Package {rd2d}

Type: Package
Title: Estimation and Inference for Boundary Discontinuity Designs
Version: 0.1.0
URL: https://rdpackages.github.io/, https://github.com/rdpackages/rd2d
BugReports: https://github.com/rdpackages/rd2d/issues
Description: Provides pointwise and uniform estimation and inference methods for boundary discontinuity (BD) designs, a causal inference design that generalizes univariate regression discontinuity (RD) designs to settings with bivariate scores. Implements local polynomial methods for location-based and distance-based analyses, including sharp and fuzzy designs, data-driven bandwidth selection, pointwise confidence intervals, and uniform confidence bands. Methodology is developed in Cattaneo, Titiunik, and Yu (2026) <doi:10.48550/arXiv.2505.05670> for location-based methods and Cattaneo, Titiunik, and Yu (2026) <doi:10.48550/arXiv.2510.26051> for distance-based methods. For an overview and empirical guidance, see Cattaneo, Titiunik, and Yu (2026) <doi:10.48550/arXiv.2511.06474>. The companion software article is Cattaneo, Titiunik, and Yu (2025) <doi:10.48550/arXiv.2505.07989>.
Imports: MASS, expm, ggplot2
Suggests: testthat (≥ 3.0.0)
License: GPL-2
Encoding: UTF-8
Maintainer: Matias D. Cattaneo <matias.d.cattaneo@gmail.com>
NeedsCompilation: no
Author: Matias D. Cattaneo [aut, cre], Rocio Titiunik [aut], Ruiqi Rae Yu [aut]
Config/testthat/edition: 3
Config/roxygen2/version: 8.0.0
Packaged: 2026-05-13 14:22:26 UTC; cattaneo
Repository: CRAN
Date/Publication: 2026-05-14 08:40:02 UTC

rd2d: Estimation and Inference for Boundary Discontinuity Designs

Description

rd2d implements pointwise and uniform estimation and inference procedures for boundary discontinuity (BD) designs using local polynomial methods. The package includes location-based and distance-based methods, sharp and fuzzy designs, automatic bandwidth selection, pointwise confidence intervals, and uniform confidence bands. Distance-based methods in this package target level effects at two-dimensional boundary points.

Included functions are: rd2d for location-based estimation and inference, rdbw2d for location-based bandwidth selection, rd2d.distance for distance-based estimation and inference, and rdbw2d.distance for distance-based bandwidth selection.

print() and summary() methods are available for all four functions.

Related Stata, R, and Python packages useful for inference in RD designs are described at:

https://rdpackages.github.io/

For an introduction to regression discontinuity designs, see Cattaneo and Titiunik (2022, doi:10.1146/annurev-economics-051520-021409) and references therein.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com. Rocio Titiunik, Princeton University. titiunik@princeton.edu. Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com.

References

See Also

Useful links:

Print Method for 2D Local Polynomial RD Estimation

Description

Prints the results of a 2D local polynomial regression discontinuity (RD) estimation, as obtained from rd2d.

Usage

## S3 method for class 'rd2d'
print(x, ...)

Arguments

x

An object of class rd2d, returned by rd2d.

...

Additional arguments passed to the method (currently ignored).

Value

No return value. This function is called for its side effects, which are to print the rd2d results.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rd2d for conducting 2D local polynomial RD estimation.

Supported methods: print.rd2d, summary.rd2d.

Print Method for 2D Local Polynomial RD Estimation (Distance-Based)

Description

Prints the results of a 2D local polynomial regression discontinuity (RD) estimation using distance-based evaluation, as obtained from rd2d.distance.

Usage

## S3 method for class 'rd2d.distance'
print(x, ...)

Arguments

x

An object of class rd2d.distance, returned by rd2d.distance.

...

Additional arguments passed to the method (currently ignored).

Value

No return value. This function is called for its side effects: it prints the rd2d.distance results.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rd2d.distance for estimation using distance-based methods in 2D local polynomial RD designs.

Supported methods: print.rd2d.distance, summary.rd2d.distance.

Print Method for Bandwidth Selection for 2D Local Polynomial RD Design

Description

The print method for bandwidth selection for 2D local polynomial RD design

Usage

## S3 method for class 'rdbw2d'
print(x, ...)

Arguments

x

Class rdbw2d objects, obtained by calling rdbw2d.

...

Additional arguments passed to the method (currently ignored).

Value

No return value, called to print rdbw2d results.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rdbw2d for bandwidth selection for 2D local polynomial RD design

Supported methods: print.rdbw2d, summary.rdbw2d.

Print Method for Bandwidth Selection (Distance-Based) in 2D Local Polynomial RD Design

Description

Print method for displaying summary information from distance-based bandwidth selection in 2D local polynomial regression discontinuity (RD) designs, as produced by rdbw2d.distance.

Usage

## S3 method for class 'rdbw2d.distance'
print(x, ...)

Arguments

x

An object of class rdbw2d.distance, returned by rdbw2d.distance.

...

Additional arguments passed to the method (currently ignored).

Value

No return value. This function is called for its side effects: it prints summary information of rdbw2d.distance.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rdbw2d.distance for distance-based bandwidth selection in 2D local polynomial RD design.

Supported methods: print.rdbw2d.distance, summary.rdbw2d.distance.

Location-Based Methods for Boundary Discontinuity Design

Description

rd2d implements location-based local polynomial boundary discontinuity (BD) point estimators with robust bias-corrected pointwise confidence intervals and uniform confidence bands. See Cattaneo, M. D., Titiunik, R., and Yu, R. R. (2026) for methodological background.

Companion commands are: rdbw2d for data-driven bandwidth selection.

