Brigham R. Frandsen

Randomization Inference in the Regression Discontinuity Design: An Application to Party Advantages in the U.S. Senate

Abstract 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.

Did Vietnam Veterans Get Sicker in the 1990s? The Complicated Effects of Military Service on Self-Reported Health

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.

Party Bias in Union Representation Elections: Testing for Manipulation in the Regression Discontinuity Design when the Running Variable is Discrete

Abstract 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.

Impacts of Unionization on Quality and Productivity: Regression Discontinuity Evidence from Nursing Homes

Using a regression discontinuity design, the authors of this article examine the effects of nursing home unionization on several labor, establishment, and consumer outcomes. They find negative effects of unionization on staffing levels and no decline in care quality, suggesting positive labor productivity effects. Some evidence suggests that nursing homes in less competitive local product markets and those with lower union density at the time of election experienced stronger union employment effects. Unionization appears to raise wages for a given worker while also shifting the composition of the workforce away from higher-earning workers. By combining credible identification of union effects and firm- and worker-level outcomes over time with measures of market-level characteristics, this study provides important new evidence on many controversial questions in the economics of unions. It also generates evidence from the service sector, which has grown in importance and where evidence has been thin.

Testing Rank Similarity

We introduce a test of the rank invariance or rank similarity assumption common in treatment effects and instrumental variables models. The test probes the implication that the conditional distribution of ranks should be identical across treatment states using a regression-based test statistic. We apply the test to data from the Tennessee STAR class-size reduction experiment and show that systematic slippages in rank can be important statistically and economically.

The Effects of Collective Bargaining Rights on Public Employee Compensation Evidence from Teachers, Firefighters, and Police

Widespread public-sector unionism emerged only in the 1960s, as individual states opened the door to collective bargaining for state and municipal workers. In this study, the author exploits differences in timing of legislative reforms across states to construct estimates of the causal effects of public-sector collective bargaining rights on pay, benefits, and employment for teachers, firefighters, and police. Perhaps surprisingly, estimates that allow for state fixed effects and state-specific trends show little effect on teachers’ pay, benefits, or employment, despite significantly increasing union presence among teachers. For firefighters, the results show a substantial positive effect on wages. For police, the wage effect was more modest but the workweek was significantly shortened.

Acceleration of Free Electrons in a Symmetric Evanescent Wave

The possibility of accelerating free electrons in a vacuum gap between closely spaced dielectric materials is explored. Plane waves impinging symmetrically on the gap from either side at oblique incidence produce an evanescent wave with net electric field along the direction of propagation. Near the critical angle, the evanescent wave propagates at the vacuum speed of light. A theoretical development and numerical simulations show that free electrons in the gap can be accelerated and accumulate energy indefinitely. This approach lies outside the purview of the Lawson-Woodward theorem, which does not apply in the vicinity of a medium. Damage thresholds of materials restrict the light intensity to far below that achievable by current high-power lasers. This limits the particle energy that might be achieved from an accelerator based on this approach.

Treatment Effects With Censoring and Endogeneity

This article develops a nonparametric approach to identification and estimation of treatment effects on censored outcomes when treatment may be endogenous and have arbitrarily heterogenous effects. Identification is based on an instrumental variable that satisfies the exclusion and monotonicity conditions standard in the local average treatment effects framework. The article proposes a censored quantile treatment effects estimator, derives its asymptotic distribution, and illustrates its performance using Monte Carlo simulations. Even in the exogenous case, the estimator performs better in finite samples than existing censored quantile regression estimators, and performs nearly as well as maximum likelihood estimators in cases where their distributional assumptions hold. An empirical application to a subsidized job training program finds that participation significantly and dramatically reduced the duration of jobless spells, especially at the right tail of the distribution.

Testing Censoring Point Independence

Identification in censored regression analysis and hazard models of duration outcomes relies on the condition that censoring points are conditionally independent of latent outcomes, an assumption which may be questionable in many settings. This article proposes a test for this assumption based on a Cramer–von-Mises-like test statistic comparing two different nonparametric estimators for the latent outcome cdf: the Kaplan–Meier estimator, and the empirical cdf conditional on the censoring point exceeding (for right-censored data) the cdf evaluation point. The test is consistent and has power against a wide variety of alternatives. Applying the test to unemployment duration data from the NLSY, the SIPP, and the PSID suggests the assumption is frequently suspect.

Exact Inference for a Weak Instrument, a Small Sample, or Extreme Quantiles

This paper describes a randomization-based inference procedure for the distribution or quantiles of potential outcomes for a binary treatment and instrument. The method imposes no parametric model for the treatment effect, and remains valid for small n, a weak instrument, or inference on tail quantiles, when conventional large-sample methods break down. The method is illustrated using simulations and data from a randomized trial of college student incentives and services.