  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.
