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# Running event studies using Stata: the estudy command

Authors:
Under review by the STATA Journal
Running event studies using Stata: the estudy
command
Fausto Pacicco
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
fpacicco@liuc.it
Luigi Vena
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
lvena@liuc.it
Andrea Venegoni
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
avenegoni@liuc.it
Abstract. This paper proposes the Stata command estudy and illustrates how it
can be used to perform an event study customizing the statistical framework, from
the estimates of abnormal returns to the tests for their statistical signiﬁcance. Our
program signiﬁcantly improves the existing modules both in terms of completeness
and users’ comprehension.
Keywords: estudy, event study, ﬁnancial econometrics
1 Introduction
If and how a given event aﬀects ﬁnancial markets is a relevant question that researchers
and practitioners aim to answer. This is why the event study framework has nowadays
become a statistical technique used in many areas, from economics to accounting, from
ﬁnance to law. According to Kothari and Warner (2008) between 1974 and 2000 almost
600 studies conducted in various ﬁelds employed such a technique. If we consider that
the mentioned analysis takes into account only four main academic journals, it is easy to
understand that the numbers describing the popularity of such a technique exponentially
grow when we extend the focus to other academic journals, as well as private and public
institutions.
This paper proposes and comments on the estudy Stata program. Such program
performs an event study permitting the user to: i) work with multiple varlists,com-
puting the Abnormal Returns (and the Average Abnormal Returns), henceforth ARs
(and AARs) as well as Cumulative Abnormal Returns and Cumulative Average Abnor-
mal Returns (henceforth, respectively CARs and CAARs)1; ii) specify up to six event
windows; iii) customize the length of the estimation window; iv) select the model for
the calculus of (ab)normal returns; v) specify the diagnostic test, among the parametric
and non-parametric ones that we propose and that are the most commonly used in the
literature; vi) customize the output table; vii) store the results into an excel ﬁle as well
as in a Stata dataset ﬁle.
1. Throughout the entire paper, we refer to ARs only for exposition’s sake.
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2Running event studies using Stata
It improves the existing modules that allow to perform an event study on Stata
under several perspectives:
computes simultaneously ARs (CARs) of more than one groups of variables (se-
curities’ returns), without repeating the command;
oﬀers the possibility to work with diﬀerent levels of aggregation, running the
event study on single ﬁrms (groups of them) computing ARs and CARs (AARs
and CAARs) and testing their statistical signiﬁcance;
provides a customizable output, according to the needs of the user;
simpliﬁes the approach for the user, resulting in an easier and faster setup.
2 The Event Study Framework
Should an event be unexpected and value relevant for some ﬁrms, it is bound to cause
an abnormal return as measured by the actual ex-post return net to the normal (or
expected) one over the same period (see for example MacKinlay 1997). The event study
technique allows to measure such abnormal return, hence allowing to assess whether a
given fact has proved able to inﬂuence ﬁrms securities’ market value. We refer generally
to ﬁrms’ securities as the event study applies most frequently on common stocks, even if
they are conducted on others securities like bonds (Bessembinder et al. 2009) or credit
default swaps (Andres et al. 2016).
The Equation 1 deﬁnes the AR of a generic ﬁrm iin the period t:
ARi,t =Ri,t E(Ri,t |Xt)(1)
where Ri,t is the actual ex-post return and E(Ri,t |Xt) is the expected return conditioned
to the information Xof period t, unrelated to the event.
2.1 Measuring abnormal returns
As pointed out by MacKinlay (1997), the conduction of the event study customarily
follows an established ﬂow divided in these steps:
1. Deﬁnition of the event window;
2. Computation of the normal returns;
a. Deﬁnition of the estimation window;
b. Choice of the estimation model;
3. Estimation of the abnormal returns;
4. Statistical testing for the signiﬁcance of the abnormal returns;
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The procedure begins with the deﬁnition of the period(s) over which the event is
supposed to inﬂuence the market return of ﬁrms’ securities, i.e. the event window(s).
Usually, each event window spans over one or more days including the event date it-
self. It is common to include the days before and/or after the event, allowing for the
possibility of news leakages preceding the event itself or delayed reactions of the markets.
