Firm size and economic concentration: An analysis from a lognormal expansion

This paper studies the distribution of the firm size for the Colombian economy showing evidence against the Gibrat's law, which assumes a stable lognormal distribution. On the contrary, we propose a lognormal expansion that captures deviations from the lognormal distribution with additional terms that allow a better fit at the upper distribution tail, which is overestimated according to the lognormal distribution. As a consequence, concentration indexes should be addressed consistently with the lognormal expansion. Through a dynamic panel data approach, we also show that firm growth is persistent and highly dependent on firm characteristics, including size, age, and leverage -these results neglect Gibrat's law for the Colombian case.

Modeling the joint distribution of firm size and firm age based on grouped data

The firm size distribution is highly skewed to the right and often follows a power law. In practice, it is common that firm size and firm age data are aggregated and released as grouped data to avoid disclosure of confidential information. We investigate multiple parametric methods for firm size and firm age modeling based on grouped data, and propose to estimate the joint distribution of firm size and firm age using the Plackett copula. The goodness-of-fit of the estimated marginal distributions are benchmarked with respect to the fit to the whole data and to the upper tails, respectively. The utilization of the proposed methods are demonstrated via an application to the 1977-2014 US firm data. Results show that the generalized lambda distribution has overall better performance in modeling both firm size and firm age data. The exponentiated Weibull distribution also works well in modeling the firm size data. As a by-product, the estimated parameter of the Plackett copula provides a measure of the association between firm size and firm age.

Percolation model for growth rates of aggregates and its application for business firm growth

Motivated by recent empirical studies of business firm growth, we develop a dynamic percolation model which captures some of the features of the economical system--i.e., merging and splitting of business firms--represented as aggregates on a d-dimensional lattice. We find the steady-state distribution of the aggregate size and explore how this distribution depends on the model parameters. We find that at the critical threshold, the standard deviation of the aggregate growth rates, sigma, increases with aggregate size S as sigma approximately S(beta), where beta can be explained in terms of the connectedness length exponent nu and the fractal dimension d(f), with beta=1(2nud(f)) approximately 0.20 for d=2 and 0.125 for d-->infinity. The distributions of aggregate growth rates have a sharp peak at the center and pronounced wings extending over many standard deviations, giving the distribution a tent-shape form--the Laplace distribution. The distributions for different aggregate sizes scaled by their standard deviations collapse onto the same curve.

Zipf distribution of U.S. firm sizes

Analyses of firm sizes have historically used data that included limited samples of small firms, data typically described by lognormal distributions. Using data on the entire population of tax-paying firms in the United States, I show here that the Zipf distribution characterizes firm sizes: the probability a firm is larger than size s is inversely proportional to s. These results hold for data from multiple years and for various definitions of firm size.