WPS iq3q
POLICY RESEARCH WORKING PAPER 1939
Second Thoughts The evidence is broadly
supportive of an asset view of
on Second Moments speculative attacks and the
importance of the variance of
. ~~~~~~~~~~~~~~monetary aggregates in
Panel Evidence on Asset-Based mntr grgtsi
predicting currency crises, but
Models of Currency Crises it cast some doubt on existing
theories.
Arturo J. Galindo
William F. Maloney
The World Bank
Latin America and the Caribbean Region
Poverty Reduction and Economic Management Unit
June 1998
POLICY RESEARCH WORKING PAPER 1939
Summary findings
The literature on speculative attacks has been given new Galindo and Maloney test two popular asset-based
impetus by the collapse of the European currency models of speculative attacks - Krugman and
arrangements beginning in 1992, by the Mexican peso Rotemberg (1992) and Calvo and Mendoza (1995) -
crisis and after-effects in 1994, and most recently by especialLy their emphasis on the second moments of
speculative attacks across Asia. monetary aggregates.
One strand of this literature stresses the importance of Analyzing monthly panels of appropriate countries in
imbalances in stocks of monetary and financial three regions, they find evidence for the importance of
aggregates rather than traditional "flow" factors, arguing money/reserve ratios predicted by both models, and their
that massive, volatile capital flows have become a variance as predicted by Calvo and Mendoza.
dominant feature of the global landscape, and that But the variance of velocity does not appear to be
exchange-rate levels and current accounts have not important, casting some doubt on the Krugman-
proved convincing as proximate causes of crises. Rotemberg target zone framework and the interpretation
of the Calvo-Mendoza results.
This paper - a product of the Poverty and Economic Management Unit of the Latin America and the Caribbean Region-
is part of a larger effort in the region to understand the determinants of macroeconomic instability. Copies of the paper
are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Marta Cervantes, room
I8-095, telephone 202-473-7794, fax 202-522-0054, Internet address mcervantes@worldbank.org. William Maloney may
be contacted at wmaloney@worldbank.org. June 1998. (27 pages)
The Policy Research Working Paper Series disseminates the findings of wore in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
Second Thoughts on Second Moments
Panel Evidence on Asset-Based Models
of Currency Crises
Arturo J. Galindo
William F. Maloney*
Keywords: Speculative attacks, target zones, currency crises, GARCH, volatility.
*We thank Menzie Chinn, Barry Eichengreen, Steve Kamin, and Andrew Rose for helpful
comments, and the Center for International Business and Economic Research at the University of
Illinois for financial support. Contactwmaloney@worldbank.org or agalindo@uiuc.edu. Previous
title: Asset Views of Speculative Attacks: Empirical Evidence.
L Introduction
The literature on speculative attacks has been given new impetus by the collapse of the
European currency arrangementsbeginningin 1]992, theMexicanPeso crisis and aftereffects in 1994,
and most recently by attacks across Asia. A comprehensive review of the numerous approaches and
findings to date is offered by Kaminsky, Lizondo, and Reinhart (1997).
One strand of this literature stresses the importance of imbalances in stocks of monetary and
financial aggregates rather than traditional "flow" factors, arguing that massive and volatile capital
flows have become a dominant feature of the global landscape, and exchange rate levels and current
accounts have not proved convincing as proximate causes of crises (see, for example, Calvo and
Mendoza, 1995). The earliest genre of these model dates from Salant and Henderson (1978) and
Krugman (1979) and have been further elaborated by Flood and Garber (1984) and Obstfeld (1986)
among others. In most, a persistent and monetized budget deficit leads to an offsetting fall in reserves.
Forward looking investors, anticipating the eventual abandonment of the peg, attack the currency
when the remaining stock of reserves equals the idecline in domestic money demanded that will occur
when the currency floats. This provides a rationale for the inclusion of ratio of reserves to money
(Bilson 1979, Edwards 1989, Kaminsky and Reiinhart 1996, Klein and Marion 1994, Sachs, Tomell
and Velasco 1996) rather than the more traditional scaling by imports (see for example, Edin and
Vredi, 1993, Frankel and Rose, 1996) or GDP (Collins 1995) and the inclusion of the rate of growth
of domestic credit (Edwards, 1989, Frankel and Rose, 1996).
However, as Calvo and Mendoza note, in the Mexican case, the apparent fiscal surplus in
1993 appears to contradict this type of speculative attack model. They argue that the focus should
rather be on the stochastic evolution of demand for monetary aggregates, particularly M2. Demand
1
for domestic assets by foreign capital or for private expenditure can suddenly evaporate leaving the
monetary authorities the choice of using sterilized intervention andweakeningthe currency, or risking
the collapse of a weak banking system. Noting that the log of the ratio of M2 to reserves appears to
follow a random walk Calvo argues that its higher volatility in Mexico raises the probability of
wandering into crisis above what it would be in Austria with a comparable reserve ratio.
