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  • Testing significance of CAR in event study

    Dear Statalists,

    i have done an Event Study as described by Princeton DSS (
    HTML Code:
    https://dss.princeton.edu/online_help/stats_packages/stata/eventstudy.html
    ) . Different from the DSS example i have CAR(s) for various event windows [-2;2] [-1;1] and [0].

    When looking at the t-statistic results i see the most of my events are not significantly different from 0 for any level from 10%-1%. I am new to statistics and therefore wonder. Before continuing with creating my regession of CARs onto other independent variables, will i need to to 'drop' all of the insignificant events?

    When i use the
    Code:
    reg CAR_MM2 if dif==0,robust
    it shows me that my overall sample of events is significantly different from 0.

    How do i go from here?


    More infos about my sample:
    - The deals are inbetween 2002 and 2016 and multiple firms have multiple events (however i believe the DSS instructions dealt with this problem)
    - Should i do any 'non-parametric' tests, such as Wilcox or Friedman? I am not sure these kind of tests apply here.
    - I do not have CRSP / U.S. data and therefor cannot use Eventus, or any other direct eventstudy command (estudy, eventstudy2) to do my analysis, many of which include these kind of robustness tests


    Please excuse if there are still open points / unclarities. I am happy to provide more informatino as well as a sample of the data. Since this seems more as a statistical reasoning rather than a 'how to compute in stata' problem i did not add it yet.

    Thank you!!

    Best regards,
    Max

  • #2
    No, you should not drop the "insignificant" events from your analysis. Even if you take statistical significance seriously here (which I would urge you not to do in the first place) it is never a useful criterion for deciding whether to continue using a variable in subsequent modeling.

    The significance habit is a difficult one to break, almost an addiction. Since you are new to statistics, it is probably better not to form it in the first place. See https://www.nature.com/articles/d41586-019-00857-9 for a pep talk about this. And then, when you have time for some serious reading, see the new American Statistical Association position on this issue at https://www.tandfonline.com/doi/full...5.2019.1583913 and the many detailed articles that accompany that.

    Comment


    • #3
      Dear Clyde,
      thank you very much for the quick response. I have included the argumentation brought forward into the articles in my work. I have seen you comment already on many articles here, also in relation to event studies, so i assume that you are quite an expert.

      From my understanding the t-test that i have done following the DSS Princeton guide is a parametric test. As for a useful non-parametric test that is easy to code in Stata, would you have any suggestions? Corrado or the more up-to-date G-Rank-T test seem very hard to code and i have not found any topic here on Statalist where somebody has posted how they have done this, unless they were using Eventus/eventstudy2.

      In case of necessity i post my data structure below. It is currently not ordered by event, therefore many different events, markets and firms can be seen the dataex.

