Search

This article analyses the distribution of firms by size in six selected countries in 2012 and 2017. Estimates are always made for the whole economy and two subgroups of firms. We compare the Visegrad Four countries (Czech Republic, Hungary, Poland and Slovakia) with similar economic activities and two neighbouring economically more developed countries (Germany and Austria). As the main objective of the article, we describe the distribution of firms by verifying the validity of Zipf's law in selected economies and their sectors. The results confirm the positively skewed distribution of company sizes measured by sales revenues, but Zipf's law does not apply to the distribution of all companies by the magnitude of sales in the whole economy (or in an economic subgroup), but only to sections in the right tail of the distribution (companies with higher turnover within the whole economy), which is in line with numerous research studies. [ABSTRACT FROM AUTHOR]

Summary: Heavy tails play an important role in modern macroeconomics and international economics. Previous work often assumes a Pareto distribution for firm size, typically with a shape parameter approaching Zipf's law. This convenient approximation has dramatic consequences for the importance of large firms in the economy. But we show that a lognormal distribution, or better yet, a convolution of a lognormal and a non‐Zipf Pareto distribution, provides a better description of the US economy, using confidential Census Bureau data. These findings hold even far in the upper tail and suggest that heterogeneous firm models should more systematically explore deviations from Zipf's law. [ABSTRACT FROM AUTHOR]

The firm size distribution (FSD) is one of the most well-known economic empirical regularity in market economies. Its functional form, postulated in macroeconomic models with heterogeneous firms, can be approximated by a parametric distribution. However, the parametric approximations proposed in the literature have long been contested due to the lack of unbiased databases and robust statistical methods. This paper addresses these shortcomings. First, a robust estimation method is proposed to test the fit of parametric distributions and to determine the one offering the best fit at different truncation thresholds. Then, by applying it to a comprehensive database of Belgian firms for the period 2006–2012, the results show that the lognormal distribution is a better approximation of the empirical FSD than the Pareto distribution. These results hold true at the aggregate, sectoral and regional levels establishing that the shape of the aggregate distribution is not an aggregation artefact arising from the potential distributional heterogeneity of sectoral or regional subsets. This empirical evidence is essential information for tracing the root causes of a plausible underlying stochastic model explaining firm dynamics. [ABSTRACT FROM AUTHOR]

This paper examines a homogeneous-good Bertrand–Edgeworth oligopoly model to explore the role of firm size and number in pricing. We consider the price impact of merger, break up, investment, divestment, entry and exit. A merger leads to higher prices only when it increases the size of the largest seller and industry capacity is neither too big nor too small post-merger. Similarly, breaking up a firm only leads to lower prices when it concerns the biggest producer and aggregate capacity is within an intermediate range. Investment and entry (weakly) reduce prices, whereas divestment and exit yield (weakly) higher prices. Taken together, these findings suggest that size matters more than number in the determination of oligopoly prices. [ABSTRACT FROM AUTHOR]

Following the ideas of prospect theory, a class of growth functions is used to characterize deterministic variations of firm size, which portrays the asymmetric efforts of the firm to achieve the desired size. Considering the differences in the ability of different firm size to cope with uncertainties, the Boltzmann equation for the evolution of firm size is constructed. Utilizing a suitable scaling limit, the Fokker–Planck equation is acquired and its explicit steady-state solution is derived. Our results illustrate that different choices of parameters in the growth function lead to various statistical laws for firm size, such as the Amoroso distribution, the lognormal distribution and Zipf's law. Under certain conditions, inequality for the distribution of firm size decreases as firm size increases. The numerical analyses are presented to illustrate our results. • A class of models for firm size evolution is constructed by using the kinetic theory. • Growth functions with prospect theory ideas are used to depict changes in firm size. • Different choices of parameters in growth function cause different statistical laws. • Inequality of firm size distribution reduces with firm size under certain conditions. [ABSTRACT FROM AUTHOR]

This note analyzes some properties of the Pareto Type III distribution. A three parameter version of the original two parameter distribution proposed by Pareto is introduced and both its density and characteristic function are derived. The analytic expression of the inverse distribution function is also obtained, together with an explicit expression of its moments of any order. Finally, a simple statistical exercise is proposed, designed to show the reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.

