Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)
This paper shows that standard empirical methods for estimating log-linearized consumption Euler equations cannot successfully uncover structural parameters like the coefficient of relative risk aversion from the dataset of simulated consumers behaving exactly according to the standard model. Furthermore, consumption growth for the simulated consumers is very highly statistically related to predictable income growth - and thus standard 'excess sensitivity' tests would reject the hypothesis that consumers are behaving according to the standard model. Results are not much better for the second-order approximation to the Euler equation. The paper concludes that empirical estimation of consumption Euler equations should not be abandoned, and discusses some alternative empirical strategies that are not subject to the problems of Euler equation estimation.