Home-Foreign Elasticity Functions and the Gains from Trade

Gains from trade are typically calculated using a constant trade elasticity estimated from substitution across foreign countries. For general homothetic preferences, we show how to calculate these gains from the initial domestic expenditure share and the home-foreign elasticity function along a price path to autarky. While this function generally depends on the specific price path, under weak separability it does not. We provide conditions for its nonparametric identification and estimate sector-level elasticity functions using tariff changes implied by trade agreements. Across WIOD and OECD ICIO data, estimated home-foreign elasticities generally rise with domestic expenditure shares. Using estimated elasticity functions in a multi-sector model with intermediate inputs, the median gain across the WIOD countries is 19.37 log points, compared with 24.43 when each country-sector elasticity is held fixed at its initial value.