Approximation Bias in Linearized Euler Equations
通过数值求解标准跨期优化问题，发现线性近似下预期消费增长与不确定性之间的关系与实际关系差异很大，并利用蒙特卡洛证据表明常用工具变量法只能部分纠正近似偏差。
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. © 2001 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology