logSi01 = β0 + β1 logSi90 + β2 log(age) + β3 logSi90*log(age) + β4 RESJUR + β5INNPRO
+ β6 INPRC + β7TECHIGH + β8TECMED + εi00 (1)
where Si01 is the employment of the ith firm in 2001; Si90 is the employment of the same
firm in 1990, and the other variables are defined in the Appendix.
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 it is greater than 1.
On the other hand, β2 will be negative if young firms have experienced a bigger growth
during the period; β3 is an interaction coefficient between age and size, and its value is
not determined; β4 will be positive if firms with limited legal liability have grown
larger; and the remaining parameters - β5, β6, β7 and β8 - will all be positive if the
growth has been larger among innovating firms of product or process, firms in high
technological sectors, or firms in sectors with medium technological development,
respectively.
The estimation of the β's by least squares with existing firms in 2001 runs the risk of
bias arising from sample attrition. The appropriate econometric method to resolve this
problem is the 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 survival in the least squares
regression for surviving firms. The probit equation we use is:
SUPERV = φ0 + φi log Si90 + φ2 log(age) + φ3 logSi90*log(age) + φ4 RESJUR + φ5
INNPRO + φ6 INPRC + φ7TECHIGH + φ8 TECMED + μi00 (2)
where SUPERV is 1 if the firm has survived until 2001, and 0 if it has closed.
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).