Trade Models, Trade Elasticities, and the Gains from Trade

We consider five models of international trade that belong to the class of models in which the trade elasticity and domestic trade share are sufficient statistics for the welfare cost of autarky. Three are fixed-variety models featuring increasing micro-level margins of adjustment: versions of the Armington model, the Ricardian model, and its variable-markup counterpart. Two are endogenous-variety models featuring monopolistic competition: versions of the Krugman model and the Melitz model. For the three fixed-variety models, we show theoretically that, although they imply the same mapping from the trade elasticity to welfare, they imply different mappings from the trade elasticity to observed order statistics of price gaps of identical goods across countries. This result implies that choosing the parameter that governs the elasticity of trade to match the same order statistics in the data differentially impacts each model's measured welfare cost of autarky. We quantify these differences for all five models.