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

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 nonlinea...

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Bibliographic Details
Published in:Quantitative economics Vol. 12; no. 1; pp. 41 - 76
Main Author: Farmer, Leland E
Format: Journal Article
Language:English
Published: New Haven, CT The Econometric Society 2021
John Wiley & Sons, Inc
Subjects:
Algorithms
Analysis
Approximation
C11
C13
discretization
DSGE models
Dynamic models
E40
E50
Econometrics
Federal Reserve monetary policy
Inflation
Interest rates
Markov analysis
Methods
Monetary policy
Nonlinear analysis
Nonlinear filtering
Phillips curve
Quantitative analysis
regime switching
Simplicity
Simulation methods
state space models
Stochastic models
Volatility
zero lower bound
ISSN:1759-7331, 1759-7323, 1759-7331
Online Access:Get full text
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Summary: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.
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ISSN:1759-7331
1759-7323
1759-7331
DOI:10.3982/QE1353