and income can be treated as exogenous for estimation is a testable proposition that section III addresses. Fi- nally, given the controversy over whether exchange-rate uncertainty affects bilateral trade, the analysis excludes the role of exchange-rate uncertainty.7

III. Estimation Results

Estimating (1) involves testing whether the con- ditioning variables (income, prices, and exchange rates) are super exogenous with respect to trade elasticities and examining whether the import- supply import-demand system is recursive. After finding support for both of these propositions, the paper applies ordinary least squares to (1) using quarterly data for 1973Q1-1985Q2.'

Based on their Monte Carlo distributions, the bilateral income elasticities (table 1) exhibit several features of interest. First, they differ across countries: Out of 56 elasticity estimates, 8 are negative, 25 vary between 0.1 and 2.0, and 23 are greater than 2. Based on the 99% confidence inter- val, 44 of the 56 elasticities are statistically significant. Second, countries belong to one of two categories depending on whether their income elasticity is below or above one. The "low" income elasticity countries are Japan and LDCs;9 the "high" income elasticity countries are Canada, Germany, the United Kingdom, the United States, and other industrial countries; the income elasticities for OPEC's bilateral imports are near unity. Third, the estimated income elasticity for imports from OPEC is either negative or not significantly different from zero. Imports from OPEC are, by and large, imports of oil which are subject to the effects of continuing technological improvements in oil requirements. This factor, as well as the potential inadequacy of the imperfect substitute model, can account for this negative income elasticity. Finally, the Band Spectrum estimates exhibit the same pattern as the OLS estimates: Out of 56 elasticity estimates, 10 are negative, 28 vary between zero and two, and 18 are greater than two; 42 out of 56 estimates are significantly different from zero; Japan and LDCs have the small- est income elasticities; and imports from OPEC have a negative or insignificant income elasticity.

All of the estimated price elasticities are negative, but half of them are not statistically significant.10 They also exhibit important differences across countries: Out of 56 elasticity estimates, 16 vary from zero to -0.5; 21 fall between -0.51 and - 1.0; 13 range between - 1.1 and - 1.5; and 6 fall below - 1.5. Note also that the range of variation for these elasticities is not uniform across countries. For example, the estimates for Japan range from - 2.8 to - 0.2 whereas other countries exhibit a smaller dispersion of elasticity estimates. Finally, the spectral estimates have both large

6 The high-frequency estimates are available on request. Equation (5) differs from the formulation of Haynes and Stone (1983) in three respects: it includes an intercept, allows for cross-price effects, and assumes homogeneity of degree zero in prices. Note that Haynes and Stone use multilateral data whereas this study relies on bilateral trade data.

See Hooper and Kohlhagen (1978), Thursby and Thursby (1985), and Cushman (1988a).

8An appendix available on request describes the data. Test- ing for super exogeneity (Engle, Hendry, and Richard, 1983) involves applying sequential Chow tests to both equation (1) and the marginal processes (the exogenous variables). The latter are modeled as a function of lagged policy variables (Marquez, 1988, appendix B). To examine recursiveness, Mar- quez (1988, appendix B) first estimates an export price equation for each bilateral trade equation and then performs two tests. The first one examines the statistical significance of bilateral imports in the price equation. The second one tests for the statistical significance of the correlation between the residual of the price equation and the residual of the associated bilateral trade equation.

9Houthakker and Magee (1969) noted the low income elasticity for imports of Japan.

10 Houthakker and Magee (1969) and Cushman (1988a) also report relatively large standard errors for price elasticities. Thursby (1988) traces this volatility in price elasticities to the interaction between specification errors and multicollinearity. The estimates for cross-price elasticities are reported in Mar- quez (1988, table 5).




TABLE 1.-INCOME AND PRICE ELASTICITIES OF WORLD BILATERAL TRADE FLOWSa LONG-RUN ESTIMATES AND TEST STATISTICS

1973Q1-1985Q2

OLS Estimates

Error Dynamic Elasticitiesb Propertiesc Specificationd Spectral Elasticities Importing

Country SOUrCe Income Std. Err. Price Std. Err. J-B AR(4) ARCH Almon URDS Chow Income Std. Err. Price Std. Err.

