Significance test in Event Study

[Mai Hang Nguyen]

Dear Statalist,

Thank to your help, I have successfully conducted my event study and calculated AR and CAR

Now I want to test the significance of abnormal return using the parametric t-test and the non-parametric generalised sign test

What codes should I use?

Thank you very much

[Marcos Almeida]

Since there is no example to work on, you may just type in Stata's command window:

help ttest
help signtest

There you will find interesting examples.

[Mai Hang Nguyen]

Since there is no example to work on, you may just type in Stata's command window:

help ttest
help signtest

There you will find interesting examples.

Hi Here an example of my data
Thank you in advance

* Example generated by -dataex-. To install: ssc install dataex
clear
input int(company_id date) double(ret market_return) float set int event_date float(group_id datenum td dif event_window count_event_obs estimation_window count_est_obs predicted_return id abnormal_return cumulative_abnormal_return ar_sd test)
 1 20663            317.45 657.14 1 20670  1 1715 1720 -5 1 4 0 200  305.5646  1  11.885394   71.15617  4.942514   3.599189
 1 20664            320.34 652.23 1 20670  1 1716 1720 -4 1 4 0 200 304.81107  1  15.528934   71.15617  4.942514   3.599189
 1 20667            326.11 648.38 1 20670  1 1717 1720 -3 1 4 0 200  304.2202  1  21.889786   71.15617  4.942514   3.599189
 1 20668            324.18 636.05 1 20670  1 1718 1720 -2 1 4 0 200 302.32794  1   21.85206   71.15617  4.942514   3.599189
 2 18770              .892 417.82 1 18777  2  362  367 -5 1 4 0 200  .6688954  2  .22310464  1.1091204 .04429332   6.260088
 2 18771              .902 402.59 1 18777  2  363  367 -4 1 4 0 200   .613057  2  .28894305  1.1091204 .04429332   6.260088
 2 18772              .883 386.36 1 18777  2  364  367 -3 1 4 0 200  .5535522  2   .3294478  1.1091204 .04429332   6.260088
 2 18773              .864 398.04 1 18777  2  365  367 -2 1 4 0 200  .5963751  2  .26762488  1.1091204 .04429332   6.260088
 3 20585              2.53 614.06 1 20592  3 1659 1664 -5 1 4 0 200 3.7104495  3 -1.1804495  -4.788177 .04866911 -24.595564
 3 20586              2.55 612.12 1 20592  3 1660 1664 -4 1 4 0 200  3.691598  3 -1.1415982  -4.788177 .04866911 -24.595564
 3 20587              2.47 610.82 1 20592  3 1661 1664 -3 1 4 0 200  3.678966  3  -1.208966  -4.788177 .04866911 -24.595564
 3 20590              2.47 615.78 1 20592  3 1662 1664 -2 1 4 0 200  3.727163  3  -1.257163  -4.788177 .04866911 -24.595564
 4 20958             26200 733.82 1 20965  4 1926 1931 -5 1 4 0 200  24461.55  4  1738.4492   12047.22 1266.4108  2.3782213
 4 20961             26900  744.1 1 20965  4 1927 1931 -4 1 4 0 200   24346.9  4   2553.098   12047.22 1266.4108  2.3782213
 4 20962             27400 740.93 1 20965  4 1928 1931 -3 1 4 0 200 24382.256  4   3017.744   12047.22 1266.4108  2.3782213
 4 20963             29100 742.74 1 20965  4 1929 1931 -2 1 4 0 200  24362.07  4  4737.9297   12047.22 1266.4108  2.3782213
 5 20031             35.03 598.39 1 20038  5 1263 1268 -5 1 4 0 200 35.453106  5  -.4231059   5.996816 1.3223332  1.1337565
 5 20032             37.15 597.01 1 20038  5 1264 1268 -4 1 4 0 200 35.470806  5   1.679194   5.996816 1.3223332  1.1337565
 5 20033             37.84 597.85 1 20038  5 1265 1268 -3 1 4 0 200 35.460033  5  2.3799665   5.996816 1.3223332  1.1337565
 5 20034 37.76000000000001 602.59 1 20038  5 1266 1268 -2 1 4 0 200  35.39924  5  2.3607614   5.996816 1.3223332  1.1337565
