OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 54,4(1992)0305-9049 $3.00

COMPARISONS OF REAL EXCHANGE RATEVOLATILITY ACROSS EXCHANGE RATE

SYSThMS

Michael Bleaney

I. INTRODUCTION

This paper uses Deutschmark real exchange rates against currencies insideand outside the European Monetary System (EMS) to make some generalpoints about comparing real exchange rate behaviour across exchange rateregimes. In particular it argues that short-run measures of real exchange ratevolatility (such as the variance of monthly or quarterly movements) need tobe supplemented by longer-run measures that take into account the persis-tence and mean-reverting tendencies in such movements. Empirical studieshave shown that short-run real exchange rate volatility is much smaller underthe EMS than under floating rates (Artis and Taylor, 1988; Cobham, 1989;Macdonald and Zis, 1989; Ungerer et al., 1986). However, this need notprevent a steady but persistent trend in intra-EMS real exchange rates whichmight ultimately engender serious misaligmnent. For example, if a high-infla-tion country uses the EMS to benefit from the anti-inflation credibility of theBundesbank, as some authors have suggested (Giavazzi and Pagano, 1986;Melitz, 1988; Wyplosz, 1989), then the high-inflation country faces theproblem that, in order to preserve the punishment for excess domestic infla-tion, it needs to allow its real exchange rate to increase if such excess inflationoccurs. It is possible to envisage circumstances in which this process wouldgenerate more serious real exchange rate misalignments than might arisefrom apparently more volatile exchange rate regimes which are not charac-terized by persistence in real exchange rate movements. Moreover, if the realexchange rate follows a random walk, its variance increases steadily withtime, which is not the case if there is reversion towards the mean. Thus bothpersisence and mean-reversion are important factors in the medium to long-run variability of real exchange rates which are not captured by short-runmeasures. Essentially this is the fable of the hare and the tortoise. The haremoved fast, but with a high variance; the tortoise moved slowly but with greatconsistency and won the race.

The purpose of the paper is to demonstrate the significance of this pointusing relatively simple descriptive measures of real exchange rate volatility,and to employ these measures to compare real exchange rate volatility

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inside and outside the EMS. The main message is that it is insufficient simplyto look at short-run volatility; equally important, if we wish to understand thepotential of an exchange rate regime to generate serious misaligmnents, is thepersistence of short-run real exchange rate movements.

II. VOLATILITY AND MISALIGNMENT OF REAL EXCHANGE RATES

By misalignment is normally meant a deviation of the real exchange rate fromits equilibrium value. Misaligmnent may be expressed in a sustained increaseor decrease in foreign exchange reserves, or in a departure of domestic policytargets from their desired values. For example, a country with an overvaluedexchange rate may avoid a loss of reserves by depressing domestic aggregatedemand. However, the point to be stressed here is that misalignment is a con-cept relating to a snapshot of the real exchange rate at a given moment. It saysnothing about how the real exchange rate moves through time. Since there isno reason to believe that the equilibrium real exchange rate should remainconstant, particularly when official price indices designed for other purposesare used in its construction, the observation of variability over time in the realexchange rate is not in itself an indication of misalignment (see Officer, 1982,for an extended discussion of these issues).

In fact economists have had great difficulty in estimating the equilibriumreal exchange rate with any accuracy, and empirical studies commonly resortto some historically observed average as the best measure available. Clearly,such uncertainty about the equilibrium rate makes misalignment a largelyunquantifiable concept, and interest has tended to focus instead on thevolatility of real exchange rates. Volatility is usually taken as some measure ofthe dispersion of real exchange rate movements over some specified period oftime. As such, it is easily measured from published data. The connectionbetween volatility and misalignment is a little tenuous. Misaligmnent does notnecessarily entail volatility, and although volatility does entail some degree ofmisalignment, it may not be of sufficient magnitude or duration to be of realconcern. However, volatility does in some sense measure the potential formisalignment: even if there is no misalignment in the mean real exchange rate,the average degree of misalignment observed will increase with volatility. Forexample if the standard deviation of movements in the real exchange rate is 5percent per quarter, the likelihood of any given degree of misalignment at anygiven moment is clearly much greater than if the standard deviation is only 1percent.

