Event study Wilcoxon signed-rank test

[Anna Papadopoulos]

Dear all,

I am doing an event study where I already calculated the CAR and mean abnormal return (to account for cross-sectional effects). Now I want to perform a Wilcoxon signed-rank test to test if the median abnormal return was significantly different from 0. I know that I need to use the "signrank" command in STATA to do so. However, do I need to set it equal to 0 since I want to test the hypothesis that the median is unequal 0? I would apply it as follows:
signrank mean_abnormal_return_daily=0

, whereby mean_abnormal_return_daily is the daily average return.

I would be grateful if you could confirm whether this is correct.

Best

Anna

[Carlo Lazzaro]

Anna:
-signrank- tests the equality of the distributions from which the matched data were drawn.
That said, if you're interested in the mean, you may want to consider -qreg-, thta also allows you to include predictors:

use "C:\Program Files\Stata17\ado\base\a\auto.dta"
. qreg price
Iteration 1: WLS sum of weighted deviations = 80174.776

Iteration 1: sum of abs. weighted deviations = 80276.5
note: alternate solutions exist.
Iteration 2: sum of abs. weighted deviations = 71102.5

Median regression Number of obs = 74
Raw sum of deviations 71102.5 (about 4934)
Min sum of deviations 71102.5 Pseudo R2 = 0.0000

------------------------------------------------------------------------------
price | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | 5079 252.0459 20.15 0.000 4576.673 5581.327
------------------------------------------------------------------------------

.

[Anna Papadopoulos]

Thank you, Carlo for your explanation. I have another question regarding the use of the t-test. I calculated the test statistics for each event as follows:

gen tstat_jday=cumul_abn_ret/(standard_Dev*sqrt(12))

Since I have multiple events per company (in total 144), I need to aggregate the test statistics in order to have a single one such as in this paper that also examines multiple events per company:

However, how can I do the t-test for these multiple event windows in STATA? I know that I need to take the cumulative abnormal return variable, however when including my event_window variable, it didn't work.

Thank you very much in advance.

Kind regards

Anna

[Carlo Lazzaro]

Anna:
if you have CARs (Y) different firms (N) mesured at different (theoretically equally spaced in time) intervals, why not considering -xtreg- (if N>T) or -xtgls- or, again, -xtregar- (if T>N)?