世界银行-税收遵从溢出效应的部分人口实验设计（英）-2025.2_81页_3mb

Framework Development

The paper develops a framework to analyze partial population experiments with heterogeneous clusters, addressing clusters of different treatment intensities. Key contributions include:

• Asymptotic Distribution: Provides an approximation for OLS estimators in the presence of cluster size and distributional heterogeneity, showing consistency and asymptotic normality.
• Variance Estimation: Demonstrates that the cluster-robust variance estimator can be upward-biased due to heterogeneity, leading to conservative inference.

Asymptotic Behavior and Power Calculations

• The distribution of OLS estimators is characterized under double-array asymptotics, allowing for unequal cluster sizes.
• Minimum Detectable Effects (MDEs) depend on cluster heterogeneity. Ignoring heterogeneity can result in severely underpowered experiments.
• Optimal Design: Derives optimal cluster-level assignment probabilities to minimize the weighted average of variance components for key estimands.

Tax Compliance Application

• In a randomized controlled trial in Argentina, personalized tax reminders were sent to 80% of randomly selected street blocks.
• Key Findings:
  • Direct effects show higher tax compliance for treated units.
  • Spillover effects on untreated neighbors are significant, especially in high saturation blocks with higher prior compliance.
• Experiments account for and validate minimal interference between blocks, confirming the validity of the counterfactual.

Key Recommendations

• Use general variance formulas accounting for cluster heterogeneity to ensure adequate power.
• Design partial population experiments by selecting saturations and within-cluster treatment probabilities based on expected outcome functions.
• Incorporate constraints (e.g., budget limits) into the probability optimization.

This summary encapsulates the core findings and methodological advances without referencing specific figures or tables.