Package {rdhte}

rdhte: RD Heterogeneous Treatment Effects Estimation and Inference

Description

Building on the recent developments in Calonico, Cattaneo, Farrell, Palomba, and Titiunik (2025), this package implements estimation and inference of heterogeneous treatment effects in RD designs. The package includes two main commands: rdhte conduct estimation and robust bias-corrected inference for conditional RD treatment effects, for a given choice of bandwidth parameter; and rdbwhte implements automatic bandwidth selection methods. We illustrate the methods implemented in the package rdhte using a canonical empirical application. We also demonstrate how the package rdhte complements, and in very specific cases recovers, the methods available in the packages rdrobust (Calonico, Cattaneo, Farrell, Titiunik (2017) and rdmulti, Cattaneo, Titiunik, VazquezBare (2020).

Commands: rdhte for estimation and inference. rdbwhte for data-driven bandwidth selection.

Related software packages useful for inference in regression discontinuity (RD) designs are described in the website: https://rdpackages.github.io/.

Author(s)

Sebastian Calonico, University of California, Davis scalonico@ucdavis.edu.

Matias D. Cattaneo, Princeton University matias.d.cattaneo@gmail.com.

Max H. Farrell, University of California, Santa Barbara mhfarrell@gmail.com.

Filippo Palomba, Princeton University filippo.palomba19@gmail.com.

Rocio Titiunik, Princeton University rocio.titiunik@gmail.com.

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.

Glance at a rdbwhte object

Description

broom-compatible glance() method. Returns a one-row summary of the bandwidth-selection call.

Usage

## S3 method for class 'rdbwhte'
glance(x, ...)

Arguments

Value

A one-row data frame.

Glance at a rdhte object

Description

broom-compatible glance() method. Returns a one-row summary of the fit (sample sizes, polynomial orders, kernel, VCE, BW selector).

Usage

## S3 method for class 'rdhte'
glance(x, ...)

Arguments

Value

A one-row data frame.

Plot rdhte heterogeneous treatment effects

Description

For an rdhte object fit with a categorical covs.hte, draw one point per group at the conventional point estimate (Estimate) with the robust bias-corrected confidence interval (ci.rb). A dashed horizontal line at zero gives a visual reference for the null effect.

Usage

## S3 method for class 'rdhte'
plot(x, sort = FALSE, point.size = 2.5,
                     errorbar.width = 0.2, zero.line = TRUE,
                     title = NULL, xlab = NULL, ylab = NULL, ...)

Arguments

Details

Continuous covs.hte (or no covs.hte) is not yet supported – the function errors with a clear message in those cases.

Requires the ggplot2 package. The intervals shown are the same robust bias-corrected CIs reported by print(x) and summary(x): they are centered on Estimate.bc (not Estimate) and use the robust standard error se.rb. Because the point and the CI center can differ slightly, the point may sit just inside or just outside the bar; this is the rdrobust convention and is not a plotting bug.

Value

Invisibly, a ggplot object.

Examples

## Not run: 
  set.seed(1)
  n <- 600
  x <- runif(n, -1, 1)
  W <- factor(sample(c("A", "B", "C"), n, replace = TRUE))
  y <- 0.5 + (x >= 0) * (W == "A") * 1.0 +
             (x >= 0) * (W == "B") * 2.0 +
             (x >= 0) * (W == "C") * 0.3 + rnorm(n)
  m <- rdhte(y = y, x = x, covs.hte = W)
  plot(m)
  plot(m, sort = TRUE)        # reorder by effect size

## End(Not run)

Internal function.

Description

Internal function.

Usage

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

Arguments

Value

No return value, called for side effects.

Internal function.

Description

Internal function.

Usage

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

Arguments

Value

No return value, called for side effects.

Internal function.

Description

Internal function.

Usage

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

Arguments

Value

The input x returned invisibly; called for side effects.

Internal function.

Description

Internal function.

Usage

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

Arguments

Value

The input x returned invisibly; called for side effects.

