Model-based small area estimation with no samples within the areas, by benchmarking to marginal cross-sectional and time-series estimates

Official monthly U.S. labour force estimation at the sub-State level (mostly counties) is based on what is known as the ‘Handbook’ (HB) method, one of the earliest uses of administrative data for small area estimation. The administrative data, however, are poor in coverage and have conceptual deficiencies. Past attempts to correct for the resulting bias of the HB estimates by informal (implicit) modelling have not been successful, due to the absence of regular direct monthly survey estimates at the sub-State level. Benchmarking the sub-State HB estimates each month to the State model dependent estimates helps to correct for an overall bias, but not in individual areas. In this article we propose benchmarking additionally to the annual model-dependent area estimates. The annual models include known administrative data as covariates, and are used to define corresponding monthly sub-State models, which in turn enable producing monthly synthetic estimates as possible substitutes for the HB estimates in real time production. Variance estimates, which account for sampling errors and the errors of the model dependent estimators are developed. Data for sub-State areas in the State of Arizona are used for illustration. Although the methodology developed in this article stems from a particular (but very important) application, it is general and applicable to other similar problems.