Panel Hausman Test
Also known as: Hausman endogeneity test, Wu-Hausman test, fixed-vs-random effects test, Hausman chi-squared test
The Hausman specification test for panel data determines whether individual-specific effects are correlated with the regressors — a correlation that would make the random effects estimator inconsistent. A statistically significant result favours the fixed effects model; a non-significant result supports the more efficient random effects model.
Key highlights
- Provides a formal, objective statistical criterion for choosing between fixed and random effects rather than relying on subjective judgment.
- Computationally simple: requires only the two sets of estimates and their covariance matrices.
- Has a known asymptotic chi-squared distribution under the null, making inference straightforward.
- Directly tests the key identifying assumption of the random effects model — orthogonality of individual effects and regressors.
- Widely implemented in all major econometric software (Stata, R, Python, EViews).
Intuition
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How it works
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When to use it
Apply the Hausman test after estimating a panel model when you are uncertain whether to use fixed or random effects. It is appropriate when the panel contains enough within-unit variation to estimate fixed effects reliably and the number of time periods is not too small. Do not use it when all regressors are time-invariant (fixed effects cannot identify them), when the panel is very short (T = 2 or 3), when the robust or clustered version of the test is not available and errors are heteroscedastic, or when theoretical reasoning already strongly mandates one specification (e.g., a designed experiment favours random effects; a self-selected cross-section favours fixed effects).
Strengths & limitations
- Provides a formal, objective statistical criterion for choosing between fixed and random effects rather than relying on subjective judgment.
- Computationally simple: requires only the two sets of estimates and their covariance matrices.
- Has a known asymptotic chi-squared distribution under the null, making inference straightforward.
- Directly tests the key identifying assumption of the random effects model — orthogonality of individual effects and regressors.
- Widely implemented in all major econometric software (Stata, R, Python, EViews).
- The classical version of the test is invalid when errors are heteroscedastic or clustered; a robust Hausman test or a regression-based Mundlak test is required in those cases.
- The test has low power in short panels (small T) or when within-unit variation is limited, potentially failing to detect endogeneity that is present.
- A rejection does not identify which specific regressor is endogenous — further investigation is needed.
- The test cannot be applied to time-invariant regressors, which disappear under fixed effects.
Common pitfalls
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Applications
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Frequently asked
What does rejecting the Hausman test mean?
A rejection (small p-value) indicates that the fixed effects and random effects estimates differ systematically. This implies that the unobserved individual-specific effects are correlated with at least one regressor, making the random effects estimator inconsistent. You should use the fixed effects model.
What should I do if the Hausman test statistic is negative?
A negative test statistic signals that the estimated covariance matrix difference is not positive semi-definite, often due to heteroscedasticity. Use the robust regression-based version of the test (Mundlak approach) or a bootstrap Hausman test instead of the classical form.
Can I run the Hausman test if my panel has time-invariant variables?
Not directly, because fixed effects sweeps out time-invariant variables. The test can only be applied to the subset of time-varying regressors. For time-invariant variables consider the Hausman-Taylor estimator or a correlated random effects approach.
Is the Hausman test the only way to choose between FE and RE?
No. The Mundlak (1978) auxiliary regression test is a flexible alternative that is robust to heteroscedasticity. Correlated random effects models (Chamberlain 1982) also test the same hypothesis. Theoretical reasoning about whether individual effects are a random draw from a population or fixed parameters is equally important.
How many degrees of freedom does the Hausman statistic have?
The degrees of freedom equal the number of time-varying regressors included in the test — typically all regressors except the constant and time-invariant variables.
Sources
- 1.Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46(6), 1251–1271.
- 2.Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.ISBN 978-0262232586
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Cite this page
ScholarGate. (2026, June 3). Panel Hausman Test. ScholarGate. https://scholargate.app/econometrics/panel-hausman-test