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EXCHANGE RATE COINTEGRATION ACROSS
CENTRAL BANK REGIME SHIFTS
by
Jose A. Lopez
Federal Reserve Bank of New York
Research Paper No. 9602
January 1996
This paper is being circulated for purposes of discussion and comment only.
The contents should be regarded as preliminary and not for citation or quotation without
permission of the author. The views expressed are those of the author and do not necessarily
reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.
Single copies are available on request to:
Public Information Department
Federal Reserve Bank of New York
New York, NY 10045
Exchange Rate Cointegration Across
Central Bank Regime Shifts
Jose A. Lopez
Research and Market Analysis Group
Federal Reserve Bank of New York
33 Liberty Street
New York, NY 10045
(212) 720-6633
Draft Date: January II, 1996
ABSTRACT: Foreign exchange rates are examined using cointegration tests over
various time
periods linked to regime shifts in central bank behavior. The number of cointeg
rating vectors
seems to vary across these regime changes within the foreign exchange market
. For example,
cointegration is not generally found prior to the Plaza Agreement of September
22, 1985, but·
it is present after that date. The significance of these changes is evaluated using
a likelihood
ratio procedure proposed by Quintos (1993). The changing nature of the cointeg
rating
relationships indicate that certain aspects of central bank activity do have long-te
rm effects on
exchange rates.
Acknowledgements: The views expressed here are those of the author and not
those of the Federal Reserve Bank of
New York or the Federal Reserve System. I thank Frank Diebold for
his extensiv e comments and suggestio ns on an
earlier draft of this paper and Carmela Quinto, for generously providing the necessar
y tables of critical values. I also
thank Roberto Mariano, Jesus Felipe, Lorenzo Giorgianni as well as several
seminar participants for helpful
discussio ns.
I Tntrorlnction
"Nevertheless, the empirical evidence, although allowing for the possibility of
short-lived effects, does not ascribe to [central bank] intervention a long-lasting
effect on the foreign exchange market." - Edison (1993)
The above quote is the concluding sentence of Edison's recent survey on the efficacy of
central bank intervention in the foreign exchange market. The short-term impact of central
bank intervention has been extensively studied, even down to the level of continuous time data
(Goodhart and Hosse, 1993). However, the long-term impact of central bank behavior in the
foreign exchange market has not been carefully examined. The long-term behavior of
exchange rates is an important area of economic research and has been addressed by Engel and
Hamilton (1990), Mark (1995) and others. An important component of this research is regime
shifts in central bank behavior, such as the Plaza Agreement of 1985. In this paper, the longterm impact of such regime shifts is examined using cointegration procedures.
Cointegration, as introduced by Engle and Granger (1987), is used to test for the
existence of long-term relationships among nonstationary economic variables. Exchange rates
are considered to be nonstationary time series, as first established by Meese and Singleton
(1982), and systems of exchange rates may exhibit cointegrating relationships. However, as
pointed out by Granger (1986), financial asset prices determined in efficient markets should
not be cointegrated. That is, if they were cointegrated, one could forecast a given series on
the basis of other series in the cointegrated system, and the efficient markets hypothesis would
not hold. Several studies have tested for cointegration in systems of foreign exchange rates,
such as Hakkio and Rush (1989), Copeland (1991), Baillie and Bollerslev (1989), and Diebold
et al. ( 1994). Using various co integration testing procedures, these studies achieve different
1
results. Specifically, Baillie and Bollerslev (1989) find cointegration in a system
of seven
daily exchange rates, but Diebold et al. (1994) find no cointegration in this system
once a
trend is explicitly modelled.
This paper attempts to extend these studies by incorporating structural breakp
oints into
the cointegration analysis. Structural breaks in data series, particularly in asset
price series,
usually indicate fundamental changes in the underlying data generating process
es. Such breaks
may significantly alter the equilibrium relationships between data series, and tests
of the longterm behavior of these series should take account of them. 1 The breakpoints examin
ed are
linked to specific regime shifts in central bank behavior in the foreign exchan
ge market.
Generally, studies of such central bank activities have been limited to intervention,
official
sales or purchases of foreign assets against domestic assets. Much research has
found these
activities to have little, if any, impact on the behavior of exchange rates. This
paper focusses
instead on transactions or official announcements by central banks that, in essence
, indicate a
regime shift in their behavior. Examples of such intervention activities are the
formation of
the European Monetary System in March 1979 and the Plaza Agreement of Septem
ber 1985.
Five such episodes are examined in this paper.
With respect to the cointegration analysis, such regime shifts may be considered
structural breaks that fundamentally alter any long-term equilibrium relationships
which may
exist. Thus, the number of cointegrating vectors present in the periods before
and after the
1
Granger and Escribano (1986) find evidence that exceptional events in the gold
and silver markets cause these
two price series, which should not be cointegrated under the efficient markets
hypothesis, to be cointegrated during
certain time periods.
2
specified structural break may differ. Quintos (1993) presents a procedure for testing whether
such differences in the number of cointegrating vectors induced by structural breaks are
statistically significant. She specifically states that the procedure addresses structural breaks
that potentially change the definition of a system's equilibrium relationship. She suggests that ·
such a change could be brought about by fundamental changes in the behavior of institutions,
such as central banks.
The main finding of this paper is that the specified incidents of central bank regime
shifts do impact the long-term behavior of exchange rates. Varying numbers of cointegrating
relationships are found before and after the structural breaks, and the changes are mostly found
to be significant. For example, no cointegrating relationships are found in the period before
the Plaza Agreement of September 22, 1985, but after that date, evidence of co integration is
found. Since the Plaza Agreement signalled concerted intervention by central banks to cause a
dollar depreciation, it is not surprising that new long-term relationships (or market equilibria)
between exchange rates arose in the post-Plaza period. Similar results are found for other
breakpoints and for a subsystem of exchange rates consisting solely of EMS currencies.
