Abstract
In this paper, we consider a semiparametric single-index panel data model with cross-sectional dependence 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 the link function for the case where both cross-sectional dimension (N) and temporal dimension (T) go to infinity. Rates of convergence and asymptotic normality 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.
Highlights
Single–index models have been studied by both econometricians and statisticians in the past twenty years or so and cover many classic parametric models by using a general function form g (x β) (e.g. Chapter 2 of Gao (2007))
We have considered a semiparametric single–index panel data model allowing for cross–sectional dependence, stationarity and unobservable heterogeneity
Some closed–form estimates have been proposed to recover the parameters of interest and the link function
Summary
Single–index models have been studied by both econometricians and statisticians in the past twenty years or so and cover many classic parametric models (e.g. linear model and logistic model) by using a general function form g (x β) (e.g. Chapter 2 of Gao (2007)). We aim at establishing consistent closed–form estimates for a semiparametric single–index panel data model with both cross–sectional dependence and stationarity for the case where both N and T go to infinity. It proposes a semiparametric single–index panel data model to simultaneously accommodate cross–sectional dependence, stationarity and unobservable heterogeneity; 2 It establishes simple and consistent closed–form estimates for the unknown index vector, and there is no restriction on the parameter space; 3. It establishes both rates of convergence and asymptotic normality results for the estimates under a general spatial error dependence structure; and.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
