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 econometric methods to extract the permanent and transitory components of the SDF process. We show how to estimate  the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009) using data on the Markov state and the SDF process. Estimating directly the eigenvalue and eigenfunction allows one to (1) construct empirically the time series of the  permanent and transitory components of the SDF process and (2 ) estimate the yield and the change of measure which characterize pricing over long investment horizons. The methodology is nonparametric , i.e., it does not impose any tight parametric restrictions on the dynamics of the state variables and the SDF process. We derive the large-sample properties of the estimators and illustrate favorable performance in simulations. The methodology is applied to study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.
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.
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econometric methods to extract the permanent and transitory components of the SDF process. We
an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we
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using data on the Markov state and the SDF process. Estimating directly the eigenvalue and eigenfunction allows one to (1) construct empirically
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of the SDF process and (2
and (ii
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The methodology is nonparametric , i.e., it does not impose any tight parametric restrictions on the dynamics of the state variables and the SDF process. We derive the large-sample properties of the estimators and illustrate favorable performance in simulations. The methodology is applied to
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