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  Attrition and disruption

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

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

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

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

How to do it  Bias if model misspecified  Polynomials used  Y i = β 0 + β 1 X i + β 2 D i + β 3 X i D i + β 4 X i 2 + β 5 X i 2 D i + e i  In STATA: rd (

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)

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)

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

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

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 Syracuse University, New York, unpublished manuscript.

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

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)

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):