Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test

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.

[1]  H. White.  Asymptotic theory for econometricians , 1985 .

[2]  W. Härdle,et al.  APPLIED NONPARAMETRIC METHODS , 1992 .

[3]  Jason A. Snyder,et al.  DETECTING MANIPULATION IN U.S. HOUSE ELECTIONS , 2005 .

[4]  Victor Chernozhukov,et al.  Likelihood Estimation and Inference in a Class of Nonregular Econometric Models , 2003 .

[5]  O. Scaillet,et al.  CONSISTENCY OF ASYMMETRIC KERNEL DENSITY ESTIMATORS AND SMOOTHED HISTOGRAMS WITH APPLICATION TO INCOME DATA , 2005, Econometric Theory.

[6]  Eugene F. Schuster,et al.  Incorporating support constraints into nonparametric estimators of densities , 1985 .

[7]  Daren B. H. Cline,et al.  Kernel Estimation of Densities with Discontinuities or Discontinuous Derivatives , 1991 .

[8]  Ming-Yen Cheng,et al.  A bandwidth selector for local linear density estimators , 1997 .

[9]  David S. Lee,et al.  Economic Impacts of New Unionization on Private Sector Employers: 1984–2001 , 2004 .

[10]  A. Deaton.  The Analysis of Household Surveys : A Microeconometric Approach to Development Policy , 1997 .

[11]  D. V. Lindley,et al.  Randomization Analysis of Experimental Data: The Fisher Randomization Test Comment , 1980 .

[12]  David Card.  The Causal Effect of Education on Learning , 1999 .

[13]  D. Rubin.  Randomization Analysis of Experimental Data: The Fisher Randomization Test Comment , 1980 .

[14]  M. C. Jones.  Discretized and Interpolated Kernel Density Estimates , 1989 .

[15]  W. V. D. Klaauw,et al.  Estimating the Effect of Financial Aid Offers on College Enrollment: A Regression-Discontinuity Approach , 2002 .

[16]  M. Stone.  Cross-validation and multinomial prediction , 1974 .

[17]  J. Marron,et al.  Transformations to reduce boundary bias in kernel density estimation , 1994 .

[18]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[19]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[20]  J. Hahn,et al.  IDENTIFICATION AND ESTIMATION OF TREATMENT EFFECTS WITH A REGRESSION-DISCONTINUITY DESIGN , 2001 .

[21]  M. Stone.  Asymptotics for and against cross-validation , 1977 .

[22]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[23]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[24]  W. Gawronski,et al.  Smoothing histograms by means of lattice-and continuous distributions , 1981 .

[25]  P. Hall.  EFFECT OF BIAS ESTIMATION ON COVERAGE ACCURACY OF BOOTSTRAP CONFIDENCE INTERVALS FOR A PROBABILITY DENSITY , 1992 .

[26]  J. Horowitz,et al.  The Bootstrap , 2018, Randomization, Bootstrap and Monte Carlo Methods in Biology.

[27]  Emmanuel Saez,et al.  Do Taxpayers Bunch at Kink Points? , 1999 .

[28]  ON DENSITY-ESTIMATION BY MEANS OF POISSONS DISTRIBUTION , 1980 .

[29]  James J. Heckman,et al.  1. The Scientific Model of Causality , 2005 .

[30]  Jianqing Fan,et al.  On automatic boundary corrections , 1997 .

[31]  David S. Lee.  The Electoral Advantage to Incumbency and Voters&Apos; Valuation of Politicians&Apos; Experience: A Regression Discontinuity Analysis of Elections to the U.S.. , 2001 .

[32]  R. John,et al.  Boundary modification for kernel regression , 1984 .

[33]  William H. Flanigan,et al.  The Theory of Political Coalitions. , 1965 .

[34]  A. Ullah,et al.  Nonparametric Econometrics , 1999 .

[35]  Ming-Yen Cheng,et al.  Minimax efficiency of local polynomial fit estimators at boundaries , 1993 .

[36]  James J Heckman,et al.  Understanding Instrumental Variables in Models with Essential Heterogeneity , 2006, The Review of Economics and Statistics.

[37]  D. Poirier,et al.  On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function , 1976 .

[38]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[39]  Ming-Yen Cheng.  On boundary effects of smooth curve estimators , 1994 .

[40]  Berwin A. Turlach,et al.  Performance of wavelet methods for functions with many discontinuities , 1996 .

[41]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1995 .