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Rocio Titiunik

Publications and source records attributed to Rocio Titiunik.

At least 19 recordsLinked to original sources
arXiv2026

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↗
arXiv2026

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↗
arXiv2026

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↗
arXiv2026

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

Randomization Inference for Before-and-After Studies with Multiple Units: An Application to a Criminal Procedure Reform in Uruguay

Learning about the immediate causal effects of large-scale policy interventions poses a significant challenge for quasi-experimental methods that rely on long-term trends or parametric modeling assumptions. As an alternative, we develop a randomization inference framework for before-and-after studies with multiple units, designed specifically for short-term causal inference and allowing for general assignment mechanisms. The method provides finite-sample-valid statistical inferences without relying on parametric time series models or extrapolation. We demonstrate its utility by analyzing a major criminal justice reform in Uruguay that switched from an inquisitorial to an adversarial system in November 2017. Our method relies on the key assumption of no local time trends near the policy adoption time, which is supported by several falsification tests in our empirical study. We find a statistically significant short-term causal effect: an increase of approximately 25 daily police reports (an 8% rise) in the first week of the new justice system. Our randomization inference framework provides a robust and flexible methodology for evaluating policy adoptions in before-and-after studies with multiple units.

stat.ME↗
arXiv2025

The Regression Discontinuity Design in Medical Science

This article provides an introduction to the Regression Discontinuity (RD) design, and its application to empirical research in the medical sciences. While the main focus of this article is on causal interpretation, key concepts of estimation and inference are also briefly mentioned. A running medical empirical example is provided.

stat.ME↗
arXiv2025

Treatment Effect Heterogeneity in Regression Discontinuity Designs

Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates, even though no formal statistical methods exist for such analyses. This has led to the widespread use of ad hoc approaches in applications. Motivated by common empirical practice, we develop a unified, theoretically grounded framework for RD heterogeneity analysis. We show that a fully interacted local linear (in functional parameters) model effectively captures heterogeneity while still being tractable and interpretable in applications. The model structure holds without loss of generality for discrete covariates. Although our proposed model is potentially restrictive for continuous covariates, it naturally aligns with standard empirical practice and offers a causal interpretation for RD applications. We establish principled bandwidth selection and robust bias-corrected inference methods to analyze heterogeneous treatment effects and test group differences. We provide companion software to facilitate implementation of our results. An empirical application illustrates the practical relevance of our methods.

econ.EM↗
arXiv2025

rdhte: Conditional Average Treatment Effects in RD Designs

Understanding causal heterogeneous treatment effects based on pretreatment covariates is a crucial aspect of empirical work. Building on Calonico, Cattaneo, Farrell, Palomba, and Titiunik (2025), this article discusses the software package rdhte for estimation and inference of heterogeneous treatment effects in sharp regression discontinuity (RD) designs. The package includes three main commands: rdhte conducts estimation and robust bias-corrected inference for heterogeneous RD treatment effects, for a given choice of the bandwidth parameter; rdbwhte implements automatic bandwidth selection methods; and rdhte lincom computes point estimates and robust bias-corrected confidence intervals for linear combinations, a post-estimation command specifically tailored to rdhte. We also provide an overview of heterogeneous effects for sharp RD designs, give basic details on the methodology, and illustrate using an empirical application. Finally, we discuss how the package rdhte complements, and in specific cases recovers, the canonical RD package rdrobust (Calonico, Cattaneo, Farrell, and Titiunik 2017).

econ.EM↗
arXiv2025

Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly different points in time. From a theoretical perspective, our uncertainty quantification methods improve on prior literature by (i) covering a large class of causal predictands in staggered adoption settings, (ii) allowing for synthetic control methods with possibly nonlinear constraints, (iii) proposing scalable robust conic optimization methods and principled data-driven tuning parameter selection, and (iv) offering valid uniform inference across post-treatment periods. We illustrate our methodology with an empirical application studying the effects of economic liberalization on real GDP per capita for Sub-Saharan African countries. Companion software packages are provided in Python, R, and Stata.

econ.EM↗
arXiv2024

A Practical Introduction to Regression Discontinuity Designs: Extensions

This monograph, together with its accompanying first part Cattaneo, Idrobo and Titiunik (2020), collects and expands the instructional materials we prepared for more than $50$ short courses and workshops on Regression Discontinuity (RD) methodology that we taught between 2014 and 2023. In this second monograph, we discuss several topics in RD methodology that build on and extend the analysis of RD designs introduced in Cattaneo, Idrobo and Titiunik (2020). Our first goal is to present an alternative RD conceptual framework based on local randomization ideas. This methodological approach can be useful in RD designs with discretely-valued scores, and can also be used more broadly as a complement to the continuity-based approach in other settings. Then, employing both continuity-based and local randomization approaches, we extend the canonical Sharp RD design in multiple directions: fuzzy RD designs, RD designs with discrete scores, and multi-dimensional RD designs. The goal of our two-part monograph is purposely practical and hence we focus on the empirical analysis of RD designs.