 6 20191          18149.94 559.54 1 20198  6 1377 1382 -5 1 4 0 200 14560.957  6   3588.983  15024.508  314.5903  11.939743
 6 20192          18149.94 558.67 1 20198  6 1378 1382 -4 1 4 0 200 14567.427  6   3582.513  15024.508  314.5903  11.939743
 6 20193          18149.94  564.5 1 20198  6 1379 1382 -3 1 4 0 200  14524.07  6  3625.8696  15024.508  314.5903  11.939743
 6 20194           18723.1 568.28 1 20198  6 1380 1382 -2 1 4 0 200 14495.958  6   4227.142  15024.508  314.5903  11.939743
 7 20073            280000 535.14 1 20080  7 1293 1298 -5 1 4 0 200 288632.38  7  -8632.375  -6153.375  5257.736 -.29258674
 7 20074            285500 518.22 1 20080  7 1294 1298 -4 1 4 0 200 281811.16  7   3688.844  -6153.375  5257.736 -.29258674
 7 20075            284000 528.45 1 20080  7 1295 1298 -3 1 4 0 200 285935.34  7 -1935.3438  -6153.375  5257.736 -.29258674
 7 20076            284500 523.09 1 20080  7 1296 1298 -2 1 4 0 200  283774.5  7      725.5  -6153.375  5257.736 -.29258674
 8 19410          21119.37 476.73 1 19417  8  820  825 -5 1 4 0 200  21324.26  8  -204.8878 -1842.3643 197.92004 -2.3271573
 8 19411          20794.46 477.69 1 19417  8  821  825 -4 1 4 0 200  21353.46  8  -559.0009 -1842.3643 197.92004 -2.3271573
 8 19414          21119.37 483.69 1 19417  8  822  825 -3 1 4 0 200 21535.975  8  -416.6046 -1842.3643 197.92004 -2.3271573
 8 19415          20307.09 465.05 1 19417  8  823  825 -2 1 4 0 200  20968.96  8  -661.8709 -1842.3643 197.92004 -2.3271573
 9 19785          15538.47 573.38 1 19792  9 1087 1092 -5 1 4 0 200 15700.824  9  -162.3542  -1140.554  118.4452  -2.407345
 9 19786          15384.63 569.97 1 19792  9 1088 1092 -4 1 4 0 200 15591.729  9  -207.0985  -1140.554  118.4452  -2.407345
 9 19787          15384.63 574.94 1 19792  9 1089 1092 -3 1 4 0 200 15750.733  9  -366.1034  -1140.554  118.4452  -2.407345
 9 19788          15461.55 578.56 1 19792  9 1090 1092 -2 1 4 0 200 15866.548  9  -404.9979  -1140.554  118.4452  -2.407345
12 19275          19740.02 393.67 1 19282 12  723  728 -5 1 4 0 200 19506.824 10   233.1958   -49.0007  222.6451 -.05502108
12 19276          19617.41 394.66 1 19282 12  724  728 -4 1 4 0 200  19509.23 10  108.17953   -49.0007  222.6451 -.05502108
12 19277           19372.2 394.19 1 19282 12  725  728 -3 1 4 0 200 19508.088 10  -135.8879   -49.0007  222.6451 -.05502108
12 19278          19249.59 392.54 1 19282 12  726  728 -2 1 4 0 200 19504.078 10 -254.48813   -49.0007  222.6451 -.05502108
14 18596 7.155000000000015 451.59 1 18603 14  238  243 -5 1 4 0 200  5.718357 11   1.436643    6.70236  .3346611   5.006827
14 18597 7.185000000000015 449.93 1 18603 14  239  243 -4 1 4 0 200  5.794424 11   1.390576    6.70236  .3346611   5.006827
14 18598 7.215000000000015 457.42 1 18603 14  240  243 -3 1 4 0 200  5.451207 11   1.763793    6.70236  .3346611   5.006827
14 18599 7.245000000000015 464.35 1 18603 14  241  243 -2 1 4 0 200  5.133651 11  2.1113486    6.70236  .3346611   5.006827
16 20901              5920 719.56 1 20908 16 1885 1890 -5 1 4 0 200  5214.721 12   705.2793  2894.7266  75.79781   9.547526
16 20902              5950 722.14 1 20908 16 1886 1890 -4 1 4 0 200  5233.901 12   716.0986  2894.7266  75.79781   9.547526
16 20905              5890 723.52 1 20908 16 1887 1890 -3 1 4 0 200  5244.161 12   645.8389  2894.7266  75.79781   9.547526
16 20906              6040 719.26 1 20908 16 1888 1890 -2 1 4 0 200   5212.49 12   827.5098  2894.7266  75.79781   9.547526
