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# Re: st: comparing equality of coefficients from two subsamples

 From Mario Jose To statalist@hsphsun2.harvard.edu Subject Re: st: comparing equality of coefficients from two subsamples Date Wed, 20 Feb 2013 22:10:42 +0000

```Thank you Rebecca for the links, they were very useful to understand
the previous Jay's comment.
I have implemented the strategy of Bill Gould (allowing for different
variances), but it appeared the message of error "weight must be
constant within id"... Anyway I do not want to introduce interactions
with all independent variables but to only one.

Below I expose what the specific problem I have.

I have a panel sample of firms, and in the middle  of the period
(2004) it was implemented  by the government a specific fiscal
measure. I want to test whether this measure had impacts on the
profits reported by firms. As I think that the measure had impacts in
a specific subsample of firms, I divided the sample in two subsamples
- group1 group2 (splitted according the debt/assets ratio of firms).

I run the model for the two groups separately:
xtreg, Y x1 control1 control2 ... i.pos i.pos#c.x1 if group==1, fe
xtreg, Y x1 control1 control2 ... i.pos i.pos#c.x1 if group==2, fe.

(pos is binary taking value 1 for years after the implementation of the policy)

and I obtain the following estimates for group 1 and 2, respectively:

*******output excerpt************

-----------------------------------------------------------------------------------
|               Robust
Y   |      Coef.   Std. Err.      t    P>|t|     [95%
Conf. Interval]
------------------+----------------------------------------------------------------
x1      |  -2.053274   .5641935    -3.64   0.000    -3.159248
-.9473006
control1 |   .5904103   .0267907    22.04   0.000     .5378933    .6429273
control2 |   .0947558   .0233539     4.06   0.000     .0489758    .1405358
... |  -.0234459   .2617354    -0.09   0.929    -.5365189
.4896271
year dum.. |
1.pos |  -.5814072   .1512517    -3.84   0.000     -.877902   -.2849124
1.pos#c.x1 |  1.256448   .4183398     3.00   0.003     .4363875    2.076508
_cons |  -6.099231   1.766059    -3.45   0.001    -9.561191   -2.637272
------------------+----------------------------------------------------------------
sigma_u |  2.1744991
sigma_e |  .77651905
rho |  .88690051   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------

-----------------------------------------------------------------------------------
|               Robust
Y    |      Coef.   Std. Err.      t    P>|t|     [95%
Conf. Interval]
------------------+----------------------------------------------------------------
x1     |  -2.047585   .6997248    -2.93   0.003     -3.41921
-.6759593
control1  |   .4552402   .0232387    19.59   0.000     .4096868    .5007936
control2 |    .028412   .0110095     2.58   0.010     .0068306    .0499933
...
year dum .. |
1.pos     |  -.4291118   .1817098    -2.36   0.018    -.7853059   -.072917
1.pos#c.x1 |.6220617   .5078439     1.22   0.221    -.3734318    1.617555
cons |  -7.341474   1.606579    -4.57   0.000    -10.49075   -4.192201
------------------+----------------------------------------------------------------
sigma_u |  2.4369753
sigma_e |  .70849863
rho |  .92206421   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------

**********end of excerpt*************

These results are in the direction of the predicted, but when I pooled
the sample for me to compare the coefs, the estimates appear to be
significantly different. They are as follows:

*******output excerpt************
--------------------------------------------------------------------------------------------------
|               Robust
Y  |      Coef.   Std. Err.      t
P>|t|     [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
x1             |  -1.601963   .5324727    -3.01
0.003    -2.645681   -.5582453
control1  |   .5435240   .0232387    19.59   0.000
.4096868    .5007936
control2 |    .03976   .0110095     2.58   0.010
.0068306    .0499933
... |
year dum .. |
1.pos |   -.382873   .1487651    -2.57   0.010
-.6744726   -.0912734
pos#c.x1  |  .5273469   .4331443     1.22   0.223
-.3216739    1.376368
1.group  |      .2575    .175552     1.47   0.142
-.0866054    .60
1.group#c.x1  |  -.8550352   .5470408    -1.56   0.118
-1.927308    .217238
1.group#pos   |  -.2539677   .1681945    -1.51   0.131
-.5836514     .075716
1.goup#pos#c.x1  |  .8948809    .528096     1.69   0.090
-.140258     1.93002
_cons |  -6.485282   1.161574    -5.58   0.000
-8.762123   -4.208441
---------------------------------+----------------------------------------------------------------
sigma_u |  2.2954577
sigma_e |  .76123454
rho |  .90092029   (fraction of variance due to u_i)

**********end of excerpt*************

Do you find something wrong with the last equation?

