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An empirical exploration of exchange-rate target-zones
Carnegie-Rochester North-Holland
Conference Series on Public Policy 35 (1991) 7-66
An empirical
exploration
of exchange-rate
target-zones
Rob,ert P: Flood &&rn’ht%‘on~~ ‘konetary
Fund
Andrew K. Rose University
of California,
Berkeley
and Donald
J . Mathieson”
International
Monetary
Fund
Abstract In the sumption determinant
context
of a flexible-price
of uncovered of exchange
interest
parity,
rates.
Daily
monetary
exchange-rate
we obtain data
model
a measure
for the
European
and
the
as-
of the fundamental Monetary
System
*The authors are, respectively: Senior Economist, Research Department, IMF; Assistant Profess0 i School of Business Administration, University of California at Berkeley; and Chief of 9 inancial Studies, Research Department, IMF. Rose thanks the International Finance Division of the Board of Governors of t,he Federal Reserve System and the Center for Research and Management at Berkeley for financial support. For comments we thank: Willem Buiter; Ricardo Caballero; Harold Cole; Susan Collins; Frank Diebold; Hali Edison; Martin Eichenbaum; Joe Gagnon; Peter Garber; Dale Henderson; Alexandra Jones; Karen Lewis; Ben McCallum; Allan Graciela Kaminsky; Eric Leeper; Leo Leiderman; Meltzer; Dick Meese; Dan Sichel; Chris Sims; Gregor Smith; Ken West; seminar participants at Ohio State and Yale Universities; workshop participants at the IMF and the Federal Reserve Board; and participants at the Carnegie-Rochester, CMSG, MSG, and NBER exchange rate conferences. Steve Phillips provided stalwart research assistance; Kellet Hannah and Hong-An11 Tran assisted with the data. We thank Lars Svensson for continuing discussions and encouragement, as well as uncovering an important error in an earlier draft. This is a condensed version of a working paper wit,h the same title, issued as IFDP 388 and NBER WP3543. The views expressed in this paper are those of the authors and do not necessarily represent t,hose of the IMF or the Federal Reserve System. 0167-2231/91/$03.50
0 1991 - Elsevier Science Publishers
B.V.
All rights reserved
are used exchange are also
to explore rates
and
considered.
the
importance
fundamentals;
of nonlinearities data
from
three
Many implications of existing
in the other
relationship
between
exchange-rate
systems
“target-zone”
exchange-rate
models are tested; little support is found for existing nonlinear models of limited exchange-rate
flexibility.
I. Introduction In this paper,
we characterize
the behavior
of nominal
exchange
rates dur-
ing managed exchange-rate regimes. When exchange-rate management takes the form of an exchange rate “target-zone,” enforcement of the zone sets up expectations that alter the relationship between the exchange rate and its fundamental determinants. Such effects are the focus of a theoretical literature concerned with exchange rate “target-zones.” We assess the empirical importance of these nonlinearities, focusing on the six long-term participants in the Exchange R.ate Mechanism (ERM) of the European Monetary System (EMS). There are two motives for this paper. First, a comprehensive description of exchange-rate behavior during managed floats is potentially of great value in comparing the merits of alt,ernative exchange-rate regimes. Second, this paper is a contribution to the sparse empirical literature on exchange-rate target-zone models. By implicitly using a. flexible-price monetary exchange-rate model and the assumption of uncovered interest parity, we are able to obtain a daily measure of the funda.mental exchange-rate determinant. With this variable, we search directly for a nonlinear relationship between the exchange rate and fundamentals. We use three different modes of analysis: graphical study; parametric testing for non1inea.r terms; and out-of-sample forecast analysis. We also test) five implications of target-zone models that do not rely on our measure of fundamentals. Our EMS findings are corroborated by data drawn from three regimes of limited exchange rate Aexibility: the post-WWII Bretton Woods era; and the inter-war and pre-WWI gold standards. Our findings are mixed. Our graphical tionship between the excha.nge-rate and it,s different” in an exchange rate target-zone change rates. However, the exchange-ra.te not resemble
that suggested
by current
analysis suggests that the relafunda,mental determinant “looks tha.n it is in freely floating exfundamentals relationship does
theories.
Our pa,rametric
testing
for
nonlinear terms usually indicates that a model that fails to account for the effects of the target-zone is misspecified; nonlinear terms are statistically significant determinants of t,hc exchange rate, although the sign pattern of the estimated coefficients is usually inconsistent with theoretical predictions. However, these effects are also nppa.rent for floating rates. 8
More importantly,
nonlinearities
do not help to predict exchange
when we examine measure
implications
of fundamentals,
of target-zones
rates out of sample. that
Finally,
do not depend on our
we find little evidence of target-zones.
Our mixed findings make us cautious in our conclusions. Our graphical analysis suggests to us that fixed exchange rates behave at least somewhat differently than freely floating exchange rates; this seems unsurprising. However, our more intensive target-zone
models.
study of the data reveals little support for existing
We think our results are not surprising.
Our more inten-
sive statistical work is often quite model dependent. The auxiliary assumptions required to derive close&form solutions for models in this literature seem to be poor assumptions that do not much aid our understanding of the data. We conclude that models of limited exchange-rate flexibility work about as poorly as do models of flexible exchange rates. In the next section of the paper, the relevant theory and our empirical strategy are outlined; Section III provides a brief survey of the existing literature, while a descript,ion of the data is contained in the following section. Section V provides a discussion of how we determine o, a parameter that is important in our model because it is required to identify exchange-rate fundamentals. Our analysis of nonlinearities in conditional means of exchange rates is contained in the next four sections, which constitute the core of the paper. Section VI provides graphical analysis of the relationship between the exchange rate and fundamentals. Parametric tests for target-zone nonlinearities are reported in t,he following section; the forecasting abilities of linear and nonlinear models are compared in Section VIII. Various auxiliary implications of target-zone models t,ha.t do not rely on measurements of fundamentals are analyzed in Section IX. A brief summary and concluding remarks are contained in Section ><.
II. Theory In this section,
we present a. simple model of exchange-rate
target-zones.
We
then use this model to derive distributional implicat,ions for the exchange rate and fundamentals. Finally. we out line our approach to measuring exchangerate fundamentals.
The model The model we use in our study is standard in the target-zone literature (e.g., Krugman (1990), and Froot and Obst,feld (19S9a)). In the model, the natural logarithm of the spot, exchange rate, et, (measured as the domestic currency price of a unit of foreign exchange), is equal tjo a scalar measure of exchange9
rate fundamentals, of change
of the exchange
In the typical that
ft, plus an opport,unity
enter
of cquat ~OII (I ). jc is a linear
market,
of money
demand;
pectation
operator,
Et,
the nature
ing” relevant in the
WC follow
is based
switch,
governing
for exalnplf,,
exchange
market
fin
to protect
order
process.
uiiglit
irl\ml\.f>
lx~lic.!.
to specific
a11 c~sclla~lp-ratc~
in rat,ioilal
f~xpf~ctatiolis is H f’llll(.tio11
additional
that
t IIC~ I’IIIIC~ iota hf> iI twicf,
of thfl
t hc currf~til,
The
precise
process
sta.tv.
form
switches.
of obscrvatioIl, In the
\2:f, co~lsiflf7~
Hencefort~lI.
atwcncf~ of’ airy
where 11 is the drift rate, During
‘A typical simple
procc3s
type
of process
benign
to alkr
neglf~t
the cours(b of that
ttic> SOIW
variable,
wit,h thrb
cont.inuousl~
I)olic.ies aii(l forcing
diffcrent,iablc procfw,f3
wtifxrf‘
on t 11f, nature
of conttmplat
\vf’ will 1ls~~all.v drop the not,atiorl
t)rocfw
s\\-it f,trfx,
f’llnfianwi~tiils
follo\v:
r/f//+ ntl:
(:I!
cT is il posit ivfx coilst ant, and & is a standard s\yitf-hf3.
flrxibl+t)rict~
changes
t IIc ,f t)rowss
IIWII~~~~I~~IIIO~ICI consists
(m - p = &j ~ rri + 5); ~IIP tlrfinit~ion
c,schange
rate.
and an asterisk
Weinri
to anot her procf5s
of: a domestic
money-demand
dc~~otr~ forclgrl
of
variahtes.
and interest, rates leads to ( 1). where t Ile fundamcnt~als 11 denotes velocity. given by L’~ = -@I?/~ + C,~ - p; (1989a)
or Svensson
interest-parity our
analysis
(199Oc).
ecpat.ion;
this
ml
for t,hc t,imcL
t lw wat cxctiange rate (q = E + and uncovered intcrcs( i)ari(y (i - i’ = I:(t/c )/dt); whr-rc 17~ is the tog of thr money p denotes the tog of t,he price level, y ctc~~ot IV, 1hr tog of real income, t dcllotcs the interest rat,f,, E is a shock t,o t lr~, doliml.ic money-demand equation, 4 denotes
equation
uf
for c~znt~~pl~~. f = .q(I. f).
f!/‘ :=
process.
from
t II~’ stat (‘:
of t 11c 9 1’1111clif>11 dqx~~ds
I, writing.
swit.cb
we mean changes
of t11c>relc\-ant state
oIII>.
\;aluv ot’ f’s\ltni71arizf3
cx-
latter
of the model,
wf‘ coIijecl,urc~
iiiotlcls.
rate
frltlctiou
t. The
‘~proccss
One
iutervent,ioIls
senii-
The
ZOII~‘.
t.ion for the exchange condit,ion
time
switching”
swit.ch
rate
here.’
and any
(1983).
of variables
intkrcst
jt, a.nd the structure
Garbcr
a
is the through
condition
and
function
interpret,ation
By “process
f; Flood
fundamentals
As is typical
variable.
of 1,11(xc~quilihriurll
to the forcing
process
0
that.
OII information
values of the only forcing
including
while
quilihrium.
elasticity includes
to the rate
rate cxxpectc~t at- I. Et(de)/dt:
derivation
money
cost, term proportional
(krtaitl
types
is discussctt
to n~ottr~ts wil Ii sticky
prjc(5.
Etirnination are defined
zt). of risk prcmia
furthrr
I)etow.
of cndogenous
y’ - p): supply. r~on~inal the
real
priers
az !I = m( + ~1~(whcrc
See, e.g., Froot and Ohst,fctd can be added to t.hr uncovcml
In fret urc work,
we plan
to ext.cn(l
dictated
by the particular
policy switch.2
Using our trial solution from (2) and invoking Ito’s lemma: E(de)ldt Substituting
from equation
= qg’(f)
(4)
+ (g”/2)g”(f)
(4) into equation
(l),
we
obtain:
s(f) = f + VS’(f) + w2/wv) Equation
(5) is a second order linear
differential
(5)
equation,
which has the
general solution.3 g(f)
= f +
07
Alezp(X1.f)
+
+
A2edhf)
(6)
where x1 = -(?]/a)
+ (l/a2)J_
x2
-
=
-(71/u)
(7)
(l/c”)+l’
+
pa’/(Y)
(8)
The integration constants Al a.nd A;! are determined by process-switching side conditions. Different side conditions result in different settings for the constants. Indeed, during periods of policy volatility, agents’ settings for the As should shift with policy perceptions. Three patterns for the setting of the constants have emerged in the literature. First, if agents pay no attention t,o the policy side conditions, then (ruling out bubbles) Al = A2 = 0.” S econdly, if the target-zone is credible, agents must anticipate that the authorities will stop the drift of fundamentals out of the zone when funcla.mcnt.als a.nd the exchange rate reach the boundaries of the target-zone. Consequently, credible target-zones give rise to “sure thing” bets about fundamentals
at the boundaries.
In order to keep
such bets about fundamentals from being translated into profit opportunities, agents require “smooth-pasting” conditions at the boundaries. These smooth-pasting conditions ensure tha.t the exchange rate will not change in response to anticipated
infinitesimal
int,ervention
at the boundaries.
Smooth
pasting requires Al < 0 and A2 > 0. This result is true for all credible zones, with or without intramarginal interventions. Thirdly, the target-zone may 2Pesenti exchange 3Tlle
Alezp(Alf) similar
allows solution
+ A+rp(A2f).
t,he drift. rate
to vary so as to induce
is f + on, Lewis
(1990)
while the d evelops
mean
reversion
in the
solution of the homogenous part is a different model with qualitatively
properties.
4Froot market;
(1990)
rate. particular
and Obstfeld see also Flood
(1989b)
provide
and Hodrick
a discussion
(1989). 11
of bubbles
in the context
of the stock
are unconstrained until not have full credibility. In t.tlis case, the constants alternative policies are specified; see, e.g., Bertola and Caballero (1990b). Most, of our empirical
work relies
ncit her an explicit
on
model
of interven-
tion nor target-zone boundaries that coincide with the declared boundaries. When we nlake use of t tit, s~wcific functional form suggested in equation 6. anr \ AZ to 1~ free parameters. In much of our work, we always allow ill we do not Thus,
even
coIlstrain
els based
on regulated
1 is a graph interventions zone.’
The model ohscrvablcs.
the rc~ducc+form
equation
work is tlirc,c-ted at the general
our empirical
I3rownian
motion
of the exchange
class of target-zone
for a single
of t.htl exchallgf, rate against, fundamentals at cretliblc exchange-rate bands are used
state
variable.
rat,e. mod-
Figure
when infinitesimal to defend the target
prc~scntctl ~II ccluat iolr ( I ) bears only a limit.cd White t hrt cschangc, rat P is ohscrvahlc almost
direct relat,ion to continuously, the
model offers little guidance on how to observe the triplet ft, CY,&(de)/dt.” We note, however. t#hat if w(‘ (-orlId observe any two mpmhers of the triplet, Our empirical t,hen, by using equation ( I), wc would have t,he third member. strategy entails obt,a.ining ~ncasur~s of o a.nd E,(de)/df and deducing a measure for exchange-rate fundamentals. Ji. ‘l’his approach obviously precludes tests of equation (I ). since thr latter is 11set1 to construct measured fundaOur st,rat.rgy rlocs. howrver, allow IIS t.o construct and compare’ mentals. reduced-form
tquat.ions
It, is relatively Sect,ion
V. Assurniikg
based
on c~q~~ation ( 1 ).
cas>’ to ol)sc,rvc, E,( dc)/dt; covc~rc~l iii1 crvst
parit.y
we defer discussion for cant t-acts of length
of 0 to h:
where: il,h is t,he interest rat<, at titnc, f (x1 domestic funds borrowed for a period of 1engt.h h; i;,h is I hrt col,rt,sl”‘rlc_lillg foreign int.ercst rate; FRt,h is the forward exchange ra.te quot~ctl at t i~nr, t for delivery at f + h.; and E& is the tevel of the spot exchange rate at t,irncx f. The rcalationship between the forward rate and the c~xp~ctrtf f1itlii.c spot rat<> is given by:
6
4 EXCHANGE RATE
2
(e)
reduced form
0 -2
----------
-4 -6
l
-6
1
0 FUNDAMENTALS
Figure 1: Credible
13
Target-zone
5 (f)
where RP,,h is the risk premium at time t for cont,ract,s of length h. If agents the foreign-exchange market IllaxirnizrL t,hca cxpccta.tion of an int,erternporallj separable
utility
funct,iolr.
tjher~:
RPt,h = [C’()l’t(l”(C’t+,~)/Pt+/~. ER,+h)]/[E,(lr’(C,+h)/p~+h] where:
Covt( ., .) denotes
in
t,he c-ovariance
opera.tor
conditional
ut ilit,y of consumption at time t; l.J’(Ct+h ) is 1.h(, nlargillal Pt+h is the price level at time t + h.
(11)
informa.tion
on
at, t,ime t + h; and First. utilit,y
We intend to ignore risk prcmia, in this study for two reasons. Svensson (1990a) ha.s shown that for constant relative risk-aversion
functions, the risk prenlium in a credible target-zone (with potentially moderate devaluation risk) is small. Second. in the empirical part of this study, we rely on daily observations of t,wo-day interest, rates. Regardless of the functiona,l form of the period llt ility funct,ion, the risk premium rmlxdtld in such short contra.cty is liI<(~l>~to I)(, nc~gligiblc, compa.rcd with the rxpect,etl rate of change of the cscl~angt~ rat(x.‘*” Once risk premia hal-t, ht~cn asslImed (IO) to yield: I:‘,( iii?,+,,
risk prrrtlium
in two-(lay
between
I”(Ct+h)/Pt+h
an(l
between
two variables
it, hard over In
t,o believe
the
our
course
view,
at, least rat,e
that.
both
risk
of the further
days
and
rat(’
prenlium
exchange
rati,.
al)nut
go
woultl Ovc,r
;rssulllillg
hotll
can
be rspected
surprises compared the
risk
to wro over short go to zero
longc,r away
fast,er
cont.ract
over wit,h prc,miurll
horizons, than
periods,
risk prernia.
conditional
Engel
would such
t,wo
covariancc covariancc
in the two magnitudes.
plans
ark sticky while
applying
‘I’he conditional
of surprises
pricing
Thr-r+,forf>,
and
bc dutx to two-day
t,o r~~atcl~ eschangr-rate
horizorl
less complacent
provide
consulnptiorl
of t.htx c,xchangc,
consumption-based much
would
WIIP~C h is two-days.
pricc>s a11d corlslllllplio11
at. till, ‘L-day
of change
cottt racts
is tllf\ (>xpcac.t(>d I)roduc(.
of two
of change
(1’)
= (I + it,,,)/( 1 + l;,J
)/I:/<,
I:‘/<,+,,
(!I) antI
quat.ions
logarit hrns of c,ach sitlc of this cquat,ion. we arrive at.:”
Taking natural . . approximations, ‘The
away. we combine
We find
to change t,he same the and
exchange, the
we think the
nluch
t.wrrdays. rate-,
rxpect~~tl t.hat
expected
as a nlont,h,
(1990) and Hodrick
t,ht, rattt
WP are (1987)
analysis
“Bertola and Svr~~sson ( I UUU):I\ low that t IIC~implied two-day forward raLe. ( I + should tw a biased predictor of ER,+,, in our &+h)E’n,/(l + i;+h) w t Lere h=two-days, dat)a samples (which arc between EMS realignmrnt,s). Standard tests of unbiasedness on our EMS data do in f;lct rcljcct tlrts 11u11 hypothesis of unbias4ness. This is a standard finding
for floating
“The
rates
approximat.ions
(Hodrick arc:
In(
( 11)X7),Drool, and Thalrr (1990)). 1 + i) - 1n(l + i*) z i - i’ and In(EtERt+~/ERt)
(&et+,, -et). The second approxirnxtion logarithm is a nonlinear opcralor, which using only t,weday forrlcasts. otlr r’rror this
assertion
exchange We found
rate that
by sirnulat.ing
t,llr> aI)pi-oxl~ilat
wit11 1.11~ zonk
bountlarieh
thcx av~ragc’
z
is lnuch the more worrisome of the two since thr irrducrs Jcnsr~n’s inquality problems. Since WC artof approximation may h(x small. WP investigated 2.25
ion rrror percent
;rl~sc~l~~lr~;il,l,rosiirl;rt,iorl
for
a credible
around f’rror
central is abolit,
t.arget-zone parity
and
on
t.hcl
o =
I. lr(, of t.hr> avrragc
1
Etet+h - et = it
h
i$,
-
(13)
When we study flexible exchange rates below, we find that our exchangerate model works well, despite our assumption of uncovered interest parity. We observe interest rates on contracts with a two-day maturity; by equation (13), that is equivalent of the exchange exchange
rate.
to observing
We treat
the two-day expected
the two-day expected
rate as the instantaneous
expected
rate of change
rate of change of the
rate of change of the exchange
rate. Succinctly, we measure exchange-rate fundamentals as fi G e, -cr(i -i*)t. Even assuming that uncovered interest parity holds, this measure will not be literally correct as long as cy is unknown; we use sensitivity analysis to account for uncertainty about cr. Also, this measure does not directly link exchange rates to “raw” fundamentals such as money and output. Nevertheless, for reasonable choices of CI, all interesting moments of the f distribution will closely match moments of t,he e distribution in the sampZe. Given the poor performance of exchange-rate models that use raw fundamentals, compelling argument for 0111‘measure of fundamentals.‘0 III. Previous
this is a
findings
Most previous empirical examinations of nonlinearities in exchange-rate behavior have focused on non-linearities that affect even moments of the exchange rate process, often the conditional variance of the exchange rate. For instance, it is known that excha.nge rates manifest substantial leptokurtosis; conditional forecast varia.nces of exchange rates also exhibit serial dependence (Meese and Rose (1991) p rovide references). However, relatively little empirical work has been done to link mentals in an intrinsically nonlinear to be no theoretical reason to pursue (1990) and Smith and Smith (1990) side conditions
imply deviations
the level of the exchange rate to fundafashion. Until recently, there appeared such avenues. The papers by Krugman p resented exchange-rate models where
from the linear exchange-rate
solution.
There is another, more important, explanation for the dearth of nonlinear empirical work on conditional means of exchange rates. Empirical work on exchange-rate determination has been dampened by the negative results of absolute expected rate of change of the exchange rat,e. We are also assuming tions costs.
away any measurement
So long as bid-ask
spreads
error which may be the result of transac-
are small in relation
to interest
differentials,
this
error is likely to be very small. “Our
methodology
fundamentals answer Obstfeld
can,
are difficult
the question
we think,
be extended
to measure,
of interest.
fruitfully
to other
so long as reduced-form
One example
(1989b).
15
is the existence
environments
estimates of bubbles;
where
allow one to Froot
and
Meese and Rogoff (1983). 11ww and Rogoff demonstrated equipped wit,h a. variety of linear structural exchange-rat,e ex post
knowledge
to forecast
more
of the, dr~terlrlinants accurat.c,ly
than
a naive
noted that ta.rget-zone modt~ls require set of fundamentals to which a(ltlitiollal presence
of a ta,rgct-zone;
at the very least,
of such random
models
that models would
walk model.
and a.ct,ual not
he abk
It should
bet
a strrlctnral linear model (that is, a nonlinear terms are tacked on in tllc>
see cqliat ion (6)) . so that. target-zone
all t,he problcnls
a forecaster
of fioating
excha.nge-rate
models
have,
models.
Only a small amount of rf,lt>vanl. clnpiricat research has been conduct~ed to date. Almost without, cxcept~ion, econon1ist.s have t,aken heed of t.he negative result,s of Meese and Rogoff and abstained from posit.ing explicit parametric much of t.hc work present,4 below is models of fundament.a.ls (in contrast,. techniques and find parametric). Meese and ROW ( 1990) use nonparametric little evidence that nonlinear models fit exchange-rat,e data hct)ter t.ha.n linear models during fixed eschangc>-rat c periods. I)icbold and Xason (19YO) and Meese and Rose (1991 ) find c~olllpa.rablc rcslllt,s hot 11 in-sample and out-ofsample during float,ing eschangc~-rat<, rcgirnc’s. using Itrrivariat e and mult ivari(1990) usfl 1.hf, ate data, rcspectivel!,. S~WIICY~I‘ ( IWO) RII~ Smit.ti and Spmcf,r method of simulated momcl~t s to a\.oitl positing an explicit) empirical model of funda.menI.als ill n~octc~ling ts. ~%=rt.ola and (:aba.llcro (199Oh) prcsr,llt. infornlal (~vidf~ncc OII t trrc>c aspects of two EMS excha.ngta rates from the ea.rly- t.tirorigtl Iriitl- l!)SOs. Svrnsson (199Ob. 199Od) uses a variety of techniques wit 11 Swctlistl data to t.c,st. and corroborate a model of target-zones with realignmcllt risks wit.hout relying on a model of frlndamcntals. Pessa.ch and Razitl (l!)!)o) is t tic paper that is closest t,o ours in spirit: they use Israeli data in a ~)ara~twt.ric fashion and fired evidence of symmetric nonlinear effects implicrl l)!- target -zfJilc ~rmflf~ls iii t hf, rate of ctiangf* of t tic exchange
rat,<,.
