International Trade Dynamics with Sunk Costs and Productivity Shocks

Abstract

This paper offers a unified framework to analyze both short- and long-run trade dynamics in a consistent manner. It explains “the international elasticity puzzle”, a low trade elasticity against temporary shocks and a high trade elasticity against permanent shocks, studied in Ruhl (2008). The model in this paper extends the idea of export sunk costs and uncertainty to more general productivity shock processes by embedding 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 characterization of the equilibrium elucidates the microfoundations of trade dynamics linking a static trade model with heterogeneous firms and an international macroeconomic model. Due to the sunk costs and uncertainty, firms do not change their export status against small temporary 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.