Bias Corrections for Two-Step Fixed Effects Panel Data Estimators

53 Pages Posted: 18 Apr 2007

See all articles by Iván Fernández‐Val

Iván Fernández‐Val

Boston University - Department of Economics

Francis Vella

Georgetown University; IZA Institute of Labor Economics

Date Written: March 2007


This paper introduces bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These include limited dependent variable models with both unobserved individual effects and endogenous explanatory variables, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time variant heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control function from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control function accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two step nature of the procedure. As these two step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.

Keywords: panel data, two-step estimation, endogenous regressors, fixed effects, bias, union premium

JEL Classification: C23, J31, J51

Suggested Citation

Fernandez-Val, Ivan and Vella, Francis, Bias Corrections for Two-Step Fixed Effects Panel Data Estimators (March 2007). Available at SSRN: or

Ivan Fernandez-Val

Boston University - Department of Economics ( email )

270 Bay State Road
Boston, MA 02215
United States


Francis Vella (Contact Author)

Georgetown University ( email )

Washington, DC 20057
United States
202-687-5573 (Phone)


IZA Institute of Labor Economics

Schaumburg-Lippe-Str. 7 / 9
Bonn, D-53072

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