Canada Germany 2.16 0.49 -0.84 0.33 0.31 0.29 0.76 - 0.03 0.47 1.11 0.44 - 0.65 0.24 Japan 3.13 0.79 -1.28 0.59 0.21 0.50 0.75 - 0.14 0.74 2.64 0.49 - 1.20 0.31 U.K. -1.75 0.68 -0.46 0.24 0.42 0.54 0.78 - 0.30 0.88 -0.73 0.45 -0.46 0.22 U.S. 2.01 0.33 -0.99 0.34 0.35 0.30 0.87 0.78 0.89 0.88 1.33 0.23 -0.12 0.32 ROECD 1.29 0.57 -1.73 1.30 0.31 0.75 0.81 0.56 0.74 0.92 1.33 0.63 0.26 1.31 LDCs 2.83 0.66 -1.17 0.45 0.07 0.92 0.59 - 0.64 0.75 2.49 0.27 -1.13 0.20 OPEC -1.11 0.74 -0.52 0.79 0.22 0.81 0.66 0.02 0.86 0.40 -4.71 1.40 -1.74 1.05

Germany Canada 2.73 0.89 -0.67 0.50 0.66 0.12 0.34 0.90 0.51 0.25 2.00 0.51 -0.74 0.27 Japan 3.89 1.05 -1.51 0.55 0.21 0.30 0.79 - 0.42 0.43 4.45 0.44 -1.22 0.49 U.K. 4.61 0.23 -0.11 0.22 0.71 0.33 0.29 - 0.34 0.83 4.55 0.44 0.42 0.24 U.S. 1.95 0.29 -0.89 0.27 0.50 0.15 0.50 - 0.87 0.20 1.66 0.33 -1.16 0.30 ROECD 2.15 0.48 -0.73 0.23 0.35 0.13 0.65 - 0.64 0.77 2.24 0.10 -0.67 0.23 LDCs 2.29 0.41 -0.16 0.16 0.08 0.85 0.92 - 0.82 0.30 2.37 0.18 -0.20 0.27 OPEC -2.99 1.20 -0.25 0.17 0.35 0.61 0.65 0.82 0.94 0.92 -1.28 1.16 -0.52 0.17

Japan Canada 0.35 0.13 - 0.36 0.17 0.48 0.40 0.02 0.06 0.26 0.69 0.46 0.14 - 0.24 0.16 Germany 0.56 0.26 - 1.31 0.64 0.67 0.95 0.07 0.69 0.58 0.23 0.68 0.27 -0.60 0.41 U.K. 0.82 0.48 -0.74 0.56 0.72 0.72 0.78 - 0.86 0.63 0.98 0.35 -0.46 0.47 U.S. 0.79 0.34 -0.72 0.41 0.62 0.63 0.74 0.76 0.55 0.15 0.81 0.19 0.04 0.27 ROECD -0.04 0.27 -2.84 1.06 0.31 0.41 0.42 - 0.78 0.34 0.29 0.34 -1.97 0.91 LDCs 1.22 0.37 -1.22 0.52 0.69 0.80 0.41 0.44 0.89 0.09 1.41 0.15 0.14 0.46 OPEC -0.42 0.51 -0.24 0.19 0.29 0.33 0.14 0.93 0.90 0.83 -0.33 0.22 -0.12 0.08

U.K. Canada 0.14 1.60 -1.62 1.21 0.86 0.09 0.14 0.69 0.40 0.56 -2.85 0.95 -0.99 0.56 Germany 5.61 1.73 -0.49 0.28 0.47 0.01 0.53 0.68 0.32 0.00 6.15 0.61 - 0.76 0.18 Japan 4.83 1.57 -0.29 0.42 0.05 0.83 0.95 0.66 0.81 0.37 5.71 1.15 - 1.08 0.34 U.S. 4.11 1.27 - 0.88 0.59 0.77 0.49 0.23 0.49 0.72 0.09 3.11 0.85 -0.74 0.24 ROECD 3.43 0.96 -0.13 0.18 0.77 0.07 0.23 0.14 0.15 0.00 3.51 0.37 -0.34 0.12 LDCs 1.45 0.56 -0.17 0.17 0.87 0.71 0.13 0.52 0.23 0.42 0.83 0.54 -0.11 0.17 OPEC -7.07 1.52 -1.94 0.21 0.10 0.26 0.90 0.63 0.69 0.19 -10.1 2.29 -0.83 0.27

