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Re: st: How to get mean coefficients and t-statistics from several regressions
From
Richard Herron <[email protected]>
To
[email protected]
Subject
Re: st: How to get mean coefficients and t-statistics from several regressions
Date
Thu, 11 Jul 2013 11:37:01 -0400
I'm not sure that you can use -xtfmb- (from SSC) in your setting. It
sounds like you want to run one pooled panel per industry, then take
the mean across industries. -xtfmb- runs cross-sectional regressions
(across all industries) each period, then takes the time series mean.
With respect to the Newey-West (1987) correction, I'm not sure that
it's appropriate here. Newey and West correct for serial correlation,
which requires ordering. What would be the correct industry order?
Newey, W.K., West, K.D., 1987. A simple, positive semi-definite,
heteroskedasticity and autocorrelation consistent covariance matrix.
Econometrica: Journal of the Econometric Society 703–708.
On Thu, Jul 11, 2013 at 11:14 AM, Nahla Betelmal <[email protected]> wrote:
> On 11 July 2013 15:54, Nahla Betelmal <[email protected]> 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 <[email protected]> wrote:
>>>
>>> Correction, the correct spelling is Petersen (not Peterson).
>>>
>>> On Tue, Jul 9, 2013 at 6:57 AM, Richard Herron
>>> <[email protected]> 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 <[email protected]>
>>> > 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 <[email protected]> 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 <[email protected]>
>>> >>> 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 <[email protected]>
>>> >>>> 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 <[email protected]> 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 <[email protected]>
>>> >>>>>> 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 <[email protected]>
>>> >>>>>>> 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
>>> >>>>>>>> <[email protected]> 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 <[email protected]>
>>> >>>>>>>>> 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
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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/
>>> >>>>>>> *
>>> >>>>>>> * 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:
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>>> >>>>> *
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>>> >>>>
>>> >>>> *
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>>> >>
>>> >> *
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>>
>>
>
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