IV. Description
of the data
The major focus of this paper is the F:1IS regime of fixed. but adjustable, exchange ra.tes. We concctntratc on t trc, ICiLlS both for its intrinsic and current. interest, and for easy comparisorl with the lit,erature. Relevant fcnt,ures of the institutional structure of the E3,IS a.re described in Folkerts-1,anda.u and (1989). Mathieson (1989) and C:ia.vazzi and Giovannini Our EMS da.ta were obtained from t.he RIS. We also use non-EMS countries. and for I’MS collntries during the period ERM.” The da.ta are daily; exchange rates arc recorded at the fixing” while int,erest rat,es arc arlnualizctl simple bid rates at,
I fi
RIS data for preceding the da.ily “official 10 a.m. Swiss
time.‘2~‘3~‘4 We focus on 2-day interest rates (which will be taken to be “the we use l-month and 12rate,” unless explicit,ly noted otherwise);
interest month
rates
t,o check our results.
Two-day
interest
rates
have been used
because they are the shortest available interest rates (they also reflect the yield on a deposit that has the same maturity as the two-day settlement period in foreign-exchange markets). l5 The interest rates are Euro-market rates and should be relatively free of political, credit, settlement and liquidity risk premia, at least for interest-rate differentials across different currencies at the same maturity. I6 Two-day
interest
rates are unavailable
for Denmark
and Ireland until February 1982 and November 1981, respectively.17 data have been checked for errors in a number of ways.” “The
rates
are averages
13Belgium
has
used
for current
EMS
rules
account
market; rate
14We treat,
each
daily
or holiday that
analysis
financial
not
The and
observat,ion time
effectively
We use
central
rate
floats
and
ignoring
any
stops
on the time-series
our
cannot
parametric
results
are never
“The that
work
risk
with
premia
different
interest
rates
political
risk
this
problem.
they
could
even
Italy. Giavazzi The longer risk,
and
liquidity
17Japanese ‘sin
and Giovannini version of this
by computing
of our
excessively dummies do differentials
from
In some
other
of
data;
our
markets domestic
reflects
payments
the
fact
systems
in
which
issues
of the
the yields
of funds
the
once
it should
the differentials currencies
matures.
be relatively
unchanged
also
during
as well as between Moreover,
this
help
a particular
domestic
wedge
for countries
discussion. (1989) p rovide further paper contains discussions of credit
risk,
free of
to alleviate
demonstrated
markets,
uniform
Euro-currency
be relatively
should
on instruments
eased
deposit
between
should
Euro-markets
de-
it is physically
this period, political risk the extent of the political
currency.
progressively
Eurc+currency
in which
deposit,
Thus,
the
of the country
period, in different
and
offshore
may
vary
over
time
such
as France
and
settlement
failure
premia.
short-t.erm
particular,
been
As much
levels.
data
day-
implicitly
we are not
significance Friday
our
of, e.g.,
we are
t.hat. day-of-the-week levels and interest-rate
in the
the bank
were relatively
in the same have
place
several
in t,he Euro-currency controls
take
in different
across bet,ween
also checked
weekends.
is
division.
on the transfer
m&u&y
controls
a wedge
and
which
to following
account
of the data,
capital controls throughout study of the EMS. While
denominated
capital
no special
in foreign-exchange
that
of denomination.
Sampling
denominated capital
the
affected.
deformation,”
out
by the government
or taxes
with
on deposits premia. If such
instruments because
vary
currencies
rate,
in the t,ransaction.
the possibilit,y
restrictions
introduce
currencies,
are involved
Italy have maintained are important in any
might
across
must,
be confronted
new
As France and considerations risk
reflects
by this period
of funds
currencies
may suddenly
located
affected
We have
at, conventional
also separated
set.tlement.
transfer
whose
“Political posit
tweday
ultimate
countries
be rejected we have
substantially
typical
the
generally below,
freely.
on holidays
worried about this assumpt,ion. Furt,her, the hypot.hesis not enter significantly into regressions of exchange-rate on a constant
official
is committed
are not
take
“time
properties
the
bank
our conclusions
identically,
By
depend
markets. Belgian
the financial
data,
effects.
economic
does
Euro-markets.
exchange
t,ransactions.
with
of-the-week
several
of dual
for the official
key results
assuming
across
a system
The
interest
we checked descriptive
rates
for outliers
st,atistics
are also unavailable from
and examining
both
levels
until and
early
1982.
log-differences
t.he datagraphically.
Some
of the series 150 apparent
IJnless rates;
otherwise
for interest,
noted, rates,
plus the int,erest
rate
work.
is trcatfld
Germany
are always differentia.ls
tli~ Dhl
pricf,
use natural
always
as t Ire “home” of 011c unit
of colllparison.
of exchange
logarithm
of one
by 100.” In our EMS so that exchange rates
divided
country,
of foreign
C~erniai~ intf~rf3l
logarithms
11se the natural
p0int.s).
(in percentagf‘
are always
For the purposes
we always
wft almost.
exchange,
ratf,s minus
and
foreign
interest-rate
interest.
WP also 11s~ data for the period
change rates t,hat preva~ilcd drlring the classical gold standard. rat,e dat,a arp taken frown Andrew ( 1910). who tabulates data
rat,es.2”
of fixed cx-
Our exchangeon weekly nom-
inal exchange rates of the 1I.S. vis-i\-vis the I1.K.. France, a.nd Germany for The rat,es are the a.vcrage of weekly t,hc National hlonet,ary (‘orrlrrlission. int,erhighs and lows. licmmcrt~r ( I!) IO) Jprovides weekly data on American est, rates. also gatherf~d for t hc Nat iollal Monet.ary (bmmission. The rate% is a week1.y average call loan ratf, for t 11(xNYSE. The National Monct,arv (‘ommissiorl ( 1910) tahlllatt,s 13ril isll call Irlonr’y rates and French “market from hack rates of disf,ollnt ..* Our (’It\rlrlall irtt c,rc,st-rat v data wcrf’ gathered issues of 7’hf ~f~ouorttrsl. ‘l‘tifb c.lassical golf1 st antlard flat a span lSS!b 190X. ‘I’hfw data arc monthly We also usf’ data OH t hc intt,r\var gold standard. a.nd are t,akrn from hrrking trud :\/orjr tclr,!J .4tntistics 1914-1941; the data ifa f~sf.hangf~ raic3 are averages of flail)span .lune 1925 t,hrorigli .July I!):< I. ‘1‘1 rates; interA rates arf’ II~llall>. s~lortbtcr111 ‘.privatf> fliscount rates.” Finally, we use mont,tily caxchangc rates. Inrlirnior~.
data
frorlr
Ttifw
data
1Irf> tjr.f,t 10~ l\‘ootls wfw‘
ol)t ainfd
regime
of adjustahtc
1‘1.0111 l,lic, OFX~I~‘s
‘l’hc ex~.l~it~~go rat (‘5 it[‘f’ Imilrt -itI-t ilrrrl spot. r;tks. q~~otf~(l l’or 1Jkrf~c~-rrrolrtII clolwst
:llnin while
pf,gged t:‘co7torrric~
the int,erest
The data are drawn frolri the lolrgf~st siriglt> l)f,riotl of f3f~~iiirigf~-ra.lc traIlqiiiliiy fliiritrg the 1960s (e.g.. t.tlo (:~~~III;III data Iqirl aftcsr t hcb\larch I !j)tiI revalllation arlcl end before the Octohr,r I!Ki!) rft\-alliat ioli ). t’i)r hot h the gold standarfl and raks
arf‘ usually
Hret,ton Figliws
b’igure
if.
‘t’rf~as~lr?;
Woods c1at.a. 1tic l..S..\. is t.rf~alf~(l as tlifl liorlw 2 and 3 colit aitr plots of’t tiv hasif, daily data
2 colitains
t illif’-s(>rioh of t Iit> Iloillillal
cxcha.llgf‘
hills.
colintry.
for t hc EMS pf,riod.” rates
(mcasrlrf~fl,
as
always, as the natural
logarithm
of the DM price of one unit of foreign ex-
change);
the upper and lower (implied)
included
in the graph.
EMS exchange-rate
Tick marks along the bottom
bands are also
of the diagrams
delin-
eate calendar years; the ticks along the top mark realignments which affected either of the two relevant currencies (e.g., either the DM, the Belgian Franc, or both, in the case of the DM/Bf r rate). Figure 3 contains time-series plots of the 2-day interest-rate differential (as always, the German rate minus the foreign rate). As is true of most of our graphics, scales are not directly comparable across countries; the Dutch exchange rate has actually been much more stable than the Italian exchange rate, even though the relevant exchange-rate bands appear wider on the graphs. The EMS
has experienced
a number
of realignments.
Our use of fine
frequency data enables us to split our data into thirteen different corresponding to the periods between the twelve different realignments EMS.22 We divide our data for a number of reasons. A split sample us to check the sensitivity of our results. Dividing the sample also
parts, of the allows allows
us to check for policy shifts such as the often-noted increasing credibility of the EMS (which should result. in changing types of nonlinearities) and timevarying capital controls. 23 Bertola and Caballero (1990a) also argue that the nature of the nonlinear relationship is expected to vary over time with the level of reserves. The thirteen different samples are tabulated below; it should be noted that the number of potential observations varies dramatically across regimes. In virtually all of regime-specific work below, data for the business 22The exact
ERM
realignments
were as follows
(percentage
changes
in bilateral
central
rates are also shown):
Regime
Date
Belgium
13-3-79
EMS Begins
Den.
24-9-79
+3.0
29-11-79
$4.74
France
Ger.
Ireland
Neth
-2.0
22-3-81
+6.0
4-10-81
+3.0
21-2-82
-5.5
+3.0
-5.5
$8.5
12-6-82 8
21-3-83
-1.5
-2.5
$5.75 +2.5
9
21-7-85
-2.0
-2.0
-2.0
10
6-486
-1.0
-1.0
11
3-8-86
t3.0
-4.25
+2.75
-4.25
-5.5
+3.5
$2.5
-3.5
-2.0
-2.0
+6.0
-2.0
-3.0
-3.0 +8.0
12
12-1-87
13
5-l-90
23Government
Italy
-2.0
-3.0
-3.0 +3.7
authorities
and differ from declared
may also defend implicit. target-zones
t,argrt-zones;
split,ting the sample
19
which change over time
may alleviate
this problem.
‘I
.05
'2b1'6 Years
"'
2i2'
Japan
Calendar
Ireland
“’
-0
-0
&, 2915 Years
“”
Belgium Relevant Realignments
o-’
- 0412
"I'
vary by Country Relevant Realignments
'-,a,,!,,, 0 Calendar
,045
Scales
165 Calendar
Y t2bi’k
Years
13
-
UK
Calendar
1990:5:
#2b1'& Years
16
Figure 3: Interest Rate Differentials
0
Denmark Relevant !?eallgnments
14’1
1979:3:
-1775.,,
-
Relevant Realignments
,’ Calendar
'2$1'& Years
-1262-m,,
0
1
USA
Calendar
I,
Netherlands
Calendar
'2b1'i
'2b1'6 Years
Years
France Relevant Realignments
0
-3.95 -,
Relevant Realignments
As
is
well-known.
t.o test work samplf,
for
t hfx ICIZIS has hf~~~iit~ illcrf3sirlgly
lxdwfw1 rfxligll1llf~lit.s
the periods
that
ot,ller
WC kntl
mallil;3t
t,o f’oc~is on
corlllt r.v; t,his is apparf7rt arc
dads),
associatfd
ncithf>r hand,
‘l‘lif77
f’ \~)lat ilit.!. \xrif,s
arc’ tllr>.
interest,-ratf%
;Issociat.fd
Ll’hilc
\ulat,ilit,>.
t.o lx
kss
recent by
wit II f~sccptionall>~
fliff;~rf~llt ial:, ~~11
time
descriptive
more
(meastlrcd
la.rgc, difff~ix~tlfx~:-~~~tm+ cx)llilt rks
art’
over
iI1 l~igltrf~ 2. 2s \vcll a.s siml)lc wit.11 lligll
empirical
as it, is a long
t argfxt-zolrf>.
dramatically
papf~).
we inknd
In our
of tjhf, MIS,
crfdihle
in t.hc sense-
longer;
crttlihilit~y.
t IIV t~~~lft Ii rcgimc
it1 t IIC b\orl;illg
tal,lllatcd
trot, grnrrally other
of iilcrtasiilg
of tl;Lt,a tlra’iz’ll 1’rotll a IJo1 fblrt iillly
Wfa 110tfx t.llat. fxdikiuge-ra1 (which
at ioIls
fxdihlc
S~Y’III t.o lx growing
for fxcl~ st.at,ist,ics
regimes
historical
low volatility. volatile
ill Imtli
morf’
arc> st an-
OII the rfxcf-ntly.
exchange-rat,c
and
ratfx volat,ililv
t hari t lit ot 11cr l:hlS
t IIC Nf,t hcrlantls ha.s much lower exchange roullt ries. Ilowf~vf7~. 110 t.ratle-off I)f+ween
exchange-rak
alItI irlt f>rf>st-tliflcrcxllt
ial \.olat ilit,?: is apparf‘nt,
Ilri’ -1 pro\:idcs
stackf~cl
intcrcst,-rat
variate
c \olat
fift,l-ortlcr
ilit.>.. I>or illst anut.
l)ar (.lli\l’th oI’s( illlfliirfl
in t,hc t1at.a.
tlf’viiIt ioIls of rf3idrlals
\..:I11 of’ irltf~rc~st -rat fx (liffcrcnt,ials
and
cscha.nge
from rates.“’
Figa bNo
m 1
2
4
5 6
3
4
5
6
Eelglum
3
stderrre
2
8
9 10
7
r-In
0 stderrrl
7
c] stderrel
11
12
1113 12
13
,
1
2
3
# stderrde
4
5
6
fl stderrdl r-I
4
5
6
Ireland
1 stderrle
1
9
10
0 stderrll
8
1113 12
11
12
13
1363
01
2
3
1 stderrfe
4
01
2
3
2833
0
1
I
2
3
stderrle
rl
5
6
Denmark
0257
01
I
1
2
3
stderrbe
4
5
6
Italy
4
8
9
10
n
9 10
7
8
9
10
0 stderrbl
7 8
0 stderrll
7
8
9
10
6
ill3
11
12
12
13
013
0
1
1
1
I
7
8
9
10
3 4
UK
O
5 6
Figure 4: Conditional
Volatility
Measures
7
2
3
stderrae
4
USA
5 6
9 10
7 8
9 10
0 stderral
8
n stderrhl
Netherlands
2
Stderrhe
France
Interest Dlfferentlal and Exchange Rate Standard Errors
Japan
7
5
0 ‘stderrfl
1113 12
11
11
12
12
13
13
-orlllslpl
0839
oiJllihi
01
1 stderree
‘1325 11111111
0249
.I243
Residtia: Standard Errors of Exchange Rate ar?d Interest Dlfferentlals Data for 13 EMS Regimes, from blvarlate 5th order VARs: Scales Varv
relationship deliver
is apparent
the same
Iwtween
the two measures
result. and are contained
(uncondit,ional
in t.hr working-paper
estimates version).
[Init-root
trst.s (allowing for wrial dependence through the rnethod sugthat unit-roots are pcrvageskd by Perron (1988)) indicat,e. unsurprisingly, sive throughout the dat,a (t hc statistics are tahula.ted in the working paper). More precisely. the null hypothesis that. a IlllitLroot exists cannot, usuall! be rejected
at conventional
fundamentals
(using
significance
Q =.l):
Itw~ls in each of: the excha.nge
alltl t,hc interest,
differential.25
While
rate:
this Inay
be the result of low power (Froot alld Ohst,feld (19901))), it, is extremely dist,urbing that the interest differential appears t.o be nonstationary. ignoring drift ~ the difference het,wcel1 t II(~ c>xchange rab and fr1ndamenta.b is the expect,ed rate change of the excha.nge ra.t,e; ullcovertd interest parity implies that, the latter is the same as the interest, different,ial. A nonstat,iona.ry irlterest diffcrelit.ial is illf-onsistcwt \vit II crcdihle target -zones: t hc persistence in t.llix seric3 which c‘;~lll~r)t I)(’ ;~c.c~ollrltc~l for 1)). f~~ll~lillll~~Ilt~~lS will ret 11r11lo haunt, 0111’tlypot tiesis t cxsts 121 t (‘I’. cannot typicall!, I)(% ‘l‘liv hypot licsis t,tiat f~t~~(l;~~~rc~titals Ilavr, ii Iinit-root Ie\:els. III fact. t,lie assumption t.liat rr:jccted at conventional sig:llifi(.allce furidalncntals follow a drift Ic+. ra~itlonl walk, while not likrally true, serwi~ t,o Iw a good
approximat
V. Deternlination Our
of
i011.”
alpha
strategy will 1-w to fiti(l a11 al)l>rol>rialc rnr,yf for 0: wv t hcW conduct 0111 for reasonal)lc \.iil~iw of 0 sl)afiliillg this range. We cst,imate 0 I)! two mct,Iiods. First. \vv 1i5v Olil' (la12 to (31 inlatr> 0. SNond, w(’ 11w cstinnat,cs aria.l;sis
frown the litcrat uw.
Estimating
CYfrom
If the increments intervention
daily data
to fare
generated
by equation
to defend a target-zone,
(3) with infinitesimal
then integrating
band
dfover one day results
in: .ft where. the discrete-time
ft-1
(14)
et
7) +
=
period is one day, 7 is the daily growth rate of fun-
damentals, and tt, which is the integral over one day of gdz, is the daily disturbance to the fprocess. Substituting from equation (14) into equation (l), we obtain: et -
el_l
=
n[Et(de)/dt] - [Et-l(de)/dt] + et
77 +
(15)
Equation (14) can For estimation we replace Et_,(de)/dt with (i,_, - &). then be used to estimate 17 and cy. The structural parameters (Y and 7 are identified because fundamentals are exogenous almost everywhere. Our estimates of alpha are presented in Figure 5. This figure graphs the point estimate of alpha with a two standard-error band.27 The estimates are almost uniformly small, although they vary considerably across country and EMS regimes. With the exception of a few imprecise estimates for Denmark and France, there is little statistical evidence that alpha exceeds .25 for EMS countries; lack of interest-rate volatility makes it much more difficult to pin down cy for non-EMS countries. Indeed, there are numerous negative estimates of alpha; the hypothesis that alpha is zero does not seem unreasonable from a purely sta.tistical point of view (although we exclude that possibility, and hence many of the point estimates, (1 ~riori).‘~
27As sample of varying 2sWe tution
have
also
of actual
typically mate
size varies
confidence tried
to estimate
exchange-rate
delivers
tional
volatilities
ARCH-like
The
the residual
purposes). plus
assumptions
than
data,
estimates
our
bands
-1.
since
One
could
correspond
could
to intervals
t,his method (this fby
approach
f; it is potentially reflect.ions
for the f process.
2.5
on McCallum’s
movements;
above,
be extended
also measure
target-zone
relies
volatilities
volat.ilities
to be f. This
about the
As discussed
differentials;
for conditional
which
of anticipated
conditional
technique
the constant
on additional are
in place
of a near
latter
specification
for estimation
error
o wit,h a technique
regime-specific
of int,erest-rate
zero.
the t,wo standard
changes
estimates
(Y by regressing
of cy near
by regime,
levels.
we have
typically would
deliver
regressing has the
(i-i’) advantage
with
of fundamentals
data
technique
tried
rates
delivers
regimes
important
also
of exchange
within
substi-
this
to esti-
on condian estimate
by employing more
on e and of not sampled can
an
observations
bias
defining
depending less finely coefficient
i
0
Estimates
of a in the literature
We have interpreted money demand,
a as the negative
of the interest-rate
semi-elasticity
of
a parameter
that plays a widespread role in both theoretical This parameter has previously been estiand empirical macroeconomics. mated in the literature; Goldfeld and Sichel (1990) provide a survey. The short-run semi-elasticities reported are quite similar to one another and average -.4.2s330 These estimates by the average
quarterly
are converted
to long-run elasticities
speed of adjustment,
.32/quarter,
by dividing
giving a long-
run semi-elasticity estimate of -1.25, which we take to be representative semi-elasticity estimates for industrial countries during normal times.
of
There are two ways to apply these estimates to daily data. First, in the spirit of the models upon which equation (1) is based, one can think of a model of continuous long-run money-market equilibrium such that an appropriate choice of o is 1.25. More rea.listically, one can think of equation (1) as resulting from a Goldfeld-style partial-adjustment model of the money market.31 In this view, it is the short-run, interest-rate semi-elasticity which is relevant to the problem; this is obtained by dividing -.4 by 90 days per quarter, giving a daily short-run semi-elasticity of -.0044, so that a=.0044 seems appropriate. Our various methods of uncovering (Y have led us to a range for this parameter. We think of cr=.l as being a reasonable value; a=1 is certainly representative of the high end of the range, especially given our point estimates. In preliminary estimation, we searched a grid of (Y values spanned by (.05, 3.0). I n most of our work below, we report results based on cu=.l 2gThe
average
units
so that
that
10 percent
estimates The
need has
change
of asset
mean
prices.
that
historical
30The periods;
Goldfeld 1962:l
Italy closely
interest-rate
semi-elasticity.
summarized
convention,
the
product
Under
report and
units
are the
units
study
interest-rate
the
Goldfeld
units and
so
Sichel
of a speed interest
of adjustment, demand,
having
or expected
annualized
interest
rates
rates
of
so our
years.
rather
than
equations. of cy are
we use two-day
Also,
too
low;
Euro-rates
increased Canzoneri
are
currency and
Diba
usually
used
substitution (1990)
as may
discuss
the
further. and
Sichel
report
involve
- 1985:4,
Japan
1966:l
- 1985:4,
it is important
chose
We choose
of money
of the
1971:1-1985:4, U.K. 1958:1-1986:l. the results for t,he US. in terms
in a single
they
as 10.
semi-elasticity
time
this
rates
estimates
1969:1-1985:4, match quite 31However,
our
of the
have
substitution
estimates Canada
but
as .lO.
quarter,
in money-demand
of currency
is -.004, entered
Sichel
inverse
interest
report, was
Throughout
domestic
rates
effects
the
semi-elasticities
Quarterly interest
per
Sichel
for example,
by 100.
and
percent are
and
year,
is ent,ered
Goldfeld
which
interest-rate
per
to be multiplied
units
units
Goldfeld
per year
estimates
which time
number 10 percent
to recall
model-determined
t,hat
the st,ate
analysis.
