Jumpy or Kinky? Regression Discontinuity without the Discontinuity

Dong, Yingying (2010): Jumpy or Kinky? Regression Discontinuity without the Discontinuity.

Abstract

Regression Discontinuity (RD) models identify local treatment effects by associating a discrete change in the mean outcome with a corresponding discrete change in the probability of treatment at a known threshold of a running variable. This paper shows that it is possible to identify RD model treatment effects without a discontinuity. The intuition is that identification can come from a slope change (a kink) instead of a discrete level change (a jump) in the treatment probability. Formally this can be shown using L'hopital's rule. The identification results are interpreted intuitively using instrumental variable models. Estimators are proposed that can be applied in the presence or absence of a discontinuity, by exploiting either a jump or a kink.

• Item Type: MPRA Paper
• Language: English
• Keywords: Regression Discontinuity, Fuzzy design, Average treatment effect, Identification, Jump, Kink, Threshold
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Angrist, J. D. and J.-S. Pischke (2008) Mostly Harmless Econometrics: An Empiricist's Companion, Princeton University Press.

Hahn, J., P. E. Todd, and W. van der Klaauw (2001), "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, 69, 201--09.

Card, D., C. Dobkin, and N. Maestas, (2008), "The Impact of Nearly Universal Insurance Coverage on Health Care Utilization: Evidence from Medicare," American Economic Review, 98, 2242--2258.

Carneiro, P., J. J. Heckman, and E. Vytlacil, (2010), "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, 78, 377--394.

Heckman, J. J. (2010), "Building Bridges Between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, 48, 356-398.

Imbens, G. W. and K. Kalyanaraman (2009), "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," NBER working paper number 14726.

Imbens, G. W. and T. Lemieux (2008), "Regression Discontinuity Designs: A Guide to Practice," Journal of Econometrics, 142, 615--35.

Imbens, G. W. and J. M. Wooldridge (2009), "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature 47, 5--86.

Jacob, B. A., and L. Lefgren, (2004) "Remedial Education and Student Achievement: A Regression-Discontinuity Analysis," Review of Economics and Statistics, 86, 226--244.

Lee, D. S. and T. Lemieux (2010), "Regression Discontinuity Designs in Economics," Journal of Economic Literature 48, 281--355.

Porter, J. R. (2003) "Estimation in the Regression Discontinuity Model," Unpublished Manuscript.

Rubin, D. B. (1974) "Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies," Journal of Educational Psychology, 66, 688--701.