Geographic disaggregation of household surveys. Modified estimators for correcting misclassification bias

We present a two-stage method to estimate spatial conditional means at a higher spatial resolution than the data actually have. In the first stage, we increase the spatial resolution of the data using classification tools and ancillary data. In the second stage, we estimate spatial conditional means (conditioning on the new spatial resolution). The estimation procedure in the second stage is not straightforward because the new finer spatial areas are subject to misclassification (measurement error). We prove that the least square (LS) estimators are biased under this framework and propose a consistent and asymptotically normal estimator under non-differential measurement errors. Given that the proposed estimator depends on unobservable terms, we also present its feasible version. Unlike most of the spatial downscaling methods, our proposal is non-model-based, and does not require area homogeneity assumptions. We assess analytical results by some Monte Carlo simulations, showing that our proposals work properly and outperform the spatial microsimulation approach. Finally, we conduct an empirical application where we analyse poverty and unemployment in one of the main urban agglomerates of Argentina known as Gran Rosario, we spatially disaggregate the original database to make inferences at a finer geographic scale.