In order to deﬁne the abnormal return, it is necessary to proceed to the second step
of the analysis and compute the normal or expected performance. This task requires
the deﬁnition of an estimation window, i.e. a sample period prior to the event window,
usually leaving a cushion of at least one month in order to exclude market returns
inﬂuenced by the event, avoiding the estimation window to include anticipation eﬀects
(and/or news leakages).
The estimation of normal returns is carried out using diﬀerent models. The two that
are most commonly used are the historical mean model (HMM) and the single index
model (SIM).
E(Ri,t|Xt)=μi(2)
E(Ri,t|Xt)=αi+βiRm,t (3)
With respect to the former (Eq. 2), the security’s historical mean return over the
estimation window represents the expected normal performance unconditioned to the
event.
Conversely, according to the single index model (see Eq. 3), the normal return depends
on the parameters αiand βi(estimated over the estimation windows), and the market
return Rm,t. A special case of this model is the market adjusted model (MAM), where
a constraint on the parameters αiand βiwants them to be set equal to 0 and 1,
respectively.
In an attempt to improve the variance explained by the single index model (hence
facilitating ARs detection), sometimes the expected return is estimated using more
than one factor, i.e. modelling a multi factor model (MFM) such as the 3 factors model
proposed by Fama and French (1993).
Once normal returns are computed, it is possible to obtain abnormal returns (ARs).
When the aim is to compute the event impact for each single security on a single day
event, it is possible to obtain ARs by applying Equation 1. Sometimes, the user can also
be interested in investigating the eﬀect of the event on a multi-day period and hence
becomes necessary to operate a time series aggregation of the ARs, obtaining the CARs
as described by Equation 4.
CARi(t1,t
2)=
t2
t=t1
ARi,t (4)
with t1<t
2and t1,t
2(event window).
If, instead, the object of interest is the impact on a pool of ﬁrms, a cross-section
aggregation becomes necessary and Average Abnormal Returns calculation can be per-
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4Running event studies using Stata
formed using Equation 5.
AARt=1
N
N
i=1
ARi,t (5)
where ARi,t represents the abnormal return estimated on the i-th security and N the
securities’ population. In the words of Kothari and Warner (2008), the cross-sectional
aggregation of abnormal returns makes sense if one aims either at studying if the event
alters, on average, the security holders’ wealth, or at testing economic models and
alternative hypotheses suggesting the sign of the mean impact.
Lastly, when the focus is on the average eﬀect over multiple days it is necessary to
perform both of the aggregations just described and compute the Cumulative Average
Abnormal Returns (CAARs), by summing over time the AARs, as shown in Equation
6.
CAAR(t1,t
2)=
t2
t=t1
AARt(6)
The literature suggests an alternative method to compute both AARs and CAARs,
named the portfolio approach. Levering on an equally weighted portfolio that groups
all securities under scrutiny (before computing the abnormal components), one can
compute the portfolio ARs (a substitute for the AARs) and CARs (instead of the
CAARs), considering the portfolio as a single security. By default, estudy program
performs both techniques.
2.2 Statistical properties of abnormal returns
Once abnormal returns are computed in any form suits the analysis, it is necessary
to study their stastical signiﬁcance. To assume economic relevance, ARs2must be
statistically signiﬁcant, i.e. their diﬀerence from zero must be veriﬁed employing an
To this end, the literature oﬀers two types of tests, parametric and non-parametric:
while the former assumes a certain distribution of returns, the latter is not anchored to
any a-priori assumption.
With respect to the former family, under the assumption of Normally distributed
securities’ returns, ARs follow a Normal distribution centered on 0, with variance σ2
AR.
Accordingly, also AARs, CARs, and CAARs are Normally distributed with mean 0 and
var ianc e σ2
AAR,σ2
CAR,andσ2
CAAR
3. We dub this test “Normal”.
Alternatively, Patell (1976) proposes a parametric test that, basing on scaled abnormal
returns, brings a twofold beneﬁt. On the one hand, the test takes into account the di-
verse standard deviation between event-period and estimation period residuals. On the
other hand, it prevents securities with large variance to heavily inﬂuence the outcome;
2. The same holds for AARs, CARs and CAARs
3. For a complete description of these variances see MacKinlay (1997) and Binder (1998) among
others.
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werefertothistestas“Patell.
Boehmer et al. (1991) (BMP test) improve Patell’s test, by taking into account the pos-
sible cross-sectional increase in the variance of the returns that may occur within the
event window.
