POLICY RESEARCH WORKING PAPER 2397
Verifying Exchange Rate One reason intermediate
exchange rate regimes have
Regim es fallen out of favor is that they
are not transparent or easy to
Jeffrey Frankel verify. A simple peg or a
Eduardo Fajnzylber simple float may be easier for
Sergio Schmukler market participants to verify
Luis Servgn than a more complicated
intermediate regime.
The World Bank
Development Research Group
Macroeconomics and Growth U
simpy flatmy0eea0r0o
POLICY RESEARCH WORKING PAPER 2397
Summary findings
Credibility and transparency are at the core of the Frankel, Fajnzylber, Schmukler, and Serv6n investigate
current debate about exchange rate regimes. The steady how difficult it is for investors to verify from observable
growth in the magnitude and variability of international data whether the authorities are in fact following the
capital flows has complicated the question of whether to exchange rate regime they claim to be following.
use floating, fixed, or intermediate exchange rate Of the various intermediate regimes, they focus on
regimes. basket pegs with bands. Statistically, it can take a
Emerging market economies are abandoning basket surprisingly long span of data for an econometrician or
pegs, crawling pegs, bands, adjustable pegs, and various investor to verify whether such a regime is actually in
combinations of these. operation.
One of several reasons intermediate regimes have The authors find that verification becomes more
fallen out of favor is that they are not transparent; it is difficult as the regime's bands widen or more currencies
very difficult to verify them. Verifiability is a concrete enter the basket peg.
example of the principle of "transparency" so often At the other extreme, they also analyze regimes
invoked in discussions of the new international financial described as free floating and find that in some cases the
architecture but so seldom made precise. A simple peg or observed exchange rate data do validate the announced
a simple float may be easier for market participants to regime.
verify than a more complicated intermediate regime.
This paper-a joint product of Macroeconomics and Growth, Development Research Group, and the Regional Studies
Program, Latin America and the Caribbean Region-is part of a larger effort in the Bank to understand alternative currency
regimes. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please
contact Emily Khine, room MC3 -347, telephone 202-473-7471, fax 202-522-3518, email address kkhine@worldbank.org.
Policy Research Working Papers are also posted on the Web at w gw.worldbank.org/research/workingpapers. The authors
may be contacted at jeffrey_frankel@harvard.edu, efajnzyl hucla.edu, sschmukler@worldbank.org, or Iserven
@worldbank.org. July 2000. (64 pages)
The Polcy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective ofthe series is toget the findings out quickly, even ifthe presentations are less than fully polished. The
papers carry the names ofthe authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
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countries they represent.
Produced by the Policy Research Dissemination Center
Verifying Exchange Rate Regimes
Jeffrey Frankel
Harvard University and NBER
Eduardo Fajnzylber
University of California, Los Angeles
Sergio Schmukler
World Bank
Luis Serv6n
World Bank
JEL Classification Codes: F31, F32, F33, F36
Keywords: verifiability, transparency, exchange rate regimes, basket peg, bands, target
zone, floating
- We are grateful to Sebastian Edwards, Miguel Kiguel, Javier Ortiz, Ilan Goldfajn, and participants at the
NBER/CEMA Inter-American Seminar on Economics for their useful feedback. Changqing Sun performed
excellent research assistance work. We also thank Klaus Schmidt-Hebbel, Roberto Steiner, Matias Tapia
Gonzalez, Alejandro Werner, and Roberto Zahler for making their data available to us. This paper was
prepared as part of the Regional Studies Program of the Latin American and Caribbean Region of the
World Bank.
E-mail addresses: jeffiey frankel(harvard.edu, efajnzvl(ucla.edu, sschmukler(wworldbank.orM
Iserven@worldbank.org
I. Introduction and The Corners Hypothesis
The choice of exchange rate regime - floating, fixed, or somewhere in between -
is an old question in international monetary economics. But the steady increase in
magnitude and variability of international capital flows has complicated the question.
This is particularly the case for the developing countries that in the 1990s became full-
fledged participants in international financial markets.
A major new element in the debate is the proposition that emerging market
countries are, or should be, abandoning basket pegs, crawling pegs, bands, adjustable
pegs, and various combinations of these. The currently-fashionable view is that countries
are being pushed to the "corners," the extremes of either free floating or firm fixing. The
intermediate regimes are said to be no longer viable. This proposition is variously called
the hypothesis of the vanishing intermediate regime, the missing middle, or the comers
solution. Its life history has gone from birth to conventional wisdom in a remarkably
short period of time.
The motivation of this paper is the observation that, as fashionable as this
proposition has become, few of its proponents, if any, have offered an analytical rationale
for it, let alone a fully worked out theoretical model. Our aim is to offer a possible
theoretical rationale. We seek to introduce the notion of verifiability, and to suggest that
a simple peg or a simple float may be more verifiable by market participants than a more
complicated intermediate regime. Verifiability is a concrete instance of the more general
principle of "transparency" that is so often invoked in recent discussions of the new
international financial architecture but so seldom made precise.
La Motivation
Consider the exchange rate regime that a number of emerging markets had in the
1990s: a band around a central parity that itself is a basket with a rate of crawl. So far as
existing theory is concerned, the complexity of this arrangement has no implications for
its credibility. But, in truth, when a central bank announces a regime of this type, the
public has no way of verifying quickly, by observing the exchange rate, whether the
central bank is doing what it claims to be doing.
A central bank does not earn credibility merely by announcing a monetary regime
with a nominal anchor such as the exchange rate, even if its intentions are sincere. The
public will judge credibility from data available to it. If the announced exchange rate
regime is a simple dollar peg, a market participant need only check that the exchange rate
today is the same as the exchange rate yesterday, in order to verify that the central bank is
indeed following its announced policy. If the announced regime is a pure float, a
participant can essentially check every month whether the central bank has intervened in
the market by seeing whether its reserve holdings have changed. Under the basket band,
by contrast, the market participant needs more months of data in order to be able to verify
that the central bank is indeed implementing the announced policy. When comparing the
corners, simple pegs tend to be more immediately verifiable than floating regimes.
Typically, a market participant needs some extra piece of information, like reserves, or
more data to check that an exchange rate is truly floating. How many months of data he
or she needs is the central analytical exercise of this paper.
We are not claiming that verifiability is necessarily the complete story behind the
purported non-viability of intermediate regimes. And we are certainly not claiming that it
2
is the only criterion, or even the most important criterion, in the larger debate about fixed
and floating exchange rate regimes. Many other factors, whether from the traditional
optimum currency area literature or the newer criteria associated with credibility and
financial markets, need to be taken into account.1 Our goal is rather to offer an attempt at
what, so far as we are aware, may be the first explicit analytical rationale for the
proposition that intermediate regimes are less viable than the corner regimes.
In this paper, we demonstrate the difficulties of verifiability for the case of a band
around a basket peg. We believe that the same difficulties apply to other intermediate
exchange rate regimes, such as a managed float or adjustable peg. One could model a
managed float, as a central target and a central bank policy of intervening partially to
offset market forces when they push the exchange rate away from that target. But one
would have to estimate the central target, and measure somehow the pressure of current
market forces in order to figure out to what extent the authorities were intervening to
resist them, a difficult econometric exercise. One could model an adjustable peg as a
fixed exchange rate with an escape clause: the central bank has an explicit or implicit rule
of abandoning the peg when an exogenous shock of a particular size occurs, and when a
particular percentage of its foreign exchange reserves have been exhausted. Verifying
that sort of rule would be even harder than the others because usually few relevant
observations will occur in the sample period, and even when the adjustment takes place,
there is little way in practice of verifying whether on the one hand the putative exogenous
shock in fact occurred, or on the other hand the government's commitment to monetary
discipline was not sincere in the first place. We choose to explore verifiability for the
case of the basket band rather than the other examples because it is a cleaner econometric
'Two recent reviews are Larrain and Velasco (1999) and Frankel (1999).
3
exercise. We also look at countries that are believed to be floating, to offer a contrast to
those that are believed to follow basket bands.
This paper explores the amount of information that it takes for market participants
to verify announced exchange rate regimes from observed data. The goal of the paper is
to show the difficulty to verify exchange rate regimes and how this varies with regimes.
To our knowledge, this is the first paper that performs this type of exercise. We use
observed exchange rate data and simulated data to provide empirical estimates. The fact
that countries vary their exchange rate regime over time allows us to run this experiment
for regimes of different complexity.
Regarding bands, the paper confirms the intuitive notion that wide bands are
harder to verify than narrow bands. It is often difficult or impossible to estimate the
weights of the central parity with only one or two years of data. Regarding regimes
announced as free-floating, the paper shows that in some cases the exchange rates
observed under such regimes are correlated with those of major currencies. In this sense,
they behave similarly to the basket countries. It is not straightforward to verify them,
when only using exchange rate data.
To complement the tests performed with real data, we run Monte Carlo
experiments to obtain more general conclusions and to provide results regarding the
amount of information necessary to estimate regimes of interest. Monte Carlo
experiments, displayed in the Appendix, confirm that more complex regimes take a larger
amount of data to be verified. The Monte Carlo exercise shows the role of a number of
factors in determining verifiability: the band size, number of currencies in the basket, the
rate of crawl, sample period, periodic adjustments of the central parity. The results
4
confirm the intuition that the amount of information necessary to verify the exchange rate
regimes increases with the complexity of the regime.
The rest of the paper is organized as follows. The rest of the introduction
introduces the verifiability problem. Section II describes the framework and empirical
strategy used to verify exchange rate regimes. Section III presents estimations for the
case of exchange rate bands. Section IV shows the results from free-floating regimes.
The main conclusions are summarized in Section V. Appendix 1 displays a small Monte
Carlo exercise extending the study of regime verification to simulated models, and
Appendix 2 gives more details on the construction of the numeraire and the estimated
models.
Lb Intellectual Origins of the Corners Hypothesis
What is known about the origins of the hypothesis of the vanishing intermediate
regime? The original reference is believed to be Eichengreen (1994). The context was
not emerging markets, but rather the European Exchange Rate Mechanism. The ERM
crisis of 1992 and band-widening of 1993 suggested to some that a gradual transition to
European Economic and Monetary Union, where the width of the target zone was
narrowed in steps, might not be the best way to proceed after all. (Crockett, 1994, made
the same point.) Obstfeld and Rogoff (1995) concluded, "A careful examination of the
genesis of speculative attacks suggests that even broad-band systems in the current EMS
style pose difficulties, and that there is little, if any, comfortable middle ground between
floating rates and the adoption by countries of a common currency." The lesson that "the
5
best way to cross a chasm is in a single jump" was seemingly borne out subsequently, by
the successful leap from wide bands to EMU in 1998-99.
After the East Asia crises of 1997-98, the hypothesis of the vanishing
intermediate regime was applied to emerging markets. In the effort to "reform the
international financial architecture" so as to minimize the frequency and severity of crisis
in the future, the proposition was rapidly adopted by the international financial
establishment as the new conventional wisdom.
For example, Summers (1 999a)2:
"There is no single answer, but in light of recent experience what is perhaps becoming
increasingly clear - and will probably be increasingly reflected in the advice that the
international community offers - is that in a world of freely flowing capital there is
shrinking scope for countries to occupy the middle ground of fixed but adjustable pegs.
As we go forward from the events of the past eighteen months, I expect that countries
will be increasingly wary about committing themselves to fixed exchange rates, whatever
the temptations these may offer in the short run, unless they are also prepared to dedicate
policy wholeheartedly to their support and establish extra-ordinary domestic safeguards
to keep them in place."
Other high-profile examples include Eichengreen (1999, p.104-105), Minton-
Beddoes (1999) and Council on Foreign Relations (1999, p.87). The International
Monetary Fund has now agreed that countries that get into trouble by following an
intermediate regime will in the future not be bailed out, though it qualified the scope of
2 Other high-profile examples include Eichengreen (1999, p.104-105), Minton-Beddoes (1999) and
Council on Foreign Relations (1999, p.87).
