A multi‐country dynamic factor model with stochastic volatility for euro area business cycle analysis

• Author: Florian Huber,Michael Pfarrhofer,Philipp Piribauer
• Date: 01 September 2020
• Published date: 01 September 2020
• DOI: http://doi.org/10.1002/for.2667

Received: 4 September 2019 Accepted: 12 January 2020

DOI: 10.1002/for.2667

RESEARCH ARTICLE

A multi-country dynamic factor model with stochastic

volatility for euro area business cycle analysis

Florian Huber1Michael Pfarrhofer1Philipp Piribauer2

1Salzburg Centre of European Union

Studies, University of Salzburg, Salzburg,

Austria

2Austrian Institute of Economic Research

(WIFO), Vienna, Austria

Correspondence

Florian Huber, Salzburg Centre of

European Union Studies, University of

Salzburg, Mönchsberg 2a, 5020 Salzburg,

Austria.

Email: florian.huber@sbg.ac.at

Funding information

Oesterreichische Nationalbank,

Grant/AwardNumber: 17382;

Austrian Science Fund (FWF),

Grant/AwardNumber: ZK 35

Abstract

This paper develops a dynamic factor model that uses euro area country-specific

information on output and inflation to estimate an area-wide measure of the

output gap. Our model assumes that output and inflation can be decomposed

into country-specific stochastic trends and a common cyclical component.

Comovement in the trends is introduced by imposing a factor structure on the

shocks to the latent states. We moreover introduce flexible stochastic volatil-

ity specifications to control for heteroscedasticity in the measurement errors

and innovations to the latent states. Carefully specified shrinkage priors allow

for pushing the model towards a homoscedastic specification, if supported

by the data. Our measure of the output gap closely tracks other commonly

adopted measures, with small differences in magnitudes and timing. To assess

whether the model-based output gap helps in forecasting inflation, we perform

an out-of-sample forecasting exercise. The findings indicate that our approach

yields superior inflation forecasts, both in terms of point and density predictions.

KEYWORDS

dynamic factor model, European business cycles, factor stochastic volatility, inflation forecasting

1INTRODUCTION

Effective policy making in central banks such as the Euro-

pean Central Bank (ECB) requires accurate measures of

latent quantities such as the output gap to forecast key

quantities of interest like inflation across euro area (EA)

member states. Since using aggregate EA data potentially

masks important country-specific dynamics, exploiting

country-level information could help in obtaining more

reliable estimates of the output gap that is consequently

used in Phillips curve-type models to forecast inflation.

In this paper, we exploit cross-sectional information

on output and inflation dynamics to construct a

multi-country model for the EA. The proposed framework

aims to combine the literature on output gap modeling

(see, among many others, Basistha & Nelson, 2007;

Kuttner, 1994; Orphanides & Van Norden, 2002; Planas

et al., 2008) that focuses on estimating the output gap based

on data for a single country/regional aggregate, the liter-

ature on dynamic factor models (Breitung & Eickmeier,

2015; Jarocinski & Lenza, 2018; Kim & Nelson, 1999; Kose

et al., 2003; Otrok & Whiteman, 1998), and the literature

on inflation forecasting (Stock & Watson, 1999, 2007).

Our model assumes that country-specific business cycles

are driven by a common latent factor, effectively exploit-

ing cross-sectional information in the data. Moreover, we

assume that output and inflation feature a nonstationary

country-specific component. To control for potential

comovement in these trend terms, we assume that the cor-

responding shocks to the states feature a factor structure.

The resulting factor model features stochastic volatility

(SV) in the spirit of Aguilar and West (2000) and thus pro-

vides a parsimonious way of controlling for heteroscedas-

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original work is properly cited.

© 2020 The Authors. Journal of Forecasting published by John Wiley & Sons, Ltd.

Journal of Forecasting. 2020;39:911–926. wileyonlinelibrary.com/journal/for 911

HUBER ET AL.

ticity. Since successful forecasting models typically allow

for SV (Clark, 2011; Clark & Ravazzolo, 2015; Huber,

2016; Huber & Feldkircher, 2019), we also allow for time

variation in the error variances across the remaining state

innovations and the measurement errors. One method-

ological key innovation is the introduction of global–local

shrinkage priors on the error variances of the state

equations describing the law of motion of the logarithmic

volatility components, effectively shrinking the system

towards a homoscedastic specification, if applicable.

