On the Proper Computation of the Hausman Test Statistic in Standard Linear Panel Data Models: Some Clarifications and New Results

We provide new analytical results for the implementation of the Hausman specification test statistic in a standard panel data model, comparing the version based on the estimators computed from the untransformed random effects model specification under Feasible Generalized Least Squares and the one computed from the quasi-demeaned model estimated by Ordinary Least Squares. We show that the quasi-demeaned model cannot provide a reliable magnitude when implementing the Hausman test in a finite sample setting, although it is the most common approach used to produce the test statistic in econometric software. The difference between the Hausman statistics computed under the two methods can be substantial and even lead to opposite conclusions for the test of orthogonality between the regressors and the individual-specific effects. Furthermore, this difference remains important even with large cross-sectional dimensions as it mainly depends on the within-between structure of the regressors and on the presence of a significant correlation between the individual effects and the covariates in the data. We propose to supplement the test outcomes that are provided in the main econometric software packages with some metrics to address the issue at hand.