6
the generalization a bit, for example, by allowing a possible exception for "systemically"
important countries.
It may be that the Economist (1999, p.15-16) is right that "Most academics now
believe that only radical solutions will work: either currencies must float freely, or they
must be tightly tied (through a currency board or, even better, currency unions)." But the
proposition remains to be modeled, let alone proven. It seems intuitively right that these
countries, facing finicky international investors and rapidly disappearing foreign
exchange reserves, had little alternative but to abandon their pegs and baskets and bands
and crawls and move to a float, unless they were prepared to go to the opposite corner.
But what is the rationale for this proposition?
I.c Lack of Theoretical Foundations
What is the analytical rationale for the hypothesis of the disappearing
intermediate regime (or the "missing middle")? Surprisingly, none currently exists, to
our knowledge.
At first glance, it appears to be a corollary to the principle of the Impossible
Trinity.' That principle says that a country must give up one of three goals: exchange
rate stability, monetary independence, and financial market integration. It cannot have all
three simultaneously. If one adds the observation that financial markets are steadily
becoming more and more integrated internationally, that forces the choice down to giving
up on exchange rate stability or giving up on monetary independence. But this is not the
3 Summers (1999b, p. 326) is explicit: "...the core principle of monetary economics is a trilemma: that
capital mobility, an independent monetary policy, and the maintenance of a fixed exchange rate objective
are mutually incompatible. I suspect this means that as capital market integration increases, countries will
be forced increasingly to more pure floating or more purely fixed exchange rate regimes."
7
same thing as saying one cannot give up on both, that one cannot have half-stability and
half-independence. There is nothing in existing theory, for example, that prevents a
country from pursuing a target zone of moderate width. The elegant line of target-zone
theory begun by Krugman (1991), in which speculation helped stabilize the currency,
always assumed perfect capital mobility. Similarly, there is nothing that prevents the
government from pursuing a managed float in which half of every fluctuation in demand
for its currency is accommodated by intervention and half is allowed to be reflected in the
exchange rate. (To model this, one need only introduce a "leaning against the wind"
central bank reaction function into a standard monetary model of exchange rate
determination.) And there is nothing that prevents a country from pursuing a peg that is
abandoned whenever there is a shock large enough to use up half its reserves.
Another justification that has been offered is that when a government establishes
any sort of exchange rate target, as did the East Asian countries, its banks and firms
foolishly underestimate the possibility of a future break in the currency value.4 As a
result, they incur large unhedged dollar liabilities abroad. When a devaluation occurs,
their domestic-currency revenues are inadequate for servicing their debts, and so they go
bankrupt, with devastating consequences for the economy. "It follows that in a world of
high capital mobility there are only two feasible approaches to exchange rate policy. One
is not just to peg the exchange rate, but to lock it in - the Argentine strategy... .The vast
majority of countries will ... have to follow the other alternative of allowing their
currencies to fluctuate. If the exchange rate moves regularly, banks and firns will have
an incentive to hedge their foreign exposures..." (Eichengreen, 1999, p.105).
8
There is little doubt that the focus on unhedged foreign-currency debt describes
accurately why the 1997-98 devaluations were economically devastating to East Asia.
But the argument, as stated, has some weaknesses. First, it appears to depend on
irrationality on the part of banks and firms. Second, it appears to imply that a country
would be better off by gratuitously introducing extra noise into the exchange rate, to deter
borrowers from incurring unhedged dollar liabilities. This seems unlikely to be right.
Third is the point emphasized by Ricardo Hausmann: because foreigners are unwilling to
take open positions in the currencies of emerging-market countries, the admonition to
avoid borrowing in dollars is to some extent an admonition to avoid borrowing at all.
(An admonition to hedge the dollar exposure is not helpful; someone has to take the other
side of the futures contract, and this will be difficult in the aggregate if foreigners are
unwilling to take the open position.) It may well be that this is the right road to go down,
that exchange rate volatility is a way to put some sand in the wheels of the excessive
capital movements, and that a lower volume of total debt is a good outcome. But if this is
the argument, the proponents should be explicit about it. In any case, it seems doubtful
that this argument could be captured by conventional models.
A third possible justification is that governments that adopt an exchange rate
target, and sometime later experience a major reversal of capital inflows, tend to wait too
late before abandoning the target. As of 1998, we thought we had learned that the one
thing an emerging-market government can do to minimize the eventual pain from a
currency crisis is to try to devalue early enough (or else raise interest rates early enough,
as would happen automatically under a currency board - anything to adjust, rather than
4 The version of this argument in Eichengreen (1999, p.104) overstates the extent to which the East Asians
had "a stated commitment to the peg," as most commentators have done as well. In fact few of the East
9
try to finance an ongoing deficit). Mexico, Thailand and Korea made the mistake of
waiting too long, until reserves ran very low, so that by the time of the devaluation there
was no good way out, no combination of interest rates and exchange rate that would
simultaneously satisfy the financing constraint externally and prevent recession
domestically. But exiting from an exchange rate target can be difficult politically. The
lesson is drawn that, to avoid this difficulty, governments should either adopt a rigid
institutional fixed-rate commitment (such as the currency boards of Hong Kong and
Argentina), or, if not prepared to do that, abandon the peg early. 5
On this basis, when Brazil in the autumn of 1998 delayed the seemingly inevitable
jettisoning of the real target, many thought this would be a repeat of the earlier mistakes.
Instead, when the devaluation finally came in January 1999, Brazil's trade balance
improved sharply, the lack of confidence subsided, and output and employment
subsequently performed far better than in neighboring Argentina. Thus it is more
difficult to generalize from recent experience than widely believed. Furthermore, if we
are to use government reluctance to exit a target arrangement as the basis of a model of
the unviability of intermediate regimes, it seems that we would again require some sort of
irrationality (or political constraints6) on the part of policy-makers.
Thus, each of the three arguments offered - the impossible trinity, the dangers of
unhedged dollar liabilities, and the political difficulty of exiting - contains some
important truth. But none seems able to stand as a theoretical rationale for the superiority
Asian countries had explicit dollar pegs.
s Even then we had a counter-example: Indonesia had widened the band right away in 1997, and yet that
didn't save it. But one could argue that political instability would have done Indonesia in no matter what.
Taiwan devalued promptly, and suffered less than the others.
6 Governments may have an incentive to postpone devaluations until after elections. See Ernesto Stein and
Jorge Streb (1998, 1999).
10
of the corner solutions over the intermediate regimes. Is the corners hypothesis, then, just
a misplaced manifestation of the temptation to believe that the grass is always greener
somewhere else?
II. Assessing Verifiability
The idea behind verifiability is that the government's announcement of an
exchange rate regime is more likely to be credible if market participants can check for
themselves from observable data that the announced regime is in fact in operation.
Specifically, the goal of our paper is to study how long it takes for financial markets to
identify from the data the rules guiding the intervention behavior of the authorities in the
foreign exchange markets
The process of verification can be modeled along the lines of statistical inference
familiar to econometricians. We are not suggesting that market participants will literally
run OLS or other sorts of regressions, but rather that they must do something similar
implicitly to process the available information.
The paper's framework encompasses a broad variety of regimes - simple and
basket pegs with bands and crawl as well as floating regimes. However, if a country
follows an exact basket peg (i.e., with no band), the problem of statistical inference is of
limited interest.7 In practice, however, there is almost always some range of variation in
the observed exchange rate data, even if it is only within a narrow bid-ask spread quoted
by the banking system, or within the +/- 1% range that constituted a fixed exchange rate
under the rules of the Bretton Woods system. Then the problem of statistical inference is
11
not trivial. For bands of substantial width, the statistical inference can in fact be difficult,
as we shall see. This is all the more true if one allows for the ever-present possibility of
shifts in the parameters-basket weights, band width, rate of crawl, or level of parity-or
changes in the regime altogether, especially if some of these shifts are not announced.
In our empirical analysis, we work with a set of emerging countries, for which we
know the announced exchange rate regimes. We will begin with an analysis of the basket
bands followed by Chile and Israel during the late 1980s and 1990s.8 Given that Chile
and Israel changed their band parameters over time, we are able to examine them under
different regime configurations. Then, we move on to the regimes officially declared as
floating followed by Brazil, Mexico, Peru, South Korea, and Thailand.
If the currency in question is in fact following a basket band, the question of
interest is how many data points are necessary, i.e., how much time must elapse, in order
to verify that the regime is in fact in operation. In general, we will consider an anchored
exchange rate regime to have been verified if it passes two tests. (1) We fail to reject the
hypothesis that the exchange rate is following the announced basket peg. (2) We can find
statistically significant basket parameters, i.e., can reject the hypothesis that the currency
is behaving like any "random" currency. These two tests are informative only if they
have adequate power. To judge the power of the tests, we perform the same tests with a
randomly generated variable and with a freely floating exchange rate as the dependent
variable. When using these latter variables we should reject the null hypothesis in (1) and
fail to reject that in (2). In the case of floating regimes, since there are no announced
In that case, the announcement of a basket of N major currencies can be verified with N+1 observations,
which is the number needed to estimate exactly the basket weights. As noted, however, this does not
constitute verification of an adjustable peg since we don't observe the terms of the "escape clause."
A detailed description of these regimes can be found in Appendix Tables A.1 and A.2.
12
pegs we only use the second test. Below we specify more explicitly the null hypotheses
under consideration.
If an announced regime of basket bands does not pass these tests, one can argue
that it is not verifiable, which suggests that the country cannot reap the credibility gains
that an anchored exchange rate regime theoretically offers-credibility in the eyes of
workers and producers who set wages and prices, and in the eyes of speculators who have
the ability to attack the central bank's reserves and bring about a crisis. If viability
requires verifiability, such a regime may not be viable.
In the case of bands, we are especially interested also in seeing how the ability to
confirm the announced nominal regime is statistically affected by features such as the
width of the band and the number of foreign currencies in the basket.
Our approach focuses on the empirical estimation of the parameters describing the
exchange rate rule at different sample sizes - e.g., 50, 100, and 200 observations. The
point estimates, their precision, and the tests of the above hypotheses constructed using
them tell us how well can market participants identify the parameters of the regime when
the latter is 10, 20, and 40 weeks old. For this empirical analysis, we need a basic
framework and a testing procedure. The rest of this section is devoted to these questions.
IIa Basic Framework
We adopt a general formulation to "nest" a number of alternative regimes. We
assume that the exchange rate for a given small country is given by a weighted
13
combination of N foreign currencies, with a possible rate of crawl d and an error term.
The exchange rate is:9
St = c + dxt + D(w,, sl)+e. (1)
where st is the spot exchange rate of the domestic currency with its value measured in
terms of a numeraire that we will explain momentarily; s, are the spot exchange rates of
the major "strong currencies" measured vis-A-vis the same numeraire; d is the rate of
crawl, which for now is assumed to be fixed during a given sample period;10 and wi are
the weights given to the currencies included in the basket. Depending on the specification
of the basket, (D may take different forms, with the simplest one being the familiar
N
D(w,i,,-:=Ywisi,t.
Simple Pegs, Basket Pegs, Crawling Pegs, Crawling Baskets
This general case captures many possible regimes, including simple pegs, basket
pegs, crawling pegs, crawling baskets, target zones, certain forms of managed floating,
and free floating. In the case of simple pegs, the value of the currency follows the
exchange rates of the foreign currency to which it is pegged, plus the crawling rule, and a
stochastic error. The latter is the error allowed or incurred by the government when
setting the exchange rate. In the case of simple pegs, N (the number of currencies in the
basket) is equal to one. Under basket pegs, N is bigger than one. Crawling pegs imply
that d>O. Under crawling baskets, N>l and d>O.
9 The precise models that we estimated are described in Appendix 2, which also provides a description of
the procedure followed by Chile and Israel to construct the basket used as central parity in their band
systems.
