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.