Mean field variational Bayes for finite mixture of random coefficients models: an application to healthcare expenditures

We develop a Markov Chain Monte Carlo (MCMC) estimator for a finite mixture random coefficients model for unbalanced panels, allowing for flexible unobserved heterogeneity through discrete latent types. We then consider a mean field variational Bayes (MFVB) approximation that achieves substantial computational gains without compromising estimation accuracy. We derive the associated predictive densities, which take the form of mixtures of non standard t-distributions, and evaluate finite-sample performance through Monte Carlo simulations. An application to healthcare expenditures in the United States using the RAND HRS panel over the period 1994–2020 shows that marginal responses vary markedly both across and within latent groups – patterns that standard estimators are intrinsically incapable of recovering.