Efficient Bayesian estimation for flexible panel models for multivariate outcomes: Impact of life events on mental health and excessive alcohol consumption

The problem we consider considers estimating a multivariate longitudinal panel data model whose outcomes can be a combination of discrete and continuous variables. This problem is challenging because the likelihood is usually analytically intractable. Our article makes both a methodological contribution and also a substantive contribution to the application. The methodological contribution is to introduce into the panel data literature a particle Metropolis within Gibbs method to carry out Bayesian inference, using a Hamiltonian Monte Carlo (Neal 2011} proposal for sampling the vector of unknown parameters. We note that in panel data models the Our second contribution is to apply our method to carry out a serious analysis of the impact of serious life events on mental health and excessive alcohol consumption. The dependence between these two outcomes may be more pronounced when consumption of alcohol is excessive and mental health poor, which in turn has implications for how life events impact the joint distribution of the outcomes.