Dependent Randomized Rounding for Budget Constrained Experimental Design

TL;DR

This paper introduces a dependent randomized rounding method for experimental design under budget constraints, improving estimator precision by inducing negative correlations while maintaining treatment probability marginals.

Contribution

It presents a novel dependent randomized rounding framework that enhances estimator accuracy in budget-constrained experiments, with theoretical guarantees and empirical validation.

Findings

Reduces variance of estimators under fixed budgets.

Maintains marginal treatment probabilities after rounding.

Demonstrates improved inference accuracy in empirical studies.

Abstract

Policymakers in resource-constrained settings require experimental designs that satisfy strict budget limits while ensuring precise estimation of treatment effects. We propose a framework that applies a dependent randomized rounding procedure to convert assignment probabilities into binary treatment decisions. Our proposed solution preserves the marginal treatment probabilities while inducing negative correlations among assignments, leading to improved estimator precision through variance reduction. We establish theoretical guarantees for the inverse propensity weighted and general linear estimators, and demonstrate through empirical studies that our approach yields efficient and accurate inference under fixed budget constraints.