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Automated Inference on Sharp Bounds

Many causal parameters involving the joint distribution of potential outcomes in treated and control states cannot be point-identified, but only be bounded from above and below. The bounds can be further tightened by conditioning on pre-treatment covariates, and the sharp version of the bounds corresponds to using a full covariate vector. This paper gives a method for estimation and inference on sharp bounds determined by a linear system of under-identified equalities (e.g., as in Heckman et al (ReSTUD, 1997)). In the sharp bounds’ case, the RHS of this system involves a nuisance function of (many) covariates (e.g., the conditional probability of employment in treated or control state). Combining Neyman-orthogonality and sample splitting, I provide an asymptotically Gaussian estimator of sharp bound that does not require solving the linear system in closed form. I demonstrate the method in an empirical application to Connecticut’s Jobs First welfare reform experiment.

Vira Semenova is an assistant professor at UC Berkeley’s Department of Economics. Her research interests are Econometrics and Machine Learning.

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