  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.
