Mixed Density based Copula Likelihood

We consider a new copula method for mixed marginals of discrete and continuous random variables. Unlike the Bayesian methods in the literature, we use maximum likelihood estimation based on closed-form copula functions. We show with a simulation that our methodology performs similar to the method of Hoff (2007) for mixed data, but is considerably simpler to estimate. We extend to a time series setting, where the parameters are allowed to vary over time. In an empirical application using data from the 2013 Household Finance Survey, we show how the copula dependence between income (continuous) and discrete household characteristics varies across groups who were affected differently by the recent economic crisis.