For other packages of RD designs, visit https://rdpackages.github.io/

Usage

rd2d(
  Y,
  X,
  assignment,
  b,
  h = NULL,
  deriv = c(0, 0),
  tangvec = NULL,
  p = 1,
  q = NULL,
  kernel = c("tri", "triangular", "epa", "epanechnikov", "uni", "uniform", "gau",
    "gaussian"),
  kernel_type = c("prod", "rad"),
  vce = c("hc1", "hc0", "hc2", "hc3"),
  masspoints = c("check", "adjust", "off"),
  cluster = NULL,
  level = 95,
  params.other = NULL,
  params.cov = NULL,
  side = c("two", "left", "right"),
  repp = 1000,
  bwselect = c("mserd", "cerrd", "imserd", "icerrd", "msetwo", "certwo", "imsetwo",
    "icertwo", "user provided"),
  bwparam = c("main", "itt"),
  method = c("dpi", "rot"),
  bwcheck = 50 + p + 1,
  scaleregul = 3,
  scalebiascrct = 1,
  stdvars = TRUE,
  fuzzy = NULL
)

Arguments

Y

Dependent variable; a numeric vector of length N, where N is the sample size.

X

Bivariate running variable (a.k.a score variable); a numeric matrix or data frame of dimension N \times 2, with each row \mathbf{X}_i = (X_{1i}, X_{2i}).

assignment

Treatment assignment indicator; a logical or binary vector indicating assignment to the treated side.

b

Evaluation points; a matrix or data frame specifying boundary points \mathbf{b}_j = (b_{1j}, b_{2j}), of dimension J \times 2.

h

Bandwidths. Either a positive scalar (same bandwidth for all dimensions and groups), or a matrix/data frame of size J \times 4, corresponding to h_{\text{control},1}, h_{\text{control},2}, h_{\text{treated},1}, h_{\text{treated},2} at each evaluation point. If not specified, bandwidth h is computed by the companion command rdbw2d; for fuzzy designs, bwparam determines whether automatic bandwidths target the fuzzy Wald ratio or the reduced-form outcome discontinuity. Default is h = NULL.

deriv

The order of the derivatives of the regression functions to be estimated; a nonnegative integer vector of length 2 specifying the number of derivatives in each coordinate (e.g., c(1,2) corresponds to \partial_1 \partial_2^2).

tangvec

Tangent vectors; a matrix or data frame of dimension J \times 2 specifying directional derivatives. Overrides deriv if provided.

p

Polynomial order for point estimation (p = 1 by default).

q

Polynomial order for robust confidence interval construction. Must satisfy q \geq p; default is q = p + 1.

kernel

Kernel function to use. Options are "tri" or "triangular" (triangular, default), "epa" or "epanechnikov" (Epanechnikov), "uni" or "uniform" (uniform), and "gau" or "gaussian" (Gaussian).

kernel_type

Kernel structure. Either "prod" for product kernels (default) or "rad" for radial kernels.

vce

Variance-covariance estimation method. Options are:

  • "hc0": heteroskedasticity-robust plug-in residual variance estimator without small-sample adjustment.

  • "hc1": heteroskedasticity-robust plug-in residual variance estimator with HC1 small-sample adjustment (default).

  • "hc2": heteroskedasticity-robust plug-in residual variance estimator with HC2 adjustment.

  • "hc3": heteroskedasticity-robust plug-in residual variance estimator with HC3 adjustment.

Default is "hc1".

masspoints

Handling of mass points in the running variable. Options are:

  • "check": detects presence of mass points and reports the number of unique observations (default).

  • "adjust": adjusts preliminary bandwidths to ensure a minimum number of unique observations within each side of the cutoff.

  • "off": ignores presence of mass points.

cluster

Cluster ID variable used for cluster-robust variance estimation with degrees-of-freedom weights. Default is cluster = NULL.

level

Nominal confidence level for intervals/bands, between 0 and 100 (default is 95).

params.other

Optional character vector requesting companion-side result tables. Options are "main.0", "main.1" for sharp fits, and "itt.0", "itt.1", "fs.0", "fs.1" for fuzzy fits. Unrequested companion tables are returned as NA. Default is NULL.

params.cov

Optional character vector requesting covariance matrices to store for later use by summary.rd2d. Options are "main", "main.0", "main.1", "itt", "itt.0", "itt.1", "fs", "fs.0", and "fs.1", subject to the sharp/fuzzy design and params.other. Default is NULL, which computes no covariance matrices.

side

Type of confidence interval. Options: "two" (two-sided, default), "left" (left tail), or "right" (right tail).

repp

Number of repetitions for critical value simulation (used in uniform confidence bands). Default is 1000.

bwselect

Bandwidth selection strategy. Options:

  • "mserd". One common MSE-optimal bandwidth selector for the boundary RD treatment effect estimator for each evaluation point (default).

  • "cerrd". CER-optimal counterpart of "mserd".

  • "imserd". IMSE-optimal bandwidth selector for the boundary RD treatment effect estimator based on all evaluation points.

  • "icerrd". CER-optimal counterpart of "imserd".

  • "msetwo". Two different MSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator for each evaluation point.

  • "certwo". CER-optimal counterpart of "msetwo".

  • "imsetwo". Two IMSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator based on all evaluation points.

  • "icertwo". CER-optimal counterpart of "imsetwo".

  • "user provided". User-provided bandwidths. If h is not NULL, then bwselect is overwritten to "user provided".

bwparam

Target parameter used for fuzzy automatic bandwidth selection. Options are "main" (default), which selects bandwidths for the linearized fuzzy Wald ratio, and "itt", which selects bandwidths for the reduced-form outcome discontinuity. This option is ignored in sharp designs and when h is supplied.

method

Bandwidth selection method for bias estimator based on local polynomials. Either "dpi" (default) for data-driven plug-in MSE optimal bandwidth selector or "rot" for rule-of-thumb bandwidth selector.

bwcheck

If a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck unique observations are used. Default is 50 + p + 1.

scaleregul

Scaling factor for the regularization term in bandwidth selection. Default is 3.

scalebiascrct

Scaling factor used for bias correction based on higher order expansions. Default is 1.

stdvars

Logical. If TRUE, the running variables X_{1i} and X_{2i} are standardized before computing automatic bandwidths. Default is TRUE. Standardization only affects automatic bandwidth selection when bandwidths are not manually provided through h.

fuzzy

Optional treatment receipt/status variable used for fuzzy RD estimation. The default is NULL, which estimates the sharp RD design.

