CAPM event study using dummy variables

[Wytse Douma]

Hi guys,

For a project i am currently working on, I am looking at the effects of the Kyoto and Paris agreement on the stock market. I acquired monthly data and with that I am running a regression to test both for volatility and abnormal return. For the abnormal return I just regress it on the dummy, for the volatility i make an interaction term with the market return. However, I experience 2 problems. Firstly, when I try to combine these, STATA eliminates the interaction term because of multicoliniarity, do you know a way to get around this? Secondly, when I regress them separately, my results show an enormous beta change for the respective months (20>), is this even possible or am i doing something wrong?


Any help is greatly appreciated!

[Ken Chui]

Welcome to Statalist.

Just to chime in about the question. Currently it's in a form that would likely get no useful response because of the lack of information.

1) Please take a moment to read the FAQ (http://www.statalist.org/forums/help) on how to ask a Stata-related question
2) As for the missing interaction, 9 out of 10 times it's due to the users including manually computed dummy variables. For that, it will be important to show how the interaction was computed and how the model output table looks.
3) For the change in beta, the change of 20 can mean from nothing to huge depending on the scale of the dependent variable and independent variable. Without the context, there is no way for us to judge.

[Wytse Douma]

Thank you for the reply, since it was my first post i didn't what to include. In this reply i added my Data, Do-file and table outcome.

Kind regards

[Ken Chui]

Thanks! And please allow me to add a couple more advice.

The preferred way to share data is through -dataex- (See item 12 in FAQ). For example, here is the dataex of your first regression:

