The Hausman Test for Fixed vs Random Effects

Random effects is attractive because it uses between-entity variation and can retain time-invariant characteristics. Its efficiency gain is worthless if a bank's persistent unobserved quality is correlated with capital, funding, or other regressors. The Hausman test makes this trade-off testable by comparing a robust but potentially less efficient estimator with the efficient estimator that rests on the stronger orthogonality assumption.

• state the null and alternative of the FE--RE Hausman test;
• compute the statistic from the coefficient and covariance differences;
• interpret rejection as evidence against RE consistency;
• explain why non-rejection is not proof that RE's economic assumption is true;
• separate the FE--RE Hausman test from an endogeneity Hausman test involving IV.

1. The estimator comparison
2. A test is not a substitute for model design