Gains from Trade Liberalization with Flexible Extensive Margin Adjustment

We propose a sufficient statistic to measure the ex-post welfare gains from trade in CES models featuring any productivity distribution and any pattern of selection into production and exporting. This statistic is based on a single data moment, the change in the market share of continuing domestic producers, and a single structural parameter, the elasticity of substitution between products. We apply our statistic to measure Canada's gains from the Canada-US Free Trade Agreement using data on observed firm selection. We find that welfare gains can substantially deviate from welfare estimates implied by formulas that assume a constant extensive margin trade elasticity.