Gravity Model of Trade

Multilateral resistance is a country's average trade barrier with all of its partners, captured by the outward (Π_i) and inward (P_j) price indices in the structural gravity equation. Trade between two countries depends on their bilateral cost relative to these multilateral terms: a country remote from everyone trades more with any given partner than its bilateral distance alone would suggest. Anderson and van Wincoop showed that omitting these terms — as pre-2003 gravity regressions did — biases the estimated effects of distance and borders, which is why they are now controlled for with exporter and importer fixed effects.

Taking logs of the multiplicative gravity equation and running OLS is biased when the error is heteroskedastic, because by Jensen's inequality the expectation of the log differs from the log of the expectation — so OLS estimates inconsistent elasticities. Log-linear OLS also cannot use observations with zero trade, which are common. Santos Silva and Tenreyro (2006) showed that estimating the equation in its multiplicative form by Poisson pseudo-maximum-likelihood is consistent under heteroskedasticity and naturally includes zero flows, making PPML the standard estimator.

Structural gravity is the partial-equilibrium estimating equation implied by a broad class of trade models (Armington/CES, Eaton-Kortum, Krugman). The estimated trade-cost elasticities and the multilateral resistance system can be embedded in a general-equilibrium framework to run counterfactuals — for example, computing the welfare effects of a new trade agreement — linking the econometrics directly to computable general equilibrium analysis.