Title

-Complete and Boundedly-Complete Distributions

Document Type

Discussion Paper

Publication Date

5-1-2011

CFDP Number

1801

CFDP 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 L 2 -completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L 2 -complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L 2 -incomplete distributions also are provided.

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