Production Function Estimation with Multi-Destination Firms

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. We exploit a novel source of variation to identify the curvature of demand: firm-level export share of sales. Ignoring the multi-destination dimension (i.e., exporting) yields biased and inconsistent inference. In contrast, our estimator performs well in Monte Carlo experiments. We estimate in French Manufacturing data increasing total returns to scale, decreasing returns to flexible inputs, demand elasticities between 3.6 and 19.4, and learning-by-exporting effects of 0-4% per year.