Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods

39 Pages Posted: 20 Mar 2012

See all articles by Joshua C. C. Chan

Joshua C. C. Chan

University of Technology Sydney (UTS) - UTS Business School; Purdue University

Rodney W. Strachan

University of Queensland - School of Economics

Date Written: March 2012

Abstract

In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macro-economic and financial data. However, many heoretically motivated models imply non-linear or non-Gaussian specifications – or both. Existing methods for estimating such models are computationally intensive, and often cannot be applied to models with more than a few states. Building upon recent developments in precision-based algorithms, we propose a general approach to estimating high-dimensional non-linear non-Gaussian state space models. The baseline algorithm approximates the conditional distribution of the states by a multivariate Gaussian or t density, which is then used for posterior simulation. We further develop this baseline algorithm to construct more sophisticated samplers with attractive properties: on based on the accept-reject Metropolis-Hastings (ARHM) algorithm, and another adaptive collapsed sampler inspired by the cross-entropy method. To illustrate the proposed approach, we investigate the effect of the zero lower bound of interest rate on monetary transmission mechanism.

Keywords: integrated likelihood, accept-reject Metropolis-Hastings, cross-entropy, liquidity trap, zero lower bound

Suggested Citation

Chan, Joshua C. C. and Strachan, Rodney W., Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods (March 2012). Available at SSRN: https://ssrn.com/abstract=2025754 or http://dx.doi.org/10.2139/ssrn.2025754

Joshua C. C. Chan (Contact Author)

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

Purdue University

West Lafayette, IN 47907-1310
United States

Rodney W. Strachan

University of Queensland - School of Economics ( email )

Brisbane, QLD 4072
Australia

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