Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol25.Issue2.2001:
Journal of Banking & Finance 25 (2001) 377±391
www.elsevier.com/locate/econbase
Testing for long horizon UIP using PPP-based
exchange rate expectations
Jan Marc Berk
a,b
, Klaas H.W. Knot
a,*
a
b
De Nederlandsche Bank, P.O. Box 98, 1000 AB Amsterdam, Netherlands
Department of Economics, Free University, de Boelelaan 1105, 1081 HV Amsterdam, Netherlands
Received 14 January 1999; accepted 18 October 1999
Abstract
This paper revisits the uncovered interest parity relation. It supplements existing
work in two ways: It focuses on long instead of short-term interest rates, and, related to
that, employs exchange rate expectations derived from purchasing power parity (PPP)
instead of actual outcomes. Among the major ¯oating currencies over the period 1975±
1997, the paper cannot support the notion of further increases in UIP-validation beyond
that associated with the wave of ®nancial market liberalization and deregulation in the
early 1980s. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: E43; E44
Keywords: Interest parity relations; Exchange rate expectations
1. Introduction
Notwithstanding the greater importance of long-term interest rates for the
business cycle in most countries, the empirical literature on international interest rate linkages focusing on short-term assets generally outnumbers the
studies using long-term rates. 1 This re¯ects the fact that ®nancial instruments
*
Corresponding author.
Recent studies involving long-term rates are Kasman and Pigott (1988), Howe and Pigott
(1991), Pigott (1993), Throop (1994), Fell (1996), Kirchg
assner and Wolters (1996), Fase and Vlaar
(1998), and Meredith and Chinn (1998).
1
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 0 0 ) 0 0 0 8 3 - 2
378
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
traded at the long end of the market generally lack a well-developed forward
market. While it is true that forward markets are most developed at the threemonth maturity and hardly exist at maturities greater than two years, even
among well-traded currencies, in the 1980s the currency swap market became
suciently developed to hedge exchange rate risk for long-term investments as
well (Popper, 1990, 1993; Fletcher and Taylor, 1996). In addition to the
gradual worldwide abolition of capital controls, this ®nancial innovation may
have increased the linkage of international long-term interest rates.
Financial innovations contribute to international capital market integration
by increasing capital mobility. This paper investigates whether this increased
capital mobility has also resulted in a greater validation of the uncovered interest rate parity (UIP) relationship, as, under these circumstances, the scope
for interest rate arbitrage increases and the impact on interest rate dierentials
of factors other than (expected) exchange rate movements and time-varying
risk premia should steadily diminish. The focus on long-term interest rates is by
itself an important contribution to the existing literature, which, as mentioned
earlier, mainly concentrates on short-term instruments. A second but related
novelty is the use of exchange rate expectations based on long-run purchasing
power parity (PPP) instead of the more common form of rational expectations
where actual exchange rate movements proxy for expected ones.
The bulk of the evidence on UIP thus far indicates not just that (actual)
exchange rates fail to move one-for-one with interest rate dierentials, but
rather that their changes are substantial and in the opposite direction to that
implied by UIP. Froot (1990) has calculated an average regression coecient
across some 75 published estimates of )0.88. A few estimates are positive, but
all of them are distinctly smaller than the null hypothesis of a coecient of +1.
McCallum (1994) and Meredith and Chinn (1998) have argued that for relatively short horizons, failure of UIP results from risk-premium shocks in the
face of endogenous monetary policy. In the longer term, in contrast, exchange
rates are driven by `fundamentals', leading to a relation between interest rates
and exchange rates that should be more consistent with UIP.
The remainder of the paper is organized as follows: Section 2 presents some
stylized facts. UIP and PPP are brie¯y discussed in Section 3, followed by a
description of the data and the methodology used. Section 4 puts the theoretical predictions to an empirical test. Section 5 concludes the paper.
2. Recent developments in international bond markets
In the aftermath of two oil crises during the second half of the 1970s many
industrialized countries experienced strong upward pressure on long-term interest rates, when in¯ation pressures rose and, around the turn of the decade,
monetary policy was tightened quite aggressively. After reaching record heights
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
379
in the early 1980s, bond yields have gradually come down and there has been a
marked worldwide convergence of nominal (and also real) long-term interest
rates. This trend broadly corresponds to the declining trend in in¯ation during
this period and the simultaneous reduction in in¯ation divergences. This process was interrupted in the periods surrounding the stock market collapse of
1987 and the tightening of United States monetary policy in 1994. In both
phases, substantial concerns about the return of in¯ationary pressures in the
US economy developed, and bond yields rose accordingly.
Table 1 documents the major swings that have taken place in international
government bond markets since 1975 in more detail. 2 Especially during the
1970s and the early 1980s, long-term interest rates across the major countries
have been pushed apart, often with accompanying movements in exchange
rates. Countries that had experienced the largest in¯ation increases toward the
end of the 1970s, such as the US, the UK, and France, had to allow for higher
yields than Germany and Japan around the turn of the decade, while their
currencies generally fell against the deutsche mark and the yen. US interest
rates rose between spring-1983 and mid-1984 while at the same time interest
rates in Europe and Japan were generally falling, partly due to the eects of US
®scal expansion in creating excess demand for domestic savings. The pressures
resulting from this divergence in long-term interest rates were also re¯ected in
the sharp appreciation of the dollar in this period, as well as by the reversal of
that appreciation that began in 1985 and occurred as US bond yields were
falling back.
For the 1990s, however, Table 1 would seem to reveal a somewhat larger
synchronization among bond yields than in the previous decades. Apart from
the correction after the Fed-tightening of 1994 and an additional hiccup during
the ®rst half of 1996, 3 the 1990s have been characterized by declining bond
yields worldwide. In view of the experience of the 1980s, it is the circumstances
surrounding the interest rate developments, and not the mere fact that they
moved together, that would seem somewhat unusual. The 1994 long-term interest rate run-ups in Europe and Japan followed a prolonged period of declining short-term interest rates and weak economic activity. The experience of
the 1990s thus suggests that the degree to which bond yields are free to vary
with national conditions should not be overstated, even under ¯oating exchange rates. 4
2
The methodology that has been adopted to classify a major swing in the bond market is similar
to that used by the NBER to date business cycles. Peaks and troughs were identi®ed using a 12month moving window. A `bull' market is de®ned as at least 6 consecutive months of declining
bond yields and a `bear' market is de®ned in the opposite way.
3
This hiccup is not identi®ed in Table 1, as the number of consecutive months with
unidirectional movements was limited to ®ve instead of the required six (see previous note).
4
In this respect, Browne and Tease (1992) ®nd little tendency for long-term interest rates to vary
systematically with the business cycle.
