Identification and Estimation of Causal Mechanisms in Clustered Encouragement Designs: Disentangling Bed Nets using Bayesian Principal Stratification.

Exploration of causal mechanisms is often important for researchers and policymakers to understand how an intervention works and how it can be improved. This task can be crucial in clustered encouragement designs (CED). Encouragement design studies arise frequently when the treatment cannot be enforced because of ethical or practical constrains and an encouragement intervention (information campaigns, incentives, etc) is conceived with the purpose of increasing the uptake of the treatment of interest. By design, encouragements always entail the complication of non-compliance. Encouragements can also give rise to a variety of mechanisms, particularly when encouragement is assigned at cluster level. Social interactions among units within the same cluster can result in spillover effects. Disentangling the effect of encouragement through spillover effects from that through the enhancement of the treatment would give better insight into the intervention and it could be compelling for planning the scaling-up phase of the program. Building on previous works on CEDs and non-compliance, we use the principal stratification framework to define stratum-specific causal effects, that is, effects for specific latent subpopulations, defined by the joint potential compliance statuses under both encouragement conditions. We show how the latter stratum-specific causal effects are related to the decomposition commonly used in the literature and provide flexible homogeneity assumptions under which an extrapolation across principal strata allows one to disentangle the effects. Estimation of causal estimands can be performed with Bayesian inferential methods using hierarchical models to account for clustering. We illustrate the proposed methodology by analyzing a cluster randomized experiment implemented in Zambia and designed to evaluate the impact on malaria prevalence of an agricultural loan program intended to increase the bed net coverage. Farmer households assigned to the program could take advantage of a deferred payment and a discount in the purchase of new bed nets. Our analysis shows a lack of evidence of an effect of the offering of the program to a cluster of households through spillover effects, that is through a greater bed net coverage in the neighborhood.