### 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 language | English (US) |
---|---|

Pages (from-to) | 242-256 |

Number of pages | 15 |

Journal | Review of Economics and Statistics |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - May 2001 |

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### ASJC Scopus subject areas

- Economics and Econometrics
- Social Sciences (miscellaneous)

### Cite this

*Review of Economics and Statistics*,

*83*(2), 242-256. https://doi.org/10.1162/00346530151143789

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

Research output: Contribution to journal › Article

*Review of Economics and Statistics*, vol. 83, no. 2, pp. 242-256. https://doi.org/10.1162/00346530151143789

}

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 -