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


From   John Antonakis <john.antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: re: ivreg2: No validity tests if just-identified?
Date   Fri, 17 Apr 2009 22:28:31 +0200

Hi Kit:

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.

I tried this too with the Wooldridge dataset (use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta) and get similar results to those you report in the Stata journal.

Thanks for the clarification.

Best,
John.
____________________________________________________

Prof. John Antonakis
Associate Dean Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland

Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305


____________________________________________________



On 17.04.2009 20:54, Christopher Baum wrote:
> <>
> John said
>
> Out of interest, if one could specify how the error terms are handled, then it is possible to test for over-identifying restrictions, correct? That is:
> y = b0 + b1x_hat + e1
> x = b11 + b12z + e12
> The covariance between e1 and e12 is estimated in ivreg, right? Hence the model is just-identified. Constraining the covariance to be orthogonal would provide for an overidentifying test. However, theoretically, estimating this covariance is necessary to account for the common cause of x and y not included in the model (so it would be an unreasonable restriction to make, unless the model is perfect). Right?
>
>
> As written, this is a recursive system (if we assume that the y equation contains x rather than 'xhat', whatever that may be). If the structural equation for y contains x, x is a stochastic linear function of z. If the errors on those two equations are distributed independently, there would be no problem with estimating the y equation with OLS. After all, what is exogenous to the y equation may well have some equation determining it.
>
> The more common setup for an IV problem would be to write y = f(x) and x = g(y, z), so that these are simultaneous equations. Then you have an endogeneity problem for each equation, and even if their errors are independently distributed, there is a correlation between regressor and error. You could estimate the y equation with IV, as it would be exactly ID using z. You could not estimate the x equation, as it would be unidentified by the order condition.
>
> I don't know how to constrain a covariance to be orthogonal; I presume what is meant is to constrain e1 and e12 to be orthogonal. But in the model as written, that would merely guarantee that OLS would be consistent.
>
> Although you cannot carry out a test of overid restrictions on an exactly ID equation, you can test whether IV methods are required for consistency (see Baum-Schaffer-Stillman, Stata Journal 7:4, 2007, preprint available below):
>
> use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta
> ivreg2 lw s expr (iq=med), endog(iq)
>
>
> Kit Baum | Boston College Economics and 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
>
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