A heterogeneous coefficient approach to the knowledge production function

ABSTRACT

Past literature has used conventional spatial autoregressive panel data models to relate patent production output to knowledge production inputs. However, research conducted on regional innovation systems points to regional disparities in both regions’ ability to turn their knowledge inputs into innovation and to access external knowledge. Applying a heterogeneous coefficients spatial autoregressive panel model, we estimate region-specific knowledge production functions (KPFs) for 94 NUTS-3 regions in France using a panel covering 21 years from 1988 to 2008 and four high-technology industries. A great deal of regional heterogeneity in the KPF relationship exists across regions, providing new insights regarding spatial spillin and spillout effects between regions.

KEYWORDS:

• knowledge production
• spatial econometrics
• region-specific parameters

JEL:

• C21
• O31
• O52
• R12

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1 A doubly stochastic matrix is one with both row and columns sums equal to 1. More will be said about normalization of the spatial weight matrix in these models when the interpretation of the model estimates is discussed.

2 In the case of our informative ridge-type priors described in the third section, the non-singularity assumption can be relaxed.

3 These are patent applications in the fields of chemistry, pharmaceutical, mechanics or materials based on the location of the inventor. Source: REGPAT-OECD database, June 2012.

4 Private R&D expenditure in the field (€, thousands). Source: R&D Survey, French Ministry of Research. This variable was lagged by two years and smoothed over a two-year period. For example, if the dependent variable reflected patents smoothed over 1990 and 1991, the R&D variable was based on 1988 and 1989.

5 Number of scientific publications in the field (affiliation’s location). Source: PASCAL (INIST-CNRS).

6 Smoothing and log-transformation tend to decrease variation over time, but are helpful scaling/smoothing transformations typically used in the knowledge production literature.

7 Figure 1 shows island regions 2A and 2B for Corsica, which were excluded from our sample.

8 To do this, we first converted our patent and R&D data from French classifications to international classifications (respectively IPC and International Standard Industrial Classification [ISIC]). This was done on the basis of the Observatoire des Sciences et Techniques (OST) report allowing use of the link between IPC and ISIC made by researchers from the Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT) (Verspagen, Moergastel and Slabbers). Using the OST report that details each scientific field, we built the concordance with the public research classification. See Autant-Bernard and LeSage (2011) for more details.

9 We used 2000 retained draws from a set of 2500, with the first 500 draws excluded as ‘burn-in’ for the MCMC sampler. Two different runs of the MCMC sampler with different starting values were used to produce a total of 4000 retained draws. From the 4000 retained draws, every fourth draw was used to eliminate serial dependence in the draws, resulting in a set of 1000 draws. These were used in the matrix expression in (10) to produce 1000 separate estimates of direct, spillin and spillout effects for each knowledge input variable.