14
In the case of an exact peg, the error term would vanish, and an OLS regression of
the domestic currency on the foreign currencies to which it is pegged would yield an 1l
equal to 1. Verification is a trivial exercise, whether the peg is simple or to a basket. This
can be easily illustrated by examining the behavior of the central parity in band regimes.
Central parities behave like simple or basket pegs (with or without crawl), depending on
the regime. Frankel, Schmukler and Serv6n (2000) report estimations of a version of
equation (1) above using as dependent variable the Chilean peso central parity. In all the
cases examined there, the weights of the central parity converge to their announced
values almost immediately. In our present context, the pegged regime is verified
instantaneously. Thus, in the remainder of this paper we concentrate on the cases of
exchange rate bands (target zones) and floating regimes.
Target Zones
In a regime of target zones, a central parity is defined as a function of a single or
multiple foreign currencies and the exchange rate is allowed to float within a pre-
specified band around this central parity. Whenever it hits the boundary, the government
intervenes to keep the exchange rate inside the band. In many cases, governments make
intra-band interventions as well.
In a target zone, the log difference between the observed spot exchange rate and
the central parity, st*, is determined by the following equation:
b if s < -b
s, ={b ifs, > b
vt otherwise
10 One alternative would be to use past domestic or future inflation rates relative to international inflation
15
where st is defined by equation (1) above and b is the band width.
According to theory, the distribution of v can be quite complicated. Even under
two simplifying assumptions made by Krugman (1991) in a famous article that generated
a sub-field of research on target zones-that the band is 100% credible and that the
authorities intervene only at the boundaries-the distribution is not normal, but rather
follows a particular S-shape." But extensive empirical investigation of the European
Exchange Rate Mechanism in the 1980s and early 1990s established that the spot rate
does not in fact obey the predicted distribution. There are a number of likely reasons for
this, among them the lack. of full credibility of the zones12 and the prevalence of intra-
marginal intervention.
For these reasons we shall assume in our work that v follows instead an
autoregressive process, of the form vt = pv-l + ut, where u is iid. In fact, we will focus on
the random walk case of p = 1, in accordance with most time series analyses of exchange
rates, which cannot reject the unit root hypothesis.3
rates, where the authorities are believed to be following an indexation policy.
" When the spot rate draws close to one edge, speculators are aware that there is a limit on how far it can
continue to move in that direction. The expected value will show a regression back toward the central
parity. As speculators respond to that expectation, they will push the spot rate away from the margin, even
without any intervention.
12 Imperfect credibility was in the event justified by realignments in the early 1980s, and especially by the
ERM crises of 1992-93. It is also relevant for the present exercise, which is entirely based on a starting
point that assumes imperfect credibility.
13 In unreported results, we found that estimates of p were practically I in most regressions using equation
(1). One extension for further research would be to use statistical distributions implied by more
sophisticated versions of the target zone theory. Another would be to take the observed statistical
distribution from historical episodes such as the ERM currencies in the 1980s or 1990s.
16
Managed Floating and Free Floating
While there are many possible patterns of exchange rate intervention, our basic
framework [equation (1)] only allows us to test whether d or w; are different from 0. In
other words, the government is using some form of nominal anchor or crawling peg rule
14
to guide its operations. Other forms of intervention are not nested in our specification
Hence, we will consider that failure to reject that d=O and wi=0 is a characterization of a
pure floating regime. 15 In such case, the disturbance term accounts for the entire variance
of the exchange rate.
The Choice of Numeraire
The question of what to use as the numeraire to measure the values of the
domestic and foreign currencies is a surprisingly subtle one. In the case of exact pegs it
makes no difference - so long of course as the same one is used for both dependent and
independent variables alike. The correct weights should emerge, with a perfect statistical
fit, regardless of the numeraire. But in the general case, the choice of numeraire does
make a difference. Past studies have used a variety of numeraires, including the
consumer basket of domestic goods (Frankel, 1993, which emphasized Asian currencies),
the SDR (Frankel and Wei, 1995, which emphasized policies of European currencies),
the Swiss franc (Frankel and Wei, 1994 and Ohno, 1999) and the dollar (Benassy-Quere,
1999).
14 It is possible to assume that the government follows a variance-reducing form of intervention but,
without imposing some a priori value for the variance of the underlying process, it is not possible to
identify the intervention parameter.
15 We use the term free-floating to refer to a case where there is no correlation between the studied currency
and any of the strong currencies. It is possible to argue that under pure free-floating, market forces might
induce some correlation with the currencies of major trade partners.
17
Upon further reflection, these measures are not quite right. We wish to consider
regimes where the central bank monitors a central parity, but routinely allows
appreciations or depreciations relative to that parity in response to such factors as
inflation, unemployment, trade deficits or surpluses, various market pressures and so on.
These factors are only partially accommodated under an intermediate regime such as a
band or managed float, but they have a role nonetheless. We have not chosen to model
explicitly these factors; they are comprised by the error term. The authorities are
presumed to be trading off the long-term credibility benefits of sticking relatively close to
their central nominal parity against the monetary-independence benefits of responding to
short-term developments. But in framing this tradeoff, there is no reason for them to
think of the departure above or below the central parity in terms of dollars or a basket of
goods, and still less reason to think in terms of Swiss francs. The most useful way to
phrase these appreciations and depreciations is, rather, in terms of an effective exchange
rate, that is, a weighted average of trading partners' currencies.
In this paper we measure values of currencies in terms of a weighted basket of the
G7 currencies. One possible set of weights is the bilateral trade shares of the smaller
country in question. This has a drawback: it leaves out the role of all the other bilateral
trade partners, as well as third-country markets and competitors. But most of those are
linked to some combination of the major currencies. Here we adopt the simple approach
of using the G7 countries' weights in gross world production. In this way it is hoped that,
for example, the large weight of the US will roughly reflect the importance of dollar-
linked countries in the trade of Chile or Indonesia beyond the share of the US in bilateral
18
trade of those two countries.' 6 Thus, the exchange rates, both of the major currencies and
the currencies under study, are calculated as the number of units of the currency
necessary to purchase a weighted basket of strong currencies.7
II.b Empirical Strategy
We use daily data in our empirical experiments.18 To assess how verifiable
different exchange rate regimes are, we use explicit statistical tests that attempt to
replicate those implicitly carried out by financial market participants to learn about the
actions of the monetary authorities. For countries that have announced a basket band -
such as Chile and Israel during the sample periods we use (examined in section III
below), we seek to establish the amount of information (days) needed to reach a
judgment on whether the data support the hypothesis that the exchange rate is following
the announced regime. In the case of currencies that have declared their regime as a pure
float - like post-crisis Mexico and Thailand (section IV below) - the purpose of the
exercise is to offer a standard of comparison for the first set of currencies.
A test that fails to reject the announced regime for the currencies following basket
bands, has low power if the same test also fails to reject an analogous hypothesis applied
to floating currencies. We wish to see whether the public can distinguish the two sorts of
policies statistically, rather than having to rely on the assumption that it can
instantaneously intuit the true policy of their central bank.
16 A second advantage of using GDP weights is that one does not need to obtain the full set of bilateral
trade data and recompute a new set of weights for each country. But using bilateral trade weights is a
possible extension for future research.
17 See Appendix 2 for a detailed description of the construction of the numeraire.
' Data on major currencies and some of the emerging countries was extracted from Bloomberg and
Datastream. Data for the case studies of Chile and Israel was downloaded from the respective Central
Banks Web pages.
19
To make this approach operational, we summarize the exchange rate regime in
terms of the basket weights in equation (1). Tests of hypotheses about the exchange rate
regime then are just tests of hypotheses regarding the basket weights. The tests we
perform are the following.
Test 1 (TI): Market participants test whether the weights obtained from empirical
estimation of equation (1) are equal to the announced weights. Conditional on the
announcement being true, we expect that this null will not be rejected. The null and
alternative hypotheses are:
HO: wi= announced weights; HA: w,# announced weights.
Test 2 (T2): The second test inquires more generally, whether we can reject that
the currency is freely floating. We assume that market participants do not know what the
government is doing, for example because the government has not explicitly announced a
regime, or else they do not necessarily believe the announced exchange rate regime. The
null hypothesis is that the value of the currency follows a random walk with or without
drift. Therefore, we think of market participants as testing if all the weights on the strong
currencies are jointly equal to zero. Formally,
HO: w;= 0 ... and ... wv,= 0; HA: wI#0 ... or... wN # 0.
One problem with this approach is that Test I might fail to reject the null due to
lack of power --e.g., if we work with too short a time sample. Market participants know
instinctively that a failure to reject the regime is an informative finding only when that
test would be capable of rejecting the regime in the case where it was false. To see if
Test 1 has power, we complement it with another experiment in which we replace the
dependent variable with fictitious data and with a floating exchange rate. Then, we test
20
the null hypothesis that the weights are equal to the ones announced by Chile and Israel.
We perform this experiment for the cases in which Test 1 fails to reject the null
hypothesis. In this experiment, we expect to reject the null, given that we are using false
weights. Analogously, to check that Test 2 is not rejecting the null hypothesis when it is
true (i.e., it is not making a Type I error), we perform a similar experiment for Test 2. In
this case, we should fail to reject the null hypothesis of Test 2.19
To estimate equation (1) and carry out inference on its parameters, a variety of
procedures are potentially applicable. In this paper we report results using a "naive"
estimation procedure, which we implicitly assume to be the one that market participants
apply to process the observed data. Specifically, we compute OLS estimates of equation
(1) in first differences. We do this for all the exchange rate regimes explored in the
paper.20 While nre complex models, such as those derived from the recent target zone
literature, might offer some advantage in terms of consistency, their estimation would
also require a vastly larger amount of data. Therefore, we work with these relatively
simple specifications to carry out our tests and illustrate the point of the paper.
As independent variables for the basket band regimes, we use those currencies
that were included in the announced basket. In some cases we found that some of these
currencies were strongly correlated over some periods (particularly the Deutsche mark
and French franc, both included in the Israeli basket), so that the estimations were
plagued by severe multicollinearity and identification of the specific weights was almost
19 Alternatively to T2, which checks the null that all weights are zero, we used another test of the null that
all the strong currencies have the same weight, obtaining very similar rejection frequencies.
20 The estimated models are described in Appendix 2. We also experimented with more general error-
correction models allowing for long-run equilibrium and short-run dynamics, with the long-term
relationship linking the level of the domestic exchange rate with the level of the strong-currency exchange
rates. In general precision was poor, and the long-run equilibrium poorly identified. To save space, we don't
report the results here.
21
impossible. To solve this problem, we opted for computing also estimates of a
"restricted" model combining the most highly correlated currencies, using the ratio of
their announced weights. We return to this below.
III. Verifying Exchange Rate Bands
Using the framework and empirical approach just described, this section focuses
on the verifiability of the exchange rate bands followed by Chile and Israel over recent
years.
III.a Chile
A number of successive exchange rate regimes have been in place in Chile since
the early 1980s.21 In 1982, Chile had a crawling peg vis-A-vis the US dollar, with daily
devaluations following the difference between domestic and external inflation. The peg
to the dollar continued until 1992, with bands of varying width around the central parity
and with realignments of the central parity. In 1992, the government decided to adopt a
target zone around a basket peg. The weights on the currencies defining the central parity
changed over time and there were realignments, but the central parity was always tied to
the US dollar (US$), the Deutsche mark (DM), and the Japanese yen (JY). Finally, in
September 1999 the central bank decided to float the peso.
The entire period of exchange rate bands can be broken down into a number of
sub-periods distinguished by different levels of the central parity, basket composition and
band width. To analyze the verifiability of Chile's exchange rate band system, we focus
21 A detailed chronology of the exchange rate system in Chile is presented in Table A. 1 in the appendix.
22
on seven of those sub-periods, selected on the basis of a minimum duration (specifically,
those comprising at least 249 daily observations, amounting to approximately one year).
The relevant parameters characterizing these sub-periods are summarized in Table La.
The first three sub-periods involve a peg to the US dollar with a band, while the last four
involve a basket peg with a band.
