Testing the Fixed Effects Restrictions? A Monte Carlo Study of Chamberlain's Minimum Chi-Squared Test

Chamberlain (1982) showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of dependent variableson all leads and lags of independent variables. Angrist and Newey (1991) suggested computing this test statistic as the degrees of freedom times the R2 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 (1978) test is used based on a contrast of the fixed and random effects specifications. We advocate the use of the Chamberlain (1982) test if the researcher wants to settle on the FE specifications, we check this test's performance using Monte Carlo experiments, and we apply it to the crime example of Cornwell and Trumbull (1994).