Abstract

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.

Highlights

  • During the last two decades or so, there has been an increasing interest in parametric linear and nonlinear panel data modeling as the double–index panel data models enable researchers to extract information that may be difficult to obtain

  • Single–index models have been studied in depth in time series setting

  • The RMAVE method was introduced for time–series single–index models by Xia et al (2002), and its asymptotic properties were established by Xia (2006)

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Summary

INTRODUCTION

During the last two decades or so, there has been an increasing interest in parametric linear and nonlinear panel data modeling as the double–index panel data models enable researchers to extract information that may be difficult to obtain. We will study a single–index panel data model with heterogeneous link functions. The RMAVE method was introduced for time–series single–index models by Xia et al (2002), and its asymptotic properties were established by Xia (2006). As there are two indices (i.e. i and t) involved and the nonlinear link functions are heterogeneous, the establishment of the asymptotic theory for the RMAVE method for model (1.1) is much more complicated than that for the time series case. Studying model (1.1) under the α–mixing dependence allows us to extend it to a dynamic panel data model where the covariates Xit contain lagged values of Yit. Section 4 discusses some conditions that ensure {Yit, t ≥ 1} to be a geometrically ergodic process for each i. Some technical lemmas and the detailed proof of the main result are given in Appendices A and B, respectively

SEMIPARAMETRIC ESTIMATION METHODS
ASYMPTOTIC THEORY
The bandwidth h satisfies
DYNAMIC SINGLE–INDEX PANEL DATA MODELS
Bandwidth Selection
An empirical example
CONCLUSION
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