We show that capital controls have large adverse effects on misallocation, exports and welfare using a dynamic Melitz-OLG model with heterogeneous firms, monopolistic competition, endogenous trade participation and collateral constraints. Static effects increase misallocation by reducing capital-labor ratios and rising firm prices, dynamic effects reduce it by incentivizing saving and delaying entry into export markets, and general equilibrium effects are ambiguous. Firms at the collateral constraint or at their optimal scale are barely affected but those in between are severely affected. Calibrated to the 1990s Chilean encaje, the model yields higher aggregate misallocation with larger effects on exporters and high-productivity firms. Social welfare falls and welfare of exporters falls significantly more. LTV regulation cuts credit by the same amount at sharply lower costs, because it spreads the burden of the cut more evenly. A panel data analysis of Chilean manufacturing firms yields strong evidence supporting the model’s predictions.