<>
I can reproduce the results below with
use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta
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 | 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
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:
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.
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