U.S. Canada 1.87 0.30 -0.80 0.25 0.12 0.00 0.19 0.33 0.82 0.75 1.44 0.24 -1.01 0.21 Germany 2.89 0.68 -1.70 0.84 0.18 0.78 0.26 0.93 0.89 0.90 1.86 0.50 -0.48 0.60 Japan 3.56 0.99 -1.13 0.62 0.24 0.96 0.64 - 0.80 0.85 3.68 0.37 -0.81 0.43 U.K. 2.69 0.73 -0.34 0.37 0.62 0.57 0.45 - 0.16 0.38 2.76 0.39 -0.84 0.21 ROECD 2.51 0.45 -1.17 0.35 0.40 0.49 0.93 0.58 0.76 0.99 2.10 0.30 -0.88 0.17 LDCs 3.04 1.00 -0.45 0.26 0.08 0.31 0.58 0.61 0.68 0.80 3.39 0.34 -0.50 0.22 OPEC -2.26 1.50 -1.29 0.75 0.26 0.20 0.32 0.43 0.33 0.96 -2.08 2.04 0.001 0.41

ROECD Canada 3.43 0.79 -0.91 0.45 0.18 0.57 0.82 - 0.89 0.72 2.83 0.71 -0.80 0.32 Germany 1.80 0.29 -0.26 0.17 0.73 0.34 0.27 - 0.92 0.64 1.87 0.25 - 0.01 0.32 Japan 2.17 1.75 -0.78 0.82 0.82 0.46 0.18 - 0.52 0.42 0.85 1.28 - 0.35 0.73 U.K. 2.66 0.55 -0.55 0.26 0.54 0.50 0.46 - 0.75 0.45 2.10 0.59 0.34 0.29 U.S. 2.32 0.61 -0.72 0.37 0.56 0.30 0.44 - 0.73 0.70 2.33 0.52 -0.61 0.24 LDCs 2.61 0.44 -0.60 0.18 0.11 0.69 0.89 - 0.59 0.41 3.20 0.50 -0.37 0.48 OPEC -0.18 0.51 -0.19 0.10 0.49 0.79 0.51 0.81 0.87 0.93 -0.15 1.36 -0.55 0.15

LDCs Canada 0.35 0.17 -0.95 0.57 0.15 0.50 0.85 - 0.83 0.15 0.56 0.08 -0.21 0.42 Germany 0.30 0.09 -1.42 0.49 0.61 0.65 0.39 - 0.22 0.19 0.13 0.06 - 0.55 0.28 Japan 0.60 0.22 -0.78 0.38 0.20 0.00 0.80 - 0.21 0.16 0.79 0.08 -0.39 0.37 U.K. 0.08 0.05 -0.15 0.12 0.16 0.66 0.84 0.01 0.66 0.11 -0.08 0.05 0.19 0.15 U.S. 0.54 0.25 - 1.45 1.20 0.57 0.60 0.43 - 0.63 0.91 0.52 0.12 -0.66 0.49 ROECD 0.47 0.15 -0.67 0.32 0.08 0.73 0.92 - 0.83 0.21 0.41 0.04 -0.18 0.25 OPEC 0.10 0.16 -0.11 0.12 0.31 0.92 0.69 - 0.13 0.55 0.07 0.27 -0.23 0.21

OPECe Canada 0.92 0.42 -1.03 0.52 0.76 0.44 0.31 0.56 0.27 0.35 0.80 0.34 -1.22 0.22 Germany 1.55 0.53 -1.18 0.49 0.26 0.12 0.60 0.30 0.26 0.64 0.94 0.56 -1.05 0.34 Japan 0.65 0.27 -0.91 0.32 0.49 0.96 0.31 0.37 0.56 0.81 0.57 0.39 -1.08 0.24 U.K. 1.14 0.43 -0.81 0.44 0.91 0.98 0.53 0.72 0.85 0.97 0.73 0.45 -0.90 0.33 U.S. 0.96 0.31 -0.52 0.29 0.26 0.55 0.09 0.86 0.91 0.93 0.81 0.33 -0.90 0.23 ROECD 1.06 0.38 -1.17 0.47 0.39 0.80 0.20 0.10 0.69 0.70 0.64 0.41 -1.10 0.26 LDCs 0.53 0.17 -1.33 - 0.39 0.81 0.09 0.40 - 0.64 0.72 -0.38 0.36 -0.80 0.24

aThe data are described in an appendix available on request; ROECD stands for the Rest of the OECD Countries. bEntries for the elasticities are the median (left column) and the scaled median deviation (right column) of their probability distributions. CEntries represent one minus the significance level needed to reject the null hypothesis: An entry of 0.99 implies that the null hypothesis can be rejected with a

