- Hausman test
The Hausman test is a statistical test in
econometrics named afterJerry Hausman . The test evaluates the significance of anestimator versus an alternativeestimator . Per Hausman, only overidentifying restrictions (assumptions) can be tested (Test of Identifying Restrictions). [ [http://economics.about.com/od/economicsglossary/g/testir.htm economics.about.com] Accessed June 18, 2008.]Details
If the linear model "y" = "bX" + "e", where "y" is
univariate and "X" is vector ofregressor s, "b" is a vector of coefficients and "e" is theerror term . We have two estimators for "b": "b"0 and "b"1. Under thenull hypothesis , both of these estimators are consistent, but "b"1 is more efficient (has smaller asymptotic variance) than "b"0. Under thealternative hypothesis , one or both of these estimators is inconsistent.We can derive the
statistic ::
where "T" is the number of observations. This statistic has
chi-square distribution with "k" (length of "b") degrees of freedom. You can find more about the "χ"2 (chi-square distribution ) distribution at the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SOCR Resource Distributions] .If we reject the null hypothesis, one or both of the estimators is inconsistent. This test can be used to check for the endogeneity of a variable (by comparing IV estimates to OLS estimates). It can also be used to check the validity of extra instruments by comparing IV estimates using a full set of instruments "Z" to IV estimates using a proper subset of "Z". Note that in order for the test to work in the latter case, we must be certain of the validity of the subset of "Z" and that subset must have enough instruments to identify the parameters of the equation.
References
*Hausman, J. A. (1978). "Specification Tests in Econometrics", Econometrica, Vol. 46, No. 6. (Nov., 1978), pp. 1251-1271.
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