      Code:
      * Example generated by -dataex-. To install: ssc install dataex
      clear
      input float date str7 co_id str28 mkt_id float(co_ret mkt_ret id dif est_win1 evt_win0 evt_win1 evt_win2 AR_MM0 AR_CMM0 AR_MM1 AR_CMM1 AR_MM2 AR_CMM2 CAR_MM0 CAR_CMM0 CAR_MM1 CAR_CMM1 CAR_MM2 CAR_CMM2)
      19179 "F929724" "SWISSMARKETSMI"              .002588438    .0001628688 627 2618 0 0 0 0 . . . . . .   .006943136   -.01795634 .0005953177  -.0001689177  -.01417982   -.0580824
      19018 "F681817" "ATHEXCOMPOSITE"             -.006546645      .03929414 283 2425 0 0 0 0 . . . . . .    .01424123    .02100774 -.014416194     .03222254 -.016796347   .02713451
      19778 "F929724" "SWISSMARKETSMI"              .006060606     .006368762 627 3045 0 0 0 0 . . . . . .   .006943136   -.01795634 .0005953177  -.0001689177  -.01417982   -.0580824
      17849 "F142423" "SWISSMARKETSMI"              -.03587444     .006519536  29 1637 0 0 0 0 . . . . . .   -.03081326  -.016486656    -.031274     -.0297847   -.1705802   -.1620966
      18813 "F289504" "BEL20"                      -.010673537    -.010750538 120 2245 0 0 0 0 . . . . . .  .0039273985  -.008754493 -.002671758 -4.786067e-06  -.04968568  -.05416608
      16736 "F912324" "OMXAFFARSVARLDENSGENERAL"    -.02262749    -.011290445 506  962 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      18639 "F142344" "WIENERBOERSEINDEXWBI"      -.0022547913     .013569785  23 2258 0 0 0 0 . . . . . .    .04342421    .04195555    .0362002     .03348896   .07993882  .073942654
      20300 "F866513" "ATHEXCOMPOSITE"                       0              0 362 3325 0 0 0 0 . . . . . .  -.018237913   -.02192285  -.02639941    .012785463  -.02916204  .019971654
      18185 "F142423" "SWISSMARKETSMI"            -.0010587613     -.00354828  31 1937 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      18851 "F992838" "SWISSMARKETSMI"               .03812879       .0437256 731 2482 0 0 0 0 . . . . . .    .04941911    .04433436   .01400598    .023595884  .001924777 .0090327095
      15448 "F905009" "DAX30PERFORMANCE"           -.015360033    -.010467138 482   58 0 0 0 0 . . . . . .    .02908565    .03021797   .05953464     .04715435   .05260552   .03737473
      15096 "F992838" "SWISSMARKETSMI"                       0              0 731 -201 0 0 0 0 . . . . . .    .04941911    .04433436   .01400598    .023595884  .001924777 .0090327095
      15397 "F912398" "SBF120"                    -.0018144147     .009499128 511  -61 1 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      16616 "F255248" "OSLOSEOBX"                    .01983003    .0032850404  57  843 0 0 0 0 . . . . . .    .01545583   .017937839 .0003230991   -.019632194  .010627563 -.007182572
      20181 "F866457" "OMXHELSINKIOMXH"                      0              0 359 3237 0 0 0 0 . . . . . .   .034064334    .03211771   .06007842     .05721098    .0804277   .08239952
      17517 "F681817" "ATHEXCOMPOSITE"             -.033613447     -.02494159 283 1352 0 0 0 0 . . . . . .    .01424123    .02100774 -.014416194     .03222254 -.016796347   .02713451
      15231 "F912398" "SBF120"                     -.013374948   -.0001530565 511 -179 1 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      17482 "F912324" "OMXAFFARSVARLDENSGENERAL"    .032978136     .005692168 506 1494 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      20563 "F929702" "SWISSMARKETSMI"            -.0032076985     .013445044 622 3719 0 0 0 0 . . . . . .  .0043128706   .001499486  .010511033     .01227404 -.013549723 -.019222394
      20437 "F142423" "SWISSMARKETSMI"              .024150943     .024625953  31 3545 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      18780 "F901152" "FTSEALLSHARE"               -.032674532    -.012145356 456 2358 0 0 0 0 . . . . . .   .002433713  .0012666273   .00564775  -.0008809131  .026370805  .011242096
      16390 "F912398" "SBF120"                     -.007199142    -.004798234 511  648 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      20688 "F912324" "OMXAFFARSVARLDENSGENERAL"   -.004201681   -.0010307153 506 3784 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      16348 "F912324" "OMXAFFARSVARLDENSGENERAL"    .028756795      .01226294 506  684 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      20618 "F912324" "OMXAFFARSVARLDENSGENERAL"   -.016632017    -.017139105 506 3734 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      19387 "F929363" "SBF120"                      .001214856    .0007158467 610 2786 0 0 0 0 . . . . . .   .015684634   .020970406 -.003865973   -.005893887 -.032097366 -.033112217
