Abstract
This paper studies the distribution of the firm size for the Colombian economy showing evidence against the Gibrat’s law, which assumes a stable lognormal distribution. On the contrary, we propose a lognormal expansion that captures deviations from the lognormal distribution with additional terms that allow a better fit at the upper distribution tail, which is overestimated according to the lognormal distribution. As a consequence, concentration indexes should be addressed consistently with the lognormal expansion. Through a dynamic panel data approach, we also show that firm growth is persistent and highly dependent on firm characteristics, including size, age, and leverage −these results neglect Gibrat’s law for the Colombian case.
Highlights
The relationship between firm size (FS) and firm growth (FG) has been extensively studied since the early seminal study of Gibrat [1]
In order to test the relation between FG and FS implicit in the Gibrat’s Law, as well as the impact of other characteristics related to the Colombian firms, we propose the following model: Growthit 1⁄4 ai þ bGrowthi;tÀ 1 þ g logðSalestÀ 1Þ þ y1logAgeit þ y21⁄2logAgeit 2 þ φLeveragei;tÀ 1 þ oROEi;tÀ 1 þ εit; ð9Þ
Where Growthit is FG calculated as the first logarithmic difference of sales; Growthi,t−1 is the first lag of FG; log(Salest−1) is a proxy of FS measured as the natural logarithm of sales, all for a specific firm i and time t; logAgeit is the logarithm of the age of the company since its foundation, which is considered in both level and quadratic form; Leveragei,t−1 is the first lag of leverage calculated as the sum of the long-term debt and short-term debt divided by the total assets; and ROEt−1 is the first lag of profits, calculated as the net profit divided by common equity
Summary
The relationship between firm size (FS) and firm growth (FG) has been extensively studied since the early seminal study of Gibrat [1]. Many small businesses coexist with a few large companies, and Gibrat’s law is used as an explanation for the high bias in FS distribution [2,3,4,5] This topic has been addressed in several studies, FS distribution is still an open question that arouses increasing interest among researchers and policymakers, since firm distribution is correlated with the degree of aggregate economic concentration and, is a cornerstone of antitrust policy [6,7,8,9]. The log-SNP distribution allowed a better adjustment in the upper quantiles without imposing a minimum threshold, which allowed us to obtain a better quantification of the Gini index This is relevant because knowing the characteristics of larger companies and having a larger share of the market is essential to analyze the entire economy.
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