These three tests (Normal, Patell and BMP), however, suﬀer from the cross-sectional
correlation of abnormal returns that heavily aﬀects their outcome in case of event
day clustering, that veriﬁes when a single event simultaneously aﬀects all securities
included in the analysis. To overcome this problem, Kolari and Pynn¨onen (2010) mod-
iﬁes both Patell and BMP tests, introducing a correction for the cross-correlation and
hence proposing the adjusted Patell (AdjPatell) and Kolari and Pynn¨onen (2010) (KP)
tests.
Being linked to the Normality assumption of the securities’ returns distributions, the
aforementioned tests may underperform when returns are not Normal. Thus, without
relying on any distribution, the test proposed by Wilcoxon (1945) check for the statis-
tical signiﬁcance of AARs considering both the signs and the magnitude of ARs, while
the Kolari and Pynnonen (2011) generalized rank test (GRANK) outperforms both the
previous rank tests and the parametric ones without suﬀering either from the serial
correlation of ARs or from the event-induced volatility.
All the listed tests are included in the estudy package.
3estudy
The estudy command performs the event study, computing the ARs and running the
proper diagnostic, as described in the previous section. The syntax for estudy is
estudy varlist1(varlist 2) ... (varlistN) , datevar(varname) evdate(date)
dateformat(string) lb1(#) ub1(#)lb1(#) ub1(#) ... lb6(#)
ub6(#) modtype(string) indexlist(varlist ) eswlbound(#) eswubound(#)
diagnosticstat(string) suppress(string) decimal(#) showpvalues nostar
outpuptfile(string) mydataset(string)
The (maximum) N varlists must be the securities logarithmic return of the ﬁnancial
instruments subject to the event study. Each varlist, with the sole exception of the ﬁrst
one, must be speciﬁed in brackets.
3.1 Options
The options for estudy can be divided in two parts, mandatory and additional. Only
the former, below indicated with an asterisk, are strictly required to make the program
work.
*datevar(varname) speciﬁes the date variable in the dataset. The program cannot
perform the event studies if the time series of securities return is not linked to a
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6Running event studies using Stata
date variable. When the variable here indicated is not date-formatted, the program
stops.
*evdate(string) speciﬁes the date of the event. No matter the format of datevar,
evdate may be expressed as “mmddyyyy ”, “ddmmyyyy ”, and “yyyymmdd”.
*dateformat(string) speciﬁes the date format of the event date (evdate). There are
three cases: MDY ”, “DMY ”, “YMD” to indicate that the evdate option has been
speciﬁed, respectively, as“mmddyyyy”, “ddmmyyyy ”, and “yyyymmdd ”.
*lb1(#) ub1(#) [ ... lb6(#) ub6(#)] specify up to six event windows around
the event date (only the ﬁrst event window is mandatory). For each event window,
both the lower and upper bounds must be speciﬁed, and both must have an integer
format.
modtype(string)speciﬁes which model must be used to compute the (ab)normal returns.
The available options are: (i)-“SIM”, single index model (dafault option). In this
case, only one variable must be speciﬁed in the indexlist option; (ii)-“MAM”,
market adjusted model. As before, the indexlist option must indicate only one
var iabl e; (iii)-“MFM”, multi-factor model. indexlist must indicate at least
two variables (factors); (iv )-HMM”, historical mean model. In this case, the
command ignores the indexlist option.
indexlist(varlist)speciﬁes the varlist useful to compute (ab)normal component of
securities returns and is conditional to the modtype option. When either the single
index model (“SIM”) or the market adjusted model (“MAM”) has been speciﬁed,
this option must indicate only one variable. With the multi-factor model (“MFM”)
more than one variable must be speciﬁed. When the historical mean model (“HMM”)
has been set, the program ignores this option.
eswlbound(#)speciﬁes the lower bound of the estimation window. By default, the
program uses the ﬁrst trading day in the database.
eswubound(#)speciﬁes the upper bound of the estimation window. By default, it
corresponds to the 30th trading day prior to the event, thus being sure to avoid an
overlap between the estimation and the event windows.
