-19-

variance of real interest rate differentials.

In table 5, short-term real interest rates are measured using two
alternative proxies for expected inflation differentials: a three-month
moving average of past inflation differentials, and the inflation forecasts
of a vector autoregression. The VAR is of the same general form described
in section 4, except that three-month domestic interbank rates are used in
place of Euromarket rates. Note that by either expected inflation measure,
short-term German/French and German/Italian real interest differentials have
been higher on average under the EMS. The opposite is true for long-term
differentials, which are constructed using a twelve-month moving average of
past inflation as a proxy for expected inflation. What matters for
comparison with our earlier results on the conditional variance of the real
exchange rate, however, is the conditional variance of the real interest
differential. For the short-term differential with lagged inflation proxy
and for the long-term differential, second-order autoregressive (AR)
Processes are used to generate predictions of next month's real interest
rate. (The results reported in table 5 are quite robust to inclusion of a
time trend and to using first- or third-order AR's.) For the short-term
differential with VAR inflation proxy, the one-month-ahead real interest
rate prediction errors are formed as follows: The VAR is used to generate
time t expectations of a) the three-month nominal interest differential in
t + 1 and b) t + 1 expectations of the inflation differential in periods t +
2 through t + 4. These are combined to form a time t forecast of the t + 1
three-month real interest differential. The realized (ex-ante) real
interest differential is then formed using the realized t + 1 nominal
interest differential together with time t + 1 expectations of inflation in
periods t + 2 through t + 4. The VAR method is consistent with rational
expectations. Obviously, there is not enough data to apply the VAR approach

to the long-term differentials.


-13-

Ti

able 3

The root-mean-squared-error of unanticipated movements in the logarithm of the real

exchange rate, using vector autoregressi

Feb. 1974 - Feb.

1979

(VAR)

one twelve
Forecast _horizon/ month months

(random walk)

one
month

twelve
months

on and random walk forecasts.°

March 1979 - March 1984

(VAR)

one
_ Month

twelve
months

one

month

(random walk )

twelve
months

Bilateral rates
versus DM

France 2.0
Italy 2.8
United States 2.7
United Kingdom 2.4
Japan 2.6
Switzerland 2.0

Multilateral
trade-weighted

exchange rates

Germany 1.9
France 1.7
Italy 2.2
United States 2.1
United Kingdom 1.6
Japan 2.2
Switzerland 2.5

To

TTAT

a

4 Real exchange rates are measured using consumer price indices (see figures 1 and 2). RMSE
See tne data appendix for the multilateral trade
weights. The vector autoregressions employ exchange rates, relative interest rates, relative
inflation rates and cumulated trade balances.

are approximately in percentage terms.

> Under the assumption that real exchanges rates follow a random walk, a one-tailed F-test
yields that the pre-EMS one-month conditional variance is significantly different from the
post-EMS conditional variance at the 5% significance level.

Cu" "10% significance level.


Data Appendix

All financial market data are end-of -month, seasonally unadjusted
observations. Spot and three-month forward exchange rates are from the
Federal Reserve Board data base. Forward rates for other maturities and
Eurocurrency interest rates are from Data Resources Inc. (Forward rates and
realized spot rates are matched according to the procedure described in
Riehl and Rodriguez (1977). Three- and twelve-month non-dollar Euro-
interest rates were constructed using covered interest parity.) Except for
trade balances, which are formed from lines 70 and 71.v of International
Financial Statistics, all the remaining data described below are from the
FRB data base.

Wholesale and consumer price indices (WPI, CPI) are: France:

wholesale prices (industrial goods), CPI; Germany: general WPI; cost of
living index; Italy: general WPI, CPI; Japan: wholesale prices (all
commodities), CPI (all items); Switzerland: WPI (total), CPI (total); U.K.:
producer price index (manufactured goods, home sales), retail price index;
U.S.: producer price index (finished goods), CPI (all items).

Domestic three-month and long-term interest rates are France: Interbank

rate (Paris), long-term public sector bond yield; Germany: Interbank loan
rates, long-term public authority loan rate; Italy: Interbank rate (Milan),
long-term government bond yield (source: 0.E.C.D. Main Economic
Indicators).

Multilateral trade weights are based on each country's share of total

trade (measured by the sum of exports plus imports) of the G-11 countries
over the period 1972 through 1976. The weights are France (.132), Germany
(.21), Italy (.091), Japan (.137), Switzerland (.036), U.K. (.121), U.S.
(.273).


-4-

deviating country will intervene and undertake changes in economic policy.
Because divergence indicator movements do not strictly obligate
intervention, and because the bilateral limits are often reached first, the
divergence indicator does not play as large a prophylactic role as
originally planned.2/

The fluctuation margins around the bilateral central rates allow the
system some scope to tolerate countries with different desired inflation
rates. As a bilateral market rate approaches its intervention limit, the
authorities can choose to move the bilateral central rate rather than
intervene (though considerable consultation and negotiation are involved. )
By making a small enough adjustment in the central rate, the authorities can
ensure that the lower tail of the new band overlaps with the upper tail of
the old band. Thus, the realignment does not necessarily precipitate a
Movement in the market rate. Given the 12 percent band for lira bilateral
rates, and 4.5 percent bands for the other rates, there can be significant
intervals between realignments even in the face of persistent inflation rate
differentials.

In practice, the EMS realignments are not typically as smooth as the
process just described. Opposing the desire to defuse speculative capital
movements is a wish to use fixed nominal exchange rates as a means of
forcing the convergence of domestic inflation rates. The hope is that
countries will undertake policy changes which would obviate the need for
exchange rate adjustment. Such thinking underlies some episodes of
substantial speculative pressures, such as March 1983, during which the
authorities hoped to avoid or at least postpone the need for a
realignment A

The formation of the EMS did not produce a rapid convergence of

inflation rates. Table 1 presents pre- and post-EMS inflation rates for

seven countries. Comparing five-year averages, there is no evidence


-34-

_
L us March 1979 2 _ FRANCE March 1979 _
a! +
ey Ey ae an ° A pn Pe ae
LUV 4.2 - 4
= 44 = 4
Lt ft J J J} J | tt Ltt ft ft tt} | | ft
Tuk “]* [7 qraty “7
— —.2 — —
fn ni 3 AAS
a 4. =
= 44 = 4
Ltttltt tt | ft ft tb Lt tt tf jt t ft jf
[SWITZERLAND 4 Fo sapan 7
> a
a J
Vv Ae
L ee 4
= 44 = _
Lt ft [| J tf tf ft fd Ltt ft [| ti tf Jt | J
1974 1976 “1978 1980 1982 1984 1974 1976 1978 1980 1982 1984

Fig. 1. Monthly movements in the log of real (CPI) exchange rates versus the DM, March 1973-March 1984.
End-of-month foreign currency/DM rates, March 1979 =0.


