Abadie, 2017 have a paper about when we should cluster. And this paper has been summarized by McKenzie here.

I used the paper of Dasgupta,2019 to link to the summarized work of McKenzie. So, in Dasgupta's paper, he examines the impact of anticollusion laws of firms' asset growth in a standard Difference-in-Differences (DID) setting with multiple groups and periods. In specific, each country will pass the anticollusion laws in different years, and he examines the impact of such law implementation on firms' asset growth.

First of all, from the definition from Wing, 2018, DID is a quasi-experimental research design. So, I am wondering if I can apply the "The Experimental Design Reason for Clustering" for DID setting as above?

Second, if my first argument is correct, in the summarized work, McKenzie mentioned that

Then if the treatment is assigned at the individual level, there is no need to cluster (*)

(*) unless you are using multiple time periods, and then you will want to cluster by individual, since the unit of randomization is individual, and not individual-time period.

So, is it in Dasgupta's case as above, he does not need to cluster at all based on the above judgment?

The schematic of the data collection scheme and experimental design of Dasgupta, 2019 is:

$$Treatment -> Countries -> Firms$$

To briefly summarize Abadie, et al., there are two reasons to cluster standard errors:

1. The sampled entity and the treated entity are not the same.
2. The treated entity and the measured entity are not the same.

In Dasgupta, 2019, it appears that the treatment condition (leniency laws) is applied to countries, while they measure the asset growth of firms within those countries. While this is a quasi-experimental design, one can imagine that every firm in a given country experiences the same random treatment errors, such as implementation details of the law, etc. To account for these random errors, it makes sense to cluster standard errors by country.

As an aside, I think it is often useful to write out a schematic of the data collection scheme and experimental design. I may be misunderstanding what was done is Dasgupta, 2019, but it seems to be something like this:

$$Treatment -> Countries -> Firms$$

Assuming this is how the data was collected, we see that there is no need to cluster for "sampling reasons" but there is reason to cluster for "treatment assignment" reasons.

• Thank you so much for your answer, so, I understand the reason that he should at least cluster for country level because "The treated entity and the measured entity are not the same.", is not it? From my understanding, the "treated entity" here is country and "measured entity" is firms, am I correct, and is it what you call "reason to cluster for "treatment assignment" reasons". However, is there any argument if I do not want to cluster due to this "treatment assignment" reason. The schematic of data collection is similar to what you documented as above, but not Industries levels. Jun 27 at 1:31
• If this is what your data collection looks like, you have no choice but to cluster your standard errors. The only reason you would not have to is if there is no country-to-country variance, but as Abadie, et al. point out, the "clustered SE" gives the same answer as the "robust SE" in that situation. To explain why this is necessary more generally, reported standard errors are meant to achieve their nominal coverage (~68% using the normal approximation). Clustered data tends to reduce the coverage, and clustered standard errors are meant to "recover" the nominal coverage. Jun 27 at 1:35
• A very thorough answer, @rishi-k , one more question about this continuous discussion that whether I must control two-way fixed effect and do cluster at the same time. For example, control for firm and year fixed effects and clustering by countries at the same time. Is it overdoing? Or we can cluster without controlling for firm and year fixed effect? Jun 27 at 1:45
• Controlling for fixed effects in this scheme shouldn't affect your estimate of the treatment effect, but it can make the graphics somewhat more interpretable. I usually use hierarchical models or stratified randomization tests that "inherently" adjust for fixed effects. Jun 27 at 1:57
• If you are performing an OLS regression, then yes, you should adjust for fixed effects (actually, it will likely widen your SEs if you do not adjust for fixed effects). Jun 27 at 2:02