27
the
following
France
countries
1964:1-1985:4,
The results for these of the magnitude of the
assumption variable
that
and
countries short-run
fundamentals
is maintained
data
Germany
throughout
can
be the
and cu=l. Several different manifestations of the data a good choice for this key paranleter; see also Diebold Given frequency
differentials
our measure tials.
that
cr=.l
is
an cy value, t,he fundament,als can be measured at the monthly and compared with t.hc tradit ionA reduced-form determinants
of flexible-price exchange-rak monthly IFS measures of Ml rithmic
indicate (1986).
between
models, money, and output.32 WC obtained and intlust.rial production,33 computed loga(icrman
of fundament,als
The regressions
and
on act.ual
are compukd
foreign
variables,
money-supply
from 1979
and
through
and
regressed
output
differen-
1990 on a count.ry-by-
country basis. Our measures of fundamentals are typically highly correlated in levels with actual money and out,put, differentials; for instance, the R2sfor our six countries have an a.verage of .63. On t,he other hand, the coefficients on actual fundamentals are not signed consist,ently, and there is substantial residual autocorrclation. 111 first-diffcrc,ncc~s. our fundamental measures arc’ essentially
uncorrelatcxtl
VI. Graphical
A direct
with
~lloncl~- nrrtl out put.
analysis
escl,,m.in,cr,,tron
tions hip In this sect.ion of the paper. LVCana.lyzc the rclat.ionship between exchanges rates and funda.mentals, using graphical tc~chniqucs. Our conclusions will 1)~ corroborated below wit,h mor(~ rigoroIls c~~)r~ornc~tric techniques. WV bc,gin with the assumption (I=. 1. Figures 6 and 7 cant aiu a wealth of descriptive information about the relationship bet,weerl t hc r~sctlangc~ rat<, (c ) and fundamentals (f). ‘l’hc~ figures contain fourk[i “slilall Ilirllt,ipk” c : j scatter-plots; one for each of the thirteen
EMS regimes.
alltl anotllcr
covering
the whole sample
from 1979
through 1990. Tl 1c USC of slnall multiple graphs allows the data. to be conipared easily across rcginles a.nd count,ries. I:or the sake of brevity, only data for the Netherlands (a rcalati\-4y credible participant in the ERM) and Italy (a relatively participants
incredible co111ltr>.) arc usctl: comparable are availa.blr in t tie working pa.l)er.
In any given
scatter-plot
. each of t tie individual
figures
for other
point,s represent,s
ERM a single
daily observation. To guide t 1lc cyc ill connecting t,he dots of the joint t,ribution, a nonparanlctric “data snloot.tltxr” is drawn as a solid line.“4 32We temporally t,o correspond 33Quarterly 3”The five) and
average fundanwnt.als (instead I hat illdust rial protluct,ion
Lo t.hr way
in the cases
smoother calculates
divides
of Bclgiaul thv
alltl
horizotlt.al
(.liv ci-osc;-l)kdiall
of
of sctcctivrly
sampling
disWC
fundamentals)
is nleasurvd.
Francc~. axis
int,o a number
of bands
f iilld f wit tlill racll band.
The
(we genrLrally
use
cross-mrdinns
arc
29
use the shapes
of these
smoothers
extensively
in our search
for nonlinear
re-
lationships between e and j The smoother can easily handle the nonlinear patterns implied by the target-zone theories above; conversely, the absence of sensible nonlinear smoother that the theories work poorly. The marginal each observation
patterns
suggests
(though
density for e is displayed to the right is represented with a single tick mark.
right of the marginal
density,
a box-and-whiskers
it does not prove) of the scatter-plot; Immediately to the
plot of the marginal
density
is also displayed. The line in the middle of the box marks the median of the marginal distribution; the box covers the interquartile range (i.e., from the 25th percentile range to the 75th percentile range). The whiskers extend p oints beyond to upper- and lower-“adjacent values”; adjacent values are usually considered outliers. 35 A comparable marginal density and box plot for fis graphed above the diagram. This combination of graphs allows one to evaluate the marginal and joint distributions simultaneously. Target-zone theories place a number of restrictions on the marginal distributions of e and f, as discussed above. For instance, the simple model of Krugman (1990) im ’ pl ies that, (with perfect credibility and infinitesimal interventions on the bands), the exchange rate is expected asymptotically to have a bimodal symmetric density which would be directly apparent in the marginal distribution, and manifest in the box-plot as a relatively wide symmetric interquartile range with sma.11 whiskers. The model of Bertola and Caballero (1990b) d e 1’ivers a very different set of restrictions. In addition, some theories (e.g., Bertola and Caballero (1990a)) present restrictions on the relationship entire sample.
between
e a.nd f across
regimes;
hence
the
scatters
for the
The (implied) EMS exchange-rate bands are drawn as horizontal lines in the figures, so that the vertical dimension of the Dutch graphs represents +/-2.25%, those of the Italian graphs +/-6% (until January 1990). Consider the top left graph in Figure 7, describing tween e and f for Italy during the first EMS regime,
the relationship which prevailed
befrom
March 13, 1979 through September 23, 1979. The data are grouped in the upper portion of the graph, indicating that the Lira was relatively strong during this period; the box-plot for e indicates that the median value of the exchange liers. The apparently
rate is moderately
high in the band,
and there
fundamentals are approximately symmetrically normal distribution. The relationship between
are no negative
out-
distributed in an e and fappears to
then connected with cubic splines. Meese and Rose (1991) use a different nonparametric smoothing technique (locally weighted regression) and arrive at results consistent with ours. See also Diebold and Nason (1990) and Meese and Rose (1990). 35Adjacent values are defined as 150% of the interquartile range rolled back to the nearest data point,. 31
he monotonic,
positive,
and liliear.
No simple general charact,trization can be made about However, a number of features do seem apparent. ships. importantly, remarkably few nonlinearities which are typica.lly vicwcd as being nlore the Dutch Guilder) Third, nonlinearities than
more
are apparent,. Second, currencies committed to the ERM (such a,s
have fewer (not more) appear t,o be growing
important;
t,he absence
the e : f relationFirst, and most
manifestations Icss important
of nonlincarities
of nonlinea.rities. over time, rather
in the twelfth
regime
is
noticeable. However. incrcastxd credibility sltould be manifest in a relationship between the exchange rate and fundamcntjals that comes increasingly to become more unlikely.% resemble Krugman’s S-shape, a.s rea1ignment.s Fourth, while some nonlincarities are apparent,, they tend not to have shapes that are even vaguely similar to those implied by extant. t,heories. Countries that have cxperienc-et1 frqIlc,nt realignments (such as It,aly) do not appear
to liavc
iuvrrtrtl
S-shapf‘s.
as implied
by the
Bertola
and
Caballero
(199Ob)
model; crctlibl~~ count rics (such as the Nc1,herlands) do not have t.hat, arf’ apparent do not Krugman’s S-shape. ‘1‘hat, is. t11(’ ilonlincarities seem to have sensible idrnt,ifiabl(* pal.t urns across eitllcr time or count,ry. Fifth, much of thca flat a is clllst,ered iI1 11~~nliddle of t,he declared exchangerat,e bands, especially for Iat(,r r(xgillles. Assuming that. the act,ual exchangcrate bands coincide wit11 the dr,clared ba~~ds, nonlinearities a.re difficult to detect visually if t,hc c,xchangc ratf’ stays in the middle of the zone.3i This may indicate that, t,hc, aut Irorit ios defeIldcd implicit, bands well within t,he declared bands: in this case our t hc~oretZical ana.lysis applies for the a.ctual implicit bands. so long as the Inarkt,t recognized t,llis fact.“’ The fact t,hat, exchange rates spend n~ucll of (heir tinIf\ irt t,he interior of the band may
instead be a small saInpI(~ prol)l~~111. C:ivc,rl the sample sizes involved and t.hc nature of t,hc forcing process IIII~W that IIIIII hypot,hcsisl we are skeptical of t,his view; however, noIllin(~arities would IW milch more difficult to detect if exchange ra.tes happened to have avoided the periphery of the bands. the t : ,f relatiouship
Finally,
appears
to be approximat,ely
linear
over t,he
entire sample. consistcxnl wit.h t Ilrx ~nodel of Bcrtola and Caballero (199Oa). Figures 6 and T rely OII our assumpt iolr (1 = .l. (‘Iearly as N falls, the scatter-plots in these figures IIIOVVcloser towards an exact affine relationship between e and f; if (1 = 0, c = .f csactly. Figllres Al and A2 are the analogues to Figures 6 and 7, comput,r~tl \vitll (1 = I. ii valurx that, is implausibly large analysis of Fkrt.ola and (‘al)aIlt=ro ( 1990a.l)) implies
3”Thr earit.irs
should
he changit~g
370n the other
hand, the eschangc
target-zone, =This Edison bands.
is t.rue as long as and
(:racicla
over
t ilnc%fro~r~arr illvvrtcti
t,hat. the shape
S-shape
tIlta problt~~r~ is vsplicltlv a s~nall sample prohlpm. rate ~rlay sp~rrd most, of its t,ime near t,he bands.
the implicit.
Kaminskv
bands
arc’ currcnt,ly
arc constant twt.ing
of the nonlin-
to Krugman’s
(as the declared t.hr, hypothesis
S-shape. In a credible
bands
of constant,
are).
Hali
implicit
in our view. These figures indicate nonlinear effects of substantively greater importance, although it is a.gain difficult to detect patterns over time or country.
Again, the smoother
by extant
exchange-rate
Comparison
shapes bear little resemblance
to those implied
models.3g
with other
exchange-rate
regimes
While the scatter-plots of Figures 6 and 7 do not seem consistent with the implications of known nonlinear exchange-rate theories, we hasten to add that countries participating in the EMS do not look similar to countries in (relatively) free floats. Figure 8 is a graph (comparable in every way to Figures 6-7) for the British Pound Sterling, an exchange rate which was floating (relatively) freely against the DM: (comparable figures for the Japanese Yen, the American Dollar, and the Swiss Franc are similar and are available in the working paper). Figure 8 also has fourteen small graphs, one for each of the thirteen regimes, a.s well as one for the whole sample. While actions such as the Louvre Agreement lead one to doubt the assumption of perfectly free floating the e : f scatters look much more linear for non-ERM countries than they do for ERM countries.40 Our model predicts e = f for flexible exchange rates: manifestly this prediction is satisfied in spite of the assumptions used to build the model. This encouraging result bolsters our confidence in the empirical framework. The EMS can also be compared with other regimes of fixed exchange rates. Figure 9 provides graphs for the post-WWII Bretton Woods regime of pegged but adjustable rates (the data a.re drawn from the 1960s); Figure 10 provides comparable data for the pre-WWI and inter-war gold standards. Both figures use cy = .1.41 The relationship between the exchange rate and fundamentals seems to be decidedly more nonlinear for the gold standard than for the EMS; the dollar/yen rate also appears t,o be nonlinearly related to funda.mentals during the Bretton
Woods era.42 However, most of the Bretton
Woods data appear
consistent with linear e : f relationships, while the smoother shapes in the gold-standard data, are not implied by existing target-zone models.43 3gThe
working-paper
40Linearity was founded; 41Using
version
cont,ains
is also the hallmark further
a higher
detail value
is available
of a (say,
in the
1) changes
working the Bretton
Woods
higher values of alpha (e.g., 1) appear unreasonable Higher alpha values (say, .5) for the gold standard
43This
however,
may
shapes upper
be, in part,
are vaguely tails
appear
the result
and
reminiscent
33
base
graphs
are extremely
wiggly.
country. before
the ERM
considerably; Below,
the
we show
in a number of different data do not greatly change
of Krugman’s
to be essentially
of movement
as the
in t.he 1970s
paper.
that much dimensions.
tails;
sloped
Italy
float.ing
do not
lower
to be positively
with
currencies
smoothers
the graphs. 42The smoother
tend
analogues
of ERM
S-shape
for parts
of the
linear.
in t,he gold points.
These
are the exchange
35
Is there
a “honeymoon
effect”?
As discussed above, the thrust of the original target-zone proposal was to make the exchange rate less responsive to fluctuations in exchange-rate fundamentals,
the celebrated
“honeymoon
effect” of Krugman
(1990).
The the-
oretical framework of Section II implies that the e : f slope should be unity in a floating rate regime, lower in a credible target-zone. If the diminished impact of fundamentals on the exchange rate in a credible target zone is the “honeymoon effect ,” then the possibility that the impact might be magnified in an incredible target-zone (Bertola and Caballero (1990a,b)) might be the “divorce effect.” It should be remembered, however, that we are studying relationships; the start of a targetgovernment policies, not interpersonal zone is more likely, we think, to be characterized by low policy credibility than high policy credibility. Estimates of the slope t,hus provide a specification test of the target-zone model. Actual estimat,es of the slopes for all countries and EMS regimes are presented in Figure 11; we simply regress et on ft and an intercept; Newey-West covariance estimators are used. These specification test,s are independent of the theory results in Section II. Consistent with the honeymoon effect (and inconsistent with the work of Bertola and Caballero (1990b)), for cy = .l, the e : f slope is often less than unity for EMS countries, though rarely by a large margin. However, for any given country, our point estimates of the slope vary considerably over time, being greater than unit)y for around a. t,hird of the regimes considered; point estimates of small slopes also tend to be imprecise. Further, there are few identifiable patterns in the slope estimates. For instance, the unstable regimes of the early 19SOs are a.ssociated with small slopes, while the credible regimes of the late 1950s seem t,o have higher slopes. Also, slope estimates for countries a.s different as Italy and the Net.herlands do not appear to be very different.
It will be shown below that the nonlinear
rise to the honeymoon the data.44 to unity.45
effect in target-zone
linsurprisingly.
non-EMS
effects, which give
models, are not usually found in
countries
have e : f slopes very close
An errors-in-variables argument leads to the conclusion that a choice of (Y which is too high will lead to an e : f slope which is too low. Given our rates
at which
costs;
the gold
ing the gold further implicit
standard.
gains were
44Slopes
bands);
however.
from
market,
hlyers
analysis. Movements EMS exchange-rat,e
declared
important
if exchange
rates
physical forces
(1931).
transportation
which
Officer
limited and
(1986).
of gold fluctuations Spiller
the smoot,her
patterns
to t,he spread statistical and
problems
fundamrntals
are very
between afflict
transportation
and
Woods
similar bands
rates
(1988)
dur-
provide
to movements in which differ from
different.
maximal the
exceed
in exchange
in the gold points are conceptually bands (when the aut.horities defend
are also unrelated
45Potentially countries
arbitrage points
and standard
are nonstationary.
minimal errors
values for
of e. non-EMS
i” I
uncertainty about cy, we conduct sensitivity analysis. Figure 12 is comparable to Figure 11 but uses cr = 1 (the graphs with c~ = .05, for which there is essentially no evidence that the e : f slope strongly differs from unity, are in the working paper version).
For cr = 1, all point estimates
(across six ex-
change rates and thirteen EMS regimes) are less than unity, virtually always by statistically significant ma.rgins. Indeed, the e : f slopes are clustered closer to zero than to unity. We view this as another manifestation of our hypothesis
that unity is an excessively
high choice for CY.
Summary Some nonlinearities are apparent in the scatter-plots between the exchange rate and fundamentals; the e : f relationship tends to look much more linear for floating exchange rates than it does for fixed exchange rates. However, in a number of different dimensions, the nonlinearities do not seem to conform to the patterns implied by target-zone models. The few nonlinearities that exist do not appear as one might expect in more credible exchange rates (such as the Dutch Guilder), more recently (e.g., since 1987), or in the S-shapes implied by existing theories. Similarly, although there is modest evidence of a “honeymoon effect ,” the size of this effect does not vary in a sensible way across regimes; in any case, the existence of the effect depends strongly on c-y,and reasonable values of o are consistent with no honeymoon effect. Our relatively naive graphical approach has yielded, at best, weak supWe now attempt to clarify the issue by port for target-zone nonlinearities. applying more econometric firepower. VII.
Parametric
In this section, nificance significant
tests for nonlinear
we estimate
of nonlinear explanatory
terms.
target-zone
effects models
directly
and test
We find tha.t the nonlinear
power in sample.
terms
the sig-
often add
However, the finding of statistically
significant nonlinearities in-sample is too robust; it, occurs for both fixed and floating exchange ra.tes. Also, coefficient signs are not those predicted by target-zone models, and a number of other aspects of the model are rejected. The structural
model which we wish to estimate ft = 71+
is:
ft-1 + et
et = or/ + ft + Ale.v(b.ft)
+ &ev(Mt)
where we selectively sample et a.nd .ft daily. In our empirical with a slight extension of (16):
39
(14) (16) work, we work
where:
;I is the estimate
of 11 from equation
rate); i1 and i2 are the roots to equation in place of true 0 and 7; 6 is the estimated
(14)
(adjusted
to an a,nnual
(7) with estimates (T and 77 used standard error of the residual of
equation (14) (adjusted to annual rates); and Al and AZ are free parameters unconstrained by zone size or credibility assumptions. We estimate (17) with OLS, ignoring any biases in $ and 6 which may result from, e.g., small-sample bias, generated regressors, or misspecifications of (14). We maintain cr = .I for most of the analysis which follows. We allow for two potential
misspecifications
of the model by including O0
and 0,; a finding either of 00 # 0 or 03 # 0 is an indication of mcdel misspecification (multicollinearity considerations often preclude free estimation of 0,). An error term ha,s also been added to the equation; Froot and Obstfeld (1989b) suggest that this can be interpreted in a domestic context as a result of time-varying income tax rates that are conditionally independent of ft. We also examine thr> serial correla,tion properties of this disturbance below. Since there a.re cross-equatiou restrict.ions, estimation of these equations should be conducted jointly; for convenience, we pursue two-step estimation below.““>“7 Thus, we estimate (13) with OLS; consistent estimates of 77 and u are obtained from the intercept a.nd standard error of the residual, respectively. These estimat,es are t,hen used t,o estimate X, and X2; (17) can then be estimated directly with OLS. ~1~ and A2 can he consistently estimated by O1 and 0,; from the latter. t.he exchange r&e bands, eL and eU can be estimated. In practice, we test the hypothesis O1 = O2 = 0(<= Al = A2 = 0). Two problems affect this work iu pract.ice. First, our regressors are exponential funct,ions, which can lead to computa.tional complexities. Such problems can be avoidetl by a.ppropriate resealing of the data. Second, there is often severe multicollinea.rity between the regressors of (17), making tests of individual coefficients unreliable. For this reason, tests of the joint hypothesis 01 = O2 = 0 are tabulated in Table estimated signs of the 0 coefficicnk. As shown and A2 are of opposite sign in most theoretical
1. Table in the
1 also presents
theoretical
target-zone
section,
the
Al
models.48
46Simultaneous estimation is complicat,rd by two facts: (1) the well-known leptokurtosis in exchange rates is manifest in gross violations of normality of t,he shocks to t,he fundamentals equation (14); and (2) choice, rather than estimation , of (Y precludes serious statistical work, unless one is willing t,o guess t,he covariances of CI with other parameters. IV estimat,ion using Durbitl’s ranked instrumental variables does not change results; Bartlett’s variant of Wald’s indicat,or iustrrrnlental variables leads to enormously higher standard errors. 47Equations for individual bilateral exchange rates can also be estimated jointly with Zellner’s seemingly unrelated tecllnique for greatrr &iciency. 4”Froot and Obstfeld (1989b). 5Ilow that 0, and 02 arr well-behaved with the additional assumptions of normality of U’~and independence of ct Froot and Obstfeld (1989b) provide further analysis. 11
Tahlc Hypothesis
Tests
Joint Hypothesis
1:
for Nonlinear
Terms,
cu=.l
Tests for Nonlinear
Terms
Relg.
Den.
France
Ireland
Italy
Beth.
.oo
n/a
.oo
n/a
.oo
.oo
11/a.
2
.oo
n/a
.OO
II/11
.oo
.oo
n/a
3
.oo
H/ii
.oo
11/a
.oo
.oo
n/a
4
.oo
n/a.
.oo
u/a.
.oo
76
n/a
5
.oo
n/a
.oo
n/a
.OO
100
n/a
6
.oo
.oo
.uo
.OS
.oo
.oo
.oo
7
.oo
.oo
.oo
.oo
.oo
.oo
.oo
8
.oo
.oo
.oo
.oo
.oo
.oo
.oo
9
.oo
.oo
.oo
.OO
.Ol
.oo
.oo
R.egime
.Japan
UIi
10
.oo
.oo
.oo
.oo
.oo
.OO
.oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
I1
.oo .oo .oo
.oo
.oo
.UCl
.OO
.oo
.oo
.oo
1
12 I :1 Entries 711~.
arc-
Regime
ant1
used,
.oo
.oo
.oo
.oo
.oo
.oo
.OO
.oo
.I)0
.oo
.OO
.oo
.oo
.OO
significanw
o = .I:
~cgililr,-sI)c,cillc..
CJ~ and r/ (ar~tl thucforr .Yc>wc-v-\Ymt,
= O2 = 0 + O,f,
+
X2) arc
wtirnat,ors
Neth.
.la~pan
ITli
+~
II/11
t-
-+
Illa
+-
-t
II/d
-t
-+
n/a
+-
II/;1
-t
it
II/A
Il/il
-+
+-
Ii/i1
t-t -+
-4
II/i, St
-t
St
1.
t +-
+-+
0,
X1 and
cova.riance
Signs of 0, and 0, l;‘laII(‘(‘ Irc~lar~tl Italy
-+
-+
icst
+ 02wp(X21;)
wit.11 six lags.
Belg.
++
Icvcl for joint
(‘I - ,f; - (II/ = 0,t.r/1(A,.f;)
+t 2 :1
.OO
.oo
Throughout~,
count,ry-
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
arc marginal
in regressiorl
USA
-+ t+i
++-+ +t-+
+-
++ +-
-+
-+
-t +
++
-+
-+
-t
+-
++
+t+
t -t -+
n/a n/a
-+
t-
IlS,Z ++ -+ t-+ -t -+ -t-
-t
++
-+
-+
~+
4
-+ -+ -+
m+
-t
tt -+
Q-Tests
for Residual
Serial Correlation
Regime
Belg.
Den.
France
Ireland
Italy
Neth.
Japan
UK
USA
1 2 3
.oo .27 .oo
n/a n/a n/a
.oo .oo .oo
n/a n/a n/a
.oo .02
n/a
.oo .Ol .oo
4 5
.oo .oo
.oo .23
n/a
.oo .oo .oo .oo
6 7 8 9 10 11 12 13
.oo .oo .oo .oo .oo .oo .oo .oo
n/a n/a .oo .oo .oo .oo .oo .17
.oo .99 .oo .oo
n/a .oo .oo .oo
.oo .oo .oo .oo
.oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo
.oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
n/a n/a n/a n/a .oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo
Entries are ma.rginal significance levels for serial correlation of wt from regression et - ft - cq = O1 exp( X,f,) + &excp( X,f,) + 03ft + Wt,ff = .l.
T-Tests Regime
Belg.
1
.97
2 3
.oo .Ol
4
.Ol
5 6
.60 .oo
7 8
.oo .oo
9 10 11 12 13
.oo .oo .oo .oo .oo
Den.
of O3 = 0
France
Ireland
Italy
Neth.
n/a da n/a n/a da
.28
n/a
.05
.13 .42 .Ol
n/a n/a n/a n/a
.54 .ll .oo .29
.oo
.33 .04
.25 .oo .oo
.oo .oo .oo
.25 .oo .oo .36
.oo .oo .oo .29
.05 .oo
.oo .52 .oo .35 .Ol .oo
.oo .oo .oo .oo .oo .oo .93 .oo .oo
.06 .04 .52 .22 .98 .17 .83 .oo .20 .45 .oo .93
Japan
n/a n/a n/a da n/a .oo .03 .24
.oo .oo .oo .57 .oo
UK
USA
.oo .31 .48 .oo
.oo .oo .oo .oo
.oo .oo
.oo .oo .09 .64
.25 .08 .03 .oo .oo .97 .53
Entries are marginal significance level of t-statistics of hypothesis 03 = 0 in regression et - ft - cyq = Olezp(X1ft) + &esp(Xzf,) + @,f,
+ UJt.
