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RE: st: RE: Hausman test for clustered random vs. fixed effects (again)


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   "Steven Archambault" <archstevej@gmail.com>, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Hausman test for clustered random vs. fixed effects (again)
Date   Thu, 2 Jul 2009 23:47:59 +0100

Steve,

> -----Original Message-----
> From: Steven Archambault [mailto:archstevej@gmail.com] 
> Sent: 02 July 2009 22:41
> To: statalist@hsphsun2.harvard.edu; Schaffer, Mark E
> Cc: austinnichols@gmail.com; Alfred.Stiglbauer@oenb.at
> Subject: Re: st: RE: Hausman test for clustered random vs. 
> fixed effects (again)
> 
> Mark,
> 
> I should have commented on this earlier, but when I eye the 
> coefficients for both the FE and RE results, I see that some 
> of them are quite different from one another. However, the 
> xtoverid result suggests RE is the one to use. Does anybody 
> see this as a problem? The numerator of the Hausman wald test 
> is the difference in coefficients of the two models. Is this 
> not missed in the xtoverid approach?

A few things here:

- The "xtoverid approach" in this case is **identical** to the traditional Hausman test in concept.  They are both vector-of-contrast tests, the contrast being between the 9 FE and RE coefficients.  The **only** difference in this case between the GMM stat reported by -xtoverid- and the traditional Hausman stat is that the former is cluster-robust.  In addition to the references on this point that I cited in my previous posting, you should also check out Ruud's textbook, "An Introduction to Classical Econometric Theory".

- The test has 9 degrees of freedom because 9 coefficients are being contrasted jointly.  This means that some can indeed be quite different, but if the others are very similar then a test of the joint contrasts can be statistically insignificant.

- The p-value reported by -xtoverid- is 10%, which a little worrisome.  If you were to do a vector-of-contrast tests focusing on a subset of coefficients instead of all 9 (not supported by -xtoverid- but do-able by hand), you could well find that you reject the null at 5% or 1% or whatever.  I don't think it's straightforward to conclude that RE is the estimator of choice.

Hope this helps.

