Marijuana and Tobacco Consumption in Colombia: A Bayesian Zero-Inflated Ordered Probit Under Submission

Abstract

This paper develops a Bayesian implementation of the zero-inflated ordered probit model introduced in Harris and Zhao (2007), providing a broad replication of the frequentist method and extending the original paper with a Bayesian implementation. Posterior distributions naturally propagate parameter uncertainty to non-linear quantities of interest—participation, consumption intensity, and associated marginal effects—without relying on asymptotic approximations such as the delta method. Performance is assessed through Monte Carlo experiments compared against maximum likelihood estimation, with empirical applications to marijuana and tobacco consumption in Colombia. Results confirm the Bayesian approach reproduces original substantive findings while providing a coherent framework for structural inference.