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

  • Chan, Joshua
  • Strachan, Rodney

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 theoretically 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: one based on the accept-reject Metropolis-Hastings (ARMH) 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.

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File URL: http://mpra.ub.uni-muenchen.de/39360/1/MPRA_paper_39360.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39360.

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Date of creation: 2012
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Handle: RePEc:pra:mprapa:39360
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  1. Neil Shephard & Thomas Flury, 2008. "Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models," Economics Series Working Papers 413, University of Oxford, Department of Economics.
  2. Iwata, Shigeru & Wu, Shu, 2006. "Estimating monetary policy effects when interest rates are close to zero," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1395-1408, October.
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  10. Reifschneider, David & Willams, John C, 2000. "Three Lessons for Monetary Policy in a Low-Inflation Era," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(4), pages 936-66, November.
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  15. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
  16. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
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