A semiparametric panel data model with common factors and spatial dependence

This paper proposes alternative estimation procedures for semiparametric panel data models that allow handling complex and relevant empirical problems simultaneously, namely (i) functional misspecification, by modelling stochastic observed common factors with a nonparametric function instead of assuming the usual parametric form; (ii) cross-sectional dependence arising simultaneously from common factors and spatial dependence; and iii) heterogeneous relations among variables. We then consider a more general panel data model with several types of cross-sectional dependence and obtain consistent and asymptotically normal estimators for both slope parameters and unknown functions by extending Pesaran’s (2006) common correlated effect (CCE) approach to this semiparametric framework. Another methodological and empirical challenge is how to test for poolability and fully parametric functional form. For both cases, simple consistent test statistics are proposed and we show that they have limiting standard distributions under the null hypothesis. The theoretical findings are further supported for small samples via several Monte Carlo experiments, and an empirical application to the knowledge capital production function is conducted.