Notes on Regression Discontinuity Methods - [athena.sas.upenn ...

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Potential Outcomes Framework • Potential outcomes associated with treated and untreated states Yi(0),Yi(1) • Framework laid out in Fisher (1951), Roy (1951), Quandt (1972), Rubin (1978) • Interest usually focuses on Yi(1) − Yi(0) • Let Wi = 1ifuniti exposed to treatment, else Wi = 0. • Observed outcome Yi =(1 − Wi)Yi(0)+WiYi(1) = Yi(0)+Wi(Yi(1) − Yi(0))
Assignment to Treatment • Let (Xi,Zi) be a vector of covariates or pretreatment variables known not to be affected by treatment (e.g. pre-test score, age) • Assignment to treatment is determined either completely or partly by the value of Xi being on either side of a fixed threshold. • Yi(0) or Yi(1) may also be associated with Xi, butthe dependence is assumed to be smooth • Discontinuities in the conditional distribution of Yi (or in its conditional expectation) are attributed to a causal effect of treatment.
Page 1 and 2: Applying Regression Discontinuity D
Page 3: • Many studies implicitly rely on
Page 8 and 9: Two Types of Designs • Fuzzy Regr
Page 10: Take the difference, use the fact t
Page 13 and 14: Define compliance status • Compli
Page 15 and 16: Interpretation of τFRD In that cas
Page 17 and 18: Comparison of RD Approach with a Ma
Page 19 and 20: Estimation • For sharp design, ne
Page 21 and 22: Boundary bias plimˆµr (c)= c+h c
Page 23 and 24: Estimation under the FRD design Aga
Page 25 and 26: Smoothing parameter selection • F
Page 27 and 28: Assessing the variance of the estim
Page 29 and 30: Should analysis condition on other
Page 31 and 32: RD Examples: Card, D., Dobkin, C.,(
Page 33 and 34: RD Examples: Lalive (2007, J of Eco
Page 39: RD Examples: Jacob, B.A., Lefgren,
Page 46 and 47: Examples: Hahn, J., Todd, P., Van D
Page 52 and 53: RD Examples Estimating the value pa
Page 54 and 55:
RD Examples: DiNardo, J., Lee, D.S.
Page 56 and 57:
RD Examples: Lee (2007, J of Econom
Page 58 and 59:
3. Examine robustness of the result
Page 60:
4. Robustness can be examined using
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