17 19912                20 591.47 1 19919 17 1178 1183 -5 1 4 0 200 19.385933 13   .6140671   2.859705  .0979916   7.295791
17 19913             20.04  591.6 1 19919 17 1179 1183 -4 1 4 0 200  19.38785 13   .6521502   2.859705  .0979916   7.295791
17 19914             20.06 584.88 1 19919 17 1180 1183 -3 1 4 0 200 19.288805 13    .771195   2.859705  .0979916   7.295791
17 19915             20.08 582.77 1 19919 17 1181 1183 -2 1 4 0 200  19.25771 13   .8222924   2.859705  .0979916   7.295791
18 20509              8800 562.82 1 20516 18 1605 1610 -5 1 4 0 200 22097.586 14 -13297.586  -54846.59  328.3264  -41.76225
18 20510              8600 566.11 1 20516 18 1606 1610 -4 1 4 0 200  22198.97 14 -13598.973  -54846.59  328.3264  -41.76225
18 20513              8000 559.37 1 20516 18 1607 1610 -3 1 4 0 200  21991.27 14  -13991.27  -54846.59  328.3264  -41.76225
18 20514              8100 561.56 1 20516 18 1608 1610 -2 1 4 0 200  22058.76 14 -13958.758  -54846.59  328.3264  -41.76225
20 20594          121666.3 614.81 1 20601 20 1666 1671 -5 1 4 0 200 110156.64 15   11509.66   45495.86  755.4941  15.055002
20 20597          121666.3 611.03 1 20601 20 1667 1671 -4 1 4 0 200 109408.55 15  12257.753   45495.86  755.4941  15.055002
20 20598          120832.9 611.62 1 20601 20 1668 1671 -3 1 4 0 200 109525.31 15  11307.588   45495.86  755.4941  15.055002
20 20599          119999.6 611.89 1 20601 20 1669 1671 -2 1 4 0 200 109578.74 15  10420.857   45495.86  755.4941  15.055002
21 19369              6470 462.69 1 19376 21  791  796 -5 1 4 0 200  6906.548 16  -436.5483  -2431.102 134.94046 -4.5040274
21 19372              6330 458.97 1 19376 21  792  796 -4 1 4 0 200  6898.755 16  -568.7549  -2431.102 134.94046 -4.5040274
21 19373              6220 461.42 1 19376 21  793  796 -3 1 4 0 200  6903.888 16  -683.8877  -2431.102 134.94046 -4.5040274
21 19374              6170 465.25 1 19376 21  794  796 -2 1 4 0 200  6911.911 16  -741.9111  -2431.102 134.94046 -4.5040274
23 20747             40600 686.39 1 20754 23 1775 1780 -5 1 4 0 200   39471.8 17  1128.1953   5623.168  486.6631   2.888635
23 20748             40400 684.83 1 20754 23 1776 1780 -4 1 4 0 200  39401.29 17   998.7148   5623.168  486.6631   2.888635
23 20751             40500 678.02 1 20754 23 1777 1780 -3 1 4 0 200  39093.46 17   1406.543   5623.168  486.6631   2.888635
23 20752             41100 676.18 1 20754 23 1778 1780 -2 1 4 0 200 39010.285 17  2089.7148   5623.168  486.6631   2.888635
24 19730              3.06 510.12 1 19737 24 1048 1053 -5 1 4 0 200  2.640727 18   .4192727  1.4841845 .05160809   7.189689
24 19731              3.09  513.9 1 19737 24 1049 1053 -4 1 4 0 200  2.678198 18   .4118017  1.4841845 .05160809   7.189689
24 19732              3.04 516.98 1 19737 24 1050 1053 -3 1 4 0 200   2.70873 18   .3312698  1.4841845 .05160809   7.189689
24 19733              3.05 518.94 1 19737 24 1051 1053 -2 1 4 0 200   2.72816 18  .32184035  1.4841845 .05160809   7.189689
25 21164             23.45 917.45 1 21171 25 2072 2077 -5 1 4 0 200 24.017366 19  -.5673664 -1.8046284   .087366   -5.16399
25 21165             23.55 927.25 1 21171 25 2073 2077 -4 1 4 0 200  24.01323 19  -.4632294 -1.8046284   .087366   -5.16399
25 21166             23.65  924.4 1 21171 25 2074 2077 -3 1 4 0 200 24.014433 19  -.3644329 -1.8046284   .087366   -5.16399
25 21167              23.6 935.85 1 21171 25 2075 2077 -2 1 4 0 200   24.0096 19  -.4095997 -1.8046284   .087366   -5.16399
