International Trade Dynamics with Sunk Costs and Productivity Shocks

This paper offers a unified framework to analyze both short- and long-run trade dynamics with heterogeneous firms in a consistent manner. The model embeds the classical theory of export hysteresis into a continuous-time trade model with heterogeneous firms, and considers the effects of both aggregate and idiosyncratic productivity shocks. A sharp analytical charac- terization of the equilibrium elucidates the microfoundations of trade dynamics, and explains the “international elasticity puzzle”, a low trade elasticity against temporary shocks and a high trade elasticity against permanent shocks. Aggregate productivity shocks and export sunk costs explain the elasticity puzzle because of the different adjustments on the extensive margin. If the productivity shocks are idiosyncratic, the economy is in a steady state, with individual firms moving around within a stationary distribution of productivities. Export hysteresis gives rise to a region of firm productivity where both exporters and non-exporters coexist given the same current productivity. The full model incorporates both types of shocks and offers realistic microfoundations of trade dynamics including simultaneous export entry and exit, an evolving productivity density of exporters, and the sluggish trade response to aggregate shocks. The framework contributes to the recent literature of partial differential equation models in macroe- conomics, and can be applied to other topics such as the evolution of labor force or income distribution