~20-

Table 5

The month-to-month conditional variance of DM/franc and DM/lira real interest rate differentials.?

Three-month real interest Long-term real interest

rate differential rate differential
(Proxy for
expected (Three-month MA (VAR model (Twelve-month MA
inflation): of lagged inflation) forecasts ) of lagged inflation)
Standard Standard Standard
deviation of deviation of deviation of
one-month b one-month one-month b
mean forecast error mean forecast error® mean forecast error
OM/franc
pre-EMS 1.3 1.4 1.2 8 2.8 45
post -EMS 1.9 1.6 2.0 9 8 62
DM/lira
pre-EMS 1.2 2.2 1.2 1.6 6.3 79
post -EMS 2.1 2.3 2.3 1.0 2.6 85

@ Means and standard deviations are in percent/year. The data is monthly. Short-term nominal
interest rates are end-of-month domestic three-month interbank rates; the series begin only in
January 1975. The long rate series begin in February 1974.

b One-month conditional forecast error based on second-order autoregressive model.

© Qne-month conditional forecast error based on vector autoregressive. model.


-26-

(The term 1 - Pa is given in Box and Jenkins, p. 245, Using the likelihood
function (A7), it is straightforward to prove that the information matrix is
diagonal and to derive the asymptotic variance of e.)

By the invariance property of maximum likelihood estimators (see Mood,

Graybill and Boes, 1974), the MLE of oe is given by
ee + Bye, (A9)

To derive the asymptotic distribution of %, we make use of a) the fact

that [(8, #) - (8, é)] 2N(0, H(8, #)), and b) the Mann-Wald theorem [see
Mann and Wald (1943)]. Together, (a) and (b) imply that (a - oe) a

N(0,V), where

4 2
~ 2 P)
G = 228 cc + 02)2 + 2021 - 02)3 = ret, ore ( age, =! ). (Alo)

2

2
a

(A consistent estimate of V may be obtained using z and 6.) Comparison of

(Al0) and (A6) reveals that for (|6| < 1), v< ¥. Thus the MLE
of oe is more efficient than the sample variance. It is straightforward to
extend to above analysis to the case of higher-order MA processes.

We can make use of the asymptotic distribution of a to obtain an
asymptotic test of whether, for example, the twelve-month forward rate
prediction error variance was higher during the EMS period than during the
pre-EMS period. By constructing the two subperiods so that the final
forecast error of the first subperiod has no overlap with the first forecast
error of the second subperiod, we can insure that the two ML estimates of

the error variances, oy and Gs are independently distributed with

asymptotic variances V, and Vj. Therefore [( 3, - 7) = (01 - o9)]


-22-

by capital controls outweight any possible macroeconomic benefits, I will
not try to argue the case here. What is clear is that if capital controls
have been substantially responsible for the success of the EMS in
stabilizing exchange rates, then the EMS experience has only limited
relevance as a model for coordination between large countries with open

capital markets.

Conclusion

Rather than repeat the main findings of this study, which are already
summarized in the introduction, I shall conclude by stressing two major
qualifications of my results. First, it should be recognized that without a
complete structural model and without knowledge of the processes governing
the exogenous disturbances, one cannot really be sure what effect the EMS
has had on the predictibility of exchange rates. The 1979 oil price
increase is but one example of a disturbance which make the results here
more difficult to interpret. By drawing on the pre-EMS experience and by
drawing on the experiences of non-EMS countries, one can provide only a very
imperfect counterfactual. Second, the EMS has not been in existence nearly
long enough for one to develop powerful statistical tests of its effects.
Is the trend rise in the real exchange rate of the lira against the deutsche
mark an equilibrium phenomenon, or an EMS-generated bubble which we would
see burst in a large sample? This is certainly one issue best left to

future research.


US March 1979 [ FRANCE March 1979

I
!
r

|
|

lot Wy ®

bp

I
!
T

|
|

lo+ iy B®

» wy

-35-

[—_ SWITZERLAND

PN Pees

*
i

js GG ee 0 | Ss

lot DO Bb
I
|

lot vy Bb

1974 1976 1978 1980 1982
[- GERMANY ;

1974 1976 1978 1980 1982 1984

T
!
iv

Fig. 2. Monthly movements in the log of trade-weighted real (CPI) exchange rates, March 1973-March 1984.
End-of-month (home currency/foreign currency basket) rates, March 1979 =O.

1984

10+ ® A

a


-17-

differentials. In the presence of money demand disturbances, for example, a
money supply policy directed at stabilizing real exchange rates is
equivalent to a policy of stabilizing real interest rate differentials. A
similar result holds if a shift in private portfolio preferences between
domestic- and foreign-currency denominated bonds is offset by a sterilized
intervention operation 2// It is true that the optimal (output stabilizing)
response to real disturbances does not necessarily involve stabilizing real
interest rate differentials, but then it does not typically involve
stabilizing real exchange rates, either. Thus if one observes that intra-
European real interest rate differentials have become more volatile since
the formation of the EMS, it would suggest that either (a) capital controls
have been a major factor in the stability of EMS exchange rates, or (b) the
EMS has been (suboptimally) stabilizing real exchange rates in the face of
real disturbances (though this normative conclusion is weakened if the
real shocks are fiscal policy shocks.) It is true that uncertainty about
the size and timing of EMS realignments would be a third candidate
explanation. But a supporter of the EMS would hardly want to argue that its
main contribution was an increase in uncertainty about policy.

