The Basics of the Mundlak and Chamberlain Projections

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.