Multi-source inference via mixture of hidden Markov models: application to regional labour statistics in Italy

Abstract The increased availability of a large amount of administrative information suggests investigating new methodological approaches for the production of estimates, based on integrating and combining administrative and statistical survey data. We show how latent variable models can be used for estimating employment proportions in the Italian regions using survey and administrative data, taking into account the deficiencies in the corresponding measurement process and the longitudinal structure of the data. To this purpose, we adopt a mixture of hidden Markov models, a longitudinal extension of latent class analysis; in the model specification, we consider covariates and unobserved heterogeneity of the latent process among the units of the population. The mixture of hidden Markov model is used to evaluate the accuracy of the available administrative sources, to define their use in the statistical production, and to produce statistics on employment status at both regional and national levels of aggregation of the entire population.