diagnosticstat(string)speciﬁes which test must be used to analyse whether ARs
statistically diﬀer from zero. The available options are: (i)-“Normal” (default
option), assuming that securities returns, and hence ARs, are Normally distribute
and heteroscedastic across the estimation and the event windows. Despite these
assumptions are often violated, this test is commonly used to evaluate the statis-
tical signiﬁcance of ARs and CARs on single securities; (ii )-“Patell”performs
the test proposed by Patell (1976); (iii)-“ADJPatell” performs the test pro-
posed by Patell (1976) with the Kolari and Pynn¨onen (2010) adjustment. (iv )-
BMP” performs the test proposed by Boehmer et al. (1991) that improves the one
by Patell, taking into account the event-induced volatility; (v)-“KP”performs
the BMP test corrected for the cross-sectional correlation of abnormal returns (see
Kolari and Pynn¨onen 2010, for further details). (vi)-“Wilcoxon”performsthe
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nonparametric signed rank test proposed by Wilcoxon (1945); (vii)-“GRANK
performs the generalized rank test (GRANK) proposed by Kolari and Pynnonen
(2011).
suppress(string) speciﬁes the format of the output table. The option suppress may be
either “group”or“ind”. With the former, the output table shows only the ARs on
each input variable, hiding those on the group as whole and on the portfolio. On the
opposite, with the latter, only group ARs and the results for the portfolio approach
are shown, with individual ARs excluded from the output table. If not speciﬁed,
the output table prints the single ARs for each security of each varlist, the portfolio
ARs and te group AR of each varlist. A horizontal line separates the varlists.
decimal(#)speciﬁes the number of decimal that must be used in the output table.
Seven is the maximum value. By default the number of decimals is set equal to two.
showpvalues speciﬁes that the output table must show the p-value of each abnormal
return. When this option is speciﬁed, p-values are shown in brackets below the
corresponding AR.
nostar speciﬁes that the output ﬁle must not contain the stars indicating the signiﬁcance
level. If not speciﬁed, ***, ** , and * denote, by default, that ARs are statistically
signiﬁcant at the 1%, 5% and 10% level, respectively.
outpuptfile(string)speciﬁes the name of the .xlsx ﬁle in which both the ARs (always
without signiﬁcance stars) and the p-values are stored in two separate sheets. The
format imposed with suppress is maintained. The program automatically replaces
the ﬁle, should it already exist.
mydataset(string)speciﬁes the name of the Stata .dta ﬁle in which ARs (always without
signiﬁcance stars) are stored. The format imposed with suppress is maintained.
The program automatically replaces the ﬁle, should it already exist. The workﬁle,
stored in the directory in use, contains a ﬁrst variable with the securities labels and
the ARs on each event window in just as many variables.
4Examples
We illustrate how estudy works, using the dataset data estudy provided by us. This
dataset contains the time series of market returns for ten companies’ shares, as well as
the Fama and French (1993) three factors and the risk-free rate. Through our example,
we show the command syntax, clarifying how each option can be used to customize the
program thus meeting the users’ needs.
As previously pointed out, the options for estudy can be divided in two groups,
required and additional. While the former is necessary, the latter can be used to cus-
tomize the analysis but do not impair the functioning of the program. We ﬁrst show the
basic model, encompassing only required options leaving to the subsequent examples
the demonstration and use of the additional ones.
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8Running event studies using Stata
Thus, we start with a simple set-up, performing an event study on two (separate)
varlists, with only one event window of seven days (from -3 to +3) around 09 July
2015, i.e. the event date. In addition to the evdate and lb1/lb2 options (useful to
specify, respectively, the event date and window) two other options are mandatory: 1)
dateformat, the format of the event date (in this case “MDY” as the event date has
the format “mmddyyyy ”); 2) datevar, the date variable present in the dataset.
Since we are not specifying any model type, (ab)normal returns are computed according
to a Single Index Model (which is set to be the default). As such, the market (or index)
return must be indicated compiling the option indexlist.
