Index
Regression Discontinuity Designs
ISBN: 978-1-78714-390-6, eISBN: 978-1-78714-389-0
ISSN: 0731-9053
Publication date: 13 May 2017
This content is currently only available as a PDF
Citation
(2017), "Index", Regression Discontinuity Designs (Advances in Econometrics, Vol. 38), Emerald Publishing Limited, Leeds, pp. 503-512. https://doi.org/10.1108/S0731-905320170000038021
Publisher
:Emerald Publishing Limited
Copyright © 2017 Emerald Publishing Limited
INDEX
Adult sanctions
, 77, 82
incapacitation effects of
, 102
Affordable Care Act
, 284
Age-based law enforcement discretion
, 95–96
Age distribution of crime
, 139
Area Median Gross Income (AMGI)
, 400–401
As-if random assignment
, 13, 157, 161
Assignment variable, measurement error in
baseline statistical model
, 459–463
continuous assignment variable and measurement error
, 484
estimation
, 490–492
imperfect compliance identification
, 489–490
perfect compliance identification
, 484–489
discrete assignment variable and measurement error
, 463
assignment variable distribution and RD treatment effect
, 473–474
conditional expectation functions and RD treatment effect
, 472–473
potential issues in practical implementation
, 476–477
simple numerical example
, 477–484
true assignment variable distribution
, 464
Medicaid takeup and crowdout
, 492–495
with regression discontinuity design
, 456
Asymptotic mean-squared error (AMSE)
, 360, 369, 423, 437
Availability of RD design
, 2
Average treatment effect (ATE)
, 3, 6, 10, 15, 16, 23, 55–57, 154, 197, 200, 211, 239, 285, 334, 335, 345, 386, 426, 440, 441
BadgerCare
, 151
BadgerCare Plus (BC+) program
, 151–152, 177
Bajari, Hong, Park, and Town’s model
, 49–54
Bandwidth
, 7, 18, 91, 156, 286, 346–347, 359, 366, 369, 384–385
and kernel
, 429
selection
, 156
“Baseline arrest”
, 83–85, 90, 92
Baseline statistical model
, 459–463
Becker’s model of crime
, 103–104
Bellman equation
, 104
Benchmark Plan
, 151
Benefit elasticity, estimates of
, 362, 375
Bias correction
, 343, 359, 424, 438
bootstrap
, 430–435, 439
Bias estimation
, 430
Bootstrap bias correction
, 430–435
Bootstrap confidence intervals for sharp RD designs
, 421
application
, 440–442
background
, 425–430
bootstrap bias correction
, 430–435
simulation evidence
, 436–440
California’s three-strikes law
, 75, 78–79
CCF (Calonico, Cattaneo, and Farrell)
, 384, 387, 388, 390, 393, 394, 410
CCFT (Calonico, Cattaneo, Farrell, and Titiunik)
, 343, 346, 347, 361
CCT (Calonico, Cattaneo, and Titiunik)
, 343, 345, 346, 347, 384, 389, 391, 393, 423, 424, 425, 428, 430, 438, 449, 453
Child Development Study (CDS)
, 457
Children’s Health Insurance Program (CHIP)
, 150, 457
copayments in
, 150–152
CJLPM (Card, Johnston, et al.)