However, the Calvo-Mendoza view shares a closer kinship with the literature on target zones
beginning with Williamson (1985), Frenkel and Goldstein (1986), and Krugman (1991), than with the
domestic credit driven models that they critique. Krugman and Rotemberg (1992) developed the
theoretical bridge to the speculative attack literature and derive the specific conditions under which
a band cannot be defended and a crisis may be expected.' The target zone framework is more
appropriate to both the European case and the major Latin American countries in the 1990's which
were more often than not managing their exchange rates within a band. It is also rich in predictions
about the role of reserve to money ratios and the second moments of monetary variables in generating
crises.
Despite the popularity of both these views, to date there has been no systematic testing of
their predictions and particularly about the importance of the volatility of monetary aggregates. This
paper attempts to do so and finds only partial support. Beginning with the target zone literature, we
generate a set of testable specifications and show their broad similarity to the Calvo Mendoza view.
We compile a data set focused on a sample of countries in the late 1980s and 1990s whose exchange
rate arrangements and capital account regulations are appropriate to the model. We then employ
'Edin and Vredin (1993) and Otker and Pazarba§ioglu (1994)also analyze attacks on
target zones but with in a very different framework that does not yield predictions about second
moments.
2
panel estimators that preserve the temporal dimension often lost in previous studies that pool
observations. We then test the predictions of both the target zone and the Calvo-Mendoza
framework.
We tightly restrict the number of variables included in the regressions. This is primarily
because our goal is to test the importance of a few heretofore unexamined variables, rather than to
predict crises per se. However, it is also the case that the choice to work over a relatively short
interval at high frequency necessarily implies that many of the variables that have appeared important
in other studies are unavailable for many or all the countries in the sample at the required frequency.
L Theoretical Background from the Target Zone Literature
In the Krugman-Rotemberg framework, the nominal exchange rate is assumed to follow a
simple, although standard, log linear monetary model of the exchange rate
s = m + V + l7E[ds]
where s is the log of the spot exchange rate, m the log of domestic money supply, v a shift term
capturing shocks to money demand including those to real income, velocity etc., and the expected
rate of depreciation times ,A the interest semi-elasticity of money demand. The term v is assumed to
evolve as a random walk with drift:
dv = udt + adz (2)
where z is a wiener process: dz-IN(O,l), and p is the rate of drift. Money supply is assumed to be
3
passive and altered only to keep the exchange rate within the target zone. As the exchange rate
moves toward the end of the band, intervention by the central bank reduces the money supply to
maintain s in bounds and the smooth pasting equilibrium holds. However, as in the earlier literature,
an attack will occur if the stock of reserves is eroded to where it equals the decline in the demand for
money that would result from the collapse. Krugnan and Rotemberg show this quantity
M/ - m = (3)
where
X - 2u +/~~ al2,u 2a (4)
)702
This implies that an attack occurs when
K < I -e T/ 5
D+R
The threshold ratio of reserves to high powered money below which an attack occurs, t, is a function
of 7, ,u, and o. An increase in the drift or the variance of the shocks to money demand, or an
increase in the sensitivity of money demand, expected depreciation, through the interest rate lowers
the threshold. The difference between the first and second elements above can be seen as an index
of proximity to the threshold that holds the promise of being a useful predictor of attacks.
Scaling the threshold by the money multiplier, equation (5) is broadly consistent with Calvo' s
focus on the log of M2 over reserves converted into domestic currency and its variance, rather than
4
that of velocity. The two measures of varian,ce diverge to the degree that purchasing power parity
fails and reserves are not proportional to incom e. In the estimations that follow, we first test explicitly
the Krugman-Rotemberg specification, and then the Calvo hypothesis.
IIL Estimation
We construct panels of up to nine years of monthly data for 14 countries. We choose this
frequency first because it seems appropriate given the rapidity with which fundamentals can change.
- -Second, it generates enough degrees of freedom to permit focusing on a restricted period, 1987-
1995, which corresponds reasonably well to ithe assumptions of the model: high degrees of short
term capital flows, reasonably open economies, and authorities committed to maintaining a target
zone or, in the limit, a peg as determined by the IMF publication, Exchange Arrangements and
Exchange Restrictions. The downside of this approach is that the availability of indicators at this
frequency sharply restricts the range of countries that can be included, and the span of data available.
This is especially the case for Asia where only Korea and Malaysia publish industrial production
numbers, the only feasible proxy forthe output variable required to calculate velocity and to estimate
interest elasticities. Since the latter managed a target zone for only a brief period, we exclude the
Asian region from this part of the work and do not include the1997 crises. In total, our sample
includes nine European countries -Austria, Denmark, France, Italy, Holland, Finland, Ireland,
Portugal and Spain- and five Latin American countries -Brazil, Chile, Colombia, Mexico, Argentina
-for which equation (5) can be tested directly. Since the Calvo-Mendoza hypothesis does not require
output measures to calculate relevant variables, in the second section we can employ a much broader
range of countries however, to remain comparable with the first section, again, we do not address
5
the most recent crises.
We generate an index of speculative pressure similar to that of Eichengreen and Wyplosz
(1995). Reserve movements and real exchange rate are standardized by their standard deviations
and combined. As in Sachs, Tomell, and Velasco, and Kaminsky, Lizondo and Reinhart, interest
rates were not included in the index due to sharp movements in Latin America that are often
unrelated to attacks.
