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# Re: st: St: interpret the result of Hausman test

 From John Antonakis To statalist@hsphsun2.harvard.edu Subject Re: st: St: interpret the result of Hausman test Date Fri, 20 Apr 2012 12:21:14 +0200

Odd that your OLS estimates is not significant and the iv estimate is. Perhaps others can shed light on this.
```
```
Are you sure you are including the same control variables (exogenous) in each model?
```
What, precisely, is the syntax for the reg and ivreg2 models?

J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
__________________________________________

On 20.04.2012 11:37, Hoang Dinh Quoc wrote:
```
```Thank you very much for your explanation, Prof.

Yes, it seems to be quite different between iv and ols; for the variable x
(suspect var for endogenous), the model ols shows the coefficient is .03589
and the p-value 0.615; but the ivreg2 shows coefficient .3302337 and p value
0.020.
Did you mean that I would better take the ovreg2 for the final result?

Best,
Quoc

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis
Sent: Friday, April 20, 2012 3:53 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test

According to the endog test, your regressor is probably endogenous
(given that you are close to the commonly-determined critical value of p
<  .05) and thus requires instrumenting.  Are the estimates of iv and ols
very different? If they are, and if your instruments are strong , which
they seem to be judging form the Anderson test and the Stock-Yogo
critical values, you may be better off trusting the inefficient iv
estimate, than the efficient (but probably inconsistent) OLS estimate.

See: http://www.stata.com/statalist/archive/2012-03/msg01264.html

Best,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
__________________________________________

On 20.04.2012 10:18, Hoang Dinh Quoc wrote:
```
```Thanks. Below is what I got by ivreg2 y (x = z), endog(x). You talked
```
```about
```
```the p-value 0.0600, right? Does this mean that we can conclude no
endogeneity problem?

Best,
Quoc

Underidentification test (Anderson canon. corr. LM statistic):
49.520
Chi-sq(1) P-val =
```
```0.0000
----------------------------------------------------------------------------
```
```--
Weak identification test (Cragg-Donald Wald F statistic):
```
```53.345
```
```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
dentified)
-endog- option:
Endogeneity test of endogenous regressors:
```
```3.538
```
```                                                     Chi-sq(1) P-val =
```
```0.0600
```
```Regressors tested:    sc_tie_weak

```
```----------------------------------------------------------------------------
```
```--
Instrumented:         sc_tie_weak
Included instruments: sc_tie_strong sex income_cat_07 alter_SIOPs
```
```head_siops
```
```                        market_close ethnic headage leader hhknown
```
```access_cre
```
```                        Cre_Con mass_media Road_constraint red_gre
no_extension_contact _Idistrict_2 _Idistrict_3
_Idistrict_4 _Idistrict_5 _Idistrict_6 _Idistrict_7
Excluded instruments: loan_bank_job

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis
Sent: Friday, April 20, 2012 3:03 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test

No. I meant -endog- and not -orthog-.

Do you have the latest version of ivreg2?

. which ivreg2
*! ivreg2 3.1.04  19mar2012
*! authors cfb&   mes
*! see end of file for version comments

If not, updated your ivreg2 file:

ssc install ivreg2, replace

Then redo the iv-regression and see what you get.

Best,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
__________________________________________

On 20.04.2012 09:50, Hoang Dinh Quoc wrote:
```
```Dear Prof. Antonakis,

Thank you very much for your suggestion.

hausman one two, sigmamore
What does that give?

The result is below; I guess something went wrong with this result,
```
```right?
```
```

b = consistent under Ho and Ha; obtained from regress

B = inconsistent under Ha, efficient under Ho; obtained from
ivregress

Test:  Ho:  difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)

=    -3.33    chi2<0 ==>    model fitted on
```
```these
```
```                                           data fails to meet the
```
```asymptotic
```
```                                           assumptions of the Hausman
```
```test;
```
```                                           see suest for a generalized
```
```test
```
```
Your comment: "ivreg2 y (x = z), endog(x)". I guess you meant option
'orthog' right? Because endog did not work on my Stata; I am using Stata
```
```10.
```
```Below is the result; according to this result, as the P-value (0.0600) is
bigger than 0.5, I guess I can conclude x is not endogenous, right?

