CFDP 1801

Examples of L 2 -Complete and Boundedly-Complete Distributions

Publication Date: May 2011

Pages: 25

Abstract: 

Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce.

In this paper, we consider an L²-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L²-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L²-incomplete distributions also are provided.

Keywords: 

Bivariate distribution, Bounded completeness, Canonical correlation, Completeness, Identification, Measurement error, Nonparametric instrumental variable regression

JEL Classification Codes:  C14