Copyright of Economic Science / Jingji Kexue is the property of Economic Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper examines a homogeneous-good Bertrand–Edgeworth oligopoly model to explore the role of firm size and number in pricing. We consider the price impact of merger, break up, investment, divestment, entry and exit. A merger leads to higher prices only when it increases the size of the largest seller and industry capacity is neither too big nor too small post-merger. Similarly, breaking up a firm only leads to lower prices when it concerns the biggest producer and aggregate capacity is within an intermediate range. Investment and entry (weakly) reduce prices, whereas divestment and exit yield (weakly) higher prices. Taken together, these findings suggest that size matters more than number in the determination of oligopoly prices.

What effect did trade have on the size distribution of firms during the first wave of globalization? Three historical datasets from the German Empire between 1875 and 1907 were collected and harmonized to answer this question. This paper combines industry census and bilateral railway trade data from the same industry and region along with industry-level tariff data. The evidence shows that increases in aggregate trade caused the share of firms to shift from smaller to larger firms. Exogenous decreases in tariffs caused an increase in the share of the largest firms. The regional distributive effects of trade on inequality between firms that are discussed in the contemporaneous literature were already present during the first wave globalization. [ABSTRACT FROM AUTHOR]

• We test whether the growth rate of SMEs contributes significantly to a modification of the size distribution of firms over a relatively long time horizon. • Although small firms tend to grow faster than larger firms, results suggest that Italian manufacturing enterprises fail to climb the size ladder; that is, they fail to progress to larger size classes. • Firms' growth is positively affected by the development of entrepreneurial and managerial abilities, although this is not true for the group of tiny enterprises, for which the lack of a significant organizational structure represents a scaling-up threat. • Higher levels of indebtedness and a larger interest rate burden exert a negative effect on firms' growth, although once the market selection has passed, better borrowing conditions may be in place, favouring firms' growth. • Competitive factors, such as innovation and export intensity may stimulate upsizing, although their impact, in the long run, is still insufficient to cause a significant change in the size distribution of firms. Firms' ability to compete in the global market crucially depends on their ability to innovate and to introduce new products or processes into the market. This typically requires more complex and structured business organization and ultimately the ability to grow. We use a representative panel of Italian manufacturing firms to investigate whether their pattern of growth entails such an ability. Although the estimates suggest that small firms grow faster than larger ones, we do not observe a significant change in the average size of companies at the end of the period under investigation. The greater propensity to grow shown by smaller firms is confined to the size class in which they are established. However, export intensity plays a significant role in affecting the size growth rate together with industry characteristics related to technological levels. [ABSTRACT FROM AUTHOR]

This study examines the relationship between market share and its rank for a comprehensive set of product categories and subcategories in the U.S consumer packaged goods industry. Based on prior research, we expect that the slope of the market share-rank relationship will be more consistent with the Zipf distribution at the higher levels of aggregation (category-level versus subcategory-level shares). Two alternative model formulations were examined: the size-rank power law and an exponential alternative used in prior research. Model parameters were estimated across categories (and subcategories) using random coefficients for both the slopes and intercepts. The overall slopes for both samples were significantly higher than −1, the slope consistent with the Zipf distribution. However, as expected, we also found that the slope associated with data from the higher level of aggregation (category level) is flatter than that from the lower level of aggregation (subcategory level). We discuss implications of these results for future research on the size-rank relationship. [ABSTRACT FROM AUTHOR]

Export superstars are important for export growth and diversification and are typically born large. Firm-level data on manufacturing trade from 32 developing countries show that the top five exporters account for on average nearly one-third of exports, 47 percent of export growth, and a third of the growth due to export diversification over a five-year period. Within countries and industries, export growth is positively correlated with the share of exports in the top five firms. Most of the top five exporters were already large five (or eight) years ago or are new firms; it is rare for these export superstars to emerge from the bottom half of the distribution of firm sizes. For countries where detailed data exist, superstars are producers, not traders, and are primarily foreign owned. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Marmara University Social Sciences Institute / Öneri is the property of Marmara University, Institute of Social Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Does banking market power contribute to the formation of nonfinancial industries populated by few, large firms, or does it instead enhance industry entry? Theoretical arguments could be made to support either side. The banking industry of European Union (EU) countries has been significantly deregulated in the early 1990s. Under the old regime, cross-border expansions were heavily constrained, while after deregulation, banks from EU countries have instead been allowed to branch freely into other EU countries. Concurrently to the process of deregulation, European banking industries have also experienced a significant process of consolidation. Exploiting such significant innovations affecting the banking industries of EU countries, this paper explores whether changes in bank competition have in fact played a role on the market structure of nonfinancial industries. Empirical evidence is derived from a panel of manufacturing industries in 29 OECD countries, both EU and non-EU members, adopting a methodology that allows controlling for other determinants of industry market structure common across industries, across countries or related to time passing. The evidence suggests that the overall process of enhanced competition in EU banking markets has led to markets in nonfinancial sectors characterized by lower average firm size. [ABSTRACT FROM AUTHOR]