.oo .oo .oo .96 .oo
1 also prr3rilts
‘I’able
two spC,cificat ioir tests
(the
restrict,iou
OO = 0 was
rq~~rt~c~l in ‘Tahlr, I ). First, the marginal O-test, to txaminc t,he serial correlation
imposed for the analysis level from a standard
significance properties
of t,he residual from ( 17) is ta hulat~cd; a low number indicates statistically significant a.utocorrc~latiorl. S~ond, the nlargirial significance level of a t-test of the hypothesis (3, = O is also prvscnt 4. also another indicat ioll of IIIO~CI failllrf‘. The
result,s
is almost
I illdicatc
of l’ablc
that
R
t JIG joint
of t,his hypot.hclsis
hypothesis
O1 = 0,
is
= 0
alwa.ys
reject rd a.t conventional significance levels. This result, is quite strong; rejections occur for n~ost c-orlnt ries and most EMS regimes. The existence of nonlinearit ivs of t,hv type implkl by targbzonc models seems, at, first blush. to hf% ov~rwllrlrrli~lg~~ sllpported. WC have also cxaminrd a numbfar of pf73urhat~ions of 1hc ha.sic rfpssion framework including: set ting o = I: and a lil~~t-cliff’c~l.c~l~c.c~cI v(‘rsioll of the test. Neither perturbation changes t,lie basic i~slili~ of l‘al)lf~ I .l‘hc rcjcction of 0, = (!I2 = 0 is also t 0: 1iw ol‘ 0 = .O.T:(.11oicf\ of :I(Ltla!, (as opposed t 0 ‘L-day int crf3t rates); the f>xact sailil)lr~ ~~riotl (\vv t ricd c>scluding hot 11 (a) 011ly ttic day antI (I)) t lie wliok niont Ir 1~(~1;1rvarrtl al’1 (‘I’ imlipniiif~ilt s); aild day-of-t hc-wcf,k f+ fects (wfx cstimatcY1 ( IT) for ))ot II ICriclaJ2i antI non-Fritlays, wpara,tcly). This wjf~rt~ion also diarac_tf~ri/,c3 a11 1II<>cilrrfwcif~s in t,llf, l3rd ton \Voods and golfl-
insf7isil.iw
st.alldard
rcgiilws
sl.rongly sampI
wjfdf~tl: nonliiif3rii
of tisc~l
ratc5.
l‘lrc IIypot Jichis
\vf’ (~oli(~lu~lt~ 1 jl;rt 1Ircx finfliiig iw
it) t II<, c.oticlit iolial
iiic’iiils
C-1, =
(32 =
of st atist,ically
of c~sf.haligc~
0 is risiiall> signifif-arlt
rak
iii-
is clilitf’
roblIst. I’hc signs iii t Ilf, thcorfd targf+milc~
time,
of Gl ailcl (3L a13~ also tabrllntccl in Tahlf~ I. As dcinonstratcd ical swt ioil. t lir~- i~rf‘ f5pf‘f.t ml t 0 hc of oppositf’ sign ill most nmdf~1s (I)ot II cwflil)lf~ aritl iircrfdihlf~). ~Irotinfl a t,hirfl of t Ilc,
1hc signs
01’ hl
alr(l
(I)2 c~c~~~f~sponfl t 0 t,llosf> irriplicd
by targf+zoue
rnoclds.
IIowcvf~r. t hft st.iLt ist ical ~irotld (low llot wit.llst alltl flirt.hcr strut iny. ‘l’hfmt is st roilg cvidciicf~ of sf>vf7~‘ rf5itlllal alltf,c-ol.rclatic,ri (Ncwey-West covariancc cst,imat~ors lla\.f> LWII IIS~YI, I)(T~IIs~~ ot’ t llis a~lt~oc.orrf~lat.ion, rcsitlual ,IRCH is also apparent ). Only ill ;I f’t~w c‘ases cari oilf~ re.j_jcl the null hypotjlicsis of 110 a~lt~of~orrelat ion. t“rlrt lwri~iow. t Iif> 1110df~l sfmns to I,f% inisspccified in that, O. is oftc,ii sigliificant,lv diti’cv~ilt 1’ro111 zero. .Igaiil, tlif3c results arc rf>latiwly robust.. hlost import alit I>.. t hexIl!.l)ot Irf3is C-11 = O2 = 0 is uslrally rf~jcctfd for float.ing f~xcliarrgf~ ratfts 2s ~(~11 as fisf~l f~x(.llailgf~ rates, as is apparerlt froni ‘I’aI)lc, 1. ‘l’his iliflicatc5 t Irat OIII’ iloiilitlc~ar lcrms r~iiiy 11fx I)ic.king rip somf~ gcllf+c niissl)facificat ioli iii 0111‘ im~lf~l that is not part icrilar to tarp-zone rcgirilf~s. II
Summary Parametric
tests
for nonlinearities
one hand, nonlinearities
leave us with a mixed verdict.
of the type implied by target-zone
On the
models seem to
be statistically significant in-sample. The hypothesis that nonlinearities do not exist in conditional means of exchange rates can easily be rejected in a robust fashion. However, these nonlinearities arise in a model which is usually rejected on other statistical criteria. In any case, the economic meaning of these terms is far from clear. Although the signs of the coefficients correspond to target-zone nonlinearities, the fact that these nonlinear terms are often significant during regimes of floating rates seems to bolster the notion that the nonlinear terms do not represent t,arget-zone effects. To study this issue further, we now turn to a forecasting methodology. VIII.
Forecasting
with
linear
and
nonlinear
models
In this section of the paper, we compare the forecasting ability of linear exchange-rate models with models that have additional nonlinear terms implied by the target-zone litera.ture. We find that the presence of additional nonlinear terms does not produce better “ex post” forecasts than those of linear models. This result, combined with the in-sample analysis of the previous section mirrors the results of Diebold and Nason (1990). Our baseline forecasting experiment proceeds as follows. Consider a given country (say, Belgium) and a given EMS regime (say, the period before the first realignment, from March 1979 through September 1979). Using the first thirty observations, we estimate the drift term for fundamentals by regressing the first-difference of exchange-rate fundamentals on a constant. This provides us with estimates of g2 and 7. Given these estimates and our choice of cr, we can solve for i1 and i2; hence, we can generate the two nonlinear terms, e.r~(i1.f~) and esp(X2fi). A We then run two regressions: (1) (the linear model)
et = 7r7)+ 7rIft + 21:; and (2) (the non-linear model) e, = & + $lft + 42e~p(ilft) + &erp(i2ft) + ~1”“. We then generate forecast errors by substituting in the actual future values of the regressors to generate
a forecast;_ thus, the one-step
nonlinear
forecast
error is given by
%“” =: et+1 - [do + $lft+l + &e3-p(ilft+l) + dw~p(hft+~)l. We then add an observation to the initial set of (30) o b servations and repeat the procedure until we arrive at the week before the next EMS realignment. The functional form of our forecasting equakion is suggested by equation (6), but we allow Al and A2 to be time dependent free parameters, unconstrained (as always) by assumptions about zone size or credibility. The square roots of the mean squared forecast errors (RMSEs) from linear and nonlinear models (computed with cy = .l) are presented in a graphical format in Figure 13; this portrays the ratio of the linear to nonlinear RMSE
for the
six different
is little
evidence
EMS
or floating
RMSEs
countries
that
currencies.
are typically
and
nonlinear
thirteen
models
different
EMS
regimes.
There
for either t,he ratios of linear to nonlinear
provide
In particular,
superior
forecasts
around one; there is no evidence that they tend to vary
systematically over time. or that they tend t,o be larger for countries with credible reputations like the Netherlands. We have checked the sensitivit,y of these results extensively. Figure 14 is the analogue
to Figure
13 but with 0 set. t,o unity.4g
A number
of other
perturbations are contained in t,he working-paper version, including: analysis of mean avera.ge errors; rolling regression techniques; the imposition of r1 = & = 1; 20-step ahead forecasts. The finding that linear models seem to forecast EMS exchange rat.es as well a.s nonlinear models appears t,o be robust to our sensit.ivit,v chccks.SO~s’
Summary It is well-known that sophisticated exchange-rate models that appear to be satisfactory on the ba.sis of in-sample criteria often do not forecast out-ofsample data better than extremely naive alternati.ves.52 In this section, we have shown that non1inea.r models do not forecast bet,ter than simpler, linear models; this finding appea.rs to be robust. We have used three different techniques to examine the nature of the relationship between exchange rat,es and fundamentals; none has yielded compelling evidence of nonlinearity, at least of the sort implied by target-zone models. There arc three pot,ential reasons for this finding: (1) mismeasurement of cr; (2) violations of uncovered interest, parity; or (3) an invalid theoretical model. Two argumeIlt,s discredit, the first explanation: low point 4gChoosing mate
(Y to maximize
“Linear
and
nonlinear
Woods
data.
around
20% smaller
the %
For
“‘One can estimated
NL
the forecast.
error
ratios
represenk
yet another
way
RMSEs
the
t.o cst,i-
n.
1 VZ,f
iidN(0, $J(T -
produce
t,han
linear
=
l8.l
+
11;““.
a test
2).5/(
1 -
Assuming
of the
$2)
between
the
RMSE
“Meese forecast extend
and better
this
equal
nonlinear
models
produce
null
s where
~1 and
for
Bretton
RMSEs
that
are
models
t,hat
E( ~1, ~2) = 0 and
hypothesis 7’ is the
~12. Under
as Student’s t with T - 2 degrees null hypothesis of equal variances from
approximately
data,
rigorously t,est the hypot,hesis of equality of forecast linear and nonlinear forecast, errors U: and upL,
W),
correlation
models
t,he gold-standard
~111 = ~22 number
can
There
of errors
and
Such
this
standard
are also many
the
vector
be computed
the null hypothesis,
of freedom.
that
error variances. Denotc and define I)~,~ = u,” -
4) is the test tests
reject.ions,
(u;“, u;““)
from
estimated
statistic often
t(T
is
- 2) = sample
is distributed
do not
a$ might
reject
the
be expected
bar-chart,s. Rogoff than
finding
(1983)
a random
showed walk;
t,o nonparametric
t,hat, linear Diebold
and
t.erhniqurs.
structural Nason
(1990)
exchange-rate and
Meese
models and
Rose
do not (1991)
1.04762
6
8
10
12
Japan Comparisons
2
4
4
5 6
6
UK
5
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
6
4
5
6
7
2
4
5
USA
3
I arat
6
7
Netherlands
2
1 hrat
4
France
2
1 frat
by EMS Regime: Alpha=.1
3
4
Italy
3
I brat
2
2
Denmark
1 drat
Figure 13: Forecast Comparison of Target Zone Models
RMSE
01 Dniii 3 5 7 9 1113 2 4 6 8 10 12
I Jrat
Ireland
1 erat
Ratlo of Linear to Non-linear RMSEs from l-step ahead Forecasts Horizontal Line marks equality of linear and no+llnear RMSEs
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
?atlo ,+I 3r ;
ni L-lrear
1
2
Japan
4
6
Ireland :Pdt
1 rrat
873 !1 t 3 1 L 1 P e I erat
tc Non
8
8
Figure
10
10
,Ta r r\ s
14: Fortcast
12
12
Comparison
Italy
1 lrat
;&lark:
I firat
6
10
12
1 hrat
6
Netherlands
1 ; Cl?.7 “1
4
France
2
I frat
Forecasts 4MSEs
of Target Zone Models
8
ilnear HMSEs frorr l-steD ahead ?q,all:!: c+ jlnear- and no?-:;rear
8
10
12
estimates
of (Y (lower (Y estimates
lead to more linear relationships);
fact that many of our results are insensitive
and the
to choice of cr. The short time
horizon leads us to believe that any risk premium
(which would violate
un-
covered interest parity) would be too small t,o account for our results. We are, therefore, attracted to the conclusion that the theory is not useful in modelling the data. Nevertheless, to confirm our doubts we now use techniques that do not rely on our mea.sure of exchange-rate fundamentals.
IX.
Other
implications
of target-zone
models
The empirical work that we have pursued so far has depended on our measure of exchange-rate fundamentals. If this measure is flawed, our empirical work will also be faulty. For this reason, we now turn to tests of target-zones that do not depend on fundamentals. Target-zone models have a variety of implications that can be examined without a measured exchange-rate fundamental (Bertola and Caballero and Smith and Spencer (1990)), given a (1990b), Svensson (1990a,b,c,d), For instance, as noted in Section II, the specific process for interventions. interest differential in a credible target-zone is expected to be declining in the deviation of the exchange rate from its central parity; the exchange rate should spend most of its time near the boundaries; and exchange-rate volatility should be greatest in the middle of the band. In this section, we examine some of these other aspects of the data. Some of these implications are dependent on specific assumptions concerning the nature of the intervention Any test of these implications would also test these tenuous asprocess. sumptions. Therefore, we simply present the data and supply some guidance as to the predictions of various t,heories.
Exchange-rate
vola,tility
by band position
Figures 15 and 16 are scatter-plots of the absolute value of the daily change in the exchange rate a,gainst the deviation of the exchange rate from its central parity (in percentage
points).
For brevity, we continue
to present results for
Italy and the Netherlands only. The upper and lower exchange-rate bands are marked by vertical lines (at +/-2.25%); a nonparametric smoother is also provided. The graphs are intended to convey a sense of the relationship between the volatility of the exchange rate and its position inside the band. It is not easy to find a clear pattern in the smoothers, either by country or by EMS regime (credible or not). The relationship is occasionally U-shaped (as suggested by Bertola and Caballero (1990b)), but the smoother is just as likely to have an invert.ed Ushape (as implied by Krugman’s (1990) model). 49
Monotonic
or flat smoothers
The evidence of the EMS;
from other
results
Interest-rate Figures
rate
17 and
II, models
should
(1990)),
and Caballero no clear
Woods
exchange-rat,t,
Figures
much
norm
modality).
Despite
paper
Another
hold closely expected
54Svensson
(1900d)
different.ials
data,
we find
imply
interest-rate
also
is also
in Section
that
there
presented derives
widespread
56Algebraically, uncovered where: Etet+r_ is the exchange il(i;)
is the
away
any
return
risk
peaks
rates
appears
indicate
EMS
bi-
credibility.
of the histograms are again
in
conclusions.
credibility in Svensson
point
should
(1990a))
to derive
to graph
the tirne-
to testming the entire
term
we use 2-day
bet,ween
of excess
proposed
(which
parametric
model
11.
for the When
position
has been parity
test. is simply
is little
implications
evidence
interest
as shown
of differences
the
slopes
and
structure
of interest,-
30.day
interest,
of various
rate
maturities
of
smoot,hers. Ieptokurtosis,
although
the
model
pre-
the 0pposit.e int,erest, parity implies rate which is expected
on a domestic
premium,
The
differential:
and gold standard
in Section
target-zone.
pat,tern
II implies
Single
exchange of increasing
Woods
Svrnsson’s
different,ial/exchange-rate
55There
are again
data.54
paper.
in the pattern
uses llncovered
rates.“’
for a credible no clear
percept.ion
target.-zone
exchange
heteroskedasticity
rate
rates.
EMS
of a change
Svensson
negative result,s
53The
of conditional
there
in the
(e.g.,
of Bertola
test>’
in a credible
future
of excha.nge
“tc>st” of t.argc+zone
(199013).
However,
in i.he working
for ot,her
for t,hc Dretton
(nonstatistical)
by Svensson
function
the model
to the interest,-ra,te
and do not I~ad to diffrrent
“simplewt
Svenssonb
slope.
parity.
the interest-
by bnnd position
result,s
indications
over time . ” . Figures the working
arc again
the widespread
we also see no clear
declining rate:
of randomness)
ana.loglles
histograms
(t.hough
to that
interest-rate
imply that
deterministic
opposite
distributions
of 2-day
t,arget-zones
evidence
graphs
19 and 20 provide
to be the
sented
irn 1I I ies the
position
is similar
rate from its central
the exchange
and goltl-st,antla.rd
Exchange-mte
scatter-plot,s
of credible
a g ainst
graphed (and
rates
version.
of the exchange
be a nonlinear
(199Ob)
patterns
Bretton
comparable
the deviat.ion
in Section
differential
of fixed exchange
the figures.“”
by band position
18 provide
against
Krugman
regimes
throughout
are in the working-paper
differential
differentials As noted
arc also apparent
possibly
Elei+k at time
(foreign)
bond
with
a ttllbious
claim
at
.iO
T days
= et[(l + it)/(l + i;)]trls6”) t to prevail at time t+lc; and to mat,urity.
1his horizon.
This
assumes
-ID
c 0 A-
rc
51
series of expected exchange-rate
future exchange
rates and see whether they lie within the
bands.
Figure 21 provides time-series plots of the exchange rates expected as of time t to prevail one year in the future. Exchange-rate bands are also presented. With the exception of the Dutch exchange rate, exchange rates expected
to prevail in a year are often outside the bands for prolonged periods
of time,
even for the more recent:
further
inconsistency
credible
twelfth
between the predictions
EMS
regime.
of credible
This is a
target-zone
models
and the EMS data.
Summary Target-zone models have a number of implications that can be examined empirically without relying on a measure of exchange-rate fundamentals. In this section, we examined: int,erest-rate differentials; exchange-rate volatility; exchange-rate distributions; and expected future exchange rates. These auxiliary (albeit informal) t.est.s provide no support for models of credible target-zones and only weak support for models with rea.lignments such as Bertola and Caballero ( 1990h).5’ 37We data
have
conducted
we found
12 (using
that
data
across
the corresponding principle J
EMS
ratio
starting 1. These
regimes
model
replication,
point. of these
Our
and
without
the
olphcr
results
carried
our
values
between
to 12. and
were
generated
.1 and
out
for two
wit,lr and
without.
using
was
long
then
and
daily
generated
from
at a random
of (Y: .I and
which
added
set
the reflection
begins
values
beliefs, noise
actual
to c was around
1). We, therefore,
fdata
data
of invest,igat,or
Using
values
generated
exchange-rate
a grid
result,s.
fundamental
set is 200 observations
we investigat,ecl were
to check
of possible
drift;
data
simulat,ion
sett,ings,
simulations
experiments
of t,he range
in the simulat,ions
in a credible
In a typical
both
simulation
the ratio
range
1. For
from
to the true
.l to
exchange
rate. Regardless that
of the match
instrumental
differentials mates
and
cantly”
less
change
than
unity.
in the
“significant“ ratr
and
rates
(t,he linear
regressions
WC always for the
deviation
replicat.ions
per simulation.
of the mean
value
found opposit,e
generating coefficient
to thr
across 500 replications is grratcr than 2. Without added noise, the forecast.ing exercise vantage 1000.
to the Ratios
fundamental
nonlinear remained
innovations.
model. greater
Ratios than
one
However, disappear
st.andard
always
such
as those
llntil
the
had adding
(the
deviation
of that
to the ex-
was set equal
are based on 500 value of the ratio of such
indicated
a huge 20 were
in the
the
“signifi-
constants
noise
noise
esti-
that
coefficient,s
in Table
volatility
small
found
of the
(15))
interest
: f slope
an e
estimation
(equat,ion signs.
We also
deliver
found
lagged
in numerically
of zero. the
using
f). These in-sample results we mean that the absolute
By %ignificant”
of an est,imated
that rate
a, we always
text
resulted
errors
of t,hese coc‘flicients
to t,he noise
in the
of c on f)
exchange
of the appropriate
the significance
the investigator’s
as instruments,
t,wo standard
Also.
in standard
n and
of n, as proposed
well within
expression
makes
the true
estimation
exchange
were
regressions
integration were
lagged
of cy which
honeymoon
I)ct.ween
variable
noise
coefficient,s
forecasting never was
ad-
less than that
of the
I
_
h
55
-2 N
cc 0
-
I
L
co
X.
Summary
and
Using uncovered
conclusion
interest
parity in a framework
that implicitly
depends on a
flexible-price exchange-rate model, we derived a measure of exchange-rate With the aid of this measure of fundamentals, we tested fundamentals. target-zone models of exchange-rate behavior in a number of ways. Graphical examination of the relationship between exchange-rate levels and fundamentals did not yield strong evidence of economically meaningful and important nonlinearities, certainly not those implied by existing target-zone models. There is little clear evidence of an important “honeymoon effect.” Explicit in-sample parametric tests of the nonlinear terms implied by targetzone models yield the conclusion that nonlinearities are usually statistically significant; however, a number of aspects of these models work poorly inMore importantly, linear sample on both economic and statistical grounds. models forecast out-of-sample data just as well as models with additional non-linear terms. Finally, a number of additional implications of targetzone models that do not depend on our measure of fundamentals have been tested and found not t,o he in accord with the data. For instance, there does not appear to be any particular relationship between exchange-rate and interest-rate volatility, and expected future exchange rates often fall outside the EMS bands. Moreover, few of the relationships between the exchange rate and (a) interest-rate different,ials, (b) exchange-rate volatility, and (c) Sucexchange-rate distributions seem to be in accord with existing theories. cinctly, we have been unable to provide a cha.racterization behavior during managed exchange-rate regimes.
of exchange-rate
We conclude that, at an empirical level, there is little advantage apparent in working with nonlinear, rather than linear, models of exchange-rate conditional mea.ns. This result is exactly analogous to the conclusions of Meese and Rose (1991) for flexible exchange-rate regimes. Our results also imply that there is little empirical support, for existing target-zone models of exchange rates. The models that we have dealt with in this paper have a number of restricFor instance, our model incorporates only a. single-state varitive features. able (thereby
ignoring st,icky prices and certain
Our simulations indicate unconditional
counterpart
that
the sample
types of devaluation
distribution
if 200 observations
of the exchange
rate
risk).58
resembles
its
are available.
‘“There is little reason to believe that either sticky prices or devaluation risk can easily reconcile target-zone models with the data. The lack of interest-rate differential variability for floating-rate shocks Further, and
from the
we find
countries goods Dutch it hard
implies
that
a model
with
markets;
however,
it is difficult
Guilder
has been
firmly
to believe
that
fixed
devaluation
sticky
to the
risk could
59
prices
to reconcile
this
must feature
Deutsche
Mark
account
for our
rely
heavily
with since
the early
negative
on data. 1983,
results.
We expect plaining
future
research
our negative
to identify
results.
the importance
of these
factors
in ex.
L.&e%
. “.,
i
t
ar
1 ar ,z!a
1
m
,I ar P
WQ
ar
ar
I
’
ar
61
“EL:. i
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192-196. of Non-
of Economic
I: Origins
and
Press).
Statistics
for
Great
Britain,
Ger-
Officer, L.H., (1986). The Effi ciency of the Dollar-Sterling 1890-1908, jJourna1 of Political Economy, 94: 1038-1073. Pesenti, P., (1990). Yale University.
P er f orate
Perron,
T ren d s and
P., (1988).
ries, Journal
of Economic
a.nd Imperforate
R.andom
Dynamics
Pessach, S. and Razin, A., (1990). pirical Investigation, IMF Working Smith, Return
Exchange
Walks
Rate Bands.
in Macroeconomic
& Control, Targeting Paper.
