Fe, Eduardo (2012): Efficient estimation in regression discontinuity designs via asymmetric kernels.

PDF
MPRA_paper_38164.pdf Download (396kB)  Preview 
Abstract
Estimation of causal eects in regression discontinuity designs relies on a local Wald estimator whose components are estimated via local linear regressions centred at an specic point in the range of a treatment assignment variable. The asymptotic distribution of the estimator depends on the specic choice of kernel used in these nonparametric regressions, with some popular kernels causing a notable loss of effciency. This article presents the asymptotic distribution of the local Wald estimator when a gamma kernel is used in each local linear regression. The resulting statistics is easy to implement, consistent at the usual nonparametric rate, maintains its asymptotic normal distribution, but its bias and variance do not depend on kernelrelated constants and, as a result, is becomes a more effcient method. The effciency gains are measured via a limited Monte Carlo experiment, and the new method is used in a substantive application.
Item Type:  MPRA Paper 

Original Title:  Efficient estimation in regression discontinuity designs via asymmetric kernels 
Language:  English 
Keywords:  Regression Discontinuity; Asymmetric Kernels; Local Linear Regression 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions 
Item ID:  38164 
Depositing User:  Eduardo Fe 
Date Deposited:  17 Apr 2012 18:18 
Last Modified:  08 Feb 2016 00:08 
References:  Alesina, A. (1988). Credibity and policy convergence in a twoparty system with rational voters. American Economic Review. 78, 796805. Almond, D. and J. Doyle (2011). After midnight: A regression discontinuity design in length of postpartum hosptial stays. American Economic Journal: Economic Pol icy. 3, 134. Almond, D., J. Doyle, A. Kowalski, and H. Williams (2010). Estimating marginal returns to medical care: Evidence from atrisk newborns. Quarterly Journal of Eco nomics. 125, 591634. Angrist, J. and V. Lavy (1999). Using Maimonides' rule to estimate the eect of class size on scholastic achievement. Quarterly Journal of Economics 114, 533{575. Battistin, E., A. Brugiavini, E. Rettore, and G. Weber (2009). The retirement consumption puzzle: Evidence from a Regression Discontinuity approach. American Economic Review 99, 2209{2226. Besley, T. and S. Coate (1997). An economic model of representative democracy. Quar terly Journal of Economics 112, 85{114. Bound, J., D. Jaeger, and R. Baker (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90, 443{450. Brown, B. and S. X. Chen (1999). BetaBernstein smoothing for regression curves with compact supports. Scandinavian Journal of Statistics. 26, 47{59. Chen, S. X. (2000). Beta kernel smoothers for regression curves. Statistica Sinica 10, 73{91. Chen, S. X. (2001). Local linear smoothers using asymmetric kernels. Annals of the Institute of Statistical Mathematics. 54, 312{323. Downs, A. (1957). An economic theory of democracy. Harper Collins. Fan, J. (1993). Local linear regression smoothers and their minimax efficiencies. Annals of Statistics 21, 196{216. Feir, D., T. Lemieux, and V. Marmer (2011). Weak identication in Fuzzy Regression Discontinuity desings. Technical report, Micro Theory Working Paper, Microeconomics. Frandsen, B., M. Frolich, and B. Melly (2011). Quantile treatment eects in the regression discontinuity design. MIMEO. Groseclose, T., S. Levitt, and M. Snyder (1999). Comparing interest group scores across time and chambers: Adjusted ada scores for the u.s. congress. The American Political Science Review 93, 33{50. Hahn, J., P. Todd, and W. van der Klaauw (1999). Evaluating the eect of an antidiscrimination law using a regressiondiscontinuity design. NBER Working Paper 7131. Hahn, J., P. Todd, and W. van der Klaauw (2001). Identication and estimation of treatment eects with a regression discontinuity design. Econometrica 69, 201{209. Hart, J. (1997). Nonparametric Smoothing and LackofFit Tests. SpringerVerlag New York. Imbens, G. and T. Lemieux (2008). Regression Discontinuity Designs: A guide to practice. Journal of Econometrics 142, 615{635. Lee, D. (2008). Randomized experiments from nonrandom selection in U.S. House elections. Journal of Econometrics 142, 675{674. 24 Lee, D., E. Moretti, and M. Butler (2004). Do voters aect or elect policies? Evidence from the U.S. House. Quarterly Journal of Economics 119, 807 { 859. Ludwig, J. and D. Miller (2007). Does a head start improve childrens' life chances? evidence from a Regression Discontinuity Design. Quarterly Journal of Economics 122, 159{208. Osborne, M. and A. Slivinski (1996). A model of political competition with citizen candidates. Quarterly Journal of Economics 111, 65{96. Porter, J. (2003). Estimation in the Regression Discontinuity model. Technical report, Harvard University. Ruppert, D., S. J. Sheather, and M. P. Wand (1995). An eective bandwidth selector for local least squares regression. Journal of the American Statistical Association 90, 1257{1270. Ruppert, D. and M. P. Wand (1994). Multivariate locally weighted least squares regression. Annals of Statistics 22, 1346{1370. Scaillet, O. (2004). Density estimation using inverse and Reciprocal Inverse Gaussian kernels. Journal of Nonparametric Statistics 16, 217{226. Seifert, B. and T. Gasser (1996). Finite sample variance of local polynomials: Analysis and solutions. Journal of the American Statistical Association 91, 267{275. Silverman, B. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall. Staiger, D. and J. Stock (1997). Instrumental variables regression with weak instruments. Econometrica 65, 557{586. Thistlethwaite, D. and D. Campbell (1960). RegressionDiscontinuity analysis: An alternative to the ex post facto experiment. Journal of Educational Psychology 51, 309{317. van der Klaauw, W. (1996). A RegressionDiscontinuity evaluation of the eect of nancial aid oers on college enrollment. Technical report, New York University, Economics Department. Wald, A. (1940). The tting of straight lines if both variables are subject to error". Annals of Mathematical Statistics 11, 284300. Wand, M. and M. Jones (1994). Kernel smoothing. Chapman and Hall/CRC. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/38164 