Cheers,
Mark

> 
> I am posting my regression results to show what I am talking 
> about more clearly.
> 
> Thanks for your input.
> -Steve
> 
> 
> Fixed-effects (within) regression               Number of obs 
>      =       404
> Group variable: id_code_id                      Number of 
> groups   =        88
> 
> R-sq:  within  = 0.2304                         Obs per 
> group: min =         1
>        between = 0.4730                                       
>  avg =       4.6
>        overall = 0.4487                                       
>  max =         7
> 
>                                                 F(9,87)       
>      =      2.47
> corr(u_i, Xb)  = -0.9558                        Prob > F      
>      =    0.0148
> 
>                             (Std. Err. adjusted for 88 
> clusters in id_code_id)
> --------------------------------------------------------------
> ----------------
>              |               Robust
>        lnfd |      Coef.   Std. Err.      t    P>|t|     [95% 
> Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>    lags |  -.0267991   .0185982    -1.44   0.153     -.063765 
>    .0101668
>      lagk |   .0964571   .0353269     2.73   0.008     
> .0262411     .166673
>     lagp |   .2210296   .1206562     1.83   0.070    
> -.0187875    .4608468
> lagdr |  -.0000267   .0000251    -1.06   0.291    -.0000767   
>  .0000232
> laglurb |   .3483909   .1234674     2.82   0.006      .102986 
>    .5937957
>    lagtra |   .1109513   .1267749     0.88   0.384    
> -.1410275    .3629301
>      lagte |   .0067764    .004166     1.63   0.107    
> -.0015039    .0150567
>     lagcr |   .0950221   .0683074     1.39   0.168    
> -.0407463    .2307905
>     lagp |   .0343752   .1291378     0.27   0.791    
> -.2223001    .2910506
>        _cons |   4.316618   1.996618     2.16   0.033      
> .348124    8.285112
> -------------+------------------------------------------------
> ----------
> -------------+------
>      sigma_u |  .44721909
>      sigma_e |   .0595116
>          rho |  .98260039   (fraction of variance due to u_i)
> --------------------------------------------------------------
> ----------------
> 
> 
> 
> Random-effects GLS regression                   Number of obs 
>      =       404
> Group variable: id_code_id                      Number of 
> groups   =        88
> 
> R-sq:  within  = 0.1792                         Obs per 
> group: min =         1
>        between = 0.5074                                       
>  avg =       4.6
>        overall = 0.5017                                       
>  max =         7
> 
> Random effects u_i ~ Gaussian                   Wald chi2(9)  
>      =     48.97
> corr(u_i, X)       = 0 (assumed)                Prob > chi2   
>      =    0.0000
> 
>                              (Std. Err. adjusted for 
> clustering on id_code_id)
> --------------------------------------------------------------
> ----------------
>              |               Robust
>        lnfd |      Coef.   Std. Err.      z    P>|z|     [95% 
> Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>    lags |    -.01138   .0135958    -0.84   0.403    -.0380274 
>    .0152673
>      lagk |   .0115314   .0180641     0.64   0.523    
> -.0238735    .0469363
>     lagp |   .2551701    .119322     2.14   0.032     
> .0213033    .4890369
> lagdr |  -6.17e-06   .0000153    -0.40   0.686    -.0000361   
>  .0000238
> laglurb |   .0657802   .0153923     4.27   0.000     .0356119 
>    .0959486
>    lagtra |   .0022183   .0579203     0.04   0.969    
> -.1113034      .11574
>      lagte |   .0048012   .0016128     2.98   0.003       
> .00164    .0079623
>     lagcr |   .1051833    .045994     2.29   0.022     
> .0150368    .1953298
>     lagp |    .184373   .1191063     1.55   0.122    
> -.0490711    .4178171
>        _cons |   9.071133   .2322309    39.06   0.000     
> 8.615968    9.526297
> -------------+------------------------------------------------
> ----------
> -------------+------
>      sigma_u |  .10617991
>      sigma_e |   .0595116
>          rho |  .76095591   (fraction of variance due to u_i)
> --------------------------------------------------------------
> ----------------
> 
> . xtoverid;
> 
> Test of overidentifying restrictions: fixed vs random effects 
> Cross-section time-series model: xtreg re robust
> Sargan-Hansen statistic  14.684  Chi-sq(9)    P-value = 0.1000
> 
> 
> 
> 
> 
> On Sat, Jun 27, 2009 at 11:31 AM, Schaffer, Mark 
> E<M.E.Schaffer@hw.ac.uk> wrote:
> > Steve,
> >
> >> -----Original Message-----
> >> From: owner-statalist@hsphsun2.harvard.edu
> >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Steven 
> >> Archambault
> >> Sent: 27 June 2009 00:26
> >> To: statalist@hsphsun2.harvard.edu; austinnichols@gmail.com; 
> >> Alfred.Stiglbauer@oenb.at
> >> Subject: st: Hausman test for clustered random vs. fixed effects 
> >> (again)
> >>
> >> Hi all,
> >>
> >> I know this has been discussed before, but in STATA 10 
> (and versions 
> >> before 9 I understand) the canned procedure for Hausman test when 
> >> comparing FE and RE models cannot be run when the data 
> analysis uses 
> >> clustering (and by default corrects for robust errors in STATA 10).
> >> This is the error received
> >>
> >> "hausman cannot be used with vce(robust), vce(cluster cvar), or 
> >> p-weighted data"
> >>
> >> My question is whether or not the approach of using xtoverid to 
> >> compare FE and RE models (analyzed using the clustered and 
> by default 
> >> robust approach in STATA 10) is accepted in the literature. This 
> >> approach produces the Sargan-Hansen stat, which is typically used 
> >> with analyses that have instrumentalized variables and need an 
> >> overidentification test. For the sake of publishing I am 
> wondering if 
> >> it is better just not to worry about heteroskedaticity, and avoid 
> >> clustering in the first place (even though 
> heteroskedaticity likely 
> >> exists)? Or, alternatively one could just calculate the 
> Hausman test 
> >> by hand following the clustered analyses.
> >>
> >> Thanks for your insight.
> >
> > It's very much accepted in the literature.  In the -xtoverid- help 
> > file, see especially the paper by Arellano and the book by Hayashi.
> >
> > If you suspect heteroskedasticity or clustered errors, 
> there really is 
> > no good reason to go with a test (classic Hausman) that is 
> invalid in 
> > the presence of these problems.  The GMM -xtoverid- approach is a 
> > generalization of the Hausman test, in the following sense:
> >
> > - The Hausman and GMM tests of fixed vs. random effects 
> have the same 
> > degrees of freedom.  This means the result cited by Hayashi 
> (and due 
> > to Newey, if I recall) kicks in, namely...
> >
> > - Under the assumption of homoskedasticity and independent 
> errors, the 
> > Hausman and GMM test statistics are numerically identical.  
> Same test.
> >
> > - When you loosen the iid assumption and allow 
> heteroskedasticity or 
> > dependent data, the robust GMM test is the natural generalization.
> >
> > Hope this helps.
> >
> > Cheers,
> > Mark (author of -xtoverid-)
> >
> >> *
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> >>
> >
> >
> > --
> > Heriot-Watt University is a Scottish charity registered 
> under charity 
> > number SC000278.
> >
> >
> > *
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> >
> 


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