Open AccessThe discretization filter: A simple way to estimate nonlinear state space models
Author(s) -
Farmer Leland E.
Publication year - 2021
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe1353
Subject(s) - discretization , nonlinear system , estimator , nonlinear filter , mathematics , upper and lower bounds , filter (signal processing) , gaussian , zero lower bound , state space , decoupling (probability) , computer science , mathematical optimization , interest rate , mathematical analysis , filter design , statistics , economics , physics , quantum mechanics , control engineering , monetary economics , computer vision , engineering
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.