Estimating Euler Equations

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 Montecarlo
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 heteroscedasticity 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 nonlinear 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.
(Copyright: Elsevier)