Nonparametric Time-Varying Coefficient Panel Data Models with Fixed Effects

The University of Adelaide School of Economics Research Paper No. 103

28 Pages Posted: 18 Sep 2010

See all articles by Jia Chen

Jia Chen

University of Adelaide - School of Economics

Degui Li

University of Adelaide - School of Economics

Jiti Gao

Monash University - Department of Econometrics & Business Statistics

Date Written: September 15, 2010

Abstract

This paper is concerned with developing a nonparametric time-varying coefficient model with fixed effects to characterize nonstationarity and trending phenomenon in nonlinear panel data analysis. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross-sectional averages, and then uses a nonparametric local linear approach to estimate the trend function and the coefficient function. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has an optimal rate of convergence that is slower than that of the trend function, which also has an optimal rate of convergence. To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross-time average from each individual. It estimates the trend function and the coefficient function with an optimal rate of convergence. The asymptotic distributions of both of the estimates are established when T tends to infinity and N is fixed or both T and N tend to infinity. Simulation results are provided to illustrate the finite sample behavior of the proposed estimation methods.

Keywords: Fixed effects, local linear estimation, nonstationarity, panel data, specification testing, time-varying coefficient function

JEL Classification: C13, C14, C23

Suggested Citation

Chen, Jia and Li, Degui and Gao, Jiti, Nonparametric Time-Varying Coefficient Panel Data Models with Fixed Effects (September 15, 2010). The University of Adelaide School of Economics Research Paper No. 103, Available at SSRN: https://ssrn.com/abstract=1677767 or http://dx.doi.org/10.2139/ssrn.1677767

Jia Chen

University of Adelaide - School of Economics ( email )

No 233 North Terrace, School of Commerce
Adelaide SA, SA 5005
Australia

Degui Li

University of Adelaide - School of Economics ( email )

No 233 North Terrace, School of Commerce
Adelaide, South Australia 5005
Australia

Jiti Gao (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

900 Dandenong Road
Caulfield East, Victoria 3145
Australia
61399031675 (Phone)
61399032007 (Fax)

HOME PAGE: http://www.jitigao.com

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