Purpose - This study aims to estimate the firm size distributions that belong to the service sector and manufacturing sector in Korea. Design/methodology/approach - When estimating the firm size distribution, the author considers the following two major factors. First, the firm size distribution can have a gamma distribution rather than traditional accepted distributions such as Pareto distribution or log-normal distribution. In particular, industry-specific enterprises can have different size distributions of the type of gamma distribution. Second, the firm size distribution that is applied to this study’s data set should reflect a number of factors. For example, estimating mixture gamma distribution for firm size distribution should be required and compared, because the total amount of configuration data is composed of small businesses, medium-sized and large companies. Findings - Using 8,230 number of firm data in 2013, the author estimates mixture gamma distribution for the firm size. Originality/value - From the comparison, empirical results are found for the following characteristics of core firm size distribution: first, the firm size distribution of the manufacturing sector has a longer tail than firm size distribution of the service sector. Second, the manufacturing firm size distribution dominates the entire country firm size distribution. Third, one factor among the three factors that make up the mixed gamma firm size distribution is described for 99 per cent of the firm size distributions. From the estimated firm size distributions of the service sector and manufacturing sector in Korea, the author simply implies the strategy and policy implications for the start-up firm.

Do the formal and informal sectors of production react symmetrically to higher frequency of corruption? The theoretical model developed in the paper qualifies the answer and explains certain empirical observations. In the informal sector while an increased frequency of corruption increases the entry cost, in the formal sector the effect remains uncertain. While abundance of firms definitely falls in the formal sector, in the informal sector it may either rise or fall in the economies with high share of formal sector employment and unambiguously falls in the economies with low share of formal sector employment. Finally, while the firm size distribution shifts towards relatively larger firms in the formal sector, in the informal sector the effect on firm size distribution remains uncertain in the economies with high share of formal sector employment and it shifts towards smaller size firms in the economies with low share of formal sector employment. [ABSTRACT FROM AUTHOR]

Most firms begin very small, and large firms are the result of typically decades of persistent growth. This growth can be understood as the result of some form of organization capital accumulation. In the US, the distribution of firm size k has a right tail only slightly thinner than 1/k. This is shown to imply that incumbent firms account for most aggregate organization capital accumulation. And it implies potentially extremely slow aggregate convergence rates. A benchmark model is proposed in which managers can use incumbent organization capital to create new organization capital. Workers are a specific factor for producing consumption, and they require managerial supervision. Through the lens of the model, the aftermath of the Great Recession of 2008 is unsurprising if the events of late 2008 and early 2009 are interpreted as a destruction of organization capital, or as a belief shock that made consumers want to reduce consumption and accumulate more wealth instead. [ABSTRACT FROM AUTHOR]

The paper investigates the statistical regularities of industry dynamics in a transition economy and its manufacturing industry over a six-year period of recession. The static analysis of distributions supports several established stylized facts on firm size and growth-rate distributions. The growth rate distribution featured a sequential, year-by-year procyclical change of the left side of distribution, suggesting that the more years an economy spends in a recession, the greater the decline in the revenue of its firms. On the "growing" side, the recession opened increasing growth opportunities for a small subset of small firms, while it diminished growth opportunities for medium and large firms. The segregation of sectors by technological intensity gives evidence that the high-tech sectors show upward trend of the growth rate distributions' right side as the recession unfolded. Sectorial concentration ratios mostly increased, while changes in the unimodality of the firm-size distribution occurred at the end of the economic downturn. [ABSTRACT FROM AUTHOR]

Empirical studies have shown that the size distribution of firms can be described as a lognormal or Pareto distribution. However, these studies have focused on developed countries and little attention has been devoted to developing countries. Using the variable of number of employees as a measure of firm size, this paper investigates the shape of firm size distribution in the food & beverages industry and also in the non-metallic mineral products industry over the period of 1997-2005. Our findings show that there is no universality of the size distribution of firms between industries. In other words, the size distribution varies in terms of kind of industry, so that our results make it clear that food & beverages industry follows lognormal distribution, conversely to other industry which a good representation of Pareto distribution. From policy point of view, knowledge about firm size distribution caused new entrance firms to decide wisely and therefore provide improvement on performance after entry.

