Assessing Target Zone Credibility
Mean Reversion and Devaluation Expectations in the EMS
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

The paper presents estimates of devaluation expectations for six EMS currencies relative to the Deutsche mark, for the period March 1979-May 1990. The estimation method is simple and operational, and consistently generates sensible results. The estimates are constructed by the adjusting interest rate differentials by subtracting estimated expected rates of depreciation within the exchange rate band. The adjustment is nontrivial because exchange rates within the ERM bands display mean reversion rather than random walk (unit root) behavior. The adjustment is essential since the expected rates of depreciation are usually of about the same magnitude as the interest rate differentials.

Abstract

The paper presents estimates of devaluation expectations for six EMS currencies relative to the Deutsche mark, for the period March 1979-May 1990. The estimation method is simple and operational, and consistently generates sensible results. The estimates are constructed by the adjusting interest rate differentials by subtracting estimated expected rates of depreciation within the exchange rate band. The adjustment is nontrivial because exchange rates within the ERM bands display mean reversion rather than random walk (unit root) behavior. The adjustment is essential since the expected rates of depreciation are usually of about the same magnitude as the interest rate differentials.

I. Introduction

This paper presents estimates of devaluation expectations for six EMS (European Monetary System) currencies relative to the Deutsche mark, for the period March 1979-May 1990. The estimation method is simple and operational, and consistently generates sensible results. The estimates are constructed by adjusting interest rate differentials by subtracting estimated expected rates of depreciation within the exchange rate band. The adjustment is nontrivial because exchange rates within the ERM (Exchange Rate Mechanism) bands display mean reversion rather than random walk (unit root) behavior. The adjustment is essential since the expected rates of depreciation within the band are usually of about the same magnitude as the interest rate differentials.

The idea of extracting devaluation expectations by adjusting interest rate differentials for expected rates of depreciation within the band was first suggested by Bertola and Svensson (1990), within the context of a theoretical model of an exchange rate target zone with stochastic time–varying devaluation risk. Lindberg, Svensson and Söderlind (1991) and Rose and Svensson (1991) have since implemented the method to estimate devaluation expectations for the Swedish krona and the French franc/Deutsche mark, respectively. These papers employ a number of different methods to estimate expected rates of depreciation within the band.

This paper presents straightforward estimates of devaluation expectations relative to the Deutsche mark for the six original currencies (besides the Deutsche mark) in the Exchange Rate Mechanism of the EMS. The estimates are straightforward because the expected rates of depreciation within the band are estimated by a simple linear regression. This makes the estimation method operational and easy to implement. 2/

The ERM is a cooperative exchange rate regime in which the exchange rate for each participating currency is restricted to fluctuate within bands defined around bilateral central rates relative to each participating currency. Each participating currency hence has a separate band relative to each other participating currency. In practice, the bands relative to the Deutsche mark have been the most important, since the Deutsche mark has often been the strongest currency in the ERM (except very recently) and the only ERM currency never to have undergone a bilateral devaluation. Therefore, for the purpose of estimating devaluation expectations relative to the Deutsche mark we shall only consider the bilateral bands relative to the Deutsche mark. 3/

Section II presents the model of expected rates of devaluation, section III presents the data and the estimation of expected rates of depreciation within the band, and section IV reports and interprets the estimates of expected rates of devaluation. Section V concludes.

It is beyond the scope of this paper to include an independent test of the validity of the estimated expected rates of devaluation. One such test is done in Rose and Svensson (1991), with some success. Possible tests of the validity of the estimated expected races of devaluation are briefly discussed in the concluding section V.

