arXiv subjects

Kyle Schindl

Publications and source records attributed to Kyle Schindl.

4 recordsLinked to original sources

arXiv2026

Distributional Discontinuity Design

Regression discontinuity and kink designs are typically analyzed through mean effects, even when treatment changes the shape of the entire outcome distribution. To address this, we introduce distributional discontinuity designs, a framework for estimating causal effects for a scalar outcome at the boundary of a discontinuity in treatment assignment. Our estimand is the Wasserstein distance between limiting conditional outcome distributions; a single scale-interpretable measure of distribution shift. We show that this weakly bounds the average treatment effect, where equality holds if and only if the treatment effect is purely additive; thus, departure from equality measures effect heterogeneity. To further encode effect heterogeneity we show that the Wasserstein distance admits an orthogonal decomposition into squared differences in $L$-moments, thereby quantifying the contribution from location, scale, skewness, and higher-order shape components to the overall distributional distance. Next, we extend this framework to distributional kink designs by evaluating the Wasserstein derivative at a policy kink; this describes the flow of probability mass through the kink. In the case of fuzzy kink designs, we derive new identification results. Finally, we apply our methods on real data by re-analyzing two natural experiments to compare our distributional effects to traditional causal estimands.

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arXiv2025

Causal Geodesy: Counterfactual Estimation Along the Path Between Correlation and Causation

We introduce causal geodesy, a framework for studying the landscape of stochastic interventions that lie between the two extremes of performing no intervention, and performing a sharp intervention that sets an exposure equal to a specific value. We define this framework by constructing paths of distributions that smoothly interpolate between the treatment density and a point mass at the target intervention. Thus, each path starts at a purely observational (or correlational) quantity and moves into a counterfactual world. Of particular interest are paths that correspond to geodesics in some metric, i.e. the shortest path. We then consider the interpretation and estimation of the corresponding causal effects as we move along the path from correlation toward causation.

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arXiv2024

Incremental effects for continuous exposures

Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands requires that everyone has some chance of receiving any level of the exposure (i.e., positivity). To avoid this assumption, we consider stochastic interventions based on exponentially tilting the treatment distribution by some parameter $\delta$ (an incremental effect); this increases or decreases the likelihood a unit receives a given treatment level. We derive the efficient influence function and semiparametric efficiency bound for these incremental effects under continuous exposures. We then show estimation depends on the size of the tilt, as measured by $\delta$. In particular, we derive new minimax lower bounds illustrating how the best possible root mean squared error scales with an effective sample size of $n / \delta$, instead of $n$. Further, we establish new convergence rates and bounds on the bias of double machine learning-style estimators. Our novel analysis gives a better dependence on $\delta$ compared to standard analyses by using mixed supremum and $L_2$ norms. Finally, we define a "reflected" exponential tilt around any interior point and show that taking $\delta \to \infty$ yields a new estimator of the dose-response curve across the treatment support.

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arXiv2024

A Unified Framework for Rerandomization using Quadratic Forms

When designing a randomized experiment, one way to ensure treatment and control groups exhibit similar covariate distributions is to randomize treatment until some prespecified level of covariate balance is satisfied; this strategy is known as rerandomization. Most rerandomization methods utilize balance metrics based on a quadratic form $\mathbf{v}^T \mathbf{A} \mathbf{v}$, where $\mathbf{v}$ is a vector of covariate mean differences and $\mathbf{A}$ is a positive semi-definite matrix. In this work, we derive general results for treatment-versus-control rerandomization schemes that employ quadratic forms for covariate balance. In addition to allowing researchers to quickly derive properties of rerandomization schemes not previously considered, our theoretical results provide guidance on how to choose $\mathbf{A}$ in practice. We find the Mahalanobis and Euclidean distances optimize different measures of covariate balance. Furthermore, we establish how the covariates' eigenstructure and their relationship to the outcomes dictate which matrix $\mathbf{A}$ yields the most precise difference-in-means estimator for the average treatment effect. We find the Euclidean distance is minimax optimal, in the sense that the difference-in-means estimator's precision is never too far from the optimal choice. We verify our theoretical results via simulation and a real data application, and demonstrate how the choice of $\mathbf{A}$ impacts the variance reduction of rerandomized experiments.

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