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

[Nahla Betelmal <nahlaib@gmail.com>]

Hi Richard, thanks for your previous comments, and sorry for the delay
in replying. I had to do some readings to see how researchers solve
this issue.

In industry-year context rather than firm-year context, authors seem
to report mean of the mean rather than just Fama-MacBeth  time series
mean.

first they perform Fama-MacBeth on each industry alone to get the time
series mean . In other words, they perform cross-sectional  on the
firms-years observations in each industry to produce  time series mean
of each industry. This could be easily obtained by the following
Fama-MacBeth command available in Stata:

tsset firm_id year

forval  i= 1/50 {
    xtfmb DV IV_1 IV_2 IV_3 if  industry== `i'
}

Therefore, there will be 50  time series mean betas, 50 mean R-square
for the 50 industries I have. This is easy to execute.

The second stage is to take the mean of these 50 time series means
beta and the mean of these 50 means R-square, and of course the
standard error and the t-stat of mean of the mean betas.

In this way, they can obtain the time series mean across industries
(rather than firms).

Unfortunately, due to my humble knowledge with Stata, I have not
figured out the command of how to get stage two (i.e. mean of the mean
betas and matched standard error). I tried the following but there is
an error

forval  i= 1/50 {
      statsby _b e(r2)  e(r2_a) , by(industry):xtfmb DV IV1 IV2 IV3 if
 industry== `i'
}

collapse (mean) _b_cons _b_IV1 _b_IV2  _b_IV3  _eq2_stat_1 _eq2_stat_2///
 (semean) _se_cons = _b_cons _se_IV1 = _b_IV1  _se_IV2 = _b_IV2
_se_IV3 = _b_IV3

foreach v in cons IV1 IV2 IV3 {
generate _t_`v' = _b_`v' / _se_`v'
 }

I got error:

no; data in memory would be lost
r(4);


If I remove  by(industry) in the first line of the loop , I got an error as well

industry not found
r(111);


I would highly appreciate it if you can help me to figure out the
right command. Also, I do hope this thread to be useful for other
people who face this issue as well.

Many thanks in advance

Nahla



On 11 July 2013 16:37, Richard Herron <richard.c.herron@gmail.com> wrote:
> 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 <nahlaib@gmail.com> wrote:
>> 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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>>>> >>>>>>>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>> >>>>>>>>> *
>>>> >>>>>>>>> *   For searches and help try:
>>>> >>>>>>>>> *   http://www.stata.com/help.cgi?search
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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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>>>
>>>
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>
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