IDENTIFYING EXCHANGE RATE COMMON FACTORS

• Published date: 01 November 2018
• Author: Donggyu Sul,Nelson C. Mark,Jyh‐Lin Wu,Ryan Greenaway‐McGrevy
• DOI: http://doi.org/10.1111/iere.12334
• Date: 01 November 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 4, November 2018 DOI: 10.1111/iere.12334

IDENTIFYING EXCHANGE RATE COMMON FACTORS∗

BYRYAN GREENAWAY-MCGREVY,NELSON C. MARK,DONGGYU SUL,AND JYH-LIN WU1

University of Auckland, New Zealand; University of Notre Dame, U.S.A., and NBER, U.S.A.;

University of Texas at Dallas,U.S.A.; National Sun Yat-Sen University, Taiwan

Using recently developed model selection procedures, we determine that exchange rate returns are driven

by a two-factor model. We identify them as a dollar factor and a euro factor. Exchange rates are thus driven

by global, U.S., and euro-zone stochastic discount factors. The identified factors can also be given a risk-based

interpretation. Identification motivates multilateral models for bilateral exchange rates. Out-of-sample forecast

accuracy of empirically identified multilateral models dominates the random walk and a bilateral purchasing

power parity fundamentals prediction model. Twenty-four-month-ahead forecast accuracy of the multilateral

model dominates those of a principal components forecasting model.

1. INTRODUCTION

Exchange rate returns (first differences of log exchange rates) show substantial cross-sectional

correlation. In a sample of 27 monthly exchange rate returns from 1999.01 to 2015.12, the average

correlation is 0.43 when the U.S. dollar (USD) is the numeraire currency. Similarly, the average

correlation is 0.32 when the euro is the numeraire and 0.39 when the Canadian dollar is the

numeraire.2Recent research has focused on understanding the source of these exchange rate

comovements. Engel et al. (2015) assume a factor structure for exchange rates and take a small

number (2 or 3) of principal components (PCs) to be the common factors. They find that the PCs

remain significant after controlling for macroeconomic fundamental determinants and use them

to predict future exchange rate returns. Verdelhan (2018) also assumes a two-factor structure

and argues that a dollar exchange rate return and a carry exchange rate return are exchange

rate common factors. He gives them a risk-based interpretation by showing that the carry and

dollar factors can account for two different cross sections of currency risk premia.

In this article, we obtain factor identification using econometric methods developed by Bai

and Ng (2002, 2006) and Parker and Sul (2016). Our analysis identifies a two-factor structure

consisting of a dollar factor and a euro factor. The analysis does not find the carry return to be a

factor, and identification is robust to the choice of the numeraire currency. The data also support

a risk-based interpretation to the factors. Using time-varying dollar and euro factor loadings

to sort currency excess returns into portfolios, the average returns are generally increasing in

their currency’s loadings on the factors. The data also reveal a geographical dimension to the

euro factor. European currencies generally load positively on the euro factor whereas all others

generally load negatively. Commodity exporting countries tend to load positively on the dollar

factor.

∗Manuscript received June 2015; revised August 2017.

1Some of the work was performed while Mark was a Visiting Fellow at the HKIMR (Hong Kong Institute for

Monetary Research) and the Federal Reserve Bank of St. Louis. Research support provided by these institutions is

gratefully acknowledged. This is a revision of a paper originally circulated in March 2012 under the title “Exchange

Rates as Exchange Rate Common Factors.” We have benefitted from comments by seminar participants at Michigan

State University and the Bank of Canada. Thoughtful comments and suggestions from two anonymous referees helped

us to improve the article. Please address correspondence to: Donggyu Sul, Department of Economics, University of

Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080-3021, U.S.A. E-mail: d.sul@utdallas.edu.

2This cross-sectional correlation has been recognized in research at least since O’Connell (1988) but has primarily

been treated as a nuisance parameter in panel data models (Mark and Sul, 2001; Engel et al., 2007)

2193

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(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

2194 GREENAWAY-MCGREVY ET AL.

The methodology we use is designed to uncover the relationship between the vector of

true but unobserved factors and a vector of economic variables put forth as candidates for

empirical factors. The first step in the procedure uses an information criterion, proposed by

Bai and Ng (2002), to determine the number of common factors kin a panel of exchange

rate returns. The second step determines the number of common factors in residuals from

regressions of exchange rate returns on unique combinations of k-element groupings of the

candidate economic variables. Identification is based on the idea that if this particular group of

kvariables are empirical factors, then there are no common factors in the residuals. If one or

more common factors are found in the residual panel, this particular set of variables is rejected

as the empirical factors.

The candidate list of economic variables is potentially large. Searching over all possibilities is

not feasible. We therefore limit empirical factor candidates to exchange rate returns. This is not

unreasonable because exchange rate returns, being the difference between countries’ (possibly

unobservable) log stochastic discount factors (SDFs), may contain information that is difficult

to observe in other macroeconomic fundamentals.

What is the value added of empirical factor identification? One is that it guides us toward

an economic interpretation of the source of exchange rate comovements (as opposed to the

descriptive PCs analysis). Drawing on the SDF approach to the exchange rate, as in Lustig

et al. (2011) and Verdelhan (2018), implies that comovements of exchange rate returns and log

SDFs across countries are heavily influenced, if not dominated, by the dynamics of the log SDF

of the U.S. and the euro zone. We mount a limited exploration into a risk-based interpretation

of the dollar and euro factors.

A second value to the identification is that it can be exploited to improve the performance

of empirical exchange rate models. Our dollar and euro factor identification suggests a mul-

tilateral model of bilateral exchange rates that contrasts with typical bilateral formulations.

That is, bilateral exchange rates in conventional models are determined by variables from the

pair of countries associated with the bilateral exchange rate.3Instead of fixating on the details

of every bilateral country pair, knowing the determinants of the dollar and the euro allows

one to understand a substantial proportion of the variation in any bilateral exchange rate. To

assess empirical model performance of the multilateral model, we employ an out-of-sample

forecasting methodology that has been a standard procedure for model assessment since Meese

and Rogoff (1983). We reserve the period from 2004.01 to 2015.12 for out-of-sample fore-

cast evaluation and generate 1, 12, and 24-month-ahead forecasts based on 60-month rolling

regressions.

In the forecasting analysis, we compare our multilateral “dollar–euro” model with alter-

native models considered in the literature. The first is the bilateral purchasing-power parity

(PPP)-based fundamentals model (Bi-PPP). We use this as a comparison model because Engel

et al. (2007) find that it gives the best forecast accuracy among several bilateral fundamentals-

based formulations considered in the literature. We find that prediction accuracy from our

dollar–euro model dominates those from the PPP-based model as well as those from the drift-

less random walk.

The empirical exchange rate literature finds that sample size matters for forecast accuracy.

Rapach and Wohar (2001) and Lothian and Taylor (1996) report significant predictive power

when working with long historical time-series data. To obtain more observations within the

post-Bretton Woods floating regime, a first generation of papers (Mark and Sul, 2001; Rapach

and Wohar, 2004; Groen, 2005) expanded observations cross sectionally with the use of panel

data methods. The panel aspect of our data expands observations by exploiting the cross

section.

Improved forecast performance over the random walk and the bilateral PPP-based model

does not fully answer the question of whether identification has predictive value in empirical

3Berg and Mark (2015) is an exception. They argue that bilateral exchange rates are driven in part by third-country

(rest of world) shocks.