Transcript Regression Discontinuity (RD)

Regression Discontinuity (RD)
Andrej Tusicisny, methodological reading group 2008
Interrupted time series (ITS)
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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
How to do it better? (ITS)
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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)
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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)
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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
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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
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Bias if model misspecified
Polynomials used
Yi = β0 + β1Xi + β2Di + β3XiDi +
β4Xi2 + β5Xi2Di + ei
In STATA: rd
(http://pped.org/stata/ciwod.pdf)
Tests
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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
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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
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Exemplary ITS:
Braga, A. et al. (2001) “Problemoriented policing, deterrence, and
youth violence: An evaluation of
Boston's Operation Ceasefire.”
Journal of Research in Crime and
Delinquency 38: 195–225
Useful references
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Comprehensive overview:
Imbens, G. W. and Lemieux, T.
(2008) “Regression discontinuity
designs: A guide to practice”.
Journal of Econometrics 142: 615–
635
Useful references
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Bias and efficiency
Black, D. et al. (2005) “Evaluating
the regression discontinuity design
using experimental data.” Syracuse
University, New York, unpublished
manuscript.
Useful references
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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
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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
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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