Measuring Diffusion over a Large Network
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This paper introduces a measure of diffusion of binary outcomes over a large, sparse, causal graph over two periods. The measure captures the aggregated spillover effect of the outcomes in the first period on their neighboring outcomes in the second period. We associate the causal graph with a set of conditional independence restrictions, and relate diffusion to observed outcomes using a version of an unconfoundedness condition which permits covariates to be high dimensional. When the causal graph is known, we show that the measure of diffusion is identified as a spatio-temporal dependence measure of observed outcomes, and develop asymptotic inference for the measure. When this is not the case, but the spillover effect is nonnegative, the spatio-temporal dependence measure serves as a lower bound for the diffusion. Using this, we propose a confidence lower bound for diffusion and establish its asymptotic validity. Our Monte Carlo simulation studies demonstrate the finite sample stability of the inference across a wide range of network configurations. We apply the method to Indian village data to measure the diffusion of microfinancing decisions over social networks of households and find that the diffusion parameter is significantly different from zero at 1 level.
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