We document that new exporters initially export small amounts, grow gradually, and are most likely to exit the export market in their first few years. We find that the standard sunk‐cost model cannot replicate these new exporter dynamics: New exporters grow too large too quickly and live too long. In a modified sunk‐cost model that can account for these facts, the entry costs needed to match the data are three times smaller than in the sunk‐cost model. Dynamic models with richer plant‐level heterogeneity are needed.