Nonparametric Stochastic Discount Factor Decomposition

Timothy Christensen

    Research output: Contribution to journalArticle

    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) 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
    JournalEconometrica
    Volume85
    Issue number5
    DOIs
    StatePublished - Sep 1 2017

    Fingerprint

    Estimator
    Stochastic discount factor
    Decomposition
    Recursive preferences
    Permanent-transitory decomposition
    Pricing
    Investment horizon
    Value function
    Asymptotic normality
    Eigenvalues
    Consumption growth
    Permanent component
    Rate of convergence
    Permanent and transitory components
    Change of measure
    Recursion
    Representative agent
    Earnings growth

    Keywords

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

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    Nonparametric Stochastic Discount Factor Decomposition. / Christensen, Timothy.

    In: Econometrica, Vol. 85, No. 5, 01.09.2017, p. 1501-1536.

    Research output: Contribution to journalArticle

    Christensen, Timothy. / Nonparametric Stochastic Discount Factor Decomposition. In: Econometrica. 2017 ; Vol. 85, No. 5. pp. 1501-1536.
    @article{42f7d9515fad4e948fc4382e3ac4a4b2,
    title = "Nonparametric Stochastic Discount Factor Decomposition",
    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) 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.",
    keywords = "Nonparametric estimation, nonparametric value function estimation, permanent-transitory decomposition, sieve estimation, stochastic discount factor",
    author = "Timothy Christensen",
    year = "2017",
    month = "9",
    day = "1",
    doi = "10.3982/ECTA11600",
    language = "English (US)",
    volume = "85",
    pages = "1501--1536",
    journal = "Econometrica",
    issn = "0012-9682",
    publisher = "Wiley-Blackwell",
    number = "5",

    }

    TY - JOUR

    T1 - Nonparametric Stochastic Discount Factor Decomposition

    AU - Christensen, Timothy

    PY - 2017/9/1

    Y1 - 2017/9/1

    N2 - 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.

    AB - 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.

    KW - Nonparametric estimation

    KW - nonparametric value function estimation

    KW - permanent-transitory decomposition

    KW - sieve estimation

    KW - stochastic discount factor

    UR - http://www.scopus.com/inward/record.url?scp=85030311940&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85030311940&partnerID=8YFLogxK

    U2 - 10.3982/ECTA11600

    DO - 10.3982/ECTA11600

    M3 - Article

    AN - SCOPUS:85030311940

    VL - 85

    SP - 1501

    EP - 1536

    JO - Econometrica

    JF - Econometrica

    SN - 0012-9682

    IS - 5

    ER -