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Re: st: heteroskedasticity test in panel data


From   "Jing Zhou" <jing.zhou@rmit.edu.au>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: heteroskedasticity test in panel data
Date   Wed, 28 Jul 2010 11:11:30 +1000

Dear Michael,

follow your suggestions, i rescaled my variables in panel model, but still the problems exist.

I tried another method.  I reexamined the first model by removing "igls", and there is no variable omitted and the SEs are acceptable. but when I run "lrtest hetero ., df('df')", the result shows wrong information as "hetero does not contain scalar e(ll)". I attached the outcomes below. Could you advise me why it happens? Thank you.

Jing



. xtgls roa tlawn genvironment aci2 size leverage age, panels (heteroskedastic)

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   no autocorrelation

Estimated covariances      =       621          Number of obs      =      2916
Estimated autocorrelations =         0          Number of groups   =       621
Estimated coefficients     =         7          Obs per group: min =         1
                                                               avg =  4.695652
                                                               max =        10
                                                Wald chi2(6)       =  15124.70
                                                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
         roa |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       tlawn |   .0713694   .0024424    29.22   0.000     .0665823    .0761564
genvironment |   .0012895   .0004232     3.05   0.002     .0004601    .0021188
        aci2 |   .0240381   .0015218    15.80   0.000     .0210555    .0270207
        size |   .0182393   .0006986    26.11   0.000       .01687    .0196085
    leverage |  -.0391871   .0030122   -13.01   0.000    -.0450909   -.0332833
         age |  -.0039249   .0001145   -34.27   0.000    -.0041493   -.0037004
       _cons |  -.3728419   .0144485   -25.80   0.000    -.4011604   -.3445234
------------------------------------------------------------------------------

. estimates store hetero

. 
. xtgls roa tlawn genvironment aci2 size leverage age

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        homoskedastic
Correlation:   no autocorrelation

Estimated covariances      =         1          Number of obs      =      2916
Estimated autocorrelations =         0          Number of groups   =       621
Estimated coefficients     =         7          Obs per group: min =         1
                                                               avg =  4.695652
                                                               max =        10
                                                Wald chi2(6)       =    372.93
Log likelihood             =  855.1189          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
         roa |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       tlawn |   .1003806   .0162142     6.19   0.000     .0686014    .1321598
genvironment |   .0015588   .0021767     0.72   0.474    -.0027075    .0058251
        aci2 |   .0244187    .006892     3.54   0.000     .0109106    .0379268
        size |   .0202311   .0034783     5.82   0.000     .0134137    .0270485
    leverage |  -.0176257   .0013651   -12.91   0.000    -.0203012   -.0149502
         age |  -.0039722   .0007833    -5.07   0.000    -.0055075    -.002437
       _cons |  -.4569187   .0729608    -6.26   0.000    -.5999192   -.3139181
------------------------------------------------------------------------------

. 
. local df=e(N_g)-1

. 
. display e(N_g)-1
620

. lrtest hetero ., df(620)
hetero does not contain scalar e(ll)
r(498);
 

>>> "Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com> 28/07/2010 2:03 am >>>
Dear Jing

   Perhaps my last bit of advice was slightly misguided... maybe the model would benefit 
from a rescaling of the outcome variable. I am just very concerned about those extremely 
tiny standard errors, because computationally I wonder how close they are to 0. (And, thus 
how many other quantities are getting close to 0). If that does not solve the problem of 
your predictors being dropped in the first model, then that problem needs to be solved 
first. My hunch is that it is an issue of multicollinearity, but I am unaware of how to 
examine that in the context of a panel model. Maybe others have suggestions?

Best luck!

