A Cost Minimization Approach to Import Demand Equations

Abstract

THE foreign sector in conventional macroeconomic models has not been properly integrated with behavioural relationships in the rest of the economy. The aggregate producing sector is usually depicted as employing primary factors, capital and labor, to produce a single output which simultaneously satisfies the demands of consumers, producers, governments, and foreigners. In this one-sector model, imports are implicitly assumed to be either final goods which enter the utility functions of consumers, or intermediate goods which are separable from primary factors in the productive process. The first assumption conflicts with empirical evidence that the bulk of international trade occurs in intermediate goods, while the second assumption involves a substantive restriction on the form of the technology which ought to be examined and justified empirically rather than assumed a priori. Most goods entering international trade require further processing before delivery to final demand. This processing requires the services of domestic primary factors of production which could be employed elsewhere. An important issue for public policy concerns the effect of trade and trade barriers on the distribution of factor income. If final demand can be satisfied either by employing domestic primary factors or by importing materials, then changes in import prices will, in general, alter the competitive returns to the primary factors. The usual assumption adopted for empirical work, namely that imports are final goods with no close domestic substitutes, rules out any income distribution effects resulting from a change in import prices. Previous investigators have estimated import demand equations by regressing the logarithm of a measure of imports on the logarithm of national income and the logarithm of the ratio of the price of imports to the price of domestic value added.' While this functional form has the advantage that the parameters measure the price and income elasticities of demand, it is not derivable from an underlying model of optimal behaviour, and it assumes that imports are final goods which are separable from all other commodities in the utility function of the consuming sector. Until very recently most empirically tractable functional forms have imposed separability restrictions a priori. Thus, even if one were to proceed from micro-economic foundations by assuming a constant elasticity of substitution functional form to model the taste or technology of the decision unit, the assumption of separability between imports and alternative factors or commodities would constitute a maintained hypothesis that could not be tested.2 The one output specification provides no way of explaining changes in the relative prices of various categories of final demand. It will only be appropriate for explaining the composition of inputs if the technology is separable with respect to a partitioning between inputs and outputs. In this case, the cost minimizing input bundle is independent of the composition of output, and, for purposes of explaining factor demands, one can pretend that a single output exists. Separability between inputs and outputs implies that marginal rates of substitution between pairs of factors are independent of the composition of output, and marginal rates of