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27 / 31

Key unconfoundedness assumption:

EY10Y00|X, WEY10Y00|X

Also need

PW 1|X1

is critical. Under (37) and (38),

  • ATT

W pXY1 Y0E 1 pX

/PW 1,

where Yt, t 0, 1 are the observed outcomes (for the same unit) and pXPW 1|Xis the propensity score. Dehejia and Wahba (1999) derived (39) for the cross-sectional case. All quantities are observed or, in the case of the pXand PW 1, can be estimated. As in Hirano, Imbens, and Ridder (2003), a flexible logit model can be used for pX; the fraction of units treated

27

(37)

(38)

(39)

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