1% significance level. Entries under J. B. belong to the test for normality; entries under AR(4) belong to the test of serial independence; entries under ARCH correspond to the test for homoskedasticity.

dEtisrepresent one minus the significance level needed to-reject the null hypothesis. Entries under A/mon belong to the test for the Almon lags; entries under URDS correspond to the test for an unrestricted dynamic specification; entries under Chow correspond to the test for parameter constancy.

eThe estimation sample for OPEC bilateral imports is 1973Q1.-1984Q4.




standard errors and frequent sign reversals and thus do not give strong support to the theoretical priors embodied in (1).

The results from the statistical tests (table 1) support the elasticity estimates associated with (1). The data are consistent with the assumptions of normality and homoskedasticity in all of the trade equations; the F-test for serial correlation supports the assumption of serial independence for the residuals in 53 out of 56 cases. For the 30 equations in which they are used, the Almon restrictions are supported by the data. The F-test comparing (1) against an unrestricted dynamic specification supports the lag structure of (1) for all of the equations. Finally, the results associated with the Chow-test indicate that it is not possible to reject the hypothesis of parameter constancy in 53 out of 56 trade equations.

IV. Implications

To examine the implications of the results, the analysis considers three questions: Are the bilateral elasticity estimates consistent with the evidence on multilateral elasticities? What are the implications of these elasticities for balance-of- payment forecasting? How serious is the loss of information involved in aggregation?

Using bilateral trade shares as weights, table 2 estimates the multilateral elasticities implied by the bilateral estimates of table 1. Based on a comparison to previous estimates (table 2), the aggregate income elasticities are consistent with the literature: they are positive, range between 1 and 2, and have a small standard error. The excep- tions are the elasticities for imports of Japan and LDCs, which are less than one, and the elasticity of OPEC's exports, which is negative. The estimated price elasticities are also consistent with the literature: they are negative, range between -0.5 and -1.1, and are statistically significant. The most notable exception is the spectral estimate for exports of the United Kingdom which is positive and insignificantly different from zero. The simi- larity between the multilateral estimates of this study and those found in the literature is the more remarkable given the differences in the sample periods used for parameter estimation. For example, the estimates of Houthakker and Magee (1969) are based on a sample that ends in 1966, prior to the sample used in this paper.

To examine the implications of bilateral elasticities for balance-of-payments forecasting, the analysis tests whether multilateral exports and imports have different income elasticities and whether the Marshall-Lerner condition holds. Based on the evidence (table 3), the income elasticity for U.S. exports is smaller than the income elasticity for U.S. imports, which is the asymmetry noted by Houthakker and Magee (1969). But the estimated standard error suggests that this asymmetry is not statistically significant, a result consistent with the spectral estimates. For both Japan and non-OPEC LDCs, the differential in income elasticities is positive and significant whereas OPEC exhibits the opposite pattern, a finding consistent with the spectral estimates. For the remaining countries, the evidence reveals no significant asymmetries in income elasticities. Testing whether the Marshall- Lerner stability condition holds involves testing whether the sum of a country's price elasticities for multilateral exports and imports is less than minus one. Based on a one-tail test, the evidence cannot reject this stability condition for Canada, Japan, the United States, the bloc of other industrial countries (ROECD), and OPEC. The point estimates for Germany and LDCs also satisfy the Marshall-Lerner condition but it is not possible to reject the hypothesis that the sum of their price elasticities is equal to minus one. The evidence from the spectral estimates is less supportive of the Marshall-Lerner condition.

To underscore the information that aggregate elasticities conceal, the analysis examines the implications of debt servicing by developing countries for trade and growth. Given prices, developing countries can service their external debt if their real exports grow faster than the real interest rate on their loans. Thus assuming a real interest rate of 6% and relying on an elasticity of 2.3 for LDC multilateral exports (table 2) implies that developing countries would be able to service their debt if the growth rate of the rest of the world is at least 2.6%. But given differences in bilateral elasticities vis-a-vis developing countries, what do these aggregate growth rates imply for LDCs' trading partners? Assuming that all bilateral exports of LDCs grow at the required 6% implies a wide range of growth rates for LDCs' trading partners: from 2.0% for the United States to 12.0% for OPEC (table 4, column 2). On the other hand, assuming that all LDC trading partners grow at




TABLE 2.-MULTILATERAL TRADE ELASTICITIES: ESTIMATION AND COMPARISON WITH SELECTED STUDIES

This Studye

OLS Band Spectrum

Houthakker-a Wilson-b Thursby-c Warner-d Std. Std. Imports Magee Takacs Thursby Kreinin Estimate Err. Estimate Err.