380
a
Market
type
US
Start
Change
Start
Germany
Change
Start
France
Change
Bull
Bear
Bull
Bear
Bull
Bear
75/09
76/12
)156
+845
75/01
)410
75/01
75/09
78/02
79/04
)80
+126
)172
+741
Bull
Bear
Bull
Bear
Bull
Bear
81/09
83/05
84/06
87/01
87/10
89/12
81/09
Bull
Bear
Bull
End
90/09
93/10
94/11
97/12
78/04
+544
)494
+318
)648
+244
)168
+105
81/09
83/03
83/12
86/04
)322
+96
)301
+367
)356
+262
)343
90/10
94/01
95/01
97/12
)339
+194
)355
UK
Start
Change
75/03
76/10
77/10
79/12
80/10
+260
)505
+374
)160
+283
)928
81/10
)719
86/08
87/10
89/08
+299
)239
+211
86/04
86/11
88/04
+204
)160
+314
90/09
94/01
95/01
97/12
)481
+252
)400
90/04
94/01
94/09
97/12
)611
+257
)381
Switzerland
Japan
Start
Change
Start
Change
75/04
)384
75/01
76/12
78/04
80/03
81/03
+19
)245
+389
)223
+139
81/09
)631
87/05
+552
90/09
93/12
94/10
97/12
)531
+160
)390
78/12
+310
81/09
83/01
85/03
)191
+72
)117
88/04
+292
90/04
93/12
94/09
97/12
)264
+149
)286
Notes: Changes are measured in basis points. Peaks and troughs were identi®ed using a 12-month moving window. A Ôbull' market is de®ned as at least
6 consecutive months of declining bond yields and a Ôbear' market is similarly de®ned for rising bond yields.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
Table 1
Peak to trough analysis of major swings in international bond marketsa
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
381
More formal evidence on the degree to which long-term interest rates have
become more synchronized with globalization can be extracted from bilateral
correlations of their changes against those in the major market. In this respect,
the US bond market is clearly the world's dominant market, with a size about
three times that of Germany, the second largest market, for instance. For the
®ve countries under investigation, Fig. 1 displays 5-year rolling correlations of
monthly changes in domestic bond yields vis-a-vis US yields since the mid1970s. Apart from the stylized fact that co-movements in long-term interest
rates among the major industrialized economies were stronger in the 1980s and
1990s than during the 1970s (see among others Frankel, 1989), by this measure
there seems to have been no systematic further increase in the bilateral synchronization since the early 1980s.
The message from Table 1 and Fig. 1 is rather mixed. This should not be too
much of a surprise, since the analysis thus far has been con®ned to bond
markets mainly, without proper reference to contemporaneous developments
in currency markets. As is well known, however, exchange rates among the
largest industrialized countries have ¯uctuated quite substantially in the period
under investigation. Below, we shall therefore introduce exchange rate movements into the analysis.
3. UIP and PPP
The eect of exchange rate movements on interest rate relations can be
described in terms of the standard UIP-relation. Its most restrictive representation assumes risk neutral investors and perfect substitutability between assets
that are comparable in all respects except their currency of denomination
(Blundell-Wignall and Browne, 1991). Dropping the assumption of risk neutrality introduces risk premia (Knot and de Haan, 1995). Following the seminal
work of Engle et al. (1987), we allow for a time-varying risk premium by estimating the UIP-relationship as the conditional mean speci®cation in a
ARCH-in-mean model. In order to preserve a parsimonious speci®cation for
the conditional variance term, we set the order of the ARCH-process equal to 1
(month), a choice that performed reasonably well in the empirical analysis
below. We therefore estimate
Et stk ÿ st
cqt t ;
a
b
ikt ÿ ik;
t
k
1
2
2
qt d /tÿ1 ;
where ikt denotes the nominal interest rate on a ®nancial instrument with a
remaining life of k periods in the home country, an asterisk its foreign
equivalent, st the natural logarithm of the nominal exchange rate (domestic
382
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
Fig. 1. Correlations of movements in domestic bond yields vis-
a-vis the US. Source: Authors' own calculations.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
383
currency price of a foreign currency unit, here one US dollar) and E denotes
the expectations operator. Conditional on past information, the residuals t are
distributed normally with mean zero and variance q2t . In this speci®cation, the
time-varying risk premium is proxied by the conditional standard deviation qt
that directly aects the interest rate dierential vis-a-vis the US, with an elasticity of c. The speci®cation conforms with a very simple model in which ®nancial market participants predict this period's variance based on information
about previous volatility. An unexpectedly large interest rate dierential will
increase the estimated variance for the next period.
In general, only interest rates are observable in Eq. (1). To overcome the
identi®cation problem with respect to the expected depreciation term, most
authors resort to the rational expectations hypothesis to justify their use of
actual exchange rate outcomes to proxy for unobservable expectations. This
way, however, UIP can only be tested in conjunction with this speci®c process
of expectations formation; in case of a subsequent rejection it remains unclear
which leg of the joint hypothesis is not being supported by the data. Moreover,
it has often been documented that participants in the foreign exchange market
do make systematic forecast errors and do not always use all information ef®ciently when forecasting (Frankel and Froot, 1987; Takagi, 1991; Cavaglia et
al., 1993; Sobiechowski, 1996). In our view, the longer the horizon of the investment in question, the more debatable this practice of inserting ex-post
realizations for ex-ante expectations becomes. 5
Instead, we propose a process of long-term expectations formation in which
the exchange rate is assumed to be ultimately guided by its `fundamental anchor' of PPP. 6 Underlying this assumption is the notion that investors, while
acknowledging the possibility that exchange rates may be misaligned for a
couple of months, quarters, or even years, will regard the persistence of this
phenomenon over the full 10-year term as rather unlikely. Questioning 200
chief London forex dealers, Allen and Taylor (1989) indeed found that at
forecast horizons of one year and longer, nearly 30% of respondents relied on
pure fundamentals and 85% judged fundamentals to be more important than
swings in market psychology as captured by `chartism'. Moreover, recent
studies that either use long-horizon or panel data sets have been quite supportive of the notion that real exchange rates are in fact mean-reverting, with
an estimated half-life for deviations from PPP of about three to four years
(Abuaf and Jorion, 1990; Froot and Rogo, 1995; Wu, 1996; Papell, 1997).
5
This need not be true for rational expectations in general. As pointed out by one referee, the
`asymptotically rational expectations theory' states exactly the opposite (Stein, 1986).
6
Note that, in general, assuming PPP is not equivalent to discarding the rational expectations
hypothesis. It is, however, at odds with the speci®c representation of the latter hypothesis in which
actual exchange rate movements proxy for expected ones.
384
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
For a 10-year horizon it therefore seems plausible to expect the exchange
rate to revert to `current wisdom' regarding its long-run equilibrium, as
measured by then prevailing estimates of PPP exchange rates. 7 One advantage of this procedure is that it only uses information that is readily available
at the time when investors decide on the diversi®cation of their portfolios.
For this purpose, annual data on PPP exchange rates were gathered from the
OECD National Accounts database, that have been interpolated into
monthly PPP observations based on developments in relative consumer prices
employing a method proposed by Boot et al. (1967). 8 Averaged over the year
the movement in the resulting series is identical to the original OECD series
while movements within the year re¯ect movements in the CPI of the country
relative to the US, which is in line with the nature of PPP. Annualized `expected' rates of depreciation are then calculated by dividing the deviation of
the actual exchange rate from its PPP-value by the term of the investment
(ten years).
4. Empirical results
This section tests for UIP vis-
a-vis the US, regressing the long-term interest
rate dierential with the US for Germany, France, the UK, Japan, and Switzerland on an intercept, the expected rate of depreciation of their currency
against the US dollar, and a time-varying risk premium. Intercepts are included
to take into account a number of country-speci®c characteristics of the ®nancial system that are less time-varying, such as for instance the liquidity of
the US bond markets vis-
a-vis those in the other countries, or dierences in
capital income taxation (McCallum, 1994).