II. Model of Expected Rates of Devaluation

Let δtitit* denote the domestic (non–German) currency’s interest rate differencial at time t, the difference between the domestic currency interest rate it and a Deutsche mark (DM) interest rate it*, both for deposits/bills/bonds of the same default-risk and the same maturity τ > 0. Furthermore, let st denote the natural logarithm of the exchange rate, the latter measured as units of domestic currency per DM. Then we can express uncovered interest parity as:

δι=Eι[ΔSt+τ]/τ,(2.1)

where Et denotes expectations conditional upon information available at time t and Δst+r ≡ st+τ - st. 4/ That is, the interest rate differential equals the expected (average) rate of depreciation of the domestic currency relative to the DM (the rate of change of the exchange rate) during a time interval, correspond in g to the maturity. Uncovered interest parity is a good approximation if the foreign, exchange risk premium is small. Svensson (1990) argues that the foreign exchange risk premium is likely to be small in exchange rate target zones, even when there is devaluation risk. 5/

It is well known that uncovered interest parity has been rejected in a large number of empirical tests (see Froot and Thaler (1990)). However, the standard test of whether the forward exchange rate is an unbiased predictor of the future exchange rate is misleading for exchange rates within exchange rate bands with realignment risk. This is so, since the realignment risk is just one example of the well-known Peso problem, which undermines the standard unbiasedness test. Put differently, with realignment risk there is the problem that the sample distribution may not be representative of the underlying distribution of the error term, unless the sample includes a large number of realignments. Interestingly, for the French franc/DM exchange rate, which has experienced a number of realignments, there is actually empirical support for uncovered interest parity, as noted by Rose and Svensson (1991).

The method of estimating expected rates of devaluation in this paper will rely on the assumption of an insignificant foreign exchange risk premium and uncovered interest parity. In the concluding section V we will briefly mention how the method can be modified to incorporate a non-zero foreign exchange risk premium.

Let ct denote (the natural logarithm of) the central parity. A realignment is a jump in the central parity. Between realignments the central parity is constant. Next, let us introduce:

xt=stct,(2.2)

the exchange rate’s (log) deviation from the central parity. We shall informally refer to xt as the exchange rate within the band.

It will be practical to consider rates of realignment rather than the absolute size of a realignment. Let us therefore rewrite the central parity as ct = st - xt, and let us write the (average) rate of realignment from time t to time t+τ as Δct+τ/τ=Δst+τ/τ-Δxt+τ/τ. It follows that:

EtΔct+τ/τ=EtΔst+τ/τEtΔxt+τ/τ.(2.3)

That is, the expected rate of realignment equals the expected (total) rate of depreciation minus the expected rate of depreciation within the band.

Let us briefly extend on how the expected rate of realignment can be interpreted. At a realignment central parity jumps to a new level and remains constant there until the next realignment. Let market expectations of realignments be modeled in the following way. Let ptτ be the probability at time t of a realignment during the period from time t to time t+τ. During the period from time t to t+τ central parity ct remains constant with probability 1ptτ, whereas it takes a jump of independent random size Δct+τ with probability ptτ. It follows that the expected change in central parity, the expected realignment, can be written:

Et[Δct+τ]=(1ptτ)•0+ptτEt[Δct+τrealignment](2.4)=PtτEt[Δct+τrealignment],

where Et[Δct+τ [realignment] denotes the expected conditional realignment size (conditional upon a realignment during the period from time t to t+τ).(The expected conditional realignment size is positive, if a devaluation is expected, negative, if a revaluation is expected.) That is, the expected realignment is the product of the probability of a realignment during the time to maturity and the expected conditional realignment size. 6/

Define the (expected average) frequency of realignment during the time to maturity as vtτ=ptτ/τ. 7/ It follows that the expected rate of realignment in (2.4) can be written as:

Et[Δct+τ]/τ=vtτEt[Δct+τrealignment].(2.5)

The expected rate of realignment is the product of frequency of realignment and the expected conditional realignment size.

Let us then go on and note that from uncovered interest parity (2.1) it follows that (2.3) can be written:

EtΔct+τ/τ=δtτEtΔxt+τ/τ.(2.6)

That is, the expected rate of realignment is equal to the interest rate differential minus the expected rate of depreciation within the band. As observed by Bertola and Svensson (1990), equation (2.6) has empirical implications: In order to find an estimate of the expected rate of realignment, EtΔct+τ/τ, it is sufficient to find an estimate of EtΔxt+τ/τ, the expected rate of depreciation within the band, and simply subtract that estimate from the interest rate differential.