```
```----------------------------------------------------------------------------
```
```--
Sargan statistic (Lagrange multiplier test of excluded instruments):
3.538
Chi-sq(1) P-val =
0.0600
-orthog- option:
Sargan statistic (eqn. excluding suspect orthogonality conditions):
0.000
Chi-sq(0) P-val =
.
C statistic (exogeneity/orthogonality of suspect instruments):
3.538
Chi-sq(1) P-val =
0.0600

Best,

Quoc

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis
Sent: Thursday, April 19, 2012 8:42 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test

Do:

hausman one two, sigmamore

What does that give? If the hausman test is still NPD try:

ivreg2 y (x = z), endog(x)

Also, did you try it in sem as I suggested?

If the p value of the endogeneity test is<    .05 then x is endogenous.

However, if your sample is small the test might not have much power (so

I would be worried about endogeneity if<    .10). If you have good reason

to believe that x is endogenous then the iv estimator should be retained.

HTH,

J.

__________________________________________

Prof. John Antonakis

Faculty of Business and Economics

Department of Organizational Behavior

University of Lausanne

Internef #618

CH-1015 Lausanne-Dorigny

Switzerland

Tel ++41 (0)21 692-3438

Fax ++41 (0)21 692-3305

http://www.hec.unil.ch/people/jantonakis

Associate Editor

__________________________________________

On 19.04.2012 10:39, Hoang Dinh Quoc wrote:

```
```Dear Prof. Antonakis,
Thank you very much for your quick support.
I followed your suggestion:
"reg y x
est store one
ivregress 2sls y (x=z)
est store two
hausman one two"
And I got this result:
Test:  Ho:  difference in coefficients not systematic
chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=        3.31
Prob>chi2 =      0.0687
(V_b-V_B is not positive definite)
With is result, can I conclude that no endogeneity problem?
Thanks,
Best,
Hoang Dinh Quoc
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John
```
```Antonakis
```
```Sent: Thursday, April 19, 2012 3:23 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test
Hi:
I am not quite sure what you have done here.
If you want to do this "by hand" do an augmented regression:
http://www.stata.com/support/faqs/stat/endogeneity.html
Else, use the -endog- option in the user-written program, ivreg2,
available from ssc (i.e., ssc install ivreg2, replace), e.g. (for
dependent variable y, endogenous regressor x, and instrument z):
ivreg2 y (x = z), endog(x).
Or do the usual hausman test via Stata, e.g.,
reg y x
est store one
ivregress 2sls y (x=z)
est store two
hausman one two
Finally, you can do this in the new Stata command, -sem- using maximum
likelihood:
sem (y<-x) (x<-z), cov(e.y*e.x)
The test of the correlation between the disturbances is the Hausman
test, as we explain in detail here:
Antonakis, J., Bendahan, S., Jacquart, P.,&     Lalive, R. (2010). On
making causal claims: A review and recommendations. The Leadership
Quarterly, 21(6). 1086-1120.
http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf
For more basic explanations see:
Antonakis, J., Bendahan, S., Jacquart, P.,&     Lalive, R. (submitted).
Causality and endogeneity: Problems and solutions. In D.V. Day (Ed.),
The Oxford Handbook of Leadership and Organizations.
http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf
HTH,
J.
__________________________________________
Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis
Associate Editor
__________________________________________
On 19.04.2012 10:14, Hoang Dinh Quoc wrote:
>     Dear Statalist members,
>
>     I would like to ask you a question regarding the result of a
```
```Hausman
```
```test.
>
>     My question is, with this result, if I conclude that I have no
```
```problem of

```
```     >     endogeneity; in other words, I have no endogenous variable?
>
>     I followed these steps:
>     1. regress (OLS) to get a residual
>     2. predict weak_rest1
>     3. regress (OLS) using weak_rest1
>     4. regress 2sls using IV
>
>     Here is the result of the t test of the residual:
>     . test weak_res1
>
>      ( 1)  weak_res1 = 0
>
>            F(  1,   355) =    3.34
>                 Prob>     F =    0.0686
>
>     With is result, can I conclude that no endogeneity problem?
>
>     Thank you very much.
>
>     Best regards,
>     Hoang Dinh Quoc
>
>
>
>
>     *
>     *   For searches and help try:
>     *   http://www.stata.com/help.cgi?search
>     *   http://www.stata.com/support/statalist/faq
>     *   http://www.ats.ucla.edu/stat/stata/
*
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*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
*
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*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```
```*

