Regression Discontinuity - Institute for Policy Research

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Frontier Approach Estimates the discontinuity along each frontier simultaneously, and applies appropriate weights to obtain the overall effect. First, estimate the treatment function, which is the average size of the discontinuity along the cutoff frontiers using parametric, semiparametric, or non-parametric approaches. Second, estimate the joint density function by using a bivariate kernel density estimator or by estimating conditional density functions for R and M separately for observations that lie within a narrow bandwidth around the frontier. Third, numerically integrate the product of treatment and joint density functions at the cutoff frontiers to obtain conditional expectations across both frontiers. Third, apply appropriate treatment weights to each discontinuity frontier. Estimates τ MRD , τ M , τ R
Centering Approach Procedure allows researcher to address the “curse of dimensionality” issue by collapsing multiple assignment scores for unit i to a single assignment variable. First, for each unit i, center assignment variables r and m to their respective cutoffs, that is r i – r c and m i – m c . Second, choose the minimum centered value z i = min(r i – r c , m i – m c ) is chosen as the unit’s sole assignment score. Third, pool units and analyze as a standard RD design with z as the single assignment variable. Estimates τ MRD
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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
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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
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 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: Estimating Treatment Effects Four P
Page 149 and 150: IV Approach (1) Rather than exclude
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Regression Discontinuity - Institute for Policy Research

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