arXiv subjects

Ruiqi Rae Yu

Publications and source records attributed to Ruiqi Rae Yu.

7 recordsLinked to original sources

arXiv2025

Boundary Discontinuity Designs: Theory and Practice

The boundary discontinuity (BD) design is a non-experimental method for identifying causal effects that exploits a thresholding rule based on a bivariate score and a boundary curve. This widely used method generalizes the univariate regression discontinuity design but introduces unique challenges arising from its multidimensional nature. We synthesize over 80 empirical papers that use the BD design, tracing the method's application from its formative stages to its implementation in modern research. We also overview ongoing theoretical and methodological research on identification, estimation, and inference for BD designs employing local polynomial regression, and offer recommendations for practice.

econ.EM↗

arXiv2025

Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods

We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We establish identification, estimation, and inference results both pointwise and uniformly along the treatment assignment boundary. We show that the geometric regularity of the boundary, a one-dimensional manifold, plays a central role in determining feasible convergence rates and valid inference procedures. Our theoretical contributions are threefold. First, we derive uniform lower and upper bounds on the convergence rate of the misspecification bias of isotropic local polynomial estimators. Second, we obtain uniform distributional approximations that justify boundary-robust inference. Third, we establish minimax lower bounds for a broad class of nonparametric isotropic regression estimators. These results yield practical guidance for empirical implementation, including new bandwidth selection rules that adapt to local irregularities of the treatment-assignment boundary. We illustrate the proposed methods using simulation evidence and an empirical application, and provide companion general-purpose software.

econ.EM↗

arXiv2025

Accuracy Limits of Causal Trees for Individualized Treatment Effects

Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning, with splitting criteria designed to identify variation in treatment effects across covariate-defined subgroups. We study causal tree estimators based on adaptive recursive partitioning and establish lower bounds on their estimation accuracy. The class we analyze includes versions with and without sample splitting, based on common treatment effect and squared-error splitting criteria. Even in a constant-effect benchmark with randomized treatment assignment, causal trees constructed via standard CART-type splitting rules can have uniform-norm errors that decrease more slowly than any power of the sample size. The underlying mechanism is that greedy recursive partitioning selects highly imbalanced splits with nonvanishing probability, producing terminal nodes containing very few observations and leading to large estimation variance. We further show that sample splitting, often called ``honesty,'' does not remove this limitation. As a consequence, causal tree estimators may converge arbitrarily slowly uniformly over the covariate space. At the same time, these estimators can have small integrated mean squared error, showing that average accuracy can mask local inaccuracy. Our results also clarify the role of balanced partition assumptions in existing theoretical guarantees for causal forests and related ensemble methods.

math.ST↗

arXiv2025

rd2d: Causal Inference in Boundary Discontinuity Designs

Boundary Discontinuity (BD) designs are used in empirical research to learn about causal treatment effects along a continuous assignment boundary defined by a bivariate score. These designs are also known as multi-score regression discontinuity (RD) designs, and include geographic RD designs as a prominent example. This article introduces \pkg{rd2d}, a statistical software package for \proglang{R}, \proglang{Python}, and \proglang{Stata} that implements local polynomial estimation and inference for BD designs using either the bivariate score or a univariate signed distance-to-boundary score. The software covers sharp and fuzzy BD designs, providing automatic bandwidth selection, robust bias-corrected pointwise inference, uniform confidence bands, cluster-robust inference with joint or separate fitting conventions, covariate-adjusted efficiency improvements, mass-point checks, and covariance regularization, among other features. We illustrate the package with an empirical application to Opportunity Zones, where eligibility has a strong first-stage effect on designation but no significant effects on early workplace-job growth.

stat.ME↗

arXiv2025

Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods

Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well as for two aggregated causal parameters: the \textit{Weighted Boundary Average Treatment Effect} (WBATE) and the \textit{Largest Boundary Average Treatment Effect} (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.

econ.EM↗

arXiv2025

Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference

This paper develops methods for uncertainty quantification in causal inference settings with random network interference. We study the large-sample distributional properties of the classical difference-in-means Hajek treatment effect estimator, and propose a robust inference procedure for the (conditional) direct average treatment effect. Our framework allows for cross-unit interference in both the outcome equation and the treatment assignment mechanism. Drawing from statistical physics, we introduce a novel Ising model to capture complex dependencies in treatment assignment, and derive three results. First, we establish a Berry-Esseen-type distributional approximation that holds pointwise in the degree of interference induced by the Ising model. This approximation recovers existing results in the absence of treatment interference, and highlights the fragility of inference procedures that do not account for the presence of interference in treatment assignment. Second, we establish a uniform distributional approximation for the Hajek estimator and use it to develop robust inference procedures that remain valid uniformly over all interference regimes allowed by the model. Third, we propose a novel resampling method to implement the robust inference procedure and validate its performance through Monte Carlo simulations. A key technical innovation is the introduction of a conditional i.i.d. Gaussianization that may have broader applications. We also discuss extensions and generalizations of our results.

stat.ME↗

arXiv2024

Strong Approximations for Empirical Processes Indexed by Lipschitz Functions

This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by Rio (1994), and if the function class is Lipschitzian, our result improves the approximation rate $n^{-1/(2d)}$ to $n^{-1/\max\{d,2\}}$, up to a $\operatorname{polylog}(n)$ term, where $n$ denotes the sample size. Remarkably, we establish a valid uniform Gaussian strong approximation at the rate $n^{-1/2}\log n$ for $d=2$, which was previously known to be valid only for univariate ($d=1$) empirical processes via the celebrated Hungarian construction (Koml\'os et al., 1975). Second, a uniform Gaussian strong approximation is established for multiplicative separable empirical processes indexed by possibly Lipschitz functions, which addresses some outstanding problems in the literature (Chernozhukov et al., 2014, Section 3). Finally, two other uniform Gaussian strong approximation results are presented when the function class is a sequence of Haar basis based on quasi-uniform partitions. Applications to nonparametric density and regression estimation are discussed.

math.ST↗