Abstract

Stochastic models for the growth of firms and cities are typically written in terms of individual firms or cities subject to exogenous shocks. In their simplest form such models yield asymptotic size distributions that deviate from empirical data (e.g., producing nonstationary size distributions). More elaborate random-growth models can get closer to the empirical results but introduce new problems, such as the wrong value for the tail exponent or excessive fluctuations. We review such models, pointing out their main weaknesses. An alternative model of coupled growth is then elaborated and illustrated for firm sizes through the movement of workers between firms, that is, when one firm grows by a single employee the firm that worker left behind shrinks by one. This model specification remedies many of the problems associated with unconstrained stochastic growth. Furthermore, it is shown, both analytically and computationally, that biasing worker flows toward larger firms is sufficient to generate a Pareto distribution of firm sizes having exponent of exactly unity, asymptotically, that is, a Zipf distribution, closely approximating empirical data. The model is calibrated using data from the US and Finland. The general specification is also applicable to city sizes.

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