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The key assumption in regression discontinuity analysis is that the distribution of potential outcomes varies smoothly with the running variable around the cutoff. In many empirical contexts, however, this assumption is not credible; and the running variable is said to be manipulated in this case. In this paper, we show that while causal effects are not point identified under manipulation, one can derive sharp bounds under a general model that covers a wide range of empirical patterns. The extent of manipulation, which determines the width of the bounds, is inferred from the data in our setup. Our approach therefore does not require making a binary decision regarding whether manipulation occurs or not, and can be used to deliver manipulation‐robust inference in settings where manipulation is conceivable, but not obvious from the data. We use our methods to study the disincentive effect of unemployment insurance on (formal) reemployment in Brazil, and show that our bounds remain informative, despite the fact that manipulation has a sizable effect on our estimates of causal parameters. [ABSTRACT FROM AUTHOR]

In regression discontinuity (RD) studies exploiting an award or admissions cutoff, causal effects are nonparametrically identified for those near the cutoff. The effect of treatment on inframarginal applicants is also of interest, but identification of such effects requires stronger assumptions than those required for identification at the cutoff. This article discusses RD identification and estimation away from the cutoff. Our identification strategy exploits the availability of dependent variable predictors other than the running variable. Conditional on these predictors, the running variable is assumed to be ignorable. This identification strategy is used to study effects of Boston exam schools for inframarginal applicants. Identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants. These estimates suggest that the causal effects of exam school attendance for 9th grade applicants with running variable values well away from admissions cutoffs differ little from those for applicants with values that put them on the margin of acceptance. An extension to fuzzy designs is shown to identify causal effects for compliers away from the cutoff. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The authors comment on the works of researchers Michael Hudgens and Thomas Lemieux who have expressed their views on articles on statistical research published in this issue. Topics discussed include the use of conditional independence assumption (CIA) and regression discontinuity (RD) in statistical analysis; directed acyclic graphs (DAGs); and the stable unit value assumption (SUTVA) method.