On benchmarking small area estimators when the model is misspecified

One of the main motivations of concern when we apply a small area es- timation model is to relate individual area estimates with some direct estimates in a larger area. External and internal benchmarked estima- tors provide adjusted model-based estimates, in order to agree with that aggregated results. The use of multiple calibration quantities in the bench- marking matrix suggests that the underlying “true” model is misspecified by the actual model equation. We examine the appropriateness of em- ploying the benchmarking matrix to account for omitted variables in the model, through an additional regression term.