help hausman dialog: hausman -------------------------------------------------------------------------------
Title
[R] hausman -- Hausman specification test
Syntax
hausman name-consistent [name-efficient] [, options]
options description ------------------------------------------------------------------------- Main constant include estimated intercepts in comparison; default is to exclude alleqs use all equations to peform test; default is first equation only skipeqs(eqlist) skip specified equations when performing test equations(matchlist) associate/compare the specified (by number) pairs of equations force force performance of test, even though assumptions are not met df(#) use # degrees of freedom sigmamore base both (co)variance matrices on disturbance variance estimate from efficient estimator sigmaless base both (co)variance matrices on disturbance variance estimate from consistent estimator
Advanced tconsistent(string) consistent estimator column header tefficient(string) efficient estimator column header -------------------------------------------------------------------------
where name-consistent and name-efficient are names under which estimation results were saved via estimates store. A period (.) may be used to refer to the last estimation results, even if these were not already stored. Not specifying name-efficient is equivalent to specifying the last estimation results as ".".
Description
hausman performs Hausman's specification test. To use hausman, one has to perform the following steps.
(1) obtain an estimator that is consistent whether or not the hypothesis is true; (2) store the estimation results under a name-consistent using estimates store; (3) obtain an estimator that is efficient (and consistent) under the hypothesis that you are testing, but inconsistent otherwise; (4) store the estimation results under a name-efficient using estimates store; (5) use hausman to perform the test
hausman name-consistent name-efficient [, options]
The order of computing the two estimators may be reversed. You have to be careful though to specify to hausman the models in the order "always consistent" first and "efficient under H0" second. It is possible to skip storing the second model and refer to the last estimation results by a period (.).
hausman may be used in any context. The order in which you specify the regressors in each model does not matter, but it is your responsibility to assure that the estimators and models are comparable, and satisfy the theoretical conditions (see (1) and (3) above).
Options
+------+ ----+ Main +-------------------------------------------------------------
constant specifies that the estimated intercept(s) be included in the model comparison; by default, they are excluded. The default behavior is appropriate for models in which the constant does not have a common interpretation across the two models.
alleqs specifies that all the equations in the models be used to perform the Hausman test; by default, only the first equation is used.
skipeqs(eqlist) specifies in eqlist the names of equations to be excluded from the test. Equation numbers are not allowed in this context, as the equation names, along with the variable names, are used to identify common coefficients.
equations(matchlist) specifies, by number, the pairs of equations that are to be compared.
The matchlist in equations() should follow the syntax
#c:#e [,#c:#e[, ...]]
where #c(#e) is an equation number of the always-consistent (efficient under H0) estimator. For instance equations(1:1), equations(1:1, 2:2), or equations(1:2).
If equations() is not specified, then equations are matched on equation names.
equations() handles the situation in which one estimator uses equation names and the other does not. For instance, equations(1:2) means that equation 1 of the always-consistent estimator is to be tested against equation 2 of the efficient estimator. equations(1:1, 2:2) means that equation 1 is to be tested against equation 1 and that equation 2 is to be tested against equation 2. If equations() is specified, options alleqs and skipeqs are ignored.
force specifies that the Hausman test be performed, even though the assumptions of the Hausman test seem not to be met, for example, because the estimators were p-weighted.
df(#) specifies the degrees of freedom for the Hausman test. The default is the matrix rank of the variance of the difference between the coefficients of the two estimators.
sigmamore and sigmaless specify that the two covariance matrices used in the test be based on a common estimate of disturbance variance (sigma2).
sigmamore specifies that the covariance matrices be based on the estimated disturbance variance from the efficient estimator. This option provides a proper estimate of the contrast variance for so-called tests of exogeneity and overidentification in instrumental variables regression.
sigmaless specifies that the covariance matrices be based on the estimated disturbance variance from the consistent estimator.
These options can only be specified when both estimators save e(sigma) or e(rmse), or with command xtreg. e(sigma_e) is saved after command xtreg with options fe or mle. e(rmse) is saved after command xtreg with option re.
sigmamore or sigmaless are recommended when comparing fixed-effects and random-effects linear regression because they are much less likely to produce a nonpositive-definite differenced covariance matrix (although the tests are asymptotically equivalent whether or not one of the options is specified).
+----------+ ----+ Advanced +---------------------------------------------------------
tconsistent(string) and tefficient(string) are formatting options. They allow you to specify the headers of the columns of coefficients that default to the names of the models. These options will be primarily of interest to programmers.
Remark: An alternative to hausman
The assumption that one of the estimators is efficient (i.e., has minimal asymptotic variance) is a demanding one. It is violated, for instance, if your observations are clustered or pweighted, or if your model is somehow misspecified. Moreover, even if the assumption is satisfied, there may be a "small sample" problem with the Hausman test. Hausman's test is based on estimating the variance var(b-B) of the difference of the estimators by the difference var(b)-var(B) of the variances. Under the assumptions (1) and (3), var(b)-var(B) is a consistent estimator of var(b-B), but it is not necessarily positive definite "in finite samples", i.e., in your application. If this is the case, the Hausman test is undefined. Unfortunately, this is not a rare event. Stata supports a generalized Hausman test that overcomes both of these problems. See suest for details.
Examples
Typing
. xtreg lny educ age, fe . est store fixed . xtreg lny educ age sex, re . hausman fixed .
presents Hausman's specification test, which tests the appropriateness of the random-effects estimator (xtreg, re).
Typing
. mlogit travmode age gender income . est store all . mlogit travmode age gender income if travmode != 2 . est store partial . hausman partial all, alleqs constant
will perform a Hausman test for independence of irrelevant alternatives (IIA).
When one estimator uses equation names and the other does not, specify the equations() option to force the comparison. This is illustrated in the comparison of the OLS estimator and the estimator of the regress part of the heckman model
. regress mpg price . est store reg . heckman mpg price, sel(foreign=weight) . hausman reg ., eq(1:1)
Comparison of the probit and selection model of the heckman
. probit foreign weight . est store probit_for . heckman mpg price, sel(foreign=weight) . hausman probit_for ., eq(1:2)
Also see
Manual: [R] hausman
Online: lrtest, suest, test, xtreg, xtregar
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