Effects of marginal specifications on copula estimation

This paper studies the effect of marginal distributions on a copula, in the case of mixed discrete-continuous random variables. The existing literature has proposed various methods to deal with mixed marginals: this paper is the first to quantify their effect in a unified Bayesian setting. Using order statistics based information for the marginals, as proposed by Ho (2007), we find that in small samples the bias and mean square error are at least half in size as compared to those of empirical or misspecified marginal distributions. The difference in the bias and mean square error enlarges with increasing sample size, especially for low count discrete variables. We employ the order statistics method on firm-level patents data, containing both discrete and continuous random variables, and consistently estimate their correlation