Linear fixed-effects estimation with nonrepeated outcomes

Abstract

We demonstrate that popular linear fixed-effects panel-data estimators are biased and inconsistent when applied in a discrete-time hazard setting, even if the data-generating process is consistent with the linear model. The bias is not just survival bias, but originates from the impossibility to transform the model such that the remaining disturbance term becomes conditional mean independent of the explanatory variables. The bias is hence present even in the absence of unobserved heterogeneity. We discuss instrumental variables estimation, using first-differences of the explanatory variables as instruments, as alternative estimation strategy. Monte Carlo simulations and an empirical application substantiate our theoretical results.

KEYWORDS:

• Absorbing state
• discrete-time hazard
• individual fixed effects
• instrumental variables estimation
• linear probability model

JEL Classification:

• C23
• C25
• C41

Acknowledgements

We would like to thank Daniel Kühnle, Helmut Herwartz, Simon Reif, Boris Hirsch, Claus Schnabel, Stefan Pichler, Jaap Abbring, Arthur van Soest, the members of the dggö Health Econometrics Working Group, and the participants in the 2019 German Stata Users Group Meeting, the Verein für Socialpolitik Annual Conference 2019, the RWI Research Seminar, the Nuremberg Research Seminar in Economics, the Tilburg School of Economics and Management Seminar: Econometrics and Statistics, the University of Zurich Research Seminar in Economics, and the Essen Health Economics Seminar for their valuable comments and suggestions. Excellent research assistance from Helene Könnecke, Sabrina Schubert, and Irina Simankova is gratefully acknowledged.

Disclosure Statement

The authors report there are no competing interests to declare.

Availability of data

The data that support the findings of empirical application of this study are openly available from the Inter-university Consortium for Political and Social Research at https://doi.org/10.3886/E113831V1, reference Brown and Laschever (2012/2019). We are happy to share the Stata^® code used for the empirical application and the simulations presented in the paper. The replications files (Stata^® code) are available in the supplementary material. (The master file Replication-Farbmacher&Tauchmann_2023-02-17.do calls all other do-files.)