Regression discontinuity inference with specification error
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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References listed on IDEAS
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- David Card & Lara D. Shore-Sheppard, 2003.
"Using Discontinuous Eligibility Rules to Identify the Effects of the Federal Medicaid Expansions on Low Income Children,"
Department of Economics Working Papers
2003-09, Department of Economics, Williams College.
- 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.
- David Card & Lara D. Shore-Sheppard, 2002. "Using Discontinuous Eligibility Rules to Identify the Effects of the Federal Medicaid Expansions on Low Income Children," NBER Working Papers 9058, National Bureau of Economic Research, Inc.
- 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.
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- Lara Shore-Sheppard, 1996. "The Precision of Instrumental Variables Estimates With Grouped Data," Working Papers 753, Princeton University, Department of Economics, Industrial Relations Section..
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- John DiNardo & David S. Lee, 2004. "Economic Impacts of New Unionization on Private Sector Employers: 1984–2001," The Quarterly Journal of Economics, Oxford University Press, vol. 119(4), pages 1383-1441.
- 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
- 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.
- 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.
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