This paper presents a monopolistic competition model of trade and multinational production that incorporates asymmetric trade barriers and international differences in production costs. The model predicts the functional form for the dependence of U.S. exports and multinational production on tariffs, distance, and production costs. To deal with simultaneity, we estimate the nonlinear equations of U.S. exports and multinational production simultaneously. In the estimation, we also include country fixed effects and allow for endogenous location choice by firms. The estimation yields reasonable estimates of the structural parameters, including the elasticity of substitution. Based on the estimates, we then simulate the effects of trade liberalization. We find that the elimination of tariffs worldwide would increase U.S. exports by 3.0% and U.S. multinational production by 21.7%. This large expansion of U.S. overseas production mainly results from an expected increase in the number of U.S. foreign affiliates in response to tariff reductions.