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Regression Discontinuity (RD)

Regression Discontinuity (RD). Andrej Tusicisny, methodological reading group 2008. Interrupted time series (ITS). Y t = f(T) + D t b + e t Single unit observed in multiple points in time We extrapolate f(T) from t 0 to t 1 F(T) should be correctly specified Autocorrelation

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Regression Discontinuity (RD)

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  1. Regression Discontinuity (RD) Andrej Tusicisny, methodological reading group 2008

  2. Interrupted time series (ITS) • Yt = f(T) +Dtb + et • Single unit observed in multiple points in time • We extrapolate f(T) from t0 to t1 • F(T) should be correctly specified • Autocorrelation • Attrition and disruption

  3. How to do it better? (ITS) • Braga et al. (2001) • 1. Assess the effect of the cause on similar outcomes that should be affected by the cause • 2. Assess the effect of the cause on similar outcomes that should not be affected by the cause

  4. How to do it better? (ITS) • 3. Assess the effect within meaningful subgroups • 4. Include time-varying covariates • 5. Compare the time trend with the time trend in similar not-treated units or populations • 6. Assess the impact of termination of the cause in addition to its initiation

  5. Regression discontinuity (RD) • Treatment function of a continuous “forcing” variable Z • Cutoff value of Z determines assignment to the treatment group • Units of either side of the cutoff exchangeable • Other covariates smooth at cutoff • Sharp RD and fuzzy RD

  6. Discontinuity • Counterfactual values extrapolated • Internal validity high • Bias can be reduced by limiting the sample to the vicinity of the discontinuity frontier, but it will decrease efficiency (Black, 2005) • External validity limited • No problem with autocorrelation

  7. How to do it • Bias if model misspecified • Polynomials used • Yi = β0 + β1Xi + β2Di + β3XiDi + β4Xi2 + β5Xi2Di + ei • In STATA: rd (http://pped.org/stata/ciwod.pdf)

  8. Tests • Imbens and Lemieux (2008) • Treatment should have zero effect on covariates • No discontinuity in covariates at the cutoff point • No unpredicted discontinuities • No manipulation of Z (McCrary, 2007)

  9. RD and IV • Z can have a direct impact on Y • Example of Z used as an instrument for an endogenous variable: Angrist and Lavy (1999)

  10. Useful references • Exemplary ITS: • Braga, A. et al. (2001) “Problem-oriented policing, deterrence, and youth violence: An evaluation of Boston's Operation Ceasefire.” Journal of Research in Crime and Delinquency 38: 195–225

  11. Useful references • Comprehensive overview: • Imbens, G. W. and Lemieux, T. (2008) “Regression discontinuity designs: A guide to practice”. Journal of Econometrics 142: 615–635

  12. Useful references • Bias and efficiency • Black, D. et al. (2005) “Evaluating the regression discontinuity design using experimental data.” Syracuse University, New York, unpublished manuscript.

  13. Useful references • What happens if manipulation of Z: • McCrary, J. (2008) “Manipulation of the running variable in the regression discontinuity design: A density test.” Journal of Econometrics 142: 698–714

  14. Useful references • Exemplary graphic presentation of RD results: • Lee, D. et al. (2004) “Do Voters Affect or Elect Policies? Evidence from the U.S. House.” Quarterly Journal of Economics 119(3)

  15. Useful references • RD and IV • Angrist, J. D. and Lavy, V. (1999) “Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement.” The Quarterly Journal of Economics 114(2): 533-575

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