The Size and Growth of Firms

Even before his Take-overs book appeared in 1971, Singh joined a related research project with Geoffrey Whittington examining statistically the size and growth rates of UK-listed corporations. Conventional wisdom during ^[1]

the 1950s was that the growth of business firms was more or less deterministic. This view was challenged, invoking what has become known as Gibrat’s Law (1931), in seminal papers by Hart and Prais (1956) in England and by Simon and Bonini (1958) in the USA. With a Gibrat-type process, firms grow (or decline) at rates that fluctuate randomly over time, and no firm is assumed in the simplest models to have an advantage or disadvantage sampling from alternative growth possibilities. Naive intuition might suggest that if firms begin a Gibrat process at relatively equal sizes, their relative sizes will be preserved as they grow at randomly determined rates. But this is not true. Some firms will be lucky and draw a string of high growth rates, and some will be similarly unlucky. Also, once a firm through good luck grows to lead its former peers, it has (ignoring scale economies and the like) an equal chance on average to sustain its relative position, and a few firms will continue to be lucky, advancing still more in size. The long-run result is a highly skewed distribution of firm sizes—asymptotically, a lognormal distribution—with a few firms towering over the rest. Since most real-world industries in fact have highly skewed size distributions, it was a matter of keen interest whether they had arrived at that state through growth processes of the Gibrat type.

To explore the Gibrat conjectures, Singh and Whittington (1968, 1975) compiled what for the time was an unusually rich database on size measures and growth rates (somewhat surprisingly, emphasizing asset account rather than sales values) for companies listed on British stock exchanges over the years 1948-1960, first for firms specializing in four industry groups and then for a much broader sample. It is amusing in hindsight, especially for one who faced the same ‘big data’ problems at the same time, to observe that the difficulties of data processing were such in those early days of computerization that Singh and Whittington chose to list their programmer on the title page of their book. Some of their findings confirmed the crude Gibrat hypothesis, for example, that average growth rates did not vary much as a function of firm size. But they found other important violations of the Gibrat assumptions, notably, the variance of growth rates was lower for larger firms, meaning that those firms enjoyed greater positional stability. Moreover, at least over relatively short intervals, the growth rates for a given firm were not truly random from year to year, but serially correlated (i.e. persistent), so that a run of what seemed to be good luck continued, increasing the relative disparity of firm sizes. In the authors’ analysis of profit along with raw firm size data, it was found that similar phenomena appeared—for example, the variance of profit rates was lower for larger firms, high profit rates showed some tendency to persist over time, and (combining the two foci) firms with higher profits tended at least in some industries to grow more rapidly. Suggesting a link to Singh’s work on take-overs, such changes of ownership (which we in the USA were calling mergers) proved to be an important cause of growth rate differences.

In short, the work by Singh and Whittington showed clearly that there were important random influences in corporate growth processes and that these seemingly random growth rate differences led over time to strikingly similar cross-sectional firm size distributions. But much remained to be explored by other investigators on the underlying reasons for observed growth rate differences and how they illuminated theories of firm and industry behaviour.

• [1] For Singh, a merger with name change meant A + B = C. 2 Ravenscraft and Scherer (1987: 70). Our sample covered approximately 6,000 corporate control transactions, of which 25 were consummated hostile take-overs, 50 were tender offers unopposed by targetcompany management, and 20 were tender offers in which a usually unopposed ‘white knight’ ratherthan the original tenderer succeeded in effecting the take-over.