Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll-call voting in the House, where sorting is both expected and found.

Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll-call voting in the House, where sorting is both expected and found. * I thank two anonymous referees for comments, the editors for multiple suggestions that substantially improved the paper, Jack Porter, John DiNardo, and Serena Ng for discussion, Jonah Gelbach for computing improvements, and Ming-Yen Cheng for manuscripts. Any errors are my own.

Frölich (2004) compares the finite sample properties of reweighting and matching estimators of average treatment effects and concludes that reweighting performs far worse than even the simplest matching estimator. We argue that this conclusion is unjustified. Neither approach dominates the other uniformly across data-generating processes (DGPs). Expanding on Frölich's analysis, this paper analyzes empirical as well as hypothetical DGPs and also examines the effect of misspecification. We conclude that reweighting is competitive with the most effective matching estimators when overlap is good, but that matching may be more effective when overlap is sufficiently poor.

We review economics research regarding the effect of police, punishments, and work on crime, with a particular focus on papers from the last twenty years. Evidence in favor of deterrence effects is mixed. While there is considerable evidence that crime is responsive to police and to the existence of attractive legitimate labor-market opportunities, there is far less evidence that crime responds to the severity of criminal sanctions. We discuss fruitful directions for future work and implications for public policy. (JEL J64, K42)