Hidden Markov models and their applications to estimation, forecasting and policy analysis in panel data settings

This dissertation proposes modelling procedures for the joint distribution of a high dimensional vector of discrete variables and of its evolution over time. This work is motivated by problems arising in the use of panel survey data to forecast the simultaneous behavior of certain characteristics of a population.;The models proposed fall under the general classification of Hidden Markov Models (HMM). A dimension reduction of chosen groups of variables is performed, which are each represented by a latent variable whose dynamics is modelled. This combines features of multiple indicator-multiple cause (MIMIC) and LISREL factor-analytic models in the sense that some interpretable structure is imposed on the relations between a given number of latent variables that generate the observations with features of filtering algorithms like the Kalman filter which are used to estimate the dynamic component of the latent variables. Estimation does not require use of simulation to perform numerical integration and can also incorporate directly missing observations hence removing the need for separate imputation procedures. Several specification tests are also discussed.;The methodology developed is applied to analyze the evolution of health conditions over an 8 year period of the HRS population and the effects of availability of Medicare insurance on the dynamics of health.