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Regression Discontinuity Inference with Specification Error

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Author Info
David S. Lee
David Card

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Abstract

A regression discontinuity (RD) research design is appropriate for program evaluation problems in which treatment status (or the probability of treatment) depends on whether an observed covariate exceeds a fixed threshold. In many applications the treatment-determining covariate is discrete. This makes it impossible to compare outcomes for observations "just above" and "just below" the treatment threshold, and requires the researcher to choose a functional form for the relationship between the treatment variable and the outcomes of interest. We propose a simple econometric procedure to account for uncertainty in the choice of functional form for RD designs with discrete support. In particular, we model deviations of the true regression function from a given approximating function -- the specification errors -- as random. Conventional standard errors ignore the group structure induced by specification errors and tend to overstate the precision of the estimated program impacts. The proposed inference procedure that allows for specification error also has a natural interpretation within a Bayesian framework.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0322.

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Date of creation: Mar 2006
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Handle: RePEc:nbr:nberte:0322

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
J0 - Labor and Demographic Economics - - General

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References listed on IDEAS
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  1. David Card & Lara D. Shore-Sheppard, 2004. "Using Discontinuous Eligibility Rules to Identify the Effects of the Federal Medicaid Expansions on Low-Income Children," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 752-766, November. [Downloadable!] (restricted)
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  2. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-38, May. [Downloadable!] (restricted)
  3. Lara Shore-Sheppard, 1996. "The Precision of Instrumental Variables Estimates With Grouped Data," Working Papers 753, Princeton University, Department of Economics, Industrial Relations Section.. [Downloadable!]
  4. repec:fth:prinin:374 is not listed on IDEAS
  5. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier. [Downloadable!] (restricted)
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  1. Bargain, Olivier & Doorley, Karina, 2009. "Caught in the Trap? The Disincentive Effect of Social Assistance," IZA Discussion Papers 4291, Institute for the Study of Labor (IZA). [Downloadable!]
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  2. David Card & Raj Chetty & Andrea Weber, 2006. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," NBER Working Papers 12639, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Jens Hainmueller & Holger Lutz Kern, 2005. "Incumbency Effects in German and British Elections: A Quasi- Experimental Approach," Public Economics 0505009, EconWPA. [Downloadable!]
  4. Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Technical Working Papers 0337, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Juan Carlos Calcagno & Bridget Terry Long, 2008. "The Impact of Postsecondary Remediation Using a Regression Discontinuity Approach: Addressing Endogenous Sorting and Noncompliance," NBER Working Papers 14194, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Marco Manacorda, 2008. "The Cost of Grade Retention," CEP Discussion Papers dp0878, Centre for Economic Performance, LSE. [Downloadable!]
  7. Rafael Lalive, 2006. "How Do Extended Benefits Affect Unemployment Duration? A Regression Discontinuity Approach," IZA Discussion Papers 2200, Institute for the Study of Labor (IZA). [Downloadable!]
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  8. David S. Lee & Thomas Lemieux, 2009. "Regression Discontinuity Designs in Economics," NBER Working Papers 14723, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. Devereux, Paul J. & Hart, Robert A, 2008. "Forced to be Rich? Returns to Compulsory Schooling in Britain," CEPR Discussion Papers 6679, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  10. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2006. "Robust Inference with Multi-way Clustering," NBER Technical Working Papers 0327, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Rafael Lalive & Jean-Philippe Wuellrich & Josef Zweimüller, 2009. "Do Financial Incentives for Firms Promote Employment of Disabled Workers? A Regression Discontinuity Approach," NRN working papers 2009-11, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria. [Downloadable!]
  12. Lemieux, Thomas & Milligan, Kevin, 2006. "Incentive Effects of Social Assistance: A Regression Discontinuity Approach," Analytical Studies Branch Research Paper Series 2006280e, Statistics Canada, Analytical Studies Branch. [Downloadable!]
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  13. Carlos Dobkin & Fernando Ferreira, 2009. "Do School Entry Laws Affect Educational Attainment and Labor Market Outcomes?," NBER Working Papers 14945, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  14. Manacorda, Marco & Miguel, Edward & Vigorito, Andrea, 2009. "Government Transfers and Political Support," CEPR Discussion Papers 7163, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  15. Alejandra Mizala & Miguel Urquiola, 2007. "School Markets: The Impact of Information Approximating Schools' Effectiveness," NBER Working Papers 13676, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  16. Thomas K. Bauer & Stefan Bender & Alfredo R. Paloyo & Christoph M. Schmidt, 2009. "Evaluating the Labor-Market Effects of Compulsory Military Service - A Regression-Discontinuity Approach," Ruhr Economic Papers 0141, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen. [Downloadable!]
  17. Marco Manacorda & Edward Miguel & Andrea Vigorito, 2009. "Government Transfers and Political Support," NBER Working Papers 14702, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  18. Douglas Almond & Joseph J. Doyle, Jr. & Amanda E. Kowalski & Heidi Williams, 2008. "Estimating Marginal Returns to Medical Care: Evidence from At-Risk Newborns," NBER Working Papers 14522, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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