Which vce cluster is appropriate, by country of by individual in the country?

[Leo Indra Wardhana]

Dear all,

I have a panel data that I will estimate with the following specification:
Y ijt = a i + bC ijt + cF jt + e ijt

Y is firm level, C is country level, F is firm level. So, the sample is firms (i) from some countries (j) for a period of time (t).
We know that in this case, not only the observations of a firm in different years are possibly correlated, but also the country level variable in different years are correlated. (Thus the residuals are correlated between firms and between country in different years).

I have looked at some cross country study paper, but they do not explained what they do with the standard error while most of econometric discussion related to this issue I found discussing only firm-years or countries-years, not firms-years-countries. There is one paper by Petersen (2009, Review of Financial Studies) discussing comprehensively about estimation of standard error in finance data set. However, I cannot find the answer for my case because the discussion is about a set of panel data in a single country (hope I didn't miss something from this paper).
There is indeed one paper that has similar case, and they adjust the se by country. But I don't know if it is appropriate or not. I notice that their country level variable is time invariant. In my case, my country level variables are time variant.

I have tried both and I got different results. The standard errors are much larger when it is clustered by country.

Could anyone kindly help me which cluster error should I adjust? By firm level or country level?


Thank you

Best regards,
Leo

[Mark Schaffer]

Leo - there is a discussion here:

http://www.statalist.org/forums/foru...ithin-clusters

along with a reference to paper by Cameron and Miller that may prove useful for you.

[Joshua D Merfeld]

A somewhat safe approach is to report the larger of the two standard errors. It may not be "appropriate" in the sense that it is guided by theory but then at least you will be conservative in your hypothesis testing, which is at least better than over-reporting a t-statistic (I would argue, anyway).

[Leo Indra Wardhana]

Thank you Mark for the link!

Thank you Joshua for your thought.

I also found an explanation by Cameron and Trivedi on their book (Microeconometric Using Stata) that Cluster robust standard error requires N → ∞, which is in line with Mark's discussion in the link he provided.

In my case, the n for country is only 58, seems that it's sufficient to satisfy the requirement N → ∞ while the N for individual level is 1400.