The stochastic theory of growth, originating with Gibrat, who borrowed it from the astronomer Kapetyn, and elaborated by Simon, Levy, Solomon, and others, is not a theory of interactions but rather a model of an individual object (e.g., firm, city) subject to exogenous shocks. It is well-known that Gibrat’s formulation of growth produces lognormal distributions of sizes that are not stationary, and thus the theory has to be modified to yield empirically observed sizes, e.g., a stationary Pareto distribution with exponent near unity, the so-called Zipf distribution. In this talk I will quantify several additional problems, both conceptual and empirical, with theories of growth based on Gibrat’s law. I will then propose an alternative stochastic specification that couples growing objects through flows of people between them, with a small bias, leading naturally to the Zipf distribution. Such movements represent job-to-job transitions in the case of firms, an empirically large and persistent feature of modern free market economies, and inter-city migration in the case of cities, well-documented in Census data.


Research Programmes