I would appreciate any help.
Best
MJ

2013/2/20 Rebecca Pope <rebecca.a.pope@gmail.com>:
> Jay has given you important advice as it pertains to the group
> residual variances.

> You are correct that Wooldridge gives an explanation of interaction
> terms. He also notes that a fully interacted model (as I assume you
> will be estimating since your initial post seemed to suggest that you
> expect different coefficients for all covariates for males and
> females) assumes group error homogeneity (pg 245 of the 4th ed).
> Unfortunately, there doesn't appear to be any discussion, at least in
> that section, of how to address heteroskedasticity between the groups.
> I didn't read through the rest of the book

> You might want to take a look at this FAQ by Bill Gould:
> http://www.stata.com/support/faqs/statistics/pooling-data-and-chow-tests/
>
> And these slides from a talk by Bobby Gutierrez:
> http://www.stata.com/meeting/fnasug08/gutierrez.pdf
>
> Only you can see your data and judge whether the constrained variance
> model is appropriate or not. I wouldn't just dismiss the issue out of
> hand though.
>
> Rebecca
>
> On Wed, Feb 20, 2013 at 5:47 AM, Mario Jose <mariojose276@gmail.com> wrote:
>> Thanks you for comments. Testing for equality of coefficients from
>> different subsamples, as suggested by Marteen, can be solved by
>> interactions.
>> There is an excellent explanation of the procedure in Wooldridge:
>> Introd.Econometrics ModernApproach; pp. 243-246 and pp. 449-450 and in
>> http://www.stata.com/support/faqs/statistics/chow-tests/
>>
>> Best,
>> MJ
>>
>> 2013/2/18 JVerkuilen (Gmail) <jvverkuilen@gmail.com>:
>>> As someone else indicated, your syntax is odd.
>>>
>>> The main question I have is whether you want to allow for different
>>> group residual variances. If not, interaction. If so, then I guess the
>>> easiest approach would be -suest-.
>>>
>>> On Mon, Feb 18, 2013 at 11:15 AM, Mario Jose <mariojose276@gmail.com> wrote:
>>>> Dear Statalisters,
>>>>
>>>> I have tryed to solve the question below, searching for help in the
>>>> Stata Archiv without too much success...
>>>>
>>>> I have estimated a fixed effects linear regression for two different
>>>> groups on my sample (say, sex male/female), using this strategy:
>>>> xtreg dv iv, if sex==male
>>>> xtreg dv iv, if sex==female
>>>>
>>>> I am interested in testing whether or not the coefficient b1 is
>>>> identical to each other in the two subsamples.
>>>>
>>>> I would really appreciate any help.
>>>> Regards
>>>> MJ
>>>> *
>>>> *   For searches and help try:
>>>> *   http://www.stata.com/help.cgi?search
>>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>>
>>> --
>>> JVVerkuilen, PhD
>>> jvverkuilen@gmail.com
>>>
>>> http://lesswrong.com/
>>>
>>> "Everybody loves progress but nobody likes change." ---Fortune cookie, 1/13/13.
>>> *
>>> *   For searches and help try:
>>> *   http://www.stata.com/help.cgi?search
>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>> 2013/2/18 JVerkuilen (Gmail) <jvverkuilen@gmail.com>:
>>> As someone else indicated, your syntax is odd.
>>>
>>> The main question I have is whether you want to allow for different
>>> group residual variances. If not, interaction. If so, then I guess the
>>> easiest approach would be -suest-.
>>>
>>> On Mon, Feb 18, 2013 at 11:15 AM, Mario Jose <mariojose276@gmail.com> wrote:
>>>> Dear Statalisters,
>>>>
>>>> I have tryed to solve the question below, searching for help in the
>>>> Stata Archiv without too much success...
>>>>
>>>> I have estimated a fixed effects linear regression for two different
>>>> groups on my sample (say, sex male/female), using this strategy:
>>>> xtreg dv iv, if sex==male
>>>> xtreg dv iv, if sex==female
>>>>
>>>> I am interested in testing whether or not the coefficient b1 is
>>>> identical to each other in the two subsamples.
