by applying Bayes rule at the numerator and at the denominator, the weighting function
can be estimated using the following specification:
dF(z|X =1) Pr(X =1|z=zi) Pr(X =0)
(15)
ψ z ( Zi ) =-------------=--
z i dF(z|X =0) Pr(X =0|z=zi) Pr(X =1)
Where, Pr(X=0) and Pr(X=1) is the unconditional probability that the IE index is equal
to zero or one respectively, while Pr(X=1| z = zi) and Pr(X=0| z = zi) are the prediction
obtained from Probit estimates of the probability that X=1 or X=0, with zi as regressors45.
Figure 3 displays the estimated counterfactual density for the firms that are not involved in
trade networks. This latter density lies between the other two showing how the similarity
on firm characteristics affects the distribution of the performance variable, however it is
still always on the left of the distribution of productivity of the plants that are engaged in
trade both upstream and downstream.
Therefore after controlling for firm characteristics we still find that there is an higher
productivity advantage associated with being both an importer and an exporter.
Fig. 3 Kernel densities of TFP
45 zi is a vector that includes the same variables used to estimate equation (3)
29