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

[Richard Herron <richard.c.herron@gmail.com>]

Peterson addresses some programming aspects on his [Website][1], which
is a companion to his 2009 RFS paper. I think -ivreg2- from SSC also
does two-way clustering (-ssc install ivreg2-).

Angrist and Pischke (2008) recommend at least 42 clusters, so with 19
years the cure may be worse than the disease. Fama tends to adjust his
rejection threshold rather than correct standard errors and usually
provides a clear, concise discussion of his logic. I recall Fama and
French (1998) set the rejection threshold at t=3 and Fama and French
(2002) set the rejection threshold at t=5.

The identification strategy is also important. Using -reg- gives you
the pooled-panel estimator, while -xtreg, fe- gives you the within
estimator (i.e., identification using within firm variation). The
Fama-MacBeth regression identifies using cross-sectional variation,
then takes the time-series average.

The approach in your paper (Fama-MacBeth by industry) is akin to
industry fixed effects, although not exactly because it allows all
coefficients to vary by industry, not just the intercept. I'm not
familiar with your literature and can't say which is the correct
specification. There may be a key paper in this literature that
justifies this approach over firm fixed effects and how they correct
standard errors for between industry correlation (or if it's
necessary).

Angrist, J.D., Pischke, J.-S., 2008. Mostly Harmless Econometrics: An
Empiricist's Companion. Princeton University Press.

Fama, E.F., French, K.R., 1998. Taxes, financing decisions, and firm
value. The Journal of Finance 53, 819–843.

Fama, E.F., French, K.R., 2002. Testing trade-off and pecking order
predictions about dividends and debt. Review of financial studies 15,
1–33.

[1]:http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/se_programming.htm

On Mon, Jul 8, 2013 at 10:49 AM, Nahla Betelmal <nahlaib@gmail.com> wrote:
> Hi Richard, I have few questions and I would be grateful if you can
> help me please. I read the two references and also
>
> Samuel B.Thompson, 2010, Simple formulas for standard errors that
> cluster by both firm and time,Journal of Financial Economics.
>
> 1- what is the difference (in terms of Stata commands) between time
> clustering  and Fama-MacBeth time effect? Petersen (2005) reports both
> in table 6. Unfortunately, he did not stated the commands he used to
> drive the results.
>
> lets assume that there is a "year" variable in the database, then :
>
> statsby _b e(r2), by(year): regress price weight         "does this
> represent Fama-MacBeth time effect"
>
> xtreg  price weight year1 year2... yeark, fe cluster (year)
> reg  price weight year1 year2... yeark, cluster (year)
> Which one of these two if any represents what Petersen reported in
> table 6, column III as  cluster by time) please note that Petersen
> included time dummies in columns I-IV
>
> regress price weight  , cluster (year)   " According to Thompson, 2010
> footnote in page 4 , this is the cluster by time command.
>
> 2- According to Thompson, 2010 we can account for both time and firm
> effects, however, we need a minimum 25 observations in both
> dimensions. In my case I have 57 sectors but only 19 years. So I can
> not follow Thomson double clustering.
>
> Again, Petersen was not clear about the double clustering he
> performed. In the text page 23. He said to account for one dimension
> (time) as dummies while cluster by the other dimension (firm).
> However, the results are confusing in Table 6.
>
> Column II should represents Firm cluster , however, it includes time
> dummies. Column IV represents Firm and time cluster which also
> includes time dummies! What is the difference between column II and
> column IV?
>
> What is the Stata command I can use to account for both time and firm effects?
>
>
> I would highly appreciate it if you help me clear things out. Thank
> you for your time and help.
>
> Regards
>
> Nahla
>
>
>
> On 5 July 2013 17:27, Nahla Betelmal <nahlaib@gmail.com> wrote:
>> 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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>>>>>> *
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>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> ---------------------------------
>>>>> Maarten L. Buis
>>>>> WZB
>>>>> Reichpietschufer 50
>>>>> 10785 Berlin
>>>>> Germany
>>>>>
>>>>> http://www.maartenbuis.nl
>>>>> ---------------------------------
>>>>> *
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>>>> *
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