Value

An object of class "rd2d", a list with components:

main

A data frame with point estimates, standard errors, t-statistics, p-values, confidence intervals, and bandwidths at each evaluation point.

b1, b2

First and second coordinate of evaluation points \mathbf{b} = (b_1,b_2).

estimate.p

Point estimate \widehat{\tau}_p(\mathbf{b}).

std.err.p

Standard error of \widehat{\tau}_p(\mathbf{b}).

estimate.q

Bias-corrected point estimate \widehat{\tau}_q(\mathbf{b}).

std.err.q

Standard error of the bias-corrected estimate \widehat{\tau}_q(\mathbf{b}).

t.value, p.value

t-statistic and p-value based on the bias-corrected estimate.

ci.lower, ci.upper

Pointwise confidence intervals.

h01, h02, h11, h12

Bandwidths used in each coordinate and group.

N.Co, N.Tr

Effective sample size for the control and treatment sides, respectively.

main.0, main.1

For sharp RD only, companion-side outcome tables requested through params.other; otherwise NA.

bw

Bandwidth and effective sample size table.

itt

For fuzzy RD only, same structure as main but for the reduced-form or intention-to-treat outcome discontinuity.

itt.0, itt.1

For fuzzy RD only, outcome summaries for the control and treated sides requested through params.other; otherwise NA.

fs

For fuzzy RD only, same structure as main but for the first-stage treatment receipt/status discontinuity.

fs.0, fs.1

For fuzzy RD only, first-stage summaries for the control and treated sides requested through params.other; otherwise NA.

tau.hat

Point estimates at each evaluation point.

tau.hat.q

Bias-corrected estimates at each evaluation point.

se.hat

Standard errors corresponding to tau.hat.

se.hat.q

Standard errors corresponding to tau.hat.q.

params.cov

List of covariance matrices for aggregate inference in summary.rd2d. Contains only entries requested through params.cov.

cb

List with pointwise confidence intervals.

pvalues

Two-sided p-values based on bias-corrected estimates.

tvalues

t-statistics based on bias-corrected estimates.

tau.itt, tau.itt.q

For fuzzy RD, reduced-form outcome estimates using polynomial orders p and q; otherwise NA.

tau.fs, tau.fs.q

For fuzzy RD, first-stage treatment receipt/status estimates using polynomial orders p and q; otherwise NA.

rdmodel

Character label describing the fitted RD model.

call

Matched function call.

opt

List of options used in the function call.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

References

See Also

rdbw2d, print.rd2d, summary.rd2d

Examples

# Simulated example
set.seed(123)
n <- 800
X1 <- rnorm(n)
X2 <- rnorm(n)
assignment <- as.numeric(X1 > 0)
Y <- 3 + 2 * X1 + 1.5 * X2 + assignment + rnorm(n)
X <- cbind(X1, X2)
b <- matrix(c(0, 0, 0, 1), ncol = 2)

# Estimate treatment effect using rd2d
result <- rd2d(Y, X, assignment, b, params.cov = "main",
               masspoints = "off", bwcheck = 10, repp = 49)
print(result)
summary(result, cbands = "main")

# Fuzzy RD example
fuzzy <- as.numeric(runif(n) < ifelse(assignment == 1, 0.8, 0.2))
Y.fuzzy <- 3 + 2 * X1 + 1.5 * X2 + 1.5 * fuzzy + rnorm(n)
result.fuzzy <- rd2d(Y.fuzzy, X, assignment, b, fuzzy = fuzzy,
                     bwparam = "main", masspoints = "off",
                     bwcheck = 10, repp = 49)
print(result.fuzzy)
summary(result.fuzzy, output = "itt")

Distance-Based Methods for Boundary Discontinuity Design

Description

rd2d.distance implements distance-based local polynomial boundary discontinuity (BD) point estimators with robust bias-corrected pointwise confidence intervals and uniform confidence bands. The command targets level effects at two-dimensional boundary points. See Cattaneo, M. D., Titiunik, R., and Yu, R. R. (2026) for methodological background.

Companion commands are: rdbw2d.distance for data-driven bandwidth selection.

For other packages of RD designs, visit https://rdpackages.github.io/

Usage

rd2d.distance(
  Y,
  distance,
  h = NULL,
  b = NULL,
  p = 1,
  q = NULL,
  kink.unknown = c(FALSE, FALSE),
  kink.position = NULL,
  kernel = c("tri", "triangular", "epa", "epanechnikov", "uni", "uniform", "gau",
    "gaussian"),
  level = 95,
  cbands = TRUE,
  side = c("two", "left", "right"),
  repp = 1000,
  bwselect = c("mserd", "cerrd", "imserd", "icerrd", "msetwo", "certwo", "imsetwo",
    "icertwo", "user provided"),
  bwparam = c("main", "itt"),
  params.other = NULL,
  params.cov = NULL,
  vce = c("hc1", "hc0", "hc2", "hc3"),
  bwcheck = 50 + p + 1,
  masspoints = c("check", "adjust", "off"),
  cluster = NULL,
  scaleregul = 1,
  cqt = 0.5,
  fuzzy = NULL
)

Arguments

Y

Dependent variable; a numeric vector of length N, where N is the sample size.

distance

Signed distance scores; a numeric matrix or data frame of dimension N \times J, where N is the sample size and J is the number of evaluation points. Non-negative values identify observations on the treated side and negative values identify observations on the control side.

h

Bandwidths. A positive scalar uses the same bandwidth for both groups and all evaluation points. A matrix/data frame of size J \times 2 uses row-specific control and treated bandwidths. If not specified, bandwidths are selected by rdbw2d.distance.

b

Optional evaluation points; a matrix or data frame specifying boundary points \mathbf{b}_j = (b_{1j}, b_{2j}), dimension J \times 2.

p

Polynomial order for point estimation. Default is p = 1.

q

Polynomial order for bias-corrected estimation. Must satisfy q \geq p. Default is q = p + 1, except when kink.unknown[1] = TRUE, where the default is q = p.