      20240 "F901152" "FTSEALLSHARE"             -.00057388644    -.002831093 456 3400 0 0 0 0 . . . . . .   .002433713  .0012666273   .00564775  -.0008809131  .026370805  .011242096
      16231 "F912324" "OMXAFFARSVARLDENSGENERAL"   -.014777438    -.004309078 506  601 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      15739 "F142423" "SWISSMARKETSMI"              .011764706     .011170127  31  189 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      20167 "F143328" "OMXAFFARSVARLDENSGENERAL"     .00882353      .00294725  34 3233 0 0 0 0 . . . . . . -.0006572679   -.02681231 -.024376865   -.004645941 -.028990664   .01104513
      17874 "F885164" "SWISSMARKETSMI"              .034883723      .05206804 389 1638 0 0 0 0 . . . . . .   .004803052   -.02724683  .009199945   -.032134645   .01353131  -.02039668
      15167 "F997371" "OMXCOPENHAGENBMARKOMXCB"     -.00253523    -.007111889 737 -346 0 0 0 0 . . . . . .   -.01802808   -.02346631  -.08322814      -.087445  -.06552885  -.06680781
      16075 "F901152" "FTSEALLSHARE"               -.018593263      .00079173 456  425 0 0 0 0 . . . . . .   .002433713  .0012666273   .00564775  -.0008809131  .026370805  .011242096
      19263 "F289504" "BEL20"                      -.013876587    .0010351235 122 2584 0 0 0 0 . . . . . .   -.02320768  -.023329295  -.07095493    -.04702564  -.10134637  -.05778605
      16681 "F912324" "OMXAFFARSVARLDENSGENERAL"    .002664406   .00015519516 506  923 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      16973 "F912398" "SBF120"                     .0012409514    .0008217164 511 1065 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      16484 "F142344" "WIENERBOERSEINDEXWBI"       -.009647272 -.000030011704  23  719 0 0 0 0 . . . . . .    .04342421    .04195555    .0362002     .03348896   .07993882  .073942654
      18536 "F866457" "OMXHELSINKIOMXH"             -.01166606     .003793858 359 2062 0 0 0 0 . . . . . .   .034064334    .03211771   .06007842     .05721098    .0804277   .08239952
      20720 "F142423" "SWISSMARKETSMI"            -.0021276595    -.004181698  31 3748 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      15887 "F912398" "SBF120"                      -.02279664     -.02151283 511  289 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      18654 "F755486" "ATHEXCOMPOSITE"              .019463087    .0014159698 327 2345 0 0 0 0 . . . . . .  .0025382736   .003811472  .011730004   .0044930745  .008244092 .0009410233
      20538 "F289374" "SBF120"                               0              0 113 3612 0 0 0 0 . . . . . .  -.032759704  -.035420228 -.026419584    -.02879615  -.03953569  -.04349659
      18994 "F912398" "SBF120"                      .012658228     .019124566 511 2508 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      18865 "F929363" "SBF120"                      .002370179    -.008691674 610 2414 0 0 0 0 . . . . . .   .015684634   .020970406 -.003865973   -.005893887 -.032097366 -.033112217
      18217 "F901152" "FTSEALLSHARE"                 .03658387     .016049128 456 1955 0 0 0 0 . . . . . .   .002433713  .0012666273   .00564775  -.0008809131  .026370805  .011242096
      15592 "F866457" "OMXHELSINKIOMXH"            -.021146953    -.001424778 359  -42 1 0 0 0 . . . . . .   .034064334    .03211771   .06007842     .05721098    .0804277   .08239952
      16503 "F681714" "AEXINDEXAEX"                 .009122086    -.005477143 282  607 0 0 0 0 . . . . . .   -.02761853  -.035791382 .0011030296   -.027905807   .04205561  .008552203
      20396 "F257636" "OMXAFFARSVARLDENSGENERAL"   -.006247944     .012644995  63 3489 0 0 0 0 . . . . . .    .02903767   .010658534   .01862141    -.00865755  -.10005783   -.1376971
      16252 "F142344" "WIENERBOERSEINDEXWBI"        -.01614999    -.002680132  23  553 0 0 0 0 . . . . . .    .04342421    .04195555    .0362002     .03348896   .07993882  .073942654
      18435 "F866457" "OMXHELSINKIOMXH"            -.016441822   -.0043415125 359 1989 0 0 0 0 . . . . . .   .034064334    .03211771   .06007842     .05721098    .0804277   .08239952
      19946 "F912398" "SBF120"                      .011587006      .01284122 511 3188 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      18441 "F681714" "AEXINDEXAEX"                  .00665595     .013712077 282 1991 0 0 0 0 . . . . . .   -.02761853  -.035791382 .0011030296   -.027905807   .04205561  .008552203
