Regression Discontinuity - Institute for Policy Research

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Variance of Impact Estimator in RA ^ Var ra (α 0 ) = σ 2 (1-R ra2 ) np(1-p)(1-ns-co) 2 • σ 2 is the variance of mean student outcomes across schools within the treatment or comparison group • R ra 2 is the square of the correlation between school outcomes and the assignment variable • np(1-p) is the total variation in treatment status across schools • ns is the no-show (via appeals) rate • co is the cross-over (via participation) rate
Power Considerations Common to Randomized Experiments and RDD 1. Sample size -- increase N 2. Distribution of outcome variable - normal if possible 3. Misallocation rates - lower the better 4. R-square of school- and student-level covariates - as high as possible 5. Clustered designs and intra-class correlations -- as low as possible or as reduced as possible through the use of covariates explaining clustering
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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
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
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: Inadequate statistical power • Ne
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 and 114: What Is The Target Parameter? • A
Page 115 and 116: Table 1: Bias At the Cutoff Adding
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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