Size Distribution Of Firms Research Articles

Firm size distribution and growth: An empirical investigation

This paper investigates the extent to which the distribution of firm sizes affects growth and productivity. The empirical analysis is underpinned by a multilevel database comprising information on manufacturing sectors of 35 countries disaggregated in five firm size classes. Three complementary strategies to assess the relationship are implemented. The first, a country-level counterfactual analysis, measures the hypothetical impact of a firm reallocation to reflect a benchmark market structure. It is followed by a decomposition exercise that illustrates the impact of both the structural and technological components on the annual productivity growth between 1991 and 2007. Finally, different econometric models are estimated to assess the statistical significance of changes in the firm size distribution on growth and the role of the concentration of the market structure in explaining the cross-country productivity discrepancies. The results suggest that the firm size is a key driver the development process.

Synergizing ventures

Venture capital (VC) and growth are examined both empirically and theoretically. Empirically, VC-backed startups have higher early growth rates and initial patent quality than non-VC-backed ones. VC-backing increases a startup’s likelihood of reaching the right tails of the firm size and innovation distributions. Furthermore, outcomes are better for startups matched with more experienced venture capitalists. An endogenous growth model , where venture capitalists provide both expertise and financing for business startups, is constructed to match these facts. The presence of venture capital, the degree of assortative matching between startups and financiers, and the taxation of VC-backed startups matter significantly for growth.

The effect of atmospheric greenhouse gases on firm value and firm size distribution

I propose a model of firm heterogeneity and limited managerial commitment within an industrial equilibrium, where firms use natural resource and produce greenhouse gases. Firms are allowed to merge and commit to reducing greenhouse gas emissions . Greenhouse gas levels produce climate shocks that can close firms. Three hypotheses are produced from the model that are empirically verified. First, firm value is negatively related to the overall greenhouse gas levels in the atmosphere, at 0.9% per year. Second, that the power-law distribution exponent of firm size is negatively related to the rising greenhouse gas levels in the atmosphere. Third, the exponent of the power-law distribution of greenhouse gas emissions is higher than that of firm size and declines with the overall level of greenhouse gas in the atmosphere. • Due to the climatic disasters caused by rising greenhouse gas levels and limited managerial commitment I propose a model that produces three hypothesis supported by empirical data: • The cost of firm equity is raised by 0.9% per year directly by greenhouse gas levels in the atmosphere, thus lowering firm value for all firms and lowering economic growth. • Firms grow bigger as greenhouse gas levels rise as managers seek to protect themselves by building up capital in case of firm failure. • The exponent of the power-law distribution of greenhouse gas emissions is higher than that of firm size and declines with the overall level of greenhouse gas in the atmosphere.

Threshold-dependent tax enforcement and the size distribution of firms: evidence from Germany

This paper investigates firms’ responses to threshold-dependent intensity of tax enforcement. We use administrative tax return data over the entire population of German firms and exploit industry variation in firm size thresholds applied by the tax administration. In our setting, each threshold marks a considerable spike in audit intensity and hence should create strong incentives to bunch below the threshold. However, we find no such effect in our large sample analysis. We attribute this empirical observation to optimization costs, particularly to the costs associated with the operational implementation of size management and to information costs. Our paper adds to the emerging field of studies on potential distortions created by threshold-dependent firm regulation. The findings are also relevant for policymakers, as they suggest that the specific design of threshold-dependent policies might allow governments to increase the efficiency of tax audits without distorting the firm size distribution.

Entry Barriers, Idiosyncratic Distortions, and the Firm Size Distribution

This paper studies the interaction between barriers to firm entry and distortions to allocative efficiency in a standard model of firm dynamics. We derive a strategy to infer entry barriers based on cross-country differences in the firm size distribution and idiosyncratic distortions. The inferred barriers resemble regulation-based indicators in advanced economies but are substantially higher in middle- and low-income countries. Regulation-based indicators cannot account for cross-country differences in average firm size and underestimate the aggregate productivity gains associated with their removal by up to 8 percent on average. (JEL D21, D24, H25, L11, L60)