, 374–375
CLPW (Card, Lee, Pei, and Weber)
, 343–346, 378n2, 378n3
Clustered data, RD designs with
, 383
application
, 399–406
distributional approximation
, 393–394
extensions
, 394–395
main results
, 388
clustering at running variable level
, 390–393
setup and notation
, 385–388
simulations
, 395–399
Cluster-robust bandwidth
, 385, 394, 396, 404, 405
“Cluster-robust” standard error formulas
, 384, 402
Comparative regression discontinuity (CRD) design
, 240
CRD-CG design
, 265
estimated bias
, 266–268
RCT results
, 265–266
statistical efficiency
, 268–269
support for functional form assumptions
, 266
CRD-pre design
, 258–260
estimated bias
, 262–263
results for
, 258–260
statistical efficiency
, 263–264
support for functional form assumptions
, 260–262, 266
data and analysis methods
, 250
causal estimates for CRD and basic RD designs
, 256–257
causal estimates for RCT design
, 254–256
checking parallel assumptions of CRD
, 253–254
comparing efficiency across designs
, 258
creating basic RD, CRD-pre and CRD-CG designs
, 251–253
study data
, 250–251
designs and within-study comparison approach
, 241
gains statistical power from CRD
, 248
identification of causal effects using
, 244–247
implementation and estimation
, 247
sensitivity test
, 269–271
testing CRD using a within-study comparison approach
, 248
Complier probability derivative (CPD)
, 319, 322, 333
fuzzy design treatment effect derivative (TED) and
, 323–324
Compound treatments
, 161–163, 220–221
Computerized Criminal History (CCH) system
, 128
Conditional cash transfers (CCTs)
, 198–200
Conditional geographic mean independence
, 160–161, 207
Confidence intervals (CIs)
, 25, 112, 273–274, 359, 361, 366, 394, 423
Continuity-based RD design
, 3, 6, 7, 10, 16
and local randomization
, 8–11
Continuous assignment variable and measurement error
, 484
estimation
, 490–492
imperfect compliance identification
, 489–490
perfect compliance identification
, 484–489
Conventional (naive) CIs
, 427, 439
Copayments in CHIP
, 150–152
County-level tax rates
, 194
Covariate balance near municipal borders
, 203–206
Covariate index
, 353–354
Covariates
, 4, 163, 170–172, 334, 369–374
Coverage error (CE)
, 346, 395, 396
Crime control policies
, 77
Cumulative distribution function (CDF)
, 32, 42, 53, 62, 104
Current Population Survey (CPS)
, 62
Data-dependent estimation approaches
, 347
Data-generating processes (DGPs)
, 343, 366, 395, 424, 427, 432, 436, 437
Density-based identification
, 32, 55
Density discontinuity approach
, 29, 33, 55–58
Bajari, Hong, Park, and Town’s model
, 49
identification
, 52–54
model
, 49–52
Doyle’s model
, 38
identification
, 41–43
inference on the discontinuity in density
, 58–64
Jales’ model
, 43–48
identification
, 48–49
Kleven and Waseem’s model
, 34
economic model
, 34–35
identification
, 36–38
statistical model
, 35–36
minimum wage
, 38
Density test
, 282, 309
Deterrence, defined
, 117
Deterrence effect of prison
, 73
arrest-level database
, 128
construction of data set
, 128
date variables
, 128–129
arrest probabilities
, 134–140
average incarceration lengths
, 129–133
data and sample
, 82
main analysis sample
, 83–86
measurement and reporting discontinuities
, 86–87
evidence on deterrence and incapacitation
, 87
age-based law enforcement discretion
, 95–96
evidence on deterrence
, 87–92
evidence on incapacitation
, 101–103
expungement of juvenile records
, 96–101
transfers of juveniles to the adult criminal court
, 92–95
existing literature
, 77–80
identification and estimation
, 80–82
predicted effects from dynamic model of crime
, 103
benchmark model calibration and predicted values for θ
, 106–110
connecting θ to broader policy elasticities
, 111–112
model
, 103–106
nonparametric bounds on policy elasticities
, 112–114
Differences-in-differences (DID)
, 152, 179
Discontinuous assignment of treatment at geographic boundary
, 152
in the absence of geo-located individual data
, 156–157
geo-location of few coarse geographic units
, 158–161
geo-location of small aggregate units
, 157–158