26 20188 6954.980000000001 554.03 1 20195 26 1376 1381 -5 1 4 0 200  6847.206 20  107.77395    -81.424  90.55653 -.22478776
26 20191 6874.110000000001 559.54 1 20195 26 1377 1381 -4 1 4 0 200  6897.718 20  -23.60777    -81.424  90.55653 -.22478776
26 20192 6793.230000000001 558.67 1 20195 26 1378 1381 -3 1 4 0 200  6889.742 20  -96.51218    -81.424  90.55653 -.22478776
26 20193 6874.110000000001  564.5 1 20195 26 1379 1381 -2 1 4 0 200  6943.188 20  -69.07799    -81.424  90.55653 -.22478776
27 19246             14900 388.88 1 19253 27  702  707 -5 1 4 0 200  15862.74 21  -962.7402 -4237.6416 218.55315  -4.847381
27 19247             14900 386.62 1 19253 27  703  707 -4 1 4 0 200  15765.64 21  -865.6406 -4237.6416 218.55315  -4.847381
27 19248             14800 388.35 1 19253 27  704  707 -3 1 4 0 200  15839.97 21 -1039.9688 -4237.6416 218.55315  -4.847381
27 19249             14600 391.36 1 19253 27  705  707 -2 1 4 0 200 15969.292 21  -1369.292 -4237.6416 218.55315  -4.847381
28 19654          20400.09 504.05 1 19661 28  994  999 -5 1 4 0 200  20339.38 22   60.70719  -1687.681  394.0988 -1.0705951
28 19655          19266.75 501.17 1 19661 28  995  999 -4 1 4 0 200  20087.81 22  -821.0605  -1687.681  394.0988 -1.0705951
28 19656          19400.09 500.75 1 19661 28  996  999 -3 1 4 0 200 20051.123 22   -651.033  -1687.681  394.0988 -1.0705951
28 19659          19400.09 496.46 1 19661 28  997  999 -2 1 4 0 200 19676.385 22 -276.29477  -1687.681  394.0988 -1.0705951
29 19143             10800 435.34 1 19150 29  629  634 -5 1 4 0 200  9171.578 23   1628.422   7793.993  397.0082   4.907954
29 19144             10700  429.2 1 19150 29  630  634 -4 1 4 0 200  8979.704 23   1720.296   7793.993  397.0082   4.907954
29 19145             10900  428.8 1 19150 29  631  634 -3 1 4 0 200  8967.204 23   1932.796   7793.993  397.0082   4.907954
29 19148             11100 416.65 1 19150 29  632  634 -2 1 4 0 200 8587.5205 23  2512.4795   7793.993  397.0082   4.907954
30 20720             29150 674.09 1 20727 30 1756 1761 -5 1 4 0 200  29039.62 24  110.38281  1056.5508  331.1244   .7976992
30 20723             28850 677.04 1 20727 30 1757 1761 -4 1 4 0 200  28965.25 24    -115.25  1056.5508  331.1244   .7976992
30 20724             29200 684.89 1 20727 30 1758 1761 -3 1 4 0 200  28767.36 24   432.6426  1056.5508  331.1244   .7976992
30 20725             29350 686.72 1 20727 30 1759 1761 -2 1 4 0 200 28721.225 24   628.7754  1056.5508  331.1244   .7976992
31 20887              14.4  715.8 1 20894 31 1875 1880 -5 1 4 0 200 13.321717 25  1.0782827   3.971292 .10934312   9.079885
31 20888             14.15 712.21 1 20894 31 1876 1880 -4 1 4 0 200 13.284055 25   .8659452   3.971292 .10934312   9.079885
31 20891              14.2 710.17 1 20894 31 1877 1880 -3 1 4 0 200 13.262654 25   .9373457   3.971292 .10934312   9.079885
31 20892              14.4 714.71 1 20894 31 1878 1880 -2 1 4 0 200 13.310282 25  1.0897182   3.971292 .10934312   9.079885
end
format %tdnn/dd/CCYY date
format %tdnn/dd/CCYY event_date

[Marcos Almeida]

To perform t tests, we are supposed to have: a) a numerical variable and 2 groups; b) a numerical variable in 2 columns. I don't see any of these situations in the data you shared.

[David Benson]

Generally, it is easier to do that calculation within EVENTUS (a WRDS data program that runs on CRSP data) to calculate the parametric t-test and the non-parametric generalized sign test (rather than within Stata).