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Δyit gi t Δwit  Δxit Δuit.

Can difference again or estimate (17) by FE. Can derive standard panel data approaches using the counterfactural framework from the treatment effects literature. For each i, t, let yit1and yit0denote the counterfactual outcomes, and assume there are no covariates. Unconfoundedness, conditional on unobserved heterogeneity, can be stated as

Eyit0|wi, ci0, ci1Eyit0|ci0E y i t 1 | w i , c i 0 , c i 1 E y i t 1 | c i 1 ,

where wi wi1, . . . , wiTis the time sequence of all treatments. If the gain from treatment only depends on t,

Eyit1|ci1Eyit0|ci0

t

20

(17)

(18) (19)

(20)

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