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I have a Group-Firm-Year panel data set (i.e., multiple firms make up a group). Suppose I have exogenous variation at the group level over time. In a panel regression with firm and time fixed effects that estimates the effect of this exogenous group variation on some firm outcome variable, should my standard errors be clustered at the firm or group level? Should I two-way cluster as well (within-time)?

Assume that the variation at the Group-year level is truly random.

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When treatment is assigned at the group level so that all firms in the same group are in the same arm, you need to cluster at the group level. That much is certain.

This is the second common reason for clustering, called the experimental design issue by Abadie, Athey, Imbens, and Wooldridge (2022). There is an accessible summary of the first version of this paper by David McKenzie here. There is also an excellent discussion of this in Cameron and Miller's 2015 JHR paper, though the original insight goes back to Moulton (1990) in Restat.

Do you need to cluster on time as well? That depends on the institutional setting. Clustering on time would also make sense if you expect simultaneous shocks that are arbitrarily correlated across multiple firms. So a shock that hits all firms in the same way at time t will get picked up by the time fixed effect, but you need time clustering to handle events like if some firms use inputs produced by another, which experiences a shock to its input prices. Time FEs cannot handle that sort of thing easily since firms are affected in many different ways by this event.

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