Gold
12-2/S:
Spencer, Monetary
the Exchange
Switching
and the
Testing Mimeo.
in ModQueen’s
in the European
the Dollar-Sterling 96: 882-892.
Svensson, L., (1990a). Th e F oreign Exchange Risk Premium with Devaluation Risk. Mimeo. Stockholm University L., (1990b). University.
The Simplest
Svensson, Stockholm
L., (199Oc). University.
Svensson, L., (1990d). a Target-zone. Mimeo. Tufte,
E.R.,
Graphics
(1983).
Press).
Target-zones
The Term Stockholm
Test of Target-zone
and
Interest
Rate
Structure of Interest University.
The Visual Display
of Q uantitative
Se-
An Em-
(1990). Estimation and and Process Switching.
Spiller, P.T. and Wood, R.O., (19S8). Arbitrage during Gold Standard, 1899-1908, Journal of Political Economy,
Stockholm
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Rate Dynamics M.G., (1990). N ominal Exchange System. Mimeo. International Monetary Fund.
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Smith, G.W. and Spencer? M.G., els of Exchange-R&e Target-zones University.
Standard,
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Credibility.
Mimeo.
Variability.
Mimeo.
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Information,
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(Cheshire,
Conference Series on Public Policy 35 (1991) 7-66
An empirical
exploration
of exchange-rate
target-zones
Rob,ert P: Flood &&rn’ht%‘on~~ ‘konetary
Fund
Andrew K. Rose University
of California,
Berkeley
and Donald
J . Mathieson”
International
Monetary
Fund
Abstract In the sumption determinant
context
of a flexible-price
of uncovered of exchange
interest
parity,
rates.
Daily
monetary
exchange-rate
we obtain data
model
a measure
for the
European
and
the
as-
of the fundamental Monetary
System
*The authors are, respectively: Senior Economist, Research Department, IMF; Assistant Profess0 i School of Business Administration, University of California at Berkeley; and Chief of 9 inancial Studies, Research Department, IMF. Rose thanks the International Finance Division of the Board of Governors of t,he Federal Reserve System and the Center for Research and Management at Berkeley for financial support. For comments we thank: Willem Buiter; Ricardo Caballero; Harold Cole; Susan Collins; Frank Diebold; Hali Edison; Martin Eichenbaum; Joe Gagnon; Peter Garber; Dale Henderson; Alexandra Jones; Karen Lewis; Ben McCallum; Allan Graciela Kaminsky; Eric Leeper; Leo Leiderman; Meltzer; Dick Meese; Dan Sichel; Chris Sims; Gregor Smith; Ken West; seminar participants at Ohio State and Yale Universities; workshop participants at the IMF and the Federal Reserve Board; and participants at the Carnegie-Rochester, CMSG, MSG, and NBER exchange rate conferences. Steve Phillips provided stalwart research assistance; Kellet Hannah and Hong-An11 Tran assisted with the data. We thank Lars Svensson for continuing discussions and encouragement, as well as uncovering an important error in an earlier draft. This is a condensed version of a working paper wit,h the same title, issued as IFDP 388 and NBER WP3543. The views expressed in this paper are those of the authors and do not necessarily represent t,hose of the IMF or the Federal Reserve System. 0167-2231/91/$03.50
0 1991 - Elsevier Science Publishers
B.V.
All rights reserved
are used exchange are also
to explore rates
and
considered.
the
importance
fundamentals;
of nonlinearities data
from
three
Many implications of existing
in the other
relationship
between
exchange-rate
systems
“target-zone”
exchange-rate
models are tested; little support is found for existing nonlinear models of limited exchange-rate
flexibility.
I. Introduction In this paper,
we characterize
the behavior
of nominal
exchange
rates dur-
ing managed exchange-rate regimes. When exchange-rate management takes the form of an exchange rate “target-zone,” enforcement of the zone sets up expectations that alter the relationship between the exchange rate and its fundamental determinants. Such effects are the focus of a theoretical literature concerned with exchange rate “target-zones.” We assess the empirical importance of these nonlinearities, focusing on the six long-term participants in the Exchange R.ate Mechanism (ERM) of the European Monetary System (EMS). There are two motives for this paper. First, a comprehensive description of exchange-rate behavior during managed floats is potentially of great value in comparing the merits of alt,ernative exchange-rate regimes. Second, this paper is a contribution to the sparse empirical literature on exchange-rate target-zone models. By implicitly using a. flexible-price monetary exchange-rate model and the assumption of uncovered interest parity, we are able to obtain a daily measure of the funda.mental exchange-rate determinant. With this variable, we search directly for a nonlinear relationship between the exchange rate and fundamentals. We use three different modes of analysis: graphical study; parametric testing for non1inea.r terms; and out-of-sample forecast analysis. We also test) five implications of target-zone models that do not rely on our measure of fundamentals. Our EMS findings are corroborated by data drawn from three regimes of limited exchange rate Aexibility: the post-WWII Bretton Woods era; and the inter-war and pre-WWI gold standards. Our findings are mixed. Our graphical tionship between the excha.nge-rate and it,s different” in an exchange rate target-zone change rates. However, the exchange-ra.te not resemble
that suggested
by current
analysis suggests that the relafunda,mental determinant “looks tha.n it is in freely floating exfundamentals relationship does
theories.
Our pa,rametric
testing
for
nonlinear terms usually indicates that a model that fails to account for the effects of the target-zone is misspecified; nonlinear terms are statistically significant determinants of t,hc exchange rate, although the sign pattern of the estimated coefficients is usually inconsistent with theoretical predictions. However, these effects are also nppa.rent for floating rates. 8
More importantly,
nonlinearities
do not help to predict exchange
when we examine measure
implications
of fundamentals,
of target-zones
rates out of sample. that
Finally,
do not depend on our
we find little evidence of target-zones.
Our mixed findings make us cautious in our conclusions. Our graphical analysis suggests to us that fixed exchange rates behave at least somewhat differently than freely floating exchange rates; this seems unsurprising. However, our more intensive target-zone
models.
study of the data reveals little support for existing
We think our results are not surprising.
Our more inten-
sive statistical work is often quite model dependent. The auxiliary assumptions required to derive close&form solutions for models in this literature seem to be poor assumptions that do not much aid our understanding of the data. We conclude that models of limited exchange-rate flexibility work about as poorly as do models of flexible exchange rates. In the next section of the paper, the relevant theory and our empirical strategy are outlined; Section III provides a brief survey of the existing literature, while a descript,ion of the data is contained in the following section. Section V provides a discussion of how we determine o, a parameter that is important in our model because it is required to identify exchange-rate fundamentals. Our analysis of nonlinearities in conditional means of exchange rates is contained in the next four sections, which constitute the core of the paper. Section VI provides graphical analysis of the relationship between the exchange rate and fundamentals. Parametric tests for target-zone nonlinearities are reported in t,he following section; the forecasting abilities of linear and nonlinear models are compared in Section VIII. Various auxiliary implications of target-zone models t,ha.t do not rely on measurements of fundamentals are analyzed in Section IX. A brief summary and concluding remarks are contained in Section ><.
II. Theory In this section,
we present a. simple model of exchange-rate
target-zones.
We
then use this model to derive distributional implicat,ions for the exchange rate and fundamentals. Finally. we out line our approach to measuring exchangerate fundamentals.
The model The model we use in our study is standard in the target-zone literature (e.g., Krugman (1990), and Froot and Obst,feld (19S9a)). In the model, the natural logarithm of the spot, exchange rate, et, (measured as the domestic currency price of a unit of foreign exchange), is equal tjo a scalar measure of exchange9
rate fundamentals, of change
of the exchange
In the typical that
ft, plus an opport,unity
enter
of cquat ~OII (I ). jc is a linear
market,
of money
demand;
pectation
operator,
Et,
the nature
ing” relevant in the
WC follow
is based
switch,
governing
for exalnplf,,
exchange
market
fin
to protect
order
process.
uiiglit
irl\ml\.f>
lx~lic.!.
to specific
a11 c~sclla~lp-ratc~
in rat,ioilal
f~xpf~ctatiolis is H f’llll(.tio11
additional
that
t IIC~ I’IIIIC~ iota hf> iI twicf,
of thfl
t hc currf~til,
The
precise
process
sta.tv.
form
switches.
of obscrvatioIl, In the
\2:f, co~lsiflf7~
Hencefort~lI.
atwcncf~ of’ airy
where 11 is the drift rate, During
‘A typical simple
procc3s
type
of process
benign
to alkr
neglf~t
the cours(b of that
ttic> SOIW
variable,
wit,h thrb
cont.inuousl~
I)olic.ies aii(l forcing
diffcrent,iablc procfw,f3
wtifxrf‘
on t 11f, nature
of conttmplat
\vf’ will 1ls~~all.v drop the not,atiorl
t)rocfw
s\\-it f,trfx,
f’llnfianwi~tiils
follo\v:
r/f//+ ntl:
(:I!
cT is il posit ivfx coilst ant, and & is a standard s\yitf-hf3.
flrxibl+t)rict~
changes
t IIc ,f t)rowss
IIWII~~~~I~~IIIO~ICI consists
(m - p = &j ~ rri + 5); ~IIP tlrfinit~ion
c,schange
rate.
and an asterisk
Weinri
to anot her procf5s
of: a domestic
money-demand
dc~~otr~ forclgrl
of
variahtes.
and interest, rates leads to ( 1). where t Ile fundamcnt~als 11 denotes velocity. given by L’~ = -@I?/~ + C,~ - p; (1989a)
or Svensson
interest-parity our
analysis
(199Oc).
ecpat.ion;
this
ml
for t,hc t,imcL
t lw wat cxctiange rate (q = E + and uncovered intcrcs( i)ari(y (i - i’ = I:(t/c )/dt); whr-rc 17~ is the tog of thr money p denotes the tog of t,he price level, y ctc~~ot IV, 1hr tog of real income, t dcllotcs the interest rat,f,, E is a shock t,o t lr~, doliml.ic money-demand equation, 4 denotes
equation
uf
for c~znt~~pl~~. f = .q(I. f).
f!/‘ :=
process.
from
t II~’ stat (‘:
of t 11c 9 1’1111clif>11 dqx~~ds
I, writing.
swit.cb
we mean changes
of t11c>relc\-ant state
oIII>.
\;aluv ot’ f’s\ltni71arizf3
cx-
latter
of the model,
wf‘ coIijecl,urc~
iiiotlcls.
rate
frltlctiou
t. The
‘~proccss
One
iutervent,ioIls
senii-
The
ZOII~‘.
t.ion for the exchange condit,ion
time
switching”
swit.ch
rate
here.’
and any
(1983).
of variables
intkrcst
jt, a.nd the structure
Garbcr
a
is the through
condition
and
function
interpret,ation
By “process
f; Flood
fundamentals
As is typical
variable.
of 1,11(xc~quilihriurll
to the forcing
process
0
that.
OII information
values of the only forcing
including
while
quilihrium.
elasticity includes
to the rate
rate cxxpectc~t at- I. Et(de)/dt:
derivation
money
cost, term proportional
(krtaitl
types
is discussctt
to n~ottr~ts wil Ii sticky
prjc(5.
Etirnination are defined
zt). of risk prcmia
furthrr
I)etow.
of cndogenous
y’ - p): supply. r~on~inal the
real
priers
az !I = m( + ~1~(whcrc
See, e.g., Froot and Ohst,fctd can be added to t.hr uncovcml
In fret urc work,
we plan
to ext.cn(l
dictated
by the particular
policy switch.2
Using our trial solution from (2) and invoking Ito’s lemma: E(de)ldt Substituting
from equation
= qg’(f)
(4)
+ (g”/2)g”(f)
(4) into equation
(l),
we
obtain:
s(f) = f + VS’(f) + w2/wv) Equation
(5) is a second order linear
differential
(5)
equation,
which has the
general solution.3 g(f)
= f +
07
Alezp(X1.f)
+
+
A2edhf)
(6)
where x1 = -(?]/a)
+ (l/a2)J_
x2
-
=
-(71/u)
(7)
(l/c”)+l’
+
pa’/(Y)
(8)
The integration constants Al a.nd A;! are determined by process-switching side conditions. Different side conditions result in different settings for the constants. Indeed, during periods of policy volatility, agents’ settings for the As should shift with policy perceptions. Three patterns for the setting of the constants have emerged in the literature. First, if agents pay no attention t,o the policy side conditions, then (ruling out bubbles) Al = A2 = 0.” S econdly, if the target-zone is credible, agents must anticipate that the authorities will stop the drift of fundamentals out of the zone when funcla.mcnt.als a.nd the exchange rate reach the boundaries of the target-zone. Consequently, credible target-zones give rise to “sure thing” bets about fundamentals
at the boundaries.
In order to keep
such bets about fundamentals from being translated into profit opportunities, agents require “smooth-pasting” conditions at the boundaries. These smooth-pasting conditions ensure tha.t the exchange rate will not change in response to anticipated
infinitesimal
int,ervention
at the boundaries.
Smooth
pasting requires Al < 0 and A2 > 0. This result is true for all credible zones, with or without intramarginal interventions. Thirdly, the target-zone may 2Pesenti exchange 3Tlle
Alezp(Alf) similar
allows solution
+ A+rp(A2f).
t,he drift. rate
to vary so as to induce
is f + on, Lewis
(1990)
while the d evelops
mean
reversion
in the
solution of the homogenous part is a different model with qualitatively
properties.
4Froot market;
(1990)
rate. particular
and Obstfeld see also Flood
(1989b)
provide
and Hodrick
a discussion
(1989). 11
of bubbles
in the context
of the stock
are unconstrained until not have full credibility. In t.tlis case, the constants alternative policies are specified; see, e.g., Bertola and Caballero (1990b). Most, of our empirical
work relies
ncit her an explicit
on
model
of interven-
tion nor target-zone boundaries that coincide with the declared boundaries. When we nlake use of t tit, s~wcific functional form suggested in equation 6. anr \ AZ to 1~ free parameters. In much of our work, we always allow ill we do not Thus,
even
coIlstrain
els based
on regulated
1 is a graph interventions zone.’
The model ohscrvablcs.
the rc~ducc+form
equation
work is tlirc,c-ted at the general
our empirical
I3rownian
motion
of the exchange
class of target-zone
for a single
of t.htl exchallgf, rate against, fundamentals at cretliblc exchange-rate bands are used
state
variable.
rat,e. mod-
Figure
when infinitesimal to defend the target
prc~scntctl ~II ccluat iolr ( I ) bears only a limit.cd White t hrt cschangc, rat P is ohscrvahlc almost
direct relat,ion to continuously, the
model offers little guidance on how to observe the triplet ft, CY,&(de)/dt.” We note, however. t#hat if w(‘ (-orlId observe any two mpmhers of the triplet, Our empirical t,hen, by using equation ( I), wc would have t,he third member. strategy entails obt,a.ining ~ncasur~s of o a.nd E,(de)/df and deducing a measure for exchange-rate fundamentals. Ji. ‘l’his approach obviously precludes tests of equation (I ). since thr latter is 11set1 to construct measured fundaOur st,rat.rgy rlocs. howrver, allow IIS t.o construct and compare’ mentals. reduced-form
tquat.ions
It, is relatively Sect,ion
V. Assurniikg
based
on c~q~~ation ( 1 ).
cas>’ to ol)sc,rvc, E,( dc)/dt; covc~rc~l iii1 crvst
parit.y
we defer discussion for cant t-acts of length
of 0 to h:
where: il,h is t,he interest rat<, at titnc, f (x1 domestic funds borrowed for a period of 1engt.h h; i;,h is I hrt col,rt,sl”‘rlc_lillg foreign int.ercst rate; FRt,h is the forward exchange ra.te quot~ctl at t i~nr, t for delivery at f + h.; and E& is the tevel of the spot exchange rate at t,irncx f. The rcalationship between the forward rate and the c~xp~ctrtf f1itlii.c spot rat<> is given by:
6
4 EXCHANGE RATE
2
(e)
reduced form
0 -2
----------
-4 -6
l
-6
1
0 FUNDAMENTALS
Figure 1: Credible
13
Target-zone
5 (f)
where RP,,h is the risk premium at time t for cont,ract,s of length h. If agents the foreign-exchange market IllaxirnizrL t,hca cxpccta.tion of an int,erternporallj separable
utility
funct,iolr.
tjher~:
RPt,h = [C’()l’t(l”(C’t+,~)/Pt+/~. ER,+h)]/[E,(lr’(C,+h)/p~+h] where:
Covt( ., .) denotes
in
t,he c-ovariance
opera.tor
conditional
ut ilit,y of consumption at time t; l.J’(Ct+h ) is 1.h(, nlargillal Pt+h is the price level at time t + h.
(11)
informa.tion
on
at, t,ime t + h; and First. utilit,y
We intend to ignore risk prcmia, in this study for two reasons. Svensson (1990a) ha.s shown that for constant relative risk-aversion
functions, the risk prenlium in a credible target-zone (with potentially moderate devaluation risk) is small. Second. in the empirical part of this study, we rely on daily observations of t,wo-day interest, rates. Regardless of the functiona,l form of the period llt ility funct,ion, the risk premium rmlxdtld in such short contra.cty is liI<(~l>~to I)(, nc~gligiblc, compa.rcd with the rxpect,etl rate of change of the cscl~angt~ rat(x.‘*” Once risk premia hal-t, ht~cn asslImed (IO) to yield: I:‘,( iii?,+,,
risk prrrtlium
in two-(lay
between
I”(Ct+h)/Pt+h
an(l
between
two variables
it, hard over In
t,o believe
the
our
course
view,
at, least rat,e
that.
both
risk
of the further
days
and
rat(’
prenlium
exchange
rati,.
al)nut
go
woultl Ovc,r
;rssulllillg
hotll
can
be rspected
surprises compared the
risk
to wro over short go to zero
longc,r away
fast,er
cont.ract
over wit,h prc,miurll
horizons, than
periods,
risk prernia.
conditional
Engel
would such
t,wo
covariancc covariancc
in the two magnitudes.
plans
ark sticky while
applying
‘I’he conditional
of surprises
pricing
Thr-r+,forf>,
and
bc dutx to two-day
t,o r~~atcl~ eschangr-rate
horizorl
less complacent
provide
consulnptiorl
of t.htx c,xchangc,
consumption-based much
would
WIIP~C h is two-days.
pricc>s a11d corlslllllplio11
at. till, ‘L-day
of change
cottt racts
is tllf\ (>xpcac.t(>d I)roduc(.
of two
of change
(1’)
= (I + it,,,)/( 1 + l;,J
)/I:/<,
I:‘/<,+,,
(!I) antI
quat.ions
logarit hrns of c,ach sitlc of this cquat,ion. we arrive at.:”
Taking natural . . approximations, ‘The
away. we combine
We find
to change t,he same the and
exchange, the
we think the
nluch
t.wrrdays. rate-,
rxpect~~tl t.hat
expected
as a nlont,h,
(1990) and Hodrick
t,ht, rattt
WP are (1987)
analysis
“Bertola and Svr~~sson ( I UUU):I\ low that t IIC~implied two-day forward raLe. ( I + should tw a biased predictor of ER,+,, in our &+h)E’n,/(l + i;+h) w t Lere h=two-days, dat)a samples (which arc between EMS realignmrnt,s). Standard tests of unbiasedness on our EMS data do in f;lct rcljcct tlrts 11u11 hypothesis of unbias4ness. This is a standard finding
for floating
“The
rates
approximat.ions
(Hodrick arc:
In(
( 11)X7),Drool, and Thalrr (1990)). 1 + i) - 1n(l + i*) z i - i’ and In(EtERt+~/ERt)
(&et+,, -et). The second approxirnxtion logarithm is a nonlinear opcralor, which using only t,weday forrlcasts. otlr r’rror this
assertion
exchange We found
rate that
by sirnulat.ing
t,llr> aI)pi-oxl~ilat
wit11 1.11~ zonk
bountlarieh
thcx av~ragc’
z
is lnuch the more worrisome of the two since thr irrducrs Jcnsr~n’s inquality problems. Since WC artof approximation may h(x small. WP investigated 2.25
ion rrror percent
;rl~sc~l~~lr~;il,l,rosiirl;rt,iorl
for
a credible
around f’rror
central is abolit,
t.arget-zone parity
and
on
t.hcl
o =
I. lr(, of t.hr> avrragc
1
Etet+h - et = it
h
i$,
-
(13)
When we study flexible exchange rates below, we find that our exchangerate model works well, despite our assumption of uncovered interest parity. We observe interest rates on contracts with a two-day maturity; by equation (13), that is equivalent of the exchange exchange
rate.
to observing
We treat
the two-day expected
the two-day expected
rate as the instantaneous
expected
rate of change
rate of change of the
rate of change of the exchange
rate. Succinctly, we measure exchange-rate fundamentals as fi G e, -cr(i -i*)t. Even assuming that uncovered interest parity holds, this measure will not be literally correct as long as cy is unknown; we use sensitivity analysis to account for uncertainty about cr. Also, this measure does not directly link exchange rates to “raw” fundamentals such as money and output. Nevertheless, for reasonable choices of CI, all interesting moments of the f distribution will closely match moments of t,he e distribution in the sampZe. Given the poor performance of exchange-rate models that use raw fundamentals, compelling argument for 0111‘measure of fundamentals.‘0 III. Previous
this is a
findings
Most previous empirical examinations of nonlinearities in exchange-rate behavior have focused on non-linearities that affect even moments of the exchange rate process, often the conditional variance of the exchange rate. For instance, it is known that excha.nge rates manifest substantial leptokurtosis; conditional forecast varia.nces of exchange rates also exhibit serial dependence (Meese and Rose (1991) p rovide references). However, relatively little empirical work has been done to link mentals in an intrinsically nonlinear to be no theoretical reason to pursue (1990) and Smith and Smith (1990) side conditions
imply deviations
the level of the exchange rate to fundafashion. Until recently, there appeared such avenues. The papers by Krugman p resented exchange-rate models where
from the linear exchange-rate
solution.
There is another, more important, explanation for the dearth of nonlinear empirical work on conditional means of exchange rates. Empirical work on exchange-rate determination has been dampened by the negative results of absolute expected rate of change of the exchange rat,e. We are also assuming tions costs.
away any measurement
So long as bid-ask
spreads
error which may be the result of transac-
are small in relation
to interest
differentials,
this
error is likely to be very small. “Our
methodology
fundamentals answer Obstfeld
can,
are difficult
the question
we think,
be extended
to measure,
of interest.
fruitfully
to other
so long as reduced-form
One example
(1989b).
15
is the existence
environments
estimates of bubbles;
where
allow one to Froot
and
Meese and Rogoff (1983). 11ww and Rogoff demonstrated equipped wit,h a. variety of linear structural exchange-rat,e ex post
knowledge
to forecast
more
of the, dr~terlrlinants accurat.c,ly
than
a naive
noted that ta.rget-zone modt~ls require set of fundamentals to which a(ltlitiollal presence
of a ta,rgct-zone;
at the very least,
of such random
models
that models would
walk model.
and a.ct,ual not
he abk
It should
bet
a strrlctnral linear model (that is, a nonlinear terms are tacked on in tllc>
see cqliat ion (6)) . so that. target-zone
all t,he problcnls
a forecaster
of fioating
excha.nge-rate
models
have,
models.