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(eFos MktRF SMB HML RMW CMA) float(IntKyoto IntParis)
                    .                     .                     .                    .                     .                     .      . .
   .06686161592043735  -.053899999999999997                 .0524               -.0192                -.0166                 .0067      0 0
   .09498062404264447   .022799999999999997                 .0837               -.1015                -.0575                -.0472      0 0
  .040807544700661356                 .0466                -.0864                .0675                 .0418   .023399999999999997      0 0
  -.10282283451584259  -.057699999999999994   -.04019999999999999  .051399999999999994   .029300000000000003                 .0444      0 0
  -.02547779056704423  -.032799999999999996                 .0012                .0556                 .0027                 .0424      0 0
   .01853610323211062   .032799999999999996                 .0431 -.013999999999999999                -.0418  -.011200000000000002      0 0
  -.03218295220398733                -.0338                -.0104                .0594                 .0242                 .0161      0 0
   .06117781718144356   .042199999999999994                -.0063               -.0137                -.0315                  .003      0 0
 -.020401029196478467                -.0524                 .0046                .0649                 .0195                 .0471      0 0
   -.0867905512219718                -.0352                -.0434                .0679                 .0567   .049699999999999994      0 0
  -.07388542318294418                -.0747                 .0067   .12240000000000001                  .062                 .0958      0 0
  -.10010361734212186                 .0137                 .0172   .07629999999999999                 -.003   .050300000000000004      0 0
   .06232377286184507                 .0187                 .0181               -.0388                -.0167                -.0385      0 0
  -.02309041231203539                -.0877   .042300000000000004                .1192                 .0287                  .087      0 0
  -.05825544084097099   -.07769999999999999                 .0063                .0712                 .0291   .046799999999999994      0 0
  .038237551535230604                 .0767  -.011399999999999999               -.0315  -.005699999999999999  -.026099999999999998      0 0
  .041415304841642964                -.0109   .027200000000000002                .0278                 .0038                 .0182      0 0
  -.07421770583499443                -.0277                 .0227                .0361 -.0014000000000000002                 .0158      0 0
 -.042155938887207256  -.026000000000000002                -.0227                .0302                 .0417   .042300000000000004      0 0
  -.06659726530994606                -.0444                   .03                .0404   .023700000000000002                 .0602      0 0
  -.15454938994359324                -.1001  -.042800000000000005                .0192   .024300000000000002                 .0379      0 0
   .02458578434413565                 .0258   .028300000000000002               -.0513  -.011399999999999999                  -.05      0 0
   -.0402414954045943                 .0553                -.0108               -.0175                -.0179                -.0331      0 0
 -.011570185393269285                 .0066                 .0048                .0134                 .0053                 .0095      0 0
  .028223327514269207  -.030699999999999998                 .0177                .0202                 .0374                 .0298      0 0
  -.01396537487180416                -.0072  .0060999999999999995                .0348                 .0449   .052300000000000006      0 0
   .05943064656718271                 .0466                 .0147                .0051 -.0007000000000000001                -.0044      0 0
  -.03725102168347397                -.0248                 .0495  .054000000000000006                 .0183                 .0478      0 0
 -.036686952597639585  .0034999999999999996  .0078000000000000005                .0332                 .0097                 .0275      0 0
  -.06554587808867875                -.0545   .026699999999999998                .0218                 .0241   .027999999999999997      0 0
  -.12769349460947796                -.0873  -.011699999999999999                .0016   .027000000000000003  .0007000000000000001      0 0
  .006047227431216677                 .0019                -.0109                .0166                 .0037  -.005600000000000001      0 0
  -.06094454698120606   -.10339999999999999                 .0315                .0104   .023399999999999997                 -.002      0 0
  -.05194941130149901                 .0594                -.0602               -.0364                -.0292 -.0007000000000000001      0 0
 -.015034963469503608   .051399999999999994 -.0039000000000000003               -.0069  -.050499999999999996                 .0192      0 0
 -.007809016900103569  -.042300000000000004                 .0264                .0355                 .0329                -.0051      0 0
   .04488270195640554                -.0273   .019799999999999998                .0084                -.0037   .005600000000000001      0 0
 -.013561702503098613                -.0184                 .0085                .0166                 .0044                -.0005      0 0
  -.05289089623068709 -.0034999999999999996                 .0037               -.0106                 .0101                 .0022      0 0
  -.01486782758830931                  .087 -.0039000000000000003               -.0075  -.024399999999999998                 .0037      0 0
   .07309456765554236                 .0658                 .0305                .0048  -.025699999999999997                 .0059      0 0
  .031708548625311965                 .0206   .022000000000000002                .0077                 .0095                -.0009      0 0
  .020124663853708282   .022000000000000002                 .0229                .0143                -.0364                 .0144      0 0
   .08280265371592854                 .0273   .028900000000000002                .0128                -.0148                 .0166      0 0
  .039098386221582834                 .0132                 .0294                 .001                 .0161                -.0031      0 0
   .03377322287533043                 .0587                 .0106                .0248                -.0207                  .017      0 0
  .031227494391190738                 .0168                -.0011                .0019                -.0032  .0060999999999999995      0 0
   .05396271391354121                 .0564                -.0147                .0095                 .0031   .004699999999999999      0 0
   .05185975455500784                 .0229                 .0281  .018500000000000003                -.0183                 .0231      0 0
   .04644610065852714                 .0192                 .0022                .0069   .011699999999999999                -.0118      0 0
 -.003777780694418079                -.0003                 .0393 .0045000000000000005                 .0118                -.0134      0 0
  -.03524383971941256  -.023399999999999997                -.0064               -.0167                 .0291                -.0076      0 0
 -.025011462170958367                 .0067                -.0155                .0023                -.0069                -.0046      0 0
