Regression Discontinuity - Institute for Policy Research

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What to do about fuzzy allocation? • RDD as an instrumental variable – Provides causal estimates if instrument is correlated with treatment and not with errors in the outcome. – Proof: Hahn, Todd, and van der Klaauw, 2001 – Examples: Angrist & Lavy, 1999; Jacob and Lefgren, 2004a, 2004b; van der Klaauw, 2002 – In this case, we implemented in a regression (two stage least squares) framework as opposed to the non-parametric wald estimator
2. Overrides to the cutoff • Multiple estimations Michigan PPVT Full sample Restricted sample Instrumental Variable % Fuzzy (8) (9) (11) 2% -2.20 -1.91 -2.75 (3.64) (4.15) (4.53) West Virginia 8% 2.75 3.66 2.42 PPVT (2.23) (2.39) (1.94) Michigan 2% 25.21* 24.98* 22.14* Print Awareness (3.48) (3.58) (3.11) West Virginia 8% 22.25* 24.49* 20.15* Print Awareness (3.59) (3.50) (2.98)
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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
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
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: 2. Dealing with Overrides to the cu
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 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
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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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