Table 2 ®rst presents estimates of the risk-adjusted UIP-model (1) with respect to the entire sample, using maximum likelihood with heteroskedasticityconsistent standard errors (Bollerslev and Wooldridge, 1992). Decade-speci®c
7
Ideally, one should use the expected PPP rate at maturity as the anchor guiding exchange rate
expectations under PPP. The dierence between the expected PPP rate k years ahead, Et sPPP
tk , and
the current PPP rate, sPPP
, will normally correspond to the expected cumulative in¯ation dierential
t
between the US and the foreign country in question over that time interval, Et pt;tk ÿ pt;tk , so
that the latter expectation should be regarded as a missing variable in our regressions (recall
PPP
PPP
Et sPPP
sPPP ÿ st Et pt;tk ÿ pt;tk sPPP ÿ st . In terms of the empirical
tk ÿ st Et stk ÿ st
implementation, however, it is not so straightforward to come up with a proxy that would
adequately capture this ten-year ahead expected in¯ation dierential.
8
The two-step procedure is as follows: First, by minimizing the sum of squares of the second
dierences a monthly series is interpolated, ensuring smoothness whilst preserving the movement of
the original series. Subsequently, monthly observations on PPP are constructed as the ®tted values
of a regression of the smooth interpolated monthly series on the quotient of monthly movements in
the consumer price index (CPI) relative to the US.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
385
Table 2
Testing for UIP: Entire sample 1975.01±1997.12a
Intercepts
1970s
1980s
1990s
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
Diagnostics
R2 -adjusted
LM[ARCH-8]
(p-value)
Q(32)
(p-value)
LM[NORM]
(p-value)
Germany
France
UK
)0.024
(44.4)
)0.030
(100.0)
)0.008
(21.7)
0.307
(32.6)
0.166
(3.1)
0.022
(47.0)
0.009
(15.4)
0.009
(24.8)
0.141
(10.6)
)0.080
(1.8)
0.066
(87.3)
0.007
(14.2)
0.020
(59.1)
0.256
(14.5)
)0.077
(1.8)
6.05E-6
(5.9)
1.127
(10.9)
8.78E-6
(4.9)
1.066
(13.2)
5.11E-6
(4.6)
1.085
(12.8)
0.64
1.02
(0.42)
23.70
(0.86)
5.76
(0.15)
ADF tests on standardized residuals
3 unit roots
15.94
(C,4)
2 unit roots
11.37
(C,4)
1 unit root
4.15
(N,2)
Conclusion
I(0)
0.20
1.65
(0.11)
54.07
(0.01)
5.96
(0.05)
0.61
1.60
(0.13)
42.51
(0.10)
3.33
(0.19)
14.64
(C,4)
9.61
(C,4)
4.43
(N,2)
I(0)
15.92
(C,4)
9.77
(C,4)
4.15
(N,1)
I(0)
Switzerland
)0.033
(66.1)
)0.062
(101.7)
)0.034
(43.6)
0.270
(17.8)
)0.027
(0.7)
4.99E-6
(4.7)
1.053
(21.6)
0.50
0.81
(0.59)
34.95
(0.33)
13.71
(0.00)
16.29
(C,4)
11.64
(C,4)
4.63
(N,1)
I(0)
Japan
0.006
(9.3)
)0.023
(20.3)
)0.002
(1.3)
)0.383
(20.9)
)0.470
(5.9)
8.25E-6
(3.9)
1.018
(14.8)
0.52
1.08
(0.38)
21.93
(0.91)
13.00
(0.00)
13.76
(C,4)
9.06
(C,4)
4.58
(N,1)
I(0)
a
Absolute t-values, computed with heteroskedasticity consistent standard errors are in parentheses.
LM[ARCH-8] is Lagrange-Multiplier test for ARCH-8; Q(32) is Ljung±Box Q-test; LM[NORM] is
Jarque±Bera test. Critical values for an ADF-test on the residuals of a cointegration relation with
three non-stationary variables are 4.35 (1%) and 3.78 (5%), respectively (Engle and Yoo, 1987).
Signi®cance of the ADF tests at the 5% ( ) and 1% ( ) level is indicated. The information within
parentheses relates to the deterministic part of the ADF-equation: T linear trend, C constant,
N neither.
intercepts were included from the outset, in order to account for structural
breaks related to matters such as the liberalization and globalization of ®nancial markets and the advent of new ®nancial instruments. This way, we also
circumvented a number of econometric problems prompted by estimation with
386
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
a single intercept, such as singularity problems (Germany, UK), or consistently
poor diagnostics (others).
Upon investigating Table 2, three features stand out. First, while four out of
®ve parameters of the expected rates of depreciation have the expected positive
sign ± Japan being the exception ± for none of the countries is the coecient
near unity, as would be implied by strict UIP. Second, despite the greater liquidity of the US bond markets, both Switzerland and Japan combine generally negative intercepts with a negative sign on the time-varying risk premia.
Both countries are characterized by a relatively closed and to some extent also
protected ®nancial system, which may be have kept domestic bond yields arti®cially low. 9 For the other countries the evidence on risk premia is more
balanced, combining negative intercepts with positive ARCH-in-mean elements (Germany) or vice versa (France and UK). Finally, despite the restrictive
character of both the UIP and the ARCH(1)-in-mean speci®cation for a decomposition of interest rate dierentials, the equations are reasonably wellbehaved ± aside from some excess kurtosis ± and capable of explaining a fair
amount of intertemporal variation in interest rate dierentials.
The lower panel of Table 2 reports on a Engle and Granger (1987) type
cointegration test for the UIP regressions estimated. From an investigation of
the time-series characteristics of individual interest rate dierentials and PPPbased expected rates of depreciation (not shown), no clear-cut picture across
countries emerged as to the order of integration of these variables. Additionally, the variance equations of Table 2 reveal a good deal of persistence in the
time-varying risk premia, possibly suggesting non-stationarity for this generated regressor as well. Table 2 therefore proceeds by investigating the
stationarity properties of the standardized residuals of the risk-adjusted UIPmodel. 10 Stationary residuals would point to the existence of cointegration
between the three stochastic variables in the risk-adjusted UIP-model (1).
From the ®nal row of Table 2 it appears that for all ®ve countries investigated
non-stationarity of the residuals can safely be rejected, thereby validating our
levels-based speci®cation in (1).
9
Switzerland has often been referred to as an Ôinterest rate islandÕ, owing to the stylized fact that
real interest rates have been lower in Switzerland than in most other industrialized countries and
that Swiss interest rates seem to be decoupled from world interest rates to a greater extent than in
other countries. These features may relate to an excess of national savings over investment for
many years, that has resulted in a persistent current account surplus and the largest ratio of net
foreign assets to GDP in the world (Mauro, 1995).
10
This standardization, common in the evaluation of (G)ARCH models, implies dividing the
residuals from the model estimated in Table 2 by their conditional standard deviation, and ensures
that the residuals are i.i.d., with zero mean and unit variance. As shown by Engle and Granger
(1987) and Engle and Yoo (1987), the critical values for the residuals-based test for cointegration
depend on the number of I(1) variables in the cointegrating regression.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
387
In order to investigate whether the apparent increases in co-movement of
bond yields across the decades ± suggested in Section 2 ± can be traced back to
a declining prevalence of exchange rate misalignments, Table 3 reports on
subsample estimates of the risk-adjusted UIP-model (1). Since the advent of
Table 3
Testing for UIP across the decadesa
(a) 1975.01±1979.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
(b) 1980.01±1989.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
(c) 1990.01±1997.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
a
Notes: See Table 2.