The results we present are those leaving the index as a continuous measure. The literature
frequently discusses the incidence of "speculative pressure" that often falls short of a full blown
attack (see Svensson, 1994). Such episodes, though falling below whatever arbitrary cut off is
employed to define a discrete "crisis" are arguably driven by similar dynamics. It may therefore be
inefficient to discard this information, create a dichotomous variable, and then employ limited
dependent variable techniques to infer the determinants of the underlying continuous latent variable.
On the other hand all measures that weight innovations by the country-specific standard deviation
treat a one standard deviation of the index as equally important episodes of speculative pressure,
whether in Austria or Mexico. This is defendable to the degree that countries differ in "normal"
movements in reserves or exchange rates, and hence also in what should be considered a crisis. But
as an altemative, we also create a binary crisis index informed by movements in the index, but
modified by what the literature recognizes as legitimate speculative attacks. All the analysis was run
using this variable both with the complete sample, and truncating each country series immediately
after a crisis to focus on the run-up to each event. However, perhaps due to the limited number of
crises relative to observations, no specification appeared remotely significant and we do not report
the results.
6
The series forthe variance and trend in velocity movements are generated in two ways. First,
individual GARCH models were fit for each of the 14 countries. The trend was derived as the
forecast of a time series model for the log of velocity of general form:2
Alog(v)=aO+ajIog(v, _)+ + a,log(v,,)+E, (6)
i=1
As conventional, we assumed that the error term is normally distributed with mean zero and
variance h1, where
p
ht=yo+E Y2 e t PA (7)
i=l =
For every country, an acceptable individual specifications was generated that removed residual
GARCH effects, usually with a GARCH(1,1) specification or a ARCH(1). Second, to provide a
smoother alternative under the assumption that longer term volatility may enter speculators'
decisions, we construct a six month rolling variance of A log(v) and use its six month moving
average for the trend.
To generate a consistent set of interest semi-elasticities, a simple model of MI in first
differences was estimated using two stage least squares. In all cases, the coefficient on money
was of the correct sign, and almost always significant. Since the available interest rates are
implicitly those paid on assets often included in M2, the estimated semi-elasticities using this
2 a more general discussion of GARC'H models see Bollerslev, Engle and Nelson
(1993). The inclusion of a "levels" effect in the mean equation is now common in estimations of
continuous time stochastic volatility models. See, for example, Andersen and Lund (1997) for an
application to short term interest rates.
7
aggregate were, unsurprisingly, very often positive. In the absence of data on returns on less
liquid assets, this means the specification can only be run with M1.3 Since we are concerned only
with the direct effect of depreciation on money demand through the interest rates, cointegration
based estimation methods were not appropriate since they generate the total impact elasticity
through all variables in the system.4 Although the literature on estimating interest response of
money demand is long and contentious, as we will see, the precision of these estimates does not
appear critical to the results. The threshold value is scaled by the money multiplier, so as to make
it consistent with the ratio of reserves to Ml, rather than base money.
Finally, unlike the European subsample, the Latin American countries adopted a target
zone or peg at different times within our sample period. Further, in the case of Argentina, the
deceleration of inflation in the early part of the stabilization plan introduced a high degree of both
real exchange variance, interest rates and other variables that was unrelated to the sustainability
of the peg per se. We therefore begin the sample in 1992:1 when inflation was falling to levels
below 50%. The effect in both cases is to generate an unbalanced panel.
As a preliminary test of the model, table la presents the thresholds calculated first using
the GARCH and then the moving average specifications of the variance, as well as the level of
RIMl for the entire sample, and table lb the same information for several countries experiencing
crises in both Europe and Latin America. As is immediately evident, on average, the reserve ratio
3 This also raises questions about the interpretation of the interest rate coefficient in
empirical tests of monetarist models of the exchange rate that employ M2, and use these same
interest rates as the opportunity cost of holding it. Estimates available on request.
4 Johansen(1995) and Lutkepol (1994) argue that the coefficient from cointegrating
regressions cannot be interpreted as the necessary partial elasticities since they capture shocks
transmitted through all other variables and cannot be allowed a ceterisparibus interpretation.
8
is far above the threshold and that, even at theiir maxima, these thresholds are very low. In the
months before crises, only in the case of Italy was the reserve to Ml ratio remotely close to
either threshold. In general, a strict interpretation of equation (5) would imply thresholds that
tend to be so low that we should virtually never see a crisis.
One possible conclusion might be that ihis arises from the inaccuracy of our estimates of
the elements of equation(5). However, figure I shows the value of the threshold to be very
insensitive to even large movements around our estimates.' First, since velocity series are either
I(1) or I(0), differencing them leaves them stationary and, not unexpectedly, with essentially no
drift, u. Very large increases would be needed to raise t to .1 even at values of o2 an order of
magnitude greater than the maxima observed.6 Given the relatively standard tools employed, it
seems unlikely that our estimates are off by these magnitudes. At current levels of o9 and u,
even large differences in the interest semi-elasticity have very little effect. Again, since our
estimates are of similar orders of magnitude to those found elsewhere, this is unlikely to be the
problem. Given reasonable values for the arguments involved, the literal application of this
model is unlikely to generate crises at the reserre ratios generally observed.