Section II describes the exchange rate data used as well as the proposed structural
breakpoints examined. Section ill outlines the cointegration techniques used in the analysis.
Section IV summarizes the literature on cointegration tests of exchange rates and presents the
cointegration results for the various specified time periods and currencies. Section V
concludes.
3
IT. The Data and Stmc tural Breakpoints
.A. The Data
The spot foreign exchange rates used in this paper are the Feder
al Reserve Bank of
New York (FRBNY) rates as recorded at noon in the New York
foreign exchange market.
The eight exchange rates examined are the British pound (BP),
the German mark (DM), the
Japanese yen (JY), the French franc (FR), the Dutch guilder (NG),
the Italian lira (Ll), the
Swiss franc (SF) and the Canadian dollar (CD); see Figures I
to 8. The exchange rates are
expressed as the natural log of foreign currency units per U.S.
dollar, and the first differences
· of these series are the daily rates of return for dollar-based invest
ors; i.e.,
B. The Time Periods
Cointegration tests examine the long-term behavior of economic
data. Thus, as
discussed by Hakkio and Rush (1991), the length of the "long
term" is an immediately relevant
question. They argue that the proper length of the "long term"
must be determined in light of
the economic question being addressed. Two factors can be used
to determine the proper time
interval over which to examine exchange rates: one is market
based, the other is forecast
based. Given the massive daily trading volume in the foreign
exchange markets,2 new
information is quickly incorporated into exchange rates; this sugge
sts a rather short "longterm" horizon for exchange rate determination. Secondly, foreca
sts based on daily data are
2
Approximately $192 billion per day in the United States alone,
according to the FRBNY Foreign Exchange
Market Survey of 1992.
4
usually made only several months ahead, as in Diebold et al. (1994).
Given these two
reasons, time periods longer than one year (approximately 250 observations) seem to be
appropriate horizons over which to examine the long-term behavior of daily exchange rates.
As shown in Table I, the principal time periods examined in this paper meet this criterion.
In addition to a period's length, the choice of its endpoints is also important. With
respect to cointegration tests, Sephton and Larsen (1991) conclude that the evidence for
cointegration is "fragile" and exhibits "temporal sensitivity" since different subsample periods
provide differing results. Given this result, testing for cointegration over an arbitrarily chosen
· time period, as in Baillie and Bollerslev (1989) and other studies, does not seem appropriate.
An alternative method for selecting a period's endpoints is to impose structural breaks .
exogenously in the spirit of Perroti (1989). In this paper, the endpoints of the 18-year period
· examined are determined by an approximation to the start of the current floating-rate regime
and by data availability, and the five proposed structural breakpoints examined are linked to
regime shifts in central bank behavior in the foreign exchange market.
The first breakpoint suggested is November I, 1978. 3 On that date, a so-called "dollarrescue package" was enacted by the U.S. to at least halt the depreciation of the dollar. The
package consisted of tightened monetary policy and the creation of an intervention fund.
The
ensuing sustained and coordinated intervention temporarily raised the value of the dollar, but it
returned to its previous level by year end. The outcome of this intervention was interpreted to
mean that substantial effects could be achieved, but that these effects would be temporary
3
This breakpoint is explicitly examined in Loopesko (1984). In-depth summaries of the events surrounding all
five breakpoints are provided in Dominguez and Frankel (1993).
5
unless supported by genuine policy changes. This change in central bank behavi
or is included
in the subsequent analysis to detelllline whether it did have a long-te!lll impact.
The second proposed breakpoint, March 13, 1979, marks the follllation of the
European Monetary System (EMS). The original members agreed to fix their
mutual
exchange rates within certain bands and float jointly against the dollar. Althou
gh other
exchange rate agreements had existed amongst European currencies, the EMS
marked the
fo!lllation of a new and more strongly codified system.
The third suggested breakpoint, February 25, 1985, primarily arises from the
data.
Five of the six European exchange rates achieve their post-1973 maximum on
that day, and the
sixth (SF) achieves its post-EMS maximum eight days later on March 5, 1985.
According to
financial news reports at the time, market participants could not cite any particu
lar event that
led to the dollar' s rapid depreciation. However, the Ge!lllan Bundesbank and
other European
central banks, as well as the Federal Reserve to a lesser extent, intervened heavily
throughout
the first quarter of 1985 to halt the appreciation of the dollar.
This intervention activity by
the U.S. was directly linked to the change in the Secretary of the Treasury; Brady
was willing
to intervene while Regan was not. Most of these intervention operations were
widely reported
and signalled the central banks' intentions to market participants.
The fourth breakpoint examined is September 23, 1985, the first trading day
after the
announcement of the Plaza Agreement. In this agreement, the G-5 central banks
stated that
"some further orderly appreciation of the main non-dollar currencies against
the dollar is
desirable" and that they would "stand ready to cooperate more closely to encour
age this when
6
to do so would be helpful. "4 After this announcement, the dollar
continued its prolonged
depreciation as central banks intervened actively in the foreign
exchange markets.
The fifth breakpoint is February 22, 1987, the day after the Louv
re Accord. The G-7
central banks, excluding Italy, "agreed to cooperate close)y to
foster the stability of exchange
rates around current levels. "5 In essenc~, the central banks agree
d to stop the depreciation of
the dollar and maintain a reference range for the major non-dollar
currencies by intervening in
the market, as necessary.
Given the dataset's endpoints and these five breakpoints, the data
can be subdivided
into the entire post-1973 period, the pre- and post-"dollar rescue
" periods, the pre- and postEMS periods, the pre- and post-peak periods, the pre- and post-P
laza periods and the pre- and
post-Louvre periods. Overall, the long-term behavior of excha
nge rates is examined in these
· 11 periods; Table· 1 lists the endpoints and the number of obser
vations for each period, and
Figur e 9 provides a graphical representation of the periods.
m.
