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

ABSTRACT

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.

KEYWORDS:

• Benchmarking
• Denton method
• mixed models
• variance estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Danny Pfeffermann

Danny Pfeffermann is the National Statistician and Head of the Central Bureau of Statistics of Israel. He is a Professor of Statistics at the Hebrew University of Jerusalem, Israel, and at the University of Southampton, UK. His main research areas are analytic inference from complex sample surveys, small area estimation, seasonal adjustment and trend estimation, non-ignorable nonresponse and more recently, mode effects and proxy surveys. He is the recipient of several prestigious awards, most recently the Julius Shiskin Award. When receiving this award, he gave a lecture which forms the basis for the present paper.

Michael Sverchkov

Michael Sverchkov is a Research Mathematical Statistician at the U.S. Bureau of Labor Statistics, Washington DC. His main research areas are analytic inference from complex sample surveys and in particular, informative samples with non-ignorable nonresponse, small area estimation and seasonal adjustment.

Richard Tiller

Richard Tiller is a Mathematical Statistician at the U.S. Bureau of Labor Statistics, Washington DC. His main research areas are small area estimation, with emphasis on problems related to modelling continuous survey series with complex sampling error correlation structure and strong seasonality. He also works on issues in seasonal adjustment.

Lizhi Liu

Lizhi Liu is a Mathematical Statistician at the U.S. Bureau of Labor Statistics, Washington DC. She works on developing statistical software for small area estimation research, as well as maintaining and improving Local Area Unemployment Statistics (LAUS). She also works on issues in seasonal adjustment.