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

From   Kit Baum <>
Subject   Re: st: re: ivreg2: No validity tests if just-identified?
Date   Sat, 18 Apr 2009 09:06:00 -0400

I can reproduce the results below with

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   |
An Introduction to Stata Programming |
   An Introduction to Modern Econometrics Using Stata  |

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:


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":


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 =

Thus, in this case, the test cannot reject the null.

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