Smoothly Mixing Regressions

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing MCMC algorithm provides access to the posterior distribution at modest computational cost. This model is competitive with existing econometric models, as documented in the paper’s illustrations. The first illustration studies quantiles of the distribution of earnings of men conditional on age and education, and shows that smoothly mixing regressions are an attractive alternative to non-Baeysian quantile regression. The second illustration models serial dependence in the S&P 500 return, and shows that the model compares favorably with ARCH models using out of sample likelihood criteria. Acknowledgement 1 Both authors acknowledge financial support from grant R01-HD37060-01, National Institutes of Health, and the first author acknowledges financial support from grants SBR-9819444 and SBR-0214303, National Science Foundation. We thank two referees, Giovanni Amisano, Justin Tobias, and participants in seminars at Brescia University, Iowa State University, University of Iowa, and University of Rome for helpful comments on previous versions of this work. Responsibility for any errors remains with the authors.