A Model of Business Firm Growth

A new method is proposed for deriving skew distributions of business finn sizes from the assumption of Gibrat's Law. The growth of the firm is decomposed into an industry-wide component and an individual component, the latter governed by a one-period Markov process. The model is fitted to data on the recent growth of large American firms. A NUMBER of stochastic models, embodying various forms of Gibrat's law of proportionate effect, have been shown to generate skew distribution functions resembling the actual size distributions of business firms. (See 2 and references cited there.) In a previous paper 1 we presented some results of the simultation of such a model permitting serial correlations over time in the size changes of individual firms. The aim of the present paper is to carry further the analysis of autocorrelated growth, by proposing an economically meaningful scheme for its analysis, and applying the scheme to some data on large American firms. In studying business firm growth, we often encounter cases where a firm suddenly acquires an impetus for growth. Perhaps by innovating in production or marketing processes, or perhaps as an effect of new management staffs or techniques, the firm grows much more rapidly than the other firms in the industry, as measured, say, by the ratio of the current firm size to its size in the previous time period. Thus, we may observe that, while most of the firms in the industry are growing at, say, 5% a year, some firms grow 10%. Furthermore, a firm that grew 10% last year is likely to grow more rapidly than average again this year as a result of the carry-over effects of an innovation that occurred in a previous year on operations in subsequent periods. This carry-over becomes more and more likely as we shorten the length of the time period we are considering from a year to a month, week, or day. Moreover, on the average, a firm which grew rapidly in one year subsequently retains a greater share of the industry assets (or market share if sales are used as a measure of firm size) from that time on than do firms that have enjoyed only the average industry growth. Therefore, not only the growth rate over and above the average growth rate, but also the period when the extra growth took place are important factors in the individual firm's growth relative to the industry growth. In this paper, we develop a model to represent such characteristics of firms' growth, so that the process may be analysed further. In the final section we estimate the key parameter of the model for the recent growth of large American business