Hausman Specification Test (FE vs RE)
Also known as: Hausman specification test, FE vs RE test, Durbin-Wu-Hausman test, Hausman Spesifikasyon Testi (FE vs RE)
The Hausman test is a specification test, introduced by Jerry A. Hausman in 1978, that decides between the fixed-effects (FE) and random-effects (RE) estimators in panel data models. The null hypothesis is that the random-effects estimator is consistent and efficient and should be preferred; the alternative is that random effects is inconsistent and fixed effects is required because the unit-specific effects are correlated with the explanatory variables.
Key highlights
- Provides a formal, widely accepted decision rule for the fixed-effects versus random-effects choice that is central to applied panel econometrics.
- Built directly on estimators you already compute, comparing the FE and RE coefficient vectors without needing an additional model.
- Has a clear asymptotic chi-square distribution, making the test statistic and its p-value easy to report and interpret.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use the Hausman test on panel (longitudinal) data with a continuous outcome once you have estimated both a fixed-effects and a random-effects model on the same specification, and you need a principled rule to choose between them. It assumes both models are correctly specified with no omitted variables, that under the null RE is consistent and efficient while FE is consistent but inefficient, and it relies on an asymptotic chi-square distribution, so a reasonable sample (at least about 50 observations) is needed. For small samples a bootstrap version of the test is recommended.
Strengths & limitations
- Provides a formal, widely accepted decision rule for the fixed-effects versus random-effects choice that is central to applied panel econometrics.
- Built directly on estimators you already compute, comparing the FE and RE coefficient vectors without needing an additional model.
- Has a clear asymptotic chi-square distribution, making the test statistic and its p-value easy to report and interpret.
- Relies on an asymptotic approximation, so it can be unreliable in small samples; a bootstrap Hausman test is preferable there.
- Assumes both models are correctly specified with no omitted variables, and a rejection can reflect general misspecification rather than only correlated effects.
- The covariance difference can be non-positive-definite in finite samples, occasionally yielding a negative or undefined statistic.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What does it mean if the Hausman test rejects the null?
Rejecting the null means the random-effects estimator is inconsistent because the unit-specific effects are correlated with the regressors. In that case you should report the fixed-effects estimates, which remain consistent even when that correlation is present.
Why choose random effects if fixed effects is always consistent?
Fixed effects is consistent but discards between-unit variation and is less efficient. When the null holds, random effects is consistent and efficient, giving smaller standard errors and allowing time-invariant regressors. The Hausman test tells you whether you can safely keep that efficiency.
Is the test reliable in small samples?
Not always. The statistic follows a chi-square distribution only asymptotically, so in short panels the approximation can be poor. A bootstrap Hausman test is recommended when the sample is small, and the Mundlak (1978) approach is a more flexible alternative.
What if the test statistic comes out negative?
A negative statistic can occur in finite samples when the difference between the FE and RE covariance matrices is not positive definite. It signals that the asymptotic assumptions are strained; a bootstrap version or a robust variant of the test is the appropriate response.
Sources
- 1.Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251–1271.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 1). Hausman Test. ScholarGate. https://scholargate.app/econometrics/hausman-test