Entering firms into a business can be a sign of economic dynamism, but to what extent do they enter according to optimal size or converge to it? The answers are given in two approaches. In the first approach, a new- entrant enterprise adjusts its size by learning market and continues to its activity. In the second approach, the enterprise does not adjust its size and exits the market. In this regard, the study of size distribution of new enterprises in Iran’s textile industry is the main purpose of this research. We collect statistical data for new textile businesses during 1997-2005 from Statistical Center of Iran. We use nonparametric method and indicators of employment, output value and value-added for evaluation of the size distribution. The results indicate that the employment size distribution follows an active learning model and does not adapt itself with market conditions. Regarding output value and value-added, the textile businesses follow a passive learning model and converge to the Lognormal distribution. The inability of firms in convergence by employment and their ability in convergence by output and value added criteria are some signs of a rigid labor market in Iran. According to these findings, reconsidering the labor law in order to making it more flexible is essential.

The proper characterization of the size distribution and growth of firms represents an important issue in economics and business. We use the Maximum Entropy approach to assess the plausibility of the assumption that firm size follows Lognormal or Pareto distributions, which underlies most recent works on the subject. A comprehensive dataset covering the universe of French firms allows us to draw two major conclusions. First, the Pareto hypothesis for the whole distribution should be rejected. Second, by discriminating across firms based on the number of products sold and markets served, we find that, within the class of multi-product companies active in multiple markets, the distribution converges to a Zipf’s law. Conversely, Lognormal distribution is a good benchmark for small single-product firms. The size distribution of firms largely depends on firms’ diversification patterns. [ABSTRACT FROM AUTHOR]

Traditional approach to the firm size and its growth rate is based on comparative statics analysis and it does not really deal with the dynamics of growth. This paper takes a dynamic approach to investigate the relationship between firm size and its growth rate for Iranian insurance firms during 2003-2009. The study applies two ways to verify the validity of Gibrat's law in Iranian insurance industry. First way is to consider the independence of two important attributes of firms including firm size and growth rates. The second way is based on panel regression estimation. The results of the study reject the validity of Gibrat’s law and indicate the fact that small firms grow faster than their larger counterparts.

We first analyze the mechanism of the influence of environmental regulation on firm size distribution based on literature review. We propose that environmental regulation is an important means of resolving resources and environmental problems. Three pathways of influence of environmental regulation are identified, namely, cost effect, innovative compensation effect and learning effect, and competition effect. Next, an empirical analysis is carried out on 9 major industries in Guangdong Province. It is found that the Pareto index of firm size distribution in Guangdong Province is far below 1. Therefore, the firm size distribution does not conform to Zipf distribution and the balance degree of firm size distribution varies greatly from one industry to another. But as the level of environmental regulation increases, the Pareto index increases as well. This means the environmental regulation has a significant promoting effect on firm size distribution and on the uniformity of firm size distribution. [ABSTRACT FROM AUTHOR]

Firm size increases with GDP per capita. The paper develops a simple framework to explore three alternative sources of variation that may explain this correlation: (1) excessive entry; (2) differences in the distribution of firm productivities; and (3) differences in returns to scale. The results show that all these sources of variation lead to substantial differences in firm size. GDP per capita is also significantly affected, but by an order of magnitude less. [ABSTRACT FROM AUTHOR]

Among the phenomena in economics that are not yet well-understood is the fat-tailed (power-law) distribution of firm sizes in the world's economies. In the present paper we discuss different mechanisms suggested in the literature to explain this distribution of firm sizes. The paper uses the China Industrial Enterprises Database to study the distribution (firm size in terms of the number of employees, capital, and gross profit) for the provinces of China for the years 1998–2008. We estimate the power-law distribution and confirm its plausibility using the KS test and the log-likelihood ratio vs. lognormal and exponential distributions. The analysis on regional levels allows an assessment of regional effects on differences in the distribution; we discuss possible explanations for the observed patterns in the light of the recent regional economic development and the economic reforms in the PRC. [ABSTRACT FROM AUTHOR]

