The Basics of the Mundlak and Chamberlain Projections

Author(s)/Creator(s)

Badi H. Baltagi, Syracuse UniversityFollow
Tom Wansbeek, University of GroningenFollow

Description/Abstract

One of the best-known results in panel data econometrics, due to Mundlak (1978), is the equality of the random-effects and fixed-effects estimators when the individual effects are correlated with the means over time of the regressors. Chamberlain (1980) showed that the same result holds when the individual effects are correlated with the regressors for all moments in time separately. In this chapter, we review basic elements of the Mundlak and Chamberlain projections. We emphasize the simplicity that is often obtained when the model is transformed into the within and between-model, following Arellano (1993). Topics that we discuss include the augmented regression model, the Hausman test, minimum-distance estimation and its link to GMM, unbalanced data, and higher-dimensional data.

Document Type

Working Paper

Date

9-8-2025

Keywords

Econometrics

Language

English

Series

Working Papers Series

Disciplines

Econometrics | Economics

ISSN

1525-3066

Additional Information

CPR Working Paper No. 272

Recommended Citation

Baltagi, Badi H. and Wansbeek, Tom, "The Basics of the Mundlak and Chamberlain Projections" (2025). Center for Policy Research. 505.
https://surface.syr.edu/cpr/505

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.