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2012-01-29
小弟才疏学浅,关于STATA下的Hausman检验有以下问题,希望各位大大不吝赐教!

1. Hausman检验的option中有constant一项,这是根据什么来选择是否添加呢?

2. 做Hausman fe re,得到的Chi2为负。添加了sigmamore或sigmaless后Chi2为正,但是前者拒绝H0而后者接受,这该如何判断?

谢谢各位大大!
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2012-2-10 11:46:02
自己回复一下,求解答哈~
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2012-2-10 11:58:42
楼主仔细看下hausman的帮助文件,详细会有收获

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 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
    --------------------------------------------------------------------------------------------------------------------------------------
    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 (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 [R] suest for details.

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2012-2-10 12:00:10
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).
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2012-4-8 22:20:35
sigmamore specifies that the covariance matrices be based on the estimated disturbance variance from the efficient estimator.
         
        sigmaless specifies that the covariance matrices be based on the estimated disturbance variance from the consistent estimator.

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