In practice, we estimate the OM as $_{E}$( Y$_{ij}$ | X$_{i}$ , A$_{i}$ = a ) and the PS as $_{E}$( A$_{i}$ = a | X$_{i}$ ) using regression approaches. More specifically, we use a stepwise selection of relevant network and sociodemographic covariates X$_{i}$ . Because P is small, we assume that over-fitting is unlikely, although cross-validation could be used to fit OM and PS models if needed. 3 Analysis of Microfinance Diffusion in Indian Villages We used the methods described above to estimate exposure effects in the adoption of microfinance loans in a collection of villages in Karnataka, India 12 based on information for 49,707 individuals located in 49 villages. In our approach, we consider each village as its own network and we assume the villages to be independent of one another. Six months before a microfinance institution entered the villages and began offering microfinance loans to villagers, investigators used surveys to collect detailed social network data about social, familial and economic ties. The microfinance institution began by inviting “leaders” ( e.g. , teachers and shopkeepers) to informational meetings and asked them to spread information about the loans to villagers. The leaders constituted 14.7% of the total population. Data was also collected on participation in savings self-help groups. Household membership and sociodemographic information, such as age and sex, was collected for 12,122 individuals. The outcome of interest, both in the original study and in our re-analyses of data, is household participation in the microfinance program by the end of the study. We describe two exposures as follows: a village (network) experiences Exposure 1 , high proportion of leaders, if the fraction of its households containing leaders is in the top quartile compared to all other villages; a village experiences Exposure 2 , high proportion of savers, if the fraction of its households that participate in the savings self-help groups is in the top quartile compared to all other villages. Exposures 1 and 2 allow investigation of whether villages with more leaders and with higher participation rates in the self-help have greater participation rates in the microfinance program. We calculate and compare the average difference in microfinance uptake between village exposure groups. A crude estimate of this quantity is obtained as the difference between exposed and unexposed villages in average household uptake of microfinance. The standard GEE accounts for the correlation of outcomes within each village. We fit two doubly-robust GEEs: (1) using only network covariates in the outcome model ( X (1) through X $^{(10)}$), and (2) using also the proportion of men in the village and the age of the villagers as covariates. PS and OM were found using stepwise variable selection. Using the model described in the previous section, the estimated uptake of microfinance in the control group is β$_{0}$ and the change in its uptake associated with both exposures is β$_{A}$ . Results are given in Table 2. 6