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

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Smoothing parameter selection • Choose h to minimize CVy (h) over a grid of possible bandwidths. h opt CV = argmin hCVy (h) • Typically, get a cross-validation "check function" • It is also possible to choose the bandwidth locally, focussing only on data points within close distance to the cut-off point c. • Can choose a separate bandwidth for estimating the regression function of Wi given Xi
Assessing the variance of the estimator • Can obtain standard errors using bootstrap methods • Bootstrap methods are useful when it is cumbersome to obtain asymptotic standard errors. (i) Generate B bootstrap subsamples from the original data (can use 100% sampling with replacement.) (ii) Estimate treatment effect within each bootstrap sample (iii) The estimate of the treatment effect is based on the original data. The empirical variation across bootstrap estimates provides an estimator of the variance.
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 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: Smoothing parameter selection • F
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

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

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