A direct relationship between the real exchange rate and the real
interest rate differential may be obtained by manipulating the uncovered
interest parity equation, which holds when capital mobility and asset

substitutibility are perfect :28/

1+ ry(k) = C1 + rek)] (Spay /Sp) (1)

In equation (1), ry (k) is the domestic k-period nominal interest rate at
*
time t; r (k) is the foreign rate. The exchange rate at time t is Spe and

tStak is the expectation at time t of the exchange rate at time ttk.


-9-

across subperiods are qualitatively unaffected. The other variability
comparisons presented below are also generally robust to using mean absolute
deviations rather than variances. Yet another issue which should be
addressed is recent evidence that forward rate prediction errors are
conditionally heteroskedastic.£/ The variance estimates in table 2 are
still meaningful in the presence of conditional heteroskedasticity, as they
are still consistent estimates of the unconditional prediction error
variances. In other words, if a regime were left in place for a long period
of time and if the process generating the prediction errors variances were
stationary, then the procedures followed here would yield a consistent
estimate of the mean prediction error variance. The mean variance is an
appropriate criterion for comparing regimes if the social loss function is
quadratic in exchange rate prediction errors and is constant over time.
Because the EMS is subject to periodic realignments, one might
conjecture that the EMS has not made exchange rates any easier to predict at
longer horizons. This does not seem to be the case, however, at least for
nominal exchange rates. The results for three-, six- (both not reported)
and twelve-month forward rate prediction errors are qualitatively extremely
similar to the one-month horizon results 2/ Note that for these longer
horizons, the sample variance is a consistent but not an efficient
estimator. When monthly data is employed, the overlapping multi-month
horizon forecast errors follow a moving average process; see, for example,
Hansen and Hodrick (1980). The estimates in table 2 are thus based on the
maximum likelihood procedure discussed in the statistical appendix.
(Qualitatively similar results obtain when sample variances or sample mean
absolute values are employed.) The appendix also discusses the asymptotic
test used to compare the pre-and post-EMS forecast error variances. (One
cannot form an F-test based on the sample variances, because the overlapping

forecast errors are serially correlated.) Even at twelve-month horizons,


~32-

Henderson, D.W., 1984, Exchange market intervention operations: Their role
in financial policy and their effects, in J.F.0. Bilson and R.C.
Marston, eds., Exchange rate theory and practice (University of
Chicago Press, Chicago).

Isard, P., 1983, An accounting framework and some issues for modeling how
exchange rates respond to the news, in J. Frenkel, ed., Exchange rates
and international macroeconomics (University of Chicago Press,
Chicago).

International Monetary Fund, 1983, Annual report on exchange arrangements
and exchange restrictions (International Monetary Fund, Washington,
0.C.).

Jarque, C.M. and A.K. Bera, 1980, Efficient tests for normality,
homoscedasticity and serial independence of regression residuals,
Economics Letters 6, 255-259.

Mann, H.B. and A. Wald, 1943, On stochastic limit and order relationships,
The Annals of Mathematical Statistics 14, Sept., 217-226.

Marston, R.C., 1984, Financial integration and the effects of an exchange-
rate union, in J. Bhandari, ed., Exchange rate management under
uncertainty (MIT Press, Cambridge, MA.).

Meese, R.A. and K. Rogoff, 1983, Empirical exchange rate models of the
seventies: Do they fit out of sample?, Journal of International
Economics 14, Feb., 3-24.

Mood, A.M., F.A. Graybill and D.C. Boes, 1974, Introduction to the theory
of statistics, (McGraw-Hill, London).

Mussa, M., 1977, A dynamic theory of foreign exchange, in M. Artis and A.
Nobay, eds., Studies in modern economic analysis: The proceedings of
the association of university teachers of economics, (Basil Blackwell,

Oxford).


-29-

weighted French franc. The hypothesis can only be rejected at the 80% level
for the trade-weighted DM.

13/ The VAR forecasting begins two months into each subsample because two
lags are required to generate a one-month ahead forecast. For the VAR, RMSE
and standard deviations are the same at one-month horizons and very similar
at longer horizons. RMSE and standard deviations are also very close at
short-horizons for the random walk model. A second-order autoregressive
model, with or without a time trend, yields in-sample one-month horizon RMSE
which are slightly higher than those of the VAR model. Michel Galy informed
me of unpublished work in which he has compared the pre- and post-EMS
volatility of the French franc using shorter time periods and different
price indices. He finds that the real franc may even have been more
variable under the EMS.

14/ The F-tests reported in table 3 yield the same results when the random
walk prediction error variances are calculated using the sample mean as when
the raridom walk model is assumed to be an unbiased forecaster. An F-test is
not valid for the VAR estimates, but it is possible to use an asymptotic
likelihood ratio test; see Mood, Graybill and Boes (1974). The asymptotic
test rejects equality of pre- and post-EMS variances for all the one-month
VAR estimates.

15/ For forward rate predition errors, the pre-EMS one-month conditional
variances for the (pound/yen, yen/dollar, pound/dollar) are (8.4, 8.8, 7.8).
Post-EMS, they are (15.3, 15.5, 11.5). For real rates, the pre-EMS random
walk mean-squared prediction errors are (8.4, 9.1, 9.9), and post-EMS

they are (15.2, 13.3, 9.5). At twelve-month horizons, the differences are
much less pronounced. I am grateful to John Flemming for suggesting that I

present results for rates between non-EMS currencies.


whatsoever of any convergence between France's, Germany's and Italy's
inflation rates. (GDP deflators yield a similar picture to the CPI rates.)
Indeed, any converging which took place was between the inflation rates of
Germany, Japan and the United Kingdom. Comparing the final twelve months
prior to the EMS, February 1978 - February 1979, with the recent twelve-
month period March 1983 through March 1984, we can detect some convergence
in EMS inflation rates. Again, however, there is a much more discernable
convergence between Germany's inflation rate and those of the U.S., U.K.,
and Japan. Even if French, German and Italian inflation rates do ultimately
converge at a low level, one should be cautious in attributing this success

to the existence of the EMS.

3. The variance of unanticipated nominal exchange rate movements, pre- and

post-EMS.

