Gibrat's Law with Mild Nonrandom Growth (Report‪)‬

Introduction The statistical proposition known alternatively as Gibrat's Law (GL) or the law of proportionate effect asserts that if firm growth is purely random, then, a priori, the probability of x percent growth is the same for all firms, regardless of their initial size. That growth, moreover, could be of output, employment, sales revenue, assets, or any other measure of firm size. Then, for example, over some specified period of time, a firm producing 100 units of output is assumed to be just as likely to grow to 150 units as a firm producing 1000 is to grow to 1500. Alternatively, as characterized by Simon and Bonini (1958, p. 609), "a firm randomly selected from those with a billion dollars in assets has the same probability of growing, say, 20%, as a firm randomly selected from those with a million dollars in assets." In effect, purely random differences in short term growth rates are expected to average out over time so that the longer term growth rate would be the same for all firms. The practical implication is that, as larger firms grow at the same percentage rate as smaller firms, the industry will become increasingly concentrated. Specifically, the emerging size distribution of firms will become lognormal, and its variance will increase over time. Hay and Morris (1991, pp. 537-38) provide a succinct mathematical presentation of these assertions.