Overview of Cointegration Procedures
A. Unit Root Test Results
Cointegration examines the relationships between nonstationary,
or I(!), variables. The
nonstationarity ofpos t-197 3 exchange rates was initially docum
ented by Meese and Singleton
(1982) and has been verified by many authors. In this paper,
three types of unit root tests are
4
G-5 Announcement of September 22, 1985. The G-5 countries
are Britain, France, Japan, the U.S. and
Germany.
s
G-7 Announcement of February 22, I 987. The G-7 countries are
the G-5 countries plus Canada and Italy.
7
used to examine the nonstationarity of exchange rates: Dickey-Fuller tests (1979), augmen
ted
Dickey-Fuller tests (Fuller, 1976) and Phillips-Perron tests (1988). Diebold and Nerlove
( 1990) state that the augmented Dickey-Fuller test is the most attractive unit root test.
The unit root tests are applied to the eight exchange rates in all 11 periods, and the null
hypothesis of unit root behavior cannot be rejected in almost all time periods at the one-side
d
1 % and 5 % levels.• That is, the null hypothesis of p
alternative hypothesis p
<
= I cannot be rejected in favor of the
I, where p is the autoregressive parameter. The only period in
which the unit root hypothesis may be rejected is the post-peak period. Given these results,
the various exchange rate series will be considered to be I( I) variables.
B. The Johanse n Proced ure
Various tests for the presence of cointegration amongst I(l) variables have·been
proposed beginning with Engle and Granger ( I 987). The test procedure used in this paper
is a
multivariate procedure based on maximum likelihood methods introduced in Johansen
· (1988,1991) and expanded upon in Johansen and Juselius (1990).
The Johansen procedure examines a vector autoregressive (VAR) model of X" an (nxl)
vector of I(l) time series. The error-correction form is written in first differences as
AX, = r1AX.-1
6
+ ... +
rk_lAX,_bl
The unit root test results are available upon request.
8
+
IIX.-k
+
µ +
+
e,
. e, - N(0,A) t = l, ... T,
where I'; for i=l. .. k-1 and II are (nxn) matrices ,µ is a (nxl) vector of constants, e, is a (nxl)
error vector and A is its (nxn) covariance matrix. Since some or all of the elements of X, are
I(l), LiX, is an I(0) process. Thus, the stationarity of the right side of the equation is achieved
only if IIX,.k is stationary.
The Johansen procedure tests the rank of II, which determines the number of
cointegrating vectors present in the system. If rank(II) = n, X,.k must be a stationary process,
and no cointegrating vectors are present. If rank(II) = 0, then II = 0, and the model reduces
to a standard VAR in differences. However, if rank(II) = r < n, then II = o:W,
both a and
where
Pare (nxr) matrices. Pis the matrix of cointegrating vectors, and the number of
such vectors is r. The cointegrating vectors have the property that
pfx,,
j = 1, ... ,r is
stationary even though X, is nonstationary; these vectors represent the long-term relationships
present in the system. Thus, the number of long-term equilibrium relationships present in a
· system is equal to the number of cointegrating vectors. Note, however, that ex and
separately identified since for any non-singular matrix P, the product of o:P and
p cannot be
P( P 1f
I
is
also II.
The Johansen cointegration tests used in this paper examine the null hypothesis against
the alternative that no cointegrating vectors are present in the system X,. The two null
hypotheses tested are that r cointegrating vectors are present in the system under the
assumption that eitherµ = 0 orµ
* 0.
The statistic chosen for testing these null hypotheses is
the trace statistic. It tests for the presence. of r cointegrating vectors in a system against the
9
alternative hypothesis that X, is stationary; i.e, the system has r
= n cointegrating vectors.
The trace statistic is a likelihood ratio (LR) statistic of the form
n
tr(r) = -T_
1
where the
5.(s
L
= r ... I
ln(l -
ii}
are the ordered solutions to the eigenvalue problem /.l.Skk - Sk S ~1S k / = 0.
0 0
0
The Sij matrices are the residual moment matrices derived from the postulated error-correction
model. The distributions of the various forms of the trace statistic depend only on (n-r) and
are tabulated in Osterwald-Lenum (1992).
C. The Quintos Procedure for Testing Rank Constancy
Quintos (1993) presents a procedure for testing the rank constancy of the cointegrating
matrix II over sample subperiods; that is, the procedure tests whether the number of
cointegrating vectors varies across sample subperiods. If the rank does vary, then the number
of driving forces in the economic system changes across the breakpoint. Both long-run and
short-run coefficients in the error-correction model may change as well. The relevant test
statistics are simply weighted averages of Johansen's LR statistics, and the weights are the
subperiod sample sizes. The test procedure is briefly summarized below.
The Quintos procedure permits one to test a wide variety· of null hypotheses, but only a
small subset of the available options will be tested in this paper. For example, the procedure
allows forJ structural breaks in the system, but throughout this paper, J
= 1.
Furthermore,
the procedure allows the breakpoints to be endogenous to the process, but in this paper, the
breakpoints used will be exogenously imposed as in Perron (1989).
The main hypothesis tested in this paper is that the number of cointegrating vectors
(or equilibrium relationships) remains constant across time; that is, H q
0
:
where q is the number of cointegrating vectors in the entire period, q and
1
= q = q2 ,
q1
~
are the number of
cointegrating vectors in the pre- and post-breakpoint periods, and O ,; q < n.
Note that the
coefficients of IT are allowed to vary across subperiods.
