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24 / 31

and

Ui Gi Vi, Vi Gi, Ti

although, because of the linearity, we can get by with the mean independence assumption EVi|Gi, Ti0. With constant treatment effect,

Yi Ti Gi GiTi Vi,

Because EVi|Gi, Ti0, the parameters in (31) can be estimated by OLS (usual DD analysis). Athey and Imbens call the extension of the usual DD model the changes-in-changes (CIC) model. Can recover

DYi0|Gi 1, Ti 1,

under their assumptions (with an extra support c o n d i t i o n ) . I n f a c t , i f F g t 0 y t h e b e c u m u l a t distribution function of DYi0|Gi g, Ti tfor i v e

24

(30)

(31)

(32)

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