Germany
France
UK
Switzerland
Japan
0.021
(41.6)
)1.227
(47.6)
0.126
(1.7)
0.052
(11.5)
)0.961
(15.0)
)1.847
(2.0)
0.038
(32.7)
)0.899
(19.5)
0.234
(1.9)
)0.001
(1.4)
)1.380
(71.5)
0.128
(2.4)
0.005
(2.8)
)0.680
(22.6)
0.063
(0.2)
3.37E-6
(2.8)
1.256
(3.7)
)0.029
(55.5)
0.317
(23.1)
)0.072
(0.8)
9.23E-6
(3.2)
1.034
(7.9)
)0.001
(1.8)
0.142
(6.5)
)0.002
(0.1)
2.52E-6
(3.7)
1.020
(10.4)
16.1E-6
(5.1)
0.384
(2.2)
0.007
(6.2)
0.174
(9.8)
0.239
(2.2)
16.0E-6
(2.8)
0.955
(7.9)
0.005
(7.3)
0.527
(14.3)
)0.477
(3.5)
3.44E-6
(3.1)
1.039
(9.3)
16.8E-6
(2.8)
1.121
(3.7)
0.005
(7.1)
0.265
(14.2)
0.246
(3.2)
14.3E-6
(4.0)
0.991
(9.6)
0.019
(54.6)
0.401
(16.3)
)0.394
(5.1)
4.08E-6
(3.6)
0.958
(7.6)
0.246E-6
(2.8)
1.483
(4.4)
)0.061
(84.6)
0.344
(19.5)
)0.200
(3.3)
10.4E-6
(3.0)
1.027
(13.2)
)0.030
(24.1)
0.148
(6.6)
)0.404
(3.9)
4.95E-6
(3.6)
0.863
(8.8)
13.1E-6
(2.9)
0.599
(3.5)
)0.045
(43.9)
0.066
(3.6)
0.303
(3.6)
13.2E-6
(3.3)
1.038
(9.1)
0.004
(3.9)
)0.517
(33.9)
)0.292
(4.4)
3.51E-6
(3.2)
1.086
(8.7)
388
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
new ®nancial instruments and the abolition of capital controls increased longterm capital mobility, the hypothesis is that in more recent decades there
should be stronger evidence in favor of UIP than in earlier decades.
Table 3 contains a mixed bag of results. 11 For a start, empirical support for
the UIP-hypothesis has clearly increased in the 1980s compared to the 1970s.
While the ®ve estimated regression coecients for the 1970s point at uncovered
interest dierentials moving consistently in the opposite direction to that implied by PPP-based exchange rate forecasts, these parameters all adopt the
expected positive sign during the 1980s. Nonetheless, there is no discernable
tendency for these coecients to further increase from the 1980s to the 1990s.
If anything, the majority of them is decreasing. Only for France and the UK
does Table 3 reveal the expected upward sloping pattern across the decades.
For the other countries, the data seem to reject the notion of steady increases in
UIP-validation over time. 12
All in all, one cannot simply conclude that our evidence supports the validity
of UIP among all `industrialized' currencies. It nevertheless appears that from
the 1980s onward and with the single exception of Japanese securities, 13 uncovered interest rate dierentials consistently adjust in the same direction as
suggested by PPP-based expected rates of depreciation, albeit less than one-forone. In this respect, the strategy of employing 10-year ahead PPP-based
exchange rate forecasts instead of ex-post realizations to proxy for (unobservable) exchange rate expectations clearly yields more support for UIP than
the various short-horizon UIP-studies summarized in Froot (1990) and
McCallum (1994).
Further investigation will have to reveal whether the relatively favorable
results presented here are due to an empirically `superior' way of gauging exchange rate expectations (by means of PPP), or whether these are simply
prompted by the use of assets with a longer maturity. McCallum (1994) and
Meredith and Chinn (1998) have argued that for relatively short horizons,
failure of UIP may result from temporary risk-premium shocks in the face of
11
For the sake of parsimonity the diagnostics have been omitted from Table 3. In general, most
diagnostics were clearly supportive of the risk-adjusted UIP speci®cation (1) across the decades,
except (again) for the presence of excess kurtosis in France and Switzerland during the 1980s and
Japan during the 1990s.
12
Since Table 3 investigates a joint UIP and PPP hypothesis, one cannot fully exclude the
possibility that PPP is loosing validation the more capital mobility increases, for example when
long-term capital ¯ows themselves induce deviations from PPP (McDonald and Marsh, 1997).
However, this alternative explanation would not seem to square very well with the recent increase in
empirical support for long-run PPP documented in Section 3.
13
The results for Japan may have been adversely aected because our method of gauging
exchange rate expectations from current PPP rates does not take account of trends in PPP, such as
the long-run upward trend that Japan has witnessed (see also Footnote 7). There is also evidence
that equilibrium exchange rates can be in¯uenced by trends in overseas net assets, which may also
have been potentially important for Japan.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
389
an endogenous monetary policy that is characterized by `leaning against the
wind' of prevailing exchange rate movements. 14 In the longer term, in contrast, exchange rates are driven by `fundamentals', leading to a relation between interest rate dierentials and exchange rates that should be more
consistent with UIP. While our PPP-based results seem to ®t into this explanation fairly well, a full-¯edged assessment of the risk-adjusted UIP model (1)
across the term structure would be needed to actually address the relevance of
their claim. This issue will feature prominently on the future research agenda.
5. Conclusion
This paper has investigated the UIP-relationship between bond yield differentials vis-
a-vis the US, Germany, France, the UK, Switzerland, and Japan
with the aid of PPP-based exchange rate expectations against the US dollar.
Globalization and integration of ®nancial markets would seem to imply a
tendency toward co-movement of bond yields, as re¯ected in a greater likelihood of validating the UIP-relation. A visual inspection of the major swings in
international bond markets would indeed suggest such a tendency. However,
the paper could not present formal evidence supporting the notion of further
increases in co-movement beyond that associated with the wave of ®nancial
market liberalization and deregulation in the early 1980s. Nonetheless, the
UIP-tests did suggest that the strategy of employing PPP-based forecasts instead of ex-post realizations to proxy for (unobservable) exchange rate expectations constitutes a promising contribution to the existing literature.
Acknowledgements
We would like to thank Tamim Bayoumi, Peter van Bergeijk, Carlo Cottarelli, Tarhan Feyzio
glu, Aerdt Houben, Lex Hoogduin, Malcolm Knight,
Zenon Kontolemis, Erik Lundback, Donogh McDonald, Kevin Ross, Nikola
Spatafora, Elmer Sterken, Job Swank, Peter Vlaar, various participants at the
1998 Annual Conferences of the Royal Economic Society and the European
Economic Association, and two anonymous referees for useful comments on
an earlier version. Henk van Kerkho provided expert research assistance.
Nonetheless, the usual disclaimer applies.
14
Unfortunately, the backward-looking speci®cation of the time-varying risk premium in our
model (1) is unable to directly pick up the type of contemporaneous risk-premium shocks that
contaminate short-horizon tests of UIP.
