Gravity Models and the Law of Large Numbers

Modern quantitative theories of international trade rely on the probabilistic representation of technology and the assumption of the Law of Large Numbers (LLN), which ensures that when the number of traded goods goes to infinity, trade flows can be expressed via a deterministic gravity equation that is log-linear in exporter-specific, importer-specific and bilateral trade cost components. This paper shows that when the number of traded goods is finite, the gravity equation has a structural stochastic component not related to the fundamental gravity forces. It provides a novel explanation of the differences in the goodness of fit of gravity models across different sectors observed in the data. It also suggests that when the LLN does not hold, the welfare gains from trade have a considerable stochastic component and should be characterized via distributions rather than point estimates. We use sectoral trade data and Monte Carlo simulations to develop a procedure with minimal data requirements that allows estimation of intervals for the welfare gains from trade.