# st: re: 2SLS and Hausman test

 From Kit Baum To statalist@hsphsun2.harvard.edu Subject st: re: 2SLS and Hausman test Date Wed, 28 Nov 2007 12:12:53 -0500

Claude said

I am getting results from Stata (see below) using the following syntax :

ivreg2 ad pse bonus leverage pricebook lnsize blockown (roa = beta
corp_gov), endog (roa)

Could you give me brief explanations concerning the following questions :

The endog test does not reject the exogeneity of "roa". Is this test done
after considering the instrumental variables (beta and corp_gov)? In other
words, could I have used an OLS regression? Could other variables in my
model suffer from endogeneity? Is this testable?

How do I know if the IVs I used are correct? Can I re-use any of the
exogeneous variables as IVS for "roa"?

Thanks very much for your help,

Claude

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

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

Number of obs =
125
F( 7, 117) =
2.56
Prob > F =
0.0173
Total (centered) SS = .1726846849 Centered R2 =
0.1285
Total (uncentered) SS = .4273419954 Uncentered R2 =
0.6478
Residual SS = .1504946844 Root MSE =
.0347

------------------------------------------------------------------------ ------
absad | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
------------- +----------------------------------------------------------------
roa | .0005476 .0010238 0.53 0.593 -.001459
.0025542
pse | -.0104876 .0046072 -2.28
0.023 -.0195176 -.0014576
bonus | .0308946 .0310179 1.00 0.319 -.0298993
.0916885
leverage | -.0180951 .0078834 -2.30
0.022 -.0335463 -.0026439
pricebook | .0003074 .0014905 0.21 0.837 -.0026138
.0032287
lnsize | -.001135 .0009475 -1.20 0.231 -.002992
.000722
blockown | -.0001686 .0001738 -0.97 0.332 -.0005094
.0001721
_cons | .1115809 .0247104 4.52 0.000 .0631495
.1600123
------------------------------------------------------------------------ ------
Underidentification test (Anderson canon. corr. LM statistic):
11.877
Chi-sq(2) P-val =
0.0026
------------------------------------------------------------------------ ------
Weak identification test (Cragg-Donald Wald F statistic):
6.090
Stock-Yogo weak ID test critical values: 10% maximal IV size
19.93
15% maximal IV size
11.59
20% maximal IV size
8.75
25% maximal IV size
7.25
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------ ------
Sargan statistic (overidentification test of all instruments):
0.927
Chi-sq(1) P-val =
0.3357
-endog- option:
Endogeneity test of endogenous regressors:
0.103
Chi-sq(1) P-val =
0.7483
Regressors tested: roa
------------------------------------------------------------------------ ------
Instrumented: roa
Included instruments: pse bonus leverage pricebook lnsize blockown
Excluded instruments: beta corp_gov
------------------------------------------------------------------------ ------

Failure to reject the null of the Durbin-Wu-Hausman test -- that the additional orthogonality condition, roa not corr with error, is appropriate -- indicates that OLS is consistent. This test contrasts the IV regression you have run with the OLS form of the same equation. It does depend on ALL of the instruments' exogeneity (both included and excluded). No, you cannot reuse the included exogenous as instruments, for as the list above shows, they are already being used as instruments.

The Sargan statistic is also encouraging, in that you are not getting any indication that among the full set of instruments in the IV regression any are seriously violating the orthogonality conditions.

You may put more than one variable in the endog() list, but as the documentation indicates, the equation must be identified under both forms of the equation. Generally you would place the additional regressors to be questioned in the LHS of ( = ) and ensure that there are adequate instruments.

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

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