      16477 "F912398" "SBF120"                      .000588224    .0002366187 511  711 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      15568 "F912324" "OMXAFFARSVARLDENSGENERAL"   -.012492444    -.009179687 506  128 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      17338 "F929724" "SWISSMARKETSMI"             -.009224091     -.01251808 627 1303 0 0 0 0 . . . . . .   .006943136   -.01795634 .0005953177  -.0001689177  -.01417982   -.0580824
      15487 "F929363" "SBF120"                       .02165237    .0041423105 607 -103 1 0 0 0 . . . . . .  -.007910261   .030593934    .0296387     .06286526   .06607094    .1667657
      18848 "F321116" "BRAZILBOVESPA"               .027951807      .05101083 199 2361 0 0 0 0 . . . . . .   -.05667364   -.08776147   -.0923568    -.14078206    -.079036  -.11580522
      20730 "F912398" "SBF120"                      .003675599    .0010843108 511 3748 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      19387 "F681714" "AEXINDEXAEX"                .0036534446     .003925087 282 2667 0 0 0 0 . . . . . .   -.02761853  -.035791382 .0011030296   -.027905807   .04205561  .008552203
      16155 "F142423" "SWISSMARKETSMI"               .05136986      .01603189  29  427 0 0 0 0 . . . . . .   -.03081326  -.016486656    -.031274     -.0297847   -.1705802   -.1620966
      17372 "F142423" "SWISSMARKETSMI"             -.013968776     -.01381238  29 1296 0 0 0 0 . . . . . .   -.03081326  -.016486656    -.031274     -.0297847   -.1705802   -.1620966
      18056 "F257636" "OMXAFFARSVARLDENSGENERAL"    -.01552284    -.003824174  63 1817 0 0 0 0 . . . . . .    .02903767   .010658534   .01862141    -.00865755  -.10005783   -.1376971
      16118 "F905009" "DAX30PERFORMANCE"            .009765928     .006240081 482  536 0 0 0 0 . . . . . .    .02908565    .03021797   .05953464     .04715435   .05260552   .03737473
      17065 "F681817" "ATHEXCOMPOSITE"              .036585364     .006848303 283 1030 0 0 0 0 . . . . . .    .01424123    .02100774 -.014416194     .03222254 -.016796347   .02713451
      19876 "F866513" "ATHEXCOMPOSITE"               .03996194     .017711774 362 3021 0 0 0 0 . . . . . .  -.018237913   -.02192285  -.02639941    .012785463  -.02916204  .019971654
      15505 "F916235" "DAX30PERFORMANCE"           -.021284336     -.03720018 531   59 0 0 0 0 . . . . . .   .002466826   -.00161159  .018081054    .023434306 -.011614387 -.010779088
      17559 "F929724" "SWISSMARKETSMI"             -.011458334    -.013679152 627 1460 0 0 0 0 . . . . . .   .006943136   -.01795634 .0005953177  -.0001689177  -.01417982   -.0580824
      20422 "F321116" "BRAZILBOVESPA"                .00857449    -.016405107 199 3485 0 0 0 0 . . . . . .   -.05667364   -.08776147   -.0923568    -.14078206    -.079036  -.11580522
      19590 "F142423" "SWISSMARKETSMI"              -.00926706   -.0004446169  29 2880 0 0 0 0 . . . . . .   -.03081326  -.016486656    -.031274     -.0297847   -.1705802   -.1620966
      17871 "F929363" "SBF120"                      -.05000896     -.05212975 607 1601 0 0 0 0 . . . . . .  -.007910261   .030593934    .0296387     .06286526   .06607094    .1667657
      15589 "F912324" "OMXAFFARSVARLDENSGENERAL"     .01199262      .02005594 506  143 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      17150 "F672626" "SWISSMARKETSMI"              .017630855     .001167873 268 1287 0 0 0 0 . . . . . .     .0403844    .04301643   .08854018     .08778267   .04440724   .04625728
      16636 "F929363" "SBF120"                       .01689697     .012688226 607  718 0 0 0 0 . . . . . .  -.007910261   .030593934    .0296387     .06286526   .06607094    .1667657
      20450 "F912398" "SBF120"                     -.017218858    -.008397464 511 3548 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      17423 "F929724" "SWISSMARKETSMI"             -.012241054     -.01187986 627 1364 0 0 0 0 . . . . . .   .006943136   -.01795634 .0005953177  -.0001689177  -.01417982   -.0580824
      19233 "F142423" "SWISSMARKETSMI"             -.015553523     -.01076213  31 2685 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      15133 "F866457" "OMXHELSINKIOMXH"              .02144772   -.0020012138 359 -369 0 0 0 0 . . . . . .   .034064334    .03211771   .06007842     .05721098    .0804277   .08239952
