Causal inference in network experiments: regression-based analysis and design-based properties

TL;DR

This paper demonstrates that regression-based estimators in network experiments can provide reliable inference for spillover effects when properly specified, offering practical advantages and improved covariance estimation methods.

Contribution

It establishes theoretical guarantees for regression-based analysis in network experiments and introduces an adjusted covariance estimator for better empirical coverage.

Findings

Regression-based estimators are theoretically sound with proper specification.

Standard errors can be derived directly from the regression fit.

An adjusted covariance estimator improves empirical coverage under nonconstant effects.

Abstract

Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing strong modeling assumptions. We show that regression-based point estimators and standard errors can have strong theoretical guarantees if the regression functions and robust standard errors are carefully specified to accommodate the interference patterns under network experiments. We first recall a well-known result that the H\'ajek estimator is numerically identical to the coefficient from the weighted-least-squares fit based on the inverse probability of the exposure mapping. Moreover, we demonstrate that the regression-based approach offers three notable advantages: its ease of implementation, the ability to derive standard errors through the same regression fit, and the potential to integrate covariates into the analysis to improve efficiency. Recognizing that the regression-based network-robust covariance estimator can be anti-conservative under nonconstant effects, we propose an adjusted covariance estimator to improve the empirical coverage rates.