Panel Data Models and the Uncovered Interest Parity Condition: The Role of Two‐Way Unobserved Components

• Date: 01 July 2016
• Published date: 01 July 2016
• Author: Nils Herger
• DOI: http://doi.org/10.1002/ijfe.1552

INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS

Int. J. Fin. Econ.21: 294–310 (2016)

Published online 1 June 2016 in Wiley Online Library

(wileyonlinelibrary.com). DOI: 10.1002/ijfe.1552

PANEL DATA MODELS AND THE UNCOVERED INTEREST PARITY

CONDITION: THE ROLE OF TWO-WAY UNOBSERVED COMPONENTS

NILS HERGER,

Study Center Gerzensee, Dorfstrasse 2, P.O. Box 21,3115 Gerzensee, Switzerland

ABSTRACT

This paper endeavours to show how the specification of the regression testing the uncovered interest parity (UIP) condition

can determine whether or not the hypothesized proportional relationship between international interest rate differences and

exchange rate changes is rejected. Across major currencies, various terms to maturity, different data frequencies and the short

as well as the long time horizon, single-equation regressions partly reject the UIP condition. However, this ‘UIP puzzle’ tends

to disappear when panel data regressions account, for example, for risk premiums by means of two-way unobserved component

specifications with random or fixed effects for both currencies and time periods. The closest concurrence with the UIP condition

arises when specifying the time-specific component as fixed effect, which provides a way to address the potential bias when

unobserved exchange rate risk premiums correlate with interest rates. Copyright © 2016 John Wiley & Sons, Ltd.

Received 9 October 2015; Revised 29 February 2016; Accepted 12 April 2016

JEL CODE: F31

KEY WORDS: Exchange rates; exchange rate risk premium; panel data; uncovered interest parity condition; uncovered interest

parity puzzle

1. INTRODUCTION

An ongoing debate in international finance is trying to get to grips with the widely found empirical rejection of

the uncovered interest parity (UIP) condition. In particular, in what is known as the UIP puzzle, regressions of

international differences in interest rates onto exchange rate changes have more often than not found a slope coef-

ficient (ˇ) at odds with the hypothesized proportional relationship (where ˇD1). The corresponding vast body of

empirical research has been surveyed by Hodrick (1987), Lewis (1995) and Engel (2014). With today’s globalized

financial markets, between which enormous amounts of capital flow across borders in search of higher returns, it

is indeed puzzling that exchange rate changes and international differences in interest rates have, arguably, no ten-

dency to work in opposite directions. Why would currency traders not exploit the profit opportunities that arise if

high interest rates are, on average, not offset by a depreciating currency?

There are some notable exceptions to the view that the UIP condition does not withstand empirical tests. In

particular, the frequency and maturity of the exchange and interest rate data seem to matter.Whilst studies that have

found a UIP puzzle have typically relied on monthly or quarterly data with terms to maturity of several months

(e.g. Flood and Rose, 1996; Huisman et al., 1998; Chinn, 2006; Sarantis, 2006), Chaboud and Wright (2005) could

not reject the proportional relationship between exchange and interest rate movements during the very short term

by looking at intraday data and the overnight maturity. Furthermore, Chinn (2006) has suggested that the evidence

against the UIP condition is weaker when looking at long-term interest rates, that is, yields on government bonds

with a 5-year or 10-year term to maturity. Another exception is reported in Lothian and Wu (2011), whose sample

covers the very long haul with two centuries worth of (yearly) interest and exchange rate data.

Notwithstanding these exceptions, because the seminal work of Fama (1984), the UIP puzzle is commonly

attributed to some form of exchange rate risk driving a wedge between assets denominated in domestic and foreign

currency. Interest earned abroad can indeed be subject to a risk premium, which might reflect conditions that are

Correspondence to: Nils Herger, Study Center Gerzensee, Dorfstrasse 2, P.O. Box 21,3115 Gerzensee, Switzerland.

E-mail:nils.herger@szgerzensee.chTel

Copyright © 2016 John Wiley & Sons, Ltd.