The statement just made makes no allowance for varying degrees ofpersistence (positive serial correlation) or mean-reversion (negative influenceof the current level) in real exchange rate movements. Clearly these factorsare as important as the volatility factor in determining the average degreeof misalignment; yet their influence is not captured by the commonly usedmeasures of volatility. Although unit root tests are habitually used to test forthe existence of a significant mean-reverting tendency, such tests are essentially

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concerned with long-run equilibrium relationships rather than with the issueof volatility. This paper investigates the merits of capturing these additionaleffects by supplementing the usual measures of volatility with longer-runvolatility indicators. The measure used is the standard deviation of the levelof the real exchange rate over a time-span of years (in this case a minimum ofsix). Since this measure is based on the level rather than the rate of change, itcaptures the effects of drift as well as persistence and short-mn volatility inthe movements of the variable of interest. It will be shown that the differencebetween EMS and non-EMS real exchange rates against the Deutschmark onshort-run and long-run volatility measures does indeed tell us somethingabout persistence and mean-reverting tendencies in the different exchangerate systems.

III. ANALYSIS OF BILATERAL DEUTSCHMARK REAL EXCHANGE RATES

The analysis is based on quarterly observations of the real exchange rate ofthe Deutschinark against eight other currencies for the years 1979-90.Exchange rates are averages of daily rates; prices are output prices of manu-facturing industry. The data were obtained from OECD Main EconomicIndicators, but this source did not publish this information prior to the fourthquarter of 1980, so for earlier observations the data were obtained from IMFInternational Financial Statistics (lines ,f and 63). The four EMS currenciesused were those of Belgium, France, Italy and the Netherlands; the non-EMScurrencies were Japan, Switzerland, the United Kingdom and the UnitedStates.

Table 1 presents a statistic similar to those used in many previous studies:the standard deviation of quarterly first differences in the log of a series ofbilateral real exchange rates. It is clear that by this measure the EMS hasachieved a dramatic reduction in real exchange rate variability within the

TABLE 1Standard Deviations of Quarterly Changes in Real Exchange Rates (in Logs, X 100)

Countriespre -EMS1973/2-1978/4

EMS1979/1-1990/4

Belgium-Germany 1.92 1.41France-Germany 4.80 1.71Germany-Italy 4.01 1.63Germany-Netherlands 1.98 1.34

Germany-Japan 5.47 4.49Germay-Switzerland 3.59 2.08Germany-UK 4.94 4.32Germany-US 5.45 5.18

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system. Under floating rates the typical standard deviation is 4-5 percent perquarter, the only exception being the small countries adjacent to Germany(Belgium, the Netherlands, Switzerland). In the pre-EMS period of floatingrates, France and Italy had as great a short-run volatility in their DM realexchange rate as non-EMS countries. Within the EMS, the standard devia-tions have all been reduced to under 2 percent. It is true that volatilityappears also to have fallen in the 1980's for the non-EMS currencies, but thestandard deviation remains above 4 percent except in the case of Switzerland.Thus the evidence is very strong that the EMS has reduced real exchange ratevolatility in the conventional, short-run sense.

However, real exchange rates inside and outside the EMS are likely tohave very different dynamics. Nominal exchange rate movements are tightlyconstrained within the EMS, except on the occasion of agreed realignments.Such realigmnents have occurred 11 times in the 12 years up to the end of1990, but not all DM exchange rates have been adjusted at each realignment.We know that inflation differentials within the EMS have been persistent,although with some tendency to decline in magnitude over time (Collins,1988). Together these facts imply that we should observe a particular type ofdynamics in intra-EMS real exchange rates. Between realignments, realexchange rates should move in the direction indicated by inflation differen-tials, provided that these inflation differentials are sufficiently large comparedwith the permitted variability of nominal exchange rates. This movement maythen be partially or wholly offset by occasional nominal exchange raterealignments.

It may be useful at this stage to examine some non-parametric indicators toisolate persistence in inflation differentials and real exchange rate move-ments. The frequency of positive and negative movements in relative pricesand real exchange rates is tabulated in Table 2. The frequency of pluses andminuses in relative price movements differed significantly from what wouldbe expected on a random basis for France, Italy,Japan, the UK and the US.This is suggestive of persistence in inflation differentials relative to Germanyfor these countries.

The modern theory of floating exchange rates treats the exchange rate asan asset price which may 'jump' virtually instantaneously in relation to news.For non-EMS real exchange rates this would suggest a random pattern ofpluses and minuses. The results in Table 2 confirm this.

Within the EMS one would expect the real exchange rate to move in thesame direction as relative prices except when there was an exchange raterealignment, in which case the opposite is likely to occur. Consequently thedisparity in sign frequency should be smaller than for relative prices. ForFrance and Italy (the only two countries where inflation differentials werelarge enough to test this) this is indeed the pattern we observe. A surprisingfeature is that the Belgian real exchange rate had a significant preponderanceof negative movements. As will become clear later, this seems to reflect the

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TABLE 2Bilateral Relative Price and Real Exchange Rate Movements of the Deutschmark: Non-

Parametric AnalysisQuarterly, ¡979/1-1990/4

Notes: *significjt at .05 level. Tests of significance for numbers of pluses and minuses arebased on the normal approximation to the binomial distribution; expected value = 24. Plus signindicates movement in favour of the first-named country.

behaviour of the nominal exchange rate, since relative price movements inthis case were small.

