We consider the recent novel two-step estimator of Iaryczower and Shum (American Economic Review 2012; 102: 202-237), who analyze voting decisions of US Supreme Court justices. Motivated by the underlying theoretical voting model, we suggest that where the data under consideration display variation in the common prior, estimates of the structural parameters based on their methodology should generally benefit from including interaction terms between individual and time covariates in the first stage whenever there is individual heterogeneity in expertise. We show numerically, via simulation and re-estimation of the US Supreme Court data, that the first-order interaction effects that appear in the theoretical model can have an important empirical implication.
