ABSTRACT
This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density of the observations with respect to a mixed measure. The treatment is quite general, although we focus on mixtures of Gaussian and Archimedean copulas. The inference is Bayesian with the estimation carried out by Markov chain Monte Carlo. We illustrate the methodology and algorithms by applying them to estimate a multivariate income dynamics model. Supplementary materials for this article are available online.
SUPPLEMENTARY MATERIALS
There is an online supplement for our article that contains the following: Section S1 gives the density, conditional distribution function, and MCMC sampling methods for the Gaussian, Gumbel and Clayton copulas. Section S2 contains a trivariate example to illustrate the methodology. Section S3 provides the proof of Lemma 3. Section S4 provides some additional empirical results.
ACKNOWLEDGEMENTS
The authors thank two anonymous referees and the associate editor for suggestions that helped improve the clarity of the article.