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Estimating Euler Equations

Authors: Orazio P. Attanasio; Hamish Low;

Estimating Euler Equations

Abstract

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of the preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the log-linearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Monte Carlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroskedasticity in the process generating income. The only exception is when discount rates are very high (e.g. 47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization and estimates using non-linear GMM are as bad. Across all our situations, estimation using a log-linearized Euler equation does better than nonlinear GMM. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted.

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Keywords

ddc:330, Schätztheorie, Gesamtwirtschaftlicher Konsum, Euler-Gleichung, Theorie, jel: jel:E2

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
95
Top 10%
Top 10%
Average
Green
bronze