arXiv subjects

Michael P. Leung

Publications and source records attributed to Michael P. Leung.

12 recordsLinked to original sources

arXiv2026

Designing Spatial Treatments

Spatial treatments are interventions assigned to locations potentially distinct from those of the responding units. We study their optimal design under a general model in which a unit's response diminishes with distance to a treated site. Our estimand of interest is an ``uncontaminated'' effect equal to the average impact of a single intervention site over all hypothetical sites. We propose a novel design based on a Matérn point process which separates treatments by a distance of at least $r$. A larger choice of $r$ reduces bias by separating interventions but increases variance by reducing their numerosity. We choose $r$ to maximize the rate of convergence of a Horvitz-Thompson estimator and prove that this is minimax rate-optimal. We provide weak conditions under which the estimator is asymptotically normal and propose a variance estimator.

econ.EM↗

arXiv2026

Identifying Treatment and Spillover Effects Using Exposure Contrasts

To report spillover effects, a common approach is to regress outcomes on statistics summarizing neighbors' treatments. This paper studies nonparametric analogs of these estimands, which we refer to as exposure contrasts. We demonstrate that they may have the opposite sign of the unit-level effects of interest even under unconfoundedness. We then provide interpretable conditions on interference and the assignment mechanism under which exposure contrasts can be represented as convex averages of the unit-level effects, thereby avoiding sign reversals. These conditions encompass cluster-randomized trials, network experiments, and observational settings with peer effects in selection into treatment.

econ.EM↗

arXiv2026

Normal Approximation in Large Network Models

We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size diverges. We argue that a modification of ``stabilization'' conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence which we utilize to establish an abstract central limit theorem. Using results in branching process theory, we derive interpretable primitive conditions for stabilization. The main conditions restrict the strength of strategic interactions and equilibrium selection mechanism. We discuss practical inference procedures justified by our results.

econ.EM↗

arXiv2025

Graph Neural Networks for Causal Inference Under Network Confounding

This paper studies causal inference with observational data from a single large network. We consider a nonparametric model with interference in both potential outcomes and selection into treatment. Specifically, both stages may be the outcomes of simultaneous equations models, allowing for endogenous peer effects. This results in high-dimensional network confounding where the network and covariates of all units constitute sources of selection bias. In contrast, the existing literature assumes that confounding can be summarized by a known, low-dimensional function of these objects. We propose to use graph neural networks (GNNs) to adjust for network confounding. When interference decays with network distance, we argue that the model has low-dimensional structure that makes estimation feasible and justifies the use of shallow GNN architectures.

econ.EM↗

arXiv2025

Neighborhood Stability in Double/Debiased Machine Learning with Dependent Data

This paper studies double/debiased machine learning (DML) methods applied to weakly dependent data. We allow observations to be situated in a general metric space that accommodates spatial and network data. Existing work implements cross-fitting by excluding from the training fold observations sufficiently close to the evaluation fold. We find in simulations that this can result in exceedingly small training fold sizes, particularly with network data. We therefore seek to establish the validity of DML without cross-fitting, building on recent work by Chen et al. (2022). They study i.i.d. data and require the machine learner to satisfy a natural stability condition requiring insensitivity to data perturbations that resample a single observation. We extend these results to dependent data by strengthening stability to "neighborhood stability," which requires insensitivity to resampling observations in any slowly growing neighborhood. We show that existing results on the stability of various machine learners can be adapted to verify neighborhood stability.

econ.EM↗

arXiv2025

Cluster-Randomized Trials with Cross-Cluster Interference

The literature on cluster-randomized trials typically allows for interference within but not across clusters. This may be implausible when units are irregularly distributed across space without well-separated communities, as clusters in such cases may not align with significant geographic, social, or economic divisions. This paper develops methods for reducing bias due to cross-cluster interference. We first propose an estimation strategy that excludes units not surrounded by clusters assigned to the same treatment arm. We show that this substantially reduces bias relative to conventional difference-in-means estimators without significant cost to variance. Second, we formally establish a bias-variance trade-off in the choice of clusters: constructing fewer, larger clusters reduces bias due to interference but increases variance. We provide a rule for choosing the number of clusters to balance the asymptotic orders of the bias and variance of our estimator. Finally, we consider unsupervised learning for cluster construction and provide theoretical guarantees for $k$-medoids.

stat.ME↗

arXiv2023

Network Cluster-Robust Inference

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster-robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network-dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster-robust methods control size better than HAC estimators. However, for important classes of networks lacking low-conductance clusters, the former can exhibit substantial size distortion. To determine the number of low-conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low-conductance clusters and spectral clustering to construct them.

econ.EM↗

arXiv2022

Rate-Optimal Cluster-Randomized Designs for Spatial Interference

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.

stat.ME↗

arXiv2021

Causal Inference Under Approximate Neighborhood Interference

This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego's response. However, this assumption is violated in common models of social interactions. We propose a substantially weaker model of "approximate neighborhood interference" (ANI) under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, effect on the ego's response. We formally verify that ANI holds for well-known models of social interactions. Under ANI, restrictions on the network topology, and asymptotics under which the network size increases, we prove that standard inverse-probability weighting estimators consistently estimate useful exposure effects and are approximately normal. For inference, we consider a network HAC variance estimator. Under a finite population model, we show that the estimator is biased but that the bias can be interpreted as the variance of unit-level exposure effects. This generalizes Neyman's well-known result on conservative variance estimation to settings with interference.

econ.EM↗

arXiv2021

Dependence-Robust Inference Using Resampled Statistics

We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that the statistics are asymptotically normal under the weak requirement that the target parameter can be consistently estimated at the parametric rate. This holds for regular estimators under many well-known forms of weak dependence and justifies the claim of dependence-robustness. We consider applications to settings with unknown or complicated forms of dependence, with various forms of network dependence as leading examples. We develop tests for both moment equalities and inequalities.

econ.EM↗

arXiv2020

Recovering Network Structure from Aggregated Relational Data using Penalized Regression

Social network data can be expensive to collect. Breza et al. (2017) propose aggregated relational data (ARD) as a low-cost substitute that can be used to recover the structure of a latent social network when it is generated by a specific parametric random effects model. Our main observation is that many economic network formation models produce networks that are effectively low-rank. As a consequence, network recovery from ARD is generally possible without parametric assumptions using a nuclear-norm penalized regression. We demonstrate how to implement this method and provide finite-sample bounds on the mean squared error of the resulting estimator for the distribution of network links. Computation takes seconds for samples with hundreds of observations. Easy-to-use code in R and Python can be found at https://github.com/mpleung/ARD.

econ.EM↗

arXiv2019

Inference in Models of Discrete Choice with Social Interactions Using Network Data

This paper studies inference in models of discrete choice with social interactions when the data consists of a single large network. We provide theoretical justification for the use of spatial and network HAC variance estimators in applied work, the latter constructed by using network path distance in place of spatial distance. Toward this end, we prove new central limit theorems for network moments in a large class of social interactions models. The results are applicable to discrete games on networks and dynamic models where social interactions enter through lagged dependent variables. We illustrate our results in an empirical application and simulation study.

econ.EM↗