GRD designs when data is geo-located
, 153–156
Discrete assignment variable and measurement error
, 463
assignment variable distribution and RD treatment effect
, 473–474
conditional expectation functions and RD treatment effect
, 472–473
potential issues in practical implementation
, 476–477
simple numerical example
, 477–484
true assignment variable distribution
, 464
imperfect compliance
, 468–472
perfect compliance
, 464–468
Discrete test for running variable manipulation
, 286–289
additional support points
, 291
choosing k
, 291–292
critical values
, 289–291
null distribution
, 289–291
power
, 289–291
test statistic
, 289–291
Distributional approximation
, 385, 393–394
Double-dose algebra
, 8, 14, 23
“Doughnut hole” design
, 166
Doyle’s model
, 38–43
extensive–margin response and imperfect compliance
, 41
identification
, 41–43
Dual-economy setting
, 44
Dynamic model of crime, predicted effects from
, 103
benchmark model calibration and predicted values for θ
, 106–110
connecting θ to broader policy elasticities
, 111–112
model
, 103–106
nonparametric bounds on policy elasticities
, 112–114
Econometric framework
, 284
discrete test for running variable manipulation
, 286–289
standard tests for running variable manipulation
, 285–286
Effect structure assumption
, 33, 54, 58, 64, 65
Elasticity
, 38, 65, 112–114, 115, 142, 144
intertemporal
, 146
Employment effects
, 31, 38, 41, 42, 43, 49
“Excess of mass”, concept of
, 43
Exclusion restriction
, 5, 11, 15–16, 18
local independence and
, 19–21
Experimental analysis under local independence
, 22–24
Experimental samples used to assess validity
, 211–213
External validity
, 210–213, 216–219, 222, 318–319, 320, 325, 337
Falsification test
, 163, 165, 167, 168, 171–175, 247, 320
Family and Medical Leave Act
, 284
FG (Fan and Gijbels)
, 343, 347, 355, 359–361
“First arrest”
, 83, 101, 103, 107
Fisherian randomization-based approach
, 5, 15–16
Fixed-G calculations
, 384, 388, 411
Florida Department of Law Enforcement (FDLE)
, 83, 95, 122, 128
Forcing variable
, 30–32, 55, 57, 58, 318
imperfect control of
, 31
Fuzzy design treatment effect derivative (TED) and complier probability derivative (CPD)
, 322–324
“Fuzzy” generalization of the sharp design
, 345
Fuzzy RD design
, 25n3, 322, 323, 329, 337, 395
Fuzzy RKD estimates
, 346, 360–361
Geographically discontinuous treatment assignments
, 147, 152
in the absence of geo-located individual data
, 156–157
application
, 168
analysis plan
, 171–172
balance results and placebo tests
, 175–179
data
, 168–171
falsification test
, 172–175
outcome estimates
, 179–180
county level tax rates
, 194
discussion
, 180–182
empirical application
, 150–152
geo-location of few coarse geographic units
, 158–161
geo-location of small aggregate units
, 157–158
GRD designs when data is geo-located
, 153–156
particularities of
, 161
compound treatments
, 161–163
interference
, 165–166
and internal validity
, 163–165
local nature of effects
, 166–167
spatial treatment effects
, 167–168
placebo tests
, 191
Geographic discontinuity design (GDD)
, 196
Geographic quasi experiment (GQE)
, 161, 164, 175, 197, 201
compound treatment irrelevance
, 220–221
covariate balance near municipal borders
, 203–206
estimates
, 209–210
experimental samples used to assess validity
, 211–213
external validity
, 210–211, 216–219
internal validity
, 210–211, 219–220
inverse-probability weighting and external validity
, 213–215
potential threats to internal validity
, 207–208
sample
, 201–203
Geographic regression discontinuity (GRD)
, 150
GRD designs when data is geo-located
, 153–156
Growth in RD empirical applications
, 2
Head Start application
, 274, 440
Head Start program
, 437, 440–442
Health care utilization
, 152, 154, 162, 165, 168, 170, 177–181, 457
trends in (2007–2008)
, 189–190
Heteroskedasticity-robust standard errors
, 394, 402
Hypothesis tests
, 423, 428
Hypothetical experiment
, 4
Identification strategy
, 40, 75, 78, 80–82, 175
IK (Imbens and Kalyanaraman)
, 384, 391
Incapacitation
defined
