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st: Re: Tests of endogeneity by ivreg2


From   Kit Baum <baum@bc.edu>
To   KvingeTorunn <Torunn.Kvinge@fafo.no>
Subject   st: Re: Tests of endogeneity by ivreg2
Date   Sat, 5 May 2007 08:25:53 -0400

Dear Torunn

The ivendog command performs the same function as the endog() option and the orthog() option in ivreg2, as the ivreg2 help file illustrates:

(Equivalence of DWH endogeneity test when regressor is endogenous...)

. ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6)

. ivendog educ

(... endogeneity test using the endog option)

. ivreg2 lwage exper expersq educ (educ=age kidslt6 kidsge6), endog(educ)

(...and C-test of exogeneity when regressor is exogenous, using the orthog option)

. ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6), orthog(educ)


The hypothesis being tested is that the variable(s) being challenged (educ in the above example) could be treated as exogenous in order to derive consistent estimates. In the first and second examples above, it is treated as endogenous, and the estimated model is contrasted with one in which educ is treated as exogenous. The Durbin-Wu-Hausman test (see our 2003 Stata Journal paper) compares the IV and OLS estimates to determine whether they are 'close enough'. If they are, there is insufficient evidence to reject the null. In the third example, we estimate the model treating the variable as exogenous, and contrast it with a model in which it is endogenous--the same test from the opposite perspective, yielding the same test statistic.

This is not the same as the test of overidentifying restrictions ("Sargan - Hansen"), as you have noted.

The statistics differ with different specifications of instruments because the model being estimated takes account of y, X and Z (the matrix of instruments). If you vary Z in IV regression you get a different set of estimates, and any test statistics based on those estimates will differ.

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




Hello,

Could you please tell me more about the Ivendog test in ivreg2? This test
statstic differs with different instruments used, see below. Does a high
significance level mean that the variable is correctly instrumented? I thought
this was a test of the possible endogeinity of a regressor (whether the
regressor is correlated with the error term) and don't understand why the
statistics differ with different instruments.

When the equation is exactly identified, the Sargan statistic does not tell
anything about the validity of the instrument used, i.e. whether the
instrument is uncorrelated with the error term.

Sincerly,
Torunn Kvinge

. ivreg2 dbrutto dvar dkap (naceand = bruttolag2 h_2) if bnrlag2==bnr&major==0,noco

Instrumental variables (2SLS) regression
----------------------------------------

Number of obs = 27336
F( 3, 27333) = 28008.10
Prob > F = 0.0000
Total (centered) SS = 79149.00578 Centered R2 = 0.7542
Total (uncentered) SS = 79240.13053 Uncentered R2 = 0.7545
Residual SS = 19453.73944 Root MSE = .84

---------------------------------------------------------------------- --------
dbrutto | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------- +----------------------------------------------------------------
naceand | -.7821335 .4831546 -1.62 0.105 -1.729099 .1648322
dvar1 | 1.102227 .0041356 266.52 0.000 1.094121 1.110332
dkap | 1.100465 .0054046 203.62 0.000 1.089872 1.111057
---------------------------------------------------------------------- --------
Sargan statistic (overidentification test of all instruments): 3.604
Chi-sq(1) P-val = 0.05764
---------------------------------------------------------------------- --------
Instrumented: naceand
Instruments: bruttolag2 h_2 dvar1 dkap
---------------------------------------------------------------------- --------

. ivendog naceand

Tests of endogeneity of: naceand
H0: Regressor is exogenous
Wu-Hausman F test: 1.43488 F(1,27332) P- value = 0.23098
Durbin-Wu-Hausman chi-sq test: 1.43502 Chi-sq(1) P- value = 0.23095

. ivreg2 dbrutto dvar dkap (naceand = bruttolag2 ) if bnrlag2==bnr&major==0,noco

Instrumental variables (2SLS) regression
----------------------------------------

Number of obs = 32422
F( 3, 32419) = 32376.15
Prob > F = 0.0000
Total (centered) SS = 95034.69372 Centered R2 = 0.7475
Total (uncentered) SS = 95234.76917 Uncentered R2 = 0.7481
Residual SS = 23991.92712 Root MSE = .86

---------------------------------------------------------------------- --------
dbrutto | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------- +----------------------------------------------------------------
naceand | -3.34325 .5468789 -6.11 0.000 -4.415113 -2.271388
dvar1 | 1.100445 .0038692 284.41 0.000 1.092862 1.108029
dkap | 1.10401 .005045 218.83 0.000 1.094122 1.113898
---------------------------------------------------------------------- --------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
---------------------------------------------------------------------- --------
Instrumented: naceand
Instruments: bruttolag2 dvar1 dkap
---------------------------------------------------------------------- --------

. ivendog naceand

Tests of endogeneity of: naceand
H0: Regressor is exogenous
Wu-Hausman F test: 34.48155 F(1,32418) P- value = 0.00000
Durbin-Wu-Hausman chi-sq test: 34.44916 Chi-sq(1) P- value = 0.00000

. ivreg2 dbrutto dvar dkap (naceand = h_2 ) if bnrlag2==bnr&major==0,noco

Instrumental variables (2SLS) regression
----------------------------------------

Number of obs = 27336
F( 3, 27333) = 28031.26
Prob > F = 0.0000
Total (centered) SS = 79149.00578 Centered R2 = 0.7544
Total (uncentered) SS = 79240.13053 Uncentered R2 = 0.7547
Residual SS = 19437.07382 Root MSE = .84

---------------------------------------------------------------------- --------
dbrutto | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------- +----------------------------------------------------------------
naceand | -.13545 .5909122 -0.23 0.819 -1.293617 1.022717
dvar1 | 1.102789 .0041444 266.09 0.000 1.094666 1.110911
dkap | 1.099174 .0054448 201.87 0.000 1.088502 1.109845
---------------------------------------------------------------------- --------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
---------------------------------------------------------------------- --------
Instrumented: naceand
Instruments: h_2 dvar1 dkap
---------------------------------------------------------------------- --------

. ivendog naceand

Tests of endogeneity of: naceand
H0: Regressor is exogenous
Wu-Hausman F test: 0.02136 F(1,27332) P- value = 0.88380
Durbin-Wu-Hausman chi-sq test: 0.02136 Chi-sq(1) P- value = 0.88379

-----End Original Message-----

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