A Theoretical Foundation for Understanding Firm Size Distributions and Gibrat's Law

This paper presents a dynamic model of the firm size distribution. Empirical studies of the firm size distribution often compare the moments to a log-normal distribution as implied by Gibrat's Law and note important deviations. Thus, the first, and basic questions we ask are how well does the dynamic industry model reproduce Gibrat's Law and how well does it match the deviations uncovered in the literature. We show that the model reproduces these results when testing the simulated output using the techniques of the empirical literature. We then use the model to study how structural parameters affect the firm size distribution. We find that, among other things, fixed and sunk costs increase both the mean and variance of the firm size distribution while generally decreasing the skewness and kurtosis. The rate of growth in an industry also raises the mean and variance, but has non-monotonic effects on the higher moments.Firm size distribution; Gibrat's Law; R&D.

Understanding the Variations in Gibrat's Law with a Markov-Perfect Dynamic Industry Model

Gibrat's Law of proportionate effect, as applied to firms, states that the growth rate of a firm is independent of its size. Empirical work on firm dynamics finds crucial deviations from Gibrat's Law such as smaller firms growing faster than larger firms (Evans, 1987, and Hall, 1987), a negative relationship between the variance of growth rates and size (Dunne and Hughes, 1994), and first-order positive autocorrelation in the growth rates (Kumar, 1995). Moreover, the degree of deviation from Gibrat's Law varies across industries. This paper contributes to our understanding of the forces that make Gibrat's Law a close, but imperfect approximation of firm size distributions and seeks to determine potential sources of cross-industry variation. Here, we employ an extension of the Ericson-Pakes (1995) theoretical framework that allows for firm growth developed by Laincz (2004a). By varying key parameters, the simulations demonstrate potential sources for the various, and sometimes conflicting, results on Gibrat's Law uncovered in the empirical literatureGibrat's Law, Firm Size Distribution, Entry, Exit

Scale Effects, An Error of Aggregation Not Specification: Empirical Evidence

In a set of influential papers, Charles Jones (1995a, 1995b, 1999) argued that R&D based endogenous growth models are inconsistent with the data. He showed, in a very striking manner, that the scale effects prediction of early endogenous growth models (e.g. Romer, 1986 and 1990, Grossman and Helpman, 1991, and Aghion and Howitt, 1992) is not borne out in the data. Standard endogenous growth models attribute constant or increasing returns in the stock of knowledge or technology to the aggregate level of resources. This assumption leads to the counterfactual prediction that the rate of productivity growth should be increasing in the aggregate amount of resources devoted to accumulating knowledge. This paper presents empirical evidence in support of R&D based endogenous growth models without scale effects (e.g. Young, 1998, Howitt, 1999, Thompson, 2001, and Peretto and Smulders, 2002). In these models the average level of workers or R&D workers per firm drives growth as opposed to the aggregate level and do not share the scale effects property in the limit. Using data for the US covering 1964-2001, we show that when the number of employees or scientists/engineers are scaled down on a per establishment basis, the empirics support the latter version of endogenous growth models. Specifically, the long-run size of establishments is stable, neither declining or growing in the long-run, where size is measured in two ways: by workers per establishment and R&D workers per establishment. Second, we demonstrate a positive effect running from average establishment size to productivity growth as predicted by the theories.

Entry and Exit in the Nonprofit Sector

We study the entry and exit dynamics of nonprofit public charities using 1989-2003 tax return data. The observed patterns can be understood using a dynamic industry model based on Jovanovic (1982) that incorporates profit-deviation and a non-redistribution constraint. Both features generate a high exit threshold which implies high net entry rates and low exit rates. The data reveal that nonprofit gross entry rates are lower than those of for-profits in services, while extremely low exit rates (across both sectors and time) result in net entry rates nearly 3 times larger than that of for-profit firms. We find that the behavior of new public charities is remarkably similar to that found in studies of private firms (e.g. new firms begin smaller than the industry mean, but grow faster). However, exit patterns diverge sharply. Besides relatively low exit rates, the survival rate of new nonprofit firms greatly exceeds those found in studies on services and manufacturing. In addition we find that the hazard rate of exit declines with age and size, and with size conditional on age.

Scale effects in endogenous growth theory: an error of aggregation not specification

Modern Schumpeterian growth theory focuses on the product line as the main locus of innovation and exploits endogenous product proliferation to sterilize the scale effect. The empirical core of this theory consists of two claims: (i) growth depends on average employment (i.e., employment per product line); (ii) average employment is scale invariant. We show that data on employment, R&D personnel, and the number of establishments in the US for the period 1964–2001 provide strong support for these claims. While employment and the total number of R&D workers increase with no apparent matching change in the long-run trend of productivity growth, employment and R&D employment per establishment exhibit no long-run trend. We also document that the number of establishments, employment and population exhibit a positive trend, while the ratio employment/establishment does not. Finally, we provide results of time series tests consistent with the predictions of these models. Copyright Springer Science+Business Media, LLC 2006Endogenous growth, R&D, Scale effects, Firm size, Establishments, E10, L16, O31, O40,

Growth on a Finite Planet: Resources, Technology and Population in the Long Run

We study the interactions between technological change, resource scarcity and population dynamics in a Schumpeterian model with endogenous fertility. We find a steady state in which population is constant and determined by resource scarcity while income grows exponentially. If labor and resources are substitutes in production, income and fertility dynamics are stable and the steady state is the global attractor of the system. If labor and resources are complements, income and fertility dynamics are unstable and drive the economy towards either demographic explosion or collapse. We calibrate the model numerically to match past US data on fertility and land scarcity, obtaining future scenarios for the current century and quantifying the response of fertility and productivity to exogenous shocks