This paper introduces persistent productivity shocks in a continuous-time mononopolistic competition model of trade with hetererogenous firms similar to Melitz (2003). In our model, the presence of sunk costs and uncertainty have three main consequences: first, firms export decisions become history-dependent. Second, the model generates firm dynamics and allows for substantial heterogeneity in export growth conditional on survival. Policy experiments modify the equilibrium along both the cross-sectional and time dimensions. Third, both the generated equilibrium firm size distribution and sales distribution of exporters into a foreign market are Pareto in the upper tail. All three consequences have been supported by empirical evidence. To solve the model we derive the stationary productivity distributions for exporters and non-exporters in general equilibrium. We point to the presence of a link between intra-industry firm heterogeneity and the degree of persistence in export status. Finally, we perform a numerical exercise to show how per-period fixed cost and up-front entry costs are differently related to persistence in export status for exporters and non-exporters.
