Hausman Test
A statistical test used to evaluate the consistency of an estimator, often employed to choose between fixed effects and random effects models or to detect endogeneity.
What is Hausman Test?
The Durbin-Wu-Hausman test compares two estimators: one that is consistent under both the null and alternative hypotheses, and one that is efficient (has smaller variance) under the null but inconsistent under the alternative. If the two estimates differ significantly, the null hypothesis is rejected, indicating that the more efficient estimator is biased (e.g., due to endogeneity or correlated unobserved heterogeneity).
Why Hausman Test Matters
The test helps researchers formally justify their modeling choices. In panel data, it dictates whether they can safely use a random-effects model (which is more efficient) or if they must use a fixed-effects model to account for unobserved variables that are correlated with the predictors.
Example
A researcher analyzing panel data on firm profitability over time runs the Hausman test. The test yields a significant p-value, prompting the researcher to reject the random-effects model in favor of a fixed-effects model to control for time-invariant, firm-specific characteristics.
Common Mistakes
- Relying solely on the Hausman test without considering its low statistical power in small samples, which might lead to falsely accepting the null hypothesis.
- Applying the test without ensuring that the standard errors are robust to heteroskedasticity or clustering, which can invalidate the test statistic.