Learning Treatment Effects during Resource Allocation via Priority-Queue Randomization

Technical Summary: Learning Treatment Effects during Resource Allocation via Priority-Queue Randomization

Problem Statement
Public service programs (e.g., housing, childcare subsidies, organ transplants) frequently manage scarce resources through tiered priority queues rather than one-time allocations. Applicants arrive over time, and resources are allocated based on priority tiers (e.g., risk scores) and arrival order (first-in-first-out within tiers). While rigorous randomized evaluation is the gold standard for estimating causal treatment effects, direct randomization (e.g., lotteries) is often administratively or ethically infeasible in these settings because bypassing high-priority applicants violates the program's core mandate to serve those with the greatest need. This creates a tension between operational priority rules and the need for credible causal inference.

Methodology
The authors propose an experimental design framework that resolves this tension by randomizing queue assignment rather than treatment allocation directly.

• Design Mechanism: Applicants with observed covariates $X$ are randomized into one of $K$ priority queues according to a policy $\theta(X)$, which specifies the probability of assignment to each queue. Once assigned, treatment is determined deterministically by the existing operational rules: resources are allocated across queues in priority order, and within queues, in order of arrival.
• Identification Strategies:
  • Exogenous Arrivals: If arrival times $A$ are independent of potential outcomes conditional on covariates ($A \perp\!\!\!\perp (Y^0, Y^1) | X$), treatment assignment is conditionally randomized. Standard estimands, such as the Average Treatment Effect (ATE), are identified by comparing treated and untreated units conditional on $X$.
  • Endogenous Arrivals: If arrival times are correlated with potential outcomes (e.g., those in greater crisis apply earlier), standard comparisons are confounded. In this regime, the random queue assignment acts as an Instrumental Variable (IV). The authors define an instrument $r_n(X, Q)$ based on the difference between an individual's expected treatment probability pre-randomization and their realized probability. This identifies a Local Average Treatment Effect (LATE) for a latent "complier" population induced by the queuing process. They further analyze a partially linear IV model to estimate a homogeneous treatment effect parameter.
• Optimization Framework: The paper formulates an optimization problem to select the queue assignment policy $\theta$. The objective is to maximize statistical efficiency (minimize the asymptotic variance of the treatment effect estimator) subject to a utility constraint ensuring that high-need individuals remain likely to be prioritized.
  • The authors derive that under specific assumptions (fixed queue proportions, stable budget, independent arrivals), the asymptotic treatment propensity score is an affine function of $\theta$.
  • They demonstrate that despite the dependence in treatment assignments induced by the queuing process, the asymptotic variance of standard estimators (e.g., Doubly Robust ATE, IV estimators) matches the standard i.i.d. efficiency bounds. This allows the use of these bounds as tractable objectives for optimization.
  • The problem is cast as a robust optimization over nuisance functions (e.g., outcome variances) to handle uncertainty, resulting in convex (or concave) optimization problems solvable via standard methods.

Key Contributions

1. Characterization of Causal Identification: The paper rigorously characterizes what causal effects are identifiable under priority-queue allocation. It establishes that exogenous arrivals allow for standard ATE identification, while endogenous arrivals require an IV approach where queue assignment instruments treatment, identifying specific LATEs.
2. Optimized Experimental Design: The authors develop a method to optimize queue-assignment probabilities to trade off statistical efficiency against the prioritization of high-need applicants. They prove that standard i.i.d. efficiency bounds remain valid design objectives even when treatment assignments are dependent due to the queuing mechanism.
3. Theoretical Guarantees: The paper provides proofs for the asymptotic normality of estimators and shows that the dependence induced by the queueing system does not inflate the leading-order variance term, justifying the use of standard efficiency bounds for design optimization.

Results
Using data from a public housing allocation program in a large U.S. county (2,317 individuals), the authors evaluate their proposed designs against heuristic baselines (a "Switch" heuristic and a "Greedy Softmax" heuristic) and a Randomized Controlled Trial (RCT) baseline.

• Efficiency vs. Utility: The optimized designs achieve a favorable Pareto frontier, offering higher statistical efficiency (lower variance) and higher utility (better prioritization of high-risk individuals) compared to heuristic methods across various queue configurations.
• Robustness: Under endogenous arrival conditions, the IV-based design remains unbiased, whereas the exogenous design (which ignores arrival endogeneity) exhibits substantial bias, particularly when high-priority queues have low treatment probabilities.
• Queue Configuration: The efficiency of the endogenous design is shown to be sensitive to the variance of treatment probabilities across queues; higher variance in treatment probabilities between queues improves the efficiency of the IV estimator.

Significance and Claims
The paper claims that incorporating randomization into priority-queue allocation schemes provides policymakers with a viable mechanism to learn about program effectiveness without sacrificing the targeting of resources to those most in need. By treating queue assignment as the randomization lever, the framework accommodates the operational constraints of dynamic settings (online arrivals, fixed budgets) while enabling credible causal inference. The authors assert that their approach expands the Pareto frontier between statistical power and prioritization utility, potentially enabling more widespread evaluation and improvement of critical public services. The work extends prior research on balancing prioritization and learning (Wilder and Welle, 2025) to dynamic, priority-based allocation settings and contributes to the literature on market design and experimental design under capacity constraints.