Regression Discontinuity - Institute for Policy Research

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The Example • Assignment variable = Age and Cutoff = Age 70 • Outcome = Medicaid expenditure level • 3-Group Design = RCT, posttest-only standard RDD, and a pretest-supplemented RDD • Main Purpose: compare RCT and pretestsupplemented RDD estimates at the cutoff and especially in all the treated area away from it to see if biased
Table 1: Bias At the Cutoff Adding a Pretest RD Function at Age 70 Bias in SD Units Relative to Polynomial Benchmark Bias in SD Units Relative to LLR Benchmark State Model Estimation Cutoff Arkansas Pretest RDD Parametric 70 0.06 0.04 New Jersey Pretest RDD Parametric 70 0.04 0.01 Florida Pretest RDD Parametric 70 -0.17 -0.16 Arkansas Pretest RDD LLR 70 0.09 0.07 New Jersey Pretest RDD LLR 70 0.11 0.08 Florida Pretest RDD LLR 70 -0.02 -0.02
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Regression-Discontinuity Design Day
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Design Overview Design Examples Vis
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RDD Visual Depiction Comparison
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RDD Visual Depiction Discontinuity,
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Two Rationales for RDD 1. Selection
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Required Assumptions for RD design
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Sharp RD Designs • Requires that
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Estimating Treatment Effects in Fuz
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“Non”-RD designs • No discont
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2. Manipulation of the assignment v
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Diagnostic test • Can perform “
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Analytic Threats to RD Design: Para
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The size of the discontinuity at th
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Functional Form • Put more techni
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Functional Form: Interactions • S
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If we superimpose the regression li
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Here we see an example where the tr
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Adding Nonlinear Terms to the Model
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Adding Nonlinear and Interaction Te
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Adding Terms, Continued • When in
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Example of Parametric Plot used aga
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Non-parametric Approach lim x¯c E[
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3. Semi-Parametric Approach Y i = t
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Problem of Incorrect Bandwidth Sele
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RDD Example 1
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RD Design assumption 1 • Probabil
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Implementation assumption 2 • No
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Analytic assumption 1 continued •
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Shadish et al. (2011) Vocabulary RD
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RDD Example 2
Page 63 and 64: Best case scenario - regression lin
Page 65 and 66: Correct specification of functional
Page 67 and 68: What to do (2) • Parametric appro
Page 69 and 70: What to do (4) 0 50 100 150 locpoly
Page 71 and 72: What to do (5) • Move to a tie br
Page 73 and 74: Example Cocaine Project • Include
Page 75 and 76: What to do (7) • Estimation throu
Page 77 and 78: 2. Dealing with Overrides to the cu
Page 79 and 80: 2. Overrides to the cutoff • Mult
Page 81 and 82: Specification of Functional Form Pa
Page 83 and 84: Specification of Functional Form No
Page 85 and 86: Overrides to cutoff (2) Alternative
Page 87 and 88: Final estimates Function al form Pa
Page 89 and 90: Addressing Potential Issues with us
Page 91 and 92: African-American Home language Span
Page 93 and 94: What about cutoff Shift in Number o
Page 95 and 96: McCrary Test for New Jersey
Page 97 and 98: Take Home Message • Like RE, the
Page 99 and 100: Inadequate statistical power • Ne
Page 101 and 102: Power Considerations Common to Rand
Page 103 and 104: What “Uniquely” Affects Power i
Page 105 and 106: Generalizing Beyond The Cut-off In
Page 107 and 108: Adding an Untreated RD Comparison F
Page 109 and 110: Creating A Regression Discontinuity
Page 111 and 112: Pretest and Posttest RD • Imagine
Page 113: What Is The Target Parameter? • A
Page 117 and 118: Summary of what the Pretest- Supple
Page 119 and 120: Additional Topic not covered in Cla
Page 121 and 122: Sample Data with Multiple Cutoffs O
Page 123 and 124: Typical estimation strategy for RDs
Page 125 and 126: Issue 1: To standardize or not stan
Page 127 and 128: Generalizing Treatment Effects Acro
Page 129 and 130: …Also Common in • Meta-Analysis
Page 131 and 132: What is Special about Pooling RD Es
Page 133 and 134: Benefits and Tradeoffs of Option 1
Page 135 and 136: Benefits and Tradeoffs of Option 2
Page 137 and 138: Distribution of Units in an RD with
Page 139 and 140: Multivariate RDD with Two Assignmen
Page 141 and 142: The Average Treatment Effect along
Page 143 and 144: Treatment Weights for τ MRD Weight
Page 145 and 146: Estimating Treatment Effects Four P
Page 147 and 148: Centering Approach Procedure allows
Page 149 and 150: IV Approach (1) Rather than exclude
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Regression Discontinuity - Institute for Policy Research

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