Production Function Estimation with Multi-Destination Firms

<jats:p>We develop a production function estimator for the case when firms endogenously select into multiple destination markets where they compete imperfectly, and when output is denominated only in value. The estimator exploits a novel source of variation to identify demand curvature: firm-level export shares. We demonstrate that ignoring the multi-destination dimension (i.e., exporting) yields biased and inconsistent inference. We estimate in French Manufacturing data increasing total returns to scale, decreasing returns to flexible inputs, and demand elasticities between -19.42 and -3.56. These estimates imply 5 to 8 times larger effects of a U.S. tariff increase compared to estimates from alternative estimators.</jats:p>