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Regression Discontinuity Inference with Specification Error

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  • David S. Lee
  • David Card

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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  1. repec:fth:prinin:374 is not listed on IDEAS
  2. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-09, January.
  3. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-70, February.
  4. Lara Shore-Sheppard, 1996. "The Precision of Instrumental Variables Estimates With Grouped Data," Working Papers 753, Princeton University, Department of Economics, Industrial Relations Section..
  5. Thomas J. Kane, 2003. "A Quasi-Experimental Estimate of the Impact of Financial Aid on College-Going," NBER Working Papers 9703, National Bureau of Economic Research, Inc.
  6. 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, August.
  7. 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.
  8. Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working papers 98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. John DiNardo & David S. Lee, 2004. "Economic Impacts of New Unionization On Private Sector Employers: 1984-2001," The Quarterly Journal of Economics, MIT Press, vol. 119(4), pages 1383-1441, November.
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