Nonparametric Stochastic Discount Factor Decomposition

TL;DR

This paper develops a nonparametric empirical framework to decompose stochastic discount factors into permanent and transitory parts, enabling analysis of long-term asset pricing and recursive preferences.

Contribution

It introduces nonparametric estimation methods for the Perron-Frobenius eigenfunction problem in SDF analysis, with theoretical guarantees and practical applications.

Findings

Consistent nonparametric estimators for eigenfunctions and eigenvalues.

Empirical recovery of permanent and transitory SDF components.

Application to recursive preferences with nonlinear growth dynamics.

Abstract

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework allows researchers to (i) recover the time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron-Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.