rdhte: RD Heterogeneous Treatment Effects Estimation and Inference

In rdhte: Heterogeneous Treatment Effects in Regression Discontinuity Designs

RD Heterogeneous Treatment Effects Estimation and Inference

Description

rdhte provides estimation and inference for heterogeneous treatment effects in RD designs using local polynomial regressions, allowing for interactions with pretreatment covariates (Calonico, Cattaneo, Farrell, Palomba and Titiunik, 2025a). Inference is implemented using robust bias-correction methods (Calonico, Cattaneo, and Titiunik, 2014)

Companion commands: rdbwhte for data-driven bandwidth selection and rdhte_lincom for testing linear restrictions of parameters.

A detailed introduction to the software is given in Calonico, Cattaneo, Farrell, Palomba and Titiunik (2025b).

Related software packages for analysis and interpretation of RD designs and related methods are available in: https://rdpackages.github.io/.

For background methodology, see Calonico, Cattaneo, Farrell, and Titiunik (2019), Calonico, Cattaneo and Farrell (2020), and Cattaneo and Titiunik (2022).

Usage

rdhte(
  y,
  x,
  c = 0,
  covs.hte = NULL,
  covs.eff = NULL,
  p = 1,
  q = NULL,
  kernel = "tri",
  weights = NULL,
  h = NULL,
  h.l = NULL,
  h.r = NULL,
  vce = "hc3",
  cluster = NULL,
  level = 95,
  bwselect = "mserd",
  bw.joint = FALSE,
  subset = NULL,
  data = NULL,
  target.contrast = NULL
)

Arguments

y	Outcome variable.
x	Running variable.
c	RD cutoff in x; default is c = 0.
covs.hte	covariates for heterogeneous treatment effects. Factor variables can be used to distinguish between continuous and categorical variables, select reference categories, specify interactions between variables, and include polynomials of continuous variables. If not specified, the RD Average Treatment Effect is computed.
covs.eff	additional covariates to be used for efficiency improvements.
p	order of the local polynomial used to construct the point estimator (default = 1).
q	order of the local polynomial used to construct the bias correction. If NULL (default), q is set to p + 1.
kernel	kernel function used to construct the RD estimators. Options are triangular (default option), epanechnikov and uniform.
weights	variable used for optional weighting of the estimation procedure. The unit-specific weights multiply the kernel function.
h	main bandwidth used to construct the RD estimator. If not specified, bandwidth h is computed by the companion command rdbwhte. More than one bandwidth can be specified for categorical covariates.
h.l	same as h, but only used for observations left of the cutoff c.
h.r	same as h, but only used for observations right of the cutoff c.
vce	character string specifying the variance-covariance matrix estimator type. Without cluster: "hc0", "hc1", "hc2", "hc3" (default "hc3"). With cluster: "cr1" (default; standard cluster-robust sandwich with small-sample correction), "cr2" (Bell-McCaffrey leverage-adjusted), "cr3" (block-jackknife). Legacy aliases: "hc0"/"hc1" + cluster are remapped to "cr1" with a warning; "hc2" -> "cr2" and "hc3" -> "cr3" similarly. "cr1", "cr2", "cr3" without cluster fall back to "hc1", "hc2", "hc3" with a warning. It is based on the R function vcovCL.
cluster	variable indicating the clustering of observations.
level	confidence level for confidence intervals; default is level = 95.
bwselect	bandwidth selection procedure to be used. Options are: mserd one common MSE-optimal bandwidth selector for the RD treatment effect estimator. msetwo two different MSE-optimal bandwidth selectors (below and above the cutoff) for the RD treatment effect estimator. msesum one common MSE-optimal bandwidth selector for the sum of regression estimates (as opposed to difference thereof). msecomb1 for min(mserd,msesum). msecomb2 for median(msetwo,mserd,msesum), for each side of the cutoff separately. cerrd one common CER-optimal bandwidth selector for the RD treatment effect estimator. certwo two different CER-optimal bandwidth selectors (below and above the cutoff) for the RD treatment effect estimator. cersum one common CER-optimal bandwidth selector for the sum of regression estimates (as opposed to difference thereof). cercomb1 for min(cerrd,cersum). cercomb2 for median(certwo,cerrd,cersum), for each side of the cutoff separately. Note: MSE = Mean Square Error; CER = Coverage Error Rate. Default is bwselect=mserd.
bw.joint	logical. If TRUE, forces all bandwidths to be the same across groups (default is bw.joint = FALSE). When covs.hte is continuous (rather than a factor or 0/1 indicator), a single joint bandwidth is always used regardless of this argument.
subset	optional vector specifying a subset of observations to be used.
data	optional data frame. When supplied, y, x, covs.hte, covs.eff, weights, cluster, and subset may be given as bare variable names referring to columns of data. covs.hte additionally accepts a one-sided formula (e.g. "~ z1 + z2") whose variables are looked up in data first.
target.contrast	(experimental, in-flight) optional contrast vector or matrix used to refit the bandwidth to be MSE-optimal for a particular contrast of the CATE vector. NULL (default) keeps the standard per-cell MSE-optimal bandwidth. API may change.

