The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models

71 Pages Posted: 17 May 2016 Last revised: 29 Apr 2020

Date Written: April 20, 2020


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 data.

Keywords: State Space, Nonlinear, Markov Chains, Discretization, Filtering, Zero Lower Bound

JEL Classification: C11, C13, C32, C51, E43, E44

Suggested Citation

Farmer, Leland, The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models (April 20, 2020). Available at SSRN: or

Leland Farmer (Contact Author)

University of Virginia ( email )

237 Monroe Hall
P.O. Box 400182
Charlottesville, VA 22904-418
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics