We develop a novel methodology for disentangling the demand and cost drivers of firm heterogeneity when firms sort themselves into different markets, and we apply it to export status differences. Our methodology results in joint estimates of firm-level productivity and of markups in every market, without imposing functional form restrictions on demand. We find that exporters, relative to nonexporters, (i) have flatter domestic demand curves—thicker domestic markets—and (ii) have higher demand conditional on productivity. Finally, (iii) these demand advantages translate to foreign markets, thereby leading to export status differences.

We study the nonparametric identification of gross output production functions under the environment of the commonly employed proxy variable methods. We show that applying these methods to gross output requires additional sources of variation in the demand for flexible inputs (e.g., prices). Using a transformation of the firm’s first-order condition, we develop a new nonparametric identification strategy for gross output that can be employed even when additional sources of variation are not available. Monte Carlo evidence and estimates from Colombian and Chilean plant-level data show that our strategy performs well and is robust to deviations from the baseline setting.