This, of course, is not in itself evidence against the target zone framework more generally
for analyzing speculative attacks. The Krugman-Rotemberg model is admittedly heuristic in
intent and departs from a simple monetary model of the exchange rate that has persistently
resisted empirical verification. Nonetheless, it is not unreasonable to expect that the arguments
5 The average multiplier for the sample is used to scale the threshold.
6In an earlier application to Colombia, Mlexico and Germany, Carasquilla (1995) found
much higher thresholds. This was due, however, to unusually high estimates of the drift term.
9
in eq (5) appear in some form among the determinants of currency crises. Our estimation
strategy is therefore first to take the model literally, and then progressively to loosen the
constraints on the underlying arguments until the final regression is
n
trsue = fo E [pR R + +pg + n
Pressure, =p+E sM, im M1i + _ii + pa,iCytji n 8
Table 2 presents the results of these regressions. Columns la and lb present the specification
with only the proximity to the threshold index calculated using the GARCH estimates of the
variance and drift, and the moving average estimates respectively. Columns 2a and 2b allow
R/MI and 'r to enter separately, again calculating the latter using the two separate measures of
variance and drift. Columns 3a and b estimate (8) above, unconstraining the arguments in r.
The results offer only partial support to the model. Standard Hausman and Breusch -
Pagan tests dictate using either pooled or variable effects estimators, depending on the
subsample. In each case, an equal number of lags for all variables were included and the lag
structure was pared down to where the last set of lags was insignificant. Contemporaneous
values were excluded since in a crisis situation, we would expect a large shock to reserves would
be reflected in RIM1. In virtually all cases, only two lagged sets of variables were significant. The
sum of the coefficients are reported and the probability value of the F-tests on their joint
significance below.
Virtually all specifications show F or X2 tests on the overall significance of the regression
significant below the 8% level and for Europe and the overall sample, below the 5% level. In all
cases, the proximity to the threshold index enters with the anticipated sign, and significantly,
10
regardless of the variance and drift measures employed. Of concern, however, is that when the
index is broken into the asset ratio and the threshold, r, the latter enters with the predicted sign
in the European sample, but is significant only ifor the GARCH specification at the 10% level.
The reserve ratio, on the other hand, emerges of the predicted sign and very high levels of
significance in virtally all specifications. This suggests that to the degree that the index was
significant, it was driven largely by the reserve ratio.
Disaggregating rinto its component parts, the drift term, A enters with correct sign and
significantly at the 10% level in the GARCH specifications for the European and the complete
samples, but insignificantly or of the wrong sign for all other specifications. The oa terms, are
also of the anticipated sign in roughly half the specifications and enter at the 11-13% level only in
the European specifications, as with drift, with the correct sign. The semi-elasticity of money
demand also shows unstable signs and never enters significantly. In sum, the only specifications
for which the variance and drift terms enter consistently with the model and of some significance
are the European specifications. However, these are also the only specifications for which the
asset ratios enter with the wrong sign. When the semi-elasticity is dropped from the regression,
the sign reverses to that anticipated although both drift and variance terms become slightly with
the latter now significant at the 15% level only. The other regressions largely unaffected (results
available on request).
The highest level of explanatory power, as measured by the R2 is for Latin America, at
only 7.2% of the variance explained. Further, to remove the possibility that the estimates of
interest elasticities were driving the aggregated specifications, they were also run with a common
value of .1. However, consistent with the discussion above, this had essentially no impact on the
11
results.
IV. Test of the Calvo-Mendoza View with an Expanded Sample
Calvo and Mendoza argue that ln(R/M2) and its variance should appear as important in
determining speculative attacks. Since we no longer calculate velocity or estimate semi-
elasticities, we do not need measures of economic activity and the sample can be expanded to
include countries previous dropped for lack of data. The sample now includes four Asian
countries- Indonesia, Korea, Malaysia, and Thailand. We also group in this category, "Asia+,"
Israel which, while clearly not sufficient as a category of its own, is an important case study for
target zones.7 To the five existing Latin American countries we add Uruguay and to Europe we
add Greece and the UK and Sweden for the M2 regressions. The African countries in the Franc
zone were not included despite their long-standing peg to the French currency since capital flows
remain largely restricted. We employ the moving average representation of the variance rather
than estimate 24 individual GARCH specifications.
Table 3 presents the ratio of reserves to M2, its log, and the standard deviations of the
latter across the sample period employed in the regressions. Figure 2 presents the evolution of
these variables across a longer period for a selection of countries. What is immediately clear
from both is that geographical generalizations are not robust. As Calvo points out, Mexico does
have a much higher variance of R/M2 relative to Austria, and this may offset the fact that it has a
higher reserve to M2 ratio. But the other two Latin countries hit in 1994-95, Argentina and
7Williamson (1996) has a detailed analysis of the crawling bands of Chile, Colombia and
Israel.