Income Elasticities Canada 1.20 1.87 1.35 1.82 1.84 0.23 1.06 0.17 Germany 1.80 1.46 1.59 1.49 1.88 0.32 2.09 0.14 Japan 1.23 1.69 1.17 0.41 0.35 0.21 0.48 0.09 U.K. 1.66 2.58 1.12 -1.10 2.51 0.56 2.09 0.31 U.S. 1.51 4.03 1.72 2.01 1.94 0.39 1.89 0.33 ROECD 2.03 0.23 2.02 0.35 LDCs 0.40 0.08 0.38 0.06 OPEC 1.07 0.17 0.59 0.20

Price Elasticities - Canada -1.46 -2.8, -1.2 -0.46 - 1.0, 0.1 - 1.02 0.23 - 0.33 0.24 Germany -0.24 -1.9, 0.1 -0.30 - 1.3, 0.5 -0.60 0.12 - 0.58 0.13 Japan -0.72 -7.7, -1.3 - 0.33 -0.9, - 0.7 - 0.93 0.21 - 0.28 0.18 U.K. 0.22 -3.2, 0.0 0.14 -2.4, -1.4 -0.47 0.13 -0.49 0.07 U.S. -0.54 -8.8, -4.8 -0.20 - 3.2, - 1.2 - 0.92 0.19 - 0.63 0.12 ROECD -0.49 0.12 -0.26 0.16 LDCs -0.81 0.29 -0.34 0.14 OPEC - 1.14 0.21 -1.30 0.13

This Study

OLS Band Spectrum

Houthakker- Wilson- Warner- Std. Std. Exports Magee Takacs Kreinin Estimate Err. Estimate Err.

Income Elasticities Canada 1.41 0.58 1.36 1.69 0.23 1.22 0.16 Germany 2.08 1.11 0.63 1.86 0.22 1.78 0.19 Japan 3.55 0.86 1.00 2.00 0.39 1.96 0.22 U.K. 0.86 1.75 0.51 2.07 0.30 1.77 0.29 U.S. 0.99 2.15 1.26 1.54 0.17 1.30 0.13 ROECD 1.75 0.24 1.70 0.09 LDCs 2.26 0.33 2.43 0.18 OPEC -1.27 0.42 -1.30 0.68

Price Elasticities ------ ----- Canada -0.59 -4.8, -0.2 -1.4, -0.2 - 0.83 0.22 - 0.88 0.15 Germany 1.70 - 5.5, -1.9 - 5.3, - 3.9 -0.66 0.16 - 0.27 0.19 Japan -0.80 -11.7, -4.9 -1.1, -0.3 - 0.93 0.25 -0.68 0.20 U.K. -0.44 -1.8, -0.4 -1.7, -0.8 -0.44 0.16 0.03 0.15 U.S. -1.51 -4.2, - 3.3 -1.5, -0.9 -0.99 0.38 - 0.52 0.17 ROECD -0.83 0.14 -0.61 0.10 LDCs -0.63 0.13 -0.44 0.17 OPEC -0.57 0.19 -0.41 0.12

aHouthakker and Magee (1969, p. 113, table 1). bWilson and Takacs (1979, pp. 271-276, tables 1-6); price homogeneity is not assumed and the entries for price elasticities in this table show the range of

coefficient estimates for the components of the relative price of imports. CThe entries represent the estimates denoted as "Accepted" by Thursby and Thursby (1984, p. 126, table 3). dWamer and Kreinin (1983, p. 100, table 2 for imports and p. 102, table 5 for exports); price homogeneity is not assumed and the entries for price elasticities

in this table show the range of coefficient estimates for the components of the relative price of imports. eMultilateral elasticities are estimated as a weighted average of bilateral elasticities using the sample mean of bilateral trade shares as weights. Data sources:

trade shares come from the Direction of Trade published by the International Monetary Fund; trade elasticities come from table 1.




TABLE 3.-MULTILATERAL TRADE ELASTICITIES: STRUCTURAL ASYMMETRIES AND STABILITY CONDITIONS

Income Elasticity Differentiala Marshall-Lemer Condition"

OLS Band Spectrum OLS Band Spectrum

Std. Std. Std. Std. Estimate Err. Estimate Err. Estimate Err. Estimate Err.

