Nonparametric identification of positive eigenfunctions

TL;DR

This paper establishes nonparametric identification conditions for positive eigenfunctions of linear operators, crucial for analyzing economic models like asset pricing and habit formation, under mild positivity and compactness assumptions.

Contribution

It provides new identification conditions for positive eigenfunctions in nonparametric models, extending analysis in economic models such as asset pricing and habit formation.

Findings

Identification achieved under mild positivity and compactness conditions.

New conditions for external habit formation models.

Application to positive eigenfunctions in dynamic asset pricing.

Abstract

Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk-return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions and a power compactness condition. Both existence and identification are achieved under a further non-degeneracy condition. The general results are applied to obtain new identification conditions for external habit formation models and for positive eigenfunctions of pricing operators in dynamic asset pricing models.