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st: General Advice on robust standard errors for event study models with multiple dummy variables


From   Thomas Jacobs <thomasjacobs@gmail.com>
To   StataList <statalist@hsphsun2.harvard.edu>
Subject   st: General Advice on robust standard errors for event study models with multiple dummy variables
Date   Fri, 1 May 2009 14:51:56 -0500

Dear Listers,

This is not stata-specific per se, but I am performing a series of
event studies with 100 days of observation, 4 variables to measure the
market return, and anywhere from 4 to 6 event days immediately
following the observation period.  In addition to introducing an event
indicator dummy variable, EventInd which is 1 on event days, I wish to
interact it with the 4 market variables to measure changes in market
risk for the modeled firm during the event period.  Thus I have the
following multivariate regression model for the study of a firm's
excess return, ESR, over the union of observation period and event
period:

reg ESR FFMkt SMB HML UMD EvInd_FFMkt EvInd_SMB EvInd_HML EvInd_UMD EvInd

for those cases where I have only 4 event days, one of the dummies
will be dropped (typically the EvInd_SMB) as I will have one more
variable only taking non-zero values during the event than event days.

My question is whether one is better to avoid robust style standard
errors (White, etc.) in such a problem, particularly if my focus is
the EventInd variable, the measure I am using to assess the existence
of an event based abnormal return?  Further, are there any concerns
about having one dummy for each event day as opposed to significantly
more event days than dummies I am trying to model?

Generally, I get dramatically larger t stats and lower standard errors
if I use the robust option for the dummy variables while I get the
usual smaller standard errors and larger t stats for the non-dummy
variables:

Linear regression                                      Number of obs =     104
                                                       F(  4,    95) =       .
                                                       Prob > F      =       .
                                                       R-squared     =  0.6173
                                                       Root MSE      =  .02282

------------------------------------------------------------------------------
             |               Robust
         ESR |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       FFMkt |   1.492736   .2175287     6.86   0.000     1.060887    1.924585
         SMB |   -1.05778   .7261422    -1.46   0.148    -2.499355    .3837943
         HML |  -.0806645   1.033502    -0.08   0.938    -2.132426    1.971097
         UMD |  -1.803929    .403835    -4.47   0.000    -2.605642   -1.002215
 EvInd_FFMkt |   9.490433   .2678862    35.43   0.000     8.958612    10.02225
   EvInd_SMB |  (dropped)
   EvInd_HML |    46.1915   1.110029    41.61   0.000     43.98782    48.39519
   EvInd_UMD |   18.60486   .4024848    46.23   0.000     17.80583    19.40389
    EventInd |   .1749979   .0030501    57.37   0.000     .1689426    .1810531
       _cons |  -.0002698   .0024144    -0.11   0.911    -.0050629    .0045234

vs. no robust option

      Source |       SS       df       MS              Number of obs =     104
-------------+------------------------------           F(  8,    95) =   19.15
       Model |  .079811878     8  .009976485           Prob > F      =  0.0000
    Residual |  .049481274    95  .000520856           R-squared     =  0.6173
-------------+------------------------------           Adj R-squared =  0.5851
       Total |  .129293152   103  .001255273           Root MSE      =  .02282

------------------------------------------------------------------------------
         ESR |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       FFMkt |   1.492736   .2052761     7.27   0.000     1.085211    1.900261
         SMB |   -1.05778   .6147571    -1.72   0.089    -2.278227     .162667
         HML |  -.0806645   .9463244    -0.09   0.932    -1.959356    1.798027
         UMD |  -1.803929   .4087782    -4.41   0.000    -2.615456   -.9924013
 EvInd_FFMkt |   9.490433   2.876476     3.30   0.001     3.779907    15.20096
   EvInd_SMB |  (dropped)
   EvInd_HML |    46.1915   10.05867     4.59   0.000     26.22251     66.1605
   EvInd_UMD |   18.60486   4.416877     4.21   0.000     9.836252    27.37347
    EventInd |   .1749979   .0619521     2.82   0.006     .0520074    .2979883
       _cons |  -.0002698   .0024621    -0.11   0.913    -.0051576    .0046181
------------------------------------------------------------------------------

Any thoughts or suggestions would be appreciated.  Note that my
problem is not amenable to the standard cumulative abnormal return
measures used in most event studies, thus my implementation of the
multi-variate regression model approach.  Thanks.

Tom
--
Thomas Jacobs
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