Nonparametric IV regression with an Archimedean dependence structure

Abstract

This paper provides a characterization of the completeness of a family of distributions in terms of the copula between the random variables. We give sufficient conditions for a family of Archimedean copulas to be (boundedly) complete. Some copulas are typically excluded in nonparametric IV regression since they have non-square integrable densities. We provide conditions under which we can identify the nonparametric IV regression model if the dependence structure between the regressors and instrument variables can be described by an Archimedean copula.