In most modern macromodels, unanticipated disturbances have far greater

effects than perfectly anticipated shocks. Thus a natural measure of
exchange rate volatility is conditional variance; that is, the variance

of unanticipated movements in the exchange rate. Throughout most of

this section, nominal exchange rate expectations will be measured using
Euromarket forward rates. The implicit assumption is that expectations are
rational and there is no exchange rate risk premium. The results are shown
not to be sensitive to allowing for the type of (small) time-varying risk

premium which has been detected in some exchange market "efficiency"

studies.
Table 2 contains estimates of the variance of the forecast error et** =
ttk ; :
log Shak - log FE » where Stak is the exchange rate in month t +k, and
ptt is the k-month ahead forward rate in period t. (Under the null

hypothesis of risk neutrality, the mean prediction error is known and equal


Table 1

A cross-country comparison of wholesale price index and consumer price index
inflation rates before and after March 1979.4

Feb. 74 - Feb. 79 Mar. 79 - Mar. 84 Feb. 78 - Feb. 79 Mar. 83 - Mar. 84
(mean 12-month rate) (mean 12-month rate)
WPI CPI WPI CPI WPT CPI WPI CPI
Germany 3.2 4.2 5.3 4.6 3.1 2.6 5.6 3.2
France 5.0 10.3 10.8 11.6 11.2 10.1 14.5 8.6
Italy 15.0 16.4 15.0 17.0 11.2 13.1 11.4 11.7
U.S. 8.4 7.9 6.7 8.0 10.3 9.9 2.9 4.7
Japan 2.2 7.8 4.6 4.3 -.9 2.5 -1.3 2.5
U.K. 16.2 15.5 9.2 10.4 8.7 9.6 6.4 5.2
Switzerland el 3.0 3.7 4.6 2.1 4.0 3.4

4 See the data appendix for a description of the indices used. Note that the CPI/WPI differential for
the early five-year subperiod is sensitive to the starting date. In some countries, the 1973 oi1 shock
passed more quickly into WPI's than into CPI's.


-18-

*
Denoting the domestic CPI by P and the foreign CPI by P, we can multiply by

both sides of equation (1) by a common factor to obtain

[1 + re (k)HPe/ePe ag /E1 + rok) TP E/pP tag)

= (Pe/SePe) (ePeak * tStak/tP tak)» (2)

Taking logarithms of both sides of equation (2) yields a relationship
between the real interest differential and the expected rate of change of

the logarithm of the real exchange rate:

*
Peak ~ tReak 7 Ut 7 tI (3)

* .
where Peek = log {[1 + Pek) I(Pe/ Peay) ts and q, = log (PL/S,P4)- To
derive a relationship in terms of conditional variances, take t-1
expectations across equation (4) and subtract the resulting equation from

(4) to obtain:

oo \
CEReak ~ teak] = 4 > take (4)

where x’ = tt - t-1%t. Referring to equation (4), consider the effect of a
money demand disturbance. Because purely nominal disturbances have no real
effects in the long run, the effect of the disturbance on the expected
future real exchange rate should be smaller than its effect on the current
real rate, at least for large enough k. (In standard sticky-price exchange-
rate models such as Frankel (1979) or Mussa (1977), the effect on % would
be greater than on tIt+k for all k.) Thus if monetary policy is used to

offset the effects of financial disturbances on current and expected future

real exchange rates, one would expect to see a decline in the conditional


-8-

to zero; thus the root-mean-squared-error (RMSE) is equal to the standard
deviation.) The data is monthly; the two subperiods considered are the five
years preceeding the EMS and the first five years of the ews 2/ Examining
the ore-month DM prediction errors, we find that the conditional variances
of the French franc/DM and lira/DM exchange rates were both approximately a
quarter as large during the EMS period as during the pre-EMS period. Using
a one-tailed F-test, the hypothesis of equality of variances can be rejected
at the 95% level for both rates. The Swiss franc/DM rate also has lower
one-month conditional variance in the EMS period, though the difference is
not statistically significant. The variances of the dollar/DM, pound/DM and
yen/DM exchange rates are all higher under the EMS; the dollar/DM rate
variance is significantly higher at the 90% level of confidence, and the
yen/DM variance is higher at the 95% significance level.

The results reported in table 2 do not appear sensitive to the
assumption of risk neutrality. One can allow for a time-varying risk
premium in the one-month forward rates by regressing the time t prediction
error, eth against San and Sarn Risk premia of this form have been
detected in other studies ./ The residual of the autoregression may be
treated as the "unanticipated" component of the forward rate forecast error.
Relaxing the assumption of risk neutrality in this fashion yields one-month
conditional variance estimates extremely similar to those reported in table
2. Another potential problem with table 2 is that variance estimates can be
quite sensitive to outliers. This is especially worrisome if the
distribution has fat tails and converges only slowly to normality. Indeed,
a joint chi-square test of the excess skewness and excess kurtosis of the
forward rate prediction errors indicates significant deviation from
normality in over half the cases _/ However, when mean absolute deviations

rather than variances are used as a measure of variability, the comparisons


-24-

Statistical Appendix

One can obtain consistent estimates of k-month forward rate prediction
error variances by sampling every kth monthly observation. When k > 1,
however, more efficient estimates may be found by employing all the data.
Under the more efficient approach, the multi-step prediction errors overlap
and thus follow a moving average process. Here we demonstrate that the
sample variance of an MA process, although still a consistent estimator of
the unconditional variance of the series, is asymptotically less efficient
than the maximum likelihood estimator (MLE). This section also develops a
test for comparing overlapping multi-step forecast error variances across
independent subsamples.

Suppose forward rates are for two month horizons and the data is
sampled monthly. Let e be the difference between the logarithm of the
realized time t + 2 spot rate, and the logarithm of the time t two-month

forward rate. Under the joint assumptions of rational expectations and risk

neutrality, e follows the MA process:
eg = ay - Ogi, (Al)

where the a's are serially uncorrelated; for convenience we will make the
further assumption that a, ~ N(O, o), though our results only require
asymptotic normality. We are interested in forming an estimate of

2 2) 2 : *2 0.0.
% = (1 + 6 )o3 + The sample variance of e, og, is given by

n
el y A2
be =F le (A2)

(Note that mean of e is known and equal to zero under the null hypothesis.)

