Gibrat’s law holds if β1 is not significantly different from 1. Small firms have grown more if
β1 is less than 1, and big firms will have grown more if β1 is greater than 1.
The estimation of the β's by least squares with existing firms in 2002 runs the risk of bias
arising from sample attrition. The appropriate econometric method to solve this problem is a
two-step method suggested by Heckman (1979). This requires the introduction of an
additional explanatory variable in the least squares regression - the inverse Mill’s Ratio -
obtained from a probit model on firm’s survival, in the least squares regression for surviving
firms. The probit equation is:
SUPERV = φo + φ1 log Si98 + ΣjφjYj + μiκ (2)
Where SUPERV takes 1 if the firm has survived until 2002, and 0 if it has closed. Yj are the
other variables included in the equation15.
Although this Heckman estimator is consistent, it is not fully efficient. Efficient estimates can
be obtained by applying an iterative procedure that uses the estimates from the Heckman
procedure as starting values and will lead, on convergence, to maximum likelihood estimates
(Maddala (1983), Weiss (1998)). Therefore, in order to test Gibrat’s law we jointly estimate
equations (1) and (2) by Heckman procedure using maximum likelihood methods.
Employment has been defined adopting four different proxies:
a. PERTOTi is total employment of the ith firm at the end of the year, independently of
working hours.
b. ASATCi is only composed by employees with full working hours of the ith firm.
c. PERS1i is a weighted employees’ measure of ith firm. It is equal to employees with
full working hours, plus half of employees with partial working hours plus one third of
temporary employees.
d. PERS2i is a weighted measure of firm’s human capital. It is the sum of employees
with a degree (bachelors and engineers) plus half of employees with an intermediate
degree, plus one third of the rest of employees.
15 Xj = Yj in Heckman model to estimate the inverse Mill’s ratio. On the Maximum Likelihood procedure it is
possible Xj ≠Yj, but we have preferred to maintain the equality.
17