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C H A P T E R 5 The Econometrics of Estimating Endowments Implicit in Trade Decisions and Measuring Country Conformity to Trade Models "Testing" theories, as that process is generally conceived, is only one of the minor preoccupations of science The very process that generates a theory (and particularly a simple generalization) goes a long way towards promising it some measure of validity . For these reasons, histories of science written in terms of the processes that discover patterns in nature would seem closer to the mark than histories that emphasize the search for data to test for hypotheses created out of whole cloth —Herbert Simon (1977) I his chapter develops methods of discovering the patterns embedded in international trade data. The patterns are summarized in estimates of the factor endowments that are implicit in trade decisions. Because these patterns are deeply hidden within the data, it is necessary to combine a complex statistical procedure with international trade theory to extract them. Moreover, given the distance between the observed phenomenon and the object of interest, the form that the statistical procedure must take is not immediately obvious. One needs a methodology for deriving that procedure—hence the use of maximumlikelihood methods in this chapter. The primary reason for using maximum-likelihood methods here does not lie in their optimal statistical properties. Rather, the usefulness of the methods is in deriving the functional form of estimators, when the nature of the estimators is not transparent from knowledge of existing procedures. The emphasis , therefore, is not on maximum likelihood as a methodology for constructing optimal estimators and testing levels of significance, but rather on maximum likelihood as a means of showing one how to extract patterns that are deeply hidden in data. A complete, formal description of the statistical methods requires the use of matrix algebra, not because of anything particularly abstruse in those methods , but simply because a matrix is worth a thousand words. Some readers will, understandably, not want to plow through the details of this algebra, yet it is important that all those who are interested in the empirical results of 142 Chapter 5 the book have some basic understanding of how those results are generated. This chapter, therefore, begins with a brief, nontechnical description of the procedures for deriving estimates of the factor endowments implicit in foreigntrade data. There follows also a summary of applications of these procedures, including the method of generating measures of the degree to which a country' s foreign trade patterns fit standard trade models. Those who do not want to bury themselves in the complexities of the econometrics should read Section 5.1 and then move on to the chapters in which the results are presented. Those who are interested in the statistical methods may find the ensuing section useful as an introduction to the more formal analysis that follows. Sections 5.2 and 5.3 develop the basic econometric techniques that underlie all the analyses of Chapters 6 and 7. Sections 5.4 and 5.5 show how one can calculate statistics that can be used to judge the accuracy of predictions derived from the use of these techniques. Section 5.6 explains how multi-year pre­ dictions can be made using a time series of trade data. In implementing the econometric procedures, it was necessary to aggregate the trade measures for each country across commodities.' Section 5.7 discusses the issues arising in the choice of aggregation procedure and the properties of the chosen proce­ dure. The chapter closes with a description of the computational techniques used to derive the estimates. 5.1. A Brief Overview of the Statistical Methods The statistical procedures begin with a relationship derived from the theory of international trade. Theory postulates that trade performance is determined by the levels of variables measuring the factor endowments of a country. There are N measures of trade performance, the endogenous variables, and 5 factor endowments, the exogenous variables. The first step in the procedure is to find a set of countries for which data on both trade performance and factor endowments can be obtained.2 Consistent with the context of the present study, let us call these the' 'Western'' countries. With the Western data, containing both exogenous and endogenous variables, one can estimate the relationship between trade performance and factor en­ dowments. The next step in the procedure entails inverting this relationship. This step is easiest to envisage when the number of factor endowments, S, is assumed to be...


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