*
The consistency of % is easily demonstrated@2/; the variance of the


International Finance Discussion Papers
Number 245

July 1984

CAN EXCHANGE RATE PREDICTABILITY BE ACHIEVED WITHOUT
MONETARY CONVERGENCE? -- EVIDENCE FROM THE EMS

by

Kenneth Rogoff

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished materials)
should be cleared with the author or authors.


-1l-

(at the 95% level). The conditional variance of the mltilateral trade-
weighted lira at three and twelve months is also significantly lower during
the post-EMS period. If bilateral trade weights had been used instead of
multilateral trade weights, the reduction in the relative variance of the
EMS country exchange rates would probably have been more pronounced, since

most EMS trade is intra-European.

4. The variance of unanticipated real exchange rate movements, pre-

and post -EMS.
Some would argue that the EMS has served to destabilize real exchange

rates, by delaying nominal exchange rate adjustments even where they are
necessary to offset inflation rate differentials. Here we shall attempt to
investigate this hypothesis. It is, unfortunately, even more difficult to
Measure expectations about the real exchange rate than the nominal exchange
rate; one cannot directly observe inflationary expectations. (The problem
is less severe at short horizons, since short-term exchange rate volatility
is typically an order of magnitude greater than short-term price level
volatility.)

Figure 1 plots the logarithm of six bilateral real exchange rates
against the DM; prices are measured using consumer price indices t1/ Note
that between March 1979 and March 1984, the lira appreciated substantially
in real terms against the DM; the change in the logarithm of the real
exchange rate was .24. By contrast, the French franc appreciated against
the DM by only 2% in real terms over the first five years of the EMS.
Herein lies the difficulty of trying to use a relatively small data set to
measure long-horizon conditional forecast error variances. Elaborate time
series techniques cannot obscure the basic fact that it is very difficult to
say whether private agents anticipated these trend movements.

Having suitably qualified our results, we now turn to our two real


-10-

the franc/DM and lira/DM rates are significantly less variable in the post-
EMS period. 22/

Though the focus of this study is on whether and how the EMS has
succeeded in stabilizing intra-EMS rates, table 2 also reports results for
multilateral trade-weighted exchange rates. The weights are based on each
country's share of total trade among the G-11 countries; see the data
appendix. (Clearly, one cannot derive a single ideal measure of the trade-
weighted exchange rate without reference to a particular theoretical model.
The measure employed here is a popular one, but it may be of interest to
apply our methodology to alternative measures.) One reason for considering
a trade-weighted exchange rate is that it is possible to construct examples
where stabilizing the bilateral rate between two countries destabilizes the
trade-weighted exchange rate of one or both countries. Canzoneri (1982)
constructs an example based on real disturbances. Marston (1984)
demonstrates that destabilization is possible even with purely financial
disturbances. He shows that when intra-European bilateral rates are fixed,
portfolio shifts between the U.S. and Germany can have a greater effect on
the trade-weighted exchange rates of third-party European countries than
such shocks would under a pure float. Since it is quite possible that
private portfolio shifts between the U.S. and Germany are an important
phenonemon, Marston's result raises the question of whether the EMS right
have destabilized the trade-weighted lira and the trade-weighted franc. The
evidence in table 2 suggests that this theoretically troublesome possibility
did not strongly manifest itself, at least for nominal rates. (As we shall
see below, the evidence is much less clear for real rates at longer forecast
horizons.) Whereas the one-month forecast error variances rose
significantly for the yen and the dollar (at the 95% level), and for the
pound (at the 90% level); the conditional variances for the DM and French

franc did not rise significantly, and the lira variance fell significantly


~31-
References

Box, E.P. and G.M. Jenkins, 1976, Time series analysis: Forecasting and
control, (Holden-Day, San Francisco).

Canzoneri, M.B., 1982, Exchange intervention policy in a multiple-country
world, Journal of International Economics 13, Nov., 267-89.

Collins, S.M., 1983, Exchange rate expectations and interest parity during
credibility crises: The French franc, March 1983, Xerox, Nov.
(Massachusetts Institute of Technology, Boston, MA.).

Cumby, R.E. and M. Obstfeld, 1984, International interest-rate and price-
level linkages under flexible exchange rates: A review of recent
evidence, in J.F.0. Bilson and R.C. Marston, eds., Exchange rate
theory and practice (University of Chicago Press, Chicago).

European Community Directorate-General for Economic and Financial Affairs,
1984, The European Community's experience of mutual economic

surveillance and monetary cooperation, Commission of the European

Communities Document 11/60/2/84-EN (Brussels).

Flood, R.P., and P.M. Garber, 1983, A model of stochastic process
switching, Econometrica 51, May, 537-551.

Frankel, J.A., 1979, On the mark: A theory of floating exchange rates
based on real interest differentials, American Economic Review 69,
Sept., 610-622.

Frankel, J.A., 1982, On the franc, Annales de l'insee 47-48,

July/Dec., 185-221.

Hannan, E.J., 1970, Multiple time series, (John Wiley and Sons, New York).

Hansen, L.P. and R.J. Hodrick, 1980, Forward exchange rates as optimal
predictors of future spot rates: An econometric analysis, Journal of

Political Economy 88,, Oct., 829-853.


-30-

16/ Frankel (1982) also analyzes the effects of French capital controls on
offshore/onshore interest rate differentials. Some of the details of French
and Italian capital controls are described in Exchange Restrictions and
Trade Restrictions, (International Monetary Fund, 1983).

17/ For a discussion of monetary stabilization policy in an open econony,
see Henderson (1984).

18/ Isard (1983) stresses the usefulness of the "identities" approach in
analyzing the relationship between real exchange rates and real interest
rates.

19/ For a recent survey of the empirical literature on sterilized
intervention, see Rogoff (1984).

20/ The fact that e is a consistent estimate of oe may be viewed as a
special case of theorem 14 in Hannan (1970), pg. 228. Hannan's theorem
demonstrates very general conditions under which sample moments are

consistent estimates of population moments.


