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

 From Christopher Baum To statalist@hsphsun2.harvard.edu Subject st: re: ivreg2: No validity tests if just-identified? Date Fri, 17 Apr 2009 14:54:21 -0400

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John said

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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?
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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.
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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.
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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.
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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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