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These crucial relationships between research effort and innovation performance may be analysed by an input-output linear model developed by Griliches (1979, 1984). Input is the new technological knowledge generated by R&D in industries and universities and output is the patented innovations. The model is
lnPATs = β1lnIR&Ds + β2lnUR&Ds + β3lnCs + POPs + εs
lnPATs is the natural logarithm of the number of patents granted to private manufacturing firms in the state S
β1lnIR&Ds is the natural logarithm of R&D expenditures by manufacturing firms in the state S
β2lnUR&Ds is the natural logarithm of R&D expenditures by universities in the state S
β3lnCs is the geographical coincidence index
POPs is the total resident population in the state S
εs is a stochastic error
Cs = Σic [UNIVic * Tpic] / [ΣicUNIV2ic]1/2 * [ΣicTP2ic]1/2
UNIVic is R&D expenditure within universities by industry i and metropolitan area c
Tpic is the number of researchers in the manufacturing sector by industry i and metropolitan area c
Applying the model for 29 US states over the period 1972-77 and 1979, 1981 Jaffe showed that corporate patenting is significantly affected by spillovers from both the private corporate R&D expenditures and research expenditures by universities, although the former (showing elasticity >0.7) have a stronger impact than the latter (elasticity <0.1), and the geographic coincidence index is only marginally statistically significant.
Applying the model for the French regions with 1991 data, Piegriovanni and Santarelli (2001) showed that spillover from university R&D are relatively more important source of innovation in private and state-owned industrial firms than industrial research itself. This is probably due to the national system of innovation in France and the familiarity of French firms with technological dissemination projects from universities and public research centers.
Sources:
Griliches, Z. (1979) ‘Issues in assessing the contribution of D&D to productivity growth’, Bell Journal of Economics, Vol.10, pp. 92-116.
Griliches, Z. (ed) (1984) R&D Patents and Productivity, Chicago: University of Chicago Press.
Jaffe, A.B. (1986) ‘Technological opportunity and spillovers of R&D: evidence from firms’ patents, profits and market value’, American Economic Revue, Vol. 79, pp. 957-70.
Piergiovanni, R., and Santarelli, E. (2001) ‘Patents and the geographic localization of R&D spillovers in French manufacturing’, Regional Studies, Vol. 35.8, pp. 697-702.