Clustering and External Validity in Randomized Controlled Trials

TL;DR

This paper extends the analysis of randomized controlled trials by incorporating stochastic shocks at individual and cluster levels, providing methods for valid inference on the average treatment effect under these conditions.

Contribution

It introduces a framework for inference in RCTs accounting for stochastic shocks, using heteroskedasticity-robust and cluster-robust standard errors.

Findings

Inference on ATE conditional on cluster shocks is possible.

Inference on ATE net of shocks can be conducted with cluster-robust errors.

The methods improve validity of RCT analysis under realistic stochastic conditions.

Abstract

The randomization inference literature studying randomized controlled trials (RCTs) assumes that units' potential outcomes are deterministic. This assumption is unlikely to hold, as stochastic shocks may take place during the experiment. In this paper, we consider the case of an RCT with individual-level treatment assignment, and we allow for individual-level and cluster-level (e.g. village-level) shocks. We show that one can draw inference on the ATE conditional on the realizations of the cluster-level shocks, using heteroskedasticity-robust standard errors, or on the ATE netted out of those shocks, using cluster-robust standard errors.