  Multilevel regression and poststratification (MRP) is a flexible modeling
technique that has been used in a broad range of small-area estimation
problems. Traditionally, MRP studies have been focused on non-causal settings,
where estimating a single population value using a nonrepresentative sample was
of primary interest. In this manuscript, MRP-style estimators will be evaluated
in an experimental causal inference setting. We simulate a large-scale
randomized control trial with a stratified cluster sampling design, and compare
traditional and nonparametric treatment effect estimation methods with MRP
methodology. Using MRP-style estimators, treatment effect estimates for areas
as small as 1.3$\%$ of the population have lower bias and variance than
standard causal inference methods, even in the presence of treatment effect
heterogeneity. The design of our simulation studies also requires us to build
upon a MRP variant that allows for non-census covariates to be incorporated
into poststratification.