Different LR statistics are used for the different pennutations of the ranks of the
full
and subperiod IT matrices. For q < q
1
and q < q2, the LR test statistic used is
q,
LR = -p 1
L
In( I
i : q·t-1
where p 1 and p 2 are the number of observations in each subperiod and the
Xj, , j = 1,2 are the
eigenvalues of the respective, estimated IT matrices. The distribution of this statistic
is a
function of scaled, n-dimensional Brownian motions and depends upon the variabl
es n, q, q1
and~- For q
> q, and q > ~. the relevant LR.statistic is
which is distributed
X(2q _ q,
_ q,)n· These statistics can also be used in case of an equality
between q and either one of the subperiod ranks. For the case q,
statistic is
and for the case ~ < q < q 1, the LR statistic is
<
q
< ~,
the relevant LR
q,
L
i
Lili' = -p 1
In( I
= q·d
Both of these statistics have distributions that are mixtures of a
x2 distribution and a function of
scaled Brownian motions. 7
IV. Empirical Test Results
A. Previous Cointegration Tests of Exchange Rates
Four studies have tested for the presence of cointegration in systems of foreign
exchange rates: Hakkio and Rush (1989), Copeland (1991), Baillie and Bollers
lev (1989) and .
Diebold et al. (1994). The first two explicitly test for the efficiency of the foreign
exchange
markets; as mentioned before, the presence of cointegration among exchange
rates would
contradict the efficient markets hypothesis by implying that current rates can
be predicted by
past deviations from the long-run cointegrating relationships. The second two
papers focus on
modeling and forecasting exchange rates.
Hakkio and Rush (1989) use the Engle-Granger cointegration procedure to examin
e
monthly spot rates for BP and DM from July 1975 to October 1986. They conclu
de that the
two rates are not cointegrated at the 5 % significance level; this result is consist
ent with the
market efficiency hypothesis. However, further tests involving the error-correcti
on
representation of the system leads the authors to reject the market efficiency hypoth
esis for
7 Carmela Quintos
was kind enough to provide the critical values necessary for some of the hypothes
is tests
conducted in this paper.
12
these two currencies. Copeland (1991) examines bivariate systems of exchange rates for
cointegration using the Johansen (1988) procedure. The data used is daily spot rates for BP,
DM, JY, FR and SF over the period 1976 to 1990. Copeland finds no cointegration among
the ten currency pairs at the 5 % significance level, which supports the efficient market
hypothesis.
Baillie and Bollerslev (1989) examine daily opening spot rates from the New York
market for the period March 1, 1980 to January 28, 1985. The seven currencies used are
BP,
DM, JY, FR, Il, SF and CD. One cointegrating vector is found in this system using the
· Johansen (1988) procedure. They conclude that the deviations from the long-term relation
ship
between these spot rates is an important component of the next period's observed rates; thus,
the efficient markets hypothesis is violated. The authors further conclude that an errorcorrection model is appropriate for modelling foreign exchange rates. However, using the
Johansen procedure, Diebold et al. (1994) find no cointegration in this dataset. Furthennore,
in a forecasting exercise, the authors find no improvements in forecast performance by the
fitted error-correction model relative to the simple martingale model. A similar result is
found
for the entire post-1973 period.
The cointegration tests in this paper extend the latter two results by using a longer time
period and a larger currency system. Furthermore, a subsystem of exchange rates consisti
ng
of the four EMS currencies is tested for the presence of cointegrating vectors. This
cointegration analysis incorporates the structural breaks discussed in Section II. The
cointegration results are derived using the Johansen procedure and the 5 % critical values
from
Osterwald-Lenum (1992). The Quintos procedure described in Section III is applied to these
13
cointegration results to determine whether the number of cointegrating vectors (or equilibr
ium
relationships) changed significantly between the pre- and post-breakpoint periods.
B. Cointegration Test Results: Post-1973 Period
To test for cointegration, error-correction models are fit to all the exchange rate
systems under study. The orders of the VAR' s are determined by minimizing the multiva
riate
Schwarz information criterion (SIC). In all cases examined, the order chosen is two;8 that
is,
A summary of these cointegration results is presented in Table 2. The results of the
cointegration analysis for the full system of exchange rates are presented in Tables 3 to
13, and
the results for the EMS subsystem are in Tables 14 to 24. As noted above, the appropriate
critical values depend upon whether I' is present in the data. Since this cannot be determi
ned a
priori, the calculated test statistics are compared to the critical values based on both
assumptions.
The 11 time periods, as determined by the five structural breakpoints discussed in
Section II, as well as the entire post-1973 period are tested for the presence of cointegration.
Two significant results arise from this analysis. First, for the entire post-1973 period, one
cointegrating vector is found; thus, indicating that this system of exchange rates has at least
one long-term cointegrating relationship. This result differs from that of Diebold et al.
(1994)
8
In the interest of space, the VAR estimation results are not presented. The various SIC statistics
and the
estimated VAR parameters are available upon request.
14
which excludes the Dutch guilder (NG) from the analysis.
Second, the .cointegration results for the pre-breakpoint periods generally indicat
e the
absence of any long-term relationships, except for the pre-EMS period. Howev
er, the postbreakpoint periods generally indicate the presence of one or more cointegrating
relationships,
with the exception of the post~Louvre period. These results seem to indicate
that the "dollar
rescue", peak and Plaza breakpoints change the nature of the underlying long-te
rm
relationships in the foreign exchange market; these regime shifts in central bank
behavior had a
long-term impact on the exchange rates. The Louvre breakpoint also seems to
have had an
impact, but its·nature is unclear. It seems that the EMS breakpoint did not have
an impact on
the entire system of exchange rates.
These results indicate that the equilibrium relationship found in the entire post-19
73
period has not necessarily remained constant. The varying number of cointeg
rating vectors in
the pre- and post-breakpoint periods indicates that the underlying market equilib
ria for this
system of exchange rates are affected by these structural breaks. To further explore
the impact
of these structural breaks, a subsystem of EMS currencies (i.e., DM, FF, NG
and Ll) is tested
for the presence of cointegration. The results of the cointegration analysis for
the EMS
subsystem are different from those of the full system. At least two cointegrating
relationships
are indicated over the entire post-1973 period for this subsystem. In addition,
cointegration is
present in all subperiods, except for the pre-Plaza period and the pre- and post-Lo
uvre periods.
Overall, these results indicate that the cointegration present in the entire system
is driven by
the cointegration present in the EMS subsystem.
