This paper deals with small area estimation of labour force characteristics like totals of employed, unemployed and inactive people and unemployment rates. Small area estimators of these quantities are derived from a multinomial logit mixed model with independent random effects on the categories of the response vector. The mean squared errors are estimated both by explicit formulas and by bootstrap methods. Two simulation experiments designed to analyze the behaviour of the introduced estimators have been carried out. Finally, an application to real data from the Spanish Labour Force Survey of Galicia is given.

The aim of the paper is the estimation of small area labour force indicators like totals of employed and unemployed people and unemployment rates. Small area estimators of these quantities are derived from four multinomial logit mixed models, including a model with correlated time and area random effects. Mean-squared errors are used to measure the accuracy of the estimators proposed and they are estimated by analytic and bootstrap methods. The methodology introduced is applied to real data from the Spanish Labour Force Survey of Galicia.

This paper introduces area-level compositional mixed models by applying transformations to a multivariate Fay–Herriot model. Small area estimators of the proportions of the categories of a classification variable are derived from the new model, and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyse the behaviour of the introduced estimators are carried out. An application to real data from the Spanish Labour Force Survey of Galicia (north-west of Spain), in the first quarter of 2017, is given. The target is the estimation of domain proportions of people in the four categories of the variable labour status: under 16 years, employed, unemployed and inactive.

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