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

[Nahla Betelmal <nahlaib@gmail.com>]

Yes, this is exactly what I meant. Thank you Richard. Especially for
the note about time correlation and the great references. Thank you so
much.

Best Regards

Nahla


On 5 July 2013 15:27, Richard Herron <richard.c.herron@gmail.com> wrote:
> 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
>>>>>>> ---------------------------------
>>>>>>> *
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>>>>>> *
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>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> ---------------------------------
>>>>> Maarten L. Buis
>>>>> WZB
>>>>> Reichpietschufer 50
>>>>> 10785 Berlin
>>>>> Germany
>>>>>
>>>>> http://www.maartenbuis.nl
>>>>> ---------------------------------
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>>>
>>>
>>>
>>> --
>>> ---------------------------------
>>> Maarten L. Buis
>>> WZB
>>> Reichpietschufer 50
>>> 10785 Berlin
>>> Germany
>>>
>>> http://www.maartenbuis.nl
>>> ---------------------------------
>>> *
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