Gravity beyond CES

We derive a linear structural gravity equation that allows for rich substitution patterns based on observable characteristics. To achieve this, we take advantage of recent econometric work to linearize an import demand system with mixed CES (Constant Elasticity of Substitution) preferences. Compared to traditional gravity models, the resulting equation features additional regressors that capture heterogeneity in the patterns of substitution across exporters. Importantly, this equation can be easily estimated through two stage least squares (2SLS) and without additional data requirements relative to traditional gravity. We implement this method using bilateral trade data and find that the data strongly rejects the Independence of Irrelevant Alternative (IIA) assumption implied by standard trade models: we find an important role for vertical and geographical differentiation so that exporters with similar prices, or originating from similar regions, are closer substitutes. We show that this pattern has important implications in the context of the recent (2018-2019) US-China trade war, in which our model can correctly predict which countries benefitted the most from the reallocation of trade flows due to US tariffs on Chinese imports.