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st: Re: short question


From   Kit Baum <baum@bc.edu>
To   emiliano.sironi@unibocconi.it
Subject   st: Re: short question
Date   Mon, 18 Aug 2008 17:08:12 -0400

Yes, you may do so. You are comparing exactly-identified IV (which by definition has a Sargan or J of zero) with 'heteroskedastic OLS' in that case:

. ivreg2 price (mpg = headroom )

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

Number of obs = 74
F( 1, 72) = 1.16
Prob > F = 0.2861
Total (centered) SS = 635065396.1 Centered R2 = 0.1828
Total (uncentered) SS = 3447834321 Uncentered R2 = 0.8495
Residual SS = 518998088.2 Root MSE = 2648

------------------------------------------------------------------------------
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------- +----------------------------------------------------------------
mpg | -141.0716 129.4705 -1.09 0.276 -394.8291 112.6859
_cons | 9169.701 2774.505 3.30 0.001 3731.772 14607.63
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 12.671
Chi-sq(1) P-val = 0.0004
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 14.876
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: mpg
Excluded instruments: headroom
------------------------------------------------------------------------------

. ivreg2 price (mpg = headroom ), endog(mpg)

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

Number of obs = 74
F( 1, 72) = 1.16
Prob > F = 0.2861
Total (centered) SS = 635065396.1 Centered R2 = 0.1828
Total (uncentered) SS = 3447834321 Uncentered R2 = 0.8495
Residual SS = 518998088.2 Root MSE = 2648

------------------------------------------------------------------------------
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------- +----------------------------------------------------------------
mpg | -141.0716 129.4705 -1.09 0.276 -394.8291 112.6859
_cons | 9169.701 2774.505 3.30 0.001 3731.772 14607.63
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 12.671
Chi-sq(1) P-val = 0.0004
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 14.876
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
-endog- option:
Endogeneity test of endogenous regressors: 0.721
Chi-sq(1) P-val = 0.3957
Regressors tested: mpg
------------------------------------------------------------------------------
Instrumented: mpg
Excluded instruments: headroom
------------------------------------------------------------------------------


In this case the large p-val shows that the null hypothesis that the endogenous regressors are orthogonal to the error term cannot be rejected, and IV estimation is not required.

You could reach the same conclusion with -ivendog- after the original estimation:

. ivendog

Tests of endogeneity of: mpg
H0: Regressor is exogenous
Wu-Hausman F test: 0.69889 F(1,71) P-value = 0.40596
Durbin-Wu-Hausman chi-sq test: 0.72132 Chi-sq(1) P-value = 0.39571


Cheers
Kit

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Aug 18, 2008, at 13:04 , Emiliano Sironi wrote:


Dear professor,
I'm a Ph.D. student from bocconi university (milan, italy) and I've just written to you few months ago to ask about your routine ivreg2 in stata. I'm writing a paper on a topic of law and economics and I bought your book "An introduction to the modern econometrics using stata". In page 211-213 (chapter 8.11) you described tests for endogeneity of regressors. The main topic illustrated in the chapter is the Durbin-Wu-Hausman test, but this test is not allowed for clustered or p-weighted data, according to Stata Program instructions.
In the chapter and in your paper on Stata Press (with Schaffer and Stillman), you present, as an alternative, the C statistic by Hansen, Sargan, Basmann which is perfectly available in my case.
The question is...in my model I have only one endogenous variable (x) with only one excluded instrument (z). Can I use the C statistic in order to test the endogeneity of x? The approach would be similar to that used at page 213, but in your example the model is overidentified.
Sorry if I've written in August, but your kindness in answering to the reasercher's questions is known among my collegues!
Best wishes,
Emiliano




--

Emiliano Sironi
Dipartimento di Scienze delle Decisioni
UniversitÓ "L. Bocconi"
Via Roentgen, 1 - Piano 3░ - Stanza D1-05
20135 Milano
Tel: +39 02 5836 5365
e-mail: emiliano.sironi@unibocconi.it



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