arXiv subjects

Gaoqian Xu

Publications and source records attributed to Gaoqian Xu.

4 recordsLinked to original sources

arXiv2026

Policy Learning with $α$-Expected Welfare

This paper proposes an optimal policy that targets the average welfare of the worst-off $α$-fraction of the post-treatment outcome distribution. We refer to this policy as the $α$-Expected Welfare Maximization ($α$-EWM) rule, where $α\in (0,1]$ denotes the size of the subpopulation of interest. The $α$-EWM rule interpolates between the expected welfare ($α=1$) and the Rawlsian welfare ($α\rightarrow 0$). For $α\in (0,1)$, an $α$-EWM rule can be interpreted as a distributionally robust EWM rule that allows the target population to have a different distribution than the study population. Using the dual formulation of our $α$-expected welfare function, we propose a debiased estimator for the optimal policy and establish its asymptotic upper regret bounds. In addition, we develop asymptotically valid inference for the optimal welfare based on the proposed debiased estimator. We examine the finite sample performance of the debiased estimator and inference via both real and synthetic data.

econ.EM↗

arXiv2026

Uniform Inference on Quantile Effects under Network Interference

This paper studies quantile treatment and spillover effects in network experiments. Average spillover effects reveal how treating a unit's neighbors affects its outcome on average, but mask the heterogeneity of these effects across the outcome distribution. We define structural quantile effects that compare outcome quantiles between exposure states, characterizing how own treatment and exposure to treated neighbors affect different parts of the outcome distribution. Building on \citet{leung2020treatment}, we first establish the weak convergence of the estimated quantile-effect process under conditions requiring the stabilization of the degree distribution and the network-dependent covariance structure. Our main contribution is to propose uniform confidence bands (UCBs) based on Gaussian approximations conditional on the realized network, avoiding these stabilization requirements. The proposed method is evaluated through extensive simulation studies and an empirical application to a randomized savings-account experiment in Nepal \citep{prina2015banking}.

econ.EM↗

arXiv2026

Policy Learning under Unobserved Confounding: A Robust and Efficient Approach

This paper develops a robust and efficient method for policy learning from observational data in the presence of unobserved confounding, complementing existing instrumental variable (IV) based approaches. We employ the marginal sensitivity model (MSM) to relax the commonly used yet restrictive unconfoundedness assumption by introducing a sensitivity parameter that captures the extent of selection bias induced by unobserved confounders. Building on this framework, we consider two distributionally robust welfare criteria, defined as the worst-case welfare and policy improvement functions, evaluated over an uncertainty set of counterfactual distributions characterized by the MSM. Closed-form expressions for both welfare criteria are derived. Leveraging these identification results, we construct doubly robust scores and estimate the robust policies by maximizing the proposed criteria. Our approach accommodates flexible machine learning methods for estimating nuisance components, even when these converge at moderately slow rates. We establish asymptotic regret bounds for the resulting policies, providing a robust guarantee against the most adversarial confounding scenario. The proposed method is evaluated through extensive simulation studies and empirical applications to the JTPA study and Head Start program.

econ.EM↗

arXiv2023

Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

math.OC↗