Question: In the text it was claimed that in a balanced sample individual-level fixed effects are orthogonal to any variable demeaned at the state level. (a)

In the text it was claimed that in a balanced sample individual-level fixed effects are orthogonal to any variable demeaned at the state level.

(a) Show this claim.

(b) Does this claim hold in unbalanced samples?

(c) Explain why this claim implies that the regressionsand Yit Bo+BState; + B Time +0Dit +it Yit=0Dit+ui+8+ + it

yield identical estimates of µ.

and Yit Bo+BState; + B Time +0Dit +it Yit=0Dit+ui+8+ + it

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