I think it is a practical headache rising when doing empirical research. I am examining the impact of anticollusion laws on firms' asset growth as Dasgupsta, 2019 uses the genralized Difference-in-Differences for multiple groups and time periods.
The result is quite good until I perform the clustering test as a robustness test as they recommend as in the rows (7) to (10) as in the picture below
The significance levels are blown away when clustering. I am wondering if we can say anything in this case that we do not need to do cluster, In my case, I run all regression with firm and year fixed effects, controlling for industry * year and region * year fixed effect already. I remember someone told me about a paper of Woodridge recently that we do not necessarily do cluster in some case.