Table 2

The variance of forward rate prediction errors, log Stag 7 log FEtK a
Exchange rates versus DM Multilateral trade-wei ghted?
exchange rates
Feb. 1974-Feb. 1979 Mar. 1979-Mar. 1984 Feb. 1974-Feb. 1979 Mar. 1979-Mar. 1984
Forecast horizon: one twelve one twelve one twelve one twelve
(months ) month months month months 4 month months . month months
Germany 4.3 41 4.3 45
(15) (17)
France 4.5¢ 72° 1.3¢ 21¢ 3.0 57 3.9 28
(26) (8) (23) (8)
Italy 10.3° 86° 2.2¢ 24c 6.6 107¢ 2.5 18¢
(21) (8) (35) (6)
United States 8.94 89 12.64 161 5.5¢ 71 9.1¢ 90
(29) (55) (21) (27)
United Kingdom 8.2 54 10.8 79 5.24 434 7.84 94d
(14) (21) (14) (29)
Japan 7.1¢ 84 14,1¢ 133 5.2¢ 69 10.8¢ 135
(21) (45) (27) (58)
Switzerland 5.2 gsc 4.2 31¢ 7.7 133 6.3 89
(26) (13) (46) (27)

4 The units are approximately Ppercent-squared/forecast horizon. Twelve-month-horizon maximum likelihood estimates
were obtained using the Multiple Time Series Arima package at the Federal Reserve Board. Standard deviations of
fhe twelve-month variance estimates are in parentheses.

c See the data appendix for a description of the trade weights.
~ Variance in pre-EMS subperiod is significantiy different from variance in post-EMS subperiod at 5% ievel. A one-
tailed F-test is used for one-month horizons; the test described in the statistical appendix is used for twelve-
gonth horizon comparisons.

Variance for pre-EMS subperiod is significantly different at 10% level.


-21-

The results are reported in table 5. For the German-French real
interest differential, the conditional variance is higher in the EMS
subperiod by any of our three measures. The evidence is mixed for the
German-Italian differential, since the variance for the short-term
differential with VAR inflation proxy is lower under the EMS. But the other
two measures do not yield lower variances for the EMS period. Taken
together, the results of tables 1, 4 and 5 suggest that the success of the
EMS in stabilizing real exchange rates cannot be attributed to monetary
policy coordination alone.

The issue of sterilized intervention has not been given much attention
thus far. One reason is that to the extent it is used to offset portfolio
disturbances, sterilized intervention should also stabilize real interest
differentials. But the main reason is the growing body of empirical evidence
that sterilized intervention has very little effect in the absence of
capital controls =2/ This does not rule out the possibility that sterilized
intervention can be "effective" in an economy with capital controls.
Consider a (not atypical) regime where foreigners may go to the home central
bank and demand foreign currency in exchange for domestic currency, but
domestic residents are not permitted to acquire foreign assets from abroad.
In such an economy, sterilized intervention essentially mops up any domestic
currency which leaks abroad and is not willingly held. Obviously, such
intervention can continue only a long as the central bank has adequate
reserves. leakage may occur through illegal capital flight, or through
current account deficits which are not financed by foreign-currency
borrowing. If the controls are sufficiently effective to slow the pace of
illegal capital flight, they can serve to (temporarily) protect the domestic
currency from sudden portfolio shifts, thereby stabilizing day-to-day
movements in the exchange rate.

Though my presumption is that the microeconomic inefficiencies caused


-27-

Footnotes

* The author has benefited from discussions with many of his colleagues in
the International Finance Division of the Federal Reserve Board. Neil
Ericsson provided valuable suggestions on the statistical appendix. This
paper represents the views of the author and should not be interpreted as
reflecting the views of the Board of Governors of the Federal Reserve
System.

1/ See Ungerer, Evans and Nyberg (1983), and the European Community
Directorate-General for Economic and Financial Affairs (1984).

2/ In addition to France, Germany and Italy, the other participants in the
EMS are Ireland, Netherlands, Belgium, Luxemborg and Denmark.

3/ Vaubel (1980) discusses some of the limitations of the divergence
indicator.

4/ Collins (1983) employs the term structure of interest rates to analyze
investors' expectations concerning the timing and the magnitude of the March
1983 realignment.

5/ It is not really possible to draw a strict demarcation between the pre-
and post--EMS regimes. The formation of the EMS was not entirely
unanticipated (indeed, it was scheduled to go into effect in January 1979,
but was delayed until mid-March.) Anticipations of the new regime might
well have affected exchange rate behavior in the old regime. Flood and
Garber (1983) study the effects of anticipated "process-switching" on
exchange rates.

6/ Hansen and Hodrick (1980) present evidence that lagged forward rate
prediction errors help predict future forward rate prediction errors. It
has proven difficult to estimate a structural model of this risk premium;

see Rogoff (1984).


controls were operative both before and after the formation of the EMS. The
presence of these controls may explain why Italy and especially France were
able to reduce fluctuations in their exchange rates against the DM without
reducing fluctuations in real interest differentials. The important role of
capital controls may limit the relevance of the EMS coordination experience
for coordination between large countries with open capital markets, such as
Germany and the United States.

Section 2 of the paper contains a brief description of the EMS, and
evidence on the convergence of inflation rates. Section 3 examines nominal
exchange rate variability, and section 4 looks at real exchange rate
variability. Section 5 investigates the relative importance of capital
controls and monetary policy coordination in stabilizing intra-EMS exchange
rates. Efficient estimation of multi-step conditional forecast error

variances is discussed in a statistical appendix.

