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Re: st: comparing equality of coefficients from two subsamples


From   Mario Jose <mariojose276@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: comparing equality of coefficients from two subsamples
Date   Fri, 22 Feb 2013 18:20:16 +0000

Dear Rebecca,

Many thanks for your helpful comments. I definitely catch the
difference between both approaches. As I do not believe that the full
model is different for both subsamples, I decided to adopt the
approach you firstly referred, which assumes same disturbance
variance.
I really appreciated your help. Thank you.
Best,
MJ

2013/2/21 Rebecca Pope <rebecca.a.pope@gmail.com>:
> The FAQ link was intended to be helpful in a "first-prinicples" sense.
> I sent it because you seemed to not understand what Jay was saying
> about constraining variances & it provided a simple introduction. You
> won't be able to use those exact steps with your problem however, not
> least because -aweight-s aren't allowed with -xtreg-.
>
> Now, let's try to clarify what you are wanting before proceeding any
> further because I want to make sure that we're clear on the use of
> "interaction".
>
> Say, for example that you are interested in the model
> log(wage) = intercept + tenure + tenure^2 + not_smsa + wks_ue
> where not_smsa indicates that the respondent doesn't live in a
> metropolitan area and wks_ue is the number of weeks she was unemployed
> in the previous year. This data is from -webuse nlswork-, the example
> given with -xtreg-.
>
> Now, suppose that you think that the effect of wks_ue differs by
> whether or not the respondent lives in an urban area. For this, you
> have a simple interaction term. (You can think of this like your
> policy indicator).
> The Stata syntax for this is:
> xtreg ln_w tenure c.tenure#c.tenure i.not_smsa##c.wks_ue, fe
>
> Now, suppose you further hypothesize that the model above does not
> apply equally to southern areas. The model could differ in multiple
> ways, but the two that are of interest
> concern the south somehow moderating the effect of unemployment and
> rural residence. You can approach this in one of two ways.
>
> The first is to simply model the difference with respect to not_smsa
> and wks_ue; all other effects are the same. The second does not
> constrain any of the coefficients to be equal across groups, here
> south/not south.
> The first syntax is: xtreg ln_w tenure c.tenure#c.tenure
> i.south##i.not_smsa##c.wks_ue, fe
> This is what you say you want in your most recent post.
>
> The second approach though is what you have written:
> xtreg ln_w tenure c.tenure#c.tenure i.not_smsa##c.wks_ue if south==0, fe
> xtreg ln_w tenure c.tenure#c.tenure i.not_smsa##c.wks_ue if south==1, fe
>
> If you estimate these equations, you get different parameter estimates
> for _all_ terms by "south". This is why I said that you were working
> with a fully-interacted model. To understand this, note that you must
> estimate the two equations above _as one_ in order to test whether
> rural unemployment differs in the south (or your government policy
> differs by firm type).
> The correct Stata syntax is:
> xtreg ln_w i.south#c.tenure i.south#c.tenure#c.tenure
> i.south##i.not_smsa##c.wks_ue, fe
>
> Do not take "simply" above to mean that it is somehow inferior. I just
> mean that the model has fewer parameters to estimate. Your choice of
> specification must be theory-driven. If you think that approach 2 is
> incorrect, then nothing stops you using approach 1. However, that
> isn't what you indicated you were estimating when you wrote 2 separate
> equations.
>
> With all of these approaches, you get 1 error term for both groups. Is
> this a problem? It depends on your groups. You have to look at your
> data and decide. If you decide you shouldn't constrain the variance,
> you'll need to choose an appropriate approach at that point.
>
> Now, what do you observe with respect to the coefficients? Probably
> that the "pooled" regression does not exactly reproduce the
> coefficients of the separate regressions with -xtreg, fe-. This
> shouldn't surprise you. -xtreg, fe- is estimating a model on the
> "demeaned" data, the so-called "within" estimator. When you pool the
> observations, you alter the calculation of the mean within the j-th
> unit. This occurs because there are some respondents, in this example,
> who have lived in and out of the south. If that weren't the case,
> "1.south" would be dropped from the FE part of our model when we
> pooled results and we would be left with a single overall intercept.
>
> Quite apart from that, if you submitted
> xtreg ln_w tenure c.tenure#c.tenure i.south##i.not_smsa##c.wks_ue, fe
>
> thinking you were going to get the same results as:
> xtreg ln_w tenure c.tenure#c.tenure i.not_smsa##c.wks_ue if south==0, fe
> xtreg ln_w tenure c.tenure#c.tenure i.not_smsa##c.wks_ue if south==1, fe
>
> you would be wrong, even if you were using simple linear regression
> because you are working with fundamentally different views of how your
> grouping variable relates to the other covariates.
>
> I hope this helps,
> Rebecca
>
>
>
> On Wed, Feb 20, 2013 at 4:10 PM, Mario Jose <mariojose276@gmail.com> wrote:
>> 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
>>
> <snip>
>
> On Wed, Feb 20, 2013 at 4:10 PM, Mario Jose <mariojose276@gmail.com> wrote:
>> 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
>>>> the following link:
>>>> 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
>>>> the following link:
>>>> 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.
>>>>> *
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>>>> *
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> *
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