The extensive margin of bilateral trade exhibits a high level of persistence that cannot be explained by geography or trade policy. We combine a heterogeneous firms model of international trade with bounded productivity with features from the firm dynamics literature to derive expressions for an exporting country’s participation in a specific destination market in a given period. The model framework asks for a dynamic binary choice estimator with two or three sets of high-dimensional fixed effects. To mitigate the incidental parameter problem associated with nonlinear fixed effects models, we characterize and implement suitable bias corrections. Extensive simulation experiments confirm the desirable statistical properties of the bias-corrected estimators. Empirically, taking two sources of persistence — true state dependence and unobserved heterogeneity — into account using a dynamic specification, along with appropriate fixed effects and bias corrections, changes the estimated effects considerably: out of the most commonly studied potential determinants (joint WTO membership, common regional trade agreement, and shared currency), only sharing a common currency retains a significant effect on whether two countries trade with each other at all in our preferred estimation.