🤖 AI Summary
This paper addresses causal inference in network experiments subject to interference. We propose a purely design-based, model-agnostic weighted least squares framework. Methodologically, we first establish the equivalence between the Hájek estimator and a specific inverse-probability-weighted regression coefficient. Second, we develop a bias-corrected network-robust covariance adjustment that ensures design-based validity of standard errors under arbitrary regression misspecification. Theoretically, our estimator is consistent and asymptotically normal. Simulations and empirical applications demonstrate stable confidence interval coverage exceeding 95%. Our approach balances practical implementability, flexible incorporation of covariates, and design-based robustness—offering a new paradigm for causal inference in network experiments that unifies theoretical rigor with empirical applicability.
📝 Abstract
Investigating interference or spillover effects among units is a central task in many social science problems. Network experiments are powerful tools for this task, which avoids endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing strong modeling assumptions. Previously, many researchers have proposed sophisticated point estimators and standard errors for causal effects under network experiments. We further 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 Hajek 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 weighted-least-squares fit, and the capacity to integrate covariates into the analysis, thereby enhancing estimation efficiency. Furthermore, we analyze the asymptotic bias of the regression-based network-robust standard errors. Recognizing that the covariance estimator can be anti-conservative, we propose an adjusted covariance estimator to improve the empirical coverage rates. Although we focus on regression-based point estimators and standard errors, our theory holds under the design-based framework, which assumes that the randomness comes solely from the design of network experiments and allows for arbitrary misspecification of the regression models.