stat.ME↗
arXiv2023

A Guide to Regression Discontinuity Designs in Medical Applications

We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity-based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias-corrected inference methods for uncertainty quantification. We also overview empirical falsification tests that can be used to support key assumptions. Our discussion focuses on two particular features that are relevant in biomedical research: (i) fuzzy RD designs, which often arise when therapeutic treatments are based on clinical guidelines but patients with scores near the cutoff are treated contrary to the assignment rule; and (ii) RD designs with discrete scores, which are ubiquitous in biomedical applications. We illustrate our discussion with three empirical applications: the effect of CD4 guidelines for anti-retroviral therapy on retention of HIV patients in South Africa, the effect of genetic guidelines for chemotherapy on breast cancer recurrence in the United States, and the effects of age-based patient cost-sharing on healthcare utilization in Taiwan. We provide replication materials employing publicly available statistical software in Python, R and Stata, offering researchers all necessary tools to conduct an RD analysis.

stat.ME↗
arXiv2022

scpi: Uncertainty Quantification for Synthetic Control Methods

The synthetic control method offers a way to quantify the effect of an intervention using weighted averages of untreated units to approximate the counterfactual outcome that the treated unit(s) would have experienced in the absence of the intervention. This method is useful for program evaluation and causal inference in observational studies. We introduce the software package scpi for prediction and inference using synthetic controls, implemented in Python, R, and Stata. For point estimation or prediction of treatment effects, the package offers an array of (possibly penalized) approaches leveraging the latest optimization methods. For uncertainty quantification, the package offers the prediction interval methods introduced by Cattaneo, Feng and Titiunik (2021) and Cattaneo, Feng, Palomba and Titiunik (2022). The paper includes numerical illustrations and a comparison with other synthetic control software.

stat.ME↗
arXiv2022

Covariate Adjustment in Regression Discontinuity Designs

The Regression Discontinuity (RD) design is a widely used non-experimental method for causal inference and program evaluation. While its canonical formulation only requires a score and an outcome variable, it is common in empirical work to encounter RD analyses where additional variables are used for adjustment. This practice has led to misconceptions about the role of covariate adjustment in RD analysis, from both methodological and empirical perspectives. In this chapter, we review the different roles of covariate adjustment in RD designs, and offer methodological guidance for its correct use.

stat.ME↗
arXiv2022

Regression Discontinuity Designs

The Regression Discontinuity (RD) design is one of the most widely used non-experimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and matured, and there is now a large number of methodological results for RD identification, estimation, inference, and validation. We offer a curated review of this methodological literature organized around the two most popular frameworks for the analysis and interpretation of RD designs: the continuity framework and the local randomization framework. For each framework, we discuss three main topics: (i) designs and parameters, which focuses on different types of RD settings and treatment effects of interest; (ii) estimation and inference, which presents the most popular methods based on local polynomial regression and analysis of experiments, as well as refinements, extensions, and alternatives; and (iii) validation and falsification, which summarizes an array of mostly empirical approaches to support the validity of RD designs in practice.

econ.EM↗
arXiv2021

Prediction Intervals for Synthetic Control Methods

Uncertainty quantification is a fundamental problem in the analysis and interpretation of synthetic control (SC) methods. We develop conditional prediction intervals in the SC framework, and provide conditions under which these intervals offer finite-sample probability guarantees. Our method allows for covariate adjustment and non-stationary data. The construction begins by noting that the statistical uncertainty of the SC prediction is governed by two distinct sources of randomness: one coming from the construction of the (likely misspecified) SC weights in the pre-treatment period, and the other coming from the unobservable stochastic error in the post-treatment period when the treatment effect is analyzed. Accordingly, our proposed prediction intervals are constructed taking into account both sources of randomness. For implementation, we propose a simulation-based approach along with finite-sample-based probability bound arguments, naturally leading to principled sensitivity analysis methods. We illustrate the numerical performance of our methods using empirical applications and a small simulation study. \texttt{Python}, \texttt{R} and \texttt{Stata} software packages implementing our methodology are available.

stat.ME↗
arXiv2020

The Regression Discontinuity Design

This handbook chapter gives an introduction to the sharp regression discontinuity design, covering identification, estimation, inference, and falsification methods.

econ.EM↗
arXiv2020

Analysis of Regression Discontinuity Designs with Multiple Cutoffs or Multiple Scores

We introduce the \texttt{Stata} (and \texttt{R}) package \texttt{rdmulti}, which includes three commands (\texttt{rdmc}, \texttt{rdmcplot}, \texttt{rdms}) for analyzing Regression Discontinuity (RD) designs with multiple cutoffs or multiple scores. The command \texttt{rdmc} applies to non-cumulative and cumulative multi-cutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects, and provides robust bias-corrected inference procedures. Post estimation and inference is allowed. The command \texttt{rdmcplot} offers RD plots for multi-cutoff settings. Finally, the command \texttt{rdms} concerns multi-score settings, covering in particular cumulative cutoffs and two running variables contexts. It also calculates pooled and cutoff-specific RD treatment effects, provides robust bias-corrected inference procedures, and allows for post-estimation estimation and inference. These commands employ the \texttt{Stata} (and \texttt{R}) package \texttt{rdrobust} for plotting, estimation, and inference. Companion \texttt{R} functions with the same syntax and capabilities are provided.

stat.CO↗