The estimation of the expected rate of depreciation within the band is made a bit complicated by the fact that the exchange rate within the band usually takes a jump at a realignment (recall that a realignment is defined as a jump in central parity). For instance, usually the exchange rate for a “weak” currency (that is, a currency that is devalued) jumps from a position near the “weak” edge of the old exchange rate band (that is, above the old central parity) to a position near or at the “strong” edge of the new exchange rate band (that is, below the new central parity). Therefore, the jump in the exchange rate is usually less than the jump in the central parity. Sometimes when the realignment is small and the new band overlaps with the old, there is no jump at all in the exchange rate.

It is complicated to estimate the expected rate of depreciation within the band inclusive of possible jumps inside the band at realignments, since there may be relatively few realignments and the sample distribution of realignments may not be representative. Then expectations of realignments and jumps inside the band may introduce a Peso problem in the estimation of the expected rate of depreciation within the band. For these reasons it seems safer to estimate the expected rate of depreciation within the band conditional upon no realignment. This practice, however, has consequences for the estimation of the expected rate of realignment that need to be clarified.

Hence, let us expand the expected change of the exchange rate within the band in two components,

Et[Δxt+τ](1ptτ)Et[Δxt+τnorealignment]+ptτEt[Δxt+τrealignment](2.7)Et[Δxt+τnorealignment]ptτ{Et[xt+τnorealignment]Et[xt+τnorealignment]},

where we recall that Ptτ is the probability of a realignment from date t up to and including date t+τ. It follows from (2.7) that (2.6) can be written as:

Et[Δct+τ]/τ+ptτ{Et[xt+τrealignment]Et[xt+τnorealignment]}/τ(2.8)=δtτEt[Δxt+τnorealignment]/τ.

We shall use the left-hand side of (2.8) as our operational definition of the expected rate of devaluation (if it is positive a devaluation is expected, if it is negative a revaluation is expected). Hence, by (2.8) the expected rate of devaluation equals the difference between the interest rate differential and the expected rate of depreciation within the band (conditional upon no realignment).

The expected rate of devaluation as we have defined it differs from the expected rate of realignment by the second term on the left–hand side in (2.8). In order to understand this term better, let us rewrite the expected rate of devaluation as:

νtτ{Et[Δct+τrealignment]+Et[xt+τrealignment]Et[xt+τnorealignment]},(2.9)

where we recall that vtτptτ/τ is the frequency of realignment. Hence, the expected rate of devaluation is the product of the frequency of realignment and the expected conditional devaluation size (conditional upon a realignment). The expected conditional devaluation size is the sum of the expected conditional realignment size and the difference between the expected exchange rate at maturity conditional upon a realignment and the expected exchange rate at maturity conditional upon no realignment.

Consider the latter difference. If the maturity τ approaches zero, the difference approaches the jump in the exchange rate within the band at a realignment. Then the expected conditional devaluation size is the expected actual jump in the (total) exchange rate at a realignment (the “true” devaluation), which differs from the jump in central parity by the jump in the exchange rate within the band. The jump in the exchange rate within the band equals the full bandwidth in the case when the exchange rate within the band jumps from the top of the band before a realignment to the bottom of the band after the realignment. For long maturities, the difference is likely to be much less, since the two expected future exchange rates within the band (conditional upon a realignment and conditional upon no realignment) are both in the interior of the band and are unlikely to be very far from the unconditional mean within the band. Therefore, for sufficiently long maturities the expected rate of devaluation is likely to be relatively close to the expected rate of realignment. 8/

For sufficiently long maturities, it is also the case that the expected rate of depreciation within the band will be approximately zero, since the maximum amount of depreciation within the band is bounded by the width of the band and then divided by a long maturity. Therefore, for sufficiently long maturities the interest rate differential is an adequate measure of the expected rate of devaluation (and also of the expected rate of realignment since the two then coincide), and there is no need to adjust the interest rate differential. However, for short maturities, the expected rate of depreciation within the band may be sizable, as we shall see.

