Regression Discontinuity - Institute for Policy Research

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Adding Nonlinear Terms to the Model • Include nonlinear functions of the assignment variable in the equation, <strong>for</strong> example: Y i = ˆb 0 + ˆb 1 d + ˆb 2 (z i - z c ) + ˆb 3 (z i - z c ) 2 + e i Where d is the treatment indicator and z is the assignment variable • There are many such nonlinear functions, so selecting the correct one is crucial
Adding Interaction Terms to the Model • One can also add interactions between treatment assignment (d) and the assignment variable (z), <strong>for</strong> example:
Page 1 and 2: Regression-Discontinuity Design Day
Page 3 and 4: Design Overview Design Examples Vis
Page 5 and 6: RDD Visual Depiction Comparison
Page 7 and 8: RDD Visual Depiction Discontinuity,
Page 9 and 10: Two Rationales for RDD 1. Selection
Page 11 and 12: Required Assumptions for RD design
Page 13 and 14: Sharp RD Designs • Requires that
Page 15 and 16: Estimating Treatment Effects in Fuz
Page 17 and 18: “Non”-RD designs • No discont
Page 19 and 20: 2. Manipulation of the assignment v
Page 21 and 22: Diagnostic test • Can perform “
Page 23 and 24: Analytic Threats to RD Design: Para
Page 25 and 26: 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 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 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
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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
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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
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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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