kink.unknown

Logical value or vector of length 2 controlling unknown-kink bandwidth adjustments. A scalar TRUE is expanded to c(TRUE, TRUE), and a scalar FALSE is expanded to c(FALSE, FALSE). With the vector form, the first element controls whether the point-estimation bandwidth is shrunk to the unknown-kink rate; the second controls whether the inference bandwidth is further shrunk. Default is c(FALSE, FALSE). The second element can be TRUE only when the first element is TRUE.

kink.position

Optional boundary positions of known kink points. Either a logical vector with one entry per boundary point, where TRUE identifies a kink point, or an integer vector with indices between 1 and the number of boundary points. Requires b so distances between boundary points can be computed. This option applies only to automatic bandwidth selection.

kernel

Kernel function to use. Options are "tri" or "triangular" (triangular, default), "epa" or "epanechnikov" (Epanechnikov), "uni" or "uniform" (uniform), and "gau" or "gaussian" (Gaussian).

level

Nominal confidence level for intervals/bands, between 0 and 100 (default is 95).

cbands

Logical. If TRUE, stores the covariance matrix needed for uniform confidence bands and aggregate inference computed by summary(..., cbands = "main"), summary(..., WBATE = weights), or summary(..., LBATE = TRUE). Default is TRUE.

side

Type of confidence interval. Options: "two" (two-sided, default), "left" (left tail), or "right" (right tail).

repp

Number of bootstrap repetitions used for critical value simulation. Default is 1000.

bwselect

Bandwidth selection strategy. Options:

  • "mserd". One common MSE-optimal bandwidth selector for the boundary RD treatment effect estimator for each evaluation point (default).

  • "cerrd". CER-optimal counterpart of "mserd".

  • "imserd". IMSE-optimal bandwidth selector for the boundary RD treatment effect estimator based on all evaluation points.

  • "icerrd". CER-optimal counterpart of "imserd".

  • "msetwo". Two different MSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator for each evaluation point.

  • "certwo". CER-optimal counterpart of "msetwo".

  • "imsetwo". Two IMSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator based on all evaluation points.

  • "icertwo". CER-optimal counterpart of "imsetwo".

  • "user provided". User-provided bandwidths. If h is not NULL, then bwselect is overwritten to "user provided".

bwparam

Target parameter used for fuzzy automatic bandwidth selection. Options are "main" (default), which selects bandwidths for the linearized fuzzy Wald ratio, and "itt", which selects bandwidths for the reduced-form outcome. Ignored in sharp designs.

params.other

Optional character vector requesting companion output tables. In sharp designs, available values are "main.0" and "main.1". In fuzzy designs, available values are "itt.0", "itt.1", "fs.0", and "fs.1".

params.cov

Optional character vector requesting covariance matrices for aggregate inference or confidence bands. Available values are "main" for sharp and fuzzy main effects, plus "main.0" and "main.1" for sharp side-specific effects, and "itt", "itt.0", "itt.1", "fs", "fs.0", and "fs.1" for fuzzy reduced-form and first-stage effects. If cbands = TRUE, "main" is added automatically.

vce

Variance-covariance estimator for standard errors. Options:

"hc0"

Heteroskedasticity-robust variance estimator without small sample adjustment (White robust).

"hc1"

Heteroskedasticity-robust variance estimator with degrees-of-freedom correction. (default)

"hc2"

Heteroskedasticity-robust variance estimator using leverage adjustments.

"hc3"

More conservative heteroskedasticity-robust variance estimator (similar to jackknife correction).

bwcheck

If a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck unique observations are used. Default is 50 + p + 1.

masspoints

Strategy for handling mass points in the running variable. Options:

"check"

(default) Check for repeated values and adjust inference if needed.

"adjust"

Adjust bandwidths to guarantee a sufficient number of unique support points.

"off"

Ignore mass points completely.

cluster

Cluster ID variable used for cluster-robust variance estimation with degrees-of-freedom weights. Default is cluster = NULL.

scaleregul

Scaling factor for the regularization term in bandwidth selection. Default is 1.

cqt

Constant controlling subsample fraction for initial bias estimation. Default is 0.5.

fuzzy

Optional treatment receipt/status variable for fuzzy RD designs. If supplied, main reports the fuzzy Wald treatment effect, itt reports the reduced-form outcome discontinuity, and fs reports the first-stage treatment receipt/status discontinuity.

Value

An object of class "rd2d.distance", a list containing:

main

Data frame of point estimates, standard errors, confidence intervals, and bandwidths:

b1

First coordinate of the evaluation point.

b2

Second coordinate of the evaluation point.

estimate.p

Point estimate with polynomial order p.

std.err.p

Standard error for estimate.p.

estimate.q

Bias-corrected estimate with polynomial order q.

std.err.q

Standard error for estimate.q.

t.value

t-statistic based on \widehat{\tau}_{\text{distance},q}(\mathbf{b}).

p.value

Two-sided p-value based on T_{\text{distance},q}(\mathbf{b}).

ci.lower

Lower bound of confidence interval.

ci.upper

Upper bound of confidence interval.

h0

Bandwidth used for the control group (negative signed distance).

h1

Bandwidth used for the treatment group (non-negative signed distance).

h0.rbc

Bandwidth used for control-side inference.

h1.rbc

Bandwidth used for treated-side inference.

N.Co

Effective sample size for the control side.

N.Tr

Effective sample size for the treatment side.

main.0

Sharp-design summary table for the control side only.

main.1

Sharp-design summary table for the treated side only.

itt

Fuzzy-design reduced-form outcome summary table.

itt.0, itt.1

Optional fuzzy-design side-specific reduced-form outcome summary tables requested through params.other.

fs

Fuzzy-design first-stage treatment receipt/status summary table.

fs.0, fs.1

Optional fuzzy-design side-specific first-stage treatment receipt/status summary tables requested through params.other.

bw

Bandwidth and effective-sample-size table.

tau.hat

Vector of point estimates \widehat{\tau}_p(\mathbf{b}).

tau.hat.q

Vector of bias-corrected estimates \widehat{\tau}_q(\mathbf{b}).

se.hat

Standard errors corresponding to \widehat{\tau}_p(\mathbf{b}).

se.hat.q

Standard errors corresponding to \widehat{\tau}_q(\mathbf{b}).

