rd2d

Boundary Regression Discontinuity Designs in Stata

Overview

rd2d implements local polynomial estimation and inference for boundary discontinuity designs in Stata. Standard RD designs use a scalar running variable with a single cutoff. Boundary RD extends this to settings where a bivariate score (X1, X2) determines treatment assignment through a one-dimensional boundary curve, as in geographic RD or multi-score threshold designs. The causal estimand is the boundary average treatment effect curve:

τ(b) = E[Y(1) − Y(0) | X = b], b ∈ B

The package supports two approaches to estimation, each motivated by different data availability and geometric constraints:

• Location-based (rd2d, rdbw2d): uses bivariate local polynomial regression directly on (X1, X2) relative to boundary points. This approach provides MSE-optimal bandwidth selection and remains valid regardless of boundary geometry, including at kinks.
• Distance-based (rd2d_dist, rdbw2d_dist): transforms the bivariate score into a signed distance to the boundary. This simplifies estimation to univariate local polynomial regression with cutoff at zero, but requires caution near boundary kinks where the misspecification bias is irreducible at rate O(h) regardless of polynomial order.

Both approaches offer pointwise and uniform robust bias-corrected inference. Post-estimation commands handle visualization, aggregation, bandwidth sensitivity, table construction, and diagnostics.

Installation

net install rd2d, from("https://raw.githubusercontent.com/gorgeousfish/rd2d/main") replace
net get rd2d, from("https://raw.githubusercontent.com/gorgeousfish/rd2d/main") replace

net install places ado and help files on the adopath. net get retrieves example do-files into the current working directory.

Quick Start

Location-Based Estimation

. rd2d y x1 x2 t, at(0 0)

Location RD estimation
-------------------------------------------------------------------------------
  Evaluation points:         1    Observations:     20000
  VCE: hc1    RBC: on    Side: two
  Bandwidth source: automatic    Kernel: triangular    Std. Vars: On (default)
-------------------------------------------------------------------------------
     Point      Est.q      SE.q    CI.low   CI.high    CB.low   CB.high
-------------------------------------------------------------------------------
       at1      .6635    .07854     .5096     .8175     .5039     .8231
-------------------------------------------------------------------------------
  Uniform bands: on    Critical value:     2.032    Repetitions:      1000

Multiple boundary points with uniform confidence bands:

. rd2d y x1 x2 t, at(0 0 0.5 0.5 -0.5 -0.5)

Location RD estimation
-------------------------------------------------------------------------------
  Evaluation points:         3    Observations:     20000
  VCE: hc1    RBC: on    Side: two
  Bandwidth source: automatic    Kernel: triangular    Std. Vars: On (default)
-------------------------------------------------------------------------------
     Point      Est.q      SE.q    CI.low   CI.high    CB.low   CB.high
-------------------------------------------------------------------------------
       at1      .6635    .07854     .5096     .8175      .497     .8301
       at2      .6764    .06205     .5548      .798     .5448      .808
       at3      .6444     .1034     .4419      .847     .4252     .8636
-------------------------------------------------------------------------------
  Uniform bands: on    Critical value:     2.121    Repetitions:      1000

Distance-Based Estimation

. rd2d_dist y D

Distance RD estimation
-------------------------------------------------------------------------------
  Evaluation points:         1    Observations:     20000
  VCE: hc1    RBC: on    Side: two
  Bandwidth source: automatic    Kernel: triangular    Kink: off
-------------------------------------------------------------------------------
     Point      Est.q      SE.q    CI.low   CI.high    CB.low   CB.high
-------------------------------------------------------------------------------
         D      .6954    .09922     .5009     .8898     .4926     .8982
-------------------------------------------------------------------------------
  Uniform bands: on    Critical value:     2.044    Repetitions:      1000

Post-Estimation

* Visualize treatment effects along the boundary
rd2d_plot

* Structured summary with diagnostics
rd2d_summary

* Aggregate effects (weighted boundary average treatment effect)
rd2d_aggregate, method(wbate)

