Robust Hausman Specification Test
Heteroscedasticity- and Autocorrelation-Robust Hausman Specification Test · Also known as: robust hausman specification test, cluster-robust hausman test, Robust Hausman Testi
The Robust Hausman Test is a heteroscedasticity- and autocorrelation-robust version of the Hausman specification test, used to choose between fixed-effects and random-effects estimators in panel-data models. It builds on Hausman's 1978 test and the robust treatment of correlated effects developed by Arellano (1993).
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When to use it
Use this test with panel data when you have at least about 50 observations and need to choose between fixed- and random-effects specifications, and especially when the panel errors may be heteroscedastic or serially correlated so that the classical Hausman test is unreliable. It assumes a panel structure is available, a consistent fixed-effects estimator exists, and that robust (cluster-robust) standard errors are applied. It is not suitable for very small panels: with fewer than 20 units a wild bootstrap is preferred, and with fewer than 10 units a permutation test is the better choice.
Strengths & limitations
- Stays valid under heteroscedasticity and autocorrelation, where the classical Hausman test can break down.
- Gives a principled, data-driven choice between fixed- and random-effects panel models.
- Builds directly on a robust variance, so it tolerates clustered and non-constant error variance common in panel data.
- Requires a reasonably sized panel (at least about 50 observations) to be trustworthy.
- Becomes unreliable in very small panels: under 20 units a wild bootstrap is preferred, and under 10 units a permutation test.
- Depends on having a consistent fixed-effects estimator and on correctly specifying the robust covariance.
Frequently asked
How is the robust Hausman test different from the classical one?
The classical Hausman test assumes the random-effects estimator is fully efficient, so its variance is the simple difference of the two estimators' variances. Under heteroscedasticity or autocorrelation that assumption fails and the statistic can be unreliable or even negative. The robust version replaces that variance with a robust (cluster-robust) covariance, giving a valid Wald-type chi-square statistic.
What does a significant result mean?
A large, significant statistic rejects the random-effects assumption: the unit effects appear correlated with the predictors, so the fixed-effects estimator is the consistent choice. A non-significant result is consistent with random effects, which is also more efficient.
What sample size do I need?
At least about 50 observations for the test to be trustworthy. With fewer than 20 panel units a wild bootstrap is preferred, and with fewer than 10 units a permutation test is more appropriate.
Do I have to use robust standard errors?
Yes. The whole point of the robust variant is that the contrast between the fixed- and random-effects estimates is weighted by a robust covariance that allows for heteroscedasticity and autocorrelation, so robust (cluster-robust) standard errors must be applied.
Sources
- Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251-1271. DOI: 10.2307/1913827 ↗
- Arellano, M. (1993). On the Testing of Correlated Effects with Panel Data. Journal of Econometrics, 59(1-2), 87-97. DOI: 10.1016/0304-4076(93)90040-C ↗
How to cite this page
ScholarGate. (2026, June 1). Heteroscedasticity- and Autocorrelation-Robust Hausman Specification Test. ScholarGate. https://scholargate.app/en/statistics/robust-hausman-test
Which method?
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