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

[Nahla Betelmal <nahlaib@gmail.com>]

On 11 July 2013 15:54, Nahla Betelmal <nahlaib@gmail.com> wrote:
>
> Thanks for the reply. The link is old (was written in 2006), I found out
> that there is a command to execute Fama-MacBeth (1973):  xtfmb. It seems
> that it has been available since 2011.
> Also, the command  xtfmb, lag () to correct for autocorrelation
> (Newey-West (1987)). I think this option could solve the issue of
> correlation among industries/firms as well ( I have seen a couple of papers
> doing so). If I understood Petersen (2005) paper right, the lag needs to be
> 9 or more for this correction of standard deviation to be unbiased.
>
> Thanks again, I highly appreciate your time.
>
> Nahla
>
>
> On 9 July 2013 12:00, Richard Herron <richard.c.herron@gmail.com> wrote:
>>
>> Correction, the correct spelling is Petersen (not Peterson).
>>
>> On Tue, Jul 9, 2013 at 6:57 AM, Richard Herron
>> <richard.c.herron@gmail.com> wrote:
>> > 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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>> >>>>>>>>
>> >>>>>>>>
>> >>>>>>>>
>> >>>>>>>> --
>> >>>>>>>> ---------------------------------
>> >>>>>>>> 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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