Canada -0.15 0.33 0.16 0.23 - 1.85 0.32 - 1,21 0.28 Germany -0.02 0.39 -0.31 0.24 - 1.26 0.20 - 0.85 0.23 Japan 1.65 0.44 1.48 0.24 - 1.86 0.33 - 0.96 0.27 U.K. -0.44 0.64 -0.32 0.42 -0.91 0.21 - 0.46 0.17 U.S. -0.40 0.43 -0.59 0.35 - 1.91 0.42 - 1.15 0.21 ROECD -0.28 0.33 -0.32 0.36 -1.32 0.18 -0.87 0.19 LDCs 1.86 0.34 2.05 0.19 -1,44 0.32 -0.78 0.22 OPEC -2.34 0.45 -1.89 0.71 -1.71 0.28 -1.71 0.18

aThe null hypothesis is that the multilateral income elasticities for exports and imports are equal against the alternative that they are not equal; source:

table 2. bThe null hypothesis is that the sum of multilateral price elasticities for exports and imports is equal to or greater than minus one; the alternative hypothesis

is that this sum is less than minus one; source: table 2.

TABLE 4.-INCOME ELASTICITIES, GROWTH, AND EXPORTS OF DEVELOPING COUNTRIES

Income Threshold Export Elasticitya Growth Rate" Growth Ratec

Canada 2.8 2.1 7.3 Germany 2.3 2.6 6.0 Japan 1.2 5.0 3.1 U.K. 1.5 4.0 3.9 U.S. 3.0 2.0 7.8 ROECD 2.6 2.3 6.8 OPEC 0.5 12.0 1.3 Aggregate 2.3 2.6 6.0

alncome elasticity for imports from non-OPEC LDCs; source: table 1 for bilateral elasticities and table 2 for the aggregate elasticity.

bGDP growth rate needed to sustain a 6% growth rate in imports from developing countries. Entries in this column are constructed as the ratio between the assumed growth rate for exports of developing countries (6% per year) and the income elasticity of column 1,

CGrowth rate of imports from developing countries when each country's annual growth rate is 2.6%. Entries in this column are constructed as the product of the growth rate (2.6% per year) and the income elasticity of column 1.

the required 2.6% implies a wide range of growth rates for imports from LDCs: from 13% for OPEC to 7.8% for the United States (table 4, column 3). By construction, these two examples give the same aggregate outcome, but they carry different implications for individual countries. Can OPEC sustain an income expansion of 12% per year? Can the United States absorb imports from LDCs at a rate of 8% per year? This paper does not address these questions, but the calculations above show that policies based on multilateral trade elasticities need not be consistent with those based on bilateral elasticities.

Sole reliance on multilateral elasticities might conceal useful information in other instances: estimating optimal bilateral tariffs, predicting the re-

sponse of the distribution of global imbalances to changes in income and prices, and determining the sensitivity of market shares to multilateral trade policies. A complete analysis of these questions is beyond the scope of this paper, but bilateral trade elasticities are certain to be an essential ingredient in addressing them.

V. Conclusions

Bilateral trade elasticities play an important role in designing trade policies and predicting how the direction of international trade responds to changes in income and relative prices. However, the empirical evidence on these elasticities is scant, outdated, and limited in country-coverage. To relax these limitations the paper estimates income and price elasticities for bilateral world trade. In addition to testing the properties of the error term, the dynamic specification, and parameter constancy, the analysis presents the first application of the Band Spectrum estimator to bilateral trade flows for all countries.

The paper finds that bilateral trade elasticities exhibit enough of a dispersion to suggest that the direction of trade is sensitive to changes in income and prices. Using the bilateral elasticities as raw data, the analysis obtains the associated multilateral estimates and finds that they are consistent with the literature and that they are suitable to addressing questions involving multilateral trade. But the evidence also reveals that sole reliance on multilateral elasticities conceals valuable information for both policy applications and empirical analyses of international trade.




Although the analysis is subject to several limitations-reliance on single equation methods, aggregation across commodities and countries, and other data considerations-eliminating them is likely to strengthen the main implication of this paper: that reliance on multilateral elasticities entails an important loss of information for the questions receiving attention in the literature whereas reliance on bilateral elasticities entails no such loss.

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