A dynamic inhomogeneous latent state model for measuring material deprivation

Material deprivation can be used to assess poverty in a society. The status of poverty is not directly observable, but it can be measured with error for instance through a list of deprivation items. Given two unobservable classes, corresponding to poor and not poor, we develop a time inhomogeneous latent Markov model which enables us to classify households according to their current and intertemporal poverty status, and to identify transitions between classes that may occur year by year. Households are grouped by estimating their posterior probability of belonging to the latent status of poverty. We then estimate an optimal weighting scheme, associated with the list of items, to obtain an optimal deprivation score. Our score is arguably better at predicting the poverty status than simple item counting (equal weighting). We use the longitudinal component of the European Union statistics Survey on Income and Living Conditions for evaluating poverty patterns over the period 2010-2013 in Greece, Italy and the UK.