12
Brazil have roughly the same degree of volatility as, and significantly higher reserve ratios than
Austria, as well as every Asian country with the exception of Malaysia. At the time of the
Tequila crisis, Colombia and Chile had levels of variance similar to those of Austria. Overall,
volatility in Latin America would be difficult to distinguish from Europe and reserve ratios are,
on average, higher.
It is true that, in table 3, the moderate Latin American volatility arises partially from
having dropped the high inflation periods in Argentina, Brazil and Mexico. We defend this on
two grounds. First, it can be argued that these are unusual periods and thus do not share the
same data generation process as the other countries in the panel. Second, the variances across
these periods dwarf the relatively small rises around the tequila period and in preliminary
regressions tended to generate the inverse correlation with crises from that predicted. These
high variances may be "real" but they may possibly arise if large increases in money supply, and
the expected proportional depreciation of the cutrrency are not coincident.
Figure 2 suggests some support for the ('alvo-Mendoza hypothesis. Chile, Colombia and
Uruguay, countries largely unaffected in the Tequila episode, had extremely low variances across
this period while Brazil and Mexico, with relatively high reserve ratios, showed rises in their
variances in the early part of 1994 to among the highest levels in the sample. On the other hand,
Italy and Spain at the end of the 1994 showed comparable levels of variance but with much
lower reserve ratios and yet experienced no crisis while Argentina showed low variance and
relatively high reserves and was still hit.
Table 4 presents the results of regressing; the pressure index on the log of reserve ratios
and their variance. For comparison with the previous section, we begin working with MI. F-tests
13
suggest 6 lags of the two variables. As before, the asset ratio is significant for the entire sample,
and Europe and for Latin America at the 7% level. However, the variance is now significant for
the whole sample, Europe, and Latin America although it enters with incorrect sign in the latter
and in Asia+. The variables taken together are statistically significant for all except the Asia+
regression, although again, the overall explanatory power is under 5% of the variance.
The results improve if we work with R/M2 as suggested by Calvo and Mendoza. The
sample size increases for Europe because Sweden publishes M2 and the U.K. publishes a proxy
for M2 (the retail component of M4) but neither publish MI. RIM2 is of the predicted sign for
all but Asia+ although it is now not significant within Latin America. The variance is very
significant and of the correct sign for all except Asia+. Again, all the regressions, with the
exception of Asia+ are very significant.
The poor performance of the model for Asia+ may results from two factors. First, since
in none of the countries was there a true speculative attack across the sample period, the
movements in the standardized index may represent noise unrelated to speculative pressure.
Moderate depreciations designed to preserve competitiveness in Korea, or Israel will get very
large weight, yet occur in relatively healthy macro-environments. The fact that the model
predicts so poorly in this case may be considered support for it overall. It also suggests that, for
the other regions, the index is not just picking up noise. It may also be, however, that despite the
loosening of capital controls over time, some countries, like Korea, still managed short term
flows and therefore do not correspond well to the model.
The fact that the variance now enters with the correct sign in the Latin subsample is
supportive of the variance of M2IR being the more appropriate of the two monetary aggregates.
14
The explanatory power also increases in every case except Asia+. This raises the question of
whether the relative success of the Calvo-Mendoza model compared to the Krugman-Rotemberg
model is solely due to using M2 rather than Ml, As empirical studies of monetary models of the
exchange rate frequently employ M2, this might have been a more desirable aggregate to employ
in section m were it not for the unavailability of corresponding interest elasticities. As an
alternate test, in table 5 we present the results of a specification analogous to that of Calvo-
Mendoza, where the variance of RIM2 is replaced by the variance of the inverse of velocity,
PY/M2. As in the more complete regressions using Ml, the results are not supportive of the
Krugman-Rotemberg specification: the variance of the velocity does not enter significantly in any
regression and the signs are the opposite of those predicted in both the overall and European
regressions.
This finding provokes some second thoughts about the more successful Calvo-Mendoza
approach as well. The shocks to broad money demand that it postulates as critical to bringing on
crises should presumably also show up in the variance of velocity yielding similar empirical
findings. The fact that they do not raises the question of what is driving the significance of the
variance of RRM2, the variance of M2, or of reserves. This is not necessarily bad news. Finding
that the second moment of reserves helps predict crises is still useful information for policy
makers even if not entirely in line with the formal motivation in terms of shocks to M2. A
possible concem is that if in the run up to a crisis, reserve losses become progressively larger,
this may show up both in the pressure indicator, that has as one component the change in
reserves, as well as in lags of the variance of M2/R. Attempting to eliminate this problem by
running a probit with the binary crisis index capturing recognized attacks, as in section II,
15j
yielded insignificant results. However, as before, this may be due to the few crises relative to
observations.
Conclusions:
The paper provides some evidence in favor of an asset view of speculative attacks and
the importance of the second moments of monetary aggregates in predicting crises. In the
regressions for both the Krugman- Rotemberg target zone model and the Calvo-Mendoza
approach, the stock of money relative to reserves appears very significant and of the predicted
sign in most specifications. The results for the drift and variance terms for the innovations in
velocity are less consistently supportive of the first model with only the GARCH specifications
for Europe and the overall sample generating the predicted signs and borderline significance.