, 117
effect
, 76–77, 79, 82
evidence on
, 101–103
Index crimes
, 84, 86, 133
Informal sectors
, 43–44, 49
Informational constraints, in medical industry
, 49–54
Instrumental variables (IVs) designs
, 3
Insurance copays
, 152–153
Internal validity
, 163–164, 210–211, 219–220
potential threats to
, 207–208
Interpretation of RD designs
, 2–5, 25, 157
Intertemporal elasticity
, 2–5, 146
Inverse-probability weighting and external validity
, 213–215
Iterated bootstrap
, 424, 430, 434, 435, 452
Jales’ model
, 43–49
identification
, 48–49
missing and excess of mass
, 47
Juvenile Justice Reform Act (JJRA) (1994)
, 86–87, 95, 140
Juvenile records
, 85, 95
expungement of
, 96–101
Juveniles
crime rates
, 78
justice system
, 78
transfers of, to adult criminal court
, 92–95
Kernel, bandwidth and
, 429
Kernel function
, 61
Kleven and Waseem’s model
, 34, 65
bunching at tax notch
, 36
economic model
, 34–35
identification
, 36–38
statistical model
, 35–36
Labor costs
, 65
Labor unions
, 282
Latent wage
, 38, 40
Lee’s framework
, 4
Leibniz integral rule
, 141
Local average response (LAR)
, 345
Local average treatment effect (LATE)
, 239, 318, 320, 326, 327
Local experiments, interpretation of RD designs as
, 4–5, 10–11
Local independence
, 18
and exclusion restriction
, 19–21
experimental analysis under
, 22–24
random assignment of score and
, 18–19
Local likelihood approach
, 63
Local polynomial estimators
, 384, 406, 416
Local randomization RD framework
, 6, 10, 11
formalizing
, 15–18
of score/treatment
, 11–12
score value
, 12–15
Low-Income Housing Tax Credits (LIHTC)
, 385, 399, 402
and neighborhood characteristics
, 399–406
Manipulation test
, 58–59, 304
Maximum likelihood estimation (MLE) framework
, 458
McCrary test with discrete data
, 292–293
McCrary’s binning-based local linear approach
, 63
Mean-squared errors (MSE)
, 343, 347
MSE minimization
, 156
MSE-optimal bandwidth
, 384, 411, 416
MSE-optimal procedure
, 361
Measurement error in assignment variable
baseline statistical model
, 459–463
continuous assignment variable and measurement error
, 484
estimation
, 490–492
imperfect compliance identification
, 489–490
perfect compliance identification
, 484–489
discrete assignment variable and measurement error
, 463
assignment variable distribution and RD treatment effect
, 473–474
conditional expectation functions and RD treatment effect
, 472–473
potential issues in practical implementation
, 476–477
simple numerical example
, 477–484
true assignment variable distribution
, 464
Medicaid takeup and crowdout
, 492–495
with regression discontinuity design
, 456
Medicaid
, 458–459, 492–495
Medicaid Analytics Extracts
, 170
Medicaid takeup and crowdout
, 492–495
Medical Expenditure Panel Survey (MEPS)
, 457
Minimum wage policy
, 32, 38, 43–45
Missing mass
, 33, 36, 38, 42–43, 68
“Missing workers”, concept of
, 38
Modifiable areal unit problem (MAUP)
, 158
Moment generating functions (MGFs)
, 466
Monte Carlo simulations
, 61, 309, 343, 364–365, 367–368
MTTE, treatment effect derivative (TED) and
, 335–336
Naïve RD interval
, 423
National Labor Relations Board (NLRB)
, 283
Neyman–Rubin framework
, 2, 3
Non-Index crimes
, 96
Notches
, 34–35
Null distribution
, 289–291
Observed information matrix (OIM)
, 119
Optimal bandwidth
, 416
Optimal bandwidth selectors
, 384–385, 406
Outer product of the gradient (OPG)
, 119
Panel Study of Income Dynamics (PSID)
, 457
“Pass/fail” threshold
, 30
Policing elasticity
, 142
Policy reforms, types of
, 76
Political parties
, 282
Popularity of RD design
, 2
Potential outcomes regression functions
, 8, 10
“Pre-asymptotic” cluster-robust standard errors
, 394
Preventive health visits
, 151
Probability of disemployment
, 32
“Proof of concept”
, 424
Punitive criminal justice sanctions
, 75, 77
Qualified Census Tract (QCT)
, 399, 400, 401, 402, 405
“Quasi-experimental” research designs
, 3
Random assignment of score and local independence
, 18–19
Randomization
, 5, 6, 11, 17
Randomized controlled trial (RCT)
, 239
causal estimates for RCT design
