Academic journal article Atlantic Economic Journal

K-Fold Cross-Validation and the Gravity Model of Bilateral Trade

Academic journal article Atlantic Economic Journal

K-Fold Cross-Validation and the Gravity Model of Bilateral Trade

Article excerpt

Introduction

The gravity model of international trade, named for its resemblance to the physics equation of gravitational attraction, is widely considered one of the most empirically sound models in economics due to its ability to explain large amounts of the variation in international trade. Originally, there was little foundational economic theory for why econometricians used the gravity model. However, this has gradually changed and the gravity model now has solid theoretical foundations. (1) Many studies on international trade focus on the determinants of trade and use the gravity model as a means of analyzing the variables, typically with panel data in an attempt to identify causality. The common gravity model has the basic form of:

log ([trader.sub.ij]) = [[beta].sub.0] + [[beta].sub.1] ln ([distance.sub.ij]) + [[beta].sub.2]log ([gdp.sub.i]) + [[beta].sub.3]log ([gdp.sub.j]) + [[beta].sub.4][borde.sub.ij] + [[beta].sub.5] [FTA.sub.ij] + [[beta].sub.6][CU.sub.ij] + ... + [[epsilon].sub.ij] (1)

where log([trade.sub.ij]) is the bilateral trade between countries i and j, [FTA.sub.ij] and C[U.sub.ij] are dummy variables for whether countries i and j are in a free trade agreement or currency union, and the remaining variables are similarly expressed. Other variables can be easily added to this model based upon the researcher's interests.

There are two main objectives in this paper. First, it proposes an alternative method for determining whether a variable is a significant determinant of bilateral trade. Most papers, such as Rose and Glick (2002); Rose (2005); van Wincoop and Rose (2001); Bergstrand and Baier (2004), and many others, use in-sample significance tests to determine whether a variable is statistically and practically significant. If the p-value is statistically significant, the coefficient is practically significant, and the assumptions of the model are met, then the variable is assumed to be significant. In general, saying the variable is significant for the in-sample data is not the correct answer to the question that the researchers are trying to answer. Frequently, the implicit question is whether or not the variable is a significant predictor of the level of bilateral trade. For example, Rose and Glick (2002) pose the policy question: "What is the trade effect of a country joining or leaving a currency union?" The answer to this question should give an indication of whether or not joining or leaving a currency union is a significant predictor of the level of bilateral trade. They use a fixed effects regression on their in-sample data and get a coefficient of .65 for currency union [[e.sup.65] [approximately equal to] 1.9]. They interpret this by saying "the estimate implies that joining a currency union leads bilateral trade to rise by about 90%, i.e., almost double. This effect is economically large, and statistically significant at conventional levels; the t-statistic is 13". Rose and Glick then continue to conduct sensitivity tests where they check the significance of the variable after restricting the fixed effects regression to certain sections of the data.

However, Rose and Glick (2002) only use in-sample significance tests. The logic of the question, especially to be useful for any policy analysis, implies the ability to predict the effects of joining or leaving a currency union. This is repeated by van Wincoop and Rose (2001), who use similar in-sample methods and state predictively that "we estimate that the [European Monetary Union] will cause European trade to rise by 50%." A measure of predictive ability requires utilizing out-of-sample data techniques and is not satisfactorily met by in-sample techniques, because in-sample statistical methods assume the model specification is known, and thus, are difficult to generalize beyond the exact data used to generate the model.

Despite the fact that out-of-sample techniques are more logically consistent with the predictive policy questions asked, few papers utilize them. …

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