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In many countries, exports are highly concentrated among a few "superstar" firms. We estimate the export decisions of superstar firms as the result of a complete information, simultaneous, discrete choice, static entry game. We employ a dataset on the universe of Danish trade transactions by firm, product and destination. We also obtain detailed information on applied, preferential tariff protection from the MAcMap-HS6 database. We find evidence of strong negative competitive effects of entry: in the absence of strategic competitive effects, firms would be 54.3 percentage points more likely to export to a given market. Next, we run two counterfactual exercises. We show that failing to account for the strategic interaction among superstar exporters leads to: (i) overstating the probability that firms would start exporting to a market following tariff elimination by 8 percentage points; and, (ii) overstating the probability that firms would stop exporting to a market if tariffs were imposed by 7.5 percentage points. We also show that competitive effects vary across export markets and competitors. This heterogeneity in the competitive effects implies that there exist multiple equilibria, both in the identity and in the number of firms.

This paper provides new evidence on how export status relates to prices and product quality. Using firm-product-level data on production, exports and imports for a sample of Danish manufacturing firms, we present three key correlations. First, exported varieties are on average sold at lower prices relative to only domestically sold varieties. Second, exported varieties have higher quality measured by "demand residuals" (i.e., they have larger sales conditional on price).Finally, exported varieties are produced using cheaper imported intermediates. We introduce the term "quality-cum-price sorting" to describe this sorting environment. The observed sorting behavior in terms of output quality and import prices works not just across firms, but also within multi-product firms across the product portfolio. In contrast, the negative exporter premium in terms of output prices vanishes once firm-level unobservables are accounted for -consistent with the idea that unobserved firm efficiency is driving the negative correlation.