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

Advances in Operations Research, 2011

We study empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on a US data set on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Both Pareto's law and Gibrat's law are often used to study firm size distribution. Their theoretical relationship is discussed, and it is shown how they are complementable with a bimodal distribution of firm size. We introduce economic mechanisms that suggest a bimodal distribution of firm size in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. Allowing for these mechanism thus will give rise to heterogeneity of firms with respect to certain characteristics. We then present different types of tests on US data on firm size which indicate a bimodal distribution of firm size.

2013

In this paper, we analyze the distributional properties of firms' growth, using an exhaustive data set of Italian firms between 1987-2006. The aim of the project is to understand the patterns of growth of firms and the relationship between growth and different financial structures.

A New Statistical Test (March 11, 2011), 2011

Abstract: We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functional forms belonging to the Subbotin family of distributions. While our hypotheses are rejected for the vast majority of sets at the sector level, we cannot reject them at the subsector level, indicating that ...

Journal of Statistical Theory and Practice, 2020

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. The inference problem is examined for maximum likelihood. Consistency is proven for the general case when all parameters are unknown. After deriving the Fisher information matrix, asymptotic normality and efficiency are established for a restricted model with the location parameter known. The asymptotic properties of the estimators are then examined using Monte Carlo simulations. To assess its goodness of fit, the ADP is applied to companies' growth rates, for which it is unequivocally favored over competing models.

Physica A: Statistical Mechanics and its Applications, 2019

The growth dynamics of firms have been object of numerous studies by econophysicists. The vast majority of these studies was done for large developed countries including the United States of America (US), France or Italy. These studies were conducted for countries with strong economies and whose business fabric has different characteristics from countries such as Portugal or Spain, with more large-sized firms and less micro-sized firms. It is thus important to study the growth dynamics of firms in Portugal and Spain, countries with economies that typically display anemic growth indexes and have a larger percentage of micro-sized firms. Considering two large samples of Portuguese and Spanish firms, we find that size distribution of firms is well fitted by the generalized Pareto distribution. Moreover, the distribution of Iberian firms annual growth rates is best approximated by the Cauchy distribution rather than the Laplace distribution. Firms growth standard deviation conditional on size is well approximated by power-law relationships with a scaling exponent close to 1 2 for micro/small-sized firms and close to 0 for medium/large-sized firms.

We describe several important features of annual firm growth rate dynamics. Specifically, we report three major findings, some of which were previously known for certain subsets of U.S. firms and are here shown to obtain for the entire universe of U.S. business firms, and others that are apparently novel. First, the distribution of log growth rates overall are well-characterized by the so-called Laplace distribution, i.e., a two-sided exponential distribution, and the closely-related Subbotin distribution; log growth rates are not normal. This has important implications for overall firm survival since the Laplace distribution has much heavier tails than the normal, meaning that some U.S. firms experience much stronger fluctuations than would be encountered if the economy were more normal (Gaussian). We argue that it is small businesses that bear the brunt of such fluctuations, since they are sufficiently numerous that a certain fraction of them always experience giant annual fluctuations. We suggest that the ostensible dynamism of the small business sector is essentially rationalized by heavy-tailed growth rates. A second finding has to do with the relatively modest differences in growth rate distributions across (two digit) sectors. Specifically, we find that the heavy-tailed character of growth rate distributions is nearly ubiquitous. This is surprising since the number of firms within such sectoral classifications differ by orders of magnitude, age cross-sections vary substantially, technological shocks are presumably quite different, and so on. The only significant deviations from Laplace-distributed growth are toward even heavier-tailed growth, not toward normality. Third, we have discovered that for data on establishments, the variance in growth rates does not depend on establishment size. This is a surprising finding from a number of perspectives. Essentially what it means is that a large establishment is as likely to lay-off 10% of its workers, say, as is a small establishment, or that it is as probable for a small firm of 10 employees to hire 2 new people as it is for a size 100 firm to hire 20 new workers. From these findings we draw a variety of conclusions, some of which may be relevant for policy. Since extreme events/large fluctuations are an inherent part of firm growth, especially for small firms, government policies the goal of which is to shield firms from fluctuations may be difficult to devise. However, policies designed to help firms ride out difficult times may go a long way in promoting firm survival. Similarly, the heavy-tailed character of positive growth fluctuations may be largely responsible for the intrinsic dynamism of small businesses, and any policy aimed at dampening these fluctuations, if effective, may have, as an unwanted side effect, a weakening of the ability of the small business sector to provide growth. An important methodological conclusion that the present investigation highlights is the need for more systematic longitudinal data on firms, primarily multi-establishment ones. For economists a further sharp result is that econometric work utilizing normal specifications of log growth rates (or lognormal specifications of absolute growth rates) is very badly misspecified. The growth of firms is a critical, even foundational, process to modern, industrial economies, involving product, labor and financial markets. A comprehensive, empirically grounded understanding of this process has yet to be fully developed. The present study, highlighting important dynamical aspects of firm growth, contributes to this research enterprise.

The European Physical Journal B, 2007

This paper investigates the statistical properties of within-country gross domestic product (GDP) and industrial production (IP) growth-rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether also within-country, time-series GDP and IP growth rates can be approximated by tent-shaped distributions. We fit output growth rates with the exponential-power (Subbotin) family of densities, which includes as particular cases both Gaussian and Laplace distributions. We find that, for a large number of OECD (Organization for Economic Cooperation and Development) countries including the US, both GDP and IP growth rates are Laplace distributed. Moreover, we show that fat-tailed distributions robustly emerge even after controlling for outliers, autocorrelation and heteroscedasticity.

Journal of Economic Dynamics and Control, 2014

We propose a hypothesis testing procedure to investigate whether the same growth rate distribution is shared by all the firms in a balanced panel or, more generally, whether they share the same functional form for this distribution, without necessarily sharing the same parameters. We apply the test to panels of US and European Union publicly quoted manufacturing firms, both at the sectoral and at the subsectoral NAICS levels. We consider the following null hypotheses about the growth rate distribution of the individual firms: i) an unknown shape common to all firms, with all the firms sharing also the same parameters, or with the firm variance related to its firm size through a scaling relationship, and ii) several functional shapes described the Subbotin family of distributions. Our empirical results indicate that firms do not have a common shape of the growth rate distribution at the sectorial NAICS level, whereas firms may typically be described by the same shape of the distribution at the subsectorial level, even if the specific shape may not be the same for different subsectors.

2022

In Marxist economic analysis, the firm-level rate of profit and the average rates of profit by industry play a central role in the study of intra-and-inter industry real competition. This paper aims to estimate the distribution of profit rates among and within industries in Colombia by employing firm-level data from the 5.032 biggest firms in the country in 2018. The econometrical methodology rests on the use of non-parametric techniques (kernel density estimations). The main empirical results are: First, a significant dispersion in the firm-level profit rates as well as in the average profit rates across industries. Second, a nonnormal unimodal tent-shape distribution for the general firm-level rates of profit as well as for the distribution of profit rates in the majority of industries. Third, negative profit rates are a structural feature of profit rate distribution at both: general and sectoral levels. Fourth, in comparison with interest rates, the firms exhibit low profitability: 60.5% of the firms yielded profit rates below the average deposit interest rate while only 14.8%, above the lending ordinary interest rate. Grosso modo, those findings are in line with Marxist economic theory but not with other economic paradigms.

2008