. use data_estudy.dta
. estudy boa ford boeing (apple netflix amazon facebook google) , datevar(date)
> evdate(07092015) dateformat(MDY) indexlist(mkt) lb1(-3) ub1(3)
By default the upper bound of the estimation window has been set to (-30)
Event date: 09jul2015, with 1 event windows specified, under the Normality assum
> ption
SECURITY CA(A)R[-3,3]
Bank of America Corporation -1.15%
Ford Motor Company -1.85%
The Boeing Company 3.48%
Ptf CARs n 1 (3 securities) 0.16%
CAAR group 1 (3 securities) 0.16%
-----------------------------------------------------------
Apple Inc -2.12%
Netflix Inc 3.00%
Amazon com Inc 4.17%
Alphabet Inc 5.33%*
Ptf CARs n 2 (5 securities) 2.08%
CAAR group 2 (5 securities) 2.08%
-----------------------------------------------------------
*** p-value < .01, ** p-value <.05, * p-value <.1
When the estimation window is not speciﬁed, as in this case, by default the program
considers it to be from the ﬁrst available to the 30th trading day prior to the event
(-30). A warning message reminds the user of this. Moreover, the header of the output
brieﬂy recaps the set-up of the event study performed, reminding the event date, the
number of event windows speciﬁed, and the diagnostic test implemented.
The ﬁrst column reports the labels of the variables on which the event study has been
performed. By default, the program adds two rows per varlist showing the results for
the portfolio approach as well as the group ARs, both useful to evaluate the average
impact of the event. The remaining column reports the ARs (CARs and CAARs over
the [-3, 3] window, in this case). Statistically signiﬁcant ARs are identiﬁed by asterisks
as explained by the legend at the bottom of the table. Horizontal lines separate the
table in panels, each showing the speciﬁed varlists.
In the next example, we customize our analysis by: (i) changing the statistical test
implemented, with the option diagnosticstat; (ii) setting a precise estimation window,
using the options eswlbound and eswubound to specify the lower and the upper bound,
respectively; (iii) and adding two event windows (options lb2,ub2,lb3,andub3).
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(Continued on next page)
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10 Running event studies using Stata
. use data_estudy.dta
. estudy boa ford boeing (apple netflix amazon facebook google) , datevar(date)
> evdate(07092015) dateformat(MDY) indexlist(mkt) lb1(-3) ub1(3) lb2(-3) ub2(-1)
> lb3(0) ub3(3) diagn(BMP) eswlb(-250) eswub(-20)
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test
SECURITY CA(A)R[-3,3] CA(A)R[-3,-1] CA(A)R[0,3]
Bank of America Corporation -1.29% -2.99%* 1.70%
Ford Motor Company -1.42% -1.43% 0.01%
The Boeing Company 3.71% 2.57% 1.14%
Ptf CARs n 1 (3 securities) 0.33% -0.62% 0.95%
CAAR group 1 (3 securities) 0.33% -0.62% 0.95%*
--------------------------------------------------------------------------------
Apple Inc -3.00% -1.72% -1.27%
Netflix Inc 3.77% 0.70% 3.07%
Amazon com Inc 4.02% -0.54% 4.56%
Alphabet Inc 5.86%** 0.42% 5.44%***
Ptf CARs n 2 (5 securities) 2.24% -0.31% 2.55%
CAAR group 2 (5 securities) 2.24% -0.31% 2.55%
--------------------------------------------------------------------------------
*** p-value < .01, ** p-value <.05, * p-value <.1
As we have set the estimation window, there is no warning message. The output
table now has two more columns showing the new event windows. The table header
recalls that the Boehmer et al. (1991) test has been implemented to test the signiﬁcance
of ARs over the three event windows speciﬁed.
Should one be interested in the mean eﬀect of an event, ARs on the single variables
can be suppressed. The option suppress(ind ) meets this need.
. use data_estudy.dta
> boa ford boeing google) , datevar(date) evdate(07092015) dateformat(MDY) modt
> ype(HMM) lb1(-3) ub1(3) lb2(-3) ub2(-1) lb3(0) ub3(3) diagn(KP) eswlb(-250) es
> wub(-20) supp(ind)
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test, with the Kolari and Pynnonen adjustment
SECURITY CA(A)R[-3,3] CA(A)R[-3,-1] CA(A)R[0,3]
Ptf CARs n 1 (3 securities) 1.71% -2.34% 4.05%**
CAAR group 1 (3 securities) 1.71% -2.34% 4.05%***
--------------------------------------------------------------------------------
Ptf CARs n 2 (3 securities) 0.94% -2.25% 3.19%
CAAR group 2 (3 securities) 0.94% -2.25%** 3.19%***
--------------------------------------------------------------------------------
Ptf CARs n 3 (3 securities) 4.96% -0.78% 5.74%**
CAAR group 3 (3 securities) 4.96%*** -0.78% 5.74%***
--------------------------------------------------------------------------------
Ptf CARs n 4 (5 securities) 2.85% -2.08% 4.93%***
CAAR group 4 (5 securities) 2.85% -2.08% 4.93%**
--------------------------------------------------------------------------------
*** p-value < .01, ** p-value <.05, * p-value <.1
As required, the table reports only the portfolio and group ARs. Furthermore, in
this case, ARs are computed according to the Historical Mean Model (HMM) speciﬁed
through the option modtype. Since normal returns are supposed to be equal to the
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historical averages, the option indexlist (specifying the market returns) is no longer
required. The output table now is divided in four panels, reporting the variables speciﬁed
in each of the four varlists.
