Modelling Sample Selection Using Copulas

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to modelling proceeds by specifying distributions for each margin, and a copula function. In this article, a number of copula functions are given, with attention focusing on members of the Archimedean class. This class of copulas is shown to be su¢ciently rich in regard to permitting various distributional attributes as may be desired when modelling. The article then proceeds by applying the copula approach to construct models for data that may su¤er from sample selection. When Archimedean copulas are used, expressions are obtained for the log-likelihood and score that facilitate maximum likelihood estimation. The literature on selection models is almost exclusively based on multivariate normal speci...cations. Consequently, the extension to multivariate non-normality made possible by adopting a copula approach, contributes a new source of modelling technique to the practitioner’s toolkit. Examples of self-selection models for labour supply, and for the duration of hospitalisation, illustrate the application of the copula approach to modelling.