Michael N. Mitchell
Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html 
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html 
Stata tidbit of the week         - http://www.MichaelNormanMitchell.com 



On 2010-07-27 1.30 AM, Jing Zhou wrote:
> Dear Michael,
>
> Thank you for your suggestions. in fact the predictor in my model is a percentage which should not be very large. however, i still follow your suggestions to divide other large regressors. the results are unchanged (p value of 1.000), and in the first model some regressors are also omitted. I am wondering how this omitted variables happened?
>
> Thanks.
>
> Jing
>
>
>>>> "Michael N. Mitchell"<Michael.Norman.Mitchell@gmail.com>  27/07/2010 6:02 pm>>>
> Dear Jing
>
>     I think this is very informative. I notice two issues...
>
> 1) The terms -aci2-, -leverage-, and the constant (_cons) were omitted from the first model.
>
> 2) The standard errors are extremely tiny, and the coefficients for the terms that are
> present are very small.
>
>     I wonder if you have an issue with the scaling of the variables, and that your model is
> not being estimated very stably because the units of the variables are very large. You
> might try dividing the predictor by a constant, e.g.
>
> . generate tlawnew = tlaw / 1000
>
>     and then entering the "new" variable. I think this might lead to a more stable estimate
> of the first model, and then different results with respect to the chi-squared test.
>
> Best regards,
>
> Michael N. Mitchell
> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html 
> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html 
> Stata tidbit of the week         - http://www.MichaelNormanMitchell.com 
>
>
>
> On 2010-07-27 12.51 AM, Jing Zhou wrote:
>> following is the command and corresponding output.
>>
>> . xtgls roa tlaw genvironment aci2 size leverage age, igls panels (heteroskedastic)
>> Iteration 1: tolerance = .01281716
>> Iteration 2: tolerance = .01676558
>> Iteration 3: tolerance = .25025852
>> Iteration 4: tolerance = .00706137
>> Iteration 5: tolerance = .04061494
>> Iteration 6: tolerance = .03815978
>> Iteration 7: tolerance = .03675714
>> Iteration 8: tolerance = .02342555
>> Iteration 9: tolerance = .00073142
>> Iteration 10: tolerance = .00832932
>> Iteration 11: tolerance = 3.144e-06
>> Iteration 12: tolerance = 1.718e-07
>> Iteration 13: tolerance = .1305574
>> Iteration 14: tolerance = .11548056
>> Iteration 15: tolerance = .08959096
>> Iteration 16: tolerance = .02050352
>> Iteration 17: tolerance = .006188
>> Iteration 18: tolerance = .02034936
>> Iteration 19: tolerance = .01040934
>> Iteration 20: tolerance = .0073191
>> Iteration 21: tolerance = .00270878
>> Iteration 22: tolerance = .00243333
>> Iteration 23: tolerance = .00237504
>> Iteration 24: tolerance = .14171418
>> Iteration 25: tolerance = .00958554
>> Iteration 26: tolerance = .00850144
>> Iteration 27: tolerance = .00094421
>> Iteration 28: tolerance = .02799819
>> Iteration 29: tolerance = 8.475e-06
>> Iteration 30: tolerance = .00224329
>> Iteration 31: tolerance = .11496823
>> Iteration 32: tolerance = .0108985
>> Iteration 33: tolerance = .00491695
>> Iteration 34: tolerance = .01146044
>> Iteration 35: tolerance = .11495675
>> Iteration 36: tolerance = .00775622
>> Iteration 37: tolerance = .00769652
>> Iteration 38: tolerance = .00452005
>> Iteration 39: tolerance = .00376106
>> Iteration 40: tolerance = .00165737
>> Iteration 41: tolerance = .00165462
>> Iteration 42: tolerance = .00148306
>> Iteration 43: tolerance = .00311958
>> Iteration 44: tolerance = .00028596
>> Iteration 45: tolerance = .00036032
>> Iteration 46: tolerance = .00211196
>> Iteration 47: tolerance = .0600343
>> Iteration 48: tolerance = .0023866
>> Iteration 49: tolerance = .01014685
>> Iteration 50: tolerance = .06387619
>> Iteration 51: tolerance = .07202545
>> Iteration 52: tolerance = .02556249
