Expectile Regression for Multi-Category Outcomes with Application to Small Area Estimation of Labour Force Participation

Author:

Dawber James1,Salvati Nicola2,Fabrizi Enrico3,Tzavidis Nikos1

Affiliation:

1. Department of Social Statistics and Demography and Southampton Statistical Sciences Research Institute University of Southampton , Southampton , UK

2. Department of Economics and Management University of Pisa , Pisa , Italy

3. DISES and DSS Università Cattolica del S. Cuore , Milan , Italy

Abstract

Abstract In many applications of small area estimation, dichotomous or categorical outcomes are the targets of statistical inference. For example, in the analysis of labour markets, proportions of working-age people in the various labour market statuses are of interest. In this paper, in line with the recent literature, we consider a classification with more than three statuses and estimate related population parameters for 611 local labour market areas using data from the 2012 Italian Labour Force Survey, administrative registers and the 2011 Census. As for the methodology, we propose multinomial expectile regression models. These models provide a means to utilise M-quantile type approaches, which have been shown to be a useful alternative to mixed model approaches when parametric assumptions on the distribution of random effects cannot be met. Via a large-scale simulation study, we show how this novel approach is much faster and provides reliable results when compared to multinomial mixed model approaches, and works for any number of categories rather than just a small number of categories as is more commonly the case with existing methods. Furthermore, the proposed approach potentially provides a framework for developing other methods for prediction with multi-category outcomes.

Publisher

Oxford University Press (OUP)

Subject

Statistics, Probability and Uncertainty,Economics and Econometrics,Social Sciences (miscellaneous),Statistics and Probability

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