Regression Discontinuity - Institute for Policy Research

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Recent Education Examples of RDDs with Multiple Assignment Variables • College financial aid offer (van der Klaauw, 2002; Kane, 2003) • Remedial education (Jacob & Lefgren, 2004a) • Teacher professional development (Jacob & Lefgren, 2004b) • High school exit exams (Martorell, 2005; Papay et al. 2010) • No Child Left Behind (Gill et al., 2007)
The Average Treatment Effect along the Cutoff Frontier (τ MRD ) τ MRD is the weighted average of conditional expectations given the single frontiers F R and F M : t MRD = E[G i | (R i , M i ) ÎF] = w R E[G i | R i ÎF R ] + w M E[G i | M i ÎF M ] = w R t R + w M t M Where G i is the average size of the discontinuity at the R and M cutoff frontiers, and f(r,m) is the joint density function <strong>for</strong> assignment variables R and M.
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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
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 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: Multivariate RDD with Two Assignmen
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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