# A Decomposition Analysis of Diffusion Over a Large Network

## TL;DR

This paper introduces a decomposition method to accurately measure diffusion over large networks, accounting for confounding covariates, and provides an inference procedure validated through Monte Carlo simulations.

## Contribution

It develops a novel decomposition analysis and asymptotic inference method for diffusion measurement that controls for omitted covariates in network data.

## Key findings

- Decomposition method effectively isolates true diffusion effects.
- Inference procedure performs well in small samples.
- Application clarifies the role of covariates in diffusion estimates.

## Abstract

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.