Misallocation and Inequality

For a large set of countries with different GDP per capita levels, we document how the distribution of labour earnings varies by development. Data reveals that the distribution of earnings changes with development in a particular way: while there is a larger mass at the left-tail, the right-tails shrinks, and moves towards the center. As a result, while the standard deviation of log earnings increases with development, the mean-to-median ratio declines. We interpret this fact within a model economy with heterogeneous workers and firms, which features industry dynamics, labor market frictions captured by a matching function, skill accumulation of workers with learning-by-doing and on-the-job training, and earnings inequality both across firms and workers. The benchmark economy is calibrated to the UK. We study how the earnings distribution changes as we increase two distortions in the benchmark economy: wedges on firms' output correlated with firm productivity and reductions in the labor market's ability to match unemployed workers and open vacancies. These distortions lead to the misallocation of resources and reduce employment and the GDP per capita. But they also affect how much firms are willing to pay to workers, how well higher skilled workers are matched with firms with higher productivity, and how much training workers receive. The model is consistent with a host of factors on how firm size distribution, firms' training decisions, and workers' life-cycle earnings profiles change with development and generates the observed patterns of changes in earnings distribution with development.

Product Innovation, Product Diversification, and Firm Growth: Evidence from Japan’s Early Industrialization

We explore how firms grow by adding products. We leverage detailed data from Japan’s cotton spinning industry at the turn of the last century to do so. This setting allows us to fully characterize the type of differentiation (vertical or horizontal) of new product introductions as well as whether the product is within or outside of the firm’s prior technological capabilities. We find that trying to introduce innovative products beyond the firm’s previous technologically feasible set, even if such trials fail, is a key to firm growth. Indeed, it mostly facilitates growth through the firm’s later success in horizontal product diversification. In long-term outcomes, the right tail of the firm size distribution becomes dominated by firms that first moved into technologically challenging products and then later applied their newly acquired technical competence to horizontal expansion of their product portfolios. Two mechanisms through which this knowledge transfer occurs are greater production system flexibility and higher product appeal to downstream buyers. (JEL D22, L11,L67, N65, N85, O31, O33)

From employee to entrepreneur: Learning, employer size, and spinout dynamics

Most new firms are founded by former employees of existing firms – spinouts. This paper explores how existing firms shape the entry and post-entry dynamics of spinouts and studies the aggregate implications of this relationship. Using micro-data from Mexico, I show that employees from small firms are more likely to form spinouts than employees of large firms. In addition, spinouts from large employers start at a larger scale and grow faster than spinouts from small employers. To reconcile these patterns, I develop a model of occupational choice and firm dynamics in which employees can learn from their employers. Using a calibrated version of the model, I analyze the implications of the link between employer size and spinout dynamics for macroeconomic outcomes within and across economies. I argue that learning efficiency – interpreted as management quality – is not only salient for understanding cross-country differences in spinout entry but also variation in the firm size distribution and output per worker. I also show that employee learning has meaningful and long-lasting implications for the creation of new firms and for workers in response to policies that target existing firms. Taken together, this paper establishes a connection between incumbent and entrant firms and shows that it is important for aggregate outcomes.

Firm Heterogeneity in Consumption Baskets: Evidence from Home and Store Scanner Data

Abstract A growing literature has documented the role of firm heterogeneity within sectors for nominal income inequality. This article explores the implications for household price indices across the income distribution. Using detailed matched U.S. home and store scanner microdata, we present evidence that rich and poor households source their consumption differently across the firm size distribution within disaggregated product groups. We use the data to examine alternative explanations, propose a tractable quantitative model with two-sided heterogeneity that rationalizes the observed moments, and calibrate it to explore general equilibrium counterfactuals. We find that larger, more productive firms sort into catering to the taste of richer households, and that this gives rise to asymmetric effects on household price indices. We quantify these effects in the context of policy counterfactuals that affect the distribution of disposable incomes on the demand side or profits across firms on the supply side.

