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Re: st: How to get mean coefficients and t-statistics from several regressions


From   Richard Herron <richard.c.herron@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to get mean coefficients and t-statistics from several regressions
Date   Fri, 5 Jul 2013 10:27:53 -0400

I think you want the mean beta across industries and the t-stat based
on the associated SE.

* begin code
sysuse auto, clear
statsby _b e(r2), by(rep78): regress price weight

* get mean betas and R2
collapse (mean) _b_cons _b_weight _eq2_stat_1 ///
(semean) _se_cons = _b_cons _se_weight = _b_weight

* get t-stat for mean betas
foreach v in cons weight {
generate _t_`v' = _b_`v' / _se_`v'
}
list
* end code

This is a different take on Fama and MacBeth (1973), who do
cross-sectional regressions each month/year then take the time series
mean and SE of the regression coefficients.

This works because in asset pricing the time series correlation is low
(i.e., random walk). Here there may be correlation between the
industries, which this technique doesn't correct and could bias down
the SEs (they could address this in the paper - I didn't read).

Mitchell Peterson (2009) provides a great summary of ways to address
panel data in finance research.

Fama, E.F., MacBeth, J.D., 1973. Risk, return, and equilibrium:
Empirical tests. The Journal of Political Economy 607–636.

Petersen, M.A., 2009. Estimating standard errors in finance panel data
sets: Comparing approaches. Review of financial studies 22, 435–480.

On Fri, Jul 5, 2013 at 9:56 AM, Nahla Betelmal <nahlaib@gmail.com> wrote:
> Thank you, I will keep looking and searching and will let you know if
> I find how to it (both statistically and command wise).
> Many thanks again, I highly appreciate it
>
> Nahla
>
> On 5 July 2013 14:48, Maarten Buis <maartenlbuis@gmail.com> wrote:
>> I agree that the mean t-statistic is not very useful. I just
>> interpreted your initial question as that you wanted to know that, so
>> I gave it to you. Also, look at the dataset that -statsby- created. If
>> you find the formula the author used, you in all likelihood want to
>> use that dataset to do the manipulations.
>>
>> -- Maarten
>>
>> On Fri, Jul 5, 2013 at 3:38 PM, Nahla Betelmal <nahlaib@gmail.com> wrote:
>>> Thanks again. This is one of the pioneer papers in the field if not
>>> the first. Again thanks for the mathematics you gave me. But I do
>>> believe that it is not the right way "statistically" to get the
>>> matched t-statistics (can not be the mathematical mean of
>>> t-statistics) . I will keep looking in other statistical references
>>> how to do it, and I will search other Stata sources for the Stata
>>> command, there must be one! The paper mentions that the authors used
>>> SAS.
>>>
>>> Thank you again, I am very grateful for your time and try to help.
>>> Very kind of you
>>>
>>> Nahla
>>>
>>> On 5 July 2013 14:26, Maarten Buis <maartenlbuis@gmail.com> wrote:
>>>> I would start with understanding the statistics before worying about
>>>> how to program it. I have only briefly looked at the paper, but I am
>>>> suspicious about its value. I might be wrong. Anyhow, what I have
>>>> given you is a way to create a dataset that contains the different
>>>> pieces of information from each regression. It is now up to you to
>>>> find a meaningful way to use those bits.
>>>>
>>>> -- Maarten
>>>>
>>>> On Fri, Jul 5, 2013 at 3:00 PM, Nahla Betelmal <nahlaib@gmail.com> wrote:
>>>>> Dear Maarten,
>>>>> Thanks for the reply, but I do not think that I misunderstood the
>>>>> articles. Kindly have a look at Table 3 and its notes, page 44 in the
>>>>> following link.
>>>>>
>>>>> http://econ.au.dk/fileadmin/Economics_Business/Education/Summer_University_2012/6308_Advanced_Financial_Accounting/Advanced_Financial_Accounting/7/Dechow_Dichev_TAR_2002.pdf
>>>>>
>>>>> Also, I have humble knowledge in statistic, according to what I know
>>>>> that we can have mean coefficients and R2, but it is wrong to attach
>>>>> the mean coefficient with mean  t-statistics (and hence standard
>>>>> error). (we can do it mathematically but it is wrong conceptually)
>>>>>
>>>>> For example we can not say that the t statistics for B1+B2 is
>>>>> t-statistic(B1) + t-statistics(B2).
>>>>>
>>>>>  It needs to be derived from the distribution of the coefficients.
>>>>> Unfortunately I do not know how to do it.
>>>>>
>>>>> I would highly appreciate any help in that
>>>>>
>>>>> Thank you again
>>>>>
>>>>> Nahla
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> On 5 July 2013 13:39, Maarten Buis <maartenlbuis@gmail.com> wrote:
>>>>>> On Fri, Jul 5, 2013 at 2:24 PM, Nahla Betelmal wrote:
>>>>>>> My data represents 100 industries  across certain time horizon. It
>>>>>>> seems from the literature that a regression is run for each industry
>>>>>>> (i.e. 100 regressions are run), however, only the mean coefficients,
>>>>>>> mean R-square, and t statistic based on the distribution of 100
>>>>>>> coefficients for each variable obtained from 100 regressions are
>>>>>>> reported.
>>>>>>>
>>>>>>> I can run the 100 regression in a loop, however, I do not know how can
>>>>>>> I get  the mean coefficients, the mean R-square, and  t statistic
>>>>>>> based on the distribution of several coefficients for each variable
>>>>>>> obtained from several regressions?
>>>>>>
>>>>>> I strongly suspect that you misunderstood what was done in those
>>>>>> articles, but you can do what you ask:
>>>>>>
>>>>>> *------------------ begin example ------------------
>>>>>> sysuse auto, clear
>>>>>> statsby _b _se e(r2), by(foreign): regress mpg gear turn
>>>>>>
>>>>>> // average coefficient for turn
>>>>>> sum _b_turn
>>>>>>
>>>>>> // average t-value for turn
>>>>>> gen t_turn = _b_turn / _se_turn
>>>>>> sum t_turn
>>>>>>
>>>>>> // average R2
>>>>>> sum _eq2_stat_1
>>>>>> *------------------- end example -------------------
>>>>>> * (For more on examples I sent to the Statalist see:
>>>>>> * http://www.maartenbuis.nl/example_faq )
>>>>>>
>>>>>> ---------------------------------
>>>>>> Maarten L. Buis
>>>>>> WZB
>>>>>> Reichpietschufer 50
>>>>>> 10785 Berlin
>>>>>> Germany
>>>>>>
>>>>>> http://www.maartenbuis.nl
>>>>>> ---------------------------------
>>>>>> *
>>>>>> *   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/
>>>>
>>>>
>>>>
>>>> --
>>>> ---------------------------------
>>>> Maarten L. Buis
>>>> WZB
>>>> Reichpietschufer 50
>>>> 10785 Berlin
>>>> Germany
>>>>
>>>> http://www.maartenbuis.nl
>>>> ---------------------------------
>>>> *
>>>> *   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:
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>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>> --
>> ---------------------------------
>> Maarten L. Buis
>> WZB
>> Reichpietschufer 50
>> 10785 Berlin
>> Germany
>>
>> http://www.maartenbuis.nl
>> ---------------------------------
>> *
>> *   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/
> *
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