A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

27 Pages Posted: 29 Jul 2005  

Alan Bester

University of Chicago Graduate School of Business

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics

Date Written: June 21, 2005

Abstract

In this paper, we consider estimation of nonlinear panel data models that include individual specific fixed effects. Estimation of these models is complicated by the incidental parameters problem; that is, noise in the estimation of the fixed effects when the time dimension is short generally results in inconsistent estimates of the common parameters due to the nonlinearity of the problem. We present a penalty for the objective function that reduces the bias in the resulting point estimates. The penalty function involves only cross-products of scores and the hessian matrix and so is simple to construct in practice. The form of the penalty also provides interesting intuition into how the bias reduction is working. We present simulation results that suggest that the penalized optimization approach may substantially reduce the bias in nonlinear fixed effects models.

Keywords: Incidental Parameters, Fixed Effects, Panel Data, Bias

JEL Classification: C10, C13, C23

Suggested Citation

Bester, Alan and Hansen, Christian, A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects (June 21, 2005). Available at SSRN: https://ssrn.com/abstract=762504 or http://dx.doi.org/10.2139/ssrn.762504

Alan Bester

University of Chicago Graduate School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-834-1714 (Phone)

Christian Hansen (Contact Author)

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States
773-834-1702 (Phone)

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