rdbw2d: Bandwidth Selection for 2D Local Polynomial RD Design

In rd2d: Boundary Regression Discontinuity Designs

Bandwidth Selection for 2D Local Polynomial RD Design

Description

rdbw2d implements bandwidth selector for bivariate local polynomial boundary regression discontinuity (RD) point estimators with robust bias-corrected pointwise confidence intervals and uniform confidence bands, developed in Cattaneo, Titiunik and Yu (2025a) with a companion software article Cattaneo, Titiunik and Yu (2025b). For robust bias-correction, see Calonico, Cattaneo, Titiunik (2014).

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,
  t,
  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", "imserd", "msetwo", "imsetwo"),
  method = c("dpi", "rot"),
  vce = c("hc1", "hc0", "hc2", "hc3"),
  bwcheck = 50 + p + 1,
  masspoints = c("check", "adjust", "off"),
  C = NULL,
  scaleregul = 1,
  scalebiascrct = 1,
  stdvars = TRUE
)

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}).
t	Treatment indicator; a logical or binary vector indicating treatment assignment (t_i = 1 if treated, t_i = 0 otherwise).
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 local polynomial estimator.
deriv	The order of the derivatives of the regression functions to be estimated; a numeric 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 "unif", "uniform" (uniform), "triag", "triangular" (triangular, default), and "epan", "epanechnikov" (Epanechnikov).
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). "imserd". IMSE-optimal bandwidth selector for the boundary RD treatment effect estimator based on all evaluation points. "msetwo". Two different MSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator for each evaluation point. "imsetwo". Two IMSE-optimal bandwidth selectors (control and treatment) for the boundary RD treatment effect estimator based on all evaluation points. "user provided". User-provided bandwidths. If h is not NULL, then bwselect is overwritten to "user provided".
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.
bwcheck	If a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck observations are used. If masspoints == "adjust", ensure at least bwcheck unique observations are used. The program stops with “not enough observations” if sample size N < bwcheck. Default is 50 + p + 1.
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.
C	Cluster ID variable used for cluster-robust variance estimation. Default is C = NULL.
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 the bandwidths. Default is TRUE. Standardization only affects automatic bandwidth selection if bandwidths are not manually provided via h.

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:

Nh0

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

Nh1

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.

method

Bandwidth estimation method.

vce

Variance estimation method.

scaleregul

Scaling factor for regularization.

scalebiascrct

Scaling factor for bias correction.

N

Total sample size N.

Author(s)

Matias D. Cattaneo, Princeton University. [e-mail]
Rocío Titiunik, Princeton University. [e-mail]
Ruiqi Rae Yu, Princeton University. [e-mail]

References

• Cattaneo, M. D., Titiunik, R., Yu, R. R. (2025a). Estimation and Inference in Boundary Discontinuity Designs

• Cattaneo, M. D., Titiunik, R., Yu, R. R. (2025b). rd2d: Causal Inference in Boundary Discontinuity Designs

• Calonico, S., Cattaneo, M. D., Titiunik, R. (2014) Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs

See Also

rd2d, print.rdbw2d, summary.rdbw2d

Examples

# Simulated example
set.seed(123)
n <- 5000
X1 <- rnorm(n)
X2 <- rnorm(n)
t <- as.numeric(X1 > 0)
Y <- 3 + 2 * X1 + 1.5 * X2 + t + rnorm(n)
X <- cbind(X1, X2)
b <- matrix(c(0, 0, 0, 1), ncol = 2)

# MSE optimal bandwidth for rd2d
bws <- rdbw2d(Y, X, t, b)

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

rd2d documentation built on Nov. 5, 2025, 6:48 p.m.