Instrumental Variables Estimation in Cluster Randomized Trials with Noncompliance : A Study of A Biometric Smartcard Payment System in India

Many policy evaluations occur in settings with treatment randomized at the cluster level and there is treatment noncompliance at the unit level within each cluster. For example, villages might be assigned to treatment and control, but residents in each village may choose to not comply with their assigned treatment status. This was the case in Andhra Pradesh, India, where the state government sought to evaluate the use of new biometric smartcards to deliver payments from two anti-poverty programs. Smartcard payments were randomized at the village level, but residents could choose to register for a smartcard or not. In some villages, more than 90% of residents complied with the treatment, while in other locations fewer than 15% of the residents complied. When noncompliance is present, investigators may choose to focus attention on either intention to treat effects or the treatment effect among the units that comply. When analysts focus on the effect among compliers, the instrumental variables framework can be used to evaluate identify and estimate causal effects. While a large literature exists on instrumental variables estimation methods, relatively little work has been focused on settings with clustered treatments. In the paper, we review extant methods for instrumental variable estimation in clustered designs. We then show that these methods depend on assumptions that are often unrealistic in applied settings. In response, we develop an estimation method that relaxes these assumptions. Specifically, our method allows for possible treatment effect heterogeneity that is correlated with cluster size and uses a finite sample variance estimator. We evaluate these methods using a series of simulations and apply them to data from the evaluation of using smartcard payments for anti-poverty programs in India. ∗We thank participants at the Penn Causal Inference Seminar for helpful comments. †Assistant Professor, University of Wisconsin, Madison, Email: hyunseung@stat.wisc.edu ‡Associate Professor, University of Pennsylvania, Email: luke.keele@uphs.upenn.edu ar X iv :1 80 5. 03 74 4v 2 [ st at .M E ] 7 J an 2 01 9