Data-Driven Optimal Bandwidth Selection for RD Heterogeneous Treatment Effects Estimation

Description

rdbwhte computes MSE- and CER-optimal bandwidths for estimating RD heterogeneous treatment effects based on covariates (Calonico, Cattaneo, Farrell, Palomba and Titiunik, 2025a).

Companion commands: rdhte for RD HTE estimation and inference, 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

rdbwhte(
  y,
  x,
  c = 0,
  covs.hte = NULL,
  covs.eff = NULL,
  p = 1,
  q = NULL,
  kernel = "tri",
  weights = NULL,
  vce = "hc3",
  cluster = NULL,
  bwselect = "mserd",
  bw.joint = FALSE,
  subset = NULL,
  data = NULL
)

Arguments

Value

A list with the following named elements:

Author(s)

Sebastian Calonico, University of California, Davis scalonico@ucdavis.edu.

Matias D. Cattaneo, Princeton University matias.d.cattaneo@gmail.com.

Max H. Farrell, University of California, Santa Barbara mhfarrell@gmail.com.

Filippo Palomba, Princeton University filippo.palomba19@gmail.com.

Rocio Titiunik, Princeton University rocio.titiunik@gmail.com.

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

rdhte, rdhte_lincom

Examples

set.seed(123)
n <- 5000
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)
rdbwhte.1 = rdbwhte(y=Y, x=X, covs.hte=factor(W))
summary(rdbwhte.1)

## Not run: 
data(rdhte_dataset)
with(rdhte_dataset, {
  summary(rdbwhte(y = y, x = x, covs.hte = factor(w_ideology),
                  cluster = cluster_var))
  summary(rdbwhte(y = y, x = x, covs.hte = factor(w_ideology),
                  cluster = cluster_var, bw.joint = TRUE))
  summary(rdbwhte(y = y, x = x, covs.hte = w_strength,
                  cluster = cluster_var))
})

## End(Not run)

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

Value

A list with the following named elements:

Author(s)

Sebastian Calonico, University of California, Davis scalonico@ucdavis.edu.

Matias D. Cattaneo, Princeton University matias.d.cattaneo@gmail.com.

Max H. Farrell, University of California, Santa Barbara mhfarrell@gmail.com.

Filippo Palomba, Princeton University filippo.palomba19@gmail.com.

Rocio Titiunik, Princeton University rocio.titiunik@gmail.com.

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)

RD Heterogeneous Treatment Effects: contrast-targeted bandwidth

Description

rdhte_contrast refits an rdhte model at the MSE-optimal bandwidth for a single user-chosen linear combination of the Estimate vector and returns the resulting point estimate, robust bias-corrected estimate, standard error, p-value, and confidence interval.

Usage

rdhte_contrast(model, contrast, refit = TRUE, level = 95, tol = 1e-10)

Arguments

Details

Use rdhte_lincom instead when you want joint Wald inference on several linear restrictions at one bandwidth.

Value

A list with the conventional estimate, robust bias-corrected estimate, robust standard error, z-statistic, p-value, confidence interval, selected bandwidth, pilot bandwidth, contrast diagnostics, and (when refit = TRUE) the refitted rdhte object.

See Also

rdhte, rdhte_lincom

Examples

## Not run: 
set.seed(123)
n <- 1000
X <- runif(n, -1, 1)
W <- rbinom(n, 1, 0.5)
Y <- 3 + 2 * X + 1.5 * X^2 + 3 * W * (X >= 0) + rnorm(n)
m <- rdhte(y = Y, x = X, covs.hte = factor(W))
rdhte_contrast(m, contrast = c(-1, 1))

## End(Not run)

Granzier-Pons-Tricaud Election Dataset for rdhte Illustrations

Description

A working extract of the data used in Granzier, Pons, and Tricaud (2023, AEJ: Applied), distributed with the rdhte package as a fixed-format example dataset for the package vignette and worked examples. The running variable x is the candidate's first-round margin against the threshold for advancing to the runoff; y is an indicator for advancing.

