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

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Interpretation of FRD when treatment response is heterogeneous • Assume that treatment effect varies by unit τFRD random • Let Wi(x) be the potential treatment status given cut-off point x, forx in a neighborhood of c. • Wi(x)=1ifuniti would take treatment if cut-off equals x • Assume monotonicity: Wi(x) is nonincreasing in x at x = c
Define compliance status • Compliers: have limx↓Xi W i(Xi)=0,limx↑Xi W i(Xi)=1, (4) would get treatment if cut-off Xi or below, would not get treatment otherwise • Nevertakers: do not get treatment either way limx↓Xi W i(Xi)=0,limx↑Xi W i(Xi)=0 (5) • Always takers: get treatment either way limx↓Xi W i(Xi)=1,limx↑Xi W i(Xi)=1 (6)
Page 1 and 2: Applying Regression Discontinuity D
Page 3 and 4: • Many studies implicitly rely on
Page 5 and 6: Assignment to Treatment • Let (Xi
Page 8 and 9: Two Types of Designs • Fuzzy Regr
Page 10: Take the difference, use the fact t
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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