Regression Discontinuity - Institute for Policy Research

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Two Rationales for RDD 1. Selection process is completely known and can be modeled through a regression line of the assignment and outcome variables – Untreated portion of the AV serves as a counterfactual 2. It is like an experiment around the cutoff – Benefit: Functional form need not be identified away from the cutoff • Empirically validated by 6 within-study comparisons (Aiken et al., 1998; Buddelmeyer & Skoufias, 2005; Black, Galdo & Smith, 2007; Berk et al., in press; Greene, 2010; Shadish et al., 2011), even though estimands differ between RE and RD and power too
Required Assumptions for RD design 1. Prob. of treatment receipt must be discontinuous at cutoff. More of those receiving treatment should be on treatment side of cutoff than the other side. If all are, then “sharp” RD. Otherwise, “fuzzy” RD 2. No discontinuity in potential outcomes in the cutoff (the “continuity restriction”). That is, no alternative interpretation should also show a discontinuity at the cutoff. If so, it would serve as a causal confound.
Page 1 and 2: Regression-Discontinuity Design Day
Page 3 and 4: Design Overview Design Examples Vis
Page 5 and 6: RDD Visual Depiction Comparison
Page 7 and 8: RDD Visual Depiction Discontinuity,
Page 9: Two Rationales for RDD 1. Selection
Page 13 and 14: Sharp RD Designs • Requires that
Page 15 and 16: Estimating Treatment Effects in Fuz
Page 17 and 18: “Non”-RD designs • No discont
Page 19 and 20: 2. Manipulation of the assignment v
Page 21 and 22: Diagnostic test • Can perform “
Page 23 and 24: Analytic Threats to RD Design: Para
Page 25 and 26: The size of the discontinuity at th
Page 27: Functional Form • Put more techni
Page 30 and 31: Functional Form: Interactions • S
Page 32 and 33: If we superimpose the regression li
Page 34 and 35: Here we see an example where the tr
Page 36 and 37: Adding Nonlinear Terms to the Model
Page 38 and 39: Adding Nonlinear and Interaction Te
Page 40 and 41: Adding Terms, Continued • When in
Page 42 and 43: Example of Parametric Plot used aga
Page 44 and 45: Non-parametric Approach lim x¯c E[
Page 46 and 47: 3. Semi-Parametric Approach Y i = t
Page 48 and 49: Problem of Incorrect Bandwidth Sele
Page 50 and 51: RDD Example 1
Page 52: RD Design assumption 1 • Probabil
Page 55 and 56: Implementation assumption 2 • No
Page 57 and 58: Analytic assumption 1 continued •
Page 59 and 60: Shadish et al. (2011) Vocabulary RD
Page 61 and 62:
RDD Example 2
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Best case scenario - regression lin
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Correct specification of functional
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What to do (2) • Parametric appro
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What to do (4) 0 50 100 150 locpoly
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What to do (5) • Move to a tie br
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Example Cocaine Project • Include
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What to do (7) • Estimation throu
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2. Dealing with Overrides to the cu
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2. Overrides to the cutoff • Mult
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Specification of Functional Form Pa
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Specification of Functional Form No
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Overrides to cutoff (2) Alternative
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Final estimates Function al form Pa
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Addressing Potential Issues with us
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African-American Home language Span
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What about cutoff Shift in Number o
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McCrary Test for New Jersey
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Take Home Message • Like RE, the
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Inadequate statistical power • Ne
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Power Considerations Common to Rand
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What “Uniquely” Affects Power i
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Generalizing Beyond The Cut-off In
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Adding an Untreated RD Comparison F
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Creating A Regression Discontinuity
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Pretest and Posttest RD • Imagine
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What Is The Target Parameter? • A
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Table 1: Bias At the Cutoff Adding
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Summary of what the Pretest- Supple
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Additional Topic not covered in Cla
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Sample Data with Multiple Cutoffs O
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Typical estimation strategy for RDs
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Issue 1: To standardize or not stan
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Generalizing Treatment Effects Acro
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…Also Common in • Meta-Analysis
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What is Special about Pooling RD Es
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Benefits and Tradeoffs of Option 1
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Benefits and Tradeoffs of Option 2
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Distribution of Units in an RD with
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Multivariate RDD with Two Assignmen
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The Average Treatment Effect along
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Treatment Weights for τ MRD Weight
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Estimating Treatment Effects Four P
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Centering Approach Procedure allows
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IV Approach (1) Rather than exclude
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Regression Discontinuity - Institute for Policy Research

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