Whereas Table 1 gives us measures of short-run volatility, the non-para-metric tests of Table 2 tell us something about persistence without saying any-thing about the magnitude of real exchange rate movements. In Table 3 theseaspects are combined in measures of the volatility of relative prices, nominalexchange rates and real exchange rates that span respectively the two halves(1979-84 and 1985-90) and the whole of the EMS period. These periodsare long enough to capture the longer-run effects of the EMS exchange ratemechanism, i.e. they are likely to include at least one nominal exchange rateadjustment. The measure used in Table 3 is the standard deviation of the levelof the variable over the whole time-span. The intuition behind this is that per-sistent movement of a variable in the same direction will be reflected inincreasing variance of the level as the time-span of measurement is increased.This is illustrated very well by the figures in Table 3 for relative prices: in allcases the 12-year standard deviation was greater than either six-year stand-ard deviation, indicating the persistence of inflation differentials. However,inflation differentials shrank dramatically for France and Italy in the secondhalf compared with the first, and less dramatically for the UK and Japan.Relative price movements against Belgium, the Netherlands, Switzerland andthe US were relatively small throughout the period.

The picture for nominal exchange rates is rather similar to that for relativeprices. In most cases the 12-year standard deviation is the highest, and for the

Relative prices Real exchange rates

Plus Minus Plus Minus

Belgium-Germany 28 20 13* 35*

France-Germany 35* 13* 25 23Germany-Italy 3* 45* 15* 33*

Germany-Netherlands 24 24 26 22

Germany-Japan 33* 15* 19 29Germany-Switzerland 26 22 24 24Germany-UK 1* 47* 27 21Germany-US 17* 31* 25 23

EMS currencies the variation was much smaller in 1985-90 than in1979-84. It appears therefore that the EMS is making good progress towardsconvergence in inflation rates and greater stability of nominal exchange rates.However, this convergence in inflation rates is not confined to the EMS, sothat it is unclear exactly what the EMS contribution is.

With respect to real exchange rates, there is no longer the dramatic differ-ence between the volatility of EMS and non-EMS rates that appeared in theshort-run measures shown in Table 1. In fact the Swiss rate has the loweststandard deviation over the entire period 1979-90, and the standard devia-tion is less for the UK than for Belgium. The distinction between the UK andthe intra-EMS currencies is much less marked than in Table 1, and the

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TABLE 3Standard Deviations of Nominal and Real Exchange Rates and Relative Prices Over

Various Time-Spans (in Logs, X 100)

Countiy6 years 6 years1979/1-1984/4 1985/1-1990/4

12 years1979/1-1990/4

RELATIVE PRICESBelgium-Germany 1.97 1.36 2.21France-Germany 11.28 2.05 14.21Germany-Italy 15.22 7.15 22.82Germany-Netherlands 2.76 4.65 5.91Germany-Japan 5.22 3.23 8.40Germany-Switzerland 1.84 1.16 2.20Germany-UK 8.46 6.52 14.75Germany-US 2.90 3.09 3.54

NOMINAL EXCHANGE RATESBelgium-Germany 10.54 1.36 10.54France-Germany 11.97 4.16 14.55Germany-Italy 11.95 5.24 17.58Germany-Netherlands 1.29 0.20 1.32Germany-Japan 15.09 7.74 17.73Germany-Switzerland 5.18 2.44 4.19Germany-UK 7.53 9.90 15.78Germany-US 17.48 20.78 20.05

REAL EXCHANGE RATESBelgium-Germany 8.70 2.10 8.70France-Germany 3.76 3.26 3.48Germany-Italy 3.96 3.16 5.75Germany-Netherlands 2.11 4.57 6.53Germany-Japan 11.53 8.13 11.23Germany-Switzerland 3.90 2.55 3.28Germany-UK 10.24 5.74 8.23Germany-US 19.18 18.29 19.10

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TABLE 4Autoregressions of Non-EMS Real Exchange Rates

Dependent variable: change in the log of the real exchange rate (Ax)Data period: 1979/2-1990/4 (47 observations)

Estimation method: OLS

NotesFigures in brackets are t-statistics.Regression based on end-period exchange rates.Serial correlation is a Lagrange Multiplier statistic which is distributed as

12-year measure suggests that the relevant split is between European andnon-European countries, with the latter having much greater long-run volatil-ity, rather than between EMS and non-EMS countries. This is indicative ofdrift in intra-EMS real exchange rates that is not present in non-EMS rates.Such drift would result from under-indexation of nominal exchange-rateadjustments, which is a well-established feature of the EMS (Cobham, 1989)and probably reflects a concern to avoid a full accommodation of domesticinflationary pressures, as mentioned above.

