This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, that is, the pattern in which adjacent outcomes tend to be more strongly correlated than nonadjacent outcomes. The graph concordance measure can be generally used to quantify the empirical relevance of a network in explaining cross-sectional dependence of the outcomes, and as shown in the paper, it can also be used to quantify the extent of homophily under certain conditions. When one observes a single large network, it is nontrivial to make inferences about the concordance pattern. Assuming a dependency graph, this paper develops a permutation-based confidence interval for the graph concordance measure. The confidence interval is valid in finite samples when the outcomes are exchangeable, and under the dependency graph, an assumption together with other regularity conditions, is shown to exhibit asymptotic validity. Monte Carlo simulation results show that the validity of the permutation method is more robust than the asymptotic method to various graph configurations.

This article 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 neighbours’ outcomes in the second period. This article 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 non-negative, 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 article applies the method to data on Indian villages to measure the diffusion of microfinancing decisions over households’ social networks.

In online procurement markets, projects are often allocated through a mechanism that allows buyers to take into account a seller’s nonprice characteristics as well as his bid. We design a methodology to recover primitives of the environment in the presence of unobserved seller heterogeneity while accommodating two important features of such markets: buyer-specific choice sets and the high turnover of sellers. We apply our method to data from an online market for programming services, to assess buyers’ welfare gains associated with the globalization enabled by the internet. We find that the internet enables buyers to substantially improve on their outside (local) option; many of the gains arise from access to the international markets.