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

From   John Antonakis <>
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:


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 = 0.0881

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

I tried this too with the Wooldridge dataset (use and get similar results to those you report in the Stata journal.

Thanks for the clarification.


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

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
> ivreg2 lw s expr (iq=med), endog(iq)
> Kit Baum | Boston College Economics and DIW Berlin | > An Introduction to Stata Programming | > An Introduction to Modern Econometrics Using Stata |
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