The model introduces a time element to the fixed-variable cost trade-off in a heterogeneous producer trade model. Thus, the dynamics of aggregate trade adjustment arise from producer-level decisions to invest in lowering their future variable export costs. The model is calibrated to match salient features of new exporter growth and provides a new estimate of the exporting technology. At the micro level, the authors find that new exporters commonly incur substantial losses in the first three years in the export market and that export profits are backloaded. At the macro level, the slow export expansion at the producer level leads to sluggishness in the aggregate response of exports to a change in tariffs, with a long-run trade elasticity that is 2.9 times the short-run trade elasticity. The authors estimate the welfare gains from trade from a cut in tariffs, taking into account the transition period. While the intensity of trade expands slowly, consumption overshoots its new steady-state level, so the welfare gains are almost 15 times larger than the long-run change in consumption. Models without this dynamic export decision underestimate the gains to lowering tariffs, particularly when constrained to also match the gradual expansion of aggregate trade flows.