Testing the fixed effects restrictions? A Monte Carlo study of Chamberlain’s Minimum Chi-Squared test

Chamberlain [Chamberlain, G., 1982. Multivariate regression models for panel data. Journal of Econometrics 18, 5–46] showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of dependent variables on all leads and lags of independent variables. Angrist and Newey [Angrist, J.D., Newey, W.K., 1991. Over-identification tests in earnings functions with fixed effects, Journal of Business & Economic Statistics 9, 317–323] suggested computing this test statistic as the degrees of freedom times the R2R2 from a regression of within residuals on all leads and lags of the exogenous variables. Despite the simplicity of these tests, they are not commonly used in practice. Instead, a Hausman [Hausman, J.A., 1978. Specification tests in econometrics, Econometrica 46, 1251–1271] test is used based on a contrast of the fixed and random effects specifications. We advocate the use of Chamberlain test if the researcher wants to settle on the FE specification and we check this test’s performance using Monte Carlo experiments and we apply it to the crime example of Cornwell and Trumbull [Cornwell, C., Trumbull, W.N., 1994. Estimating and economic model of crime with panel data. Review of Economics and Statistics 76, 360–366].