Only a small amount of rf,lt>vanl. clnpiricat research has been conduct~ed to date. Almost without, cxcept~ion, econon1ist.s have t,aken heed of t.he negative result,s of Meese and Rogoff and abstained from posit.ing explicit parametric much of t.hc work present,4 below is models of fundament.a.ls (in contrast,. techniques and find parametric). Meese and ROW ( 1990) use nonparametric little evidence that nonlinear models fit exchange-rat,e data hct)ter t.ha.n linear models during fixed eschangc>-rat c periods. I)icbold and Xason (19YO) and Meese and Rose (1991 ) find c~olllpa.rablc rcslllt,s hot 11 in-sample and out-ofsample during float,ing eschangc~-rat<, rcgirnc’s. using Itrrivariat e and mult ivari(1990) usfl 1.hf, ate data, rcspectivel!,. S~WIICY~I‘ ( IWO) RII~ Smit.ti and Spmcf,r method of simulated momcl~t s to a\.oitl positing an explicit) empirical model of funda.menI.als ill n~octc~ling t
rat,<,.
IV. Description
of the data
The major focus of this paper is the F:1IS regime of fixed. but adjustable, exchange ra.tes. We concctntratc on t trc, ICiLlS both for its intrinsic and current. interest, and for easy comparisorl with the lit,erature. Relevant fcnt,ures of the institutional structure of the E3,IS a.re described in Folkerts-1,anda.u and (1989). Mathieson (1989) and C:ia.vazzi and Giovannini Our EMS da.ta were obtained from t.he RIS. We also use non-EMS countries. and for I’MS collntries during the period ERM.” The da.ta are daily; exchange rates arc recorded at the fixing” while int,erest rat,es arc arlnualizctl simple bid rates at,
I fi
RIS data for preceding the da.ily “official 10 a.m. Swiss
time.‘2~‘3~‘4 We focus on 2-day interest rates (which will be taken to be “the we use l-month and 12rate,” unless explicit,ly noted otherwise);
interest month
rates
t,o check our results.
Two-day
interest
rates
have been used
because they are the shortest available interest rates (they also reflect the yield on a deposit that has the same maturity as the two-day settlement period in foreign-exchange markets). l5 The interest rates are Euro-market rates and should be relatively free of political, credit, settlement and liquidity risk premia, at least for interest-rate differentials across different currencies at the same maturity. I6 Two-day
interest
rates are unavailable
for Denmark
and Ireland until February 1982 and November 1981, respectively.17 data have been checked for errors in a number of ways.” “The
rates
are averages
13Belgium
has
used
for current
EMS
rules
account
market; rate
14We treat,
each
daily
or holiday that
analysis
financial
not
The and
observat,ion time
effectively
We use
central
rate
floats
and
ignoring
any
stops
on the time-series
our
cannot
parametric
results
are never
“The that
work
risk
with
premia
different
interest
rates
political
risk
this
problem.
they
could
even
Italy. Giavazzi The longer risk,
and
liquidity
17Japanese ‘sin
and Giovannini version of this
by computing
of our
excessively dummies do differentials
from
In some
other
of
data;
our
markets domestic
reflects
payments
the
fact
systems
in
which
issues
of the
the yields
of funds
the
once
it should
the differentials currencies
matures.
be relatively
unchanged
also
during
as well as between Moreover,
this
help
a particular
domestic
wedge
for countries
discussion. (1989) p rovide further paper contains discussions of credit
risk,
free of
to alleviate
demonstrated
markets,
uniform
Euro-currency
be relatively
should
on instruments
eased
deposit
between
should
Euro-markets
de-
it is physically
this period, political risk the extent of the political
currency.
progressively
Eurc+currency
in which
deposit,
Thus,
the
of the country
period, in different
and
offshore
may
vary
over
time
such
as France
and
settlement
failure
premia.
short-t.erm
particular,
been
As much
levels.
data
day-
implicitly
we are not
significance Friday
our
of, e.g.,
we are
t.hat. day-of-the-week levels and interest-rate
in the
the bank
were relatively
in the same have
place
several
in t,he Euro-currency controls
take
in different
across bet,ween
also checked
weekends.
is
division.
on the transfer
m&u&y
controls
a wedge
and
which
to following
account
of the data,
capital controls throughout study of the EMS. While
denominated
capital
no special
in foreign-exchange
that
of denomination.
Sampling
denominated capital
the
affected.
deformation,”
out
by the government
or taxes
with
on deposits premia. If such
instruments because
vary
currencies
rate,
in the t,ransaction.
the possibilit,y
restrictions
introduce
currencies,
are involved
Italy have maintained are important in any
might
across
must,
be confronted
new
As France and considerations risk
reflects
by this period
of funds
currencies
may suddenly
located
affected
We have
at, conventional
also separated
set.tlement.
transfer
whose
“Political posit
tweday
ultimate
countries
be rejected we have
substantially
typical
the
generally below,
freely.
on holidays
worried about this assumpt,ion. Furt,her, the hypot.hesis not enter significantly into regressions of exchange-rate on a constant
official
is committed
are not
take
“time
properties
the
bank
our conclusions
identically,
By
depend
markets. Belgian
the financial
data,
effects.
economic
does
Euro-markets.
exchange
t,ransactions.
with
of-the-week
several
of dual
for the official
key results
assuming
across
a system
The
interest
we checked descriptive
rates
for outliers
st,atistics
are also unavailable from
and examining
both
levels
until and
early
1982.
log-differences
t.he datagraphically.
Some
of the series 150 apparent
IJnless rates;
otherwise
for interest,
noted, rates,
plus the int,erest
rate
work.
is trcatfld
Germany
are always differentia.ls
tli~ Dhl
pricf,
use natural
always
as t Ire “home” of 011c unit
of colllparison.
of exchange
logarithm
of one
by 100.” In our EMS so that exchange rates
divided
country,
of foreign
C~erniai~ intf~rf3l
logarithms
11se the natural
p0int.s).
(in percentagf‘
are always
For the purposes
we always
wft almost.
exchange,
ratf,s minus
and
foreign
interest-rate
interest.
WP also 11s~ data for the period
change rates t,hat preva~ilcd drlring the classical gold standard. rat,e dat,a arp taken frown Andrew ( 1910). who tabulates data
rat,es.2”
of fixed cx-
Our exchangeon weekly nom-
inal exchange rates of the 1I.S. vis-i\-vis the I1.K.. France, a.nd Germany for The rat,es are the a.vcrage of weekly t,hc National hlonet,ary (‘orrlrrlission. int,erhighs and lows. licmmcrt~r ( I!) IO) Jprovides weekly data on American est, rates. also gatherf~d for t hc Nat iollal Monet.ary (bmmission. The rate% is a week1.y average call loan ratf, for t 11(xNYSE. The National Monct,arv (‘ommissiorl ( 1910) tahlllatt,s 13ril isll call Irlonr’y rates and French “market from hack rates of disf,ollnt ..* Our (’It\rlrlall irtt c,rc,st-rat v data wcrf’ gathered issues of 7’hf ~f~ouorttrsl. ‘l‘tifb c.lassical golf1 st antlard flat a span lSS!b 190X. ‘I’hfw data arc monthly We also usf’ data OH t hc intt,r\var gold standard. a.nd are t,akrn from hrrking trud :\/orjr tclr,!J .4tntistics 1914-1941; the data ifa f~sf.hangf~ raic3 are averages of flail)span .lune 1925 t,hrorigli .July I!):< I. ‘1‘1 rates; interA rates arf’ II~llall>. s~lortbtcr111 ‘.privatf> fliscount rates.” Finally, we use mont,tily caxchangc rates. Inrlirnior~.
data
frorlr
Ttifw
data
1Irf> tjr.f,t 10~ l\‘ootls wfw‘
ol)t ainfd
regime
of adjustahtc
1‘1.0111 l,lic, OFX~I~‘s
‘l’hc ex~.l~it~~go rat (‘5 it[‘f’ Imilrt -itI-t ilrrrl spot. r;tks. q~~otf~(l l’or 1Jkrf~c~-rrrolrtII clolwst
:llnin while
pf,gged t:‘co7torrric~
the int,erest
The data are drawn frolri the lolrgf~st siriglt> l)f,riotl of f3f~~iiirigf~-ra.lc traIlqiiiliiy fliiritrg the 1960s (e.g.. t.tlo (:~~~III;III data Iqirl aftcsr t hcb\larch I !j)tiI revalllation arlcl end before the Octohr,r I!Ki!) rft\-alliat ioli ). t’i)r hot h the gold standarfl and raks
arf‘ usually
Hret,ton Figliws
b’igure
if.
‘t’rf~as~lr?;
Woods c1at.a. 1tic l..S..\. is t.rf~alf~(l as tlifl liorlw 2 and 3 colit aitr plots of’t tiv hasif, daily data
2 colitains
t illif’-s(>rioh of t Iit> Iloillillal
cxcha.llgf‘
hills.
colintry.
for t hc EMS pf,riod.” rates
(mcasrlrf~fl,
as
always, as the natural
logarithm
of the DM price of one unit of foreign ex-
change);
the upper and lower (implied)
included
in the graph.
EMS exchange-rate
Tick marks along the bottom
bands are also
of the diagrams
delin-
eate calendar years; the ticks along the top mark realignments which affected either of the two relevant currencies (e.g., either the DM, the Belgian Franc, or both, in the case of the DM/Bf r rate). Figure 3 contains time-series plots of the 2-day interest-rate differential (as always, the German rate minus the foreign rate). As is true of most of our graphics, scales are not directly comparable across countries; the Dutch exchange rate has actually been much more stable than the Italian exchange rate, even though the relevant exchange-rate bands appear wider on the graphs. The EMS
has experienced
a number
of realignments.
Our use of fine
frequency data enables us to split our data into thirteen different corresponding to the periods between the twelve different realignments EMS.22 We divide our data for a number of reasons. A split sample us to check the sensitivity of our results. Dividing the sample also
parts, of the allows allows
us to check for policy shifts such as the often-noted increasing credibility of the EMS (which should result. in changing types of nonlinearities) and timevarying capital controls. 23 Bertola and Caballero (1990a) also argue that the nature of the nonlinear relationship is expected to vary over time with the level of reserves. The thirteen different samples are tabulated below; it should be noted that the number of potential observations varies dramatically across regimes. In virtually all of regime-specific work below, data for the business 22The exact
ERM
realignments
were as follows
(percentage
changes
in bilateral
central
rates are also shown):
Regime
Date
Belgium
13-3-79
EMS Begins
Den.
24-9-79
+3.0
29-11-79
$4.74
France
Ger.
Ireland
Neth
-2.0
22-3-81
+6.0
4-10-81
+3.0
21-2-82
-5.5
+3.0
-5.5
$8.5
12-6-82 8
21-3-83
-1.5
-2.5
$5.75 +2.5
9
21-7-85
-2.0
-2.0
-2.0
10
6-486
-1.0
-1.0
11
3-8-86
t3.0
-4.25
+2.75
-4.25
-5.5
+3.5
$2.5
-3.5
-2.0
-2.0
+6.0
-2.0
-3.0
-3.0 +8.0
12
12-1-87
13
5-l-90
23Government
Italy
-2.0
-3.0
-3.0 +3.7
authorities
and differ from declared
may also defend implicit. target-zones
t,argrt-zones;
split,ting the sample
19
which change over time
may alleviate
this problem.
‘I
.05
'2b1'6 Years
"'
2i2'
Japan
Calendar
Ireland
“’
-0
-0
&, 2915 Years
“”
Belgium Relevant Realignments
o-’
- 0412
"I'
vary by Country Relevant Realignments
'-,a,,!,,, 0 Calendar
,045
Scales
165 Calendar
Y t2bi’k
Years
13
-
UK
Calendar
1990:5:
#2b1'& Years
16
Figure 3: Interest Rate Differentials
0
Denmark Relevant !?eallgnments
14’1
1979:3:
-1775.,,
-
Relevant Realignments
,’ Calendar
'2$1'& Years
-1262-m,,
0
1
USA
Calendar
I,
Netherlands
Calendar
'2b1'i
'2b1'6 Years
Years
France Relevant Realignments
0
-3.95 -,
Relevant Realignments
As
is
well-known.
t.o test work samplf,
for
t hfx ICIZIS has hf~~~iit~ illcrf3sirlgly
lxdwfw1 rfxligll1llf~lit.s
the periods
that
ot,ller
WC kntl
mallil;3t
t,o f’oc~is on
corlllt r.v; t,his is apparf7rt arc
dads),
associatfd
ncithf>r hand,
‘l‘lif77
f’ \~)lat ilit.!. \xrif,s
arc’ tllr>.
interest,-ratf%
;Issociat.fd
Ll’hilc
\ulat,ilit,>.
t.o lx
kss
recent by
wit II f~sccptionall>~
fliff;~rf~llt ial:, ~~11
time
descriptive
more
(meastlrcd
la.rgc, difff~ix~tlfx~:-~~~tm+ cx)llilt rks
art’
over
iI1 l~igltrf~ 2. 2s \vcll a.s siml)lc wit.11 lligll
empirical
as it, is a long
t argfxt-zolrf>.
dramatically
papf~).
we inknd
In our
of tjhf, MIS,
crfdihle
in t.hc sense-
longer;
crttlihilit~y.
t IIV t~~~lft Ii rcgimc
it1 t IIC b\orl;illg
tal,lllatcd
trot, grnrrally other
of iilcrtasiilg
of tl;Lt,a tlra’iz’ll 1’rotll a IJo1 fblrt iillly
Wfa 110tfx t.llat. fxdikiuge-ra1 (which
at ioIls
fxdihlc
S~Y’III t.o lx growing
for fxcl~ st.at,ist,ics
regimes
historical
low volatility. volatile
ill Imtli
morf’
arc> st an-
OII the rfxcf-ntly.
exchange-rat,c
and
ratfx volat,ililv
t hari t lit ot 11cr l:hlS
t IIC Nf,t hcrlantls ha.s much lower exchange roullt ries. Ilowf~vf7~. 110 t.ratle-off I)f+ween
exchange-rak
alItI irlt f>rf>st-tliflcrcxllt
ial \.olat ilit,?: is apparf‘nt,
Ilri’ -1 pro\:idcs
stackf~cl
intcrcst,-rat
variate
c \olat
fift,l-ortlcr
ilit.>.. I>or illst anut.
l)ar (.lli\l’th oI’s( illlfliirfl
in t,hc t1at.a.
tlf’viiIt ioIls of rf3idrlals
\..:I11 of’ irltf~rc~st -rat fx (liffcrcnt,ials
and
cscha.nge
from rates.“’
Figa bNo
m 1
2
4
5 6
3
4
5
6
Eelglum
3
stderrre
2
8
9 10
7
r-In
0 stderrrl
7
c] stderrel
11
12
1113 12
13
,
1
2
3
# stderrde
4
5
6
fl stderrdl r-I
4
5
6
Ireland
1 stderrle
1
9
10
0 stderrll
8
1113 12
11
12
13
1363
01
2
3
1 stderrfe
4
01
2
3
2833
0
1
I
2
3
stderrle
rl
5
6
Denmark
0257
01
I
1
2
3
stderrbe
4
5
6
Italy
4
8
9
10
n
9 10
7
8
9
10
0 stderrbl
7 8
0 stderrll
7
8
9
10
6
ill3
11
12
12
13
013
0
1
1
1
I
7
8
9
10
3 4
UK
O
5 6
Figure 4: Conditional
Volatility
Measures
7
2
3
stderrae
4
USA
5 6
9 10
7 8
9 10
0 stderral
8
n stderrhl
Netherlands
2
Stderrhe
France
Interest Dlfferentlal and Exchange Rate Standard Errors
Japan
7
5
0 ‘stderrfl
1113 12
11
11
12
12
13
13
-orlllslpl
0839
oiJllihi
01
1 stderree
‘1325 11111111
0249
.I243
Residtia: Standard Errors of Exchange Rate ar?d Interest Dlfferentlals Data for 13 EMS Regimes, from blvarlate 5th order VARs: Scales Varv
relationship deliver
is apparent
the same
Iwtween
the two measures
result. and are contained
(uncondit,ional
in t.hr working-paper
estimates version).
[Init-root
trst.s (allowing for wrial dependence through the rnethod sugthat unit-roots are pcrvageskd by Perron (1988)) indicat,e. unsurprisingly, sive throughout the dat,a (t hc statistics are tahula.ted in the working paper). More precisely. the null hypothesis that. a IlllitLroot exists cannot, usuall! be rejected
at conventional
fundamentals
(using
significance
Q =.l):
Itw~ls in each of: the excha.nge
alltl t,hc interest,
differential.25
While
rate:
this Inay
be the result of low power (Froot alld Ohst,feld (19901))), it, is extremely dist,urbing that the interest differential appears t.o be nonstationary. ignoring drift ~ the difference het,wcel1 t II(~ c>xchange rab and fr1ndamenta.b is the expect,ed rate change of the excha.nge ra.t,e; ullcovertd interest parity implies that, the latter is the same as the interest, different,ial. A nonstat,iona.ry irlterest diffcrelit.ial is illf-onsistcwt \vit II crcdihle target -zones: t hc persistence in t.llix seric3 which c‘;~lll~r)t I)(’ ;~c.c~ollrltc~l for 1)). f~~ll~lillll~~Ilt~~lS will ret 11r11lo haunt, 0111’tlypot tiesis t cxsts 121 t (‘I’. cannot typicall!, I)(% ‘l‘liv hypot licsis t,tiat f~t~~(l;~~~rc~titals Ilavr, ii Iinit-root Ie\:els. III fact. t,lie assumption t.liat rr:jccted at conventional sig:llifi(.allce furidalncntals follow a drift Ic+. ra~itlonl walk, while not likrally true, serwi~ t,o Iw a good
approximat
V. Deternlination Our
of
i011.”
alpha
strategy will 1-w to fiti(l a11 al)l>rol>rialc rnr,yf for 0: wv t hcW conduct 0111 for reasonal)lc \.iil~iw of 0 sl)afiliillg this range. We cst,imate 0 I)! two mct,Iiods. First. \vv 1i5v Olil' (la12 to (31 inlatr> 0. SNond, w(’ 11w cstinnat,cs aria.l;sis
frown the litcrat uw.
Estimating
CYfrom
If the increments intervention
daily data
to fare
generated
by equation
to defend a target-zone,
(3) with infinitesimal
then integrating
band
dfover one day results
in: .ft where. the discrete-time
ft-1
(14)
et
7) +
=
period is one day, 7 is the daily growth rate of fun-
damentals, and tt, which is the integral over one day of gdz, is the daily disturbance to the fprocess. Substituting from equation (14) into equation (l), we obtain: et -
el_l
=
n[Et(de)/dt] - [Et-l(de)/dt] + et
77 +
(15)
Equation (14) can For estimation we replace Et_,(de)/dt with (i,_, - &). then be used to estimate 17 and cy. The structural parameters (Y and 7 are identified because fundamentals are exogenous almost everywhere. Our estimates of alpha are presented in Figure 5. This figure graphs the point estimate of alpha with a two standard-error band.27 The estimates are almost uniformly small, although they vary considerably across country and EMS regimes. With the exception of a few imprecise estimates for Denmark and France, there is little statistical evidence that alpha exceeds .25 for EMS countries; lack of interest-rate volatility makes it much more difficult to pin down cy for non-EMS countries. Indeed, there are numerous negative estimates of alpha; the hypothesis that alpha is zero does not seem unreasonable from a purely sta.tistical point of view (although we exclude that possibility, and hence many of the point estimates, (1 ~riori).‘~
27As sample of varying 2sWe tution
have
also
of actual
typically mate
size varies
confidence tried
to estimate
exchange-rate
delivers
tional
volatilities
ARCH-like
The
the residual
purposes). plus
assumptions
than
data,
estimates
our
bands
-1.
since
One
could
correspond
could
to intervals
t,his method (this fby
approach
f; it is potentially reflect.ions
for the f process.
2.5
on McCallum’s
movements;
above,
be extended
also measure
target-zone
relies
volatilities
volat.ilities
to be f. This
about the
As discussed
differentials;
for conditional
which
of anticipated
conditional
technique
the constant
on additional are
in place
of a near
latter
specification
for estimation
error
o wit,h a technique
regime-specific
of int,erest-rate
zero.
the t,wo standard
changes
estimates
(Y by regressing
of cy near
by regime,
levels.
we have
typically would
deliver
regressing has the
(i-i’) advantage
with
of fundamentals
data
technique
tried
rates
delivers
regimes
important
also
of exchange
within
substi-
this
to esti-
on condian estimate
by employing more
on e and of not sampled can
an
observations
bias
defining
depending less finely coefficient
i
0
Estimates
of a in the literature
We have interpreted money demand,
a as the negative
of the interest-rate
semi-elasticity
of
a parameter
that plays a widespread role in both theoretical This parameter has previously been estiand empirical macroeconomics. mated in the literature; Goldfeld and Sichel (1990) provide a survey. The short-run semi-elasticities reported are quite similar to one another and average -.4.2s330 These estimates by the average
quarterly
are converted
to long-run elasticities
speed of adjustment,
.32/quarter,
by dividing
giving a long-
run semi-elasticity estimate of -1.25, which we take to be representative semi-elasticity estimates for industrial countries during normal times.
of
There are two ways to apply these estimates to daily data. First, in the spirit of the models upon which equation (1) is based, one can think of a model of continuous long-run money-market equilibrium such that an appropriate choice of o is 1.25. More rea.listically, one can think of equation (1) as resulting from a Goldfeld-style partial-adjustment model of the money market.31 In this view, it is the short-run, interest-rate semi-elasticity which is relevant to the problem; this is obtained by dividing -.4 by 90 days per quarter, giving a daily short-run semi-elasticity of -.0044, so that a=.0044 seems appropriate. Our various methods of uncovering (Y have led us to a range for this parameter. We think of cr=.l as being a reasonable value; a=1 is certainly representative of the high end of the range, especially given our point estimates. In preliminary estimation, we searched a grid of (Y values spanned by (.05, 3.0). I n most of our work below, we report results based on cu=.l 2gThe
average
units
so that
that
10 percent
estimates The
need has
change
of asset
mean
prices.
that
historical
30The periods;
Goldfeld 1962:l
Italy closely
interest-rate
semi-elasticity.
summarized
convention,
the
product
Under
report and
units
are the
units
study
interest-rate
the
Goldfeld
units and
so
Sichel
of a speed interest
of adjustment, demand,
having
or expected
annualized
interest
rates
rates
of
so our
years.
rather
than
equations. of cy are
we use two-day
Also,
too
low;
Euro-rates
increased Canzoneri
are
currency and
Diba
usually
used
substitution (1990)
as may
discuss
the
further. and
Sichel
report
involve
- 1985:4,
Japan
1966:l
- 1985:4,
it is important
chose
We choose
of money
of the
1971:1-1985:4, U.K. 1958:1-1986:l. the results for t,he US. in terms
in a single
they
as 10.
semi-elasticity
time
this
rates
estimates
1969:1-1985:4, match quite 31However,
our
of the
have
substitution
estimates Canada
but
as .lO.
quarter,
in money-demand
of currency
is -.004, entered
Sichel
inverse
interest
report, was
Throughout
domestic
rates
effects
the
semi-elasticities
Quarterly interest
per
Sichel
for example,
by 100.
and
percent are
and
year,
is ent,ered
Goldfeld
which
interest-rate
per
to be multiplied
units
units
Goldfeld
per year
estimates
which time
number 10 percent
to recall
model-determined
t,hat
the st,ate
analysis.
