Fig. 2 Kernel densities of TFP
On the other hand, these findings can derive from the different, and not observed,
characteristics of the firms that belong to the two groups. However, following Di Nardo et
al (1996) is possible to construct a counterfactual density distribution of the productivity
of firms for which the IE index is equal to zero. This counterfactual density is calculated
associating a greater weight to the firms that are not involved in international networks but
that have observable characteristics similar to those firms that are involved.
Since the density function of the TFP index conditional to the realization of the IE index is
the integral of the cumulative conditional probability function. For the case of firms that
are not involved in foreign networks but have the same zi characteristics of firms that are
both importers and exporters we have that:
f (TFP | X = 0)= ∫ f (TFP | z,X = θ) dF(z | X = 1) = ∫ f (TFP | z,X = θ) dFzZ] X = 1) dF(z | X = 0) (13)
z z dF(z | X = 0)
Thus, with dF(z | X—1) = ψz(z) as weighting function, we have that the estimated
dF(Z |X =0)
counterfactual kernel density function will be:
1 n (TFP
fh = ʒ ∑Ψz * K( i
njhi=1 I
TFP11 ( X = 0)
(14)
28