(namely working requirements, compulsory licensing, and revocation of patents), three types of enforcement mechanisms, and the duration of patents relative to international standards.<sup>5</sup> Each component ranges between zero and one, and thus the composite index we use in the empirical exercises also varies between 0 and 1, with higher values indicating stronger IPR protections and enforcement. Summary descriptive statistics of the three variables and the list of 67 countries that appear in our sample are reported in the Appendix.

Finally, the data on IPRs are available in ve year intervals, with the updated data from 19602000 available from Park's web site.<sup>6</sup> These data, like the educational attainment data, are thus also available for the initial year of each ve-year period in our estimation sample. And both variables therefore can be treated as pre-determined or weakly exogenous with respect to the R&D variable in a temporal sense. Moreover, the educational attainment variable reects educational enrollment decisions made roughly during ages 6-25, and therefore are unlikely to be due in a causal sense to the share of R&D observed in the subsequent 4 years. The IPR index is largely a summary indicator of the laws that establish the coverage and enforcement of IPR laws, which are the result of past international negotiations and legislative activity. Consequently it is dicult to believe that the index is caused by subsequent realizations of R&D.

# 3.2 Model specication

As mentioned, the theoretical model predicts that the relationship between R&D as a share of GDP and human capital and IPRs can be characterized by a non-linear function. Under the expectation of non-linear relationships, the ideal estimator would be a non-parametric estimator capable of estimating local derivatives over the data sample. Unfortunately, non-parametric estimators commonly used in empirical analyses tend to breakdown in the presence of multi-variate relationships and especially in the presence of xed eects.<sup>7</sup> A more tractable alternative is to apply linear estimators to exible functional forms using Taylor or Fourier approximations to non-linear functions of unknown form. The disadvantage of this general approach is the well known curse of dimensionality, whereby the addition of higher-order polynomials or trigonometric terms in linear functions reduces the power of standard specication tests, such as the t-statistic, and thus we are unable to ascertain the statistical signicance of each element in the high-order functions. On the other hand, we can apply standard F-tests to test the null hypothesis of insignicant higher-order and interactive terms in the chosen functions.<sup>8</sup> We apply three econometric approaches to assess the existence of

> 5Regarding the enforcement mechanisms, the sub-index includes three de jure enforcement mechanisms: (a) Preliminary (pre-trial) injunctions, (b) Contributory infringement, and (c) Burden of proof reversal (see Ginarte and Park 1997, p. 287-88; and Park 2008).

> 6http://www.american.edu/cas/econ/faculty/park.htm

> 7See, for example, Stone (1980), White (1980) and Yatchew (2003).

> 8We thank Francisco Rodriguez of Wesleyan University for highlighting these econometric issues. See also his paper on growth empirics, Rodriguez (2007).

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