Trade elasticities, heterogeneity, and optimal tariffs

We develop a structural estimator for heterogeneous supply and demand in the absence of instrumental variables. Using only readily available bilateral trade data we show how to leverage variation in prices and quantities across multiple markets in order to consistently estimate heterogeneous elasticities. Our elasticity estimates follow intuitive patterns of importer and exporter market power and produce believable distributions and magnitudes. To highlight the flexibility of the estimator, we extend the cornerstone theories of non-cooperative optimal trade policy to a setting where exporters have heterogeneous supply elasticities. Applying our estimates to trade and tariff data worldwide, we show that heterogeneous export supply elasticities provide new avenues for identification. We demonstrate statistically positive and persistent links between non-cooperative optimal tariffs and applied tariffs worldwide.