Figure 1 displays the observed exchange rate in terms of the weighted basket
numeraire, along with the announced bands. The figure shows that the trend of the peso
has been to depreciate over time, with significant appreciations and depreciations on
several occasions, and highlights the fluctuations of the exchange rate within the band, as
well as the gradual widening of the latter. In some periods, like 1991-92, the exchange
rate is close to the lower band. In other periods, like 1994-95, the exchange rate
fluctuates farther inside the band. After suffering pressure on the peso, the authorities
decided to narrow the band from 12% to 3.5% in September 1998 to show their
commitment to the value of the peso. The band was widened back to 8% in December
1998.
Table 1.b reports the results of the verifiability tests using the Chilean exchange
rate data, based on first-difference OLS estimates of the basic equation. For each of the
seven sub-periods under consideration, the table presents the cumulative rejection
frequencies of the null hypotheses of Test 1 and Test 2 at increasing sample sizes - 50,
100 and 200 observations. For example, a rejection frequency of 100 for 50 observations
in Test 2 means that in 100 percent of the estimations with sample sizes smaller than 50
we can reject the null hypothesis that the weights are equal to 0.2 In addition, the table
also reports point estimates and standard errors of the weight of the US$ in the basket
23
defining the central parity (to save space, we omit the estimated weights of the other
currencies). Finally, the last two columns of the table give a measure of the precision of
the estimates, in terms of their mean absolute error - that is, the sum of absolute
deviations of the estimated weights from their announced values.23
For periods 4-7, when the central parity is defined by a basket of several
currencies, the table presents two sets of results. The first set is based on an unrestricted
version of the model, in which we attempt to estimate the individual weights of all
currencies in the basket. As already mentioned, however, this procedure may run into
difficulties due to the high correlation among some of these currencies in some sub-
periods, and therefore we also present results from a restricted model version combining
the most highly-correlated currencies in the proportions dictated by the announced
weights. In the Chilean case, this involved combining in such fashion the US dollar and
the yen. 24
The results in Table 1.b show a clear difference between periods 1-3 and 4-7,
regardless of whether we use the restricted or unrestricted model in the latter sub-periods.
In the former sub-periods, the point estimates of the US dollar weight approach fairly
quickly the announced weight (equal to one), especially in periods 1-2. In these two
periods the estimated weights are not statistically different from the announced value
(Test 1), but are statistically different from zero (Test 2) for any sample size. In turn, in
sub-period 3, with an increased bandwidth (equal to 5%) relative to periods 1-2, the point
estimate of the US dollar weight still approaches its announced value, although at a
22 The first estimation starts with the minimum number of observations required to estimate the models.
23 Since the announced weights sum up to 1, no rescaling is required.
24 The correlation between the first differences of these two currencies exceeds .85 in some of the sub-
periods of analysis.
24
somewhat slower pace than in periods 1-2. However, we also find a higher rejection rate
in Test I and a somewhat reduced rejection rate in Test 2. On the whole, these results
tend to suggest that the widening band makes verification more difficult.
In contrast, for periods 4-7, characterized by a currency basket and much wider
bands, none of the estimates in Table lb - whether restricted or unrestricted - appears
close to the announced values even after a reasonably large number of observations.
Precision is much poorer than in the earlier periods, although the restricted estimates are
in general substantially more precise than the unrestricted ones (see the last two columns
in the table). In any case, both sets of estimates appear clearly biased; indeed, some point
estimates are even negative. As a result, while Test 2 generally rejects the null of zero
weights, Test 1 also rejects the announced weights in most samples, and this applies both
to the restricted and unrestricted estimates.
These results can be more easily understood with the help of Figure 3, which
presents scatter plots of the observed exchange rate of the Chilean peso against the
central parity. In the first three sub-periods, the points cluster along the 45-degree line,
reflecting a relatively close match between the peso and the central parity. As the band
widens in the last four periods, the peso can fluctuate further away from the central
parity. This is particularly apparent in periods 5-7, whose scatter plots display little or no
clustering along the 45-degree line. Thus, it is not surprising that in the first three periods
the basket weights defining the central parity can be estimated fairly precisely from the
observed exchange rate data, while this is not the case in later periods.25
2' The scatter diagram, along with Figure 1, also provides some clues for the relatively poorer verifiability
of the third period vis-h-vis the first two. In the early part of the third period (approximately 50
observations), the exchange rate was practically pegged to the upper part of the band, but starting in early
1990 the peso started appreciating until it finally reached the lower band. This marked break in the
25
On the whole, the results for Chile strongly suggest that the widening of the band,
together with the adoption of multiple instead of simple pegs, make verification of the
announced regime more difficult using simple econometric estimates. 26
III.b Israel
Israel presents another interesting experience of basket band with weight changes
and progressive widening of the band. During the periods on which we will focus, the
band included the same five currencies [US dollar (US$), Deutsche mark (DM), British
pound (BP), French franc (FF), and Japanese yen (JY)] and the bandwidth rose from 3%
to 15%.
The Bank of Israel had already introduced an exchange rate band around a basket
in 1976.27 It lasted for a year before being replaced with a floating exchange rate,
followed in turn by a dollar peg in 1985 and a basket peg in 1986, with basket weights
determined by trade shares and subject to relatively frequent revisions.28
At the beginning of 1989, the Bank of Israel reintroduced a band system by
allowing the exchange rate to fluctuate within a region of ±3% around the currency
basket defined by the five currencies already mentioned. The band was later widened to
trajectory of the peso, clearly visible from the scatter plot in Figure 3, is behind the poorer performance of
Tests 1 and 2 in the third period that is apparent from Table lb.
26 One could object that the contrast between the results we obtain for the earlier and later periods of Chile's
band regime might be due instead to some underlying change in the behavior of the strong currencies or in
the way the peso moved within the band. However, the intuition that verifiability is more difficult with
wider bands and baskets with more currencies is confirmed by the Monte Carlo experiments in Appendix 1,
which are not subject to those objections.
27 For a detailed account of the exchange rate policy in Israel, see http://www.bankisrael.gov.il and
Appendix Table A.2.
28 The number of units of each currency in the new basket was originally determined according to its share
in trade during the previous calendar year and to international cross rates. Since then, the trade shares were
revised annually and when significant changes produced, the weights and units in the basket were
recalculated. The number of units of each currency in the basket is kept constant, but its weight -
26
5% in March 1990, 7% in May 1995, and then gradually since June 1997, to reach 15%
by the end of that year.29 Most importantly, since December 1991 a pre-announced,
constant rate of crawl was added to both the midpoint and the band - a system known as
a crawling band.
Figure 2 shows the evolution of the Israeli exchange rate and the exchange rate
band. One feature that stands out is the frequency of realignments of the central parity,
particularly in the early years of the band. For the analysis of verifiability, we divided the
sample into different sub-periods characterized by different bandwidth, basket weights
and/or rate of crawl of the exchange rate band. Table 2.a lists the periods under
consideration, their beginning and ending dates, and the relevant parameters of the band.
In the case of Israel, collinearity among basket currencies is more of an issue than
in Chile due to the larger number of currencies and, especially, to the simultaneous
inclusion of the French franc and DM in the basket. 30 Thus, for the restricted model
estimation we combined the DM with the franc and the US dollar with the yen, using in
each period the ratio of announced weights.
The empirical results for Israel are reported in Table 2.b, which is analogous to
Table 1.b for Chile. It is apparent from the table that the exchange rate system can be
unambiguously verified by our procedure only in the third sub-period (labeled 2.2 in the
table), when the announced weights cannot be rejected by Test 1 and zero weights are
clearly rejected by Test 2 - particularly when using the restricted model estimates. In the
understood as the share in the total cost of the basket - can change daily according to changes in cross rates
(see Appendix 2 for more details).
29 Appendix Table A.2 provides more details on the developments of exchange rate policy in Israel since
1986.
3o The correlation between these two currencies exceeds .98 in some of the sub-periods under
consideration.
27
other sub-periods, the unrestricted estimates wander off very far from the announced
values, and lead to rejection of both null hypotheses in the majority of cases, even though
their precision is extremely poor. In turn, the restricted estimates are much more precise,
and generally closer to the announced weights. In general, they lead to rejection of the
null of zero weights for sufficiently large samples in all sub-periods, but tend also to lead
eventually to rejection of the announced weights except in period 2.2.
Like in the case of Chile, the scatter plots presented in Figure 4 help understand
these empirical results. Period 2.2 is the only one in which the observed exchange rate
behaved in a fashion similar to the central parity. During this period, which coincides
with the introduction of a crawl in the path of the central parity, the exchange rate
hovered around the midpoint of the band, and the boundaries were never reached.
In contrast, during periods 1 and 2.1 the frequent level adjustments to the band
already mentioned are reflected in the disconnected scatter plots of Figure 4. From the
perspective of verifiability, these jumps make identification of the basket weights more
difficult. Finally, in the wider-band periods 3-6, the scatter plots are more reminiscent of
those corresponding to the multiple-currency periods of the Chilean band: they show little
correspondence between the central parity and the observed exchange rate.
In summary, one interpretation for the poor verifiability results in the Israeli case
probably lies in the additional complexity induced by the presence of five mutually
correlated currencies in the central basket. Even after reducing to three the number of
regressors, identification is still poor. The sharp discontinuous changes in the central
parity in the earlier periods, and the augmented band width in the later ones, are also
likely obstacles to the verification of the regime.
28
III.c Is the Test Informative?
We conclude this section with a reassessment of the robustness of our findings for
the cases in which we achieved verification (periods 1-2 in Chile and 2.2 in Israel). We
do this by constructing a randomly generated variable and using it to replace the observed
exchange rate as dependent variable in the empirical estimation and testing procedures
performed earlier. The results are reported in Table 3, from which it is apparent that Test
1 rejects the announced weights in most cases, and Test 2 fails to reject the zero weights
in all the cases. This suggests that problems with test power are not behind the success in
verifying the exchange regime in these episodes.
As a final exercise to reassess the robustness of our findings, we replace the
Chilean peso and the Israeli shekel with the Swiss franc. We choose the Swiss franc
because Switzerland had a floating regime during the periods of interest. Table 3 shows
that we reject the null hypothesis that the weights are equal to the announced weights. As
reported before, for the same periods, the estimations with the Chilean peso and the
Israeli shekel fail to reject the announced weights. Therefore, one can conclude that
periods 1-2 in Chile and period 2.2 in Israel are verifiable.
Table 3 also shows that the Swiss franc rejects the null hypothesis that the weights
are equal to zero. This rejection does not mean that the Swiss franc is not freely floating
during the periods under consideration. Exchange rates are correlated for other reasons
than government intervention. This tends to yield rejections of zero correlation. The
next section of the paper explores whether it is possible to fail to reject free floating using
the methodology applied for band regimes.
29
IV. Verifying Free-Floating Regimes
We now turn to the verification of free-floating regimes. The concept of
verifiability has a different meaning under floating regimes. Under these regimes,
governments do not make a commitment to a nominal anchor. There are no exchange
rate rules to be verified, except that the exchange rate is floating or that the government is
not intervening in the market. Applying the methodology used for exchange rate bands,
market participants can check if the exchange rate is uncorrelated with major exchange
rates.
A rejection of no correlation is not a rejection of a free-floating regime. Using
observed exchange rate data, it is generally difficult to fail to reject that weights are equal
to zero, either because governments intervene or because exchange rates co-move.
Rejecting zero weights is not necessarily a sign of intervention. However, failing to
reject zero weights is a clear sign of no intervention (or no pegging to other currencies).
We rejected zero weights in the case of the Swiss franc above. Now, we move to the case
of emerging markets.
Before proceeding with the estimations, note that there are other alternative ways
of verifying free-floating regimes. Market participants can essentially check every month
whether the central bank has intervened by seeing whether its reserve holdings have
changed. Also, banks usually know who is participating in the market, so they can tell
the difference between a system where the central bank never intervenes and where it
intervenes occasionally. These methods require some type of additional information,
30
beyond observed exchange rates. In this paper, for ease of comparison with the previous
section, we stick to verifiability just using exchange rate data.
