Approximation Bias in Linearized Euler Equations

49 Pages Posted: 10 Jul 2000 Last revised: 24 Feb 2023

See all articles by Christina H. Paxson

Christina H. Paxson

Princeton University; National Bureau of Economic Research (NBER)

Sydney C. Ludvigson

New York University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: March 1999

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 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 commonly used to estimate the parameters correct some, but not all, of the approximation bias.

Suggested Citation

Paxson, Christina H. and Ludvigson, Sydney C., Approximation Bias in Linearized Euler Equations (March 1999). NBER Working Paper No. t0236, Available at SSRN: https://ssrn.com/abstract=226647

Christina H. Paxson

Princeton University ( email )

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Sydney C. Ludvigson (Contact Author)

New York University - Department of Economics ( email )

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