PANEL DATA MODELS AND THE UIP 295

specific to a given currency (time-constant premium), but also pertain to specific periods (day, month or year)

and hence be time varying (e.g. Huisman et al., 1998; Sarantis, 2006). However, as long as the degree with

which uncertainties are thought to imperil a foreign investment is not directly observable, they give rise to del-

icate econometric issues (Sarantis, 2006, p.1169). In particular, whilst the currency-specific risk premium can

be attributed to the intercept (˛) of the UIP regression (e.g. Chinn, 2006, p.9), time-varying risk premiums are

much more difficult to handle. Single-equation regressions, which have typically been employed to document the

UIP-puzzle, require, arguably, explicit theoretical or empirical assumptions to control for time-varying risk com-

ponents (e.g. Berk and Knot, 2001; Sarantis, 2006). By way of contrast, this paper follows a small literature

exploiting the well-known idea that panel data offer unique advantages when dealing with unobserved compo-

nents (also called unobserved effects) such as exchange rate risk premiums. In particular, Flood and Rose (1996)

and Chinn (2006) have estimated the common relationship between exchange and interest rate movements for

a range of currencies with a panel data estimator with fixed effects pertaining to individual currencies. Huisman

et al. (1998) have employed a UIP regression with random time effects, which tend to move the slope coefficient

ˇsubstantially closer to the hypothesized value of one. However, panel data have hitherto not been a panacea

to resolve the UIP puzzle in the sense that the contributions mentioned previously still reject the UIP condition

when forward premiums are small (Huisman et al., 1998), exchange rates are freely floating (Flood and Rose,

1996) and terms to maturity are shorter than 5 years (Chinn, 2006). This paper endeavours to contribute to the

literature by, as far as I can see, being the first to carry out a more comprehensive panel data analysis when

estimating the UIP regression. In particular, this includes two-way unobserved component specifications account-

ing simultaneously for effects pertaining to specific currencies and time periods. Such two-way panel regressions

are connected with the earlier discussion that exchange rate risk premiums could have a time-constant and a

time-varying dimension.

The results suggest that the specification of the panel UIP regression is crucial. For exchange rates of the French

Franc/Euro, the Japanese Yen, Sterling and the Swiss Franc vis-à-vis the US dollar, the UIP puzzle does arise

with single-equation regressions or the one-way panel data specifications that have hitherto been popular in the

literature. Conversely, the puzzle tends to disappear when turning to two-way unobserved component models. The

closest concurrence with the UIP condition arises when specifying the time-specific component as fixed effect,

which can handle the likely correlation between latent time-varying exchange rate risk premiums and international

interest rate differences. It is therefore perhaps not surprising that, after including time-specific fixed effects, the

hypothesized proportional relationship between international interest rate differences and exchange rate changes

cannot be rejected. This finding is robust to various measures of interest rates, different terms to maturity (overnight

to one year) and frequencies (daily, monthly, quarterly and yearly) of the data, as well as samples covering the

recent years since 1999 or the very long haul with annual observations dating back to the 19th century. The paper

is organized as follows. Section 2 discusses briefly the theoretical background and the empirical strategy. Section

3 provides an overview of the data and reports the results. Section 4 summarizes and concludes.

2. THEORETICAL BACKGROUND AND EMPIRICAL STRATEGY

The UIP condition combines several hypotheses.1Firstly, for each currency jD1;:::;N and time period tD

1;:::;T , the domestic interest rate ijt is thought to be equivalent to a corresponding foreign return, which consists

of the foreign interest rate i

tand the forward premium/discount fjt sjt. The latter accrues when, upon maturity

at tCm, foreign earnings are converted back at the forward rate fjt into domestic currency. Formally, this yields

the covered interest parity (CIP) condition (defined in logarithmic values), that is,

ijt Di

tC.fjt sjt/(1)

Equation (1) is strongly supported by the data.2Secondly, rational expectations are thought to imply that deviations

of the realized future exchange rate sj;tCmfrom the value se

j;tCmexpected today arise because of stochastic,

zero-valued prediction errors jt. Hence,

sj;tCmDse

j;tCmCjt with e

jt D0(2)

Copyright © 2016 John Wiley & Sons, Ltd. Int. J. Fin. Econ.21: 294–310 (2016)

DOI: 10.1002/ijfe