params.cov

List containing covariance matrices requested for aggregate or uniform inference.

cb

Pointwise confidence interval endpoints.

pvalues

Two-sided p-values based on bias-corrected estimates.

tvalues

t-statistics based on bias-corrected estimates.

tau.itt, tau.itt.q, tau.fs, tau.fs.q

Fuzzy reduced-form and first-stage point estimates with polynomial orders p and q; these are NULL in sharp designs.

rdmodel

Character label describing the fitted RD model.

call

Matched function call.

opt

A list of estimation options (e.g., p, q, kernel, level, etc.) and internal variables such as sample size N.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

References

See Also

rdbw2d.distance, rd2d, print.rd2d.distance, summary.rd2d.distance

Examples

set.seed(123)
n <- 800

# Generate running variables x1 and x2
x1 <- rnorm(n)
x2 <- rnorm(n)

# Define treatment assignment: treated if x1 >= 0
assignment <- as.numeric(x1 >= 0)

# Generate outcome variable Y with some treatment effect
Y <- 3 + 2 * x1 + 1.5 * x2 + 1.5 * assignment + rnorm(n, sd = 0.5)

# Define evaluation points (e.g., at the origin and another point)
eval <- data.frame(x.1 = c(0, 0), x.2 = c(0, 1))

# Compute Euclidean distances to evaluation points
distance.a <- sqrt((x1 - eval$x.1[1])^2 + (x2 - eval$x.2[1])^2)
distance.b <- sqrt((x1 - eval$x.1[2])^2 + (x2 - eval$x.2[2])^2)

# Combine distances into a matrix
distance <- as.data.frame(cbind(distance.a, distance.b))

# Assign positive distances for treatment group, negative for control
assignment_expanded <- matrix(rep(2 * assignment - 1, times = ncol(distance)),
                              nrow = nrow(distance), ncol = ncol(distance))
distance <- distance * assignment_expanded

# Run the rd2d.distance function
result <- rd2d.distance(Y, distance = distance, b = eval, cbands = FALSE,
                    masspoints = "off", bwcheck = 10)

# View the estimation results
print(result)
summary(result)

# Fuzzy distance-based fit with a user-supplied bandwidth
fuzzy <- as.numeric(runif(n) < ifelse(assignment == 1, 0.8, 0.2))
Y.fuzzy <- 3 + 2 * x1 + 1.5 * x2 + 1.5 * fuzzy + rnorm(n, sd = 0.5)
fuzzy.result <- rd2d.distance(Y.fuzzy, distance = distance, h = 0.8, b = eval, fuzzy = fuzzy,
                          cbands = FALSE, masspoints = "off")
summary(fuzzy.result)

Bandwidth Selection for Location-Based Methods for Boundary Discontinuity Design

Description

rdbw2d implements bandwidth selectors for location-based local polynomial boundary discontinuity (BD) estimation and inference. See Cattaneo, M. D., Titiunik, R., and Yu, R. R. (2026) for methodological background.

Companion commands are: rd2d for point estimation and inference procedures.

For other packages of RD designs, visit https://rdpackages.github.io/

Usage

rdbw2d(
  Y,
  X,
  assignment,
  b,
  p = 1,
  deriv = c(0, 0),
  tangvec = NULL,
  kernel = c("tri", "triangular", "epa", "epanechnikov", "uni", "uniform", "gau",
    "gaussian"),
  kernel_type = c("prod", "rad"),
  bwselect = c("mserd", "cerrd", "imserd", "icerrd", "msetwo", "certwo", "imsetwo",
    "icertwo"),
  bwparam = c("main", "itt"),
  method = c("dpi", "rot"),
  vce = c("hc1", "hc0", "hc2", "hc3"),
  bwcheck = 20,
  masspoints = c("check", "adjust", "off"),
  cluster = NULL,
  scaleregul = 1,
  scalebiascrct = 1,
  stdvars = TRUE,
  fuzzy = NULL
)

Arguments

Y

Dependent variable; a numeric vector of length N, where N is the sample size.

X

Bivariate running variable (a.k.a score variable); a numeric matrix or data frame of dimension N \times 2, with each row \mathbf{X}_i = (X_{1i}, X_{2i}).

assignment

Treatment assignment indicator; a logical or binary vector indicating assignment to the treated side.

b

Evaluation points; a matrix or data frame specifying boundary points \mathbf{b}_j = (b_{1j}, b_{2j}), of dimension J \times 2.

p

Polynomial order of the local polynomial estimator. Default is p = 1.

deriv

The order of the derivatives of the regression functions to be estimated; a nonnegative integer vector of length 2 specifying the number of derivatives in each coordinate (e.g., c(1,2) corresponds to \partial_1 \partial_2^2).

tangvec

Tangent vectors; a matrix or data frame of dimension J \times 2 specifying directional derivatives. Overrides deriv if provided.

kernel

Kernel function to use. Options are "tri" or "triangular" (triangular, default), "epa" or "epanechnikov" (Epanechnikov), "uni" or "uniform" (uniform), and "gau" or "gaussian" (Gaussian).

kernel_type

Kernel structure. Either "prod" for product kernels (default) or "rad" for radial kernels.

bwselect

Bandwidth selection strategy. Options:

  • "mserd". One common MSE-optimal bandwidth selector for the boundary RD treatment effect estimator for each evaluation point (default).

  • "cerrd". CER-optimal counterpart of "mserd".

  • "imserd". IMSE-optimal bandwidth selector for the boundary RD treatment effect estimator based on all evaluation points.

  • "icerrd". CER-optimal counterpart of "imserd".

  • "msetwo". Two different MSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator for each evaluation point.

  • "certwo". CER-optimal counterpart of "msetwo".

  • "imsetwo". Two IMSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator based on all evaluation points.

  • "icertwo". CER-optimal counterpart of "imsetwo".

bwparam

Target parameter used for fuzzy bandwidth selection. Options are "main" (default), which selects bandwidths for the linearized fuzzy Wald ratio, and "itt", which selects bandwidths for the reduced-form outcome discontinuity. This option is ignored in sharp designs, where only "main" is used.

method

Bandwidth selection method for bias estimator based on local polynomials. Either "dpi" (default) for data-driven plug-in MSE optimal bandwidth selector or "rot" for rule-of-thumb bandwidth selector.

vce

Variance-covariance estimation method. Options are:

  • "hc0": heteroskedasticity-robust plug-in residual variance estimator without small-sample adjustment.