390
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
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www.elsevier.com/locate/econbase
Testing for long horizon UIP using PPP-based
exchange rate expectations
Jan Marc Berk
a,b
, Klaas H.W. Knot
a,*
a
b
De Nederlandsche Bank, P.O. Box 98, 1000 AB Amsterdam, Netherlands
Department of Economics, Free University, de Boelelaan 1105, 1081 HV Amsterdam, Netherlands
Received 14 January 1999; accepted 18 October 1999
Abstract
This paper revisits the uncovered interest parity relation. It supplements existing
work in two ways: It focuses on long instead of short-term interest rates, and, related to
that, employs exchange rate expectations derived from purchasing power parity (PPP)
instead of actual outcomes. Among the major ¯oating currencies over the period 1975±
1997, the paper cannot support the notion of further increases in UIP-validation beyond
that associated with the wave of ®nancial market liberalization and deregulation in the
early 1980s. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: E43; E44
Keywords: Interest parity relations; Exchange rate expectations
1. Introduction
Notwithstanding the greater importance of long-term interest rates for the
business cycle in most countries, the empirical literature on international interest rate linkages focusing on short-term assets generally outnumbers the
studies using long-term rates. 1 This re¯ects the fact that ®nancial instruments
*
Corresponding author.
Recent studies involving long-term rates are Kasman and Pigott (1988), Howe and Pigott
(1991), Pigott (1993), Throop (1994), Fell (1996), Kirchg
assner and Wolters (1996), Fase and Vlaar
(1998), and Meredith and Chinn (1998).
1
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 0 0 ) 0 0 0 8 3 - 2
378
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
traded at the long end of the market generally lack a well-developed forward
market. While it is true that forward markets are most developed at the threemonth maturity and hardly exist at maturities greater than two years, even
among well-traded currencies, in the 1980s the currency swap market became
suciently developed to hedge exchange rate risk for long-term investments as
well (Popper, 1990, 1993; Fletcher and Taylor, 1996). In addition to the
gradual worldwide abolition of capital controls, this ®nancial innovation may
have increased the linkage of international long-term interest rates.
Financial innovations contribute to international capital market integration
by increasing capital mobility. This paper investigates whether this increased
capital mobility has also resulted in a greater validation of the uncovered interest rate parity (UIP) relationship, as, under these circumstances, the scope
for interest rate arbitrage increases and the impact on interest rate dierentials
of factors other than (expected) exchange rate movements and time-varying
risk premia should steadily diminish. The focus on long-term interest rates is by
itself an important contribution to the existing literature, which, as mentioned
earlier, mainly concentrates on short-term instruments. A second but related
novelty is the use of exchange rate expectations based on long-run purchasing
power parity (PPP) instead of the more common form of rational expectations
where actual exchange rate movements proxy for expected ones.
The bulk of the evidence on UIP thus far indicates not just that (actual)
exchange rates fail to move one-for-one with interest rate dierentials, but
rather that their changes are substantial and in the opposite direction to that
implied by UIP. Froot (1990) has calculated an average regression coecient
across some 75 published estimates of )0.88. A few estimates are positive, but
all of them are distinctly smaller than the null hypothesis of a coecient of +1.
McCallum (1994) and Meredith and Chinn (1998) have argued that for relatively short horizons, failure of UIP results from risk-premium shocks in the
face of endogenous monetary policy. In the longer term, in contrast, exchange
rates are driven by `fundamentals', leading to a relation between interest rates
and exchange rates that should be more consistent with UIP.
The remainder of the paper is organized as follows: Section 2 presents some
stylized facts. UIP and PPP are brie¯y discussed in Section 3, followed by a
description of the data and the methodology used. Section 4 puts the theoretical predictions to an empirical test. Section 5 concludes the paper.
2. Recent developments in international bond markets
In the aftermath of two oil crises during the second half of the 1970s many
industrialized countries experienced strong upward pressure on long-term interest rates, when in¯ation pressures rose and, around the turn of the decade,
monetary policy was tightened quite aggressively. After reaching record heights
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
379
in the early 1980s, bond yields have gradually come down and there has been a
marked worldwide convergence of nominal (and also real) long-term interest
rates. This trend broadly corresponds to the declining trend in in¯ation during
this period and the simultaneous reduction in in¯ation divergences. This process was interrupted in the periods surrounding the stock market collapse of
1987 and the tightening of United States monetary policy in 1994. In both
phases, substantial concerns about the return of in¯ationary pressures in the
US economy developed, and bond yields rose accordingly.
Table 1 documents the major swings that have taken place in international
government bond markets since 1975 in more detail. 2 Especially during the
1970s and the early 1980s, long-term interest rates across the major countries
have been pushed apart, often with accompanying movements in exchange
rates. Countries that had experienced the largest in¯ation increases toward the
end of the 1970s, such as the US, the UK, and France, had to allow for higher
yields than Germany and Japan around the turn of the decade, while their
currencies generally fell against the deutsche mark and the yen. US interest
rates rose between spring-1983 and mid-1984 while at the same time interest
rates in Europe and Japan were generally falling, partly due to the eects of US
®scal expansion in creating excess demand for domestic savings. The pressures
resulting from this divergence in long-term interest rates were also re¯ected in
the sharp appreciation of the dollar in this period, as well as by the reversal of
that appreciation that began in 1985 and occurred as US bond yields were
falling back.
For the 1990s, however, Table 1 would seem to reveal a somewhat larger
synchronization among bond yields than in the previous decades. Apart from
the correction after the Fed-tightening of 1994 and an additional hiccup during
the ®rst half of 1996, 3 the 1990s have been characterized by declining bond
yields worldwide. In view of the experience of the 1980s, it is the circumstances
surrounding the interest rate developments, and not the mere fact that they
moved together, that would seem somewhat unusual. The 1994 long-term interest rate run-ups in Europe and Japan followed a prolonged period of declining short-term interest rates and weak economic activity. The experience of
the 1990s thus suggests that the degree to which bond yields are free to vary
with national conditions should not be overstated, even under ¯oating exchange rates. 4
2
The methodology that has been adopted to classify a major swing in the bond market is similar
to that used by the NBER to date business cycles. Peaks and troughs were identi®ed using a 12month moving window. A `bull' market is de®ned as at least 6 consecutive months of declining
bond yields and a `bear' market is de®ned in the opposite way.
3
This hiccup is not identi®ed in Table 1, as the number of consecutive months with
unidirectional movements was limited to ®ve instead of the required six (see previous note).
4
In this respect, Browne and Tease (1992) ®nd little tendency for long-term interest rates to vary
systematically with the business cycle.
