Synthetic Area Weighting for Measuring Public Opinion in Small Areas.

The comparison of subnational areas is ubiquitous but survey samples of these areas are often biased or prohibitively small. Researchers turn to methods such as multilevel regression and poststratification (MRP) to improve the efficiency of estimates by partially pooling data across areas via random effects. However, the random effect approach can pool observations only through area-level aggregates. We instead propose a weighting estimator, the synthetic area estimator, which weights on variables measured only in the survey to partially pool observations individually. The proposed method consists of two-step weighting: first to adjust differences across areas and then to adjust for differences between the sample and population. Unlike MRP, our estimator can directly use the national weights that are often estimated from pollsters using proprietary information. Our approach also clarifies the assumptions needed for valid partial pooling, without imposing an outcome model. We apply the proposed method to estimate the support for immigration policies at the congressional district level in Florida. Our empirical results show that small area estimation models with insufficient covariates can mask opinion heterogeneities across districts.