Re: st: re: ivreg2: No validity tests if just-identified?

[John Antonakis <john.antonakis@unil.ch>]

Hi Kit:

Thanks for clarifying further; I agree with your reasoning.

As for your question, yes, the estimates change substantially for the 
second-stage equation (the first stage are, of course, unchanged):

                                                   Two-Tailed
                   Estimate       S.E.  Est./S.E.    P-Value
 LW       ON
   IQ                 0.004      0.001      3.805      0.000
   S                  0.094      0.007     13.667      0.000
   EXPR               0.046      0.006      7.231      0.000
   Cons               3.911      0.110     35.652      0.000


This is what they were before (with the error estimated):
LW       ON
   IQ                 0.022      0.012      1.815      0.070
   S                  0.040      0.038      1.050      0.294
   EXPR               0.051      0.008      6.280      0.000
   Cons               2.789      0.771      3.618      0.000

This is what ivreg2 with liml gives:


	
	
	
	
	
	
lw 	Coef. 	Std. Err. 	z 	P>z 	[95% Conf. 	Interval]

	
	
	
	
	
	
iq 	0.02194 	0.012088 	1.81 	0.07 	-0.00175 	0.045632
s 	0.039556 	0.037688 	1.05 	0.294 	-0.03431 	0.113424
expr 	0.050968 	0.008116 	6.28 	0 	0.03506 	0.066875
_cons 	2.789476 	0.771075 	3.62 	0 	1.278197 	4.300754


Best,
John.

____________________________________________________

Prof. John Antonakis
Associate Dean Faculty of Business and Economics
University of Lausanne
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On 18.04.2009 15:06, Kit Baum wrote:
> <>
> I can reproduce the results below with
>
> > use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta
> > ivreg2 lw s expr (iq=med), endog(iq) liml first
>
> using LIML rather than FIML. Indeed, your intuition that restricting 
> the two equations' errors to be uncorrelated gives rise to the 
> Wu-Hausman endogeneity statistic is correct. However in terms of 
> semantics I would not describe the restriction of the equations' error 
> covariance as an 'identifying restriction'. It is certainly true that 
> restrictions on error covariances may be used to identify equations, 
> but in this case the equation is already identified by the order and 
> rank conditions. If you impose that restriction a priori, it seems to 
> me that you're using a different estimation procedure. Do the results 
> from the constrained estimation differ from OLS results for the LW 
> equation?
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |   
> http://ideas.repec.org/e/pba1.html
>                               An Introduction to Stata Programming  
> |   http://www.stata-press.com/books/isp.html
>    An Introduction to Modern Econometrics Using Stata  |   
> http://www.stata-press.com/books/imeus.html
>
>
>
> On Apr 18, 2009, at 02:33 , John wrote:
>
> > Thanks for the note.  I like the endog option and I see what your endog
> > test is doing--it seems to me that it is constraining the residual
> > covariance to zero (this is what I meant by overidentifying test--which
> > I see is not one in the classical sense). As for constraining the
> > residuals I can accomplish this (and obtain a similar result to what
> > your endog test does) using Mplus to estimate the system of equations
> > you note below. The estimator is maximum likelihood estimation.
> > Estimating the covariance I obtain:
> >
> >
> >                     Estimate       S.E.  Est./S.E.    P-Value
> >
> > IQ       ON
> >    S                 2.876      0.205     14.022      0.000
> >    EXPR        -0.239      0.207     -1.153      0.249
> >    MED           0.482      0.164      2.935      0.003
> >    Cons         60.467      2.913     20.759      0.000
> >
> > LW       ON
> >    IQ              0.022      0.012      1.815      0.070
> >    S                0.040      0.038      1.050      0.294
> >    EXPR        0.051      0.008      6.280      0.000
> >    Cons          2.789      0.771      3.618      0.000
> >
> > Note: I explicitly correlated the residuals of IQ and LW and obtained:
> >
> > LW       WITH
> >    IQ                -2.412      1.638     -1.472      0.141
> >
> > (this residual covariance is not different from zero)
> >
> > Also, the model is just-identified, just as in ivreg2:
> >
> > TESTS OF MODEL FIT
> >
> > Chi-Square Test of Model Fit
> >
> >          Value                              0.000
> >          Degrees of Freedom                     0
> >          P-Value                           0.0000
> >
> >
> > These estimates are pretty much the same as the ivreg2 estimates from 
> > Stata.
> >
> > Now, when I constrain the covariance between the two error terms of the
> > endogenous variables to be to be zero, I have what I termed "an
> > overidentifying restriction":
> >
> > TESTS OF MODEL FIT
> >
> > Chi-Square Test of Model Fit
> >
> >          Value                              2.914
> >          Degrees of Freedom                     1
> >          P-Value                           0.0878
> >
> > This test is is about the same as your endog test:
> >
> > Endogeneity test of endogenous regressors:     2.909
> >                                                   Chi-sq(1) P-val =
> > 0.0881
> >
> > Thus, in this case, the test cannot reject the null.
>
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