In summary, we shall estimate the expected rate of devaluation as defined in (2.9), remembering that it differs from the expected rate of realignment in that it takes into account the possibility that the exchange rate within the band may jump at realignments.

III. Estimates of Expected Rates of Depreciation within the Band

Data

The data used is part of a database created by Andrew Rose from BIS data. The database is used and described by Flood, Rose and Mathieson (1990). Daily data for the seven initial ERM currencies are included: the Belgian/Luxembourg franc (BF), the Danish krone (DK), the Deutsche mark (DM), the French franc (FF), the Italian lira (IL), the Irish pound (IP) and the Netherlands guilder (NG). The period covered is

March 13, 1979, through May 16, 1990. 9/The spot exchange rates are recorded at the daily “official fixing”; interest rates are annualized bid rates for 1 month Euro-market bills at around 10 a.m. Swiss time.

Figures 1a-f show time-series plots of the log of the BF/DM, …, NG/DM exchange rates and their bands. The exchange rates are expressed in percentage deviation of the log exchange rate from the initial log central parity. (The scale is the same for all exchange rates except the IL/DM rate.) The realignment dates and central parities are given in Table 1. The band-width is ±2.25 percent for all currencies except the Italian lire which had a ±6 percent band before January 8, 1990, and a ±2.25 percent from then on. Table 1 also shows the number of days (excluding weekends) in each subsample between realignments (including the observations within r before each realignment).

Figure 1a.
Figure 1a.

BF/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 1b.
Figure 1b.

DK/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 1c.
Figure 1c.

FF/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 1d.
Figure 1d.

IL/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 1e.
Figure 1e.

IP/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 1f.
Figure 1f.

NG/DM log exchange rate

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Table 1.

Realignment Dates and Bilateral Central DM Rates in the EMS

article image
Source: Ungerer, Hauvonen, Lopez-Claros and Mayer (1990, Table 4). The last column gives the number of days (excluding weekdays) to the next realignment. The last date of sample is 90:05:16.

Figures 2a-f show the corresponding log exchange rates within the band. (The scale is the same for all exchange rates except the IL/DM rate.) Figures 4a-f show the interest rate differentials between the BF, …, NG interest rates and the DM Interest rate. (The scale is the same for all interest rate differentials.)

Figure 2a.
Figure 2a.

BF/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 2b.
Figure 2b.

DK/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 2c.
Figure 2c.

FF/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 2d.
Figure 2d.

IL/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 2e.
Figure 2e.

IP/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 2f.
Figure 2f.

NG/DM log exchange rate within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

In section II we mentioned that the exchange rate within the band usually jumps at a realignment. As examples we can take the realignments of the FF/DM exchange rate in October 1981 and June 1982 (see Figure 2c). Then the realignments were larger than the devaluations, in our terminology. We also mentioned that there are cases when the old and the new exchange rate overlap at a realignment and the exchange rate does not jump at all. Then there is a realignment but no devaluation, in our terminology. As examples we can take the realignments of the IL/DM exchange rate in September 1979 and January 1987 (see Figure 1d).

Estimation

We wish to estimate the expected rate of depreciation within the band, Et[Δxt+τ[no realignment]/τ =Et[xt+τ- xt+τ[no realignment]/τ, conditional upon information available at time t, where τ is 1/12 year (which corresponds to about 22 daily observations), and conditional upon no realignment between date t and date t+τ. (From now on, “expected depreciation within the band” should be understood to be conditional upon no realignment unless explicitly stated otherwise.) In the Bertola-Svensson model the single determinant of the expected future rate of depreciation within the band is the current exchange rate band within the band, xt. Although in principle the relation between the expected rate of depreciation within the band is nonlinear, Bertola and Svensson suggests that a linear approximation may be acceptable for typical parameters. Lindberg, Svensson and Söderlind (1991) and Rose and Svensson (1991) consider a number of different estimation methods, functional forms, and explanatory variables. 10/ Their results combined indicate that a simple linear regression of realized rates of depreciation within the band on the current exchange rate consistently generates sensible results; whereas fancier techniques sometimes generate clearly unreasonable results. Consequently we shall use the simple linear regression here.