15
C. Quintos Rank Constancy Tests
To determine whether these differences in the number of cointegrating vectors are
significant, the Quintos tests described in Section ill is applied to the cointegration results.
(i). Full System of Exchange Rates
Table 25 contains the results of the Quintos tests applied to the cointegration results for
the full system of exchange rates over the entire post-1973 period. Given the various
combinations of the estimated full and subperiod ranks examined, various LR statistics
described in Section ill are used.
For all cases, other than the EMS breakpoint, the null hypothesis of rank constancy
with unstable coefficients is rejected. Several implications immediately follow from these
results. The most prominent is that these episodes of central bank intervention did have an
impact on the long-term relationships (or equilibria) in this system of exchange rates. Thus,
certain central bank activities can have a long-term impact on the foreign exchange market.
The meaning of these results for the individual breakpoints requires further study. The
"dollar rescue" package, as described in Section II, did not have a strong impact on the market
since shortly after its enactment, the market countered all of the gains the package provided.
Yet, according to the Quintos test results, the cointegrating relationships across this breakpoint
did change. On the other hand, the EMS breakpoint, which one would expect to have an
impact on the system since it explicitly imposes a long-term relationship on the exchange rates,
does not change the rank of the cointegrating matrix. The results for the peak, Plaza and
Louvre breakpoints are as expected; these breakpoints seem cause a significant change in the
16
cointegrating relationships in the system. Furthermore, the similarity between the peak and
Plaza breakpoints is as expected.
To supplement these full-period results while recognizing the drop in power due to
reduced sample size, subperiods around these breakpoints are examined in order to isolate the
effects of a single breakpoint. The relevant test results are contained in Table 27. 9 This
subperiod analysis seems to cast some light on the impact of the "dollar rescue" breakpoint.
The null of rank constancy with unstable coefficients is rejected for the start-EMS breakpoint
period and cannot be tested for the longer start-peak and start-Plaza breakpoint periods. These
results seem to indicate thatthe "dollar rescue" breakpoint had little overall impact and that its
impact with respect to the entire post- 1973 period is mainly due to the events surrounding the
peak and Plaza breakpoints. However, the results for subperiods surrounding the EMS, peak
and Plaza breakpoints indicate that they did impact the system's cointegrating relationships.
(ii). EMS Subsystem of Exchange Rates
Table 26 contains the results of the Quintos test applied to the cointegration results for
the EMS subsystem of exchange rates over the entire post-1973 period. For all cases, the null
hypothesis of rank constancy with unstable coefficients is clearly rejected. Several
implications follow from this set of results. The proposed central bank regime shifts seem to
have an impact on the long-term relationships present in this subsystem of exchange rates.
The "dollar rescue" breakpoint results are mixed in that the null hypothesis is rejected at the
9
Complete test results are available upon request.
17
5% significance level but not at the 1 % level. The result that the "dollar rescue" period
may
not impact the EMS subsystem as strongly as the whole system is understandable since the
event did not focus specifically on the EMS currencies.
To supplement these results, subperiods around these breakpoints are examined as
before, while still acknowledging the decline in power due to reduced sample size. The
results
of this analysis are contained in Table 28. The interesting result here regards the Plaza
breakpoint. The subperiods examined for this breakpoint begin at the four previous
breakpoints and end at the Louvre breakpoint; i.e., the post-Louvre period is excluded from
the analysis: For the first·three startpoints, q = q = 'h ; thus, the null of rank constanc
y
1
cannot be rejected. For the subperiod starting at the peak breakpoint, the null can be rejected
.
These results seem to indicate that, for the EMS subsystem, the effects of Plaza breakpo
int
were not as strong as for the whole system.
V Conclusions
The long-term impact of central bank activities, broadly defined, on the foreign
exchange market is an issue that has not been directly examined. This paper attempts to
address this question using cointegration analysis that incorporates structural breaks linked
to
regime changes in central bank behavior. The five breakpoints examined are instances of
changes in central bank behavior that may have substantially altered the long-term relations
hips
among the eight currencies examined.
Using the Johansen procedure, cointegrating relationships are found for the full system
of exchange rates and a subset consisting of four EMS currencies. The number of
18
cointegrating vectors in the periods before and after the suggested breakpoints are found to be
different in several cases. Furtherm ore, these differences are found to be statistically
significant using the testing procedure proposed by Quintos (1993). Structural changes ofthe
type that alter the definition of the system's equilibria seem to have occurred at these
breakpoints. Thus, regime shifts in central bank behavior do have a long-term impact on
foreign exchange rates.
Further research into this finding is warranted, both along methodological and
theoretical lines. With respect to methodological issues, the rich structure of the Quintos test
procedure should ·be used to endogenize the breakpoints as well as test for more than one
breakpoint at a time. In addition, extensions of the cointegration results, such as fractional
cointegration analysis proposed by Baillie and Bollerslev (1993) and further explored in Lopez
· · (1995), should be examined. With respect to theoretical issues, another outstanding question
is what the existence of cointegrating vectors implies with respect to models of exchange rate
determination. If cointegration is a feature of the data, models incorporating it must be
constructed and possibly be made robust to structural breaks.
19
References
Baillie, R.T. and Bollerslev, T., 1989. "Common Stochastic Trends in a System of Exchang
e
Rates," Journal of Finance, 44, 167-81.
Baillie, R.T. and Bollerslev, T., 1994. "Cointegration, Fractional Cointegration and
Exchange Rate Dynamics," Journal of Finance, 49, 737-745.
Copeland, L.S., 1991. "Cointegration Tests with Daily Exchange Rate Data," Oxford Bulletin
of Economics and Statistics, 53, 185-198.
Dickey, D.A. and Fuller, W.A., 1979. "Distribution of the Estimators for Autoregressive
Time Series with a Unit Root," Journal of the American Statistical Association, 74,
427-31.
