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A spatial econometric panel data examination of endogenous versus exogenous interaction in Chinese province-level patenting

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Abstract

We examine the provincial-level relationship between domestic Chinese intellectual property (IP) and knowledge stocks using a space–time panel model and data set covering monthly patent activity over the period 2002–2010. The goal of the modeling exercise is to explore the elasticity response of IP to knowledge stocks classified by type of creator (universities and research institutes, enterprises, and individuals). A focus is on spatial and time dependence in the relationship between knowledge stocks and IP, which implies spatial spillovers and diffusion over time. Many past studies of regional knowledge production have focused on patent applications as a proxy for regional output from the knowledge production process. However, this ignores the distinction between patent applications and patents granted, with the latter reflecting a decision and ability to convert knowledge produced into IP. This study differs in its focus on the regional relation between IP and knowledge stocks and the space–time dynamics of these. Using patents granted as a proxy for IP, and past patent applications as a proxy for regional knowledge stocks, allows us to explore the implied quality of knowledge production by various types of creators. Because Chinese patent applications have grown by 22 %, questions have been raised about the quantity versus quality of these applications. Our findings shed light on this issue.

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Notes

  1. 2012 World Intellectual Property Indicators, WIPO Economics & Statistics Series, WIPI hereafter. Available at www.wipo.int/ipstats.

  2. A utility model is an exclusive right granted for an invention, which prevents others from commercially using the protected invention for a limited period of time. In its basic definition is similar to a patent, and these are sometimes referred to as “petty patents” or “innovation patents.” The requirements for a utility model are less stringent than for patents, so these are often sought for incremental innovations that may not meet patentability requirements.

  3. An industrial design is an IP right that protects the visual design of objects that are not purely utilitarian. For example, creation of a shape, configuration or composition of pattern or color, or combination of pattern and color in three dimensional form containing esthetic value.

  4. The Office of Harmonization for the Internal Market (OHIM) registers the Community Trade Mark in the European Union.

  5. Li and Pai (2007) highlight problems with the WIPO (2007) report by enumerating reasons why patent applications should not be treated as a matured innovation indicator truly reflecting the innovation capacities of North East Asia with special emphasis on China.

  6. IP5Statistics Report 2011 Edition.

  7. Shanghai implemented China’s first patent subsidy policy in 1999. Since 2003, almost all provinces have had subsidy policies in place, and many cities have their own subsidies for patent applications which compensate applicants for fees.

  8. See LeSage and Fischer (2012) for a similar development.

  9. See Parent and LeSage (2011, 2012a) for a discussion of issues pertaining to models that do not condition on the initial period observation, but treat this as endogenous. The arguments sets forth here apply to both types of models.

  10. If the improper priors for models being compared are different, they will not cancel each other properly, or if the models being compared have different numbers of parameters with improper priors, model probabilities become ill-defined (Koop 2003, 40–42). This is not the case here.

  11. The web site states that discrepancies between the English and Chinese language data files should be resolved in favor of the Chinese language versions of the files.

  12. This includes both government and private firms.

  13. Also has the name “non-service” on the website.

  14. These are groups such as Red Cross and other NPO as well as government sectors.

  15. This is posted on http://www.sipo.gov.cn/yw/2011/201101/t20110121_568361.html.

  16. A similar result arises for the case of the DSTU specification, where the partial derivatives are slightly more complicated (see Debarsy et al. 2012).

  17. See LeSage (2013) for a detailed description of the expressions required to calculate log-marginal likelihoods using univariate numerical integration. Monte Carlo results are also provided showing that these methods work well in practice.

  18. Methods used for calculating these were discussed in Sect. 3.2.

  19. Averaging over the eight different models simply involves combining the set of 1,000 effects estimates based on 1,000 parameter draws from all models. Since the effects are nonlinear functions of the parameters, we calculate effects, then average over these. See LeSage and Pace (2009, Chapter 6) for an explanation of the issues involved here.

  20. We used 0.15, which is approximately the average indirect effect estimate reported for individuals and enterprises in Table 4 for both models, with 4.5 being the average number of neighboring provinces.

  21. Most researches treat the geographically coastal province Guangxi as an inland province, as does the Chinese government for many purposes, and we follow this convention.

