Event study difference-in-difference regression

I am currently writing my master thesis, and I have run into some problems where I hope someone can help me. My primary goal is to investigate whether High ESG companies were more resilient than low ESG companies during the Covid-19 stock market crash.

My research approach follows the following paper: https://academic.oup.com/rcfs/article/9/3/593/5868419?login=true#208403379

Thus, my difference-in-difference regression looks like this:

reg2 <- plm(Panel$AR_ESIUWRF2 ~ Panel$ESG_Treated*Panel$Post_Covid + Panel$ESG_Treated*Panel$Post_Fiscal, data = Panel, index = c("id", "t"), model = "within", effect = "twoways")

Where AR_ESIUWRF2 represents the daily abnormal return, ESG_Treated is a dummy variable equal to one, if the company's ESG score is in the top quartile of the sample, Post_Covid is a dummy variable equal to 1 from the 24th of February till the 31st of march and Post_Fiscal is a dummy variable equal to 1, from the 18th of March till the 31st of March. Thus the methodology should be the same as in the paper. To cluster standard errors by day and firm, is used the command.

summary(reg2, vcov = vcovDC)

providing the following regression results:

Twoways effects Within Model

Note: Coefficient variance-covariance matrix supplied: vcovDC

plm(formula = Panel$AR_ESIUWRF2 ~ Panel$ESG_Treated * Panel$Post_Covid + 
    Panel$ESG_Treated * Panel$Post_Fiscal, data = Panel, effect = "twoways", 
    model = "within", index = c("id", "t"))

Balanced Panel: n = 781, T = 63, N = 49203

      Min.    1st Qu.     Median    3rd Qu.       Max. 
-53.857565  -1.194027  -0.028801   1.145946  36.063013 

                                    Estimate Std. Error t-value Pr(>|t|)
Panel$ESG_Treated:Panel$Post_Covid  -0.10660    0.11550 -0.9229   0.3560
Panel$ESG_Treated:Panel$Post_Fiscal  0.10777    0.22922  0.4702   0.6382

Total Sum of Squares:    466630
Residual Sum of Squares: 466610
R-Squared:      4.3827e-05
Adj. R-Squared: -0.017409
F-statistic: 0.432663 on 2 and 48358 DF, p-value: 0.64878

The results are confusing me, though. Even though it is acceptable that I could not find the expected effects (High ESG companies outperform low ESG companies), I am confused about the adjusted R-square. As far as I know, the negative adjusted R-square suggests that the model is a bad fit for the data. Does that mean I should use a different regression model? If yes, how should it look like? Or can I still use the model in the master thesis paper and conclude that I did not find any effect. I am worried because I have never seen an article (or master thesis) that includes models with negative adjusted R-Square values.

I hope that someone can help me :slight_smile:

The adjusted R-square (and the F-statistic) are telling you that taken as a whole your independent variables explain essentially nothing. Sometimes that's just the facts. It doesn't mean the regression is misspecified. It does mean that the regression can't identify any effect.

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