*   For searches and help try:

*   http://www.stata.com/help.cgi?search

*   http://www.stata.com/support/statalist/faq

*   http://www.ats.ucla.edu/stat/stata/

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis
Sent: Thursday, April 19, 2012 8:42 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test

Do:

hausman one two, sigmamore

What does that give? If the hausman test is still NPD try:

ivreg2 y (x = z), endog(x)

Also, did you try it in sem as I suggested?

If the p value of the endogeneity test is<    .05 then x is endogenous.

However, if your sample is small the test might not have much power (so
I would be worried about endogeneity if<    .10). If you have good reason
to believe that x is endogenous then the iv estimator should be retained.

HTH,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
__________________________________________

On 19.04.2012 10:39, Hoang Dinh Quoc wrote:
```
```Dear Prof. Antonakis,

Thank you very much for your quick support.

I followed your suggestion:
"reg y x
est store one
ivregress 2sls y (x=z)
est store two
hausman one two"

And I got this result:

Test:  Ho:  difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=        3.31
Prob>chi2 =      0.0687
(V_b-V_B is not positive definite)

With is result, can I conclude that no endogeneity problem?

Thanks,
Best,
Hoang Dinh Quoc

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John
```
```Antonakis
```
```Sent: Thursday, April 19, 2012 3:23 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: St: interpret the result of Hausman test

Hi:

I am not quite sure what you have done here.

If you want to do this "by hand" do an augmented regression:

http://www.stata.com/support/faqs/stat/endogeneity.html

Else, use the -endog- option in the user-written program, ivreg2,
available from ssc (i.e., ssc install ivreg2, replace), e.g. (for
dependent variable y, endogenous regressor x, and instrument z):

ivreg2 y (x = z), endog(x).

Or do the usual hausman test via Stata, e.g.,

reg y x
est store one
ivregress 2sls y (x=z)
est store two
hausman one two

Finally, you can do this in the new Stata command, -sem- using maximum
likelihood:

sem (y<-x) (x<-z), cov(e.y*e.x)

The test of the correlation between the disturbances is the Hausman
test, as we explain in detail here:

Antonakis, J., Bendahan, S., Jacquart, P.,&     Lalive, R. (2010). On
making causal claims: A review and recommendations. The Leadership
Quarterly, 21(6). 1086-1120.
http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf

For more basic explanations see:

Antonakis, J., Bendahan, S., Jacquart, P.,&     Lalive, R. (submitted).
Causality and endogeneity: Problems and solutions. In D.V. Day (Ed.),
The Oxford Handbook of Leadership and Organizations.
http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf

HTH,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
__________________________________________

On 19.04.2012 10:14, Hoang Dinh Quoc wrote:
>     Dear Statalist members,
>
>     I would like to ask you a question regarding the result of a
```
```Hausman
```
```test.
>
>     My question is, with this result, if I conclude that I have no
```
```problem of
```
```     >     endogeneity; in other words, I have no endogenous variable?
>
>     I followed these steps:
>     1. regress (OLS) to get a residual
>     2. predict weak_rest1
>     3. regress (OLS) using weak_rest1
>     4. regress 2sls using IV
>
>     Here is the result of the t test of the residual:
>     . test weak_res1
>
>      ( 1)  weak_res1 = 0
>
>            F(  1,   355) =    3.34
>                 Prob>     F =    0.0686
>
>     With is result, can I conclude that no endogeneity problem?
>
>     Thank you very much.
>
>     Best regards,
>     Hoang Dinh Quoc
>
>
>
>
>     *
>     *   For searches and help try:
>     *   http://www.stata.com/help.cgi?search
>     *   http://www.stata.com/support/statalist/faq
>     *   http://www.ats.ucla.edu/stat/stata/

*
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*   http://www.ats.ucla.edu/stat/stata/

*
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*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```
```*
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```
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```
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*
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```
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```