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

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Two Types of Designs • Fuzzy Regression-Discontinuity (FRD) Design • Prob of receiving treatment need not change from 0 to 1 at the threshold, but there there is a discontinuous jump in the probability, so that limx↓cE(Wi|Xi = x) − limx↑cE(Wi|Xi = x) = 0 or,equivalently, limx↓cPr(Wi = 1|Xi = x) − limx↑cPr(Wi = 1|Xi = x) = 0 • Treatment effect can be obtained by the ratio τFRD = lim x↓cE(Yi|Xi = x) − limx↑cE(Yi|Xi = x) limx↓cE(Wi|Xi = x) − limx↑cE(Wi|Xi = x) (3)
Why? Assume constant treatment effect τFRD. Yi = Yi(0)+Wi[Yi(1) − Yi(0)] Yi = Yi(0)+WiτFRD limx↓cE(Yi|Xi = x)= limx↓cE(Yi(0)|Xi = x)+limx↓cE(Wi|Xi = x)τFRD limx↑cE(Yi|Xi = x)= limx↓cE(Yi(0)|Xi = x)+limx↑cE(Wi|Xi = x)τFRD
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 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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