It is interesting to examine the behaviour of non-EMS real exchange ratesa little further. Their relatively better performance on long-run measures ofvolatility could reflect either a lower degree of persistence (positive serialcorrelation) in quarterly movements or a degree of mean reversion. Somesimple autoregressions are presented in Table 4. The change in the log of thereal exchange rate was regressed on a constant, one lagged value of itself andthe immediate past level of the real exchange rate (in logs). Use of quarterlyaverages of the real exchange rate introduces some artificial persistence intoexchange rate movements because of the moving-average effect, so end-period observations of nominal exchange rates (International Financial Statis-tics line ae) were used (replacing quarterly average by end-period exchangerates made little difference to the results reported earlier).

The persistence effects are small (but statistically significant in the case ofJapan). Mean-reversion appears to exert a much greater influence in the caseof the two European countries (Switzerland ànd the UK) than in the case ofJapan and the US. The comparison between Japan and the UK in Tables 3

Regressor Japan Switzerland UK US

constant 0.591 2.44 -0.554 -0.061(2.24) (2.83) (-3.40) (-0.17)

x_1 -0.130 -0.351 -0.281 -0.061(-2.25) (-2.83) (-3.37) (-1.21)

Ax_1 0.312 0.099 0.097 0.167(2.24) (0.63) (0.72) (1.13)

adjusted R2 0.12 0.12 0.17 0.08standard error 0.045 0.027 0.045 0.065serial correlation 1.06 0.83 0.21 0.30

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and 4 is interesting: whereas both have the same standard error in Table 4,indicating similar short-run volatility, the greater persistence and lower mean-reversion of Japan translate into higher long-run volatility in Table 3. How-ever, the lower long-run volatility of the Swiss real exchange rate (relative tothat of the UK) is essentially a reflection of its lower short-run volatility, sincepersistence and mean-reversion are similar in the two cases.

IV. CONCLUSIONS

If exchange rate volatility is a matter of concern principally because of thepossibility that it may generate serious misalignment, then conventionalshort-run measures of volatility are inadequate, because they fail to takeaccount of either persistence or mean-reversion in the dynamics of the realexchange rate. Exchange rate regimes that limit short-run variability mayincorporate some degree of persistence which under certain circumstancesmight cause serious misaligmnent and threaten the stability of the regimeitself. There is evidence of persistence of this kind within the EMS, which wasreflected in the long-run measure of volatility suggested in this paper. As aresult the difference between the volatility of intra-EMS and extra-EMS realexchange rates is much less striking on this longer-run measure than onconventional shorter-run measures; indeed, for the two European non-EMScurrencies examined, there was little difference between their longer-runvolatility against the Deutschmark and that of EMS currencies. This reflectsthe absence of persistence and the presence of fairly strong mean-revertingtendencies in the European non-EMS rates.

Department of Economics,Univeisity of Nottingham.

Date of Receipt of Final Manuscript: April1992

REFERENCES

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Cobham, D. (1989). 'Strategies for monetary integratioñ revisited', Journal ofCommon Market Studies, Vol. 27, pp. 203-18.

Collins, S. M. (1988) 'Inflation and the European Monetary System', Chapter 5, inGiavazzi, F., Micossi, S. and Miller, M. (eds), The European Monetary System,Cambridge University Press, Cambridge.

Giavazzi, F. and Pagano, M. (1986). 'The advantage of tying one's hands', EuropeanEconomic Review, Vol. 32, pp. 105 5-82.

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Macdonald, F. and Zis, G. (1989). 'The European Monetary System: towards 1992and beyond', Journal of Common Market Studies, Vol. 27, pp. 183-202.

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Ungerer, H., Evans, O., Mayer, T. and Young, P. (1986). The European MonetarySystem: Recent Developments, !MF, Occasional Paper No. 48, IMF, Washington,D.C.

Wyplosz, C. (1989). 'Asymmetry in the EMS: intentional or systemic', EuropeanEconomic Review, Vol.35, pp.310-20.

Zis, G. (1984). 'The European Monetary System 1979-84: an assessment', Journal ofCommon Market Studies, Vol. 23, pp. 45-72.