Abstract: In the analysis of the Griliches' knowledge capital production function, previous works pointed out the relevance of incorporating slope heterogeneity in the technological parameters, cross-sectional dependence arising simultaneously from common factors and spillovers, and possible nonlinear effects of relevant common observed variables. In order to solve the above problems, in this article we introduce a semi-parametric model in a partially linear form that copes simultaneously with all the previous specification issues. The asymptotic properties of the resulting estimators are obtained and the theoretical findings are further supported for small samples via several Monte Carlo experiments and an empirical application

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