This increased flexibility, however, is costly in terms

of additional parameters to estimate. We thus follow

the recent literature on state-space modeling (Belmonte

et al., 2014; Bitto & Frühwirth-Schnatter, 2019; Feldkircher

et al., 2017; Frühwirth-Schnatter & Wagner, 2010; Kastner

& Frühwirth-Schnatter, 2014) and exploit a noncentered

parametrization of the model (see Frühwirth-Schnatter

& Wagner, 2010) to test whether SV is supported by the

data. The noncentered parametrization allows treating the

square root of the process innovationvariances as standard

regression coefficients, implying that conventional shrink-

age priors can be used. Here we follow Griffin and Brown

(2010) and use a variant of the Normal-Gamma (NG)

shrinkage prior that introduces a global shrinkage compo-

nent that applies to all process variances simultaneously,

forcing them towards zero.Local shrinkage parameters are

then used to drag sufficient posterior mass away fromzero

even in the presence of strong global shrinkage, allowing

for nonzero process variances if required.

When applied to data for 10 EA countries over the time

period from 1997:Q1 to 2018:Q4, we find that our out-

put gap measure closely tracks other measures reported in

previous studies (Jarocinski & Lenza, 2018; Planas et al.,

2008) as well as gaps obtained by utilizing standard tools

commonly used in policy institutions. We moreover per-

form historical decompositions to gauge the importance

of area-wide as opposed to country-specific shocks for

describing inflation movements. These measures reveal

that inflation is strongly driven by common business cycle

dynamics, underlining the importance of controlling for a

common business cycle. Wethen turn to assessing whether

there exists a Phillips curve across EA countries by sim-

ulating a negative one standard deviation business cycle

shock. This exercise points towards a robust relationship

between the common gap component and inflation, with

magnitudes differing across countries.

The main part of the empirical application applies our

modeling approach to forecast inflation, paying particular

attention to whether the inclusion of a common output

gap improves predictive capabilities. Since inflation across

countries is driven by a term measuring trend inflation and

the output gap, our framework can be interpretedas a New

Keynesian Phillips curve, akin to Stella and Stock (2013).

Compared to a set of simpler alternatives that range from

univariate benchmark models to models that use alterna-

tive ways to calculate the output gap, the proposed model

yields more precise point and density forecasts for infla-

tion.

The remainder of the paper is structured as follows.

Section 2 describes the econometric framework. After

providing an overview of the model, we discuss the

Bayesian prior choice and briefly summarize the main

steps involved in estimating the model. Section 3 presents

the empirical application, starting with a summary of the

data set, and inspects various key features of our model.

The section moreover studies the dynamic impact of busi-

ness cycle shocks to the country-specific output and infla-

tion series. In a forecasting exercise, Section 4 compares

the out-of-sample predictive performance of our model

with other specifications. The final section summarizes

and concludes the paper.

2ECONOMETRIC FRAMEWORK

2.1 A dynamic factor model for the EA

In this section we describe the framework to estimate the

EA output gap using disaggregate country-level informa-

tion. Let it and it denote output and inflation for country

i=1,…,Nin period t=1,…,T, respectively. For

notational simplicity, we define k∈{, }.

Country-specific output and inflation are driven by

unobserved common nonstationary trend components

kit that aim to capture low-frequency movements,

while a common cyclical component gttracks mid- to

high-frequency fluctuations in inflation and output. These

unobserved (latent) quantities are related to the observed

quantities through a set of measurement equations:

it =it +igt+it,(1)

it =it +igt+it,(2)

kit ∼(0,ehkit).(3)

These equations imply that the trend components can

loosely be interpreted as country-specific trend inflation

and potential output for the ith country, respectively.

Moreover, the stationary component of output and infla-

tion depends on the common cycle gtthroughasetof

idiosyncratic factor loadings iand iand measurement

errors that feature time-varying variances ehkit.Itisworth

stressing that Equation (2) represents a country-specific

Phillips curve that establishes a relationship between infla-

tion and the area-wide output gap gt. One key goal of this

paper is to assess whether there exists a Phillips curve

across EA countries by inspecting iand functions thereof.

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