For the verification of floating regimes, we focus on Brazil, Mexico, Peru, South
Korea, and Thailand during specific periods in the 1990s. These countries provide a good
opportunity to compare periods of intervention with periods of free-floating. Brazil,
Mexico, South Korea, and Thailand suffered exchange rate crises in the 1990s, which
forced them to abandon previous exchange rate arrangements and adopt systems
officially described as free-floating by their respective authorities. Therefore, for these
countries we perform the same statistical tests for periods labeled as free floating and for
periods during which other regimes were in operation - namely periods of managed
floating, bands, crawling pegs, and basket pegs. Peru, on the other hand, is an interesting
case because despite declaring a free-floating regime for the entire decade, several papers
have noted that the Peruvian exchange rate has remained surprisingly steady. (See Calvo
and Reinhart, 2000, Hausmann, Panizza, and Stein, 2000, and Edwards and Savastano,
1999, for characterizations of floating regimes.) As in other cases, the observed pattern
calls into question whether the government is in truth following the regime that it says.
Following the methodology used in the previous section, we estimate our basic
equation (1) for each of these countries over the periods noted in Table 4 and dictated by
data availability over the 1990s. We allow for a constant rate of crawl, include as
regressors the five major currencies (US dollar, yen, DM, British pound and French
franc), and as before estimate the model by OLS in first differences.3'
3t As we are only testing the hypothesis of all the weights being equal to zero (a standard goodness of fit
test), we are not concerned by the potential multicollinearity problem.
31
In free-floating regimes, we expect to fail to find any peg of the exchange rate vis-
i-vis foreign exchange rates, so we would expect Test 2 not to reject the null of zero
weights. Table 4 reports the percentage of observations for which the test does reject the
null hypothesis that weights are equal to zero. If the exchange rate is in fact free-floating,
one would expect to find low values in the table, meaning that we only find a relationship
between the local currency and strong currencies in very rare occasions. On the other
hand, when the central bank follows a specific rule relative to one or several strong
currencies, we expect to find large values in the tables (mostly rejections of the
hypothesis that weights are equal to zero).
For ease of comparison, the shaded areas in Table 4 correspond to periods labeled
as free-floating. The results displayed in the table show that in the case of pegs, bands,
and managed floating regimes we reject in almost every sample the null hypothesis that
the weights are equal to zero. The only exception is the case of Brazil, during part of her
period of managed floating. On the other hand, in the episodes declared as free-floating
we generally fail to reject the same hypothesis. There are two exceptions, however: Peru
and most of the post-Tequila period in Mexico.
The samples used for the tests reported in Table 4 start at the beginning of the
year except when a specific date is known for the transition to floating. As an alternative
approach, Figure 5 shows the rejection percentage (right-hand scale) of the zero-weights
hypothesis in rolling samples of 100 observations during the 1990s, together with the
exchange rate vis-A-vis the US$ (in the left-hand scale).
The pattern is similar to that shown in Table 4. It is possible to see how rejection
rates fall dramatically right after a major devaluation in the three countries affected by the
32
late 1990s crisis: Brazil, Korea, and Thailand. In the last two cases, we observe a similar
pattern in the sense that after approximately one year has elapsed since the large
devaluation, rejection rates appear to rise again. In the Mexican case, rejection rates fall
only during short periods after the late 1994 crisis. Much interest has been devoted to the
Mexican free-floating regime that followed the Tequila episode of 1994, particularly
during the stable period starting in late 1995. Edwards and Savastano (1998) found that
the volatility of the exchange during 1996 was not smaller than that of other currencies
widely considered as free-floating, but there seemed to be some form of feedback rule
from the exchange rate to monetary policy.
Finally, it is also clear from the figure that periods of marked stability of the
exchange rate are matched by rejections of the zero-weights hypothesis. Examples of this
are the Brazilian band period (1995-1998), the Korean, Mexican, and Thai pre-crisis
periods, and the Peruvian free-floating regime of the 1990s.
V. Summary and Concluding Remarks
The new conventional wisdom is that intermediate exchange rate regimes, such as
baskets, crawls, and bands, are no longer viable. According to this proposition, countries
are being pushed to the "corners," the extremes of either free floating or firm fixing. We
have argued that a theoretical rationale for this proposition is currently lacking; none of
the candidates offered - the impossible trinity, the dangers of unhedged foreign liabilities,
or government reluctance to abandon ship in time - is quite up to the job. We offered
such a rationale, by introducing the notion of verifiability. By verifiability we mean the
ability of a market participant to infer statistically from observed data that the exchange
33
rate regime announced by the authority is in fact in operation. Verifiability is an instance
of transparency, a means to credibility. Our point is that a simple regime such as a clear
dollar peg, or even a free float, may be more verifiable by market participants than a
complicated intermediate regime.
In this paper we have made a first attempt at assessing empirically the verifiability
of various exchange rate regimes. We first focused on the verification of exchange rate
bands, drawing from the experiences of Chile and Israel. In the case of Chile, when the
band was relatively narrow and the peg involved only the dollar, verification is relatively
easy to achieve. But from 1992 to 1999, when the band became wider and the peg
involved additional currencies, our simple statistical procedures fail to achieve
verification. In the case of Israel, whose basket involved five currencies, two of which
were very strongly correlated, we only achieve verification in a period of relatively
narrow band in which the central parity does not experience sharp realignments, and only
when using a restricted specification involving a reduced number of currencies. In wider-
band periods, and in narrow-band periods with frequent realignments, our procedures
again fail to achieve verification of the regime. This is precisely the result we expected.
On the whole, the results suggest that higher bandwidth, as well as the adoption of
multiple instead of simple basket pegs, and frequent parity realignments, all make more
difficult the econometric verification of the announced regime.
The finding that Chile and Israel fail to reject the announced weights for some
particular periods seems to be an informative test. For the same time periods, we reject
those weights when we replaced the peso and shekel by a randomly generated variable
34
and by the Swiss franc. This means that for narrow bands we are able to verify the
announced exchange rate regime.
We also examined the verifiability of regimes self-declared as free floating in
several Latin American and East Asian countries in the 1990s - Brazil, Mexico, Peru,
South Korea, and Thailand. Even though there are different ways to verify floating
regimes, we followed the same methodology used for bands. We tested whether
supposedly floating exchange rates are correlated with major exchange rates. Our tests
do not show significant evidence against the hypothesis that the exchange rates of these
countries are indeed floating, with the exception of Peru and part of the post-Tequila
period in Mexico. In these cases, we find some evidence that the exchange rate is in fact
moving along with some weighted combination of strong currencies. This appears to
agree with the conclusions reached by other researchers. In sum, we fail to reject free-
floating regimes, although cross-currency correlations tend to reject free-floating - even
when governments do not intervene. Whether these findings can be extended for long
periods of free floating, after the high volatility in the aftermath of crises has vanished, is
a question for future research.
The analysis in the main text was complemented by means of Monte Carlo tests
reported in Appendix 1 assessing the effects of bandwidth and number of currencies in
the basket on the time needed to verify exchange rate bands. On the whole, the results
agree with the above findings. As expected, when the range of variability of the
exchange rate is relatively large, the number of observations needed to verify the regime
increases considerably with the width of the band. The number of observations needed to
differentiate the crawling basket from a random variable in at least half of the samples is
35
under 100 days when the band width is 2%, as it was for Chile from 1985 to 1987, but is
over 500 days when the band width is 10%, as it was for Chile from 1992 to 1998.
Regarding the role of the number of currencies in the basket, we find that moving from a
single-currency parity to a 3-currency basket increases the amount of data needed to
distinguish the basket from a random currency by an extra year's worth of observations
(assuming a 10% band, and again using the criterion of finding statistically significant
weights at least half the time).
If we are right that it is hard for a central bank to establish credibility for its
proclaimed monetary regime without verifiability, then our results confirm that
complicated combinations of baskets, crawls, and bands, are less likely to satisfy
skeptical investors than are simpler regimes. We thus offer a possible and much-needed
rationale for the hypothesis of the vanishing intermediate exchange rate regime.
36
References
Benassy-Quere, Agnes, 1999, "Exchange Rate Regimes and Policies: An Empirical
Analysis," in Exchange Rate Policies in Emerging Asian Countries, edited by Stefan
Collignon, Jean Pisani-Ferry, and Yung Chul Park (Routledge: London), 40-64.
Calvo, Guillermo and Carmen Reinhart, 2000, "Fear of Floating," mimeo, University of
Maryland.
Council on Foreign Relations, 1999, Safeguarding Prosperity in a Global Financial
System: The Future International Financial Architecture, published by Institute for
International Economics, Washington, DC, 1999.
Crockett, Andrew, 1994, "Monetary Policy Implications of Increased Capital Flows,"
Changing Capital Markets: Implications for Monetary Policy, Symposium sponsored
by Federal Reserve Bank of Kansas City, Jackson Hole, August 1993.
The Economist, "Global Finance: Time for a Redesign?" January 30, 1999, p. 1-18.
Edwards, Sebastian and Miguel Savastano, 1998, "The Morning After: The Mexican
Peso in the Aftermath of the 1994 Currency Crisis" NBER Working Paper No. 4661.
April.
Edwards, Sebastian and Miguel Savastano, 1999, "Exchange Rates in Emerging
Economies: What Do We Know? What Do We Need to Know?" NBER Working
Paper No. 7228, July.
Eichengreen, Barry, 1994, International Monetary Arrangements for the 21st Century,
Brookings Institution, Washington DC.
Eichengreen, Barry, 1999, Toward a New Financial Architecture: A Practical Post-Asia
Anda, Institute for International Economics, Washington, DC.
Frankel, Jeffrey, 1993, "Is Japan Creating a Yen Bloc in East Asia and the Pacific?" in
Regionalism and Rivalry: Japan and the U.S. in Pacific Asia, edited by Jeffrey
Frankel and Miles Kahler, University of Chicago Press, Chicago, 1993, 53-85.
Frankel, Jeffrey, 1999, "No Single Exchange Rate Regime is Right for All Countries or at
All Times," Graham Lecture, Princeton University Press. NBER Working Paper No.
7338.
Frankel, Jeffrey, Sergio Schmukler, and Luis Serv6n, 2000, "Verifiability and the
Vanishing Intermediate Exchange Rate Regime," working paper.
Frankel, Jeffrey, and Shang-Jin Wei, 1994, "Yen Bloc or Dollar Bloc? Exchange Rate
Policies of the East Asian Economies" in Macroeconomic Linkages: Savings.
Exchange Rates, and Capital Flows, NBER - East Asia Seminar on Economics,
Volume 3, Takatoshi Ito and Anne Krueger, editors, University of Chicago Press,
1994.
Frankel, Jeffrey, and Shang-Jin Wei, 1995, "Emerging Currency Blocs," in The
International Monetary System: Its Institutions and its Future, edited by Hans
Genberg, Springer, Berlin, 1995, 111-143.
Hausmann, Ricardo, Ugo Panizza, and Ernesto Stein, 2000, "Why Do Countries Float the
Way they Float?" mimeo, Inter-American Development Bank.
Krugman, Paul, 1991, "Target Zones and Exchange Rate Dynamics," Quarterly Journal
ofEconomics CVI, 669-682.
Larrain, Felipe, and Andres Velasco, 1999, "Exchange Rate Policy for Emerging
Markets: One Size Does Not Fit All," July, forthcoming, Essays in International
Fiaag, Princeton University Press.
37
Minton-Beddoes, Zanny, 1999, "From EMU to AMU? The Case for Regional Currency
Blocs," Foreign Affairs.
Obstfeld, Maurice, and Kenneth Rogoff, 1995, "The Mirage of Fixed Exchange Rates,"
NBER Working Paper No. 5191.
Stein, Ernesto and Jorge Streb, 1998, "Political Stabilization Cycles in High Inflation
Economies," Journal ofDevelopment Economics, 56, 159-180, June.