  • "hc1": heteroskedasticity-robust plug-in residual variance estimator with HC1 small-sample adjustment (default).

  • "hc2": heteroskedasticity-robust plug-in residual variance estimator with HC2 adjustment.

  • "hc3": heteroskedasticity-robust plug-in residual variance estimator with HC3 adjustment.

Default is "hc1".

bwcheck

If a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck unique observations are used. Default is 20.

masspoints

Handling of mass points in the running variable. Options are:

  • "check": detects presence of mass points and reports the number of unique observations (default).

  • "adjust": adjusts preliminary bandwidths to ensure a minimum number of unique observations within each side of the cutoff.

  • "off": ignores presence of mass points.

cluster

Cluster ID variable used for cluster-robust variance estimation with degrees-of-freedom weights. Default is cluster = NULL.

scaleregul

Scaling factor for the regularization term in bandwidth selection. Default is 1.

scalebiascrct

Scaling factor used for bias correction based on higher order expansions. Default is 1.

stdvars

Logical. If TRUE, the running variables X_{1i} and X_{2i} are standardized before computing the bandwidths. Default is TRUE.

fuzzy

Optional treatment receipt/status variable used to construct bandwidth selectors for fuzzy RD estimation. If supplied, bwparam controls whether the selector targets the fuzzy Wald ratio or the reduced-form outcome discontinuity.

Value

A list of class "rdbw2d" containing:

bws

Data frame of estimated bandwidths for each evaluation point:

b1

First coordinate of the evaluation point.

b2

Second coordinate of the evaluation point.

h01

Estimated bandwidth for X_{1i} in the control group (\mathcal{A}_0).

h02

Estimated bandwidth for X_{2i} in the control group (\mathcal{A}_0).

h11

Estimated bandwidth for X_{1i} in the treatment group (\mathcal{A}_1).

h12

Estimated bandwidth for X_{2i} in the treatment group (\mathcal{A}_1).

mseconsts

Data frame of intermediate quantities used in bandwidth calculation:

N.Co

Effective sample size for the control group \mathcal{A}_0.

N.Tr

Effective sample size for the treatment group \mathcal{A}_1.

bias.0

Bias constant estimate for the control group.

bias.1

Bias constant estimate for the treatment group.

var.0

Variance constant estimate for the control group.

var.1

Variance constant estimate for the treatment group.

reg.bias.0

Bias correction adjustment for the control group.

reg.bias.1

Bias correction adjustment for the treatment group.

reg.var.0

Variance of the bias estimate for the control group.

reg.var.1

Variance of the bias estimate for the treatment group.

opt

List containing:

p

Polynomial order used for estimation.

kernel

Kernel function used.

kernel_type

Type of kernel (product or radial).

stdvars

Logical indicating if standardization was applied.

bwselect

Bandwidth selection strategy used.

bwparam

Target parameter for fuzzy bandwidth selection.

method

Bandwidth estimation method.

vce

Variance estimation method.

scaleregul

Scaling factor for regularization.

scalebiascrct

Scaling factor for bias correction.

N

Total sample size N.

call

Matched function call.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

References

See Also

rd2d, print.rdbw2d, summary.rdbw2d

Examples

# Simulated example
set.seed(123)
n <- 800
X1 <- rnorm(n)
X2 <- rnorm(n)
assignment <- as.numeric(X1 > 0)
Y <- 3 + 2 * X1 + 1.5 * X2 + assignment + rnorm(n)
X <- cbind(X1, X2)
b <- matrix(c(0, 0, 0, 1), ncol = 2)

# MSE optimal bandwidth for rd2d
bws <- rdbw2d(Y, X, assignment, b, masspoints = "off", bwcheck = 10)

# View the bandwidth selection results
print(bws)
summary(bws)

# Fuzzy bandwidth selection can target the Wald ratio or the reduced form
fuzzy <- as.numeric(runif(n) < ifelse(assignment == 1, 0.8, 0.2))
Y.fuzzy <- 3 + 2 * X1 + 1.5 * X2 + 1.5 * fuzzy + rnorm(n)
bws.fuzzy <- rdbw2d(Y.fuzzy, X, assignment, b, fuzzy = fuzzy, bwparam = "main",
                    masspoints = "off", bwcheck = 10)
print(bws.fuzzy)

Bandwidth Selection for Distance-Based Methods for Boundary Discontinuity Design

Description

rdbw2d.distance implements bandwidth selectors for distance-based local polynomial boundary discontinuity (BD) estimation and inference. The command targets level effects at two-dimensional boundary points. See Cattaneo, M. D., Titiunik, R., and Yu, R. R. (2026) for methodological background.

Usage

rdbw2d.distance(
  Y,
  distance,
  b = NULL,
  p = 1,
  kink.unknown = c(FALSE, FALSE),
  kink.position = NULL,
  kernel = c("tri", "triangular", "epa", "epanechnikov", "uni", "uniform", "gau",
    "gaussian"),
  bwselect = c("mserd", "cerrd", "imserd", "icerrd", "msetwo", "certwo", "imsetwo",
    "icertwo"),
  bwparam = c("main", "itt"),
  vce = c("hc1", "hc0", "hc2", "hc3"),
  bwcheck = 20 + p + 1,
  masspoints = c("check", "adjust", "off"),
  cluster = NULL,
  scaleregul = 1,
  cqt = 0.5,
  fuzzy = NULL
)

Arguments

Y

Dependent variable; a numeric vector of length N, where N is the sample size.

distance

Signed distance scores; a numeric matrix or data frame of dimension N \times J, where N is the sample size and J is the number of evaluation points. Non-negative values identify observations on the treated side and negative values identify observations on the control side.

b

Optional evaluation points; a matrix or data frame specifying boundary points \mathbf{b}_j = (b_{1j}, b_{2j}), dimension J \times 2.