Usage

data("rdhte_dataset")

Format

A data frame with 39,534 observations on the following variables.

y

Outcome: indicator (0/1) for advancing to the runoff.

x

Running variable: first-round margin against the qualifying threshold (the cutoff is at zero).

cluster_var

Cluster identifier (district).

w_left

Binary: 1 if the candidate's party is left of center, 0 otherwise.

w_ideology

Unordered categorical (4 levels): party ideology bucket.

w_strength

Continuous: candidate's average prior national-level vote share, used as a proxy for ex-ante candidate strength.

w_strong

Binary: above-median strength (w_strength).

w_strength_qrt

Ordered categorical (4 levels): quartile bucket of w_strength.

Source

Granzier, R., V. Pons, and C. 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.

Examples

data(rdhte_dataset)
str(rdhte_dataset)

RD Heterogeneous Treatment Effects. Linear combinations of parameters

Description

rdhte_lincom computes point estimates, p-values, and robust bias-corrected confidence intervals for linear combinations of parameters after any estimation using rdhte (Calonico, Cattaneo, Farrell, Palomba and Titiunik, 2025a). Inference is implemented using robust bias-correction methods (Calonico, Cattaneo, and Titiunik, 2014). It is based on the R function glht.

Companion commands: rdhte for estimation and inference of RD-HTE and rdbwhte for data-driven bandwidth selection.

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_lincom(model, linfct, level = 95, digits = 3)

Arguments

Value

A list with two data frames:

individual

One row per hypothesis. Columns: hypothesis, estimate (conventional point estimate of the linear combination), z_stat (asymptotic z-statistic from the bias-corrected fit), p_value (two-sided p-value from the standard normal), conf.low, conf.high (robust bias-corrected CI bounds at the requested confidence level).

joint

One row. Columns: statistic (Wald chi-squared from the bias-corrected fit), df (number of restrictions), p_value.

Numeric columns are rounded to digits decimal places.

Author(s)

Sebastian Calonico, University of California, Davis scalonico@ucdavis.edu.

Matias D. Cattaneo, Princeton University matias.d.cattaneo@gmail.com.

Max H. Farrell, University of California, Santa Barbara mhfarrell@gmail.com.

Filippo Palomba, Princeton University filippo.palomba19@gmail.com.

Rocio Titiunik, Princeton University rocio.titiunik@gmail.com.

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

rdhte, rdbwhte

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))
linfct <- c("`factor(W)0` - `factor(W)1` = 0")
rdhte_lincom(model = m1, linfct = linfct)

## Not run: 
data(rdhte_dataset)
with(rdhte_dataset, {
  rd_ideology <- rdhte(y = y, x = x, covs.hte = factor(w_ideology),
                       cluster = cluster_var)
  rdhte_lincom(rd_ideology,
               linfct = c("`factor(w_ideology)4` - `factor(w_ideology)3` = 0",
                          "`factor(w_ideology)4` = 0"))
})

## End(Not run)

Summary method for rdbwhte objects.

Description

Summary method for rdbwhte objects.

Usage

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

Arguments

Value

An S3 object inheriting from rdbwhte with class summary.rdbwhte; printed by print.summary.rdbwhte.

Summary method for rdhte objects.

Description

Summary method for rdhte objects.

Usage

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

Arguments

Value

An S3 object inheriting from rdhte with class summary.rdhte; printed by print.summary.rdhte.

Tidy a rdbwhte object

Description

broom-compatible tidy() method. Returns one row per heterogeneity subgroup (factor case) or one row labelled "Overall" (continuous).

Usage

## S3 method for class 'rdbwhte'
tidy(x, ...)

Arguments

Value

A data frame with columns term, h.left, h.right.

Tidy a rdhte object

Description

broom-compatible tidy() method. Returns one row per heterogeneity subgroup (factor case) or per series term (continuous case).

Usage

## S3 method for class 'rdhte'
tidy(x, ...)

Arguments

Value

A data frame with columns term, estimate (conventional), std.error (robust SE), statistic, p.value, conf.low, conf.high (robust BC CI), estimate.bc, h.left, h.right, n.eff.left, n.eff.right.