Stein, Ernesto and Jorge Streb, 1999, "Elections and the Timing of Devaluations,"
working paper, InterAmerican Development Bank.
Summers, Lawrence, 1999a, testimony before the Senate Foreign Relations
Subcommittee on International Economic Policy and Export/Trade Promotion,
January 27.
Summers, Lawrence, 1999b "Building an International Financial Architecture for the 21st
Century," Cato Journal, 18, no. 3, 321-330.
38
Appendix 1: Monte Carlo Simulations
We turn now to the Monte Carlo simulations, which offer a more general testing
ground for verifiability of intermediate regimes. For our experiments, we generate 1,000
samples according to the simple model described by equation (1), using for the baskets
actual data on the exchange rates of the major currencies (valued in terms of the GDP-
weighted numeraire). We use daily data between February 1986 and September 1999.
The parameters of the data-generating process are c (level of exchange rate), d (yearly
rate of crawl), w;... w3 (weights on US$, DM, and JY), a (standard deviation of the error
term), and to (initial observation). We use a log linear version of equation (1). The log
error term is generated as i.i.d. normal with mean zero. Based on this basic framework,
we study the effect of different model specifications on the amount of time to reject our
proposed null hypotheses. For each sample, we calculate the number of observations
necessary to obtain 10 rejections of the null hypothesis that both the weights and the rate
of crawl are zero (Test A) and the null hypothesis that the weights are zero (Test B).
Role ofBand Size
Clearly, it should be harder to verify a basket regime with a wide band than one
with a narrow band, and harder to verify a basket regime with a loosely managed float
(i.e., a small tendency to intervene when the exchange rate drifts from the parity) than
another with a tightly managed float (a strong tendency to intervene). To verify the role
of band size in determining tne amount of information needed to reject the proposed null
hypotheses, we generate sets of 1,000 samples. Each set has a different standard
deviation of the underlying disturbance (a), representing different band sizes.
39
For this exercise, we generate the samples using a level parameter equal to 1, a
rate of crawl of 1% per year, and equal weights for all major currencies, and starting from
observation 1 (2/24/1986). We let the standard deviation a vary from 1% to 10%. In this
regard, recall that 2% was the width of Chile's band from mid-1985 to 1987, and 10%
was the width of the band during the period 1992-97. For purposes of comparison, 24%
was the width of the ERM target zone followed by many European countries up until
1992 (and still followed today by Denmark), 6% is the width of the ERM target zone
followed by Italy and the United Kingdom up to 1992, and 15% is the width of the ERM
zone for France and others from 1992 until the beginning of EMU in January 1999.
The results appear in Appendix Figure 1. The graphs plot the quantiles of Test A
and Test 2 against the standard error (a) used to generate the samples. Each line
corresponds to one quantile, and depicts the number of observations needed to achieve
rejection of the null hypothesis (at the 5% level) in x% of the 1,000 samples-where x is
the quantile in question.
As expected, the graphs show that, for both tests, the number of observations
needed to reject the null of zero weights and rate of crawl in any given percentage of the
samples rises steadily with Y. This is reflected by the fact that the lines corresponding to
the various quantiles have positive slopes. In other words, wider bands make it more
difficult for investors to reject specific hypotheses concerning the weights of the central
parity-they need more time to get an accurate assessment of the parameter values. And
the additional time needed is not negligible. For Test B, for example, the number of
observations needed to reject the null in 50% of the samples ranges from under 100 days
40
for an (old-) EMU-sized band (2% width) to over 500 for a Chilean-sized one (10%
width).
Role ofNumber of Currencies in Basket
Intuitively, the larger the number of unknown parameters that need to be
estimated, the harder it should be to verify that the data match the announced policy
regime. This applies not only to the number of currencies in the basket, but also to the
presence of a non-zero rate of crawl.
To verify this assertion, we next examine the impact of different basket sizes on
the amount of information needed to reject the nulls underlying Tests A and B. For this
purpose, different numbers of currencies were included in the Data Generating Process
(DGP). We construct a simple peg (the US dollar), a two-currency basket (the US dollar
and the Deutsche mark), and a three-currency basket (the dollar, the Deutsche mark, and
the Japanese yen). In each basket the currencies are equally weighted. The other
assumptions are like in the previous exercise.
The results are portrayed in Appendix Figure 2. To avoid cluttering the pictures,
only the medians of Test A and Test B (defined as before) are presented. They are
plotted against alternative values of the standard deviation of the random disturbance
assumed in the simulation.
As expected, increasing the number of currencies in the basket shifts the quantile
lines upward, reflecting the fact that for any given value of the standard deviation more
observations become necessary to reject the null hypotheses. As before, the increase in
information requirements is sometimes substantial. For example, with a bandwidth of
41
10% (as observed in Chile in recent times), moving from a single to a 3-currency basket
raises the 50% quantile of Test B by over 200 observations-implying that an extra year
of data becomes necessary to reject the null hypothesis.
Role of Rate of Crawl
What about the rate of crawl? Intuitively, its value should have little consequence
for Test B, which is concerned only with the basket weights. However, for Test A it can
make a big difference-rates of crawl further away from zero must help reject the null
hypothesis more quickly, since the latter involves a zero rate of crawl.
This is verified in Appendix Figure 3, which shows the effects of different rates of
crawl on the verification time, as reflected by the 50% quantile of Test A and Test B. For
a given value of a, we generate different samples assuming increasing rates of crawl. As
expected, the time to reject Test A (measured by the left scale) declines steadily as the
rate of crawl rises away from zero, while the time to reject Test B (measured by the right
scale) shows only modest variation.
Role ofPeriod
The power of these tests depends on the precision of the parameter estimates,
itself given by the noise-to-signal ratio-or the relative size of the variances of the
dependent and independent variables. When the variance of the dependent variable is
large relative to the variance of the independent variable, the estimates are imprecise and
it is difficult to reject a given null hypothesis. Since these relative variances are not
42
constant over time, the verifiability of a given model may depend on the specific time
period over which it is observed.
This can be assessed using data from different time periods to carry out the Test A
and B. Since our experiments use actual data on the hard currencies, any differences in
time to reject Test A and B across replications, using hard-currency data from different
time periods, should be attributed to changes over time in the variance-covariance matrix
of the hard currencies.
The results of such an experiment are reported in Appendix Figure 4, which
shows the median values of the time to reject Test A and B, obtained when the
simulations use hard-currency data from different periods in 1986-96 and assuming a
three-currency basket with equal weights.
To facilitate the interpretation of the results, we also show in the figure a measure
of the variance of the hard currencies-specifically, the inverse of the average of their
standard deviations. As the graph shows, variability of the hard-currency exchange rates
was particularly high in the first and fourth periods considered. This results in a clear
reduction in time to reject Test A and B in such periods, relative to the rest.
43
Appendix 2: Construction of Numeraire and Estimated Models
In this appendix, we describe how we constructed the weighted basket numeraire
and the precise models we estimated in the case studies of Chile, Israel, and the floating
regimes.
Construction of the Weighted Basket Numeraire
The numeraire was constructed using the bilateral exchange rates of seven strong
currencies weighted by the GDP share in 1992. The specific units of each currency in the
basket were chosen so that the basket is valued in 1 US dollar on January 2, 1990. The
value, in US$, of the weighted basket (WB) at a given point in time is:
WBt = a, + a2 DMt + a3 BPt + a4 FFt + as JYt + a6 CD, + a7 II4 (Al)
such that all the exchange rates are expressed in US$ over local currency. IL stands for
the Italian lira and CD for the Canadian dollar.
Using 1991 GDP at market prices (constant 1995 US$) data from the World
Development Indicators report, we defined the following weights:
Currency US$ DM BP FF JY CD IL
Weight 35.72% 13.01% 5.79% 8.34% 28.25% 2.97% 5.92%
These weights represent the share of the cost of each currency in the total value of
the basket at the reference date (in this case 1/2/1990). Based on this definition, we can
calculate the units of each currency (a, ... a7):
wi= a / WBo ai= w,*WBo (A2)
W2 a2 DMo/ WBo 4 a2 W2* WBo / DMo
44
W3= a3 BPo/ WBo 4 a3 = w3* WB0 / BPO
The resulting units are the following:
Currency US$ DM BP FF JY CD IL
Units (a) 0.3572 0.2192 0.03566 0.4803 40.707 0.0499 91.245
Using these units and equation (Al), we obtained the value of the weighted basket
at any point in time. In order to obtain any exchange rate as a function of this numeraire,
we just multiply the exchange rate of the local currency in terms of the US$ by WBt.
Estimation of Basket Weights in Case Studies of Chile, Israel and free-floating regimes
In the two case studies undertaken in this paper, the baskets were, in fact,
constructed in a similar way to our weighted basket numeraire. When the basket is
defined for the first time, some strong currencies are selected. Initial weights are
calculated according to trade weighs. The units of each currency that are used for the
calculation of the basket from that moment on are defined according to the procedure
described above. The units remain constant over time, but the actual weights of each
currency depend on the bilateral exchange rates movements.
In order to complete the definition of the exchange rate regime, a path must be
defined for the value of the basket (Be). In some cases, this value is to remain constant, to
increase at a constant rate or to vary with internal or external inflation rates. The local
exchange rate, in the case of a basket peg, is determined by the equality of the
45
predetermined path for the value of the basket (B) and the actual value of the basket,
given the units chosen, the bilateral foreign exchange rates and the local rate:
Bt = bi St + b2 St*DII + b3 St*BPt + b4 St*FFt + b5 St*JYt,
where St represents the local currency (in this example the Israeli Shekel vis-h-vis the
US$). Using a formula analogous to (A2), we can express the previous equation in terms
of the original weights:
B/Bo= w, St/SO+ W2 (StDM)/( SODMO)+ w3 (St*BPt)/( SoBPO)+ w4 (St*FFt)/( SoFFo)+ w5
(St*JYt)/( SoYo).
Rewriting the previous expression with the local currency on the LHS, we have:
So/St = w, Bo/Bt + w2 Bo/Bt*DMt/DMo + w3 Bt/B*BPt/BPO + W4 B0Bt*FFt/FFo + w5
Bo/B *JYt/JYo.
Finally, multiplying both sides of the previous equation by WBo/WBt we obtain
an equation where all the exchange rates are expressed in terms of the numeraire.
Redefining variables, we obtained the following equation:
Y, = w, XUSt + w2 XDM + W3 XBPt + W4 XFFt + w5 XJYt. (A3)
In the case of basket bands, the actual value of the basket is allowed to fluctuate
around the predetermined path, usually with a given percentage above or below (the band
width). In those cases, we refer to the reference path as central parity. Equivalently, the
band defined for the basket implies an analogous band for the local exchange rate vis-A-
vis the numeraire.
In our analysis, we try to recover the original announced weights from the
observed exchange rate, the bilateral exchange rates between the strong currencies and
the predetermined path for the central parity. The movements of the observed exchange
46
rate inside the band give rise to an error term. A stationarity assumption is certain to fail
in a time series for the level of the exchange rate. A simple way to deal with this is to
work with first differences. The basic equation we estimate in this paper, expressed in
first differences, is the following:
AY, = do + w1 AXUSt + W2 AXDM + W3 AXBPt + W4 A Ft 5 AXJ-Yt + et. (A3)
For the Chilean case, in the first three periods we included only the US$ and in the
following four periods, the US$, the DM, and the JY.
As described in the next section, we finally used a restricted version of equation (A3) for
the case studies of Chile and Israel but in the case of the free-floating countries, we
estimated equation (A3) without worrying about the multicollinearity problem.
Dealing with Multicollinearity
As mentioned in the text, strong correlation between the included regressors
(particularly between AXDMt and AXFFt and between AXUSt and AXJYt in some
periods) gave rise to a significant multicollinearity problem. In order to deal with it, we
combined pairs of regressors, using the ratio of announced weights:
AYt = do + w, (AXUSt + w50 / w10 AXJYt) + w2 (AXDM + W40 / W20 AXFFt)+
w3 AXBPt + et, (A5)
where w10, w20, w40 and w50 represent the announced weights (which are known
constants). With this specification, we were able to identify only the following
parameters: do, wI, w2 and w3.