In contrast should one be interested only in the ARs on each variable, the option
suppress(group) may be speciﬁed.
. use data_estudy.dta
> boa ford boeing google) , datevar(date) evdate(07092015) dateformat(MDY) modt
> ype(MFM) indexlist(mkt smb hml) lb1(-3) ub1(3) lb2(-3) ub2(-1) lb3(0) ub3(3) d
> iagn(KP) eswlb(-250) eswub(-20) supp(group) showpvalues nostar
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test, with the Kolari and Pynnonen adjustment
SECURITY CAAR[-3,3] CAAR[-3,-1] CAAR[0,3]
Bank of America Corporation 0.25% -2.03% 2.28%
(0.9181) (0.1942) (0.2076)
Ford Motor Company -1.07% -1.21% 0.14%
(0.7036) (0.5100) (0.9464)
The Boeing Company 3.30% 2.32% 0.98%
(0.2198) (0.1878) (0.6293)
--------------------------------------------------------------------------------
IBM Corp 1.48% 0.48% 1.00%
(0.5680) (0.7778) (0.6093)
(0.8076) (0.5830) (0.8781)
Apple Inc -3.93% -2.31% -1.63%
(0.1743) (0.2235) (0.4575)
--------------------------------------------------------------------------------
Netflix Inc 3.55% 0.57% 2.98%
(0.6047) (0.8989) (0.5654)
The Coca-Cola Company 3.72% 1.64% 2.08%
(0.1030) (0.2717) (0.2283)
Amazon com Inc 3.05% -1.13% 4.18%
(0.5393) (0.7284) (0.2658)
--------------------------------------------------------------------------------
(0.8076) (0.5830) (0.8781)
Bank of America Corporation 0.25% -2.03% 2.28%
(0.9181) (0.1942) (0.2076)
Ford Motor Company -1.07% -1.21% 0.14%
(0.7036) (0.5100) (0.9464)
The Boeing Company 3.30% 2.32% 0.98%
(0.2198) (0.1878) (0.6293)
Alphabet Inc 5.30% 0.09% 5.22%
(0.0397) (0.9593) (0.0074)
--------------------------------------------------------------------------------
p-values in parentheses
Contrary to the previous example, the table now reports only ARs on single secu-
rities, hiding those on the portfolio and of the group as a whole. Moreover, the option
showpvalues prints in brackets the p-value of each signiﬁcance test below the ARs
which is referred to. Although some ARs are statistically diﬀerent from zero, asterisks
do not appear in the table, due to option nostar. ARs are computed according to
the Fama and French (1993) 3 factors model, through the options modtype(MFM )and
indexlist(mkt smb hml ).
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12 Running event studies using Stata
4.1 Export
Table 1 and 2 show what the program exports when the option outputfile is speciﬁed,
using the same set-up of the last example4. This option creates, or replace should it
already exist, an .xlsx ﬁle containing two sheets, respectively reporting ARs and p-
values. In both cases, the program stores in the ﬁrst column the labels of securities
on which the event study is performed (i.e. those included in each varlist), whereas
the speciﬁed event windows are reported in the ﬁrst row. In Table 1 (Table 2), each
intersection is ﬁlled with the corresponding ARs (p-values).
Table 1: Output results: ARs
[-3,3] [-3,-1] [0,3]
Bank of America Corporation 0.0025... -0.0203... 0.0228...
Ford Mo t o r C ompany -0.0107... -0.0121... 0.0014...
The Boeing Company 0.033... 0.0232... 0.0098...
Ptf CARs n 1 (3 securities) 0.0083... -0.0031... 0.0113...
CAAR group 1 (3 securities) 0.0083... -0.0031... 0.0113...