>>>>
>>>> I would really appreciate any help.
>>>> Regards
>>>> MJ
>>>> *
>>>> *   For searches and help try:
>>>> *   http://www.stata.com/help.cgi?search
>>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>>
>>> --
>>> JVVerkuilen, PhD
>>> jvverkuilen@gmail.com
>>>
>>> http://lesswrong.com/
>>>
>>> "Everybody loves progress but nobody likes change." ---Fortune cookie, 1/13/13.
>>> *
>>> *   For searches and help try:
>>> *   http://www.stata.com/help.cgi?search
>>> *   http://www.stata.com/support/faqs/resources/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/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
>
> On Wed, Feb 20, 2013 at 5:47 AM, Mario Jose <mariojose276@gmail.com> wrote:
>> Thanks you for comments. Testing for equality of coefficients from
>> different subsamples, as suggested by Marteen, can be solved by
>> interactions.
>> There is an excellent explanation of the procedure in Wooldridge:
>> Introd.Econometrics ModernApproach; pp. 243-246 and pp. 449-450 and in
>> http://www.stata.com/support/faqs/statistics/chow-tests/
>>
>> Best,
>> MJ
>>
>> 2013/2/18 JVerkuilen (Gmail) <jvverkuilen@gmail.com>:
>>> As someone else indicated, your syntax is odd.
>>>
>>> The main question I have is whether you want to allow for different
>>> group residual variances. If not, interaction. If so, then I guess the
>>> easiest approach would be -suest-.
>>>
>>> On Mon, Feb 18, 2013 at 11:15 AM, Mario Jose <mariojose276@gmail.com> wrote:
>>>> Dear Statalisters,
>>>>
>>>> I have tryed to solve the question below, searching for help in the
>>>> Stata Archiv without too much success...
>>>>
>>>> I have estimated a fixed effects linear regression for two different
>>>> groups on my sample (say, sex male/female), using this strategy:
>>>> xtreg dv iv, if sex==male
>>>> xtreg dv iv, if sex==female
>>>>
>>>> I am interested in testing whether or not the coefficient b1 is
>>>> identical to each other in the two subsamples.
>>>>
>>>> I would really appreciate any help.
>>>> Regards
>>>> MJ
>>>> *
>>>> *   For searches and help try:
>>>> *   http://www.stata.com/help.cgi?search
>>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>>
>>> --
>>> JVVerkuilen, PhD
>>> jvverkuilen@gmail.com
>>>
>>> http://lesswrong.com/
>>>
>>> "Everybody loves progress but nobody likes change." ---Fortune cookie, 1/13/13.
>>> *
>>> *   For searches and help try:
>>> *   http://www.stata.com/help.cgi?search
>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>> 2013/2/18 JVerkuilen (Gmail) <jvverkuilen@gmail.com>:
>>> As someone else indicated, your syntax is odd.
>>>
>>> The main question I have is whether you want to allow for different
>>> group residual variances. If not, interaction. If so, then I guess the
>>> easiest approach would be -suest-.
>>>
>>> On Mon, Feb 18, 2013 at 11:15 AM, Mario Jose <mariojose276@gmail.com> wrote:
>>>> Dear Statalisters,
>>>>
>>>> I have tryed to solve the question below, searching for help in the
>>>> Stata Archiv without too much success...
>>>>
>>>> I have estimated a fixed effects linear regression for two different
>>>> groups on my sample (say, sex male/female), using this strategy:
>>>> xtreg dv iv, if sex==male
>>>> xtreg dv iv, if sex==female
>>>>
>>>> I am interested in testing whether or not the coefficient b1 is
>>>> identical to each other in the two subsamples.
>>>>
>>>> I would really appreciate any help.
>>>> Regards
>>>> MJ
>>>> *
>>>> *   For searches and help try:
>>>> *   http://www.stata.com/help.cgi?search
>>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>>
>>> --
>>> JVVerkuilen, PhD
>>> jvverkuilen@gmail.com
>>>
>>> http://lesswrong.com/
>>>
>>> "Everybody loves progress but nobody likes change." ---Fortune cookie, 1/13/13.
>>> *
>>> *   For searches and help try:
>>> *   http://www.stata.com/help.cgi?search
>>> *   http://www.stata.com/support/faqs/resources/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/faqs/resources/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/faqs/resources/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/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/
```