The authors derive a nonparametric identification formula for the average treatment effect that combines experimental data with observational data on a post-outcome remotely sensed proxy and provide n^{-1/2} inference robust to misspecification.
By the definition of˜Yε and Assumption 1, Pr( ˜Yε =y|S=e,X=x,D=d)= Z y′∈By(ε) fY (y′ |S=e,X=x,D=d)dy ′ = Z y′∈By(ε) fY(d) (y′ |S=e,X=x)dy ′ =Pr{Y(d)∈B y(ε)|S=e,X=x}
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Program Evaluation with Remotely Sensed Outcomes
The authors derive a nonparametric identification formula for the average treatment effect that combines experimental data with observational data on a post-outcome remotely sensed proxy and provide n^{-1/2} inference robust to misspecification.