Gibrat's Law-The Law of Proportionate Effect (LPE) +tbe firm size in period 0 s, the firm size in period 1 B1>proportional growth rate for period s1=501+81)→1og(1)=1og5)+log(1tg t-1 (1) X, log(s,), t=l log(1+g.) is the normally distributed error term with variances The LPE makes two assumptions a) there is no correlation between a firms size and growth between periods Cov (X t-1 )=0 b)no correlation between successive growth rates. Cov(e t’t-s 0 Then this equation yields for period 1 ) Var(X)+ Varley 2 but the last term on the R.h.s. is zero since we have assumed that the growth of the firm is independent of its initial size. Then For period 2: 2 +s with t var(X,),s= Var(e+) Generalising to period t N s =0 t-1 In other words the variance of log size will be the product of the variance of growth rate times the number of periods that have elapsed. Clearly from (4) 1im (5) ie, the variance (spread)of the firm sizes increases indefinitely over time. This is the testable implication of Gibrat's law. Note that since the random variable follows the normal distribution with variance