  This study aims to analyze the methodologies that can be used to estimate the
total number of unemployed, as well as the unemployment rates for 28 regions of
Portugal, designated as NUTS III regions, using model based approaches as
compared to the direct estimation methods currently employed by INE (National
Statistical Institute of Portugal). Model based methods, often known as small
area estimation methods (Rao, 2003), "borrow strength" from neighbouring
regions and in doing so, aim to compensate for the small sample sizes often
observed in these areas. Consequently, it is generally accepted that model
based methods tend to produce estimates which have lesser variation. Other
benefit in employing model based methods is the possibility of including
auxiliary information in the form of variables of interest and latent random
structures. This study focuses on the application of Bayesian hierarchical
models to the Portuguese Labor Force Survey data from the 1st quarter of 2011
to the 4th quarter of 2013. Three different data modeling strategies are
considered and compared: Modeling of the total unemployed through Poisson,
Binomial and Negative Binomial models; modeling of rates using a Beta model;
and modeling of the three states of the labor market (employed, unemployed and
inactive) by a Multinomial model. The implementation of these models is based
on the \textit{Integrated Nested Laplace Approximation} (INLA) approach, except
for the Multinomial model which is implemented based on the method of Monte
Carlo Markov Chain (MCMC). Finally, a comparison of the performance of these
models, as well as the comparison of the results with those obtained by direct
estimation methods at NUTS III level are given.
