Front Matter Page
IMF Institute
Authorized for distribution by Mohsin S. Khan
Contents
Summary
I. Introduction
II. The model
III. Estimation Results
A. Unit Root Test
B. Import Demand Equations
IV. Small-Sample Properties of the ols and fm estimators
A. Small-Sample bias of the Short- and Long-run Elasticities
B. Small-Sample Distribution of the t-Statistic
V. Conclusions
References
Tables
1. The four possible model specifications
2. Augmented-Dickey-Fuller test for variables entering the import demand equation
3. Import demand equations
4. Bias for short- and long-run elasticities for OLS and Fully-Modified estimators (percent)
5. OLS t-statistic critical values for the import demand equation parameters
6. Fully-Modified t-statistic critical values for the import demand equation parameters
7. OLS t-statistic critical values for long-run import price and income elasticities
8. Fully-Modified t-statistic critical values for long-run import price and income elasticities
SUMMARY
The traditional import demand function is specified as a log-linear function of the relative price of imports and real income. Because of data constraints and the empirical success of this specification, it has dominated the empirical literature for more than a quarter century, but questions about its microeconomic foundation arise because it has not been derived from utility maximization. Another issue that has been largely ignored in the literature is the problem of nonstationarity, which is found in most macroeconomic variables and invalidates classical statistical inference: if the variables that enter the import demand equation contain a unit root, ignoring nonstationarity in these variables may cause serious inference problems.
The paper seeks to address these problems, first, by deriving an empirically tractable import demand equation that can be estimated for a large number of countries, using recent time-series techniques that address the nonstationarity present in the data. Second, because the statistical properties of the different estimators have been derived only asymptotically, the paper derives the small-sample properties of both the ordinary least squares (OLS) and the fully modified (FM) estimators of the short- and long-run elasticities, using Monte Carlo methods. It is shown that the FM estimators dominate the OLS estimators, even in small samples. Both price and income elasticities generally have the expected sign and are precisely estimated. The average price elasticity is close to zero in the short run but is slightly higher than unity in the long run. A similar pattern holds for income elasticities: the short-run income elasticities are on average less then 0.5, while the long-run income elasticities are close to 1.5.