Trade costs are often additive. Well-known examples are quotas, per unit tariffs, and, in part, transportation costs. In spite of this, we have no broad and systematic evidence of the magnitude of these costs. In this paper, we develop a new empirical framework for estimating additive trade costs from standard firm-level trade data. Our results suggest that additive barriers are on average 14%, expressed relative to the median price. The point estimates are strongly correlated with common proxies for trade costs. Using our microestimates, we show that an additive import tariff reduces welfare and trade by more than an equal-yield multiplicative tariff.

We investigate to what extent worker heterogeneity explains the well-known wage and productivity exporter premiums, employing a matched employer-employee data set for Norwegian manufacturing. The wage premium falls by roughly 50% after controlling for observed and unobserved worker characteristics, while the total factor productivity premium falls by 25% to 40%, suggesting that sorting explains up to half of these premiums. Recent trade models emphasize the role of within-industry reallocation of labor in response to various shocks to the economy. Our findings suggest that aggregate productivity gains due to reallocation may be overstated if not controlling for sorting between firms and workers.