Firm Size, Employment and Value Added in African Manufacturing Firms: Why Ghana Needs Its 1%

AbstractIn this paper, we use manufacturing firm census data to examine the size distribution of firms in Ghana for 1962, 1987 and 2003 and the distribution of employment and value added across the size distribution for 2003. We make four contributions to the literature on firm size in Africa. First, we compare the Tybout procedure, of matching employment shares to that implied by a Paretian distribution, to obtain the shape parameter from the Paretian distribution with a direct estimate from the firm size distribution. We show they differ. Our second contribution is to follow up on Tybout’s suggestion that a policy undistorted environment would produce a Paretian distribution and show that such a distribution can describe firm size, for both the 1987 and 2003 censuses, for firms with more than nine employees. The implication we draw is that processes of firm growth are quite different for firms above and below the nine employees’ threshold. Rather than there being a ‘missing middle’ of mid-sized firms, the data are better described as a ravine at nine employees, whereby the density of the distribution of firm size collapses at this point. Our third contribution is to show that the increasing dominance of the small, which has characterised firm growth in Ghana over this period, implies an increasing proportion of employment in the low productivity part of the size spectrum. Finally, we show that in 2003 while 95% of firms have less than ten employees, they produce only 14% of value added. At the other end of the size spectrum, less than 1% of the firms produced nearly 80% of value added.

Entrepreneurs, Managers, and the Firm Size Distribution

ABSTRACT Small firms can contribute to job creation and aggregate income. However, small firms are volatile and only a fraction of those can transition into larger firms, which create high-paying jobs. Entrepreneurs self-select for the transition. This study examines the pattern of entrepreneur self-selection. The main determinants of the self-selection are ability distribution of entrepreneurs and business environment, which represents skill distribution of laborers and social capital. This study predicts that firm-size distribution is truncated with the entrepreneur self-selection and aggregate income is larger when the business environment is better. This study contributes to the literature on firm-size distribution.

Bank liquidity provision across the firm size distribution

We use supervisory loan-level data to document that small firms (SMEs) obtain shorter maturity credit lines than large firms, post more collateral, have higher utilization rates, and pay higher spreads. We rationalize these facts as the equilibrium outcome of a trade-off between lender commitment and discretion. Using the COVID recession, we test the prediction that SMEs are subject to greater lender discretion. Consistent with this hypothesis, SMEs did not draw down whereas large firms did, even in response to similar demand shocks. PPP recipients reduced non-PPP loan balances, indicating the program bolstered their liquidity and alleviated the shortfall.

Rozkład wielkości firm w Polsce - czy ma zastosowanie prawo potęgowe?

This article focuses on the existence of power laws in the firm-size distribution in Poland. Specifically, we empirically test whether the size distribution of companies in Poland has the characteristics of Zipf ’s law, a special case of power law observed in many different contexts in empirical economic literature. Our analysis uses 2019 data on the 2,000 largest companies in Poland as ranked by the Rzeczpospolita daily newspaper in its “Lista 2000” (Top 2,000 List). We reviewed theoretical mechanisms generating power laws and used several estimators of the power-law exponent in our empirical analysis. Our results confirm statistically significant deviations from Zipf ’s law in the firm-size distribution in Poland. We found evidence that the power law cannot satisfactorily approximate the sales-based distribution of firms.

Labor market competition over the business cycle

AbstractWith a duopsony model, we study how earnings inequality, firm size distribution, and labor market slack vary across local labor markets and the business cycle. In booms, due to high aggregate productivity, there is fierce competition with resulting high wages and full employment. During recessions, there is labor market slack and firms enjoy local market power. In periods in which the economy is moving into or out of a recession, there is an “accommodation” phase, with firms shrinking their labor forces and paying lower wages instead of competing for poached workers. We show that the impact of economic shocks on wage dispersion and inequality may vary not only due to the nature of the shock, but also based on which equilibrium the economy may have settled in.

Human capital and average firm size

This note embeds an O-ring production function of Kremer (1993) into the standard Lucas (1978) model of firm size distribution. We show that an increase in the stock of human capital can raise average firm size. Empirical evidence confirms this finding. These findings help explain the positive relationship between average firm size and development documented in the recent literature. • We study average firm size in a model marrying Kremer (1993) and Lucas (1978). • We show that an increase in worker human capital raises average firm size (AFS). • Cross-country data confirms the positive relationship between human capital and AFS. • The results help explain why AFS rises with development.

