The pattern of trade observed from firm-product-country data calls for a new generation of models. To address the unexplained variation in the data, we propose a new model of monopolistic competition where varieties enter preferences non-symmetrically, capturing both horizontal and vertical differentiation in an unprecedented way. Together with a variable elasticity of substitution, competition effects, varying markups and prices across countries, this results in a tractable model that rationalizes the empirical finding that firm-product quantities show systematically more variability than prices across export destinations. Accounting for unexplained data variation, our model can thus be used to improve demand identification.
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