Gibrat’s Law (skewed distribution of firm size)

Xt - size of a firm at time t, et - random (normally distributed) variable representing idiosyncratic, multiplicative growth shock over the period of time (t-1:t) The distribution of firm size is asymmetric: in statistical terms such distributions are qualified as “positive skewed”: the tail on the right side is longer (or fatter) than the tail on the left side. Gibrat's law of proportionate effect states that the proportional change in the size of a firm is independent of its absolute size. An implication of this is that large and small firms have the same average proportionate rates of growth. Gibrat’s law has been very popular in economic research because: it explains very asymetric firm size distributions (that is with a frequency of small firms much higher than a normal distribution would predict; there is empirical evidence supporting the idea that firm grwoth rates are largely erratic and hard to predict However, research has also shown that: - small firms grow faster - but they have a lower survival probability - the relation between firm size and growth is moderated by firm age (which has a negative correlation with firm growth and positive with survival) - Gibrat’s law is supported among firms above a certain threshold Ubiquitous fat tails are a sign of some underlying correlating mechanism which one would rule out if growth events were normally distributed, small and independent.