Aggregate Properties of Open Economy Models with Expanding Varieties

We present a unified dynamic framework to study the interconnections between international trade and business cycle models. We prove an aggregate equivalence between a competitive, representative firm model that has aggregate production externalities and dynamic trade models that feature monopolistic competition, endogenous entry, and heterogeneous firms. The production externalities in the representative firm model have to be introduced in the intermediate and final good sectors so that the model is isomorphic to dynamic trade models that embody love-of-variety and selection effects. In a quantitative exercise with multiple shocks, we show that to improve the fit of the dynamic trade models with the data, the most important ingredient is negative capital externality in the intermediate good sector. We conclude that this presents a puzzle for the literature as standard dynamic trade models provide micro-foundations for positive capital externality.