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Take the case of panel data with a time dimension in years and a cross-sectional dimension in plants (production units of firms). Each firm has many plants.

I understand I cannot include plant fixed effects (FE) and firm FE (or any FE that nests plants) together in the same regression. The plant FE would absorb the firm FE. However, is it possible to include plant FE and firm-by-year FE in the same regression?

An equivalent example would a firms organized in industries. Can we include industry-by-year FE and firm FE in the same regression?

Stata seems to do it without producing errors, but intuitively for me including both would still be wrong since in the same way firm FE are perfectly collinear with a linear combination of plant FE, there is a linear combination of firm-by-year FE that is perfectly collinear with plant FE...

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