Gains from Trade with Flexible Extensive Margin Adjustment

We propose a new sufficient statistic to measure the gains from trade in models where the extensive margin trade elasticity is not necessarily constant. This statistic is a function of one data moment, the market share of continuing domestic products, and one parameter, the elasticity of substitution between products. It measures the gains from trade in a Ricardian model with any productivity distribution or a Melitz model with any productivity distribution and any pattern of selection into production and exporting. We apply our statistic to measure Canada's gains from the Canada-US Free Trade Agreement and find that they are smaller than suggested by statistics that assume a constant extensive margin response of trade.