Industrial districts, innovation and I-district effect: territory or industrial specialization?

5. PARAMETRIC MODELLING OF THE I-DISTRICT
EFFECT

5.1. The model

To test the existence of a district effect on innovation (I-district effect) and
model its determinants, Boix and Galletto (2008a) depart from the knowledge
production function introduced by Griliches (1979) and implemented by
Pakes and Griliches (1984). The enhanced function relates innovation to
R&D inputs and to idiosyncratic effects associated to each typology of LPS
so that the equation is specified as a fixed effects model:

logi_j=γ+βlogr_j+δ^* +ε_j      (1)

, where i is the average innovation per worker, r is average R&D per
worker in the LPS j, and δ^* are the fixed effects by typology of LPS. After
subtracting the effect of inputs, the remaining differential is due to the
characteristics associated to each type of production system. The seven fixed
coefficients capture the different performances of each typology of LPS and
inform whether they are statistically significant⁸.

Two modifications to this model are proposed. First, if it is assumed
that the innovation effect is caused by the dominant specialization of the LPS
and not by their territorial typology, the territorial fixed effect δ^* should be
replaced by the specialization-industry effect λ^*:

logi_j=γ+βlogr_j+λ^* +ε_j      (2)

Second, to contrast the hypothesis of dominance of the territorial
effect, it is necessary to separate the territorial typology and the specialization
of each LPS. The estimation of a two-way fixed effect model including δ^*
and λ^* is not a good strategy because territorial typology and specialization
are correlated. A better approach is to introduce a combined fixed effect δλ^*
so that for each specialization it is possible to compare the performance of
the different territorial typologies or vice versa:

logi_j=γ+βlogr_j+δλ^* +ε_j     (3)

⁸ In a posterior step Boix and Galletto (2008a) relate the fixed effects to the existence
of external economies: δ^* = f(Zj).

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