As the exchange rate, foreign demand, and production costs evolve, domestic producers are continually faced with two choices: whether to be an exporter and, if so, how much to export. We develop a dynamic structural model of export supply that characterizes these two decisions. The model embodies plant‐level heterogeneity in export profits, uncertainty about the determinants of future profits, and market entry costs for new exporters. Using a Bayesian Monte Carlo Markov chain estimator, we fit this model to plant‐level panel data on three Colombian manufacturing industries. We obtain profit function and sunk entry cost coefficients, and use them to simulate export responses to shifts in the exchange‐rate process and several types of export subsidies. In each case, the aggregate export response depends on entry costs, expectations about the exchange rate process, prior exporting experience, and producer heterogeneity. Export revenue subsidies are far more effective at stimulating exports than policies that subsidize entry costs.