In the Regression Discontinuity (RD) design, units are assigned a treatment based on whether their value of an observed covariate is above or below a fixed cutoff. Under the assumption that the distribution of potential confounders changes continuously around the cutoff, the discontinuous jump in the probability of treatment assignment can be used to identify the treatment effect. Although a recent strand of the RD literature advocates interpreting this design as a local randomized experiment, the standard approach to estimation and inference is based solely on continuity assumptions that do not justify this interpretation. In this article, we provide precise conditions in a randomization inference context under which this interpretation is directly justified and develop exact finite-sample inference procedures based on them. Our randomization inference framework is motivated by the observation that only a few observations might be available close enough to the threshold where local randomization is plausible, and hence standard large-sample procedures may be suspect. Our proposed methodology is intended as a complement and a robustness check to standard RD inference approaches. We illustrate our framework with a study of two measures of party-level advantage in U.S. Senate elections, where the number of close races is small and our framework is well suited for the empirical analysis.

The veterans disability compensation (VDC) program, which provides a monthly stipend to disabled veterans, is the third largest American disability insurance program. Since the late 1990s, VDC growth has been driven primarily by an increase in claims from Vietnam veterans, raising concerns about costs as well as health. We use the draft lottery to study the long-term effects of Vietnam-era military service on health and work in the 2000 Census. These estimates show no significant overall effects on employment or work-related disability status, with a small effect on non-work-related disability for whites. On the other hand, estimates for white men with low earnings potential show a large negative impact on employment and a marked increase in non-work-related disability rates. The differential impact of Vietnam-era service on low-skill men cannot be explained by more combat or war-theatre exposure for the least educated, leaving the relative attractiveness of VDC for less skilled men and the work disincentives embedded in the VDC system as a likely explanation.

This paper shows nonparametric identi…cation of quantile treatment e¤ects (QTE) in the regression discontinuity design. The distributional impacts of social programs such as welfare, education, training programs and unemployment insurance are of large interest to economists. QTE are an intuitive tool to characterize the e¤ects of these interventions on the outcome distribution. We propose uniformly consistent estimators for both potential outcome distributions (treated and non-treated) for the population of interest as well as other function-valued e¤ects of the policy including in particular the QTE process. The estimators are straightforward to implement and attain the optimal rate of convergence for one-dimensional nonparametric regression. We apply the proposed estimators to estimate the e¤ects of summer school on the distribution of school grades, complementing the results of Jacob and Lefgren (2004).

Conventional tests of the regression discontinuity design's identifying restrictions can perform poorly when the running variable is discrete. This paper proposes a test for manipulation of the running variable that is consistent when the running variable is discrete. The test exploits the fact that if the discrete running variable's probability mass function satisfies a certain smoothness condition, then the observed frequency at the threshold has a known conditional distribution. The proposed test is applied to vote tally distributions in union representation elections and reveals evidence of manipulation in close elections that is in favor of employers when Republicans control the NLRB and in favor of unions otherwise.