2. Convergence of inflation rates.

The EMS is something of a hybrid between a crawling peg system and a
fixed but adjustable rate system. There are bilateral central rates for
each pair of currencies, around which fluctuations of up to +2.25 percent
are permitted (6 percent for the lira). Theoretically, when the margins are
reached, the participating central banks are obliged to intervene in
unlimited amounts. However, the central banks sometimes change the central
rate instead. The bilateral intervention limits are supplemented by a
"divergence indicator", which may be viewed as measuring the deviation of a
country's weighted average EMS-currency exchange rate from a weighted
average of its bilateral central rates. When a currency reaches its
"threshold of divergence", set at 75 percent of the maximum possible

divergerice spread, there is a "presumption" that the authorities in the


-14-

the hypothesis of equality of pre- and post-EMS variances for both the
franc/DM and the lira/DM rates. The Swiss franc/DM rate variance a’so fell
significantly. The one-month conditional variance of the real dollar/DM,
pound/DM and yen/0M rates were all higher during the EMS subperiod, but only
the yen rise is statistically significant 24/

The trade-weighted real exchange rates are plotted in figure 2, and
their conditional forecast error RMSE are presented in table 3. Note that
there has been no significant trend movement in the real trade-wei ghted
lira. The one-month horizon random walk results indicate that the variance
of the real trade-weighted lira was significantly lower during the EMS
period and the real trade-weighted Swiss franc variance was also lower
(though only at the 90% level). The real trade-weighted exchange rate
variance of the DM and French franc did not change significantly, whereas
the conditional variances of the trade-weighted real pound, yen and dollar
(90%) all rose significantly in the second subperiod.

The point estimates for the twelve-month horizon RMSE present a
somewhat similar picture for the DM bilateral rates. (No formal tests are
presented.) Note though, that the fall in the volatility of the real
lira/DM rate is much less decisive at twelve months, whether measured by the
VAR or by the random walk model. The twelve-month horizon trade-wei ghted
results are even more ambiguous. Using the random walk model, the real
trade-weighted DM RMSE doubled during the post-EMS period; using the VAR
model, the RMSE for the yen halved. Thus one cannot entirely dismiss the
empirical relevance for the EMS of the Canzoneri-Marston point: Attempts to
stabilize a bilateral rate may destabilize the trade-weighted rate.

One comparison that has not been made thus far is to ask what has
happened to the variability of exchange rates between non-EMS currencies.
Could it be that the post-EMS period is characterized by increased

volatility between EMS and non-EMS currencies, but decreased volatility for


-16-

Table 4

Offshore/onshore three-month interest differentials for France and Italy.

Jan. 1975 - Feb. 1979 March 1979 - March 1984

standard standard

mean maximum deviation mean maximum deviation
France® 2.0 4.6 1.2 3.2 14.3 4.1
Italy® 5.0 24.8 5.5 3.8 18.5 4.6

4 Three-month Eurofranc rate minus the three-month Paris interbank rate (end-
of-month data, annual percentage rates).

b Three-month Eurolira rate minus the three-month Milan interbank rate (end-
of-month data, annual percentage rates).


-2-

years; this result holds for nominal exchange rates at horizons from one
month through one year. Real exchange rate volatility was also
significantly lower at short horizons, though the evidence is not decisive
at twelve-month horizons. In contrast, the DM exchange rates of the dollar,
yen and pound were all more variable (though not always statistically
significantly) during the EMS period than during the pre-EMS period.
Bilateral cross-exchange rates for the dollar, yen and pound have also
generally become more volatile since March 1979. Nor do results based on
multilateral trade-weighted exchange rates reverse the conclusion that EMS
members have experienced more forecastable exchange rates, at least at
short-term horizons.

Whereas there is substantial evidence that the EMS period has been
characterized by reduced intra-European exchange rate volatility, it is not
certain how much this success should be attributed to increased monetary
policy coordination. For one thing, only recently has there been any
perceptible convergence between French, German and Italian inflation rates.
Also, the evidence presented here suggests that the EMS has not led to a
reduction in the conditional variance of real interest rate differentials
between France and Germany. (The results are mixed for differentials
between Italy and Germany.) This is troublesome because in the presence of
financial disturbances, an optimal intervention policy directed at reducing
unanticipated movements in real exchange rates should also end up reducing
unanticipated movements in real interest rate differentials. It is true
that the above result does not hold for real disturbances, but then standard
intervention models do not prescribe fixing the exchange rate (a la EMS)
in response to real disturbances. The relationship between the conditional
variances of real interest differentials and real exchange rates also breaks
down in the presence of capital controls. A comparison of onshore and

offshore interest rates for the lira and the franc suggests that capital


~25-

*
asymptotic distribution of oe is given by

<
q

=n) prim (n71/2 y (ef - of) 7? (A3)

nvtptim {n7 Ly(ay - @a¢_3)? - oSILY (ag - Gag_3)? - 01} (Aa)
t s

n7! ptim {n7? 5 [lag - ay 4)? - Palig
t

+ 27} Y Clay ~ oag_y)? - oe IE (ag - ay 9)? - oe]}, (A5)
t

(To obtain expression (A5) from (A4), note that crossproduct terms involving
s #t +1, t, or t - 1, are all zero.) Expression (A5) can be evaluated to
obtain:

4
* 2
Ve =a [(1 + 02)? + 2677. (A6)

To derive the MLE of a, a, and its asymptotic variance, V, we employ

the likelihood function for the MA process defined in (Al):

ag}, (A7)

n
L(Gsaglen) = (of) -TM/2E(1 - 0*2)/(1 - 62)1°/? exp { Sy}

4 t=0

(see Box and Jenkins (1976), p 272). By maximizing log L with respect to 6
and “, one can obtain the nonlinear equations in {e} for the ML estimates
of @ and a The asymptotic covariance matrix of 6 and a, H(6, ), is
given by the inverse of the asymptotic information matrix:

2
~ oI - 1-6 0
H(@, 32) = nt ; (a8)
a


Can Exchange Rate Predictability be Achieved without Monetary

Convergence? --Evidence from the EMS, by Kenneth Rogoff*

1. Introduction

When the European Monetary System was founded in March 1979, many
skeptics argued that countries with widely divergent and highly variable
inflation rates could not possibly hope to stabilize their bilateral nominal
exchange rates. In one sense, the skeptics were right: the EMS experienced
seven central parity realignments during its first five years.

