A statistical illusion of large firm conformity to Gibrat's law

 

Abstract: When the growth of sufficiently large firms is progressively less than proportionate to initial size, the resulting growth rates are shown to have three characteristics which increasingly resemble those that would result from proportionate growth as assumed by Gibrat’s Law.  The increasingly strong resemblance can render the two growth processes statistically indistinguishable and create an illusion of large firm conformity to the Gibrat assumption of equal and size-independent growth rates for all firms.  Final inferences about conformity to the law require testing, therefore, of its long run implication of a lognormal size distribution with secularly increasing variance.  The increasing variance reflects the law’s critical implication of continuously growing firm size inequality and is expected to occur if actual firm growth is proportionate (Gibrat’s Law), but not if progressively less than proportionate.  The illusion is demonstrated by a test of the Gibrat growth assumption on the less-than-truckload sector of the U.S. trucking industry.  The large firm growth rate characteristics show consistency with both growth processes, allowing less than proportionate growth to create an illusion of proportionate growth.  The size distributions for all industry segments give a poor fit to lognormal, however, and there is never a significant increase in the variance, so the law is rejected among all firms, large and small.  Thus, testing the growth rate characteristics alone, as in many recent studies, can lead to a false confirmation of the law among larger firms.