27
the
following
France
countries
1964:1-1985:4,
The results for these of the magnitude of the
assumption variable
that
and
countries short-run
fundamentals
is maintained
data
Germany
throughout
can
be the
and cu=l. Several different manifestations of the data a good choice for this key paranleter; see also Diebold Given frequency
differentials
our measure tials.
that
cr=.l
is
an cy value, t,he fundament,als can be measured at the monthly and compared with t.hc tradit ionA reduced-form determinants
of flexible-price exchange-rak monthly IFS measures of Ml rithmic
indicate (1986).
between
models, money, and output.32 WC obtained and intlust.rial production,33 computed loga(icrman
of fundament,als
The regressions
and
on act.ual
are compukd
foreign
variables,
money-supply
from 1979
and
through
and
regressed
output
differen-
1990 on a count.ry-by-
country basis. Our measures of fundamentals are typically highly correlated in levels with actual money and out,put, differentials; for instance, the R2sfor our six countries have an a.verage of .63. On t,he other hand, the coefficients on actual fundamentals are not signed consist,ently, and there is substantial residual autocorrclation. 111 first-diffcrc,ncc~s. our fundamental measures arc’ essentially
uncorrelatcxtl
VI. Graphical
A direct
with
~lloncl~- nrrtl out put.
analysis
escl,,m.in,cr,,tron
tions hip In this sect.ion of the paper. LVCana.lyzc the rclat.ionship between exchanges rates and funda.mentals, using graphical tc~chniqucs. Our conclusions will 1)~ corroborated below wit,h mor(~ rigoroIls c~~)r~ornc~tric techniques. WV bc,gin with the assumption (I=. 1. Figures 6 and 7 cant aiu a wealth of descriptive information about the relationship bet,weerl t hc r~sctlangc~ rat<, (c ) and fundamentals (f). ‘l’hc~ figures contain fourk[i “slilall Ilirllt,ipk” c : j scatter-plots; one for each of the thirteen
EMS regimes.
alltl anotllcr
covering
the whole sample
from 1979
through 1990. Tl 1c USC of slnall multiple graphs allows the data. to be conipared easily across rcginles a.nd count,ries. I:or the sake of brevity, only data for the Netherlands (a rcalati\-4y credible participant in the ERM) and Italy (a relatively participants
incredible co111ltr>.) arc usctl: comparable are availa.blr in t tie working pa.l)er.
In any given
scatter-plot
. each of t tie individual
figures
for other
point,s represent,s
ERM a single
daily observation. To guide t 1lc cyc ill connecting t,he dots of the joint t,ribution, a nonparanlctric “data snloot.tltxr” is drawn as a solid line.“4 32We temporally t,o correspond 33Quarterly 3”The five) and
average fundanwnt.als (instead I hat illdust rial protluct,ion
Lo t.hr way
in the cases
smoother calculates
divides
of Bclgiaul thv
alltl
horizotlt.al
(.liv ci-osc;-l)kdiall
of
of sctcctivrly
sampling
disWC
fundamentals)
is nleasurvd.
Francc~. axis
int,o a number
of bands
f iilld f wit tlill racll band.
The
(we genrLrally
use
cross-mrdinns
arc
29
use the shapes
of these
smoothers
extensively
in our search
for nonlinear
re-
lationships between e and j The smoother can easily handle the nonlinear patterns implied by the target-zone theories above; conversely, the absence of sensible nonlinear smoother that the theories work poorly. The marginal each observation
patterns
suggests
(though
density for e is displayed to the right is represented with a single tick mark.
right of the marginal
density,
a box-and-whiskers
it does not prove) of the scatter-plot; Immediately to the
plot of the marginal
density
is also displayed. The line in the middle of the box marks the median of the marginal distribution; the box covers the interquartile range (i.e., from the 25th percentile range to the 75th percentile range). The whiskers extend p oints beyond to upper- and lower-“adjacent values”; adjacent values are usually considered outliers. 35 A comparable marginal density and box plot for fis graphed above the diagram. This combination of graphs allows one to evaluate the marginal and joint distributions simultaneously. Target-zone theories place a number of restrictions on the marginal distributions of e and f, as discussed above. For instance, the simple model of Krugman (1990) im ’ pl ies that, (with perfect credibility and infinitesimal interventions on the bands), the exchange rate is expected asymptotically to have a bimodal symmetric density which would be directly apparent in the marginal distribution, and manifest in the box-plot as a relatively wide symmetric interquartile range with sma.11 whiskers. The model of Bertola and Caballero (1990b) d e 1’ivers a very different set of restrictions. In addition, some theories (e.g., Bertola and Caballero (1990a)) present restrictions on the relationship entire sample.
between
e a.nd f across
regimes;
hence
the
scatters
for the
The (implied) EMS exchange-rate bands are drawn as horizontal lines in the figures, so that the vertical dimension of the Dutch graphs represents +/-2.25%, those of the Italian graphs +/-6% (until January 1990). Consider the top left graph in Figure 7, describing tween e and f for Italy during the first EMS regime,
the relationship which prevailed
befrom
March 13, 1979 through September 23, 1979. The data are grouped in the upper portion of the graph, indicating that the Lira was relatively strong during this period; the box-plot for e indicates that the median value of the exchange liers. The apparently
rate is moderately
high in the band,
and there
fundamentals are approximately symmetrically normal distribution. The relationship between
are no negative
out-
distributed in an e and fappears to
then connected with cubic splines. Meese and Rose (1991) use a different nonparametric smoothing technique (locally weighted regression) and arrive at results consistent with ours. See also Diebold and Nason (1990) and Meese and Rose (1990). 35Adjacent values are defined as 150% of the interquartile range rolled back to the nearest data point,. 31
he monotonic,
positive,
and liliear.
No simple general charact,trization can be made about However, a number of features do seem apparent. ships. importantly, remarkably few nonlinearities which are typica.lly vicwcd as being nlore the Dutch Guilder) Third, nonlinearities than
more
are apparent,. Second, currencies committed to the ERM (such a,s
have fewer (not more) appear t,o be growing
important;
t,he absence
the e : f relationFirst, and most
manifestations Icss important
of nonlincarities
of nonlinea.rities. over time, rather
in the twelfth
regime
is
noticeable. However. incrcastxd credibility sltould be manifest in a relationship between the exchange rate and fundamcntjals that comes increasingly to become more unlikely.% resemble Krugman’s S-shape, a.s rea1ignment.s Fourth, while some nonlincarities are apparent,, they tend not to have shapes that are even vaguely similar to those implied by extant. t,heories. Countries that have cxperienc-et1 frqIlc,nt realignments (such as It,aly) do not appear
to liavc
iuvrrtrtl
S-shapf‘s.
as implied
by the
Bertola
and
Caballero
(199Ob)
model; crctlibl~~ count rics (such as the Nc1,herlands) do not have t.hat, arf’ apparent do not Krugman’s S-shape. ‘1‘hat, is. t11(’ ilonlincarities seem to have sensible idrnt,ifiabl(* pal.t urns across eitllcr time or count,ry. Fifth, much of thca flat a is clllst,ered iI1 11~~nliddle of t,he declared exchangerat,e bands, especially for Iat(,r r(xgillles. Assuming that. the act,ual exchangcrate bands coincide wit11 the dr,clared ba~~ds, nonlinearities a.re difficult to detect visually if t,hc c,xchangc ratf’ stays in the middle of the zone.3i This may indicate that, t,hc, aut Irorit ios defeIldcd implicit, bands well within t,he declared bands: in this case our t hc~oretZical ana.lysis applies for the a.ctual implicit bands. so long as the Inarkt,t recognized t,llis fact.“’ The fact t,hat, exchange rates spend n~ucll of (heir tinIf\ irt t,he interior of the band may
instead be a small saInpI(~ prol)l~~111. C:ivc,rl the sample sizes involved and t.hc nature of t,hc forcing process IIII~W that IIIIII hypot,hcsisl we are skeptical of t,his view; however, noIllin(~arities would IW milch more difficult to detect if exchange ra.tes happened to have avoided the periphery of the bands. the t : ,f relatiouship
Finally,
appears
to be approximat,ely
linear
over t,he
entire sample. consistcxnl wit.h t Ilrx ~nodel of Bcrtola and Caballero (199Oa). Figures 6 and T rely OII our assumpt iolr (1 = .l. (‘Iearly as N falls, the scatter-plots in these figures IIIOVVcloser towards an exact affine relationship between e and f; if (1 = 0, c = .f csactly. Figllres Al and A2 are the analogues to Figures 6 and 7, comput,r~tl \vitll (1 = I. ii valurx that, is implausibly large analysis of Fkrt.ola and (‘al)aIlt=ro ( 1990a.l)) implies
3”Thr earit.irs
should
he changit~g
370n the other
hand, the eschangc
target-zone, =This Edison bands.
is t.rue as long as and
(:racicla
over
t ilnc%fro~r~arr illvvrtcti
t,hat. the shape
S-shape
tIlta problt~~r~ is vsplicltlv a s~nall sample prohlpm. rate ~rlay sp~rrd most, of its t,ime near t,he bands.
the implicit.
Kaminskv
bands
arc’ currcnt,ly
arc constant twt.ing
of the nonlin-
to Krugman’s
(as the declared t.hr, hypothesis
S-shape. In a credible
bands
of constant,
are).
Hali
implicit
in our view. These figures indicate nonlinear effects of substantively greater importance, although it is a.gain difficult to detect patterns over time or country.
Again, the smoother
by extant
exchange-rate
Comparison
shapes bear little resemblance
to those implied
models.3g
with other
exchange-rate
regimes
While the scatter-plots of Figures 6 and 7 do not seem consistent with the implications of known nonlinear exchange-rate theories, we hasten to add that countries participating in the EMS do not look similar to countries in (relatively) free floats. Figure 8 is a graph (comparable in every way to Figures 6-7) for the British Pound Sterling, an exchange rate which was floating (relatively) freely against the DM: (comparable figures for the Japanese Yen, the American Dollar, and the Swiss Franc are similar and are available in the working paper). Figure 8 also has fourteen small graphs, one for each of the thirteen regimes, a.s well as one for the whole sample. While actions such as the Louvre Agreement lead one to doubt the assumption of perfectly free floating the e : f scatters look much more linear for non-ERM countries than they do for ERM countries.40 Our model predicts e = f for flexible exchange rates: manifestly this prediction is satisfied in spite of the assumptions used to build the model. This encouraging result bolsters our confidence in the empirical framework. The EMS can also be compared with other regimes of fixed exchange rates. Figure 9 provides graphs for the post-WWII Bretton Woods regime of pegged but adjustable rates (the data a.re drawn from the 1960s); Figure 10 provides comparable data for the pre-WWI and inter-war gold standards. Both figures use cy = .1.41 The relationship between the exchange rate and fundamentals seems to be decidedly more nonlinear for the gold standard than for the EMS; the dollar/yen rate also appears t,o be nonlinearly related to funda.mentals during the Bretton
Woods era.42 However, most of the Bretton
Woods data appear
consistent with linear e : f relationships, while the smoother shapes in the gold-standard data, are not implied by existing target-zone models.43 3gThe
working-paper
40Linearity was founded; 41Using
version
cont,ains
is also the hallmark further
a higher
detail value
is available
of a (say,
in the
1) changes
working the Bretton
Woods
higher values of alpha (e.g., 1) appear unreasonable Higher alpha values (say, .5) for the gold standard
43This
however,
may
shapes upper
be, in part,
are vaguely tails
appear
the result
and
reminiscent
33
base
graphs
are extremely
wiggly.
country. before
the ERM
considerably; Below,
the
we show
in a number of different data do not greatly change
of Krugman’s
to be essentially
of movement
as the
in t.he 1970s
paper.
that much dimensions.
tails;
sloped
Italy
float.ing
do not
lower
to be positively
with
currencies
smoothers
the graphs. 42The smoother
tend
analogues
of ERM
S-shape
for parts
of the
linear.
in t,he gold points.
These
are the exchange
35
Is there
a “honeymoon
effect”?
As discussed above, the thrust of the original target-zone proposal was to make the exchange rate less responsive to fluctuations in exchange-rate fundamentals,
the celebrated
“honeymoon
effect” of Krugman
(1990).
The the-
oretical framework of Section II implies that the e : f slope should be unity in a floating rate regime, lower in a credible target-zone. If the diminished impact of fundamentals on the exchange rate in a credible target zone is the “honeymoon effect ,” then the possibility that the impact might be magnified in an incredible target-zone (Bertola and Caballero (1990a,b)) might be the “divorce effect.” It should be remembered, however, that we are studying relationships; the start of a targetgovernment policies, not interpersonal zone is more likely, we think, to be characterized by low policy credibility than high policy credibility. Estimates of the slope t,hus provide a specification test of the target-zone model. Actual estimat,es of the slopes for all countries and EMS regimes are presented in Figure 11; we simply regress et on ft and an intercept; Newey-West covariance estimators are used. These specification test,s are independent of the theory results in Section II. Consistent with the honeymoon effect (and inconsistent with the work of Bertola and Caballero (1990b)), for cy = .l, the e : f slope is often less than unity for EMS countries, though rarely by a large margin. However, for any given country, our point estimates of the slope vary considerably over time, being greater than unit)y for around a. t,hird of the regimes considered; point estimates of small slopes also tend to be imprecise. Further, there are few identifiable patterns in the slope estimates. For instance, the unstable regimes of the early 19SOs are a.ssociated with small slopes, while the credible regimes of the late 1950s seem t,o have higher slopes. Also, slope estimates for countries a.s different as Italy and the Net.herlands do not appear to be very different.
It will be shown below that the nonlinear
rise to the honeymoon the data.44 to unity.45
effect in target-zone
linsurprisingly.
non-EMS
effects, which give
models, are not usually found in
countries
have e : f slopes very close
An errors-in-variables argument leads to the conclusion that a choice of (Y which is too high will lead to an e : f slope which is too low. Given our rates
at which
costs;
the gold
ing the gold further implicit
standard.
gains were
44Slopes
bands);
however.
from
market,
hlyers
analysis. Movements EMS exchange-rat,e
declared
important
if exchange
rates
physical forces
(1931).
transportation
which
Officer
limited and
(1986).
of gold fluctuations Spiller
the smoot,her
patterns
to t,he spread statistical and
problems
fundamrntals
are very
between afflict
transportation
and
Woods
similar bands
rates
(1988)
dur-
provide
to movements in which differ from
different.
maximal the
exceed
in exchange
in the gold points are conceptually bands (when the aut.horities defend
are also unrelated
45Potentially countries
arbitrage points
and standard
are nonstationary.
minimal errors
values for
of e. non-EMS
i” I
uncertainty about cy, we conduct sensitivity analysis. Figure 12 is comparable to Figure 11 but uses cr = 1 (the graphs with c~ = .05, for which there is essentially no evidence that the e : f slope strongly differs from unity, are in the working paper version).
For cr = 1, all point estimates
(across six ex-
change rates and thirteen EMS regimes) are less than unity, virtually always by statistically significant ma.rgins. Indeed, the e : f slopes are clustered closer to zero than to unity. We view this as another manifestation of our hypothesis
that unity is an excessively
high choice for CY.
Summary Some nonlinearities are apparent in the scatter-plots between the exchange rate and fundamentals; the e : f relationship tends to look much more linear for floating exchange rates than it does for fixed exchange rates. However, in a number of different dimensions, the nonlinearities do not seem to conform to the patterns implied by target-zone models. The few nonlinearities that exist do not appear as one might expect in more credible exchange rates (such as the Dutch Guilder), more recently (e.g., since 1987), or in the S-shapes implied by existing theories. Similarly, although there is modest evidence of a “honeymoon effect ,” the size of this effect does not vary in a sensible way across regimes; in any case, the existence of the effect depends strongly on c-y,and reasonable values of o are consistent with no honeymoon effect. Our relatively naive graphical approach has yielded, at best, weak supWe now attempt to clarify the issue by port for target-zone nonlinearities. applying more econometric firepower. VII.
Parametric
In this section, nificance significant
tests for nonlinear
we estimate
of nonlinear explanatory
terms.
target-zone
effects models
directly
and test
We find tha.t the nonlinear
power in sample.
terms
the sig-
often add
However, the finding of statistically
significant nonlinearities in-sample is too robust; it, occurs for both fixed and floating exchange ra.tes. Also, coefficient signs are not those predicted by target-zone models, and a number of other aspects of the model are rejected. The structural
model which we wish to estimate ft = 71+
is:
ft-1 + et
et = or/ + ft + Ale.v(b.ft)
+ &ev(Mt)
where we selectively sample et a.nd .ft daily. In our empirical with a slight extension of (16):
39
(14) (16) work, we work
where:
;I is the estimate
of 11 from equation
rate); i1 and i2 are the roots to equation in place of true 0 and 7; 6 is the estimated
(14)
(adjusted
to an a,nnual
(7) with estimates (T and 77 used standard error of the residual of
equation (14) (adjusted to annual rates); and Al and AZ are free parameters unconstrained by zone size or credibility assumptions. We estimate (17) with OLS, ignoring any biases in $ and 6 which may result from, e.g., small-sample bias, generated regressors, or misspecifications of (14). We maintain cr = .I for most of the analysis which follows. We allow for two potential
misspecifications
of the model by including O0
and 0,; a finding either of 00 # 0 or 03 # 0 is an indication of mcdel misspecification (multicollinearity considerations often preclude free estimation of 0,). An error term ha,s also been added to the equation; Froot and Obstfeld (1989b) suggest that this can be interpreted in a domestic context as a result of time-varying income tax rates that are conditionally independent of ft. We also examine thr> serial correla,tion properties of this disturbance below. Since there a.re cross-equatiou restrict.ions, estimation of these equations should be conducted jointly; for convenience, we pursue two-step estimation below.““>“7 Thus, we estimate (13) with OLS; consistent estimates of 77 and u are obtained from the intercept a.nd standard error of the residual, respectively. These estimat,es are t,hen used t,o estimate X, and X2; (17) can then be estimated directly with OLS. ~1~ and A2 can he consistently estimated by O1 and 0,; from the latter. t.he exchange r&e bands, eL and eU can be estimated. In practice, we test the hypothesis O1 = O2 = 0(<= Al = A2 = 0). Two problems affect this work iu pract.ice. First, our regressors are exponential funct,ions, which can lead to computa.tional complexities. Such problems can be avoidetl by a.ppropriate resealing of the data. Second, there is often severe multicollinea.rity between the regressors of (17), making tests of individual coefficients unreliable. For this reason, tests of the joint hypothesis 01 = O2 = 0 are tabulated in Table estimated signs of the 0 coefficicnk. As shown and A2 are of opposite sign in most theoretical
1. Table in the
1 also presents
theoretical
target-zone
section,
the
Al
models.48
46Simultaneous estimation is complicat,rd by two facts: (1) the well-known leptokurtosis in exchange rates is manifest in gross violations of normality of t,he shocks to t,he fundamentals equation (14); and (2) choice, rather than estimation , of (Y precludes serious statistical work, unless one is willing t,o guess t,he covariances of CI with other parameters. IV estimat,ion using Durbitl’s ranked instrumental variables does not change results; Bartlett’s variant of Wald’s indicat,or iustrrrnlental variables leads to enormously higher standard errors. 47Equations for individual bilateral exchange rates can also be estimated jointly with Zellner’s seemingly unrelated tecllnique for greatrr &iciency. 4”Froot and Obstfeld (1989b). 5Ilow that 0, and 02 arr well-behaved with the additional assumptions of normality of U’~and independence of ct Froot and Obstfeld (1989b) provide further analysis. 11
Tahlc Hypothesis
Tests
Joint Hypothesis
1:
for Nonlinear
Terms,
cu=.l
Tests for Nonlinear
Terms
Relg.
Den.
France
Ireland
Italy
Beth.
.oo
n/a
.oo
n/a
.oo
.oo
11/a.
2
.oo
n/a
.OO
II/11
.oo
.oo
n/a
3
.oo
H/ii
.oo
11/a
.oo
.oo
n/a
4
.oo
n/a.
.oo
u/a.
.oo
76
n/a
5
.oo
n/a
.oo
n/a
.OO
100
n/a
6
.oo
.oo
.uo
.OS
.oo
.oo
.oo
7
.oo
.oo
.oo
.oo
.oo
.oo
.oo
8
.oo
.oo
.oo
.oo
.oo
.oo
.oo
9
.oo
.oo
.oo
.OO
.Ol
.oo
.oo
R.egime
.Japan
UIi
10
.oo
.oo
.oo
.oo
.oo
.OO
.oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
I1
.oo .oo .oo
.oo
.oo
.UCl
.OO
.oo
.oo
.oo
1
12 I :1 Entries 711~.
arc-
Regime
ant1
used,
.oo
.oo
.oo
.oo
.oo
.oo
.OO
.oo
.I)0
.oo
.OO
.oo
.oo
.OO
significanw
o = .I:
~cgililr,-sI)c,cillc..
CJ~ and r/ (ar~tl thucforr .Yc>wc-v-\Ymt,
= O2 = 0 + O,f,
+
X2) arc
wtirnat,ors
Neth.
.la~pan
ITli
+~
II/11
t-
-+
Illa
+-
-t
II/d
-t
-+
n/a
+-
II/;1
-t
it
II/A
Il/il
-+
+-
Ii/i1
t-t -+
-4
II/i, St
-t
St
1.
t +-
+-+
0,
X1 and
cova.riance
Signs of 0, and 0, l;‘laII(‘(‘ Irc~lar~tl Italy
-+
-+
icst
+ 02wp(X21;)
wit.11 six lags.
Belg.
++
Icvcl for joint
(‘I - ,f; - (II/ = 0,t.r/1(A,.f;)
+t 2 :1
.OO
.oo
Throughout~,
count,ry-
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
arc marginal
in regressiorl
USA
-+ t+i
++-+ +t-+
+-
++ +-
-+
-+
-t +
++
-+
-+
-t
+-
++
+t+
t -t -+
n/a n/a
-+
t-
IlS,Z ++ -+ t-+ -t -+ -t-
-t
++
-+
-+
~+
4
-+ -+ -+
m+
-t
tt -+
Q-Tests
for Residual
Serial Correlation
Regime
Belg.
Den.
France
Ireland
Italy
Neth.
Japan
UK
USA
1 2 3
.oo .27 .oo
n/a n/a n/a
.oo .oo .oo
n/a n/a n/a
.oo .02
n/a
.oo .Ol .oo
4 5
.oo .oo
.oo .23
n/a
.oo .oo .oo .oo
6 7 8 9 10 11 12 13
.oo .oo .oo .oo .oo .oo .oo .oo
n/a n/a .oo .oo .oo .oo .oo .17
.oo .99 .oo .oo
n/a .oo .oo .oo
.oo .oo .oo .oo
.oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo
.oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
n/a n/a n/a n/a .oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo .oo
.oo .oo .oo .oo .oo .oo .oo .oo .oo
Entries are ma.rginal significance levels for serial correlation of wt from regression et - ft - cq = O1 exp( X,f,) + &excp( X,f,) + 03ft + Wt,ff = .l.
T-Tests Regime
Belg.
