Measuring firm size distribution with semi-nonparametric densities

In this article, we propose a new methodology based on a (log) semi-nonparametric (log-SNP) distribution that nests the lognormal and enables better fits in the upper tail of the distribution through the introduction of new parameters. We test the performance of the lognormal and log-SNP distributions capturing firm size, measured through a sample of US firms in 2004-2015. Taking different levels of aggregation by type of economic activity, our study shows that the log-SNP provides a better fit of the firm size distribution. We also formally introduce the multivariate log-SNP distribution, which encompasses the multivariate lognormal, to analyze the estimation of the joint distribution of the value of the firm's assets and sales. The results suggest that sales are a better firm size measure, as indicated by other studies in the literature.