The name is absent

7. Robustness checks: Semiparametric analysis

The parametric results reported up to here become weaker when we try to control for
endogeneity biases. The most interesting results derive from multivariate correlation
exercises. We are not able to conclude if trade practices generate productivity advantages
or if it is the case that more productive firms chose to export or import. However
additional extensions of the analysis are suggested by the fact that recent industrial
organization literature has highlighted the importance of heterogeneity of firms within
sectors. To investigate this feature we examine whether the participation in trade networks
affects the distribution of firms’ productivity uniformly or not.

The density distribution of the productivity index conditional on the fact that firms
participate in foreign networks can be estimated with the following kernel density
function:
where K() is a kernel function⁴², h is the bandwidth, I() is an indicator function equal to 1
if the trade index X is equal to j that can be either zero or one, nj is the number of firms
for which the index X is equal to j. Figure 2 shows the kernel density of the productivity
index for firms that are both importers and exporters and for firms that are not⁴³.The
distribution of firms that participate in foreign networks shows a good degree of
heterogeneity however the probability of having an higher productivity level⁴⁴ is greater
for firms that are both importer and exporter. In fact, the density distribution of firms for
which the IE index is greater that zero lies on the right of the density distribution of firms
for which the index is equal to zero. For a more rigorous test, in Appendix B we also
report the Stochastic dominance tests on the cumulative distributions.

⁴² in this application, a Gaussian kernel function will be used.

⁴³ Whether the IE index (5) is equal to zero or to one.

⁴⁴ Above the “mean” which corresponds, for the TFP Index, to the value “1” on the horizontal axis.

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