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Gravity equations have been widely used to infer trade flow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfounded. We develop a method that (i) consistently and efficiently estimates a theoretical gravity equation and (ii) correctly calculates the comparative statics of trade frictions. We apply the method to solve the famous McCallum border puzzle. Applying our method, we find that national borders reduce trade between industrialized countries by moderate amounts of 20-50 percent. (JEL F10, F15)
The gravity equation is one of the most empirically successful in economics. It relates bilateral trade flows to GDP, distance, and other factors that affect trade barriers. It has been widely used to infer trade flow effects of institutions such as customs unions, exchange-rate mechanisms, ethnic ties, linguistic identity, and international borders. Contrary to what is often stated, the empirical gravity equations do not have a theoretical foundation. The theory, first developed by Anderson (1979), tells us that after controlling for size, trade between two regions is decreasing in their bilateral trade barrier relative to the average barrier of the two regions to trade with all their partners. Intuitively, the more resistant to trade with all others a region is, the more it is pushed to trade with a given bilateral partner. We will refer to the theoretically appropriate average trade barrier as "multilateral resistance." The empirical gravity literature either does not include any form of multilateral resistance in the analysis or includes an atheoretic "remoteness" variable related to distance to all bilateral partners. The remoteness index does not capture any of the other trade barriers that are the focus of the analysis. Moreover, even if distance were the only bilateral barrier, its functional form in the remoteness index is at odds with the theory.1
The lack of theoretical foundation of empirical gravity equations has two important implications. First, estimation results are biased due to omitted variables. Second, and perhaps even more important, one cannot conduct comparative statics exercises, even though this is generally the purpose of estimating gravity equations.2 In order to conduct a comparative statics exercise, such as asking what the...