The discretization filter: A simple way to estimate nonlinear state space models

• 成果类型: Article
• 署名作者: Farmer, Leland E.
• 署名单位: University of Virginia
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1353
• 发表日期: 2021
• 页码: 41-76
• 关键词: Nonlinear filtering; Discretization; regime switching; state space models; DSGE models; zero lower bound

摘要

Existing methods for estimating nonlinear dynamic models are either highly computationally costly or rely on local approximations which often fail adequately to capture the nonlinear features of interest. I develop a new method, the discretization filter, for approximating the likelihood of nonlinear, non-Gaussian state space models. I establish that the associated maximum likelihood estimator is strongly consistent, asymptotically normal, and asymptotically efficient. Through simulations, I show that the discretization filter is orders of magnitude faster than alternative nonlinear techniques for the same level of approximation error in low-dimensional settings and I provide practical guidelines for applied researchers. It is my hope that the method's simplicity will make the quantitative study of nonlinear models easier for and more accessible to applied researchers. I apply my approach to estimate a New Keynesian model with a zero lower bound on the nominal interest rate. After accounting for the zero lower bound, I find that the slope of the Phillips Curve is 0.076, which is less than 1/3 of typical estimates from linearized models. This suggests a strong decoupling of inflation from the output gap and larger real effects of unanticipated changes in interest rates in post Great Recession.