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st: How to run a chow test for endogenous variables

 From Yuval Arbel To statalist Subject st: How to run a chow test for endogenous variables Date Sat, 5 May 2012 19:19:27 +0300

```Dear statalisters,

I appreciate very much your assistance in the following question.

I ran a 3sls regression for a system of two equations. The system
includes two endogenous variables (cesarean and private_dum) and the
sample includes two groups (yeshiva0 and yeshiva1).

I tried to run a Chow test to compare the coefficients of the two

http://www.stata.com/support/faqs/stat/chow3.html

and I defined the following variables:

gen yeshiva0=0
replace yeshiva0=1 if (jewish==1 & yeshiva==0) | muslim==1
gen yeshiva1=0
replace yeshiva1=1 if (jewish==1 & yeshiva==1) | muslim==1

gen private0=yeshiva0*private_dum
gen private1=yeshiva1*private_dum
gen children0=yeshiva0*former_children1
gen children1=yeshiva1*former_children1
gen age0=yeshiva0*mother_age2
gen age1=yeshiva1*mother_age2
gen cesarean0=yeshiva0*cesarean
gen cesarean1=yeshiva1*cesarean
gen usa0=yeshiva0*mother_usa
gen usa1=yeshiva1*mother_usa
gen ysm0=yeshiva0*ysm
gen ysm1=yeshiva1*ysm

The problem is that if I try to combine private0 and private1 (and
cesarean0 and cesarean1) the algorithm treats these variables as
exogenous and reverses the sign of the coefficient of private_dum from
negative to positive - as if the estimate is a simple ols instead of
3sls. Based on the Wu-Hausman test, it seems the 3sls is supported
statistically.

My question is: does anyone have an idea how to carry out the Chow
test while accounting for the endogeneity between cesarean and
private_dum?

Here is a detailed output:

. reg3 (cesar:cesarean = yeshiva0 private_dum children0
c.children0#c.children0 age0 yeshiva1 children1 c.children1
> #c.children1 age1,noconstant) (private: private_dum=yeshiva0 cesarean usa0 canada0 ysm0 yeshiva1 usa1 canada1 ysm
> 1, noconstant) if jewish==1 | muslim==1, noconstant 3sls

Three-stage least-squares regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
cesar           24773      9    .2848849    0.0828    3487.71   0.0000
private         24773      9    .2484733    0.0885    3284.34   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
cesar        |
yeshiva0 |   .2005305   .0097253    20.62   0.000     .1814693    .2195917
private_dum |  -.1368681   .0306297    -4.47   0.000    -.1969012    -.076835
children0 |  -.0196644   .0042478    -4.63   0.000    -.0279899   -.0113388
|
c.children0#|
c.children0 |    .000097   .0002631     0.37   0.712    -.0004187    .0006126
|
age0 |   .0118617   .0011359    10.44   0.000     .0096353    .0140881
yeshiva1 |   .1539818   .0052103    29.55   0.000     .1437698    .1641938
children1 |  -.0302777   .0020532   -14.75   0.000    -.0343019   -.0262535
|
c.children1#|
c.children1 |   .0014059   .0001736     8.10   0.000     .0010656    .0017462
|
age1 |   .0109493   .0005162    21.21   0.000     .0099376    .0119611
-------------+----------------------------------------------------------------
private      |
yeshiva0 |  -.0455058   .0075655    -6.01   0.000    -.0603338   -.0306777
cesarean |   .3621419   .0350277    10.34   0.000     .2934889     .430795
usa0 |   .2123353   .0296337     7.17   0.000     .1542543    .2704163
canada0 |   .4636214   .0878011     5.28   0.000     .2915344    .6357084
ysm0 |   .0065901   .0304892     0.22   0.829    -.0531676    .0663477
yeshiva1 |    .020335   .0032178     6.32   0.000     .0140283    .0266417
usa1 |   .2161742    .006092    35.48   0.000     .2042341    .2281143
canada1 |   .1860172   .0203964     9.12   0.000      .146041    .2259934
ysm1 |  -.0265531   .0111081    -2.39   0.017    -.0483245   -.0047816
------------------------------------------------------------------------------
Endogenous variables:  cesarean private_dum
Exogenous variables:   yeshiva0 children0 c.children0#c.children0 age0
yeshiva1 children1 c.children1#c.children1 age1 usa0 canada0 ysm0 usa1
------------------------------------------------------------------------------

. test [cesar]yeshiva0=[cesar]yeshiva1

( 1)  [cesar]yeshiva0 - [cesar]yeshiva1 = 0

chi2(  1) =   16.34
Prob > chi2 =    0.0001

Yours sincerely,
Yuval

--
Dr. Yuval Arbel