Diebold, F.X., Gardeazabal, J. and Yilmaz, K., 1994. "On Cointegration and Exchange
Rate
Dynamics," Joumal'of Finance, 49, 727-735.
Diebold, F.X. and Nerlove, M., 1990. "Unit Roots in Economic Time Series: A Selectiv
e
Survey," in Advances in Econometrics, 8, 3-69. Greenwich, CT: JAi Press.
Dominguez, K.M. and Frankel, J.A., 1993. Does Foreign Exchange Intervention Work?,
Washington, D.C. : Institute for International Economics.
Edison, H.J., 1993. "The Effectiveness of Central Bank Intervention: A Survey of the
Literature after 1982," Special Papers in International Economics No. 18, International
Finance Section, Department of Economics, Princeton University.
· Engel, C. and Hamilton, J.D., 1990. "Long Swings in the Dollar: Are They in the Data
and
Do Markets Know It?," American Economic Review, 80, 689-713.
Engle,R.F. and Granger, C.W.J., 1987. "Cointegration and Error Correction:
Representation, Estimation and Testing," Econometrica, 55, 251-76.
Federal Reserve Bank of New York, 1986. "Summary of the Results of the U.S. Foreign
Exchange Market Survey Conducted in April 1986," September 1986.
Federal Reserve Bank of New York, 1989. "Summary of the Results of the U.S. Foreign
Exchange Market Survey Conducted in April 1989," September 1989.
Federal Reserve Bank of New York, 1992. "Summary of the Results of the U.S. Foreign
Exchange Market Survey Conducted in April 1992," September 1992.
20
Fuller, W.A., 1976. Introduction to Statistical Time Series, New York: John Wiley and
Sons.
Goodhart, C.A.E. and Hosse, T., 1993. "Central Bank Forex Intervention Assessed in
Continuous Time," Journal of International Money and Finance, 12, 368-389.
Granger, C.W.J., 1986. "Developments in the Study of Cointegrated Economic Variables,"
Oxford Bulletin of Economics and Statistics, 48, 213-228.
Granger, C.W.J. and Escribano, A., 1986. "The Long-Run Relationship between Prices from
an Efficient Market: The Case of Gold and Silver," Manuscript, University of
California, San Diego.
Hakkio, C.S. and Rush, M., 1989. "Market Efficiency and Cointegration: An Application to
the Sterling and Deutschemark Exchange Markets," Journal of International Money
and Finance, 8, 75-88.
Hakkio, C.S. and Rush, M., 1991. "Cointegration: How Short is the Long Run?," Journal of
International Money and Finance, IO, 571-581.
Johansen, S., 1988. "Statistical Analysis of Cointegration Factors," Tnnrnal of Fconomic·
Dynamics and Control, 12, 231-54.
Johansen, S., 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian
Vector Autoregressive Models," Econometrica, 59, 1551-1581.
Johansen, S. and Juselius, K., 1990. "Maximum Likelihood Estimation and Inference on
Cointegration - With Applications to the Demand for Money," Oxford Bulletin of
Economics and Statistics, 52, 169-210.
Loopesko, B.E., 1984. "Relationships among Exchange Rates, Intervention and Interest
Rates: An Empirical Investigation," Journal of International Money and Finance, 3,
257-277.
Lopez, J.A., 1994. "The Long-Term Behavior of Exchange Rates: Fractional Integration and
Fractional Cointegration," Manuscript, Research and Market Analysis Group, Fecleral
Reserve Bank of New York.
Mark, N.C., 1995. "Exchange Rates and Fundamentals: Evidence on Long-Horizon
Predictability," American Economic Review, 85, 201-218.
Meese, R.A. and Singleton, K.J., 1982. "On Unit Roots and the Empirical Modeling of
Exchange Rates," Journal of Finance, 37, 1029-35.
21
Osterwald-Lenum, M., 1992. "A Note with Quantiles of the Asymptotic Distribution of the
Maximum Likelihood Cointegration Rank Test Statistics", Oxford Bulletin of
Economics and Statistics, 54, 461-472.
Perron, P., 1989. "The Great Crash, the Oil Price Shock and the Unit Root Hypothesis",
Econometrica, 57, 1361-1401.
Phillips, P.C.B. and Perron, P., 1988. "Testing for a Unit Root in a Time Series
Regression," Biometrika, 75, 335-46.
Quintos, C.E., 1993. "Rank Constancy Tests in Cointegrating Regressions," Manuscript,
John M. Olin School of Business, Washington University.
Sephton, P.S. and Larsen, H.K., 1991. "Tests of Exchange Rate Efficiency: Fragile Evidence
from Cointegration Tests," Journal of International Money and Finance, 10, 561-570.
22
Table 1: Summary the 11 Time Periods Examined
Start Date
End Date
Post-1973 Period
01/04/74
12/31/91
4513
Pre-"Dollar Rescue" Period
01/04/74
11/01/78
1213
Post-"Dollar Rescue" Period
11/02/78
12/31/91
3300
Pre-EMS Period
01/04/74
03/13/79
1301
Post-EMS Period
03/14/79
12/31/91
3212
Pre-Peak Period
01/04/74
02/25/85
2791
Post-Peak Period
02/26/85
12/31/91
1722
Pre-Plaza Period
01/04/74
09/20/85
2938
Post-Plaza Period
09/23/85
12/31/91
1575
Pre-Louvre Period
01/04/74
02/20/87
3291
Post-Louvre Period
02/23/87
12/31/91
1222
23
Observations
Table 2:
. Summary of the Johansen Cointegration Results for the Syste
ms of FX Rates
Time Period
Number of Cointegrating Vectors under H (r)
2
Full System
F,MS Subsystem
Post-I 973 Period
I
2
Pre-"Dollar Rescue" Period
0
I
Post-"Dollar Rescue" Period
l
2
Pre-EMS Period
l
l
Post-EMS Period
l
l
Pre-Peak Period
0
l
Post-Peak Period
3
l
Pre-Plaza Period
0
0
Post-Plaza Period
3
l
Pre-Louvre Period
0
0
Post-Louvre Period
0
0
24
Tables 3-24: Johanse n Cointeg ration Test Results
The 5 % critical values for the two folllls of the H(r) hypothesis tests using the trace
statistic are listed below. The source for these critical values is Osterwald-Lenum (1992).
