2 Estimates Outcome and Propensity Score Model Parameters In this section, the distribution for the degree of all individuals in the Karnataka dataset is displayed. We also provide details on the outcome and propensity score models used in Section 3 of the main paper. Figure 3 shows the empirical log-log distribution of degree for the Karnataka dataset. 2.1 Karnataka Degree Distribution Figure 3: The empirical degree distribution for the Karnataka dataset. The x -axis shows the log degree, and the y -axis shows the log proportion of individuals with degree exceeding the corresponding degree. Karnataka Dataset Degree Distribution 0.5 1.0 1.5 2.0 −4 −3 −2 −1 0 Log Degree Log Survival In this subsection, we report on the outcome models (OM) and propensity score (PS) models that were fit using a stepwise procedure for inclusion in the doubly-robust (DR) estimation procedure in Section 3 of the main paper. Tables 1, 2 and 3 provide the results of fitting these models; the exposure of interest was the fraction of households that include village leaders. 2.2 Exposure 1: Fraction of Households Reported As Containing Leaders 22