This paper explores semi-monotonicity constraints in the distribution of potential outcomes, first, conditional on an instrument, and second, in terms of the response function. The imposed assumptions are strictly weaker than traditional instrumental variables assumptions and can be gainfully...

This paper explores semi-monotonicity constraints in the distribution of potential outcomes, first, conditional on an instrument, and second, in terms of the response function. The imposed assumptions are strictly weaker than traditional instrumental variables assumptions and can be gainfully...

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive...

In this article, I develop a novel identification result for estimating the effect of an endogenous treatment using a proxy of an unobserved imperfect instrument. I show that the potential outcomes distributions are partially identified for the compliers. Therefore, I derive sharp bounds on the...

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive...

We develop novel regression discontinuity inferences where the binary treatment and/or continuous assignment variable may contain measurement errors. For a measurement error of the binary treatment, the standard estimator is inconsistent for the causal parameter. To solve the problem, we develop...

A breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the...

This paper extends the identification results in Nevo and Rosen (2012) to nonparametric models. We derive nonparametric bounds on the average treatment effect when an imperfect instrument is available. As in Nevo and Rosen (2012), we assume that the correlation between the imperfect instrument...

Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value...

Dummy endogenous variables are commonly encountered in program evaluations using observational data. Motivated by the increasing availability of rich micro data, we develop a two-stage approach to estimate the dummy endogenous treatment effect using high-dimensional instrumental variables (IV)....