  This paper introduces a measure of the diffusion of binary outcomes over a
large, sparse network, when the diffusion is observed in two time periods. The
measure captures the aggregated spillover effect of the state-switches in the
initial period on their neighbors' outcomes in the second period. This paper
introduces a causal network that captures the causal connections among the
cross-sectional units over the two periods. It shows that when the researcher's
observed network contains the causal network as a subgraph, the measure of
diffusion is identified as a simple, spatio-temporal dependence measure of
observed outcomes. When the observed network does not satisfy this condition,
but the spillover effect is nonnegative, the spatio-temporal dependence measure
serves as a lower bound for diffusion. Using this, a lower confidence bound for
diffusion is proposed and its asymptotic validity is established. The Monte
Carlo simulation studies demonstrate the finite sample stability of the
inference across a range of network configurations. The paper applies the
method to data on Indian villages to measure the diffusion of microfinancing
decisions over households' social networks.