These results cannot be seen as strong evidence in favor of the target zone framework or as
offering much confidence in the elusive measure of proximity to crisis that it theoretically offers.
The variance of reserves to the money aggregates suggested by the Calvo-Mendoza approach,
however interpreted, appears more significantly and may contribute additional explanatory
power to models seeking to predict crises.
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Appendix I: Data
MO: All from line 14 of IFS statistics except: Italy 1995 from Banca D'Italia, Economic Bulletin,
Number 22, Feb 1996.Colombia, Banco de la Republica.
MI: line 34 IFS or, if unavailable, Ml. Colombia, Banco de la Repuiblica. Not available for U.K.
or Sweden.
M2: line 34 + line 35 quasi money, IFS. VK: Building Societies pay interest on demand deposits.
In 1989, some became banks. Bank of England continued calculating Ml without new banks
18
until 1990. Then stopped. M2 is the retail component of M4, The Bank of England suggested the
omitting very large depositors who had some market power and who were unlikely to be using
M4 for transactions purposes was the correct measure. 1987-1994 from Bank of England,
Statistical Abstract, 1995 part 2 Detailed monetary statistics. 1995 values provided by the Bank
of England. Colombia, Banco de la Republica.
Money multipliers: Ratios of MI to Base money'. Chile, Boletin Mensual, Banco Central de
Chile.
Industrial Production: All from line 66 of IFC except: Portugal: June 1994- Boletim Mensal de
Estadistica, Instituto Nacional de Estatistica, Bank of Portugal; Chile, Boletin Mensual, Banco
Central de Chile; Colombia, Banco de la Repuibliica, Brazil, Banco Garantia; Argentina;
Real Exchange Rate: IFS line reu or rec. For Latin America, EP*/P where P* is weighted
average of the WPI of the principal commercial partners of each country. US WPI.
Interest rates: IFS line 601 or closest market determined rate. Argentina, Informe Econ6mico,
Ministerio de Economia y Obras y Servicios Nblicos.
Our thanks for essential help collecting data to: I)avid Willoughby, Bank of England, Charles
Goodhart, LSE for the UK; Hemando Vargas, Banco de la Republica, Colombia; Jose Guerra,
Cental Bank of Venezuela; Rodrigo Azevedo, Banco Garantia, Brazil; Ricardo Bebzuk and Abel
Viglione, Argentina.
Appendix II: Countries and Sample Periods
Asia: Israel 1987:1-95:12,Indonesia 1987:1-95:12, Korea 1988:12-1995:12; Malaysia 1987:1-
1988:12.
Europe: Austria, Denmark, France, Italy, Holland, Finland, Greece, Ireland, Portugal, Spain,
Sweden, UK; all 1987: 1-1995:12
Latin America: Argentina 1992:01-95:12; Brazil 1994:07-95:12; Chile 1987:1-95:12; Colombia
1987:1-95:12; Mexico 1991:11-95:12; Uruguay 1990:12-95:12.
19
Table la: Complete Sample Summary Statistics
_Mean S.D. Max Min
Pressure Index -0.000 0.025 0.444 -0.319
'T1 0.016 0.022 0.212 0.000
T2 0.019 0.021 0.169 0.001
R/M1 0.706 0.710 3.562 0.054
Ca21 0.003 0.005 0.042 0.000
III -0.004 0.056 0.369 -0.249
(e2 0.007 0.015 0.180 0.000
p2 -0.002 0.023 0.070 -0.190
fn 0.684 0.688 2.010 0.069
Notes: ti =tbreshold, ai =variance of innovations, .i= drift using GARCH.
¶Z 2, 2 using moving average. RIMl = resrves in domestic Currency
divided by narrow money. Tj = semi-elasticity of money demand.
Table lb: Thresholds and Reserve Ratios for
Selected Speculative Attacks
Country Crisis -1 ¶1 T2 R/Mi
Argentina 1994:11 0.036 0.036 0.885
BraZil 1994:11 0.072 0.024 1.658
Mexico 1994:11 0.010 0.007 0.322
Finland 1992:08 0.009 0.001 0.165
Italy 1992:08 0.031 0.012 0.054
Spain 1992:08 0.023 0.014 0.382
Portugal 1992:08 0.011 0.010 1.146
Spain 1992:10 0.034 0.015 0.356
Portugal 1992:10 0.014 0.017 0.947
Spain 1993:04 0.025 0.031 0.299
Portugal 1993:04 0.018 0.015 0.828
Spain 1993:06 0.004 0.032 0.323
Portugal 1993:06 0.010 0.015 0.826
France 1993:06 0.001 0.002 0.119
Notes: Ti = threshold using GARCH, I using moving average. Crisis-1l
month before crisis.