380
a
Market
type
US
Start
Change
Start
Germany
Change
Start
France
Change
Bull
Bear
Bull
Bear
Bull
Bear
75/09
76/12
)156
+845
75/01
)410
75/01
75/09
78/02
79/04
)80
+126
)172
+741
Bull
Bear
Bull
Bear
Bull
Bear
81/09
83/05
84/06
87/01
87/10
89/12
81/09
Bull
Bear
Bull
End
90/09
93/10
94/11
97/12
78/04
+544
)494
+318
)648
+244
)168
+105
81/09
83/03
83/12
86/04
)322
+96
)301
+367
)356
+262
)343
90/10
94/01
95/01
97/12
)339
+194
)355
UK
Start
Change
75/03
76/10
77/10
79/12
80/10
+260
)505
+374
)160
+283
)928
81/10
)719
86/08
87/10
89/08
+299
)239
+211
86/04
86/11
88/04
+204
)160
+314
90/09
94/01
95/01
97/12
)481
+252
)400
90/04
94/01
94/09
97/12
)611
+257
)381
Switzerland
Japan
Start
Change
Start
Change
75/04
)384
75/01
76/12
78/04
80/03
81/03
+19
)245
+389
)223
+139
81/09
)631
87/05
+552
90/09
93/12
94/10
97/12
)531
+160
)390
78/12
+310
81/09
83/01
85/03
)191
+72
)117
88/04
+292
90/04
93/12
94/09
97/12
)264
+149
)286
Notes: Changes are measured in basis points. Peaks and troughs were identi®ed using a 12-month moving window. A Ôbull' market is de®ned as at least
6 consecutive months of declining bond yields and a Ôbear' market is similarly de®ned for rising bond yields.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
Table 1
Peak to trough analysis of major swings in international bond marketsa
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
381
More formal evidence on the degree to which long-term interest rates have
become more synchronized with globalization can be extracted from bilateral
correlations of their changes against those in the major market. In this respect,
the US bond market is clearly the world's dominant market, with a size about
three times that of Germany, the second largest market, for instance. For the
®ve countries under investigation, Fig. 1 displays 5-year rolling correlations of
monthly changes in domestic bond yields vis-a-vis US yields since the mid1970s. Apart from the stylized fact that co-movements in long-term interest
rates among the major industrialized economies were stronger in the 1980s and
1990s than during the 1970s (see among others Frankel, 1989), by this measure
there seems to have been no systematic further increase in the bilateral synchronization since the early 1980s.
The message from Table 1 and Fig. 1 is rather mixed. This should not be too
much of a surprise, since the analysis thus far has been con®ned to bond
markets mainly, without proper reference to contemporaneous developments
in currency markets. As is well known, however, exchange rates among the
largest industrialized countries have ¯uctuated quite substantially in the period
under investigation. Below, we shall therefore introduce exchange rate movements into the analysis.
3. UIP and PPP
The eect of exchange rate movements on interest rate relations can be
described in terms of the standard UIP-relation. Its most restrictive representation assumes risk neutral investors and perfect substitutability between assets
that are comparable in all respects except their currency of denomination
(Blundell-Wignall and Browne, 1991). Dropping the assumption of risk neutrality introduces risk premia (Knot and de Haan, 1995). Following the seminal
work of Engle et al. (1987), we allow for a time-varying risk premium by estimating the UIP-relationship as the conditional mean speci®cation in a
ARCH-in-mean model. In order to preserve a parsimonious speci®cation for
the conditional variance term, we set the order of the ARCH-process equal to 1
(month), a choice that performed reasonably well in the empirical analysis
below. We therefore estimate
Et stk ÿ st
cqt t ;
a
b
ikt ÿ ik;
t
k
1
2
2
qt d /tÿ1 ;
where ikt denotes the nominal interest rate on a ®nancial instrument with a
remaining life of k periods in the home country, an asterisk its foreign
equivalent, st the natural logarithm of the nominal exchange rate (domestic
382
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
Fig. 1. Correlations of movements in domestic bond yields vis-
a-vis the US. Source: Authors' own calculations.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
383
currency price of a foreign currency unit, here one US dollar) and E denotes
the expectations operator. Conditional on past information, the residuals t are
distributed normally with mean zero and variance q2t . In this speci®cation, the
time-varying risk premium is proxied by the conditional standard deviation qt
that directly aects the interest rate dierential vis-a-vis the US, with an elasticity of c. The speci®cation conforms with a very simple model in which ®nancial market participants predict this period's variance based on information
about previous volatility. An unexpectedly large interest rate dierential will
increase the estimated variance for the next period.
In general, only interest rates are observable in Eq. (1). To overcome the
identi®cation problem with respect to the expected depreciation term, most
authors resort to the rational expectations hypothesis to justify their use of
actual exchange rate outcomes to proxy for unobservable expectations. This
way, however, UIP can only be tested in conjunction with this speci®c process
of expectations formation; in case of a subsequent rejection it remains unclear
which leg of the joint hypothesis is not being supported by the data. Moreover,
it has often been documented that participants in the foreign exchange market
do make systematic forecast errors and do not always use all information ef®ciently when forecasting (Frankel and Froot, 1987; Takagi, 1991; Cavaglia et
al., 1993; Sobiechowski, 1996). In our view, the longer the horizon of the investment in question, the more debatable this practice of inserting ex-post
realizations for ex-ante expectations becomes. 5
Instead, we propose a process of long-term expectations formation in which
the exchange rate is assumed to be ultimately guided by its `fundamental anchor' of PPP. 6 Underlying this assumption is the notion that investors, while
acknowledging the possibility that exchange rates may be misaligned for a
couple of months, quarters, or even years, will regard the persistence of this
phenomenon over the full 10-year term as rather unlikely. Questioning 200
chief London forex dealers, Allen and Taylor (1989) indeed found that at
forecast horizons of one year and longer, nearly 30% of respondents relied on
pure fundamentals and 85% judged fundamentals to be more important than
swings in market psychology as captured by `chartism'. Moreover, recent
studies that either use long-horizon or panel data sets have been quite supportive of the notion that real exchange rates are in fact mean-reverting, with
an estimated half-life for deviations from PPP of about three to four years
(Abuaf and Jorion, 1990; Froot and Rogo, 1995; Wu, 1996; Papell, 1997).
5
This need not be true for rational expectations in general. As pointed out by one referee, the
`asymptotically rational expectations theory' states exactly the opposite (Stein, 1986).
6
Note that, in general, assuming PPP is not equivalent to discarding the rational expectations
hypothesis. It is, however, at odds with the speci®c representation of the latter hypothesis in which
actual exchange rate movements proxy for expected ones.
384
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
For a 10-year horizon it therefore seems plausible to expect the exchange
rate to revert to `current wisdom' regarding its long-run equilibrium, as
measured by then prevailing estimates of PPP exchange rates. 7 One advantage of this procedure is that it only uses information that is readily available
at the time when investors decide on the diversi®cation of their portfolios.
For this purpose, annual data on PPP exchange rates were gathered from the
OECD National Accounts database, that have been interpolated into
monthly PPP observations based on developments in relative consumer prices
employing a method proposed by Boot et al. (1967). 8 Averaged over the year
the movement in the resulting series is identical to the original OECD series
while movements within the year re¯ect movements in the CPI of the country
relative to the US, which is in line with the nature of PPP. Annualized `expected' rates of depreciation are then calculated by dividing the deviation of
the actual exchange rate from its PPP-value by the term of the investment
(ten years).
4. Empirical results
This section tests for UIP vis-
a-vis the US, regressing the long-term interest
rate dierential with the US for Germany, France, the UK, Japan, and Switzerland on an intercept, the expected rate of depreciation of their currency
against the US dollar, and a time-varying risk premium. Intercepts are included
to take into account a number of country-speci®c characteristics of the ®nancial system that are less time-varying, such as for instance the liquidity of
the US bond markets vis-
a-vis those in the other countries, or dierences in
capital income taxation (McCallum, 1994).
