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

Farmer, Leland

doi:10.2139/ssrn.2780166

Cited by 8 publications

(8 citation statements)

References 32 publications

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“…The proof of this second part, which makes arguments for

M \to normal∞

, is detailed in Propositions 1 and 2 and Lemmas 4 and 5. These results and their proofs can be found in Appendix A and Appendix D, respectively, available in the Online Supplementary Material and in the replication file (Farmer (2021)).…”

Section: Asymptotic Properties Of the Maximum Likelihood Estimatormentioning

confidence: 91%

“…This result represents a new contribution to the literature on discrete approximations of Markov chains with continuous valued states. All intermediate results and proofs can be found in Appendix E in the replication file (Farmer (2021)).…”

Section: Asymptotic Properties Of the Maximum Likelihood Estimatormentioning

confidence: 99%

“…1 Approximate the State Dynamics: Construct a discrete grid {x m M } M m=1 and its associated transition matrix P θ M using Algorithm 2 in Appendix B (Farmer (2021)) or any other method appropriate for the process X t being considered.…”

Section: Evaluating the Likelihoodmentioning

confidence: 99%

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

Farmer

2021

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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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“…The proof of this second part, which makes arguments for

M \to normal∞

Section: Asymptotic Properties Of the Maximum Likelihood Estimatormentioning

confidence: 91%

Section: Asymptotic Properties Of the Maximum Likelihood Estimatormentioning

confidence: 99%

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

Farmer

2021

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“…Our method can be used to solve a life cycle model with a realistic income process by matching the dynamics of these higher order moments. Our method can also be used for estimating nonlinear, non-Gaussian state space models (Farmer, 2016). In this paper we considered only tensor grids since our applications involved only one or two state variables.…”

Section: Me Methods Perturbationmentioning

confidence: 99%

“…For example, our method can be used to facilitate the estimation of nonlinear state space models. In parallel work, Farmer (2016) shows that by discretizing the dynamics of the state variables, one can construct an approximate state space model with closed-form expressions for the likelihood and filtering recursions, as in Hamilton (1989). The parameters of the model can then be estimated using standard likelihood or Bayesian techniques.…”

Section: Introductionmentioning

confidence: 99%

Discretizing nonlinear, non-Gaussian Markov processes with exact conditional moments

Farmer

Toda

2017

Quantitative Economics

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Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process. and seminar participants at Duke, McGill, UCSD, University of Technology Sydney, and the 2016 Computing in Economics and Finance Conference for helpful comments and feedback. We are especially grateful to four anonymous referees for constructive comments and suggestions that significantly improved the paper. Matlab codes are posted in a supplementary file on the journal website,

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Filtered likelihood for point processes

Giesecke

Schwenkler

2018

Journal of Econometrics

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

Cited by 8 publications

References 32 publications

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

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

Discretizing nonlinear, non-Gaussian Markov processes with exact conditional moments

Filtered likelihood for point processes

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