p

Polynomial order for point estimation. Default is p = 1.

kink.unknown

Logical value or vector of length 2 controlling unknown-kink bandwidth adjustments. A scalar TRUE is expanded to c(TRUE, TRUE), and a scalar FALSE is expanded to c(FALSE, FALSE). With the vector form, the first element controls whether the point-estimation bandwidth is shrunk to the unknown-kink rate; the second controls whether the inference bandwidth is further shrunk in rd2d.distance. For bandwidth selection, only the first element is used. Default is c(FALSE, FALSE).

kink.position

Optional boundary positions of known kink points. Either a logical vector with one entry per boundary point, where TRUE identifies a kink point, or an integer vector with indices between 1 and the number of boundary points. Requires b so distances between boundary points can be computed.

kernel

Kernel function to use. Options are "tri" or "triangular" (triangular, default), "epa" or "epanechnikov" (Epanechnikov), "uni" or "uniform" (uniform), and "gau" or "gaussian" (Gaussian).

bwselect

Bandwidth selection strategy. Options:

  • "mserd". One common MSE-optimal bandwidth selector for the boundary RD treatment effect estimator for each evaluation point (default).

  • "cerrd". CER-optimal counterpart of "mserd".

  • "imserd". IMSE-optimal bandwidth selector for the boundary RD treatment effect estimator based on all evaluation points.

  • "icerrd". CER-optimal counterpart of "imserd".

  • "msetwo". Two different MSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator for each evaluation point.

  • "certwo". CER-optimal counterpart of "msetwo".

  • "imsetwo". Two IMSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator based on all evaluation points.

  • "icertwo". CER-optimal counterpart of "imsetwo".

bwparam

Target parameter used for fuzzy automatic bandwidth selection. Options are "main", which selects bandwidths for the linearized fuzzy Wald ratio, and "itt", which selects bandwidths for the reduced-form outcome. Ignored in sharp designs.

vce

Variance-covariance estimator for standard errors. Options:

"hc0"

Heteroskedasticity-robust variance estimator without small sample adjustment (White robust).

"hc1"

Heteroskedasticity-robust variance estimator with degrees-of-freedom correction. (default)

"hc2"

Heteroskedasticity-robust variance estimator using leverage adjustments.

"hc3"

More conservative heteroskedasticity-robust variance estimator (similar to jackknife correction).

bwcheck

If a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck unique observations are used. Default is 20 + p + 1.

masspoints

Strategy for handling mass points in the running variable. Options:

"check"

(default) Check for repeated values and adjust inference if needed.

"adjust"

Adjust bandwidths to guarantee a sufficient number of unique support points.

"off"

Ignore mass points completely.

cluster

Cluster ID variable used for cluster-robust variance estimation with degrees-of-freedom weights. Default is cluster = NULL.

scaleregul

Scaling factor for the regularization term in bandwidth selection. Default is 1.

cqt

Constant controlling subsample fraction for initial bias estimation. Default is 0.5.

fuzzy

Optional treatment receipt/status variable used for fuzzy RD bandwidth selection. If supplied, bwparam controls whether the selector targets the fuzzy Wald ratio or the reduced-form outcome.

Value

An object of class "rdbw2d.distance", containing:

bws

Data frame of optimal bandwidths for each evaluation point:

b1

First coordinate of the evaluation point b1.

b2

Second coordinate of the evaluation point b2.

h0

Bandwidth for observations with negative signed distance.

h1

Bandwidth for observations with non-negative signed distance.

mseconsts

Data frame of intermediate bias and variance constants used for MSE/IMSE calculations, including N.Co and N.Tr, the effective sample sizes for observations with negative and non-negative signed distances, respectively.

opt

A list of options and settings used in estimation, including p, kernel, sample size N, and user-specified choices.

call

Matched function call.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

References

See Also

rd2d.distance, rd2d, summary.rdbw2d.distance, print.rdbw2d.distance

Examples

set.seed(123)
n <- 800

# Generate running variables x1 and x2
x1 <- rnorm(n)
x2 <- rnorm(n)

# Define treatment assignment: treated if x1 >= 0
assignment <- as.numeric(x1 >= 0)

# Generate outcome variable Y with some treatment effect
Y <- 3 + 2 * x1 + 1.5 * x2 + 1.5 * assignment + rnorm(n, sd = 0.5)

# Define evaluation points (e.g., at the origin and another point)
eval <- data.frame(x.1 = c(0, 0), x.2 = c(0, 1))

# Compute Euclidean distances to evaluation points
distance.a <- sqrt((x1 - eval$x.1[1])^2 + (x2 - eval$x.2[1])^2)
distance.b <- sqrt((x1 - eval$x.1[2])^2 + (x2 - eval$x.2[2])^2)

# Combine distances into a matrix
distance <- as.data.frame(cbind(distance.a, distance.b))

# Assign positive distances for treatment group, negative for control
assignment_expanded <- matrix(rep(2 * assignment - 1, times = ncol(distance)),
                              nrow = nrow(distance), ncol = ncol(distance))
distance <- distance * assignment_expanded

# Run the rdbw2d.distance function
bws <- rdbw2d.distance(Y, distance = distance, b = eval, masspoints = "off", bwcheck = 10)

# View the estimation results
print(bws)
summary(bws)

# Fuzzy distance-based bandwidths
fuzzy <- as.numeric(runif(n) < ifelse(assignment == 1, 0.8, 0.2))
Y.fuzzy <- 3 + 2 * x1 + 1.5 * x2 + 1.5 * fuzzy + rnorm(n, sd = 0.5)
bws.fuzzy <- rdbw2d.distance(Y.fuzzy, distance = distance, b = eval, fuzzy = fuzzy,
                         bwparam = "main", masspoints = "off",
                         bwcheck = 10)
print(bws.fuzzy)

Summary Method for 2D Local Polynomial RD Estimation

Description

Summarizes estimation and bandwidth results from a 2D local polynomial regression discontinuity (RD) design, as produced by rd2d.

Usage

## S3 method for class 'rd2d'
summary(object, ...)

Arguments

object

An object of class rd2d, typically returned by rd2d.

...

Optional named arguments. Unsupported option names produce an error. Supported options include:

  • cbands: Optional character vector requesting uniform confidence bands for displayed outputs. Options are "main", "main.0", "main.1", "itt", "itt.0", "itt.1", "fs", "fs.0", and "fs.1", subject to the sharp/fuzzy design and covariance matrices stored by rd2d.

  • WBATE: Optional numeric weights for a weighted boundary average treatment effect row. The weights must match the full set of evaluation points for the selected output. The selected output must have a matching covariance matrix stored by rd2d.

  • LBATE: Logical. If TRUE, prints a largest boundary average treatment effect row. The selected output must have a matching covariance matrix stored by rd2d.

  • subset: Integer vector of indices of evaluation points to display. Aggregates and uniform-band critical values are still computed using all evaluation points. Defaults to all evaluation points.

  • output: Character. Use "main" to display sharp or fuzzy main results; "main.0" or "main.1" to display sharp control- or treatment-side main results; "itt", "itt.0", or "itt.1" to display fuzzy reduced-form or intention-to-treat results; "fs", "fs.0", or "fs.1" to display fuzzy first-stage treatment receipt/status results; and "bw" to display bandwidth information. If omitted, summary() prints all default and requested estimate tables and does not print "bw". Use output = "bw" to print bandwidth information.

  • sep: Integer vector of length three. Controls spacing in the output. sep[1] controls spacing for the columns of bandwidths, estimation, t-statistic, and p-value in the "main" table. sep[2] controls spacing for the confidence interval (confidence bands) in the "main" table. sep[3] controls spacing for the columns in the "bw" table. Default is c(7, 17, 8).

Value

Invisibly returns a list with displayed tables and uniform confidence bands requested through cbands. Each returned estimate table has the same columns as the corresponding rd2d output, with cb.lower and cb.upper added only when uniform bands are requested. Requested WBATE and LBATE rows are appended to the corresponding returned table.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rd2d for estimation using 2D local polynomial RD design.

Supported methods: print.rd2d, summary.rd2d.

Summary Method for 2D Local Polynomial RD Estimation (Distance-Based)

Description

Summarizes estimation and bandwidth results from a 2D local polynomial regression discontinuity (RD) design using distance-based methods, as returned by rd2d.distance.

Usage

## S3 method for class 'rd2d.distance'
summary(object, ...)

Arguments

object

An object of class rd2d.distance, returned by rd2d.distance.

...

Optional arguments. Supported options include:

  • cbands: Character vector. Use cbands = "main" to display uniform confidence bands for the main distance-based estimates. Other stored outputs can be requested when their covariance matrices were stored through params.cov. The default displays pointwise confidence intervals.

  • WBATE: Optional numeric weights for a weighted boundary average treatment effect row. The weights must match the full set of evaluation points and are normalized internally. The fitted object must contain the covariance matrix stored by rd2d.distance(cbands = TRUE) or requested through params.cov.

  • LBATE: Logical. If TRUE, prints a largest boundary average treatment effect row. The fitted object must contain the covariance matrix stored by rd2d.distance(cbands = TRUE) or requested through params.cov.

  • subset: Integer vector of indices of evaluation points to display. Defaults to all evaluation points.

  • output: Character vector. Use "main" to display treatment effect estimates or "bw" to display bandwidth information. In sharp designs, "main.0" and "main.1" display side-specific estimates. In fuzzy designs, "itt" and "fs" display reduced-form and first-stage estimates, and "itt.0", "itt.1", "fs.0", and "fs.1" display requested side-specific companion estimates.

  • sep: Integer vector of length three. Controls spacing in the output. sep[1] controls spacing for the columns of boundary points, estimation, t-value, and p-value in the "main" table. sep[2] controls spacing for confidence intervals (or bands) in the "main" table. sep[3] controls spacing for the columns in the "bw" table. Default is c(7, 17, 8).

Value

Invisibly returns an object of class "summary.rd2d.distance", a list with elements:

Requested WBATE and LBATE rows are appended to the returned estimation table(s), except for output = "bw". The function is also called for its side effect of printing a formatted summary.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rd2d.distance for estimation using distance-based 2D local polynomial RD design.

Supported methods: print.rd2d.distance, summary.rd2d.distance.

Summary Method for Bandwidth Selection for 2D Local Polynomial RD Design

Description

Summary method for objects of class rdbw2d, displaying bandwidth selection results for 2D local polynomial regression discontinuity designs.

Usage

## S3 method for class 'rdbw2d'
summary(object, ...)

Arguments

object

An object of class rdbw2d, typically returned by rdbw2d.

...

Optional arguments. Supported options include:

  • subset: Integer vector of indices of evaluation points to display. Defaults to all evaluation points.

  • sep: Integer. Controls spacing in the output. Default is 8.

Value

No return value. Called for its side effects of printing a formatted summary of rdbw2d results.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rdbw2d for bandwidth selection in 2D local polynomial RD design.

Supported methods: print.rdbw2d, summary.rdbw2d.

Summary Method for Bandwidth Selection in 2D Local Polynomial RD Design (Distance-Based)

Description

Summarizes bandwidth selection results from a 2D local polynomial regression discontinuity (RD) design using distance-based methods, as returned by rdbw2d.distance.

Usage

## S3 method for class 'rdbw2d.distance'
summary(object, ...)

Arguments

object

An object of class rdbw2d.distance, returned by rdbw2d.distance.

...

Optional arguments. Supported options include:

  • subset: Integer vector of indices of evaluation points to display. Defaults to all evaluation points.

  • sep: Integer vector of length two. Controls spacing in the output. sep[1] controls spacing for the columns of evaluation points in the table. sep[2] controls spacing for the columns of bandwidths in the table. Default is c(8, 14).

Value

No return value. This function is called for its side effects: it prints a formatted summary of rdbw2d.distance results.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. raeyuuuu@gmail.com

See Also

rdbw2d.distance for bandwidth selection using 2D local polynomial RD design with distance-based methods.

Supported methods: print.rdbw2d.distance, summary.rdbw2d.distance.