When evaluating the effects of trade frictions on bilateral trade, it is important to consider firm level heterogeneity and multilateral resistance. This paper is the first to do so simultaneously.   Helpman, Melitz & Rubinstein[1] show that ignoring firm heterogeneity leads to an overestimate of the effect of reduced frictions on firm-level trade. Well-specified gravity models predict that trade is not only a function of frictions between a pair of countries, but frictions relative to those with the rest of the world, captured by multilateral resistance (MR).  The estimation procedure we follow controls for country-selection into exports and firm heterogeneity while our comparative statics between two or more countries accounts for MR. 

We model MR in a tractable framework by developing a Taylor approximation to the non-linear system developed by Anderson & Van Wincoop (2003).[2]  Our framework accommodates asymmetric trade flows between countries and is consistent with an empirical strategy in which a two-stage procedure is used to control for firm heterogeneity and country selection. It allows for easy estimation and provides a straightforward method for identifying the MR effects in comparative statics, even if they remain unidentified in the regression.

Treating MR explicitly points to some interactions between the size of trading countries and the impact of changes in trade costs on bilateral trade between them. Moreover, the joint modeling of firm heterogeneity and MR highlights that these interactions are present for changes to both variable and fixed costs of trade.

We show that interactions between country size and changes in trade frictions depend crucially on the nature of those changes - be they unilateral, bilateral or multilateral. Our model indicates that the elasticity of bilateral trade is increasing in the size of trading countries for multilateral changes in trade costs, but decreasing in the size of trading countries for bilateral changes in trade costs.  Unilateral changes in trade frictions have larger effects on bilateral trade as the importing country gets larger, but bilateral trade liberalizations have smaller effects on bilateral trade as the importing country gets larger.

Orthogonal to MR issues, our analysis highlights the finding that the overall effect for a pair of countries is underestimated by OLS relative to the two-stage procedure, even though it has recently been established that the firm-level effect is overestimated. 

Our simulations illustrate our theoretical findings.  They allow us to quantify the effects of ignoring multilateral resistance in simulations. When simulating the effects of multilateral trade cost reductions on bilateral trade, one simply cannot ignore multilateral resistance. For simulations of bilateral friction reduction for a typical pair of countries, which are small, ignoring multilateral resistance is innocuous.