>> Iteration 53: tolerance = .00008123
>> Iteration 54: tolerance = .00004186
>> Iteration 55: tolerance = .00175812
>> Iteration 56: tolerance = .05552171
>> Iteration 57: tolerance = .01552817
>> Iteration 58: tolerance = .01716332
>> Iteration 59: tolerance = .02063742
>> Iteration 60: tolerance = .01274508
>> Iteration 61: tolerance = .00920043
>> Iteration 62: tolerance = .12077282
>> Iteration 63: tolerance = .00905253
>> Iteration 64: tolerance = .01079828
>> Iteration 65: tolerance = .03328352
>> Iteration 66: tolerance = .01233767
>> Iteration 67: tolerance = .00929827
>> Iteration 68: tolerance = .05281334
>> Iteration 69: tolerance = .03867031
>> Iteration 70: tolerance = .01011156
>> Iteration 71: tolerance = .00011164
>> Iteration 72: tolerance = .00999907
>> Iteration 73: tolerance = 7.644e-08
>>
>>
>> Cross-sectional time-series FGLS regression
>>
>> Coefficients:  generalized least squares
>> Panels:        heteroskedastic
>> Correlation:   no autocorrelation
>>
>> Estimated covariances      =       621          Number of obs      =      2916
>> Estimated autocorrelations =         0          Number of groups   =       621
>> Estimated coefficients     =         3          Obs per group: min =         1
>>                                                                  avg =  4.695652
>>                                                                  max =        10
>>                                                   Wald chi2(3)       =  4.40e+13
>> Log likelihood             =   4073.23          Prob>   chi2        =    0.0000
>>
>> ------------------------------------------------------------------------------
>>            roa |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>>           tlaw |    .000556   8.73e-09  6.4e+04   0.000      .000556     .000556
>> genvironment |   .0013927   4.93e-08  2.8e+04   0.000     .0013926    .0013928
>>           aci2 |  (omitted)
>>           size |   .0003605   5.94e-08  6065.32   0.000     .0003604    .0003606
>>       leverage |  (omitted)
>>            age |  -.0030722   6.90e-09 -4.5e+05   0.000    -.0030722   -.0030722
>>          _cons |  (omitted)
>> ------------------------------------------------------------------------------
>>
>> . estimates store hetero
>>
>> . xtgls roa tlaw genvironment aci2 size leverage age
>>
>> Cross-sectional time-series FGLS regression
>>
>> Coefficients:  generalized least squares
>> Panels:        homoskedastic
>> Correlation:   no autocorrelation
>>
>> Estimated covariances      =         1                Number of obs      =      2916
>> Estimated autocorrelations =       0              Number of groups   =       621
>> Estimated coefficients     =         7                  Obs per group: min =         1
>>                                                                           avg =  4.695652
>>                                                                           max =        10
>>                                                                   Wald chi2(6)       =    372.93
>> Log likelihood             =  855.1189          Prob>   chi2        =    0.0000
>>
>> ------------------------------------------------------------------------------
>>            roa |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>>           tlaw |   .0010038   .0001621     6.19   0.000      .000686    .0013216
>> genvironment |   .0015588   .0021767     0.72   0.474    -.0027075    .0058251
>>           aci2 |   .0244187    .006892     3.54   0.000     .0109106    .0379268
>>           size |   .0202311   .0034783     5.82   0.000     .0134137    .0270485
>>       leverage |  -.0176257   .0013651   -12.91   0.000    -.0203012   -.0149502
>>            age |  -.0039722   .0007833    -5.07   0.000    -.0055075    -.002437
>>          _cons |  -.4569186   .0729608    -6.26   0.000    -.5999192   -.3139181
>> ------------------------------------------------------------------------------
