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.