From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties.

This paper emphasizes the importance of two sufficient statistics to characterize firm-level heterogeneity in the workhorse heterogeneous firms trade model: the Cumulative Distribution Function (CDF) and the mean of firm-level sales. Contradicting the strong focus on the CDF, a close fit to average sales proves to be critical for model performance. Moreover, this average varies largely across finite sample draws due to sales being heavy-tailed, providing evidence that individual firms can influence the aggregate economy. As a result, modeled aggregate trade elasticities and Gains From Trade are unlikely to materialize: they are biased in finite samples and underlying characterizations of firm-level heterogeneity are rejected by the data.