Value

A list with the following named elements:

Estimate	Vector of conventional local-polynomial RD estimates, one per group level (or per slope-coefficient for continuous covs.hte). Also available as coef.
Estimate.bc	Vector of bias-corrected estimates. Also available as coef.bc.
se.rb	Vector of robust bias-corrected standard errors.
ci.rb	Matrix (n.lev x 2) of robust bias-corrected confidence-interval bounds.
t.rb	Vector of asymptotic z-statistics (named t.rb for legacy reasons; the underlying inference is Gaussian).
pv.rb	Vector of two-sided p-values from the standard normal.
vcov	Group-level variance-covariance matrix of Estimate.bc.
coef.full	Full coefficient vector from the underlying joint local-polynomial regression (used by rdhte_lincom).
vcov.full	Full variance-covariance matrix of coef.full.
W.lev	Group-level identifiers (or coefficient names for continuous covs.hte).
W.names	Display labels for the rows of Estimate.
kernel	Kernel type used (e.g. "Triangular").
bwselect	Bandwidth selection procedure used.
vce	Variance estimator display label (e.g. "CR1", "HC3").
vce_select	Canonical lowercase variance-estimator name (e.g. "cr1", "hc3").
c	Cutoff value.
h	An n.lev x 2 matrix of left/right bandwidths, one row per group.
p	Order of the polynomial used for estimation.
q	Order of the polynomial used for bias correction.
N	Length-2 vector c(N_left, N_right) of pre-bandwidth sample sizes.
Nh	An n.lev x 2 matrix of effective sample sizes (per group, per side).
covs.cont	Logical; TRUE for continuous covs.hte (or no covs.hte), FALSE for factor.
level	Confidence level used.
rdmodel	Human-readable model description string.

Author(s)

Sebastian Calonico, University of California, Davis [e-mail].

Matias D. Cattaneo, Princeton University [e-mail].

Max H. Farrell, University of California, Santa Barbara [e-mail].

Filippo Palomba, Princeton University [e-mail].

Rocio Titiunik, Princeton University [e-mail].

References

Calonico, Cattaneo, Farrell, Palomba and Titiunik (2025): rdhte: Conditional Average Treatment Effects in RD Designs. Working paper.

Calonico, Cattaneo, Farrell, Palomba and Titiunik (2025): Treatment Effect Heterogeneity in Regression Discontinuity Designs. Working paper.

Cattaneo and Titiunik. 2022. Regression Discontinuity Designs. Annual Review of Economics, 14: 821-851.

Calonico, Cattaneo, and Farrell. 2020. Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs. Econometrics Journal, 23(2): 192-210.

Calonico, Cattaneo, Farrell, and Titiunik. 2019. Regression Discontinuity Designs using Covariates. Review of Economics and Statistics, 101(3): 442-451.

Calonico, Cattaneo, and Titiunik. 2014a. Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs. Econometrica 82(6): 2295-2326.

Granzier, Pons, and Tricaud. 2023. Coordination and Bandwagon Effects: How Past Rankings Shape the Behavior of Voters and Candidates. American Economic Journal: Applied Economics, 15(4): 177-217.

See Also

rdbwhte, rdhte_lincom

Examples

set.seed(123)
n <- 1000
X <- runif(n, -1, 1)
W <- rbinom(n, 1, 0.5)
Y <- 3 + 2*X + 1.5*X^2 + 0.5*X^3 + sin(2*X) + 3*W*(X>=0) + rnorm(n)
m1 = rdhte(y = Y, x = X, covs.hte = factor(W))
summary(m1)

## Not run: 
# Empirical examples using the bundled Granzier, Pons, and Tricaud data.
data(rdhte_dataset)
with(rdhte_dataset, {
  rd_left <- rdhte(y = y, x = x, covs.hte = factor(w_left),
                   cluster = cluster_var)
  summary(rd_left)
  rdhte_lincom(rd_left,
               linfct = "`factor(w_left)1` - `factor(w_left)0` = 0")

  summary(rdhte(y = y, x = x, covs.hte = factor(w_left),
                cluster = cluster_var, bw.joint = TRUE))
  summary(rdhte(y = y, x = x, covs.hte = factor(w_left):factor(w_strong),
                cluster = cluster_var))
  summary(rdhte(y = y, x = x, covs.hte = w_strength,
                kernel = "uni", cluster = cluster_var))
})

## End(Not run)

rdhte documentation built on May 27, 2026, 1:06 a.m.