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This exploratory research note investigates the frequency and activity of HighGrowth Firms (HGFs) in Peru using panel data on Peru's largest firms for the years 2001-2016. Firms in our dataset enjoyed strong growth in revenues during the period. Compared to other countries, HGFs are relatively common in Peru although the share they represent of all firms in the database decreased over the time span of our analysis. We confirm several previous findings, such as the heavy-tailed growth rates distribution, and the superior growth performance of small and young firms.

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.

Debate on the validity of the Law of Proportionate Effect (LPE) on firm growth is ongoing decades after it was postulated by Gibrat in 1931. The theoretical model which asserts that firm growth follows a random walk has been largely tested in developed economies using data from non-incubated firms, with scanty research in developing regions like Africa. This paper, therefore, aims to address this gap by being the first to assess the validity of Gibrat's law on incubated small, medium, and micro enterprises (SMMEs) in South Africa. The study utilised four-year panel data from 300 incubated SMMEs across the country, for the period between 2018 to 2021. Utilising the Law's generalised growth rate model, the generalised least square regression modelling was harnessed, using R Software. The findings, using sales as firm size proxy, confirmed Gibrat’s Law. The results showed that firm size had no effect on the sales growth rate of incubated firms, on the other hand when employment proxied performance the LPE was rejected. The findings provide important implications for both practitioners and pertinent stakeholders in the SMME sector in South Africa.

Debate on the validity of the Law of Proportionate Effect (LPE) on firm growth is ongoing decades after it was postulated by Gibrat in 1931. The theoretical model which asserts that firm growth follows a random walk has been largely tested in developed economies using data from non-incubated firms, with scanty research in developing regions like Africa. This paper, therefore, aims to address this gap by being the first to assess the validity of Gibrat's law on incubated small, medium, and micro enterprises (SMMEs) in South Africa. The study utilised four-year panel data from 300 incubated SMMEs across the country, for the period between 2018 to 2021. Utilising the Law's generalised growth rate model, the generalised least square regression modelling was harnessed, using R Software. The findings, using sales as firm size proxy, confirmed Gibrat’s Law. The results showed that firm size had no effect on the sales growth rate of incubated firms, on the other hand when employment proxied performance the LPE was rejected. The findings provide important implications for both practitioners and pertinent stakeholders in the SMME sector in South Africa.

Debate on the validity of the Law of Proportionate Effect (LPE) on firm growth is ongoing decades after it was postulated by Gibrat in 1931. The theoretical model which asserts that firm growth follows a random walk has been largely tested in developed economies using data from non-incubated firms, with scanty research in developing regions like Africa. This paper, therefore, aims to address this gap by being the first to assess the validity of Gibrat's law on incubated small, medium, and micro enterprises (SMMEs) in South Africa. The study utilised four-year panel data from 300 incubated SMMEs across the country, for the period between 2018 to 2021. Utilising the Law's generalised growth rate model, the generalised least square regression modelling was harnessed, using R Software. The findings, using sales as firm size proxy, confirmed Gibrat’s Law. The results showed that firm size had no effect on the sales growth rate of incubated firms, on the other hand when employment proxied performance the LPE was rejected. The findings provide important implications for both practitioners and pertinent stakeholders in the SMME sector in South Africa.

This paper maps out the structure and relative dynamics of cities of various size classes in India. It aims to address their hierarchical distribution, by employing the rank-size rule, Gibrat’s law, and a primacy index. The implications of urban concentrations for GDP, banking system, FDI, civic amenities, and various urban externalities (such as pollution and spatial exclusion) are also examined. It shows that India’s urban system, though it follows the rank-size rule, is huge and top-heavy. It follows also Gibrat’s law of proportionate growth. Although India’s cities collectively account for less than one third of the total population, they command more than three fourths of the country’s GDP. Megacities have become congested, clogged, polluted, and also show significant social polarization. There is a gridlock situation for the cities, inhibiting their potential for becoming effective economic and social change sites. The top-heavy character of India’s urban system also adversely impacts the balanced regional development of the country.

The paper introduces a dynamic model for firm growth, demonstrating that Gibrat’s law is associated with a Laplace distribution of growth rates. By considering the relationship between size and growth rate, the analytical model predicts heavier tails than those observed in the Laplace distribution, indicating that Gibrat’s law is not generally applicable. The theory is validated through an analysis of companies in the pharmaceutical sector, showing strong alignment with empirical data without the need for free parameters.

Although campsites are an important segment of the tourist sector, few applied articles have analyzed their growth path and tested Gibrat's Law for firms within this industry. This knowledge can be of importance to the authorities when analyzing the regional impacts of growth in this sector. With government statistics from the last decade, we use a GMM framework to test the stricter version of Gibrat's Law, which consist of three parts: the campsites' growth trend, how they carry over success and failure, and how volatile their size is. The first and third part are rejected for Norwegian campsites, leading to a rejection of Gibrat's Law. To see if firms of different sizes follow different dynamics, we split the sample in three parts. Here, we find evidence of a threshold size, as large campsites follow a fundamentally different dynamic than small and medium campsites. Specifically, large campsites gain no stability in revenue by further increases in size, whereas they carry over success/failure across years. The opposite is true for the rest of the sector. Gibrat's Law is rejected on at least one count for each of the sub-samples. Lastly, we supplement the analysis with economy-wide and firm-specific variables to test further hypotheses.

This study aims to examine the relationship between firm size and firm growth in Vietnam. The literature does not in general give support to Gibrat’s Law stating that the expected increase in firm size is proportionate to its initial size, or that firm growth rates are independent of firm size. The present study relies on a sample of 578 listed Vietnamese companies representing eight different industries and covering the period 2010 to 2020. The analysis reveals that growth in firm revenues does not give support to a hypothesis of independence of initial firm sizes. When the firm size is measured by total assets the opposite result appears, i.e. the Gibrat’s Law is not rejected. When including also the age of the firms in the test methodology the conclusion will be that firm growth – measured by revenue or assets – in all cases will decrease with firm size.

In this research, we used Spanish wealth distribution microdata for the period 2015–2020 to provide a general framework for comparing different models and explaining different empirical datasets related to wealth distribution. We present a methodology to output the current value of assets and participations held by the population in order to calculate their real and current distribution. We propose a new methodology for mixture analysis, whereby we identify and analyze subpopulations and then go on to study their influence on wealth distribution. We use concepts of symmetry to identify two internal processes that are characteristic of the wealth accumulation process for the subpopulations of entrepreneurs and non-entrepreneurs. Finally, we propose a method to adjust these results to other empirical data in other countries and periods, providing a methodology for comparing results output with differing data granularity.