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 nite sample behavior of the proposed estimation method.
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