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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 perform 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
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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 ".".
Menu
Statistics > Postestimation > Tests > Hausman specification test
Description
hausman performs Hausman's specification test. To use hausman, perform the following steps.
(1) obtain an estimator that is consistent whether or not the hypothesis is true;
(2) store the estimation results under name-consistent by 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 name-efficient by 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 you must ensure that the estimators and models are comparable and that they 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, because 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, the alleqs and skipeqs options 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 pweighted or the data were clustered.
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 be specified only when both estimators save e(sigma) or e(rmse), or with the
xtreg command. e(sigma_e) is saved after the xtreg command with the fe or mle option. e(rmse) is
saved after the xtreg command with the re option.
sigmamore or sigmaless are recommended when comparing fixed-effects and random-effects linear
regression because they are much less likely to produce a non-positive-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 of interest primarily to programmers.
Remark: An alternative to hausman
The assumption that one of the estimators is efficient (that is, 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", that is, 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 [R] suest for details.
Examples
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Setup
. webuse nlswork4
. xtreg ln_wage age msp ttl_exp, fe
. estimates store fixed
. xtreg ln_wage age msp ttl_exp, re
Test the appropriateness of the random-effects estimator (xtreg, re)
. hausman fixed ., sigmamore
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