IBM Corp 0.0148... 0.0048... 0.01...
Apple Inc -0.0393... -0.0231... -0.0163...
Ptf CARs n 2 (3 securities) -0.0107... -0.0099... -0.0009...
CAAR group 2 (3 securities) -0.0107... -0.0099... -0.0009...
Netﬂix Inc 0.0355... 0.0057... 0.0298...
The Coca-Cola Company 0.0372... 0.0164... 0.0208...
Amazon com Inc 0.0305... -0.0113... 0.0418...
Ptf CARs n 3 (3 securities) 0.0344... 0.0036... 0.0308...
CAAR group 3 (3 securities) 0.0344... 0.0036... 0.0308...
Bank of America Corporation 0.0025... -0.0203... 0.0228...
Ford Mo t o r C ompany -0.0107... -0.0121... 0.0014...
The Boeing Company 0.033... 0.0232... 0.0098...
Alphabet Inc 0.053... 0.0009... 0.0522...
Ptf CARs n 4 (5 securities) 0.014... -0.0039... 0.018...
CAAR group 4 (5 securities) 0.014... -0.0039... 0.018...
4. We omit the option suppress in order to obtain the most complete tables.
Under review by the STATA Journal
13
Table 2: Output results: p-values
[-3,3] [-3,-1] [0,3]
Bank of America Corporation 0.9181... 0.1942... 0.2076...
Ford Mo t o r C ompany 0.7036... 0.51... 0.9464...
The Boeing Company 0.2198... 0.1878... 0.6293...
Ptf CARs n 1 (3 securities) 0.5787... 0.7523... 0.3135...
CAAR group 1 (3 securities) 0.4945... 0.7806... 0.076...
IBM Corp 0.568... 0.7778... 0.6093...
Apple Inc 0.1743... 0.2235... 0.4575...
Ptf CARs n 2 (3 securities) 0.5448... 0.3949... 0.9488...
CAAR group 2 (3 securities) 0.5738... 0.2965... 0.9488...
Netﬂix Inc 0.6047... 0.8989... 0.5654...
The Coca-Cola Company 0.103... 0.2717... 0.2283...
Amazon com Inc 0.5393... 0.7284... 0.2658...
Ptf CARs n 3 (3 securities) 0.2603... 0.857... 0.1825...
CAAR group 3 (3 securities) 0.0131... 0.5092... 0...
Bank of America Corporation 0.9181... 0.1942... 0.2076...
Ford Mo t o r C ompany 0.7036... 0.51... 0.9464...
The Boeing Company 0.2198... 0.1878... 0.6293...
Alphabet Inc 0.0397... 0.9593... 0.0074...
Ptf CARs n 4 (5 securities) 0.258... 0.628... 0.0553...
CAAR group 4 (5 securities) 0.2478... 0.6121... 0.0599...
For exposition ease we have truncated both ARs and p-values to the fourth decimal.
Yet, the program always exports numbers with 16 decimals.
5 References
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bond performance. Review of Financial Studies 22(10): 4219–4258.
Binder, J. 1998. The event study methodology since 1969. Review of quantitative
Finance and Accounting 11(2): 111–137.
Boehmer, E., J. Musumeci, and A. B. Poulsen. 1991. Event-study methodology under
conditions of event-induced variance. Journal of ﬁnancial economics 30(2): 253–272.
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bonds. Journal of ﬁnancial economics 33(1): 3–56.
Kolari, J. W., and S. Pynn¨onen. 2010. Event study testing with cross-sectional correla-
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## Supplementary resource (1)

Data
August 2018
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
In event study analyses of abnormal returns on a single day, Corrado's (1989) nonparametric rank test and its modification in Corrado and Zivney (1992) have good empirical power properties, but problems arise in their application to cumulative abnormal returns (CARs). This paper proposes a generalized rank (GRANK) testing procedure that can be used for testing both single day and cumulative abnormal returns. Asymptotic distributions of the associated test statistics are derived and empirical properties of the test statistics are studied with simulations of CRSP returns. The results show that the proposed GRANK procedure outperforms previous rank tests of CARs and is robust to abnormal return serial correlation and event-induced volatility. Moreover, the GRANK procedure exhibits superior empirical power relative to parametric tests by Patell (1976) and Boehmer, Musumeci, and Poulsen (1991).
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