The Gibrat Effect

Abstract

We begin this chapter by setting out a simple model of the growth of firms, normally ascribed to the French engineer Gibrat (1931) although it can be traced to Kapteyn (1903) and beyond. Suppose that in each period of time the probability that any particular firm will experience any particular growth rate is the same. Suppose that the growth performance of a firm in each period is independent of its performance in other periods: a fast-growing firm is no more or less likely than any other to grow more rapidly in subsequent years. And suppose that there is no single period which is so important in the life of firms as to remain a dominant influence on their fortunes indefinitely thereafter — there is no period whose effect cannot be thrown off, given sufficient time. If these three assumptions hold, the growth process conforms to what has become known as the Law of Proportionate Effect. The distribution of firms’ sizes will tend over time to become lognormal, and the variance of this distribution will increase steadily. A lognormal distribution is one whose logarithms are normally distributed, and its characteristic skew shape is illustrated in Figure 7.1. Its properties are described in detail in Aitchison and Brown (1957), but the proposition outlined above is easy to check.