On a Class of Statistical Distance Measures for Sales Distribution: Theory, Simulation and Calibration

While firm-level and micro issue analysis become an important part in research of international trade, only a few work is concerned about the goodness-of-fit for size distribution of firms. In this paper, we revisit the statistical aspects of firm productivity and sales revenue, in order to compare different definitions of statistical distances. We first deduce the exact form of size distribution of firms by only implementing the assumptions of productivity and demand function, and then introduce the famous g-divergence as well as its statistical implications. We also do the simulation and calibration so as to compare those different divergences, moreover, tests the combined assumptions. We conclude that minimizing Pearson x2 and Neyman x2 produces similar results and minimizing Kullback-Leibler divergence is likely to take the expense of other distance measures. Additionally, selection among different statistical distances is much more significant than demand functions.