This paper by Justin McCrary explores the manipulation of the running variable in the regression discontinuity design (RDD), a common econometric method used to estimate causal effects. The author proposes a density test to detect manipulation, which is particularly relevant when the treatment assignment rule is public knowledge. The test is based on the continuity of the density function of the running variable around the cutoff point. The methodology is applied to two settings: popular elections to the U.S. House of Representatives and roll-call voting in the House. In the former, the density function of Democratic vote shares is found to be smooth, indicating no manipulation. In the latter, strong evidence of manipulation is found, suggesting that representatives may coordinate to influence vote tallies. The paper also discusses the estimation and inference procedures, including bandwidth selection and bias reduction techniques. The density test complements existing specification checks and can be useful when pre-determined characteristics are not available or relevant.This paper by Justin McCrary explores the manipulation of the running variable in the regression discontinuity design (RDD), a common econometric method used to estimate causal effects. The author proposes a density test to detect manipulation, which is particularly relevant when the treatment assignment rule is public knowledge. The test is based on the continuity of the density function of the running variable around the cutoff point. The methodology is applied to two settings: popular elections to the U.S. House of Representatives and roll-call voting in the House. In the former, the density function of Democratic vote shares is found to be smooth, indicating no manipulation. In the latter, strong evidence of manipulation is found, suggesting that representatives may coordinate to influence vote tallies. The paper also discusses the estimation and inference procedures, including bandwidth selection and bias reduction techniques. The density test complements existing specification checks and can be useful when pre-determined characteristics are not available or relevant.