Table 2 ®rst presents estimates of the risk-adjusted UIP-model (1) with respect to the entire sample, using maximum likelihood with heteroskedasticityconsistent standard errors (Bollerslev and Wooldridge, 1992). Decade-speci®c
7
Ideally, one should use the expected PPP rate at maturity as the anchor guiding exchange rate
expectations under PPP. The dierence between the expected PPP rate k years ahead, Et sPPP
tk , and
the current PPP rate, sPPP
, will normally correspond to the expected cumulative in¯ation dierential
t
between the US and the foreign country in question over that time interval, Et pt;tk ÿ pt;tk , so
that the latter expectation should be regarded as a missing variable in our regressions (recall
PPP
PPP
Et sPPP
sPPP ÿ st Et pt;tk ÿ pt;tk sPPP ÿ st . In terms of the empirical
tk ÿ st Et stk ÿ st
implementation, however, it is not so straightforward to come up with a proxy that would
adequately capture this ten-year ahead expected in¯ation dierential.
8
The two-step procedure is as follows: First, by minimizing the sum of squares of the second
dierences a monthly series is interpolated, ensuring smoothness whilst preserving the movement of
the original series. Subsequently, monthly observations on PPP are constructed as the ®tted values
of a regression of the smooth interpolated monthly series on the quotient of monthly movements in
the consumer price index (CPI) relative to the US.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
385
Table 2
Testing for UIP: Entire sample 1975.01±1997.12a
Intercepts
1970s
1980s
1990s
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
Diagnostics
R2 -adjusted
LM[ARCH-8]
(p-value)
Q(32)
(p-value)
LM[NORM]
(p-value)
Germany
France
UK
)0.024
(44.4)
)0.030
(100.0)
)0.008
(21.7)
0.307
(32.6)
0.166
(3.1)
0.022
(47.0)
0.009
(15.4)
0.009
(24.8)
0.141
(10.6)
)0.080
(1.8)
0.066
(87.3)
0.007
(14.2)
0.020
(59.1)
0.256
(14.5)
)0.077
(1.8)
6.05E-6
(5.9)
1.127
(10.9)
8.78E-6
(4.9)
1.066
(13.2)
5.11E-6
(4.6)
1.085
(12.8)
0.64
1.02
(0.42)
23.70
(0.86)
5.76
(0.15)
ADF tests on standardized residuals
3 unit roots
15.94
(C,4)
2 unit roots
11.37
(C,4)
1 unit root
4.15
(N,2)
Conclusion
I(0)
0.20
1.65
(0.11)
54.07
(0.01)
5.96
(0.05)
0.61
1.60
(0.13)
42.51
(0.10)
3.33
(0.19)
14.64
(C,4)
9.61
(C,4)
4.43
(N,2)
I(0)
15.92
(C,4)
9.77
(C,4)
4.15
(N,1)
I(0)
Switzerland
)0.033
(66.1)
)0.062
(101.7)
)0.034
(43.6)
0.270
(17.8)
)0.027
(0.7)
4.99E-6
(4.7)
1.053
(21.6)
0.50
0.81
(0.59)
34.95
(0.33)
13.71
(0.00)
16.29
(C,4)
11.64
(C,4)
4.63
(N,1)
I(0)
Japan
0.006
(9.3)
)0.023
(20.3)
)0.002
(1.3)
)0.383
(20.9)
)0.470
(5.9)
8.25E-6
(3.9)
1.018
(14.8)
0.52
1.08
(0.38)
21.93
(0.91)
13.00
(0.00)
13.76
(C,4)
9.06
(C,4)
4.58
(N,1)
I(0)
a
Absolute t-values, computed with heteroskedasticity consistent standard errors are in parentheses.
LM[ARCH-8] is Lagrange-Multiplier test for ARCH-8; Q(32) is Ljung±Box Q-test; LM[NORM] is
Jarque±Bera test. Critical values for an ADF-test on the residuals of a cointegration relation with
three non-stationary variables are 4.35 (1%) and 3.78 (5%), respectively (Engle and Yoo, 1987).
Signi®cance of the ADF tests at the 5% ( ) and 1% ( ) level is indicated. The information within
parentheses relates to the deterministic part of the ADF-equation: T linear trend, C constant,
N neither.
intercepts were included from the outset, in order to account for structural
breaks related to matters such as the liberalization and globalization of ®nancial markets and the advent of new ®nancial instruments. This way, we also
circumvented a number of econometric problems prompted by estimation with
386
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
a single intercept, such as singularity problems (Germany, UK), or consistently
poor diagnostics (others).
Upon investigating Table 2, three features stand out. First, while four out of
®ve parameters of the expected rates of depreciation have the expected positive
sign ± Japan being the exception ± for none of the countries is the coecient
near unity, as would be implied by strict UIP. Second, despite the greater liquidity of the US bond markets, both Switzerland and Japan combine generally negative intercepts with a negative sign on the time-varying risk premia.
Both countries are characterized by a relatively closed and to some extent also
protected ®nancial system, which may be have kept domestic bond yields arti®cially low. 9 For the other countries the evidence on risk premia is more
balanced, combining negative intercepts with positive ARCH-in-mean elements (Germany) or vice versa (France and UK). Finally, despite the restrictive
character of both the UIP and the ARCH(1)-in-mean speci®cation for a decomposition of interest rate dierentials, the equations are reasonably wellbehaved ± aside from some excess kurtosis ± and capable of explaining a fair
amount of intertemporal variation in interest rate dierentials.
The lower panel of Table 2 reports on a Engle and Granger (1987) type
cointegration test for the UIP regressions estimated. From an investigation of
the time-series characteristics of individual interest rate dierentials and PPPbased expected rates of depreciation (not shown), no clear-cut picture across
countries emerged as to the order of integration of these variables. Additionally, the variance equations of Table 2 reveal a good deal of persistence in the
time-varying risk premia, possibly suggesting non-stationarity for this generated regressor as well. Table 2 therefore proceeds by investigating the
stationarity properties of the standardized residuals of the risk-adjusted UIPmodel. 10 Stationary residuals would point to the existence of cointegration
between the three stochastic variables in the risk-adjusted UIP-model (1).
From the ®nal row of Table 2 it appears that for all ®ve countries investigated
non-stationarity of the residuals can safely be rejected, thereby validating our
levels-based speci®cation in (1).
9
Switzerland has often been referred to as an Ôinterest rate islandÕ, owing to the stylized fact that
real interest rates have been lower in Switzerland than in most other industrialized countries and
that Swiss interest rates seem to be decoupled from world interest rates to a greater extent than in
other countries. These features may relate to an excess of national savings over investment for
many years, that has resulted in a persistent current account surplus and the largest ratio of net
foreign assets to GDP in the world (Mauro, 1995).
10
This standardization, common in the evaluation of (G)ARCH models, implies dividing the
residuals from the model estimated in Table 2 by their conditional standard deviation, and ensures
that the residuals are i.i.d., with zero mean and unit variance. As shown by Engle and Granger
(1987) and Engle and Yoo (1987), the critical values for the residuals-based test for cointegration
depend on the number of I(1) variables in the cointegrating regression.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
387
In order to investigate whether the apparent increases in co-movement of
bond yields across the decades ± suggested in Section 2 ± can be traced back to
a declining prevalence of exchange rate misalignments, Table 3 reports on
subsample estimates of the risk-adjusted UIP-model (1). Since the advent of
Table 3
Testing for UIP across the decadesa
(a) 1975.01±1979.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
(b) 1980.01±1989.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
(c) 1990.01±1997.12
Intercept
PPP-based expected
depreciation
Time-varying risk
premium
Variance equations
Intercept
ARCH(1)
a
Notes: See Table 2.
