Therefore, in order to test Gibrat’s law we jointly estimate equations (1) and (2) by
Heckman procedure using maximum likelihood methods. The set of estimators is
reported in the next section.
Results of the estimation
The results of the estimated models are reported in Table V: columns 2 to 5 show the
estimators for the four groups the sample is divided, meanwhile column 6 includes the
whole sample estimations.
Gribrat’s law holds for the whole sample and for developped regions, as can be seen in
columns 1 and 2 and the test for β1. On the contrary, in less developped provinces the
test rejects the law and in provinces of group 3 the growth is higher for big firms.
Another important conclusions can be obtained from Table V: the likelihood test shows
that the equations are not independent in any of the groups, what means that a least
square estimation with the survival sample would be biased. In fact, the significance of
parameters Sigma and Rho in the estimation shows that we have to take into account an
important bias introduced by the existence of firms that disappeared over the period of
analysis. The second additional conclusion is that innovation, both process or product, is
the main characteristic to explain survival of firms, independently of the region they are
located. Only in the less developed provinces product innovation has no effect.
Conclusions
Gibrat’s law test for different regions in Spain, classified depending on the degree of
technological development of the region, has show an heterogynous behaviour: small
firms located in the most developed areas of Spain, concretely Madrid and Barcelona,
have grown higher than big firms; on the contrary, in less developed regions Gibrat’s
law is rejected and even big firms have grown higher in group 3 provinces, since the