We compare the classes of empirical Bayes and composite estimators of the population means of the districts (small areas) of a country and show that the commonly adopted modelling strategy of searching for a well-fitting random coefficient (two-level) model and using it for estimation of the district-level means can be ineffective. In particular, we show that variables with small district-level variation are not useful as covariates even when they are strong predictors of the target variable.
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