A Markov Switching Factor‐Augmented VAR Model for Analyzing US Business Cycles and Monetary Policy
| Date | 01 June 2018 |
| Published date | 01 June 2018 |
| Author | Manfred M. Fischer,Florian Huber |
| DOI | http://doi.org/10.1111/obes.12227 |
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©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 3 (2018) 0305–9049
doi: 10.1111/obes.12227
A Markov Switching Factor-Augmented VAR Model
forAnalyzing US Business Cycles and Monetary
Policy*
Florian Huber† and Manfred M. Fischer†
†Vienna University of Economics and Business, Welthandelsplatz 1 1020, Vienna, Austria
(e-mail: fhuber@wu.ac.at)
Abstract
This paper develops a Markov switching factor-augmented vector autoregression to in-
vestigate the transmission mechanisms of monetary policy for distinct stages of the US
business cycle. We assume that autoregressive parameters and covariance matrices of
the error terms are regime dependent, driven by an unobserved Markov indicator. Endo-
genously determined transition probabilities are governed by an underlying probit model
that features a large set of possible predictors. The empirical findings provide evidence for
differences in the transmission of monetary policy shocks that mainly stem from hetero-
geneity in the responses of financial market quantities.
I. Introduction
The present paper introduces a new econometric model – a synthesis of multivariateMarkov
switching (MS) models1with time-varying transition probabilities and factor-augmented
vector autoregressive (FAVAR) models (see Bernanke, Boivin and Eliasz, 2005). The pro-
posed model allows for discrete shifts in the autoregressive parameters and the error
variances over time, with switches being determined by a latent Markov indicator with
time-varying transition probabilities. The transition probabilities depend on a large set of
possible covariateswithin a probit formulation. A combination of different shrinkage priors
permits reliable estimation of the model and provides additional inferential opportunities.
Within this framework,we analyse the transmission of monetary policy shocks to the wider
macroeconomy for distinct stages of the business cycle.
Compared to the existing literature on MS models, our approach explicitly allows
for discriminating between expansionary and recessionary regimes while exploiting, in
a parsimonious way, large information sets through a relatively small number of latent
JEL Classification numbers: C30, E52, F41, E32.
*The authors gratefully acknowledge the valuable advice of twoanonymous reviewers, and the Associate Editor,
Jonathan Temple as well as Gregor Kastner for comments on earlier versions of the paper.
1For textbook introductions to MS models, see Krolzig (1997), Kim and Nelson (1999), Fr¨uhwirth-Schnatter
(2006).
576 Bulletin
factors. These factors capture the co-movement of a wide range of macroeconomic and
financial variables throughout the evolution of the business cycle, with any nonlinearities
stemming from changes in the law of motion of the latent factors. This is in contrast to
existing small-scale business cycle models that exploit the co-trending behaviour of a
handful of real activity indicators (see Filardo, 1994; Kim and Nelson, 1998). Another
important novelty of our modelling approach is that the transition distributions of the
underlying hidden Markov chain are parameterized by a probit model that features a great
variety of predictors, as opposed to the existing literature that either assumes constant
transition probabilities (Hamilton, 1989) or introduces time-varying transition probabilities
that are governed by only a small number of possibleexogenous regressors (Filardo, 1994;
Kaufmann, 2010, 2015; Amisano and Fagan, 2013; Billio et al., 2016).
Given the fact that our model is highly parameterized, weadopt a Bayesian approach to
estimation and inference, and use shrinkage priors to alleviate potential overfitting issues.
Since the set of possible regressors that determine the time-varying transition probabilities
may be large, we impose a stochastic search variable selection (SSVS) prior (George and
McCulloch, 1993) on the underlying regression coefficients of the probit regression to draw
inferences about the (relative) importance of the variables for business cycle transitions.
For the coefficients of the state equation of the FAVAR model, we utilize a hierarchical
variant of the Minnesota prior (Doan, Litterman and Sims, 1984; Sims and Zha, 1998;
Giannone, Lenza and Primiceri, 2015) to push the system towards a multivariate random
walk.
In the empirical application we first evaluate whether our proposed model is supported
by the data, and then provide evidence that transition probabilities change over time, a
feature that proves to be important if the goal is to achieve a high level of concordance
between the extracted, model-based cycle and the NBER (National Bureau of Economic
Research) reference cycle. To gain further insights into the driving forces of business
cycle transitions, the proposed SSVS prior is used to identify a small subset of important
covariates.
Turning to the structural analysis, weinvestigate whether the transmission mechanisms
of monetary policy depend on the prevailing state of the business cycle. The monetary
policy shock is identified by means of standard sign restrictions in the spirit of Uhlig
(2005) that allow for simultaneous relations between monetary policy and financial market
quantities. Our findings, corroborating recent empirical evidence provided in Eickmeier,
Metiu and Prieto (2016), suggest that the impact of monetary policy on financial markets is
more pronounced during expansions than recessions. This result, however, does not carry
over to variablesrepresenting the real side of the economy.To gain a comprehensive picture
on how monetary policy actions impact business cycle transitions, our model allows the
analysis of changes of transition probabilities with respect to exogenous monetary policy
shocks.
The paper is organized as follows. Section II presents the proposed model with time-
varying transition distributions along with a detailed account of the Bayesian estimation
strategy. Section III describes the data employed and provides model evidence. Section IV
investigates the time-variation in the transition probabilities and uses the non-parametric
concordance statistic to check the degree of synchronization of the business cycle ex-
tracted with our model and the NBER reference cycle. The regime-dependent dynamic
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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