, 254–256
Rdrobust software
, 91, 156
Regression functions
, 6, 8, 13, 19, 20, 24, 154, 255, 386
Regression kink design (RKD)
, 319, 341, 342
data and analysis sample
, 349–350
estimation and inference, review of
, 345–347
estimation results
, 355
alternative estimators, comparison of
, 361–369
comparison with Missouri RKD application in card
, 374–375
covariates, estimates with
, 369–374
fuzzy RKD estimates
, 360–361
reduced form kinks in treatment and outcome variables
, 355–360
graphical overview of the effect of kinks in the UI benefit schedule
, 350–355
identification, review of
, 344–345
unemployment insurance (UI) benefit schedule in Austria
, 348–349
Reimbursement schemes
, 49–54
Relative punitiveness
, 78, 117
Root-mean-squared error (RMSE)
, 363, 366, 380n20
Running variable
, 2–3, 5, 13, 19, 21, 23, 57, 80, 82, 149–150, 154–155, 157–158, 282–288, 291–301, 303, 304, 309, 315, 319, 321, 329, 335, 371, 384–388, 390, 392, 396–399
“Second arrest”
, 83, 101, 107
Sector-specific density of wages
, 46
Selection-on-observables assumption
, 3, 164, 211
Sharp design, “fuzzy” generalization of
, 345
Sharp design treatment effect derivative (TED)
, 321–322
Sharp RD designs, bootstrap confidence intervals for. See Bootstrap confidence intervals for sharp RD designs
“Sharp” RKD
, 344
Simulation evidence
, 436–440
Simulation extrapolation (SIMEX) method
, 458, 489–490, 492, 496, 498
Small aggregate units, geo-location of
, 157–158
Smoothness-based RD methods
, 155
Stable unit treatment value assumption (SUTVA)
, 153, 165, 320, 336
Standard Plan
, 151
Standard tests for running variable manipulation
, 285–286
Survey of Income and Program Participation (SIPP)
, 458
Tax system
, 34, 35, 65
Taylor expansion
, 37, 412, 424
Testing stability of regression discontinuity models
, 317
covariates
, 334
empirical examples
, 325–334
fuzzy design treatment effect derivative (TED) and complier probability derivative (CPD)
, 322–324
literature review
, 320–321
sharp design treatment effect derivative (TED)
, 321–322
stability
, 324–325
treatment effect derivative (TED) and MTTE
, 335–336
Test statistic
, 61, 63, 284, 287, 289–291
Threshold
, 31–34, 49, 318–320, 326, 327, 329, 330, 331, 333, 335–336, 337
Treatment effect derivative (TED)
, 318–319, 324
fuzzy design TED and complier probability derivative (CPD)
, 322–324
and MTTE
, 335–336
sharp design
, 321–322
Treatment effect ratio
, 57–58
Treatment-on-the-treated (TOT)
, 239, 241, 244, 249, 255, 257, 345
Triangular kernel function
, 61
Two-stage least squares (2SLS)
, 331
Unemployment insurance (UI) benefit schedule in Austria
, 348–349
graphical overview of the effect of kinks in
, 350–355
Unemployment Insurance (UI) records
, 329
Variance components
, 450
“Victimless” offenses
, 96
Weibull models
, 121
Wild bootstrap
, 424, 430, 433, 437, 438
Wisconsin CHIP program
, 151, 152
Wisconsin–Illinois border
, 159, 163, 167–168
housing prices at
, 172
Wisconsin–Illinois boundary
, 154
- Prelims
- On Interpreting the Regression Discontinuity Design as a Local Experiment
- Identification and Estimation Using a Density Discontinuity Approach
- The Deterrence Effect of Prison: Dynamic Theory and Evidence
- An Overview of Geographically Discontinuous Treatment Assignments with an Application to Children’s Health Insurance
- External and Internal Validity of a Geographic Quasi-Experiment Embedded in a Cluster-Randomized Experiment
- The Comparative Regression Discontinuity (CRD) Design: An Overview and Demonstration of its Performance Relative to Basic RD and the Randomized Experiment
- Party Bias in Union Representation Elections: Testing for Manipulation in the Regression Discontinuity Design when the Running Variable is Discrete
- Testing Stability of Regression Discontinuity Models
- Regression Kink Design: Theory and Practice
- Regression Discontinuity Designs with Clustered Data
- Bootstrap Confidence Intervals for Sharp Regression Discontinuity Designs
- The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable
- Index