Model instability in predictive exchange rate regressions

• DOI: http://doi.org/10.1002/for.2620
• Published date: 01 March 2020
• Author: Niko Hauzenberger,Florian Huber
• Date: 01 March 2020

RESEARCH ARTICLE

Model instability in predictive exchange rate regressions

Niko Hauzenberger

1,2

| Florian Huber

2

1

Department of Economics, WU Vienna

University of Economics and Business,

Vienna, Austria

2

Salzburg Centre of European Union

Studies (SCEUS), Paris Lodron University

of Salzburg, Salzburg, Austria

Correspondence

Niko Hauzenberger, Department of

Economics, Vienna University of

Economics and Business (WU),

Welthandelsplatz 1, 1020 Vienna, Austria.

Email: niko.hauzenberger@wu.ac.at

Funding information

Oesterreichische Nationalbank, Grant/

Award Number: Jubilaeumsfond grant no.

17650; Austrian Science Fund (FWF);

Austrian Academy of Sciences (ÖAW),

Grant/Award Number: Zukunftskolleg ZK

35

Abstract

In this paper we aim to improve existing empirical exchange rate models by

accounting for uncertainty with respect to the underlying structural representa-

tion. Within a flexible Bayesian framework, our modeling approach assumes that

different regimes are characterized by commonly used structural exchange rate

models, with transitions across regimes being driven by a Markov process. We

assume a time‐varying transition probability matrix with transition probabilities

depending on a measure of the monetary policy stance of the central bank at

home and in the USA. We applythis model to a set of eight exchange rates against

the US dollar. In a forecasting exercise, we show that model evidence varies over

time, and a model approach that takes this empirical evidence seriously yields

more accurate density forecasts for most currency pairs considered.

KEYWORDS

empirical exchangerate models, exchange rate fundamentals, Markov switching

1|INTRODUCTION

Since the end of the Bretton Woods system in 1971, econo-

mists have been confronted with the challenging issue of

designing empirical models of bilateral exchange rates,

which are also useful for forecasting applications. In a sem-

inal contribution, Meese and Rogoff (1983) provided some

early evidence that exchange rates are difficult to predict,

at least in the short run. Using a set of theoretical models

in the spirit of Dornbusch (1976), Frankel (1979), and

Hooper and Morton (1982), to guide the choice of covari-

ates included in a forecasting regression, Meese and Rogoff

(1983) found that a simple random walk benchmark is dif-

ficult to outperform for most major exchange rate pairs.

One reason for the dismal performance of most empirical

and structural models is that, within a standard asset pric-

ing framework, the high persistence of the underlying fun-

damentals in light of a discount factor near unity translates

into highly persistent exchange rates. As a consequence, a

random walk appears to be a benchmark difficult to beat

(see Engel & West, 2005).

Over the years, a plethora of alternative econometric

techniques emerged that provide more sophisticated

means for analyzing exchange rate data to successfully

improve longer term predictions. The literature on unit

roots and cointegration, for example, provided tools to

explicitly discriminate between short‐term movements of

a given currency pair and its long‐run behavior. Mark

(1995), for instance, applied an error correction model to

a set of four exchange rates against the US dollar. Within

this error correction framework, the exchange rate is

assumed to return to its long‐run equilibrium value deter-

mined by a simple monetary model, with short‐run fluc-

tuations driven by lagged changes of the exchange rate

and its fundamentals. The finding that exchange rates

tend to be predictable in the medium and long run

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the

original work is properly cited.

© 2019 The Authors Journal of Forecasting Published by John Wiley & Sons Ltd

Received: 9 April 2019 Revised: 2 July 2019 Accepted: 6 July 2019

DOI: 10.1002/for.2620

Journal of Forecasting. 2020;39:168–186.

wileyonlinelibrary.com/journal/for

168

sparked a series of related contributions that corroborate

this result for different periods and currency pairs (Groen,

2000; Mark & Sul, 2001; Rapach & Wohar, 2002).