>>
>> . local df=e(N_g)-1
>>
>> . display e(N_g)-1
>> 620
>>
>> .
>> end of do-file
>>
>> . lrtest hetero ., df(620)
>>
>> Likelihood-ratio test                                            LR chi2(620)=  -6436.22
>> (Assumption: hetero nested in .)                       Prob>   chi2 =    1.0000
>>
>>
>> Thank you.
>>
>> Jing
>>
>>>>> "Michael N. Mitchell"<Michael.Norman.Mitchell@gmail.com>   27/07/2010 5:37 pm>>>
>> Dear Jing
>>
>>      Based on reading the FAQ (at http://www.stata.com/support/faqs/stat/panel.html) and the
>> results you report, it sounds like your data do not show heteroskedasticity across panels.
>> But, at the same time, I share your concern about getting a p value of 1.000. Perhaps you
>> could post your commands and output (suppressing any output that you need to suppress for
>> privacy/confidentiality) so we might be able to see any clues of trouble.
>>
>> Best regards,
>>
>> Michael N. Mitchell
>> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html 
>> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html 
>> Stata tidbit of the week         - http://www.MichaelNormanMitchell.com 
>>
>>
>>
>> On 2010-07-26 11.40 PM, Jing Zhou wrote:
>>> Dear Michael,
>>>
>>> Thank you for your kind assistance. follow the recommended commands on FAQs, and your suggestion, i run this test in stata. the result is however a little weird. the value of df is large (620), and Prob>    chi2 =    1.0000. Can i just conclude that my panel data is not exposed to heteroskedasticity from this result? or there still exists some problem in the process? Thanks!
>>>
>>> Jing
>>>
>>>
>>>>>> "Michael N. Mitchell"<Michael.Norman.Mitchell@gmail.com>    27/07/2010 3:24 pm>>>
>>> Dear Jing
>>>
>>>       Based on your example, it looks like you could do this...
>>>
>>> . xtgls..., igls panels (heteroskedastic)
>>> . estimates store hetero
>>> . xtgls...
>>> . display e(N_g)-1
>>>
>>>       The last command will show, I believe, the number of groups minus 1. It looks like your
>>> example uses this for the degrees of freedom. Say that number was 157. You could then type
>>>
>>> . lrtest hetero ., df (157)
>>>
>>>       and it looks like it would use 157 as the df. I am out of my element here, so I trust
>>> that someone else will correct me if I am off base. But I hope this helps.
>>>
>>> Michael N. Mitchell
>>> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html 
>>> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html 
>>> Stata tidbit of the week         - http://www.MichaelNormanMitchell.com 
>>>
>>>
>>>
>>> On 2010-07-26 9.58 PM, Jing Zhou wrote:
>>>> thank you Michael, for the command "lrtest hetero ., df ('df')", how can i get the value of df?
>>>>
>>>> Jing
>>>>
>>>>>>> "Michael N. Mitchell"<Michael.Norman.Mitchell@gmail.com>     27/07/2010 2:23 pm>>>
>>>> Greetings
>>>>
>>>>        I wonder if this would help...
>>>>
>>>> . set matsize 800
>>>>
>>>>        (or select another number in place of 800).
>>>>
>>>> Hope that helps,
>>>>
>>>> Michael N. Mitchell
>>>> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html 
>>>> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html 
>>>> Stata tidbit of the week         - http://www.MichaelNormanMitchell.com 
>>>>
>>>>
>>>>
>>>> On 2010-07-26 7.57 PM, Jing Zhou wrote:
>>>>> Dear All,
>>>>>
>>>>> I am going to test the heteroskedasticity in my panel data. by using the recommended commands on FAQ which are specified as:
>>>>>
>>>>> xtgls..., igls panels (heteroskedastic)
>>>>> estimates store hetero
>>>>> xtgls...
>>>>> local df=e (N_g)-1
>>>>> lrtest hetero., df ('df')
>>>>>
>>>>> the result shows wrong information as "matsize too small - should be at least 621". Could you please advise me what is the potential cause to this problem? and how can i refine it?
>>>>>
>>>>> Many thanks!
>>>>>
>>>>> Jing
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
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