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

Abstract

In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macroeconomic and …nancial data. However, many theoretically motivated models imply non-linear or non-Gaussian speci…cations -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 acceptreject Metropolis-Hastings (ARMH) algorithm, and another adaptive collapsed sampler inspired by the cross-entropy method. To illustrate the proposed approach, we investigate the e¤ect of the zero lower bound of interest rate on monetary transmission mechanism.

A Bounded Model of Time Variation in Trend Inflation, Nairu and the Phillips Curve

“…The fact that our latent states are bounded implies our model is not a Gaussian linear state space model and, accordingly, conventional econometric methods cannot be used. Accordingly, we use an algorithm that is an extension of those developed in Chan & Jeliazkov (), Chan & Strachan () and Chan et al , ().…”

A Noncausal Autoregressive Model with Time-Varying Parameters: An Application to U.S. Inflation

“…In this case the IF are around 1. Because of the very high dimension of the TVP models, the IF are typically reported to be much higher (see, e.g., Primiceri (2005), Chan and Strachan (2012), and ), the averages of IF ranging from 2 to more than 100. We follow and report the 50th, 25th, and 75th percentiles of the IF for the parameters of the TVP-AR(0,4) and TVP-AR(1,3) models discussed in the text.…”

A Bounded Model of Time Variation in Trend Inflation, NAIRU and the Phillips Curve

“…The fact that our latent states are bounded implies our model is not a Gaussian linear state space model and, accordingly, conventional econometric methods cannot be used. Accordingly, we use an algorithm which is an extension of the ones developed in Chan and Jeliazkov (2009), Chan and Strachan (2012) and Chan, Koop and Potter (2013).…”