We develop a procedure to estimate production functions, elasticities of demand, and productivity when firms endogenously select into multiple destination markets where they compete imperfectly, and when researchers observe output denominated only in value. We show that ignoring the multi-destination dimension (i.e., exporting) yields biased and inconsistent inference. Our estimator extends the two-stage procedure of Gandhi et al. (2020) to this setting, which allows for cross-market complementarities. In Monte Carlo simulations, we show that our estimator is consistent and performs well in finite samples. Using French manufacturing data, we find aver- age total returns to scale greater than 1, average returns to variable inputs less than 1, price elasticities of demand between -21.5 and -3.4, and learning-by-exporting effects between 0 and 4% per year. Alternative estimation procedures yield unrealistic estimates of returns to scale, demand elasticities, or both.