Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

In this paper, we study semiparametric estimation for a single–index panel data model where the nonlinear link function varies among the individuals. We propose using the so–called refined minimum average variance estimation based on a local linear smoothing method to estimate both the parameters in the single–index and the average link function. As the cross–section dimension N and the time series dimension T tend to infinity simultaneously, we establish asymptotic distributions for the proposed parametric and nonparametric estimates. In addition, we provide two real–data examples to illustrate the finite sample behavior of the proposed estimation method in this paper.