In Diff-in-Diff estimator, I did not see people using lag of outcome variable as an explanatory variable to deal with auto-correlation problem, even in some paper where the outcome variable is accounting variable, which is easily to be correlated as Dasgupta, 2019

In Diff-in-Diff, in most case, people will cluster at the unit level (or at the group-level depending on how you identify the heteroskedasticity and autocorrelation as mentioned by 1muflon1 here) What I am of curiousity now is how cluster deal with auto-correlation.

I read this book from Scott Cunningham and saw that

You simply adjust standard errors by clustering at the group level, as we discussed in the earlier chapter, or the level of treatment. For state-level panels, that would mean clustering at the state level, which allows for arbitrary serial correlation in errors within a state over time. This is the most common solution employed.

In his example, state-level is unit-level (he bases on a research of Card and Krueger (1994)). It seems that he explain that clustering at the unit level deals with autocorrelation by allowing arbitrary serial correlation in errors within a unit over time. However, I still not yet fully understand this approach. Is there any intuitive way to explain how cluster deal with auto-correlation mentioned here ?



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