Studies on the firm's size distribution (FSD) can set a good foundation to know about the growth path and mechanism of e-commerce firms. The purpose of this paper is to understand features of the China's listed e-commerce firms by testing Gibrat's law and Zipf's law within the Internet sectors. From a macroscopic perspective, with the approach of OLS estimation, Zipf's coefficient of the FSD is calculated to test whether Zipf's law holds. From a microscopic perspective, the relationship between e-commerce firm size and growth is explored by quantile regression method. The results indicate that from 2005 to 2014, Zipf's law cannot be rejected, with the relationship changing over time, Gibrat's law holds partly. It implies that competition status among China's e-commerce firms becomes more stable. [ABSTRACT FROM AUTHOR]

This paper exploits a comprehensive data set on business credit decisions to examine the importance of financing constraints for the evolution of the firm size distribution. The survey of small business finances provides information on whether a firm was in need of external financing. Firms without access to external financing-either because they were denied credit or because they did not apply for credit because they expected to be denied credit-are significantly smaller. To tighten the link between financing constraints and firm dynamics, I estimate the effect of financing constraints on subsequent employment growth and find that firms without access to external financing exhibit up to 3.5 % points lower annual employment growth than do their unconstrained counterparts. These findings suggest that financing constraints are a potentially important factor for understanding firm dynamics. [ABSTRACT FROM AUTHOR]

This paper presents a simple model of firm and consumer behavior. We formulate a sub-market entry game, where boundedly rational firms decide on investing in R&D for inventing new products that will appeal to targeted groups of consumers. The success depends on the amount of resources available for the project as well as on the firm's familiarity with market characteristics. Successful innovation feeds back into the firm size and (potentially into) market knowledge and increases the future R&D productivity. A new product decreases the market-shares of incumbents. However, this business stealing effect is asymmetric across incumbent population. We identify the section of parameter space where firms have an incentive to diversify horizontally. In this section, the model results in rich industrial dynamics. Firm size heterogeneity emerges endogenously in the model. Equilibrium firm size distributions are heavy tailed and skewed to the right. The heaviness of the tail depends on submarket specificity of firm's market knowledge. This relationship is non-monotonic, emphasizing two different effects of innovation on industrial dynamics (positive feedback and asymmetric business stealing). [ABSTRACT FROM AUTHOR]

In this paper, an endogenous credit network model of firm–bank agents is constructed. The model describes the endogenous formation of firm–firm, firm–bank and bank–bank credit relationships. By means of simulations, the model is capable of showing some obvious similarities with empirical evidence found by other scholars: the upper-tail of firm size distribution can be well fitted with a power-law; the bank size distribution can be lognormally distributed with a power-law tail; the bank in-degrees of the interbank credit network as well as the firm–bank credit network fall into two-power-law distributions. [ABSTRACT FROM AUTHOR]

The upper tail of the firm size distribution is often assumed to follow a Power Law. Several recent papers, using different estimators and different data sets, conclude that the Zipf Law, in particular, provides a good fit, implying that the fraction of firms with size above a given value is inversely proportional to the value itself. In this article we compare the asymptotic and small sample properties of different methods through which this conclusion has been reached. We find that the family of estimators most widely adopted, based on an OLS regression, is in fact unreliable and basically useless for appropriate inference. This finding raises doubts about previously identified Zipf behavior. Based on extensive numerical analysis, we recommend the adoption of the Hill estimator over any other method when individual observations are available. [ABSTRACT FROM AUTHOR]

This study examines the firm size distribution of US banks and credit unions. A truncated lognormal distribution describes the size distribution, measured using assets data, of a large population of small, community-based commercial banks. The size distribution of a smaller but increasingly dominant cohort of large banks, which operate a high-volume low-cost retail banking model, exhibits power-law behaviour. There is a progressive increase in skewness over time, and Zipf’s Law is rejected as a descriptor of the size distribution in the upper tail. By contrast, the asset size distribution of the population of credit unions conforms closely to the lognormal distribution. [ABSTRACT FROM PUBLISHER]