      19361 "F143328" "OMXAFFARSVARLDENSGENERAL"   -.019507553    .0008827943  34 2657 0 0 0 0 . . . . . . -.0006572679   -.02681231 -.024376865   -.004645941 -.028990664   .01104513
      19577 "F866513" "ATHEXCOMPOSITE"              -.02097902    .0002376503 362 2808 0 0 0 0 . . . . . .  -.018237913   -.02192285  -.02639941    .012785463  -.02916204  .019971654
      18710 "F929363" "SBF120"                       .03753656     .014097045 610 2303 0 0 0 0 . . . . . .   .015684634   .020970406 -.003865973   -.005893887 -.032097366 -.033112217
      16975 "F912398" "SBF120"                       .02419024      .00312544 511 1067 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      20278 "F912398" "SBF120"                      .025091726      .02435177 511 3426 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      19540 "F866513" "ATHEXCOMPOSITE"              .013333334     .004542398 362 2781 0 0 0 0 . . . . . .  -.018237913   -.02192285  -.02639941    .012785463  -.02916204  .019971654
      16684 "F289504" "BEL20"                       .007491216     .004596795 120  724 0 0 0 0 . . . . . .  .0039273985  -.008754493 -.002671758 -4.786067e-06  -.04968568  -.05416608
      17612 "F142344" "WIENERBOERSEINDEXWBI"                 0              0  23 1525 0 0 0 0 . . . . . .    .04342421    .04195555    .0362002     .03348896   .07993882  .073942654
      15025 "F912324" "OMXAFFARSVARLDENSGENERAL"    .011946387     .003406768 506 -261 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      14990 "F142423" "SWISSMARKETSMI"             -.009287925    .0018080556  31 -346 0 0 0 0 . . . . . .  -.016263746  -.010894367 -.030405626   -.016775474 -.019161943 -.009279845
      20782 "F905009" "DAX30PERFORMANCE"             .01802677     .002515372 482 3868 0 0 0 0 . . . . . .    .02908565    .03021797   .05953464     .04715435   .05260552   .03737473
      20024 "F929363" "SBF120"                      .013095614     .005062712 610 3241 0 0 0 0 . . . . . .   .015684634   .020970406 -.003865973   -.005893887 -.032097366 -.033112217
      17539 "F289504" "BEL20"                       .005254126  -.00002684708 122 1352 0 0 0 0 . . . . . .   -.02320768  -.023329295  -.07095493    -.04702564  -.10134637  -.05778605
      19243 "F901152" "FTSEALLSHARE"                .006607774    .0043141814 456 2689 0 0 0 0 . . . . . .   .002433713  .0012666273   .00564775  -.0008809131  .026370805  .011242096
      20130 "F912398" "SBF120"                      -.00844773    -.003363874 511 3320 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      20228 "F143328" "OMXAFFARSVARLDENSGENERAL"   -.005568862    .0006131443  34 3276 0 0 0 0 . . . . . . -.0006572679   -.02681231 -.024376865   -.004645941 -.028990664   .01104513
      15805 "F912398" "SBF120"                     -.033334404    -.024779627 511  231 0 0 0 0 . . . . . . -.0007772278  -.011772524   .00790539  -.0019163864  .010006465 -.006362977
      15887 "F929363" "SBF120"                      -.01682478     -.02151283 607  183 0 0 0 0 . . . . . .  -.007910261   .030593934    .0296387     .06286526   .06607094    .1667657
      16498 "F912324" "OMXAFFARSVARLDENSGENERAL"     .02042843     .001576145 506  792 0 0 0 0 . . . . . .   .006504399 -.0034989566  .002967647     -.0144485  .008382416 -.005604689
      17429 "F936775" "SBF120"                    -.0010373445    -.007398046 704 1419 0 0 0 0 . . . . . .  -.012069792 -.0035411105  .006372496    .003377718 -.025049094  .017601376
      17637 "F755486" "ATHEXCOMPOSITE"               .01906275    .0009294553 327 1618 0 0 0 0 . . . . . .  .0025382736   .003811472  .011730004   .0044930745  .008244092 .0009410233
      19375 "F866513" "ATHEXCOMPOSITE"               .02951389     .000976091 362 2664 0 0 0 0 . . . . . .  -.018237913   -.02192285  -.02639941    .012785463  -.02916204  .019971654
      20006 "F929363" "SBF120"                     -.028121656    -.016209353 610 3229 0 0 0 0 . . . . . .   .015684634   .020970406 -.003865973   -.005893887 -.032097366 -.033112217
      end
      format %tdYMD date
      Best wishes,
      Max

      Comment


      • #4
        The simplest non-parametric analog to the two-sample t-test is the Wilcoxon rank sum test (also known as the Mann-Whitney U-test). The command, -ranksum- is part of official Stata, and the syntax is just like that of the -ttest- command.

        I am not familiar with the Corrado or G-rank-T tests you refer to, so I can't comment about them.

        Comment

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