Table 2: Determinants of Speculative Attacks on Target Zones, 1987-1995
________ ~~~~ALL EUROPE - IATIN AMERICA - -
_la lb 2a 2b 3a 3b Ia lb 2a 2b 3a 3b la lb 2a 2b 3a 3b
Index1 E-03 -4.37 -0.302 -7.82
0.000 0.014 0.000
Index2 E-03 4.28 -0.243 -7.87
0.000 0.047 0.000
R/M I E-03 4.26 -2.70 -4.56 4.23 -0.788 -0.674 0.35 0.375 -7.44 -5.38 -7.31 -3.75
0.000 0.000 0.000 0.000 0.035 0.039 0.041 0.028 0.000 0.010 0.000 0.007
Ti E-02 -0.613 8.15 -6.4
0.366 0.100 0.664
-C2E-02 -8.61 4.48 -14.8
0.082 0.697 0.287
iti E-02 1.41 3.85 -0.63
0.070 0.066 10.218
12 13-02 -3.56 0.73 -1.88
0.010 0.438 0.337
aI E-01 1.21 2.09 -5.22
0.638 0.109 0.840
02 L-Ui -0.117 0.863 -5.75
0.667 0.128 0.267
ij E-04 -1.2 -2.96 5.89 4.7 6.33 -7.840
0.915 0.785 0.420 0.5 0.144 0.874
constantE-03 2.78 2.770 2.87 3.37 2.71 2.97 0.721 0.691 0.076 0.322 -0.405 -0.326 9.310 9.310 11.2 11.90 10.90 10.50
0.007 0.007 0.008 0.002 0.066 0.027 0.498 0.512 0.951 0.813 0.723 0.762 0.088 0.090 0.068, 0.040 0.144 I 0.126
R 0.045 0.041 0.043 0.046 0.044 0.047 0.010 0.010 0.012 0.010 0.017 0.017 0.054 0.050 0.048 0.054 0.072 0.059
Obs 1091 1091 1091 1091 1091 1091 828 828 828 828 828 828 263 263 263 263 263 1 263
OverallSignif. 26.59 24.65 13.29 14.08 8.16 8.67 8.47 6.13 11.04 7.24 14.14 14.79 8.40 7.96 4.32 4.77 2.83 3.33
P value 0.000 0.000 0.000 0.000 0.000 0.000 0.015 0.047 0.026 0.124 0.048 0.039 0.000 0.00 0.002 0.001 0.007 0.002
Notes: Results are the sunmation of the estimated parameters of the first two lags of the variables and beneath them, the P-value of tests under the null hypothesis that the coefficients are jointly equal to zero.
Specification 'a' uses the GARCH estimates of the vaiance and drift while specification "b" employs a six month moving average. Tau is the threshold level of RA41 at which an attack would be expected.
The sample size is 1987:1- 1995:12 for Europe while those for Latin Ametica depend on the individual country ( See appendix II). The complete sample and Latin American models are pooled regressions while the
European specification employs a randorn Effects estimator as dictated by lausman and Breusch-Pagan tests. F tsts for the pooled regressions and Chi squared tests for the random effects estimators were used to
evaluate the significance ofthe estimated parameters and of the averal rgession.
Table 3: Sample Means and Standard Deviations
S.D.
Country RIM2 L~o(R/M21) Log(!oR!)
Europe
Austria 0.08 -2.57 0.16
Denmark 0.12 -2.12 0.23
Finland 0.12 -2.14 0.22
France 0.06 -2.83 0.16
Greece 0.15 -2.04 0.51
Ireland 0.28 -1.28 0.21
Italy 0.07 -2.67 0.31
Netherlands 0.09 -2.43 0.21
Portugal 0.26 -1.42 0.36
Spain 0.13 -2.06 0.22
Sweden 0.17 -1.82 0.39
United Kingdom 0.07 -2.62 0.17
Latin America
Argentina 0.27 -1.31 0.14
Brazil 0.24 -1.44 0.18
Chile 0.50 -0.74 0.27
Colombia 0.45 -0.84 0.25
Mexico 0.20 -1.67 0.32
Uruguay 0.14 -2.05 0.33
Other
Israel 0.16 -1.82 0.19
Indonesia 0.18 -1.73 0.19
Korea 0.16 -1.85 0.14
Malaysia 0.30 -1.20 0.09
Thailand 0.22 -1.52 0.23
Notes: moments correspond to sanple period used in estimations
(See appendix 2).
Table 4: Tests of the Calvo-Mendoza Hypothesis,1987-1995
Sample: All Europe Latin Asia+
I America _
M1
Log(R/Ml) E-03 -2.03 -0.439 -17.0 -2.04
0,004 0.039 0.070 0.478
VJLog(RIMI)] E-02 4.77 11.2 -3.76 -10.8
0.003 0.000 0.001 0.646
Constant E-03 -0.258 -1.05 -6.41 -0.649
0.001 0.142 0.106 0.446
R2 0.018 0.049 0.080 0.000
Observations 1 577 960 232 289
Overall Significance 3.39 49.06 2.67 0.69
0.000 0 000 0.002 0.763
M2
Log(RlM2) E-03 -2.47 -0.764 -3.16 0.044
0.0)01 0.037 0.150 0.894
V[Log(R/MZ)J E-02 7,43 15.4 13.7 -1.82
0.000 0.000 0.000 0.591
Constant E-03 -5.99 -2.19 -12.1 4.29
0.004 0.177 0.220 0.530
Ri 0.029 0.061 0.111 0.000
Observations 1769 1152 232 289
Overall Significance 5.38 74.34 3.41 0.55
___________________________ 0.000 0.000 0.000 0.879
Notes: We report the summation of the fust six I of each variable and below it the P-Value ofthe test under
the null that the coefEicients an jointly equal to zero. All models are estimated as pooled mgressions except the
European ones where Hausman and Breusch-Pagan tests dictated a random effet model. F-tests for the pooled
and Chi squared for the random effects regiessions were used to evaluate the overall significance of the specification.
