A Cross-Sectional Analysis of Growth and Profit Rate Distribution: The Spanish Case

David Vidal-Tomás,Omar Blanco-Arroyo,Simone Alfarano,Alba Ruiz-Buforn

doi:10.3390/math10060926

David Vidal-Tomás, Omar Blanco-Arroyo + Show 2 more

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https://doi.org/10.3390/math10060926

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Abstract

We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.

Highlights

Gibrat (1931) [1] was the first scholar to propose a stochastic process in order to model the growth of firms based exclusively on general probabilistic concepts.His basic hypothesis states that the logarithmic growth rate of a firm’s size is independent of its level and it is normally distributed
We observe that the Laplace distribution provides a relatively poor fit for the profit rate distribution, since, at the 5% significance level, we reject the null hypothesis of α = 1 in 11 out of 19 years
We shed some light on the firm dynamics literature by analysing to what extent the Laplace distribution describes the Spanish long-lived firms’ distribution of profit and growth rate, against its alternative more general distributions, namely Subbotin and AEP

Summary

Introduction

Gibrat (1931) [1] was the first scholar to propose a stochastic process in order to model the growth of firms based exclusively on general probabilistic concepts His basic hypothesis states that the logarithmic growth rate of a firm’s size is independent of its level and it is normally distributed. The logarithmic growth rate of a firm in a given time period (one year, for instance) can be decomposed as a sum of a large number of shocks hitting the firm at a higher frequency (e.g., daily) Within this time decomposition, the emergence of the normal distribution of growth rates is a natural consequence of the CLT, assuming that the shocks are independent and identically distributed. Gibrat’s statistical approach has been generalised in order to account for other economic phenomena, such as the entry and exit of firms in a market and the turbulence and the learning of firms, leading

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