Approximation bias in linearized Euler equations

Sydney Ludvigson, Christina H. Paxson

    Research output: Contribution to journalArticle

    Abstract

    A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from linear regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental-variables methods that are commonly used to estimate the parameters correct some, but not all, of the approximation bias.

    Original languageEnglish (US)
    Pages (from-to)242-256
    Number of pages15
    JournalReview of Economics and Statistics
    Volume83
    Issue number2
    DOIs
    StatePublished - May 2001

    Fingerprint

    trend
    uncertainty
    saving behavior
    Consumption growth
    Euler equations
    Bias approximation
    regression
    Coefficients
    Uncertainty
    Prudence
    evidence
    Approximation
    literature

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Social Sciences (miscellaneous)

    Cite this

    Approximation bias in linearized Euler equations. / Ludvigson, Sydney; Paxson, Christina H.

    In: Review of Economics and Statistics, Vol. 83, No. 2, 05.2001, p. 242-256.

    Research output: Contribution to journalArticle

    Ludvigson, Sydney ; Paxson, Christina H. / Approximation bias in linearized Euler equations. In: Review of Economics and Statistics. 2001 ; Vol. 83, No. 2. pp. 242-256.
    @article{40494eb126f844918caa3f67ca9a0a3b,
    title = "Approximation bias in linearized Euler equations",
    abstract = "A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from linear regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental-variables methods that are commonly used to estimate the parameters correct some, but not all, of the approximation bias.",
    author = "Sydney Ludvigson and Paxson, {Christina H.}",
    year = "2001",
    month = "5",
    doi = "10.1162/00346530151143789",
    language = "English (US)",
    volume = "83",
    pages = "242--256",
    journal = "Review of Economics and Statistics",
    issn = "0034-6535",
    publisher = "MIT Press Journals",
    number = "2",

    }

    TY - JOUR

    T1 - Approximation bias in linearized Euler equations

    AU - Ludvigson, Sydney

    AU - Paxson, Christina H.

    PY - 2001/5

    Y1 - 2001/5

    N2 - A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from linear regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental-variables methods that are commonly used to estimate the parameters correct some, but not all, of the approximation bias.

    AB - A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from linear regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental-variables methods that are commonly used to estimate the parameters correct some, but not all, of the approximation bias.

    UR - http://www.scopus.com/inward/record.url?scp=0035590515&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0035590515&partnerID=8YFLogxK

    U2 - 10.1162/00346530151143789

    DO - 10.1162/00346530151143789

    M3 - Article

    AN - SCOPUS:0035590515

    VL - 83

    SP - 242

    EP - 256

    JO - Review of Economics and Statistics

    JF - Review of Economics and Statistics

    SN - 0034-6535

    IS - 2

    ER -