Hausman test

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The Hausman test is a test in econometrics named after Jerry Hausman. The test evaluates the significance of an estimators versus an alternative estimator.

If the linear model y = bX + e, where y is univariate and X is vector of regressors, b is a vector of coefficients and e is the error term. If we have two estimators for b:

we can derive the statistic

H = T(b₀ − b₁)'Var(b₀ − b₁) ^{− 1}(b₀ − b₁),

where T is the number of observations. This statistic has chi-square distribution with k (length of b) degrees of freedom.

[edit] Literature

Hausman, J. A. (1978). Specification Tests in Econometrics, Econometrica, Vol. 46, No. 6. (Nov., 1978), pp. 1251-1271.