The expected rates of depreciation are estimated by linear regression of the equation:

12(xt+22xt)=Σjβ0jdj+β1xt+ϵt+22.(3.1)

This regression is run separately for each of the six cross DM exchange rates: BF/DM, …, NG/DM. The variable dj is a dummy for “regime j ”, that is, each period between realignments. (For instance, for the BF/DM exchange rate we see in Table 1 that there are 6 realignments and hence 7 regimes.) Hence, for each exchange rate the intercepts are allowed to vary across regimes. For reasons detailed below, the slopes are restricted to be identical across regimes.

Estimating the expected future exchange rate depreciation within the band is of course equivalent to estimating the expected future exchange rate within the band. That is, estimation of (3.1) is equivalent to estimation of

xt+22=Σjγ0jdj+γ1xt+ηt+22,(3.2)

where the coefficients and error terms of (3.1) and (3.2) are related by γ0j ≡ β0j/12, γ1 ≡ β1/12 + 1, and ηt+22 ≡ εt+22/12. Equation (3.2) highlights the mean-reversion in the data. Table 2 shows the result of OLS estimation of (3.2). Newey-West standard errors allowing for both serial correlation and heteroskedasticity are computed, since the data are overlapping and in addition heteroskedasticity is likely.

Table 2.

Expected Future Exchange Rate within the Band, (3.2)

article image
OLS on (3.2) with Newey-West standard errors within parentheses (22 lags). Regressand is xt+22 (%) (22 daily observations correspond to one month), regressor is xt (%), where x= ln(BF/DM), …, ln(NG/DM). A vertical bar for a realignment date indicates that the corresponding currency was not realigned and that the estimate straight above applies.

Table 2 shows the regression results for the 6 exchange rates, with standard errors within parentheses. For instance, in column (6) we see that the NG/DM exchange rate has 2 realignments (79:09:24 and 83:03:31) and 3 regimes. Regime 1 (79:03:13-79:09:23) has intercept 0.52; regime 2 (79:09:24-83:03:20) has intercept -0.13; and regime 3 (83:03:21-90:5:16) has intercept 0.00. The slope, restricted to be the same across regimes, is 0.73. The number of observations varies across the exchange rates. It is lower with more realignments, since the estimation is conditional upon no realignment and therefore 22 observations before each realignment are excluded (in order not to include the jump in the exchange rate within the band that usually occurs at a realignment). 11/

The slopes vary between 0.73 and 0.90. They are estimated precisely, with standard errors between 0.04 and 0.07. They appear significantly less than unity, indicating mean-reversion in the exchange rate within the band. However, it is known that if the true slope is unity, there is a downward bias in the estimate of the coefficient (Fuller (1976)) and the usual t-distribution does not apply. The “t-values” for the coefficient being less than unity is between-3.80 and -5.71 for all exchange rates, except IL/DM for which it is -2.77. The critical level for a standard Dickey-Fuller test on a 5 percent significance level is -2.86 for this sample size (Fuller (1976, Table 8.5.2)). Therefore a unit root can be rejected (and mean-reversion be asserted) at 5 percent significance level for all exchange rates except the IL/DM exchange rate (for which the marginal significance level nevertheless is less than 10 percent). 12/

Table 3 shows the result of OLS estimation of (3.1). Table 3 can of course be constructed from Table 2; the standard errors in Table 3 are 12 times the standard errors in Table 2, etc. We see that the intercepts for the expected rates of depreciation within the band vary between -6.67 (regime 10 for IL/DM) and 13.89 (regime 4 for BF/DM) percent per year. Some of the intercepts for the short regimes are fairly imprecisely estimated. The slopes of the expected rates of depreciation within the band vary between -1.16 and -3.29 per year, with standard errors of between 0.42 and 0.86 per year. 13/

Table 3.