1
.97
2 3
.oo .Ol
4
.Ol
5 6
.60 .oo
7 8
.oo .oo
9 10 11 12 13
.oo .oo .oo .oo .oo
Den.
of O3 = 0
France
Ireland
Italy
Neth.
n/a da n/a n/a da
.28
n/a
.05
.13 .42 .Ol
n/a n/a n/a n/a
.54 .ll .oo .29
.oo
.33 .04
.25 .oo .oo
.oo .oo .oo
.25 .oo .oo .36
.oo .oo .oo .29
.05 .oo
.oo .52 .oo .35 .Ol .oo
.oo .oo .oo .oo .oo .oo .93 .oo .oo
.06 .04 .52 .22 .98 .17 .83 .oo .20 .45 .oo .93
Japan
n/a n/a n/a da n/a .oo .03 .24
.oo .oo .oo .57 .oo
UK
USA
.oo .31 .48 .oo
.oo .oo .oo .oo
.oo .oo
.oo .oo .09 .64
.25 .08 .03 .oo .oo .97 .53
Entries are marginal significance level of t-statistics of hypothesis 03 = 0 in regression et - ft - cyq = Olezp(X1ft) + &esp(Xzf,) + @,f,
+ UJt.
.oo .oo .oo .96 .oo
1 also prr3rilts
‘I’able
two spC,cificat ioir tests
(the
restrict,iou
OO = 0 was
rq~~rt~c~l in ‘Tahlr, I ). First, the marginal O-test, to txaminc t,he serial correlation
imposed for the analysis level from a standard
significance properties
of t,he residual from ( 17) is ta hulat~cd; a low number indicates statistically significant a.utocorrc~latiorl. S~ond, the nlargirial significance level of a t-test of the hypothesis (3, = O is also prvscnt 4. also another indicat ioll of IIIO~CI failllrf‘. The
result,s
is almost
I illdicatc
of l’ablc
that
R
t JIG joint
of t,his hypot.hclsis
hypothesis
O1 = 0,
is
= 0
alwa.ys
reject rd a.t conventional significance levels. This result, is quite strong; rejections occur for n~ost c-orlnt ries and most EMS regimes. The existence of nonlinearit ivs of t,hv type implkl by targbzonc models seems, at, first blush. to hf% ov~rwllrlrrli~lg~~ sllpported. WC have also cxaminrd a numbfar of pf73urhat~ions of 1hc ha.sic rfpssion framework including: set ting o = I: and a lil~~t-cliff’c~l.c~l~c.c~cI v(‘rsioll of the test. Neither perturbation changes t,lie basic i~slili~ of l‘al)lf~ I .l‘hc rcjcction of 0, = (!I2 = 0 is also t 0: 1iw ol‘ 0 = .O.T:(.11oicf\ of :I(Ltla!, (as opposed t 0 ‘L-day int crf3t rates); the f>xact sailil)lr~ ~~riotl (\vv t ricd c>scluding hot 11 (a) 011ly ttic day antI (I)) t lie wliok niont Ir 1~(~1;1rvarrtl al’1 (‘I’ imlipniiif~ilt s); aild day-of-t hc-wcf,k f+ fects (wfx cstimatcY1 ( IT) for ))ot II ICriclaJ2i antI non-Fritlays, wpara,tcly). This wjf~rt~ion also diarac_tf~ri/,c3 a11 1II<>cilrrfwcif~s in t,llf, l3rd ton \Voods and golfl-
insf7isil.iw
st.alldard
rcgiilws
sl.rongly sampI
wjfdf~tl: nonliiif3rii
of tisc~l
ratc5.
l‘lrc IIypot Jichis
\vf’ (~oli(~lu~lt~ 1 jl;rt 1Ircx finfliiig iw
it) t II<, c.oticlit iolial
iiic’iiils
C-1, =
(32 =
of st atist,ically
of c~sf.haligc~
0 is risiiall> signifif-arlt
rak
iii-
is clilitf’
roblIst. I’hc signs iii t Ilf, thcorfd targf+milc~
time,
of Gl ailcl (3L a13~ also tabrllntccl in Tahlf~ I. As dcinonstratcd ical swt ioil. t lir~- i~rf‘ f5pf‘f.t ml t 0 hc of oppositf’ sign ill most nmdf~1s (I)ot II cwflil)lf~ aritl iircrfdihlf~). ~Irotinfl a t,hirfl of t Ilc,
1hc signs
01’ hl
alr(l
(I)2 c~c~~~f~sponfl t 0 t,llosf> irriplicd
by targf+zoue
rnoclds.
IIowcvf~r. t hft st.iLt ist ical ~irotld (low llot wit.llst alltl flirt.hcr strut iny. ‘l’hfmt is st roilg cvidciicf~ of sf>vf7~‘ rf5itlllal alltf,c-ol.rclatic,ri (Ncwey-West covariancc cst,imat~ors lla\.f> LWII IIS~YI, I)(T~IIs~~ ot’ t llis a~lt~oc.orrf~lat.ion, rcsitlual ,IRCH is also apparent ). Only ill ;I f’t~w c‘ases cari oilf~ re.j_jcl the null hypotjlicsis of 110 a~lt~of~orrelat ion. t“rlrt lwri~iow. t Iif> 1110df~l sfmns to I,f% inisspccified in that, O. is oftc,ii sigliificant,lv diti’cv~ilt 1’ro111 zero. .Igaiil, tlif3c results arc rf>latiwly robust.. hlost import alit I>.. t hexIl!.l)ot Irf3is C-11 = O2 = 0 is uslrally rf~jcctfd for float.ing f~xcliarrgf~ ratfts 2s ~(~11 as fisf~l f~x(.llailgf~ rates, as is apparerlt froni ‘I’aI)lc, 1. ‘l’his iliflicatc5 t Irat OIII’ iloiilitlc~ar lcrms r~iiiy 11fx I)ic.king rip somf~ gcllf+c niissl)facificat ioli iii 0111‘ im~lf~l that is not part icrilar to tarp-zone rcgirilf~s. II
Summary Parametric
tests
for nonlinearities
one hand, nonlinearities
leave us with a mixed verdict.
of the type implied by target-zone
On the
models seem to
be statistically significant in-sample. The hypothesis that nonlinearities do not exist in conditional means of exchange rates can easily be rejected in a robust fashion. However, these nonlinearities arise in a model which is usually rejected on other statistical criteria. In any case, the economic meaning of these terms is far from clear. Although the signs of the coefficients correspond to target-zone nonlinearities, the fact that these nonlinear terms are often significant during regimes of floating rates seems to bolster the notion that the nonlinear terms do not represent t,arget-zone effects. To study this issue further, we now turn to a forecasting methodology. VIII.
Forecasting
with
linear
and
nonlinear
models
In this section of the paper, we compare the forecasting ability of linear exchange-rate models with models that have additional nonlinear terms implied by the target-zone litera.ture. We find that the presence of additional nonlinear terms does not produce better “ex post” forecasts than those of linear models. This result, combined with the in-sample analysis of the previous section mirrors the results of Diebold and Nason (1990). Our baseline forecasting experiment proceeds as follows. Consider a given country (say, Belgium) and a given EMS regime (say, the period before the first realignment, from March 1979 through September 1979). Using the first thirty observations, we estimate the drift term for fundamentals by regressing the first-difference of exchange-rate fundamentals on a constant. This provides us with estimates of g2 and 7. Given these estimates and our choice of cr, we can solve for i1 and i2; hence, we can generate the two nonlinear terms, e.r~(i1.f~) and esp(X2fi). A We then run two regressions: (1) (the linear model)
et = 7r7)+ 7rIft + 21:; and (2) (the non-linear model) e, = & + $lft + 42e~p(ilft) + &erp(i2ft) + ~1”“. We then generate forecast errors by substituting in the actual future values of the regressors to generate
a forecast;_ thus, the one-step
nonlinear
forecast
error is given by
%“” =: et+1 - [do + $lft+l + &e3-p(ilft+l) + dw~p(hft+~)l. We then add an observation to the initial set of (30) o b servations and repeat the procedure until we arrive at the week before the next EMS realignment. The functional form of our forecasting equakion is suggested by equation (6), but we allow Al and A2 to be time dependent free parameters, unconstrained (as always) by assumptions about zone size or credibility. The square roots of the mean squared forecast errors (RMSEs) from linear and nonlinear models (computed with cy = .l) are presented in a graphical format in Figure 13; this portrays the ratio of the linear to nonlinear RMSE
for the
six different
is little
evidence
EMS
or floating
RMSEs
countries
that
currencies.
are typically
and
nonlinear
thirteen
models
different
EMS
regimes.
There
for either t,he ratios of linear to nonlinear
provide
In particular,
superior
forecasts
around one; there is no evidence that they tend to vary
systematically over time. or that they tend t,o be larger for countries with credible reputations like the Netherlands. We have checked the sensitivit,y of these results extensively. Figure 14 is the analogue
to Figure
13 but with 0 set. t,o unity.4g
A number
of other
perturbations are contained in t,he working-paper version, including: analysis of mean avera.ge errors; rolling regression techniques; the imposition of r1 = & = 1; 20-step ahead forecasts. The finding that linear models seem to forecast EMS exchange rat.es as well a.s nonlinear models appears t,o be robust to our sensit.ivit,v chccks.SO~s’
Summary It is well-known that sophisticated exchange-rate models that appear to be satisfactory on the ba.sis of in-sample criteria often do not forecast out-ofsample data better than extremely naive alternati.ves.52 In this section, we have shown that non1inea.r models do not forecast bet,ter than simpler, linear models; this finding appea.rs to be robust. We have used three different techniques to examine the nature of the relationship between exchange rat,es and fundamentals; none has yielded compelling evidence of nonlinearity, at least of the sort implied by target-zone models. There arc three pot,ential reasons for this finding: (1) mismeasurement of cr; (2) violations of uncovered interest, parity; or (3) an invalid theoretical model. Two argumeIlt,s discredit, the first explanation: low point 4gChoosing mate
(Y to maximize
“Linear
and
nonlinear
Woods
data.
around
20% smaller
the %
For
“‘One can estimated
NL
the forecast.
error
ratios
represenk
yet another
way
RMSEs
the
t.o cst,i-
n.
1 VZ,f
iidN(0, $J(T -
produce
t,han
linear
=
l8.l
+
11;““.
a test
2).5/(
1 -
Assuming
of the
$2)
between
the
RMSE
“Meese forecast extend
and better
this
equal
nonlinear
models
produce
null
s where
~1 and
for
Bretton
RMSEs
that
are
models
t,hat
E( ~1, ~2) = 0 and
hypothesis 7’ is the
~12. Under
as Student’s t with T - 2 degrees null hypothesis of equal variances from
approximately
data,
rigorously t,est the hypot,hesis of equality of forecast linear and nonlinear forecast, errors U: and upL,
W),
correlation
models
t,he gold-standard
~111 = ~22 number
can
There
of errors
and
Such
this
standard
are also many
the
vector
be computed
the null hypothesis,
of freedom.
that
error variances. Denotc and define I)~,~ = u,” -
4) is the test tests
reject.ions,
(u;“, u;““)
from
estimated
statistic often
t(T
is
- 2) = sample
is distributed
do not
a$ might
reject
the
be expected
bar-chart,s. Rogoff than
finding
(1983)
a random
showed walk;
t,o nonparametric
t,hat, linear Diebold
and
t.erhniqurs.
structural Nason
(1990)
exchange-rate and
Meese
models and
Rose
do not (1991)
1.04762
6
8
10
12
Japan Comparisons
2
4
4
5 6
6
UK
5
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
6
4
5
6
7
2
4
5
USA
3
I arat
6
7
Netherlands
2
1 hrat
4
France
2
1 frat
by EMS Regime: Alpha=.1
3
4
Italy
3
I brat
2
2
Denmark
1 drat
Figure 13: Forecast Comparison of Target Zone Models
RMSE
01 Dniii 3 5 7 9 1113 2 4 6 8 10 12
I Jrat
Ireland
1 erat
Ratlo of Linear to Non-linear RMSEs from l-step ahead Forecasts Horizontal Line marks equality of linear and no+llnear RMSEs
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
?atlo ,+I 3r ;
ni L-lrear
1
2
Japan
4
6
Ireland :Pdt
1 rrat
873 !1 t 3 1 L 1 P e I erat
tc Non
8
8
Figure
10
10
,Ta r r\ s
14: Fortcast
12
12
Comparison
Italy
1 lrat
;&lark:
I firat
6
10
12
1 hrat
6
Netherlands
1 ; Cl?.7 “1
4
France
2
I frat
Forecasts 4MSEs
of Target Zone Models
8
ilnear HMSEs frorr l-steD ahead ?q,all:!: c+ jlnear- and no?-:;rear
8
10
12
estimates
of (Y (lower (Y estimates
lead to more linear relationships);
fact that many of our results are insensitive
and the
to choice of cr. The short time
horizon leads us to believe that any risk premium
(which would violate
un-
covered interest parity) would be too small t,o account for our results. We are, therefore, attracted to the conclusion that the theory is not useful in modelling the data. Nevertheless, to confirm our doubts we now use techniques that do not rely on our mea.sure of exchange-rate fundamentals.
IX.
Other
implications
of target-zone
models
The empirical work that we have pursued so far has depended on our measure of exchange-rate fundamentals. If this measure is flawed, our empirical work will also be faulty. For this reason, we now turn to tests of target-zones that do not depend on fundamentals. Target-zone models have a variety of implications that can be examined without a measured exchange-rate fundamental (Bertola and Caballero and Smith and Spencer (1990)), given a (1990b), Svensson (1990a,b,c,d), For instance, as noted in Section II, the specific process for interventions. interest differential in a credible target-zone is expected to be declining in the deviation of the exchange rate from its central parity; the exchange rate should spend most of its time near the boundaries; and exchange-rate volatility should be greatest in the middle of the band. In this section, we examine some of these other aspects of the data. Some of these implications are dependent on specific assumptions concerning the nature of the intervention Any test of these implications would also test these tenuous asprocess. sumptions. Therefore, we simply present the data and supply some guidance as to the predictions of various t,heories.
Exchange-rate
vola,tility
by band position
Figures 15 and 16 are scatter-plots of the absolute value of the daily change in the exchange rate a,gainst the deviation of the exchange rate from its central parity (in percentage
points).
For brevity, we continue
to present results for
Italy and the Netherlands only. The upper and lower exchange-rate bands are marked by vertical lines (at +/-2.25%); a nonparametric smoother is also provided. The graphs are intended to convey a sense of the relationship between the volatility of the exchange rate and its position inside the band. It is not easy to find a clear pattern in the smoothers, either by country or by EMS regime (credible or not). The relationship is occasionally U-shaped (as suggested by Bertola and Caballero (1990b)), but the smoother is just as likely to have an invert.ed Ushape (as implied by Krugman’s (1990) model). 49
Monotonic
or flat smoothers
The evidence of the EMS;
from other
results
Interest-rate Figures
rate
17 and
II, models
should
(1990)),
and Caballero no clear
Woods
exchange-rat,t,
Figures
much
norm
modality).
Despite
paper
Another
hold closely expected
54Svensson
(1900d)
different.ials
data,
we find
imply
interest-rate
also
is also
in Section
that
there
presented derives
widespread
56Algebraically, uncovered where: Etet+r_ is the exchange il(i;)
is the
away
any
return
risk
peaks
rates
appears
indicate
EMS
bi-
credibility.
of the histograms are again
in
conclusions.
credibility in Svensson
point
should
(1990a))
to derive
to graph
the tirne-
to testming the entire
term
we use 2-day
bet,ween
of excess
proposed
(which
parametric
model
11.
for the When
position
has been parity
test. is simply
is little
implications
evidence
interest
as shown
of differences
the
slopes
and
structure
of interest,-
30.day
interest,
of various
rate
maturities
of
smoot,hers. Ieptokurtosis,
although
the
model
pre-
the 0pposit.e int,erest, parity implies rate which is expected
on a domestic
premium,
The
differential:
and gold standard
in Section
target-zone.
pat,tern
II implies
Single
exchange of increasing
Woods
Svrnsson’s
different,ial/exchange-rate
55There
are again
data.54
paper.
in the pattern
uses llncovered
rates.“’
for a credible no clear
percept.ion
target.-zone
exchange
heteroskedasticity
rate
rates.
EMS
of a change
Svensson
negative result,s
53The
of conditional
there
in the
(e.g.,
of Bertola
test>’
in a credible
future
of excha.nge
“tc>st” of t.argc+zone
(199013).
However,
in i.he working
for ot,her
for t,hc Dretton
(nonstatistical)
by Svensson
function
the model
to the interest,-ra,te
and do not I~ad to diffrrent
“simplewt
Svenssonb
slope.
parity.
the interest-
by bnnd position
result,s
indications
over time . ” . Figures the working
arc again
the widespread
we also see no clear
declining rate:
of randomness)
ana.loglles
histograms
(t.hough
to that
interest-rate
imply that
deterministic
opposite
distributions
of 2-day
t,arget-zones
evidence
graphs
19 and 20 provide
to be the
sented
irn 1I I ies the
position
is similar
rate from its central
the exchange
and goltl-st,antla.rd
Exchange-mte
scatter-plot,s
of credible
a g ainst
graphed (and
rates
version.
of the exchange
be a nonlinear
(199Ob)
patterns
Bretton
comparable
the deviat.ion
in Section
differential
of fixed exchange
the figures.“”
by band position
18 provide
against
Krugman
regimes
throughout
are in the working-paper
differential
differentials As noted
arc also apparent
possibly
Elei+k at time
(foreign)
bond
with
a ttllbious
claim
at
.iO
T days
= et[(l + it)/(l + i;)]trls6”) t to prevail at time t+lc; and to mat,urity.
1his horizon.
This
assumes
-ID
c 0 A-
rc
51
series of expected exchange-rate
future exchange
rates and see whether they lie within the
bands.
Figure 21 provides time-series plots of the exchange rates expected as of time t to prevail one year in the future. Exchange-rate bands are also presented. With the exception of the Dutch exchange rate, exchange rates expected
to prevail in a year are often outside the bands for prolonged periods
of time,
even for the more recent:
further
inconsistency
credible
twelfth
between the predictions
EMS
regime.
of credible
This is a
target-zone
models
and the EMS data.
Summary Target-zone models have a number of implications that can be examined empirically without relying on a measure of exchange-rate fundamentals. In this section, we examined: int,erest-rate differentials; exchange-rate volatility; exchange-rate distributions; and expected future exchange rates. These auxiliary (albeit informal) t.est.s provide no support for models of credible target-zones and only weak support for models with rea.lignments such as Bertola and Caballero ( 1990h).5’ 37We data
have
conducted
we found
12 (using
that
data
across
the corresponding principle J
EMS
ratio
starting 1. These
regimes
model
replication,
point. of these
Our
and
without
the
olphcr
results
carried
our
values
between
to 12. and
were
generated
.1 and
out
for two
wit,lr and
without.
using
was
long
then
and
daily
generated
from
at a random
of (Y: .I and
which
added
set
the reflection
begins
values
beliefs, noise
actual
to c was around
1). We, therefore,
fdata
data
of invest,igat,or
Using
values
generated
exchange-rate
a grid
result,s.
fundamental
set is 200 observations
we investigat,ecl were
to check
of possible
drift;
data
simulat,ion
sett,ings,
simulations
experiments
of t,he range
in the simulat,ions
in a credible
In a typical
both
simulation
the ratio
range
1. For
from
to the true
.l to
exchange
rate. Regardless that
of the match
instrumental
differentials mates
and
cantly”
less
change
than
unity.
in the
“significant“ ratr
and
rates
(t,he linear
regressions
WC always for the
deviation
replicat.ions
per simulation.
of the mean
value
found opposit,e
generating coefficient
to thr
across 500 replications is grratcr than 2. Without added noise, the forecast.ing exercise vantage 1000.
to the Ratios
fundamental
nonlinear remained
innovations.
model. greater
Ratios than
one
However, disappear
st.andard
always
such
as those
llntil
the
had adding
(the
deviation
of that
to the ex-
was set equal
are based on 500 value of the ratio of such
indicated
a huge 20 were
in the
the
“signifi-
constants
noise
noise
esti-
that
coefficient,s
in Table
volatility
small
found
of the
(15))
interest
: f slope
an e
estimation
(equat,ion signs.
We also
deliver
found
lagged
in numerically
of zero. the
using
f). These in-sample results we mean that the absolute
By %ignificant”
of an est,imated
that rate
a, we always
text
resulted
errors
of t,hese coc‘flicients
to t,he noise
in the
of c on f)
exchange
of the appropriate
the significance
the investigator’s
as instruments,
t,wo standard
Also.
in standard
n and
of n, as proposed
well within
expression
makes
the true
estimation
exchange
were
regressions
integration were
lagged
of cy which
honeymoon
I)ct.ween
variable
noise
coefficient,s
forecasting never was
ad-
less than that
of the
I
_
h
55
-2 N
cc 0
-
I
L
co
X.
Summary
and
Using uncovered
conclusion
interest
parity in a framework
that implicitly
depends on a
flexible-price exchange-rate model, we derived a measure of exchange-rate With the aid of this measure of fundamentals, we tested fundamentals. target-zone models of exchange-rate behavior in a number of ways. Graphical examination of the relationship between exchange-rate levels and fundamentals did not yield strong evidence of economically meaningful and important nonlinearities, certainly not those implied by existing target-zone models. There is little clear evidence of an important “honeymoon effect.” Explicit in-sample parametric tests of the nonlinear terms implied by targetzone models yield the conclusion that nonlinearities are usually statistically significant; however, a number of aspects of these models work poorly inMore importantly, linear sample on both economic and statistical grounds. models forecast out-of-sample data just as well as models with additional non-linear terms. Finally, a number of additional implications of targetzone models that do not depend on our measure of fundamentals have been tested and found not t,o he in accord with the data. For instance, there does not appear to be any particular relationship between exchange-rate and interest-rate volatility, and expected future exchange rates often fall outside the EMS bands. Moreover, few of the relationships between the exchange rate and (a) interest-rate different,ials, (b) exchange-rate volatility, and (c) Sucexchange-rate distributions seem to be in accord with existing theories. cinctly, we have been unable to provide a cha.racterization behavior during managed exchange-rate regimes.
of exchange-rate
We conclude that, at an empirical level, there is little advantage apparent in working with nonlinear, rather than linear, models of exchange-rate conditional mea.ns. This result is exactly analogous to the conclusions of Meese and Rose (1991) for flexible exchange-rate regimes. Our results also imply that there is little empirical support, for existing target-zone models of exchange rates. The models that we have dealt with in this paper have a number of restricFor instance, our model incorporates only a. single-state varitive features. able (thereby
ignoring st,icky prices and certain
Our simulations indicate unconditional
counterpart
that
the sample
types of devaluation
distribution
if 200 observations
of the exchange
rate
risk).58
resembles
its
are available.
‘“There is little reason to believe that either sticky prices or devaluation risk can easily reconcile target-zone models with the data. The lack of interest-rate differential variability for floating-rate shocks Further, and
from the
we find
countries goods Dutch it hard
implies
that
a model
with
markets;
however,
it is difficult
Guilder
has been
firmly
to believe
that
fixed
devaluation
sticky
to the
risk could
59
prices
to reconcile
this
must feature
Deutsche
Mark
account
for our
rely
heavily
with since
the early
negative
on data. 1983,
results.
We expect plaining
future
research
our negative
to identify
results.
the importance
of these
factors
in ex.
L.&e%
. “.,
i
t
ar
1 ar ,z!a
1
m
,I ar P
WQ
ar
ar
I
’
ar
61
“EL:. i
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