Nonparametric Stochastic Discount Factor Decomposition

Timothy M. Christensen

    Research output: Contribution to journalArticlepeer-review


    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) construct 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.

    Original languageEnglish (US)
    Pages (from-to)1501-1536
    Number of pages36
    Issue number5
    StatePublished - Sep 2017


    • Nonparametric estimation
    • nonparametric value function estimation
    • permanent-transitory decomposition
    • sieve estimation
    • stochastic discount factor

    ASJC Scopus subject areas

    • Economics and Econometrics


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