Bayesian Estimation of Non-Stationary Markov Models Combining Micro and Macro Data

We develop a Bayesian framework for estimating non-stationary Markov models in situations where macro population data is available only on the proportion of individuals residing in each state, but micro-level sample data is available on observed transitions between states. Posterior distributions on non-stationary transition probabilities are derived from a micro-based prior and a macro-based likelihood using potentially asynchronous data observations, providing a new method for inferring transition probabilities that merges previously disparate approaches. Monte Carlo simulations demonstrate how observed micro transitions can improve the precision of posterior information. We provide an empirical application in the context of farm structural change.