Germany
France
UK
Switzerland
Japan
0.021
(41.6)
)1.227
(47.6)
0.126
(1.7)
0.052
(11.5)
)0.961
(15.0)
)1.847
(2.0)
0.038
(32.7)
)0.899
(19.5)
0.234
(1.9)
)0.001
(1.4)
)1.380
(71.5)
0.128
(2.4)
0.005
(2.8)
)0.680
(22.6)
0.063
(0.2)
3.37E-6
(2.8)
1.256
(3.7)
)0.029
(55.5)
0.317
(23.1)
)0.072
(0.8)
9.23E-6
(3.2)
1.034
(7.9)
)0.001
(1.8)
0.142
(6.5)
)0.002
(0.1)
2.52E-6
(3.7)
1.020
(10.4)
16.1E-6
(5.1)
0.384
(2.2)
0.007
(6.2)
0.174
(9.8)
0.239
(2.2)
16.0E-6
(2.8)
0.955
(7.9)
0.005
(7.3)
0.527
(14.3)
)0.477
(3.5)
3.44E-6
(3.1)
1.039
(9.3)
16.8E-6
(2.8)
1.121
(3.7)
0.005
(7.1)
0.265
(14.2)
0.246
(3.2)
14.3E-6
(4.0)
0.991
(9.6)
0.019
(54.6)
0.401
(16.3)
)0.394
(5.1)
4.08E-6
(3.6)
0.958
(7.6)
0.246E-6
(2.8)
1.483
(4.4)
)0.061
(84.6)
0.344
(19.5)
)0.200
(3.3)
10.4E-6
(3.0)
1.027
(13.2)
)0.030
(24.1)
0.148
(6.6)
)0.404
(3.9)
4.95E-6
(3.6)
0.863
(8.8)
13.1E-6
(2.9)
0.599
(3.5)
)0.045
(43.9)
0.066
(3.6)
0.303
(3.6)
13.2E-6
(3.3)
1.038
(9.1)
0.004
(3.9)
)0.517
(33.9)
)0.292
(4.4)
3.51E-6
(3.2)
1.086
(8.7)
388
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
new ®nancial instruments and the abolition of capital controls increased longterm capital mobility, the hypothesis is that in more recent decades there
should be stronger evidence in favor of UIP than in earlier decades.
Table 3 contains a mixed bag of results. 11 For a start, empirical support for
the UIP-hypothesis has clearly increased in the 1980s compared to the 1970s.
While the ®ve estimated regression coecients for the 1970s point at uncovered
interest dierentials moving consistently in the opposite direction to that implied by PPP-based exchange rate forecasts, these parameters all adopt the
expected positive sign during the 1980s. Nonetheless, there is no discernable
tendency for these coecients to further increase from the 1980s to the 1990s.
If anything, the majority of them is decreasing. Only for France and the UK
does Table 3 reveal the expected upward sloping pattern across the decades.
For the other countries, the data seem to reject the notion of steady increases in
UIP-validation over time. 12
All in all, one cannot simply conclude that our evidence supports the validity
of UIP among all `industrialized' currencies. It nevertheless appears that from
the 1980s onward and with the single exception of Japanese securities, 13 uncovered interest rate dierentials consistently adjust in the same direction as
suggested by PPP-based expected rates of depreciation, albeit less than one-forone. In this respect, the strategy of employing 10-year ahead PPP-based
exchange rate forecasts instead of ex-post realizations to proxy for (unobservable) exchange rate expectations clearly yields more support for UIP than
the various short-horizon UIP-studies summarized in Froot (1990) and
McCallum (1994).
Further investigation will have to reveal whether the relatively favorable
results presented here are due to an empirically `superior' way of gauging exchange rate expectations (by means of PPP), or whether these are simply
prompted by the use of assets with a longer maturity. McCallum (1994) and
Meredith and Chinn (1998) have argued that for relatively short horizons,
failure of UIP may result from temporary risk-premium shocks in the face of
11
For the sake of parsimonity the diagnostics have been omitted from Table 3. In general, most
diagnostics were clearly supportive of the risk-adjusted UIP speci®cation (1) across the decades,
except (again) for the presence of excess kurtosis in France and Switzerland during the 1980s and
Japan during the 1990s.
12
Since Table 3 investigates a joint UIP and PPP hypothesis, one cannot fully exclude the
possibility that PPP is loosing validation the more capital mobility increases, for example when
long-term capital ¯ows themselves induce deviations from PPP (McDonald and Marsh, 1997).
However, this alternative explanation would not seem to square very well with the recent increase in
empirical support for long-run PPP documented in Section 3.
13
The results for Japan may have been adversely aected because our method of gauging
exchange rate expectations from current PPP rates does not take account of trends in PPP, such as
the long-run upward trend that Japan has witnessed (see also Footnote 7). There is also evidence
that equilibrium exchange rates can be in¯uenced by trends in overseas net assets, which may also
have been potentially important for Japan.
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
389
an endogenous monetary policy that is characterized by `leaning against the
wind' of prevailing exchange rate movements. 14 In the longer term, in contrast, exchange rates are driven by `fundamentals', leading to a relation between interest rate dierentials and exchange rates that should be more
consistent with UIP. While our PPP-based results seem to ®t into this explanation fairly well, a full-¯edged assessment of the risk-adjusted UIP model (1)
across the term structure would be needed to actually address the relevance of
their claim. This issue will feature prominently on the future research agenda.
5. Conclusion
This paper has investigated the UIP-relationship between bond yield differentials vis-
a-vis the US, Germany, France, the UK, Switzerland, and Japan
with the aid of PPP-based exchange rate expectations against the US dollar.
Globalization and integration of ®nancial markets would seem to imply a
tendency toward co-movement of bond yields, as re¯ected in a greater likelihood of validating the UIP-relation. A visual inspection of the major swings in
international bond markets would indeed suggest such a tendency. However,
the paper could not present formal evidence supporting the notion of further
increases in co-movement beyond that associated with the wave of ®nancial
market liberalization and deregulation in the early 1980s. Nonetheless, the
UIP-tests did suggest that the strategy of employing PPP-based forecasts instead of ex-post realizations to proxy for (unobservable) exchange rate expectations constitutes a promising contribution to the existing literature.
Acknowledgements
We would like to thank Tamim Bayoumi, Peter van Bergeijk, Carlo Cottarelli, Tarhan Feyzio
glu, Aerdt Houben, Lex Hoogduin, Malcolm Knight,
Zenon Kontolemis, Erik Lundback, Donogh McDonald, Kevin Ross, Nikola
Spatafora, Elmer Sterken, Job Swank, Peter Vlaar, various participants at the
1998 Annual Conferences of the Royal Economic Society and the European
Economic Association, and two anonymous referees for useful comments on
an earlier version. Henk van Kerkho provided expert research assistance.
Nonetheless, the usual disclaimer applies.
14
Unfortunately, the backward-looking speci®cation of the time-varying risk premium in our
model (1) is unable to directly pick up the type of contemporaneous risk-premium shocks that
contaminate short-horizon tests of UIP.
390
J.M. Berk, K.H.W. Knot / Journal of Banking & Finance 25 (2001) 377±391
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