Design-Based and Network Sampling-Based Uncertainties in Network Experiments

TL;DR

This paper investigates the causal interpretation and inference challenges of OLS estimators in network experiments, addressing design and sampling uncertainties, contamination bias, and proposing a robust variance estimator.

Contribution

It provides a detailed analysis of biases in OLS estimators due to network correlations and introduces a network-robust variance estimator for better inference.

Findings

Contamination bias can significantly inflate spillover effect estimates.

Correlations among regressors induce bias, complicating causal interpretation.

The proposed variance estimator improves inference accuracy in network experiments.

Abstract

Ordinary least squares (OLS) estimators are widely used in network experiments to estimate spillover effects. We study the causal interpretation of, and inference for the OLS estimator under both design-based uncertainty from random treatment assignment and sampling-based uncertainty in network links. We show that correlations among regressors that capture the exposure to neighbors' treatments can induce contamination bias, preventing OLS from aggregating heterogeneous spillover effects for a clear causal interpretation. We derive the OLS estimator's asymptotic distribution and propose a network-robust variance estimator. Simulations and an empirical application demonstrate that contamination bias can be substantial, leading to inflated spillover estimates.