Regression-Discontinuity Design - Institute for Policy Research

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How to Detect Nonlinearities • Visual Inspection of relationship between assignment and outcome prior to treatment (e.g., if archival data is used). • Visual Inspection of the Graph • Computer Programs (e.g, Cook and Weisberg) • Analysis: Overfitting the model (more on this later).
Adding Nonlinear Terms to the Model • Include nonlinear functions of the assignment variable in the equation, <strong>for</strong> example: Y i = ˆβ 0 + ˆβ 1 d + ˆβ 2 (z i − z c ) + ˆβ 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
Page 1 and 2: Regression‐Discontinuity Design D
Page 3 and 4: Design Overview Design Examples Vis
Page 5 and 6: Real Examples of RD Reading First b
Page 7 and 8: RDD Visual Depiction Comparison Tre
Page 9 and 10: Two Rationales for RDD 1. Selection
Page 11 and 12: Two Rationales for RDD 1. Selection
Page 13 and 14: 1. Overrides to the cutoff: Sharp,
Page 15 and 16: Fuzzy RD Designs • Requires a dis
Page 17 and 18: Requirements for Estimating Treatme
Page 19 and 20: Implementation Threats to RD Design
Page 21 and 22: Example: AYP Data from Texas Densit
Page 23 and 24: What to do? • This is a big probl
Page 25 and 26: Analytic Threats to RD Design: Miss
Page 27 and 28: Nonlinearities in Functional Form
Page 29 and 30: Here we see a discontinuity between
Page 31 and 32: Functional Form: Interactions • S
Page 33 and 34: If we superimpose the regression li
Page 35: Here we see an example where the tr
Page 39 and 40: Adding Nonlinear and Interaction Te
Page 41 and 42: Adding Terms, Continued • When in
Page 43 and 44: Example of Parametric Plot used aga
Page 45 and 46: Non‐parametric Approach lim x↓c
Page 47 and 48: Non‐parametric plot Local linear
Page 49 and 50: Semi‐Parametric Plot RD data from
Page 51 and 52: What to do? • Check to see whethe
Page 53 and 54: Shadish, Galindo, Wong, V., Steiner
Page 55 and 56: RD Design assumption 2 • Continui
Page 57 and 58: Implementation assumption 2 • No
Page 59 and 60: Analytic assumption 1 continued •
Page 61 and 62: Shadish et al. (under review) Vocab
Page 63 and 64: RDD Example 2
Page 65 and 66: Best case scenario - regression lin
Page 67 and 68: Correct specification of functional
Page 69 and 70: What to do (2) • Parametric appro
Page 71 and 72: What to do (4) • State‐of‐art
Page 73 and 74: What to do (5) • Move to a tie br
Page 75 and 76: Example Cocaine Project • Include
Page 77 and 78: What to do (7) • Estimation throu
Page 79 and 80: 2. Dealing with Overrides to the cu
Page 81 and 82: 2. Overrides to the cutoff • Mult
Page 83 and 84: Specification of Functional Form Pa
Page 85 and 86: Specification of Functional Form No
Page 87 and 88:
Overrides to cutoff (2) Alternative
Page 89 and 90:
Final estimates Function al form Pa
Page 91 and 92:
Addressing Potential Issues with us
Page 93 and 94:
IS Wong et al. a Fallible RD or Ins
Page 95 and 96:
African‐American Home language Sp
Page 97 and 98:
Fallible RD? • Now we look for di
Page 99 and 100:
McCrary Test for New Jersey
Page 101 and 102:
Summarizing Checks - Conditional Me
Page 103 and 104:
Other Kinds of Threats with RD 1. L
Page 105 and 106:
Variance of Impact Estimator in RA
Page 107 and 108:
Variance of Impact Estimator in RDD
Page 109 and 110:
Power Considerations Unique to RDD
Page 111 and 112:
Generalizing Beyond The Cut‐off I
Page 113 and 114:
Observed vs Counterfactual Outcomes
Page 115 and 116:
Questions About Generalizing From R
Page 117 and 118:
What Do We Mean By Comparison Group
Page 119 and 120:
Our Purpose • Use experimental da
Page 121 and 122:
What Is The Target Parameter? • A
Page 127 and 128:
What About The Above The Cut‐Off
Page 129 and 130:
Root Mean Square Error In Experimen
Page 131 and 132:
Post-Treatment Medicaid Expenditure
Page 133 and 134:
Results For Number of Unpaid Worker
Page 135 and 136:
Results For Expenditures With Expen
Page 137 and 138:
Conclusions re Using a Comparison R
Page 139 and 140:
Implications for Practice • Which
Page 141 and 142:
RD with Multiple Cutoffs Design (as
Page 143 and 144:
Analyzing RDs with Multiple Cutoffs
Page 145 and 146:
Examples • Black, Galdo, and Smit
Page 147 and 148:
Issue 2: To pool or not pool across
Page 149 and 150:
Pooling is Already Common in Social
Page 151 and 152:
What is Special about Pooling RD Es
Page 153 and 154:
Estimating Treatment Effects across
Page 155 and 156:
Estimating Treatment Effects across
Page 157 and 158:
Generalizing Across Multiple Assign
Page 159 and 160:
Multivariate RDD with Two Assignmen
Page 161 and 162:
Recent Education Examples of RDDs w
Page 163 and 164:
Frontier‐specific Effect (τ R )
Page 165 and 166:
Requirements for a valid Multivaria
Page 167 and 168:
Frontier Approach Estimates the dis
Page 169 and 170:
Univariate Approach Addresses dimen
Page 171 and 172:
Monte Carlo Study Wong, V., Steiner
Page 173:
Implications for Practice • Which
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