  .006059605869911141   .023799999999999998                 .0248                .0102                 .0102                  .001      0 0
   .01890612631213596                -.0379                -.0121                .0233                 .0207                -.0037      0 0
 -.020669447399846344                 .0036                 -.005                .0125                 .0046                 -.005      0 0
   .05700180220606725                 .0215   .012199999999999999                .0048                -.0053                -.0013      0 0
   .02378614144433403                 .0256                 .0051                .0013                 .0044                 .0075      0 0
  .047460367957734784                 .0538                 .0222                .0126                -.0138                 .0042      0 0
  .005831728373126388                  .038                 .0008                .0054 -.0014000000000000002  .0034000000000000002      0 0
  .054836083609272765  -.019299999999999998                 .0241                .0148                  .021                -.0023 -.0193 0
   .08528666760678276   .029900000000000003                 .0062                .0141   .011200000000000002                 .0049      0 0
 -.002473420676644332                -.0202                -.0026                .0155  .0040999999999999995   .005699999999999999      0 0
  -.08548513808957672  -.026000000000000002  -.009300000000000001                .0005                 .0038                -.0032      0 0
 -.005206336968235089                 .0143  -.009399999999999999               -.0008                -.0069  .0028000000000000004      0 0
   .05978003208566742                 .0123                 .0208                .0163                 .0084                 .0005      0 0
   .07170245862141628                 .0354                 .0102               -.0015                 -.002 -.0045000000000000005      0 0
   .08854584243301496                 .0104                 .0064                 .008                 .0021                 .0038      0 0
   .07459114627976583                 .0208                -.0019                .0096   .005699999999999999                -.0079      0 0
  -.09624646974658474                -.0268 -.0014000000000000002                .0023                -.0129                 .0037      0 0
  .013533396888031986   .028999999999999998  .0007000000000000001               -.0074                -.0059                -.0108      0 0
  .026484292798595918                 .0258   .021400000000000002               -.0053                 .0075                -.0069      0 0
   .12312707770349125                 .0452                 .0278                .0141                -.0076  -.011399999999999999      0 0
 -.005635178080147207                -.0046                -.0063  .013500000000000002  -.011200000000000002   .005600000000000001      0 0
  .055328507495805306   .024300000000000002   .019799999999999998                .0043                -.0054 -.0034999999999999996      0 0
   .06341157322348193                 .0287  .0055000000000000005                .0132                 .0137                -.0037      0 0
   -.0675255019849891                -.0412                -.0204  .011699999999999999                 .0091                 .0128      0 0
  -.04874385962005515                -.0059                -.0163                 .001                  .006 -.0028000000000000004      0 0
-.0009295559288442865                -.0025                -.0278                 .025                 .0032                  .008      0 0
 -.010791290783090154                 .0223                 .0013               -.0074                -.0058  .0060999999999999995      0 0
  -.10868048322281965                  .006  -.013300000000000001                 .005                -.0004   .011399999999999999      0 0
  -.00344750064708469                 .0333                 .0046               -.0037                 .0049                -.0084      0 0
  .021176440500820598                 .0229                  .003                 .004                -.0004                -.0026      0 0
  -.00315359126273294   .018500000000000003                -.0012  .013600000000000001                -.0006                 .0037      0 0
   .00526366443318161   .009300000000000001   .009300000000000001                .0013                -.0037                 .0063      0 0
 -.025351440312506586 -.0055000000000000005                 .0151 .0078000000000000005  .0014000000000000002                 .0005      0 0
 -.009605563761485941                 .0176                 .0022                .0048                 .0046                 -.002      0 0
  .006801419565466694                 .0371  -.008100000000000001                .0031                 .0037                 .0024      0 0
  .029321286679706415   .024900000000000002                -.0077                .0063                  .005                -.0021      0 0
 -.009213067694048366                -.0079                 .0108                .0006                 .0111                -.0032      0 0
  -.03390320785948763  -.023700000000000002                 .0023 -.009000000000000001                 .0069                -.0085      0 0
   -.0863264033144388  -.011399999999999999                -.0348               -.0048 -.0017000000000000001                 .0086      0 0
  .032661594184631736   .044199999999999996  -.023399999999999997               -.0163                -.0022                -.0233      0 0
  .023361596428267958                 .0318                 .0066               -.0301                 .0116                -.0144      0 0
  -.09850794549154177   -.04650000000000001                -.0339 -.006500000000000001                 .0083                   .02      0 0
 .0002333588477546186  -.015300000000000001                -.0083                .0076                 .0013 -.0007000000000000001      0 0
  -.07918912709002007                -.0785  -.008100000000000001                .0268  -.011699999999999999                 .0245      0 0
   .04097058981788167                -.0004                 .0202 -.008199999999999999                 .0168                -.0121      0 0
  -.04611274233086763                -.0125  -.005600000000000001                .0147                 .0001                 .0187      0 0
end

Second, I did download your files and ran all 16 regressions inside, none of them showed any "omitted due to collinearity". So, at the end I can't make any diagnosis. However, I did spot that the interaction terms were manually calculated:

generate IntKyoto = Kyoto*MktRF
generate IntParis = Paris*MktRF

And also in the regression models that used these interaction terms, their original terms (Kyoto, MktRF, Paris) were not included. That would not be a full interaction test, cause the reference groups are now different.

In Stata, there is a much better way to indicate interaction in a model by use #, ##, i., and c.. Use the command below to learn more:

help fvvarlist

Third, because there were 16 models, I also was not sure which one is the >20 you referred to in #1.

Briefly, should you decide to keep digging what's wrong with the analysis, I'd strong encourage you to edit your question with the mindset that we are all trying to be helpful but also rather busy. Try your best to make your questions easy for us, by narrowing down to the problematic area.

I hope this helps.

[Wytse Douma]

Thank you for helping me! Under a little time pressure so i was not able to read the entire FAQ. I added the data into the question and re posted it.