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Grupo de Estudos Monetários e Financeiros

Estudos do GEMF, N.º 04 de 2015


Size Distribution of Portuguese Firms between 2006 and 2012

Rui Pascoal
Faculdade de Economia da Universidade de Coimbra

Mário Augusto
Faculdade de Economia da Universidade de Coimbra

Ana Margarida Monteiro
Faculdade de Economia da Universidade de Coimbra e GEMF

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, emphasizing the interpretation of SCL coefficients and its analogy with thermodynamics. Methods of estimation include Maximum Likelihood, modified Ordinary Least Squares in log-log scale and Nonlinear Least Squares considering the Levenberg-Marquardt algorithm. We apply these approaches to Portuguese firm data. In the sales case, the evolution of estimated parameters in both lognormal and SCL reflects the existence of a recession period more pronounced after 2008.

JEL Classification: C11; C13; C44; C58; C63; C87; G11; G32.

Keywords: Firms size, lognormal law, Zipf's law, simplified canonical law, Shannon entropy

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