Large and influential: Firm size and governments’ corporate tax rate choice

AbstractTheory suggests that large firms are more likely to engage in lobbying behaviour and are geographically more mobile compared with smaller entities. Conditional on jurisdiction size, policy choices are thus predicted to depend on the shape of a jurisdiction's firm size distribution, with more business‐oriented policies being enacted if jurisdictions host large firms. The paper empirically tests this prediction using local business taxation in Germany as a testing ground. Exploiting rich and exogenous variation in municipalities’ firm size structures, we find evidence for an inverse relationship between the size of hosted entities and municipalities’ local business tax choices. The effect is statistically significant and quantitatively relevant, suggesting that the rising importance of large businesses may trigger shifts towards a more business‐friendly design of (tax) policies.

The added value of management skill in the explanation of the distribution of firm size

The stochastic explanations of skewed distribution of firm size question the value added of management theories that trace differences in market share and profits of firms to strategy and organization choices, which are in turn linked to better entrepreneurial skills. This paper explains the distribution of firm size as the market equilibrium outcome of individual occupational choices of working as entrepreneurs or employees. The distribution of size and profit of firms in the equilibrium is directly related to the distribution of skills within the group of individuals who, in the same equilibrium, choose to work as entrepreneurs, restoring the importance of management choice in the performance of firms. The paper highlights the importance of having a theoretical model as guidance in the interpretation of regularities observed in the distribution of firm size, and the ability to distinguish between “resembling” and “true” power laws of such distributions.

A simulation of the insurance industry: the problem of risk model homogeneity

We develop an agent-based simulation of the catastrophe insurance and reinsurance industry and use it to study the problem of risk model homogeneity. The model simulates the balance sheets of insurance firms, who collect premiums from clients in return for insuring them against intermittent, heavy-tailed risks. Firms manage their capital and pay dividends to their investors and use either reinsurance contracts or cat bonds to hedge their tail risk. The model generates plausible time series of profits and losses and recovers stylized facts, such as the insurance cycle and the emergence of asymmetric firm size distributions. We use the model to investigate the problem of risk model homogeneity. Under the European regulatory framework Solvency II, insurance companies are required to use only certified risk models. This has led to a situation in which only a few firms provide risk models, creating a systemic fragility to the errors in these models. We demonstrate that using too few models increases the risk of nonpayment and default while lowering profits for the industry as a whole. The presence of the reinsurance industry ameliorates the problem but does not remove it. Our results suggest that it would be valuable for regulators to incentivize model diversity. The framework we develop here provides a first step toward a simulation model of the insurance industry, which could be used to test policies and strategies for capital management.

A Simulation of the Insurance Industry: The Problem of Risk Model Homogeneity

We develop an agent-based simulation of the catastrophe insurance and reinsurance industry and use it to study the problem of risk model homogeneity. The model simulates the balance sheets of insurance firms, who collect premiums from clients in return for ensuring them against intermittent, heavy-tailed risks. Firms manage their capital and pay dividends to their investors, and use either reinsurance contracts or cat bonds to hedge their tail risk. The model generates plausible time series of profits and losses and recovers stylized facts, such as the insurance cycle and the emergence of asymmetric, long tailed firm size distributions. We use the model to investigate the problem of risk model homogeneity. Under Solvency II, insurance companies are required to use only certified risk models. This has led to a situation in which only a few firms provide risk models, creating a systemic fragility to the errors in these models. We demonstrate that using too few models increases the risk of nonpayment and default while lowering profits for the industry as a whole. The presence of the reinsurance industry ameliorates the problem but does not remove it. Our results suggest that it would be valuable for regulators to incentivize model diversity. The framework we develop here provides a first step toward a simulation model of the insurance industry for testing policies and strategies for better capital management.

A stochastic analysis of firm dynamics: Their impact on the firm size distribution

Abstract The Pareto distribution is known for its wide range of applications, including the distribution of firm sizes. Exhaustive databases on firm sizes showed deviations from the Pareto firm size distribution for the smallest and largest firm sizes. Therefore, stochastic models of firm dynamics reproducing a Pareto firm size distribution could be further generalized in order to also reproduce these deviations. Based on Cordoba (2008), we build a model of firm dynamics which can generate a wide variety of steady-state distributions and we make clear the relationship between the growth dynamics of the firms and the resulting shape of the firm size distribution. To the light of our model, we analyse the links between the observed firm dynamics and the shape of firm size distribution in Belgium between 2006 and 2013.