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.
____________________________________________________
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University of Lausanne
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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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