  22. As before, these estimates reflect an average of the partial derivatives over the eight different time horizons.

  23. Significance was determined using 0.01 and 0.99 intervals constructed from the set of 1,000 draws from the maximum likelihood estimate of the variance–covariance matrix of the parameters. As in the case of results reported in Table 4, averaging over the eight different models simply involves combining the set of 1,000 effects estimates constructed from the 1,000 parameter draws from all models.

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Correspondence to James P. LeSage.

Appendix

Appendix

Deriving the log-marginal likelihood used for model comparison purposes in our study involves a combined strategy that relies on analytical integration for some parameters of the model and numerical integration over the space and time dependence parameters. This approach was introduced in Fischer and LeSage (2014), and analogous expressions for the case of a static panel data model are presented in LeSage (2013). The main development involves a computationally efficient expression for \(e'e\), which is needed to evaluate the log-marginal likelihood used to calculate posterior probabilities for models. We start with analytical integrating out the parameters \(\delta \), which involves concentrating out the parameters \(\delta \) using:

$$\begin{aligned} \hat{\delta }&= (Z' Z)^{-1} Z' (A \otimes B) y \nonumber \end{aligned}$$

which can be strategically written using the following expressions:

$$\begin{aligned} \hat{\delta }&= \left( \delta _0 - \phi \delta _{\phi } - \rho \delta _{\rho } - \theta \delta _{\theta } \right) \nonumber \\ \delta _0&= (Z' Z)^{-1} Z' (F \otimes I_N) y \nonumber \\ \delta _{\phi }&= (Z' Z)^{-1} Z' (L \otimes I_N) y \nonumber \\ \delta _{\rho }&= (Z'Z)^{-1} Z' (F \otimes W) y \nonumber \\ \delta _{\theta }&= (Z' Z)^{-1} Z' (L \otimes W) y \nonumber \end{aligned}$$

where

$$\begin{aligned} L&= \left( \begin{array}{ccccc} -1 &{} 0 &{} 0 &{}\ldots &{} 0 \\ 0 &{} -1 &{} 0 &{} \ldots &{} 0 \\ \vdots &{} &{} \ddots &{} \ddots &{} \vdots \\ 0&{} \ldots &{} 0 &{} -1 &{} 0 \\ \end{array} \right) \nonumber \\ F&= \left( \begin{array}{ccccc} 0 &{} 1 &{} 0 &{} \ldots &{} 0 \\ 0 &{} 0 &{} 1 &{} &{} \vdots \\ \vdots &{} &{} \ddots &{} \ddots &{} 0 \\ 0 &{} \ldots &{} &{} 0 &{} 1 \\ \end{array} \right) \nonumber \end{aligned}$$

with \(L\) and \(F\) being \((T-1) \times T\) matrices.

Now consider the errors: \(e = (A \otimes B) y - Z \delta \), which can be written using:

$$\begin{aligned} e&= \left( \begin{array}{llll} 1&-\phi&-\rho&-\theta \end{array} \right) \left( \begin{array}{l} E^{(1)} \\ E^{(2)} \\ E^{(3)} \\ E^{(4)} \end{array} \right) \nonumber \\ E^{(1)}&= (F \otimes I_N)g - Z (Z' Z)^{-1} Z' (F \otimes I_N) g \nonumber \\ E^{(2)}&= (L \otimes I_N) g - Z (Z' Z)^{-1} Z'(L \otimes I_N) g \nonumber \\ E^{(3)}&= (F \otimes W) g - Z (Z' Z)^{-1} Z' (F \otimes W) g \nonumber \\ E^{(4)}&= (L \otimes W) g - Z (Z' Z)^{-1} Z' (L \otimes W) g \nonumber \\ e' e&= \tau ' Q \tau \nonumber \\ \tau&= \left( \begin{array} {llll} 1&-\phi&-\rho&-\theta \end{array} \right) \nonumber \\ Q_{ij}&= \text{ tr } (E^{(i)'} E^{(j)}), \ \ \ i=1,\ldots ,4 \ \ \ j=1,\ldots ,4. \nonumber \end{aligned}$$

The advantage of this specification is that the sum of squared residuals \(e'e\) can be expressed as a function of only the parameters \(\phi , \rho , \theta \) in the vector \(\tau \) plus sample data information \(y, Z, W\).

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LeSage, J.P., Sheng, Y. A spatial econometric panel data examination of endogenous versus exogenous interaction in Chinese province-level patenting. J Geogr Syst 16, 233–262 (2014). https://doi.org/10.1007/s10109-014-0198-7

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