Nevertheless, recent studies by the International Monetary Fund and the
European Community conclude that there has been less month-to-month
volatility in intra-EMS exchange rates --both nominal and real-- since the
formation of the ens.2/

One purpose of the present paper is to investigate whether the EMS has
coincided with reduced variability in unanticipated nominal and real
exchange rate movements. Exchange rate expectations are measured using
Euromarket forward rates, as well as random walk and vector autoregressive
forecasting models. This study also extends earlier analyses by considering
volatility at horizons greater than one month. (The efficient estimation of
‘multi-month conditional forecast error variances turns out to require
estimation of a moving average process.) In order to examine the frequent
assertion that the EMS provides a blueprint for reducing exchange rate
variability among the world's largest currencies, the analysis focuses on
France, Germany and Italy.2/

Our findings based on conditional variances (variances of forecast
errors) are broadly similar to the unconditional variance results reported
in the IMF and EC studies. The variances of the French franc and Italian
lira exchange rates against the deutsche mark (DM) were significantly lower

during the first five years of the EMS than during the preceeding five


-33-

Riehl, H. and R. Rodriguez, 1977, Foreign exchange markets, (McGraw-Hill,
New York).

Rogoff K., 1984, On the effects of sterilized intervention: An analysis of
weekly data, Journal of Monetary Economics 13, Sept., forthcoming.

Ungerer, H., 0. Evans and P. Nyberg, 1983, The European Monetary System:

The experience, 1979-82, International Monetary Fund Occasional Paper

fo. 19, May, (I.M.F., Washington, D.C.).
Vaubel, R., 1980, The return to the new European Monetary System, in K.
Brunner and A.H. Meltzer, eds., Monetary institutions and the policy

Process, Carnegie-Rochester Conference 13 (North-Holland Publishing

Company, Amsterdam).


-28-

7/ The test for normality is based on Jarque and Bera (1980) who
demonstrate that the statistic T/6 (5/45) + Eg/u) - 31°/4}

is distributed chi-square with two degrees of freedom, where Wy is the ith
sample moment about the mean and T is the sample size.

8/ See, for example, Cumby and Obstfeld (1984).

9/ The multi-horizon prediction errors are constructed so that there is no
overlap between the last prediction error of the first subperiod, and the
first prediction error of the second subperiod. Twelve-month forward rate
prediction errors are based, for example, on forward rate data for February
1974 - February 1978, and for March 1979 through March 1983.

10/ For the three-month conditional forecast errors, both a test based on
the maximum likelihood estimates and an F-test based on nonoverlapping data
were constructed. These tests similarly reject the hypothesis of equality
of the pre-EMS and post-EMS conditional forecast error variances, for both
the French franc/DM and lira/DM rates.

11/' The CPI indices in figures 1 and 2 have been seasonally adjusted,
though the estimated seasonal adjustment factors are very small.

12/ A likelihood ratio test (with a degrees of freedom correction) fails to
reject the restriction that lag lengths are three instead of four in all
twenty-six cases (across exchange rates and subsamples). The test rejects
lag lengths of two in only four cases. (Three-month interbank interest
rates from IFS were used in the lag length tests.) The short-horizon
conditional variance of the real exchange rate generally changes little when
a time trend is included. A likelihood ratio test rejects (at the 95%
level) the hypothesis that all the coefficients in the two subsample VAR's

are equal for the French franc/DM, lira/DM, trade-weighted lira, and trade-


-12-

exchange rate forecasting models. One is the random walk model, whicn
predicts that the real exchange rate at any future date will be the same as
today's real exchange rate. The out-of-sample forecasting results presented
in Meese and Rogoff (1983) suggest that this naive forecasting model is
difficult to significantly improve upon. The other forecasting model

is a vector autoregression (VAR) which includes the logarithm of the real
exchange rate, CPI inflation rate differentials, twelve-month Euromarket
interest rate differentials, and the difference between the home and foreign
cumulated trade balance (each measured in dollars and normalized by their
respective mean absolute values). The VAR's include contemporaneous values
and two lags of each variable; monthly seasonal dummies are also included.
To allow for a structural break at the point of formation of the EMS,
separate VAR's are estimated for the pre-EMS and post -EMS periods 22/ The
estimated VAR forecast error variances are “in-sample"; that is, the
forecast errors are based on coefficients estimated over the entire
subsample. Given Meese and Rogoff's results that most (nominal) exchange
rate models fit poorly out-of-sample, one might argue that the in-sample VAR
estimates provide a lower bound on the forecast errors, and the random walk
model provides an upper bound. (The VAR forecasts might be improved though,
by taking into account oi] prices and/or structural breaks occurring at
important elections.)

Table 3 lists the root-mean-squared-errors for the two forecasting
models 23/ At one-month horizons, the RMSE for the VAR model are equal to
or lower than those of the random walk model, but the differences are
generally small. Using either measure, the results for one-month
conditional real exchange rate forecasts are quite similar to those obtained
for nominal exchange rates. Again, this is not surprising since price level
movements are relatively predictable at short horizons. Using a one-tailed

F-test on the random walk variances (assuming unbiasedness), one can reject


-15-

both intra-EMS rates and intra-non-EMS rates? The answer is no, at least
for the major bilateral exchange rates which are the focus of this study.
The one-month forward rate prediction error variances. for the pound/yen,
yen/dollar and pound/dollar exchange rates all rose significantly in the
post-EMS period. Using the random walk model for real rates, the real
pound/yen and yen/dollar one-month variances also rose significantly after

March 1979; the pound/dollar variance fell insignificantly.22/

5. Capital controls or monetary policy coordination?

It would appear that the EMS has indeed coincided with greater real
exchange rate stability within Europe, at least in the sense that short-term
movements in real exchange rates have become more predictable. How has this
"success" been achieved? ‘ ;

Italian and especially French capital controls have certainly played an
important role in the EMS. Table 4 illustrates the significant
differentials between Euromarket and domestic interest rates for franc and
lira assets. The higher offshore rates probably cannot be attributed to a
risk premium or taxes, since both these factors would presumably tend to go
in the other direction. As table 4 illustrates, capital controls existed
before the EMS, and indeed the analysis presented below does not rest on the
assumption that the intensity of controls has varied over time. (Though
French capital controls are generally thought to have become tighter after
May 1981,25/ ) The effects of capital controls on the volatility of any
given exchange rate depend in part on the objectives of the monetary
authorities.

If capital controls were insignificant, and if monetary policy
coordination were solely responsible for reducing the conditional variance
of real exchange rates under the EMS, one might well expect to observe a

reduction in the conditional variances of intra-EMS real interest rate