If a
trace statistic for the H(r) hypotheses is significant under µ
= 0, it is marked with *; if it is
significant under µ"0, it is marked with **; and if it is significant for both, it is marked
with
#.
Dimension of II
(n::r)
I
2
3
4
5
6
7
8
H(r)
/1
-
Q
' 8.176
17.953
31.525
48.280
70.598
95.177
124.253
157.109
µ,
"O_
3.762
15.410
29.680
47.410
68.524
94.155
124.243
155.999
25
Table 3.
Johansen Cointegration Test Results for the Full System in the Post-1973 Period
'7
6
5
4
3
2
1
0
Trace Statistics
ll(I)
1.4816
5.7237
16.9077
32.3175
47.9406
68.6433
110.0213
160.2744#
Table 4.
Johansen Cointegration Test Results for the Full System in the Pre-Dollar Rescue Period
'
7
6
5
4
3
2
I
0
Teare Statistics
ll(I)
0.1340
6.7796
17.0687
31.0271
49.4256
69.2059
105.3181
155.8310
Table 5,
Johansen Cointegrntion Test Results for the Full System in the Post-Dollar Rescue Period
'7
6
5
4
3
2
I
0
Teare Statistics
ll(I)
2.6645
6.3700
15.8702
31.4557
58.5751
88.2633
120.9527
164.0304#
Table 6.
Johansen Cointegrntioo Test Results for the Full System in the Pre-El\1S Period
r
7
6
5
4
3
2
1
0
Teare Statistlc.s
ll(I)
1.6814
4.9382
14.6901
25.4597
42.0717
65.8132
104.4806
156.4098**
Table 7.
Johansen Cointegrntioo Test Results for the Full System in the Post-El\lS Period
r
7
6
5
4
3
2
I
0
Teare Statistics
ll(I)
2.4110
6.2067
17.3797
31.3092
54.8606
79.4686
112.3466
162.6838 #
26
Table 8.
Johansen Cointegratiou Test Results for the Full System in the Pre-Peak Period
Trace Statistics
r
7
6
5
4
3
2
H(r)
0.1244
4.9693
10.4071
23.2316
I
40.5152
58.5681
90.7833
0
137.8266
Table 9.
Johansen Coiutegratiou Test Results for the Full System in the Post-Peak Period
Trace Statistics
r
7
6
5
4
3
2
I
0
H(r)
3.3206
9.5549
22.5927
44.2406
68.5852 **
98.0516 #
142.3415 #
267.1033 #
Table 10.
Joluwsen Coiutegrntiou Test Results for the Full System in the Pre-Plaza Period
~
r
7
6
5
4
3
2
I
0
H(r)
0.0348
5.0068
11.7034
24.1218
40.5794
60.4225
91.0500
127.0183
Table 11.
Johansen Coiutegrntion Test Results for the Full System in the Post-Pl:.11.a Period
Tu('e Statistics
[
7
6
5
4
3
2
I
0
H(r)
4.2605
13.2175
23.0940
42.2340
64.5921 •
95.3069 #
133.2467 #
179.5316 #
Table 12.
Johansen Cointegrotion Test Results for the Full System iu the Pre-Louvre Period
Teare Statistics
[
H(r)
7
6
1.5130
6.1328
11.7505
25.0944
39.9255
59.9189
90.8637
128.4835
5
4
3
2
I
0
27
Table 13,
Johansen Coiutegration Test Results for the Full System in the Post-Louvre Period
Trace Statistics
r
7
l!(r)
1.5472
6
6.9431
16.7302
31.8432
49.6656
77.4124
110.6171
150.850
5
4
3
2
I
0
Table 14,
Johansen Cointegration Test Results for the EMS Subsystem in the Post-1973 Period
Trace Statistics
r
3
2
I
0
l!(r)
1.6127
14.8994
32.5348 #
63.8383 #
Table 15.
Johansen Cointegrntion Test Results for the El\,[S Subsystem in the Pre-Dollnr Rescue Period
Trace Statistics
[
3
2
I
0
l!(r)
1.1814
4.8994
16.3359
48.6840 #
Table 16.
Johansen Cointegrntiou Test Results for the EJ\.IS Subsystem in the Post-Dollar Rescue Period
Trace Statistics
t
3
2
I
0
ll(r)
1.7818
12.8313
29.7344 #
58.5574 #
Table 17.
Johnusen Cointegration Test Results for the El\lS Subsystem in the Pre-EMS Period
Trace Statistics
t
3
2
I
0
l!(r)
2.2075
6.3416
18.1843
54.9489 #
Table 18.
Johansen Cointegrntion Test Results for the EMS Subsystem in the Post-EMS Period
Trace Statistics
r
3
2
I
0
l!(r)
2.2459
IS.7156 ••
36.5782 #
71.0912 #
28
Table 19.
Johanse n Colntegrntioo Test Results for the El\,IS Subsystem
in the PI·e-Peak Period
'.Crare Statistics
r
ll(r)
3
0.4921
2
8.5004
I
26.7178
0
50.1560 H
Table 20.
Johanse n Colntegration Test Results for the El\,IS Subsystem
in the Post-Peak Period
Trace Statistics
r
ll(r)
3
5.5125
2
14.3179
1
· 30.6567**
0
69.0913 #
Table 21.
Johanse n Cointegration Test Results for the El\lS Subsystem
in the Pre-Plaza Period
Trace Statislics
r
ll(r)
3
0.0001
2
1
0
8.0007
19.7551
45.2917
Table 22.
