Size distribution of Portuguese firms between 2006 and 2012

Abstract

This study aims to describe the size distribution of Portuguese firms, as measured by annual sales and total assets, between 2006 and 2012, giving an economic interpretation for the evolution of the distribution along the time. Three distributions are fitted to data: the lognormal, the Pareto (and as a particular case Zipf) and the Simplified Canonical Law (SCL). We present the main arguments found in literature to justify the use of distributions and emphasize the interpretation of SCL coefficients. Methods of estimation include Maximum Likelihood, modified Ordinary Least Squares in log–log scale and Nonlinear Least Squares considering the Levenberg–Marquardt algorithm. When applying these approaches to Portuguese’s firms data, we analyze if the evolution of estimated parameters in both lognormal power and SCL is in accordance with the known existence of a recession period after 2008. This is confirmed for sales but not for assets, leading to the conclusion that the first variable is a best proxy for firm size.