47
Figure 1: Chilean Exchange Rate and Exchange Rate Band - 1986-1999
Chilean Peso Relative to Weighted Basket
105
Period 1 Period 2 Period 3
band band band
width =2% width=3% width=5%
85
75
65
55
Period 4 Period 51 Period 6 Period 7
band band band band
width width width width
=10% =10% =10% =12.5%
25-r -
n_ In 1ý
oot- t. r 00 0 00 0 0ý äi, c,00 0 - - e l e n en f l f 0 ' 0 f 0 0 00 c0
00~~~~ 00 00 OP 00 00 <30 00 00 00 00 0 cO ý0 ~ 6 \ 0~0 ~ 0 ~ 0 ~ 0 ~ O~0 ' 0 ~ 0 ~ 0
t
Figure 2: Israeli Exchange Rate and Exchange Rate Band - 1989 - 1999
New Israeli Shequel Relative to Currency Basket
5.95
basket peg Period 1 Period 2.1 Period 2.2
5.45 band No Crawl With Crawl
witdth Band Band
4.95 - =3% width=5% width=5%
4.45
3.95
3.45
2.95
2.45 Period 3 Period 4 Period 5
band band expanding
width width band width
1.95 =7% =7% -15%
1.45 - 1 . I 1 1 1.
',0 '.0 r- t- t- 00 00 00 2h, C> O-N C> 0: < cq M en VI~ tn tr .0 ',0 ko t r - t-0 00 cp
00000000 oo O000 c 0ý 0ý l ' ,s ýc
1ý C1 1 C1 1 C1 1 ch
e~o6~ 6,!. ~O> ! O 01~ 6 . bl'.> - bQ 1 bl 0 . bl u. ~o6 s ~»6 ~! ~o6 ~ ~a b.
Ini> ~ 4 0~> O ~ ~ i >~ > ~ 4
Figure 3: Chilean Peso and Central Parity - Scatter Plots
(Chilean Peso / Weighted Basket)
280 550
260.
240. 500-
j 220 -
450-
200 -
180. 400
160 t
Perod Period 4
140 : , , ., 350
140 160 180 200 220 240 260 280 350 400 450 500 550
Clkan Peso Cilean Peo
270 520
500
260
480 -1 1
250
460
240 440-
2304 Period 2 401Peri 'od 5
230 240 250 260 270 420 440 460 480 500 520
Chlelan Peso
450 520
400 500l
-350 c 480
0. 0.
5 300 460
250 440-
Period 3 Period 6
200 . , , , 420-
200 250 300 350 400 450 420 440 460 480 500 520
Chilean Peso Chian Peso
500
480
460
440
420
Period 7
400·
400 420 440 460 480 500
Chilan Pes
Figure 4: Israeli Shekel and Central Parity - Scatter Plots
(Israeli Shekel / Weighted Basket)
2.05 3.8
2.00- 3.7
1.95. 3.6
S1.90 3.5
1.85. 3.4
1.80 3.3
Peiod 1 Peiod 3
1.75 3.2
1.75 1.80 1.85 1.90 1.95 2.00 2.05 3.2 3.3 3.4 3.5 3.6 3.7 3.8
lendi Sh9d landi Shd
2.6 4.0
2.4. 3.8.
2.2. 3.6
0 0
2.0 3.4
Period 2.1 Ptiod 4
1.8 3.2 ,
1.8 2.0 2.2 2.4 2.6 3.2 3.4 3.6 3.8 4.0
Isni Shcd Isri Shdcc
4.0 5.0
3.5 4.5
1+
& 3.0 & 4.0
2.5 3.5
Period 2.2 Priod 5
2.0 3.0
2.0 2.5 3.0 3.5 4.0 3.0 3.5 4.0 4.5 5.0
-Isndi Sh&d cnd Shed
5.0
4.8
4.6
& 4.4
4.2
4.0
Priod 6
3.8
3.8 4.0 4.2 4.4 4.6 4.8 5.0
budi Shed
Figure 5: Exchange Rates Against US Dollar and Percentages of Rejections
Rejection Rate Corresponds to Testing HO: Weights=O
Model Tested Is First Differences of Domestic Currency on Major World Currencies
(Exchange Rates expressed as Domestic Currency / US$ )
Brazilian Real S. Korean Won
2 1 2W0O
1.8 0.909
Rejecti n Rate (Right Scale)
1.8 . 2D
14 0.7 Rejection Rate (Right Scale) o.
1.2 0.6 1500 0.6
1 ange Rate 0. o
0.8 04 10004
0.6 0.3 03
0.4 0.2 SO Exchange Rate o 2
11 .2 0.101
201 0
Mexican Peso Thai Bat
12 1 801
71-7 0.9 s Rejectin Rate (Right Scale)0.
Rejection Rate (Right Scale)
07 40
0.6 0.
8 0.5 30 0.0
4-0.4 20change e 0.4
0.3 0.3
- - -hanRge, Rate 0.2 -
2 10
0.1 0.1
0 0 0 0
-AB
Peruvian Sol
4 4
0.8
3.0
0.8
0.70
2.5 C.A
2 Exchange Ra a 0.6
1.6 0.4
0.3
10
0.2
o PRejection Rate (Right Scale) 0.1
0
Table 1.a: Chilean Exchange Rate
Description of Exchange Rate Regimes
Period Weights of Central Parity
Begin End Number of Band U.S. Deutsche Japanese
Observations Width (+/-) Dollar Mark Yen
1 February 24, 1986 January 4, 1988 434 2% 100% 0% 0%
2 January 5, 1988 June 5, 1989 340 3% 100% 0% 0%
3 June 6, 1989 April 2, 1991 449 5% 100% 0% 0%
4 July 1, 1992 October 31,1994 580 10% 50% 30% 20%
5 November 30, 1994 November 30, 1995 236 10% 45% 30% 25%
6 December 1, 1995 January 20, 1997 264 10% 45% 30% 25%
7 January 21, 1997 June 24, 1998 326 12.5% 80% 15% 5%
Only periods with at least 250 observations are listed. During these periods there were no changes in the exchange
rate regime. The bands' width, the weights of the central parity, and the level of the central parity were held
constant. The periods excluded include discrete devaluations /revaluations of the central parity. For more details
about the exchange rate regimes in Chile, see Appendix table. The announced weights correspond to the relative
importance of the respective currency in the first day when any new weight is defined. With relative movements
between the foreign currencies, those weights vary with time. The estimation procedure, however, is designed to
estimate the initial weight.
Table 1.b: Chilean Exchange Rate
Percentage of Observations for Which Null Hypothesis Is Rejected (1%)
Period Obs OLS OLS Precision
First Differences First Differences ilw-wol
Unrestricted Model Restricted Model
Test 1 Test 2 Point Test 1 Test 2 Point OLS OLS
Ho: Ho: Estimate Ho: Ho: Estimate First First
Weights Weights WusS Weights weights Wuss Differences Differences
=0 (s.e.) - 0 (s.e.) Unrestricted Restricted
announe announcMoe Mdl
~flfOUfC ~fflOflCModel Model
1 50 0 100 0.94 (0.06) 0.06
US$ band 100 0 100 0.90(0.07) 0.10
width=2% 200 0 100 0.92 (0.05) 0.08
W1ss=1
2 50 0 100 1.27 (0.19) 0.27
US$ band 100 0 100 1.09(0.13) 0.09
width=3% 200 0 100 1.00 (0.07) 0.00
Wuss=1
3 50 21 92 0.80 (0.09) 0.20
US$ band 100 22 97 0.85 (0.05) 0.15
width=5% 200 '34 98 0.90 (0.07) 0.10
WUSS=1
4 50 100 100 1.10(0.15) 100 100 1.08(0.15) 0.90 0.87
basket 100 100 100 1.10 (0.09) 100 100 1.09 (0.08) 1.08 0.90
width=10% 200 100 100 1.04 (0.06) 100 100 1.04 (0.06) 1.06 0.87
Wuss=0.5
5 50 68 68 1.01 (0.55) 68 79 1.38 (0.26) 1.37 1.07
basket 100 86 86 1.67 (0.28) 86 91 1.02 (0.09) 1.69 0.95
width=10% 200 94 94 1.19 (0.22) 94 96 1.07 (0.08) 1.19 0.97
Wuss=0.45
6 50 58 50 0.37 (0.44) 45 45 0.95 (0.21) 1.44 0.86
basket 100 82 78 0.81 (0.25) 76 76 1.10 (0.12) 1.31 0.98
width=10% 200 91 90 1.02(0.17) 89 89 1.12(0.08) 1.27 1.00
Wuss=0.45
7 50 13 100 1.08 (0.14) 26 100 0.97 (0.07) 0.38 0.25
basket 100 63 100 1.14(0.11) 68 100 1.03(0.04) 0.44 0.33
width=12.5% 200 82 100 0.83 (0.16) 85 100 0.95 (0.07) 0.38 0.31
Wuss=0.8
In periods 1-3, only the US$ was considered in the estimation. Precision is calculated as the sum of
absolutes deviations of the estimated weights at 50, 100 and 200, with respect to the announced weights. In
the restricted model, for periods 4 to 7, the JY and the US$ were combined in one variable, using the relative
announced weights. See Appendix 2 for details.
Table 2.a: Israeli Exchange Rate
Description of Exchange Rate Regimes
Period Weights of Central Parity
Begin End Number Band U.S. Deutsche Japanese French British
of Width Dollar Mark Yen Franc Pound
Observations (+/-)
1 January 3, February 291 3% 60% 20% 5% 5% 10%
1989* 28, 1990
2.1 March 1, December 443 5% 60% 20% 5% 5% 10%
1990 16, 1991 no crawl
2.2 December May 30, 851 5% 60% 20% 5% 5% 10%
17, 1991 1995 crawling
3 May 31, April 29, 222 7% 54.8% 24.2% 1% 5.6% 8.3%
1995 1996
4 April 30, June 17, 273 7% 60.3% 21% 5.6% 5.1% 8%
1996 1997
5 June 18, December 374 15%** 60.3% 21% 5.6% 5.1% 8%
1997 31, 1998
* The basket was introduced with the presented weights in August, 1986, but the exchange rate was allowed
to vary around a 3% band in January 1989.
