Modeling Sample Selection: A Copula Approach

• Activity Number: 171
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Business & Economics Statistics Section
• Author(s): Murray Donald Smith*+
• Companies: University of Sydney
• Keywords: Sample selection ; double-selection ; copulas ; copula approach ; Archimedean

Abstract

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 statistical modeling proceeds by specifying distributions for each margin and a copula function. In this article, a number of families of copula functions are given, with attention on those that fall within the Archimedean class. Members of this class of copulas are shown to be rich in various distributional attributes that are desired when modeling. The article then proceeds by applying the copula approach to the particular case of the double-selection model. When copulas from the Archimedean class are used, the resulting expressions for the double-selection log-likelihood and score functions facilitate maximum likelihood estimation. The literature on double-selection models is almost exclusively based on multivariate normal specifications (this can be said of the wider literature on many types of sample selection models). What the copula approach facilitates is model construction based on multivariate non-normality.