A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identified choice for these vectors). In previous work, such priors have been found to greatly complicate computation. In this article, we develop algorithms to carry out efficient posterior simulation in cointegration models. In particular, we develop a collapsed Gibbs sampling algorithm which can be used with just-identifed models and demonstrate that it has very large computational advantages relative to existing approaches. For over-identifed models, we develop a parameter-augmented Gibbs sampling algorithm and demonstrate that it also has attractive computational properties.

Background: Vietnam is undergoing a fast-aging process that poses potential critical issues for older people and central among those is demand for healthcare utilization. However, healthcare utilization, here measured as count data, creates challenges for modeling because such data typically has distributions that are skewed with a large mass at zero. This study compares empirical econometric strategies for the modeling of healthcare utilization (measured as the number of outpatient visits in the last 12 months) and identifies the determinants of healthcare utilization among Vietnamese older people based on the best-fitting model identified.Methods: Using the Vietnam Household Living Standard Survey in 2006 (N = 2426), nine econometric regression models for count data were examined to identify the best-fitting one. We used model selection criteria, statistical tests and goodness-of-fit for in-sample model selection. In addition, we conducted 10-fold cross-validation checks to examine reliability of the in-sample model selection. Finally, we utilized marginal effects to identify the factors associated with the number of outpatient visits among Vietnamese older people based on the best-fitting model identified.Results: We found strong evidence in favor of hurdle negative binomial model 2 (HNB2) for both in-sample selection and 10-fold cross-validation checks. The marginal effect results of the HNB2 showed that ethnicity, region, household size, health insurance, smoking status, non-communicable diseases, and disability were significantly associated with the number of outpatient visits. The predicted probabilities for each count event revealed the distinct trends of healthcare utilization among specific groups: at low count events, women and people in the younger age group used more healthcare utilization than did men and their counterparts in older age groups, but a reverse trend was found at higher count events.Conclusions: The high degree of skewness and dispersion that typically characterizes healthcare utilization data affects the appropriateness of the econometric models that should be used in modeling such data. In the case of Vietnamese older people, our study findings suggest that hurdle negative binomial models should be used in the modeling of healthcare utilization given that the data-generating process reflects two different decision-making processes.

This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma stochastic volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse gamma and generalized inverse gamma processes can greatly outperform the commonly used log normal volatility processes with Student’s t errors or jumps in the mean equation.