Semiparametric Single-Index Panel Data Models With Cross-Sectional Dependence

In this paper, we consider a semiparametric single index panel data model with cross–sectional dependence, high–dimensionality and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then establish some consistent closed–form estimates for both the unknown parameters and a link function for the case where both N and T go to ∞. Rates of convergence and asymptotic normality consistencies are established for the proposed estimates. Our experience suggests that the proposed estimation method is simple and thus attractive for finite–sample studies and empirical implementations. Moreover, both the finite–sample performance and the empirical applications show that the proposed estimation method works well when the cross-sectional dependence exists in the data set.