Table 5: Test of Simplified Krugman Model, 1987-1995
(Calvo-Mendoza with variance of velocity)
Sample: All Europe Latin
.I Ameiica
M2
Log(RlM2) E-03 -3.35 -0.732 -6.75
0.000 0.001 0.044
V[(YP)/M21 E-02 -2.38 -2.89 31.8
0.689 0.188 0.837
Constant E-03 -6.99 -0.622 -1.54
0.003 0.736 0.207
R2 0.028 0.030 0.056
Observations 1192 960 232
Overall Significance 3.24 2.72 1.34
_______________________ 0.000 _0.001 0.198
Notes: We report the sumnmation of the first six lags of each variable and below it the P-value
of the test under the null that the coefficients are jointly equal to zero. All models estimated
are estimated as pooled regressions. F tests were used to evaluate the overall significance of the
specification.
Figure 1: Sensitivity of Xr to variance, drift, and semi-elasticity of
money demand
C8=.01 --1
/ i
r~~~~~~~~~~~~
0.3~~~z~
-.1 A ;~~~~~~~~~~
T01.0
Figure 2: R/M2 and VAR(n(R/M2)
LATIN AMERICA
ARGENTINA COLOMBIA
0.45 3.125 0.60 0175
0.40 0.55 l.0150
Ii ~~~~~~~~~~~~~.100
0.35 t 9 0 : X . .- O.S0I .o .0125
0.35
0.0754 0.45 1
lolj LO~~ II.011
0.15 , ,, , ' > ,^ ,.- -.J ...... }.WW 025 , ,0.35 , ,.0050
0.20 0~~~~~~~~.025 I '
Lj I 0.30 I I02
0.15 * . '' 1. .00 0.25 ..-09
1990 1991 1992 1993 1994 1995 1990 1991 1992 1993 .994 1995
BRAZIL MEXICO
0.440 _ 0.09 0.30 .16
/ _. _ -
0.400 W 0.0 i.14
0.360 . .07 0.25 0.12
0.320 I .01 o.as
0.402gt ^ I _0 0.20 I 1
.0.240 0 II
02W -0~~~~~~~.031~
0.250 O..0OS0
0.1S9 19U 1959 1990 1991 1992 1"N 1994 1995 IS90 1991 1992 1993 1994 199
0.120 I; .0. 0.10.02
3.0 0.05 . .. .. .0.0
99 191 192 '1993' 1994 1995 1990 1s99 1992 1993 1994 199
CHILE URUGUAY
0.70 -01so 0.200 .045
0.60 ~~~~~~~~~~II .0~~~~~~125 0.175 ]
0.55 I .0~~~ ~ ~~~~~~~ ~ ~~~~100 0.150 II I.5
0.50 I- 4 -I
5.45 It1 I
0.40 I 0.000 0.100 0015
I I ~~~~~~~~~~~~~~~~~~~~~0 ~~~~~~~.015
I I .000~~02 007
0.30 III .02 .050.005
0.25 'ii ,Si'S ii'gi..... -.0000 14'99
1987' 16 19910191 199193 1994 1995 1W ii 92 12 9
Figure 2, cont.
EIUROPE
AUSTRIA PORTUGAL
0.112 012 0.40 10.112
0104 Ii0.35
j .010
o.ot o.3o 1.am
mi ootr 11 yV
o.ou 1& 0.15 18 h0n
s ~~~~~~~~~~~~~~~~~~.008IiI
0.088 0.05
1987 1983199 1920 1991IM1993 1994 1995 71987 I M 5 IM M 1S2 IM z19% 1"
0.80-FRANCE SPAIN
I RM-
0o072 - .035 0.1" o
0.070 II 0.0 0.15
I ~~~~~~~~~~~~l 0.10~~~~~~~~~~~~~~~~~~.2
0.056 - 0,.0 ' ' .A O 0.132 ~
1987 19St 198S 1990 1991 1992 1993 1994 1995 1987 198S 1S99 1990 19S1 1992 199 1994 19 00
FRANCY SNIEAINGO
0.080 _ C4. 0.1U 1.022
II~~~~~~~~~~OI
0.010 _.0410 0.OSS 1
'.045 I .02 O.O20 I5 01*5
I I ji I 0I 01
0.058 * 0.010 0.092 jI
0.050 / i Is l 0.012 0.104
O.OS t t~~~~~~~~~~~~~11 &072 tl 005
0,04 1 ' I, .005
0.0459I .0451 0.084 I III
0.040 ., . , ~ . , , .0(0- 0.072 . Y.., ' co
0.11041 0.064
0.03 1i
0.08~~~~~~~~~4,04
i,I '~~~~199 2 9 ,o ,m''i ik193I I
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