More recently, several studies emphasized the useful-

ness of accounting for nonlinearities in the underlying

econometric models to provide more precise exchange

rate predictions (see, for example, Byrne, Korobilis, &

Ribeiro, 2016; Canova, 1993; Huber, 2016, 2017; Huber

& Zörner, 2019; Mark, 2009; Sarno, Valente, & Wohar,

2004). The majority of this literature deals with the ques-

tion on whether a given empirical model, that is loosely

based on an underlying structural model, outperforms a

set of competing models. In this context, introducing non-

linearities boils down to allow for time‐varying error var-

iances and/or time‐varying regression coefficients for a

certain structural model.

However, another key source of nonlinearities could

stem from the fact that the underlying theoretical model

changes over time, potentially jeopardizing the predictive

fit of the econometric specification.

1

For instance, the

recent success of Taylor rule‐based models (see Engel &

West, 2006; Molodtsova, Nikolsko‐Rzhevskyy, & Papell,

2008, 2011; Molodtsova & Papell, 2009) can be attributed

to the fact that involved central banks adopted a policy

rule closely related to a Taylor rule. With short‐term

interest rates reaching the zero lower bound (ZLB) and

central banks starting to implement unconventional

monetary policy measures, the question arises whether

a Taylor rule still proves to be an adequate exchange rate

model. In fact, recent literature on nonlinear Taylor rules

suggests that during the ZLB, Taylor rule‐based models

loose their momentum against simple random walk spec-

ifications (Byrne et al., 2016; Huber, 2017).

In this paper, we contribute to the literature by

acknowledging this empirical evidence and propose a

modeling framework capable of handling model instabil-

ity over time in a flexible manner. This is achieved by

proposing a Markov‐switching (MS) regression model

with each regime being characterized by different covari-

ates arising from a set of structural exchange rate models.

In contrast to the existing literature, which relies on

dynamic Bayesian model averaging techniques, our

approach is an integrated modeling device. In addition,

the introduction of time‐varying transition probabilities

allows assessment of how the likelihood of a given struc-

tural model changes over time, depending on selected

early‐warning indicators. As signal variables, we adopt

the (lagged) interest rates of the home country and the

USA. This specification is motivated by the observation

that Taylor rule fundamentals are good predictors in the

period before the global financial crisis (with policy rates

being significantly larger than zero), but are known for

their weak performance in the aftermath of the crisis

(characterized by policy rates close to zero).

We assess the merits of the proposed approach using a

forecasting exercise for eight different exchange rates

against the US dollar. By considering the resulting regime

allocation and the transition probabilities, we examine

whether structural models indeed tend to change and

how this is related to movements in policy rates. The

findings indicate that allowing for time‐varying probabil-

ities is a key feature, pointing towards a strong relation-

ship between policy rates and the underlying transition

distribution of the Markov process. In terms of forecast-

ing, we find that our proposed model improves upon

the random walk for selected currencies, both in terms

of point and density predictions. The improvements for

point forecasts are, however, muted. Comparing different

model features reveals that a model based on a larger set

of fundamentals from various structural models is also

competitive when combined with shrinkage priors and

nonlinearities (in the form of MS).

The remainder of this paper is organized as follows.

Section 2 discusses the four structural exchange rate

models adopted, while Section 3 proposes the economet-

ric framework. The empirical application is presented in

Section 4. The final section summarizes and concludes

the paper. A technical Appendix provides details on the

estimation algorithm adopted.

2|THEORETICAL EXCHANGE

RATE MODELS

In this section, we briefly discuss the main theoretical

underpinnings to be used to guide covariate inclusion in

the empirical model as well as to structurally identify

the different regimes considered in our nonlinear regres-

sion framework.

The point of departure for the discussion is a set of

macroeconomic and financial quantities stored in an R‐

dimensional vector X

t

:

with i

t−1

denoting the lagged short‐term interest rate, π

t

inflation, x

t

output gap, m

t

money supply, y

t

income, p

t

price level, while the real exchange rate is denoted by q

t

and the nominal exchange rate by e

t

.

2

The subsets of

1

Recent contributions, dealing with this issue, are Wright (2008),

Beckmann and Schüssler (2016), Beckmann, Koop, Korobilis, and

Schüssler (2018), and Byrne, Korobilis, and Ribeiro (2018).

2

Asterisks denote US quantities. Moreover, y

t

,m

t

,p

t

,q

t

and e

t

are mea-

sured in logarithms. For simplicity, we suppress subset‐specific

intercepts.

HAUZENBERGER AND HUBER 169