rdbw2d: 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
)

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 \(N\).

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.

Author

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu
Rocío Titiunik, Princeton University. titiunik@princeton.edu
Ruiqi Rae Yu, Princeton University. rae.yu@princeton.edu

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

Examples

Run this code

# 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)

Run the code above in your browser using DataLab