Expected Exchange Rate Depreciation within the Band, (3.1)

article image
OLS on (3.1) with Newey-West standard errors within parentheses (22 lags). Regressand is xt+22-xt)/τ (%/yr),τ=1/12 year (22 daily observations), regressor is xt (%), where x = ln(BF/DM),…, ln(NG/DM). A vertical bar for a realignment date indicates that the corresponding currency was not realigned and that the estimate straight above applies.

Figures 3a-f give a time-series plot of the resulting estimates of the expected rates of depreciation within the band. (The scale is the same for all exchange rates.) We see that the expected rates of depreciation within the band are sizable, usually between ±5 percent per year, although occasionally they are as large as 10 percent per year or more. The expected rate of depreciation within the band of the NG/DM exchange rate is smaller in magnitude than those of the other exchange rates, particularly after the first few years of the EMS.

Figure 3a.
Figure 3a.

BF/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 3b.
Figure 3b.

DK/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 3c.
Figure 3c.

FF/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 3d.
Figure 3d.

IL/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 3e.
Figure 3e.

IP/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 3f.
Figure 3f.

NG/DM expected rate of depreciation within band

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

IV. Estimates of Expected Rates of Devaluation

In order to estimate the expected rates of devaluation the interest rate differentials in Figures 4a-f should be adjusted for the estimated expected rates of depreciation within the band in Figures 3a-f, by equation (2.8). The resulting time-series of estimated expected rates of devaluation are displayed in Figures 5a-f. (The scale in Figures 3-5 is the same for all exchange rates. For the FF/DM during the last days before the realignment on March 21, 1983, the interest rate differential in Figure 4c and the expected rate of devaluation in Figure 5c extend beyond the top edge of the graph to about 80 percent per year.)

Figure 4a.
Figure 4a.

BF/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 4b.
Figure 4b.

DK/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 4c.
Figure 4c.

FF/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 4d.
Figure 4d.

IL/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 4e.
Figure 4e.

IP/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 4f.
Figure 4f.

NG/DM interest rate differential

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5a.
Figure 5a.

BF/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5b.
Figure 5b.

DK/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5c.
Figure 5c.

FF/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5d.
Figure 5d.

IL/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5e.
Figure 5e.

IP/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

Figure 5f.
Figure 5f.

NG/DM expected rate of devaluation

Citation: IMF Working Papers 1991, 096; 10.5089/9781451949964.001.A001

The NG/DM exchange rate has the smallest and least variable expected rates of devaluation. The expected rates of devaluation for the BF/DM exchange rate are also rather small and stable after 1984.

The average expected rates of devaluation are smaller after 1984 for all exchange rates, but not by much for some of the exchange rates. After 1984 expected rates of devaluation of 5 percent per year have been quite common, and sometimes they have reached 10 percent per year. There has also been a fair amount of fluctuation in the expected rates of devaluation (for instance for DK/DM and FF/DM). The expected rates of devaluation have usually been higher before realignments, and much smaller after (sometimes even negative, indicating an expected revaluation).

Is it really necessary to adjust the interest rate differentials for the expected rates of depreciation within the band, or could we do almost as well with just the interest rate differentials as estimates of expected rates of devaluation? If the exchange rates within the band had unit roots and followed a random walk within the band, the expected rates of depreciation within the band would be zero and no adjustment of the interest rate differentials would be warranted. Since the exchange rates within the band indeed do display clear mean reversion, expected rates of depreciation within the band are generally nonzero. Nevertheless, they could still be of such small magnitude that the adjustment does not matter much. However, the expected rates of depreciation within the band are usually of the same magnitude as the interest rate differentials (often around 5 percent per year, as we have seen), so the adjustment is indeed essential, except possibly for the very large interest rate differentials sometimes observed immediately before realignments.