** Widening band designed to reach 15% by end of 1997.
Table 2.b: Israeli Exchange Rate
Percentage of Observations for Which Null Hypothesis Is Rejected (1%)
Period Obs OLS OLS Precision
First Differences First Differences Y1'w-wo1
Unrestricted Model Restricted Model
Test 1 Test 2 Point Test 1 Test 2 Point OLS OLS
Ho: Ho: Estimate Ho: Ho: Estimate First First
Weights Weights Wuss Weights weights Wuss Differences Differences
=0 (s.e.) =0 (s.e.) Unrestricted Restricted
announc announc Model Model
1 50 29 92 -1.37 (0.40) 0 89 0.64 (0.10) 3.94 0.06
basket 100 69 97 -2.52 (0.25) 0 95 0.45 (0.10) 6.19 0.29
width=3% 200 86 98 0.43 (0.02) 44 98 0.43 (0.02) 0.48 0.27
Wus$=0.6
2.1 50 100 100 -5.10 (0.24) 0 0 0.31 (0.34) 11.49 0.79
basket 100 100 100 -5.30 (0.15) 0 7 -0.12 (0.25) 11.98 0.91
width=5% 200 100 100 0.15 (0.07) 46 40 0.09 (0.06) 1.33 0.68
(w/o crawl)
Wuss=0.6
2.2 50 0 89 -0.54 (0.36) 0 97 0.53 (0.07) 2.42 0.14
basket 100 0 95 0.01 (0.31) 0 99 0.57 (0.08) 1.55 0.11
width=5% 200 :2 98 0.22 (0.13) 0 99 0.55 (0.05) 0.80 0.07
(with crawl)
Wuss=0.6
3 50 63 100 -1.28 (0.44) 39 100 0.60 (0.15) 5.23 0.29
basket 100 84 100 -0.62 (0.30) 67 100 0.84 (0.08) 3.89 0.47
width=7% 200 93 100 -1.52 (0.21) 85 100 0.73 (0.08) 6.37 0.36
Wuss=0.548
4 50 100 100 -3.59 (0.45) 0 0 0.53 (0.25) 11.35 0.82
basket 100 100 100 -2.89 (0.32) 55 55 0.55 (0.17) 9.54 0.55
width=7% 200 100 100 -2.97 (0.25) 76 79 0.47 (0.12) 9.30 0.40
Wuss=0.603
5 50 100 100 -5.54 (0.46) 0 0 0.91 (0.30) 15.39 0.67
basket 100 100 100 -4.52 (0.36) 15 51 0.97(0.17) 13.18 0.62
width-15% 200 100 100 -4.36 (0.28) 60 77 0.96 (0.10) 12.62 0.50
expanding
band
Wuss=0.603
Precision is calculated as the sum of absolutes deviations of the estimated weights at 50, 100 and 200, with
respect to the announced weights. In the restricted model, the DM and the FF on the one hand, and the US$
and the JY on the other, were combined using the relative announced weights, to form new variables. See
Appendix 2 for details.
Table 3: Swiss Franc and Randomly Generated Variable as Dependent Variable
Percentage of Observations for Which Null Hypothesis Is Rejected (1%)
Swiss Franc Random
Period Obs Test 1 Test 2 Test 1 Test 2
H0: Ho: Ho: Ho:
Weights = Weights Weights= Weights
announced = 0 announced = 0
Announcement: 50 100 100 97 0
Chile-Period 1 100 100 100 99 0
200 100 100 99 0
Announcement: 50 100 100 89 0
Chile-Period 2 100 100 100 95 0
200 100 100 98 0
Announcement: 50 100 100 76 0
Israel-Period 2.2 100 100 100 90 0
200 100 100 95 0
The rejection percentages were recalculated for the referred country periods, replacing in each case
the local currency with the Swiss franc and a randomly generated data. Fictitious data were
generated following an AR(1) process with parameters obtained by fitting an AR(1) model to the
original dependent variable.
Table 4: Floating Exchange Rate Regimes - First Differences Linear Model
Percentage of Observations for Which HO: Weights=O Is Rejected (1%)
Brazil
obs. 1992 1993 1994 1995 1996 1997 1998 1999
Managed Floating Band Free Floating
20 0 0 0 0 90.9 100 90.9 0
50 0 0 0 73.2 97.6 100 97.6 0
100 0 41.8 2.2 87.9 98.9 100 98.9 0
150 0 62.4 1.4 92.2 99.3 100 99.3 0
200 0 72.3 1 94.2 99.5 100 99.5
Mexico
obs. 1991.) 1991 1992 1993 1994 1995 1996 1997 1998 1999
Cra%k ling Peg Free Floating
20 100 72.7 100 100 100 0 0 18.2 0 36.4
50 100 92.7 100 100 95.1 29.3 2.4 29.3 58.5 78
100 100 96.7 100 100 97.8 60.4 56 68.1 48.4 90.1
150 100 97.9 100 100 98.6 74.5 71.6 79.4 47.5 93.6
200 100 98.4 100 100 99 81.2 79.1 84.8 61.3 -
Peru
obs. 1993 1994 1995 1996 1997 1998 1999
Free Floating
20 0 9.1 0 0 9.1 90.9 0
50 51.2 70.7 14.6 63.4 56.1 97.6 70.7
100 78 86.8 61.5 83.5 79.1 98.9 68.1
150 85.8 91.5 75.2 89.4 86.5 99.3 79.4
200 89.5 93.7 81.7 92.1 . 99.5
S. Korea
obs. 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Managed Floating Free floating
20 100 90.9 100 63.6 45.5 54.5 18.2 18.2 0 0
50 100 97.6 100 90.2 85.4 87.8 61 26.8 0 0
100 100 98.9 100 95.6 93.4 94.5 82.4 67 0 0
150 100 99.3 100 97.2 95.7 96.5 88.7 78.7 14.2 32.6
200 100 99.5 100 97.9 96.9 97.4 91.6 84.3
Thailand
obs. 1990 1991 1992 1993 1994 1995 1996 1997 (1"halO 1997 (2n" half 1998 1999
Basket Peg Free Floating
20 100 90.9 81.8 100 100 100 63.6 100 0 0 0
50 100 97.6 95.1 100 100 100 90.2 100 0 0 0
100 100 98.9 97.8 100 100 100 95.6 100 0 0 9.9
150 100 99.3 98.6 100 100 100 97.2 . . 0 41.8
200 100 99.5 99 100 100 100 97.9 . 0
Appendix Figure 1: Monte Carlo Simulations-Role of Band Size
Quantiles of Test A (Weights=Rate of Crawl=O)
350-
300-
250-
200-
150-
0
- 100-
50-
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Sigma
--+ 5% -* 25% A+- 50%/6 75% W-+ 95%
Quantiles of Test B (Weights=O)
1200 -
1000 -
800 -
600 -
C' 400-
200
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Sigma
---- 5% -U- 25% --- 50% 75% -)- 95%
Parameters of estimations: 500 samples; weights on dependent variables 1/3 for US$, DM, and JY; initial
observation February 24, 1986; constant=1; rate of crawl=0.10; sigma--{0.01; 0.028; 0.046; 0.064; 0.082;
0.1}. Quantile values are calculated for the first 10 rejections.
Appendix Figure 2:
Monte Carlo Simulations-Role of Number of Currencies in Basket
Quantiles of Test A (Weights=Rate of Crawl=O)
350-
300-
250-
200-
150-
100-
50-
0-
0.01 0.048 0.086 0.124 0.162 0.2
Sigma
--- US only --- US + DM -A--- US + DM + JY
Quantiles of Test B (Weights=O)
700-
600-
500-
400-
300-
200-
100-
0 - III-I
0.01 0.048 0.086 0.124 0.162 0.2
Sigma
US only ---- US + DM ---- US + DM + JY
Parameters of estimations: 500 samples; initial observation February 24, 1986; constant=1; rate of
crawl=F0.10; sigma= {0.01; 0.048; 0.086; 0.124; 0.162; 0.2}; weights on dependent variables are 1, 1/2, and
1/3, for 1, 2, and 3 currencies in the basket respectively. Quantile values are calculated for the first 10
rejections.
Appendix Figure 3: Monte Carlo Simulations-Role of Rate of Crawl
Median Valules for Tests A & B
Test A Test B
400 - 650
350 - 600
S300 550
0 250 -
0200- 500
150 - 450
* 100-
50 - 400
0 350
0 0.1 0.2 0.3 0.4 0.5
Crawl
---Test A -+-- Test B
Test A: Weights=Rate of Crawl=O Test B: Weights=0
Parameters of estimations: 500 samples; initial observation February 24, 1986; constant=1; rate oferawl=
{0.01; 0.108; 0.206; 0.304; 0.402; 0.5}; sigma=O.1; weights on dependent variables are equal to 1/3 for each
currency in the basket. Median values are calculated for the first 10 rejections.
Appendix Figure 4:
Monte Carlo Simulations-Role of Period and Variability of Regressors
Median Values for Test A
180 -
160-
140-
120-
100-
80 -
60 -
40-
20
Mar-86 Mar-88 Mar-90 Mar-92 Mar-94 Mar-96
M Inverse Variance of US$, DM, JY Median Test A
Median Values for Test B
180 -
160-
140-
120 -
100--
80 --
60--
40
20
0
Mar-86 Mar-88 Mar-90 Mar-92 Mar-94 Mar-96
Inverse Variance of US$, DM, JY Median Test B
Parameters of estimations: 500 samples; weights on dependent variables 1/3 for US$, DM, and JY;
constant=1; rate of crawl=0.10; sigma=0.005. Median values are calculated for the first 10 rejections.
"Inverse Variance" is the inverse of the average standard error of the three currencies, for the first 50
observations of each respective period.
Appendix Table A.1: Exchange Rate Policy in Chile 19982-1999
Date Policy
September, 1982 * Daily devaluations in line with domestic inflation in the preceding month
minus an estimate of external inflation
August 1, 1984 * Band of +/- 0.5%
June, 1985 * Widening to 2%
January 5, 1988 * Widening to 3 %
June 6, 1989 * Widening to 5%
* Accelerate the rate of real depreciation, which was achieved by reducing the
estimate of international inflation
* Adjustment of central parity: previous month inflation minus estimated
international inflation
April 3, 1991 * 2% revaluation of central parity
January 23, 1992 * Band widened to 10% (from +1-5%)
* Discrete 5% revaluation of central parity
March, 1992 * Managed floating is authorized
July, 1992 * Central parity: 50% U.S. dollar, 30% Deutsche mark, 20% Japanese yen
November, 1994 * Central parity: 45% U.S. dollar, 30% Deutsche mark, 25% Japanese yen
November 30, 1994 * 9.66% revaluation of central parity
December, 1995 * 2% revaluation; 2% annual revaluation
January 21, 1997 * 4% revaluation of central parity
* New band: +/- 12.5%
* New weight: 80% U.S. dollar, 15% Deutsche mark, 5% Japanese yen
June 25, 1998 * 2% annual revaluation
* New asymmetric band: +2%, -3,5%
September 16, 1998 * New band: +/- 3.5%
* The band is widened progressively until it accumulates and additional 1.5%
in each extreme , such that by the end of the year the band would be +/- 5%
* New estimates of annual international inflation from 2.4% to 0% for the rest
of the year
* The relevant internal inflation rate is the inflation target and not past
inflation
December 23, 1998 * New band: +/-8%
* No change in other parameters (central parity adjusts only with internal
inflation and the band continue widening daily by 0,013575%)
January 1, 1999 * Deutsche mark is replaced by the euro, with the same weight
September 2, 1999 * Free floating with managed intervention only in exceptional cases
* Release of new information regarding interventions in the foreign exchange
markets
Source: Central Bank of Chile, Hussey and Morand (1996), and Vergara (1994)
Appendix Table A.2: Exchange Rate Policy in Israel 1986-1999
Date Policy
August 1, 1986 * Beginning of basket peg without crawl
* Initial weights: 60% US$, 20% DM, 10% BP, 5% FF, 5% JY
January 3, 1989 * Central parity is devaluated 13% in a week
* A ±3% band is introduced
June 23, 1989 * Midpoint raised by 6%
March 1, 1990 * Midpoint raised by 6%
* Band widened to ±5%
September 10, 1990 * Midpoint raised by 10%
March 11, 1991 * Midpoint raised by 6%
December 17, 1991 * Introduction of crawling band
* Midpoint raised by 3%
* Slope of band 9%
November 9, 1992 * Midpoint raised by 3%
* Slope reduced to 8%
July 26, 1993 * Midpoint raised by 2%
* Slope reduced to 6%
May 31, 1995 * Midpoint raised by 0.8%
* Band widened to ±7%
* No change to slope
* Weights: 54.8% US$, 24.2% DM, 8.3% BP, 5.6% FF, 7.1% JY
April 30, 1996 * Weights: 60.3% US$, 21% DM, 8% BP, 5.1% FF, 5.6% JY
June 18, 1997 * Band widened to reach ±15% by end of year
* Slope of lower limit 4%
* Slope of upper limit 6%
August 17, 1998 * Slope of lower limit 2%
* Slope of upper lin-t 6%
January 4, 1999 * DM and FF are replaced by Euro
* Weights: 61.4% US$, 8.9% BP, 5.2% JY, 24.5% Euro
Source: Bank of Israel, "Foreign Currency Exchange Rates In Israel 1999," January 2000.
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