Johanse n Cointegration Test Results for the El\lS Subsystem
in the Post-Plnzn Period
Ttace Statistics
r
ll(r)
3
2.9823
2
10.8225
I
25.8553
0
51.5630 #
Tnble 23.
Joluwse n Coiutegn1tion Test Results for the EMS Subsystem
in the Pre-Louvre Period
1J:ace St:alistic'.s
r
ll(r)
3
I. 1206
2
10.4934
1
22.0338
0
46.7566
Table 24.
Johnnsen Cointegrntion Test Results for the EMS Subsystem
in the Post-Louvre Period
Trace Statistics
r
ll(r)
3
1.3289
2
7.7759
I
20.1681
0
39.7472
29
Table 25.
Quintos Cointegration Test Results for the Full System
in the Post-1973 Period
Breakpoint
!I
Q1
Q2
LR Statistic
"Dollar
Rescue"
0
1
LR'= 48.51
EMS
1
0
3
LR'=
11515
I
*
Plaza
0
3
LR'=
13014
I
*
Louvre
0
0
LR'= 76.27
Peak
1
Note: The LR statistics that are significant at the 5% level are labelled with
*
*
*.
Table 26.
Quintos Cointegration Test Results for the EMS Subsystem
in the Post-1973 Period
Breakpoint
!I
"Dollar
Rescue"
2
EMS
2
1
Peak
2
Plaza
Louvre
Q,
Q2
LR Statistic
2
LR'= 11.71
*
1
LR'= 27.80
*
1
LR'= 34.47
*
2
0
LR'= 52.07
*
2
0
0
LR'= 67.65 *
Note: The LR statistics that are significant at the 5% level are labelled with
30
*.
Table 27.
Quintos Cointegration Test Results for the Full.System in the Defined Subperiods
Snbperiod
q
q,
q,
l.R Statistic
"Dollar
Resc11e
Start-EMS
Start-Peak
Start-Plaza
1
0
0
0
0
0
1
0
0
LR#= 48.51
EMS
Start-Peak
Start-Plaza
"DR"-Peak
"DR"-Plaza
0
0
0
0
1
1
1
1
0
0
0
0
LR=
LR=
LR=
LR=
Eeak
Start-Plaza
"DR"-Plaza
EMS-Plaza
0
0
0
0
0
0
3
3
3
LR= 167.05
LR= 167.05
LR= 167.05
*
*
:eiaza
Start-Louvre
11
DR 11 Louvre
EMS-Louvre
Peak-Louvre
0
0
0
1
0
0
0
3
2
2
2
2
LR=
LR=
LR=
LR=
124.25
124.25
124.25
154.64
*
l DJIVre
"DR"-End
EMS-End
Peak-End
Plaza-End
1
1
3
3
0
0
1
2
0
0
0
0
LR#=
LR#=
LR# =
LR# =
75.65 *
77.02 *
200.32 *
154.65 *
11
*
54.06 *
54.06 *
55.94 *
55.94 *
*
*
*
*
Note:. The LR statistics that are significant at the 5 % level are labelled with *. The critical
values were provided by Cannela Quintas and are based on 1000 Monte Carlo repititions.
31
Table 28.
Quintos Cointegration Test Results for the EMS Subsystem in the Defined Subperiods
Subperiod
q
Q1
Cb
LR Statistic
"Dollar
RescHe
Start-EMS
Start-Peak
Start-Plaza
I
I
0
I
I
I
2
0
0
LR= 27.57
LR= 31.24
LR= 31.33
EMS
Start-Peak
Start-Plaza
"DR"-Pe ak
"DR"-Pla za
I
0
0
0
I
I
2
2
0
0
0
0
LRn = 19.10 *
LR= 14.92 *
LR= 60.83 *
LR= 60.83 *
Eeak
Start-Plaza
"DR"-Plaza
EMS-Plaza
0
0
0
I
0
0
I
1
1
LR= 65.86
LR= 19.14
LR= 19.14
*
*
*
0
0
0
1
0
0
0
I
0
0
0
0
LR#= 22.93
*
2
1
1
1
0
0
1
0
0
0
0
0
LR#=
LRn =
LRn =
LRn =
11
*
*
*
:eJaza
Start-Louvre
"DR"-
Louvre
EMS-Louvre
Peak-Louvre
I.ouvre
"DR"-End
EMS-End
Peak-End
Plaza-End
63.03 *
41.05 *
19.28 *
42.20 *
Note: The LR statistics that are significant at the 5 % level are labelled with *. The critical
values were provided by Cannela Quintos and are based on 1000 Monte Carlo repititions.
32
Figur e 1.
Daily Spot .BP/$ Exchange Rate
Figure 2.
Daily Spot DM/$ Exchange Rate
1974-1992
1974-1992
2
Figur e 3.
Daily Spot JY/$ Exchange Rate
Figure 4.
Daily Spot FR/$ Exchange Rate
1974-1992
1974-1992
16
33
76
aO
82
34
Sb
88
BO
Figure 5.
Daily Spot NG/$ Exchange Rate
1974-1992
Figure 6.
Daily Spot LI/$ Exchange Rate
1974-1992
1000
Figure 7.
Daily Spot SF/$ Exchange Rate
1974-1992
Figure 8.
Daily Spot CD/$ Exchange Rate
1974-1992
'
,.,
2
34
Figure 9. Timeline of Proposed Structural Breakpoints
)1-~7~41---t,,_10---+l-1-+f1-e+I_1+-fe_o+--I_,,+--02__,1---t,,-04---+l-1-+,e-a+I_,+-,e_e+-I_1,i--uo--+---,11u2
1
Pre-Dollar Rescue Perio
27%
I
Pre-EMS Period
28%
1
Post-Doller Rescue Period
73%
Post-EMS Period
72%
I
I
Pre-Peak Period
Post-Peak Period
62%
38%
I
I
Pre-Plaza Period
Post-Pleze Period
65%
35%
I
Pre-louvre Period
Post-louvre Period
73%
27%
35
@FedFRASER