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st: RE: Negative Hausman value?


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Negative Hausman value?
Date   Mon, 16 Oct 2006 12:31:33 +0100

Pavlos,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Pavlos C. Symeou
> Sent: 16 October 2006 11:58
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Negative Hausman value?
> 
> Dear Statalisters,
> 
> I attempt to compare between FE and RE transformations in 
> Stata using the hausman command, yet the chi^2 for the test 
> is negative (how can a square be negative?).

This can happen in finite samples, unless the same estimate of the error
variance is used throughout the H statistic - see, e.g., Baum et al.
(2003) in the Stata Journal or the Boston College working paper version.

This can generally be handled in Stata with the -sigmamore- or
-sigmaless- options to the -hausman- command.  What I am not sure of is
whether -xtreg- stores the right sigma internally in the right place
where -hausman- can make use of it.  I have a vague memory that in
earlier version of Stata, -xtreg- did not store sigma in a way that was
compatible with this option, but maybe that's been fixed.  You need to
check.

> I provide below 
> the commands that I use to estimate the models, store the 
> model's estimates and compare them with hausman. Stata 
> produces a note with the output which states that the 
> differenced variance matrix does not equal the number of 
> coefficients being tested.

This can happen when the RE estimator is able to estimate the
coefficient for a time-invariant variable that the FE sweeps out with
the within transformation.  In that case, the right number of degrees of
freedom is the smaller number (= number of coeffs of FE estimator not
including the constant).  You can force this with the -df- option of
-hausman-.

Hope this helps.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
 

> I have noticed that in the output 
> provided below and used in the calculations of the hausman 
> test, the yearly dummy "_Iyear_2004" is not included. Please 
> bear in mind that this yearly dummy is dropped in the initial 
> FE and RE model estimations because of collinearity.
> 
> I hope this helps previous threads to understand why we 
> encounter negative values in the hausman test.
> 
> Your feedback would be appreciated.
> 
> 
> 
> xi: xtreg f m lagm m2 lib_fixed lib_mobile t d1-d24 i.year, 
> fe est store fe
> xi: xtreg f m lagm m2 lib_fixed lib_mobile t d1-d24 i.year, 
> re hausman fe .
> 
> 
> Note: the rank of the differenced variance matrix (52) does 
> not equal the number of coefficients being tested (53); be 
> sure this is what you expect, or there may be problems 
> computing the test.  Examine the output of your estimators 
> for anything unexpected and possibly consider scaling your 
> variables so that the coefficients are on a similar scale.
> 
> ---- Coefficients ----
> 		(b)          	(B)            	(b-B)
> sqrt(diag(V_b-V_B))
> 		fe           	.          		Difference
> S.E.
> 
> m     		4.126995     	4.210606       	-.0836103
> .
> lagm    		-3.659119    	-3.719283         .060164
> .
> m2    		-.0035987    	-.0037695     	
> .0001707               .
> lib_fixed    	-.7893976    	-.6248966        	-.164501
> .
> lib_mobile     	.8347247     .	8552306        	
> -.020506               .
> t     		.1057887     	.0839587          	.02183
> .
> d1     		1.591341     1.425241        	
> .1661004               .
> d2      		1.73248     1.566447        	.1660332
> .
> d3      		1.33496     1.175148        	.1598117
> .
> d4     		1.163786     1.009243       	 
> .1545424               .
> d5     		1.130861     .9795363      	  
> .1513244               .
> d6      		1.53821     1.372196        	.1660132
> .
> d7     		1.787398     1.618786        	
> .1686119               .
> d8     		2.030746     1.871618        	
> .1591281               .
> d9     		2.329689     2.175233       	 
> .1544567               .
> d10     		2.474566     2.379384        	.0951821
> .
> d11     		2.530941     2.391151        	.1397903
> .
> d12     		2.702182     2.548153         	.154029
> .
> d13     		3.072654     2.923146       	 .1495087
> .
> d14     		3.200262     3.048934        	.1513281
> .
> d15     		3.434791     3.299563        	.1352286
> .
> d16     		4.161894     4.040091        	 .121803
> .
> d17     		4.693086     4.604569       	 .0885171
> .
> d18     		4.813464     4.765931       	 .0475332
> .
> d19     		4.874817     4.829945        	.0448717
> .
> d20     		4.763858     4.696174       	 .0676834
> .
> d21     		4.007245     3.914138        	.0931068
> .
> d22      		3.38889     3.261472       	 .1274171
> .
> d23     		2.073858     1.891516       	 .1823422
> .
> d24     		2.133198      1.90412       	 .2290783
> .
> _Iyear_1981     .1057826     .1715391      	 -.0657565      
>          .
> _Iyear_1982      .429569     .5114474    	 	  -.0818784
> .
> _Iyear_1983      .779513     .8763522    		   -.0968392
> .
> _Iyear_1984     1.270724     1.382196     	  -.1114715     
>           .
> _Iyear_1985     1.598364     1.731791      	 -.1334276      
>          .
> _Iyear_1986     1.724753      1.88993      	 -.1651769      
>          .
> _Iyear_1987     2.117019     2.295973      	 -.1789541      
>          .
> _Iyear_1988     2.463715     2.660981       	-.1972662       
>         .
> _Iyear_1989     2.808268     3.025018        	 -.21675               .
> _Iyear_1990     3.237237     3.452751      	 -.2155147      
>          .
> _Iyear_1991     3.653473     3.891927       	-.2384541       
>         .
> _Iyear_1992     4.006215     4.272213     	  -.2659985     
>           .
> _Iyear_1993     4.307211     4.585079      	 -.2778678      
>          .
> _Iyear_1994     4.561733     4.852067      	 -.2903343      
>          .
> _Iyear_1995     4.596097     4.878367     	  -.2822704     
>           .
> _Iyear_1996     4.680343     4.956875      	 -.2765316      
>          .
> _Iyear_1997     4.754712     4.997591      	  -.242879      
>          .
> _Iyear_1998     4.427386       4.6229        	-.195514               .
> _Iyear_1999     3.808497      3.95841       	-.1499126       
>         .
> _Iyear_2000     3.243333     3.354241       	 -.110908       
>         .
> _Iyear_2001     2.610181     2.692871      	 -.0826899      
>          .
> _Iyear_2002     1.963031     2.033931     	  -.0708998     
>           .
> _Iyear_2003     1.108533      1.15696       	-.0484275       
>         .
> 
> b = consistent under Ho and Ha; obtained from xtreg B = 
> inconsistent under Ha, efficient under Ho; obtained from xtreg
> 
> Test:  Ho:  difference in coefficients not systematic
> 
> chi2(52) = (b-B)'[(V_b-V_B)^(-1)](b-B) =   -30.11
> chi2<0 ==> model fitted on these data fails to meet the 
> asymptotic assumptions of the Hausman test; see suest for a 
> generalized test
> 
> 
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