* Bandwidth sensitivity
rd2d_bwsens

* Publication table via esttab
rd2d_table

Commands

Estimation

Command	Purpose	Minimal Syntax
rdbw2d	MSE-optimal bandwidth selection (location)	yvar x1 x2 tvar, at(b1 b2)
rd2d	Treatment effect estimation and inference (location)	yvar x1 x2 tvar, at(b1 b2)
rdbw2d_dist	Bandwidth selection (distance)	yvar distvar
rd2d_dist	Treatment effect estimation and inference (distance)	yvar distvar

Post-Estimation

Command	Purpose
rd2d_plot	Effect plots and boundary heat maps
rd2d_summary	Structured result display with bandwidth diagnostics
rd2d_aggregate	Aggregation: WBATE, AATE, LBATE
rd2d_table	Publication table construction (esttab-compatible)
rd2d_diagnostics	Fit conditioning, support, and covariance checks
rd2d_bwsens	Bandwidth sensitivity analysis

Key Options

Option	Default	Description
p(#)	1	Local polynomial order for point estimation
q(#)	p+1	Polynomial order for bias correction
kernel()	triangular	Kernel:triangular, uniform, epanechnikov, gaussian
bwselect()	mserd	Bandwidth selector:mserd, imserd, msetwo, imsetwo
vce()	hc1	Variance estimator:hc0–hc3; cluster-robust for hc0/hc1
cluster()	—	Cluster variable for cluster-robust inference
cbands	on	Gaussian-simulation uniform confidence bands
kink(on)	off	Nonsmooth-boundary convention (distance commands)
stdvars	off	Standardize coordinates for bandwidth selection
masspoints()	check	Mass-point handling:check, adjust, off
tangvec()	—	Directional derivative target (location commands)
scaleregul()	3	Regularization scale for bandwidth selection

Stored Results

Estimation commands post results in e():

Object	Content
e(results)	Point estimates, SEs, pointwise CIs, and band endpoints per target
e(bws)	Final bandwidths (h01, h02, h11, h12 or h0, h1) and local sample sizes
e(diagnostics)	Fit conditioning and generalized-inverse flags
e(cov_q)	Q-order covariance matrix for uniform inference
e(cb_crit)	Simulated critical value for confidence bands
e(masspoints)	Mass-point support diagnostics
e(b), e(V)	Stata estimation conventions for postestimation

Bandwidth selectors post results in r():

Object	Content
r(bws)	Selected side-specific bandwidths
r(mseconsts)	MSE expansion constants used by the selector
r(masspoints)	Support diagnostics

Scope and Limitations

The package requires:

• A continuous bivariate running variable or a user-constructed signed-distance score.
• Known boundary location (specified via at() for location commands).
• Stata 16 or newer. No R runtime dependency.

Diagnostics are reporting aids, not identification proofs. They help a table script decide what to disclose or rerun before publishing a row, but they do not replace the assumptions, data provenance, or design-specific sensitivity checks required for an empirical application.

References

Cattaneo, M. D., Titiunik, R., & Yu, R. R. (2025). Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods. arXiv preprint arXiv:2505.05670.

Cattaneo, M. D., Titiunik, R., & Yu, R. R. (2025). rd2d: Causal inference in boundary discontinuity designs. arXiv preprint arXiv:2505.07989.

Cattaneo, M. D., Titiunik, R., & Yu, R. R. (2026). Estimation and inference in boundary discontinuity designs: Distance-based methods. Journal of Econometrics, 256, 106266.

BibTeX

@unpublished{cattaneo2025boundaryrd,
  title={Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods},
  author={Cattaneo, Matias D. and Titiunik, Rocio and Yu, Ruiqi},
  year={2025},
  note={arXiv:2505.05670}
}

@unpublished{cattaneo2025rd2d,
  title={{rd2d}: Causal Inference in Boundary Discontinuity Designs},
  author={Cattaneo, Matias D. and Titiunik, Rocio and Yu, Ruiqi},
  year={2025},
  note={arXiv:2505.07989}
}

@article{cattaneo2026distance,
  title={Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods},
  author={Cattaneo, Matias D. and Titiunik, Rocio and Yu, Ruiqi},
  journal={Journal of Econometrics},
  volume={256},
  pages={106266},
  year={2026}
}

Authors

Methodology:

• Matias D. Cattaneo, Princeton University
• Rocio Titiunik, Princeton University
• Ruiqi Yu, Princeton University

Implementation:

• Xuanyu Cai, City University of Macau
• Wenli Xu, City University of Macau