This paper introduces idiosyncratic firm efficiency shocks into a continuous-time general equilibrium model of trade with heterogeneous firms. The presence of sunk export entry costs and efficiency uncertainty gives rise to hysteresis in export market participation. A firm will enter into the export market once it achieves a given size, reflecting its efficiency, but may keep exporting even after its efficiency has fallen below its initial entry level. Some exporters will not be selling as much in the domestic market as other firms that never entered the foreign market. The model captures the qualitative features of firm birth, growth, export market entry and exit, and death found in the empirical literature. We calibrate the model to match relevant statistics of firms' turnover and export dynamics in the United States, and show that the mode of globalization (a reduction in sunk costs as opposed to overhead costs), matters for a firm's selection and persistence in export status. Trade liberalization via a reduction in sunk export entry costs reduces a firm's export status persistence, while the opposite happens when liberalization takes place through a reduction in overhead export costs.