Unconditional Randomization Tests for Interference

2024-09-14

AI Summary

Testing for interference between units (e.g., crime displacement) in causal inference often fails due to network dependence and complex clustering. This paper proposes Partial Null Randomization Tests (PNRTs): a design-based, model-free framework that enables valid finite-sample inference via unconditional randomization and pairwise difference statistics. Our key contribution is the first integration of unconditional randomization with pairwise comparisons—yielding robustness to arbitrary network structures, theoretical validity under minimal assumptions, and computational simplicity. PNRTs combine permutation inference with simulation-based calibration. Applied to Bogotá’s hot-spot policing experiment, PNRTs robustly detect significant violent crime displacement. Simulation studies demonstrate that PNRTs achieve substantially higher statistical power than existing methods across diverse interference patterns, including spatial spillovers and heterogeneous treatment effects.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

When conducting causal inference or designing policy, researchers are often concerned with the existence and extent of interference between units, which may be influenced by factors such as distance, proximity, and connection strength. However, complex correlations across units pose significant challenges for inference. This paper introduces partial null randomization tests (PNRTs), a novel framework for testing interference in experimental settings. PNRTs adopt a design-based approach, combining unconditional randomization testing with pairwise comparisons to enable straightforward implementation and ensure finite-sample validity under minimal assumptions about network structure. To illustrate the method's broad applicability, this paper applies it to a large-scale experiment by Blattman et al. (2021) in Bogota, Colombia, which evaluates the impact of hotspot policing on crime using street segments as units of analysis. The findings indicate that increasing police patrolling time in hotspots has a significant displacement effect on violent crime but not on property crime. A simulation study calibrated to this dataset further demonstrates the strong power properties of PNRTs and their suitability for general interference scenarios.

Problem

• Testing interference in causal inference with complex dependencies
• Developing robust framework for interference assessment in experiments
• Evaluating effects of hotspot policing on crime displacement

Innovation

• Pairwise imputation-based randomization test (PIRT)
• Unconditional randomization testing for interference
• Minimal assumptions about network structure