Specifically, consider the DK/DM exchange rate during 1989. The interest rate differential in Figure 4b was around 2.5 percent per year for most of the year. The expected rate of depreciation within the band in Figure 3b was around -2.5 percent per year. Hence, the expected rate of devaluation in Figure 5b was around 5 percent per year, double the interest rate differential, during most of 1989. (If the expected rate of depreciation within the band had instead been around +2.5 percent per year, the expected rate of devaluation would have been around zero.) Clearly the adjustment of the interest rate differential is necessary here for a precise estimation of devaluation expectations.

Let us recall how an expected rate of devaluation of 5 percent per year should be interpreted. By expression (2.9) the expected rate of devaluation can be interpreted as the expected conditional devaluation size (conditional upon a realignment) times the frequency of realignment. Suppose the expected conditional devaluation size is 2.5 percent. (In Figure 1b we see that the realignments after 1982 have been of about that size.) Then the corresponding frequency of realignment is as high as 2 per year. Put differently, the expected time to a realignment (the reciprocal of the frequency) is as short as 6 months. The probability of a realignment within a month is about 17 percent [(2 per year)•(l/12 year)]. If instead the expected conditional devaluation size is 5 percent, the expected frequency is 1 per year, the expected time to a realignment is 1 year, and the probability of a realignment within one month is about 8 percent.

Let me also comment on the results for the IL/DM exchange rate after the time of the realignment of January 8, 1990. The central parity was increased by 3.75 percent. At the same time the bandwidth was reduced from ±6 percent to ±2.25 percent, as we can see in Figures 1d and 2d. As a consequence the upper edge of the band remained constant whereas the lower edge was increased by 7.5 percent. The exchange rate did not jump at the realignment, but the exchange rate within the band jumped from the upper part of the old band to the center of the new band.

We see in Figure 5d that the expected rate of devaluation took an upward jump after the realignment. This is a bit odd since usually the expected rate of devaluation drops at an increase in the central parity. The upward jump in the expected rate of devaluation is not due to any jump in the interest rate differential but due solely to a downward jump in the estimated expected rate of depreciation within the band, as we can see in Figures 3d and 4d. The downward jump in the expected rate of depreciation within the band is in turn due to the large negative intercept (-6.67 percent per year) estimated for regime 90:01:08-90:05:16 (Table 3, column (4)). This intercept is an outlier among the other intercepts. Even though the intercept is fairly precisely estimated, with a standard deviation of 0.88, I believe the estimate is misleading and biased downwards because of a small-sample problem.

The reason why a large negative intercept is precisely estimated is apparent from Figure 2d. There we see that the exchange rate within the band appreciated rapidly and very steadily after the realignment in January 1990 up to the end of the sample in May 1990, which naturally results in such an estimate of the intercept. However, the rapid and steady appreciation within the band is not representative and cannot be sustained, since then the exchange rate within the band would shortly end up outside the band. Clearly, an extension of the sample period to include later observations would by necessity result in a less negative estimate. For this reason the estimate of the intercept for this regime is biased downwards and misleading. 14/

V. Conclusions

In summary, I argue that the “naive” measure of devaluation expectations for a currency with an exchange rate band, the interest rate differential, can be considerably improved upon by adjusting the interest rate differential for the expected rate of depreciation within the band. The reason such adjustment is essential is that exchange rates within ERM bands display clear mean reversion, causing expected rates of depreciation within the band to be of about the same magnitude as the interest rate differentials. The expected rates of depreciation within the band have been estimated with a very simple and operational method, which consistently delivers sensible results.

The expected rates of depreciation within the band has been found to be sizable for the short maturity of one month that we have examined. We have noted that for sufficiently long maturities the expected rates of depreciation within the band must be approximately zero, though, since the maximum amount of depreciation within the band is bounded by the width of the band and then divided by a long maturity. Therefore, for sufficiently long maturities the interest rate differential itself is an adequate measure of the expected rate of devaluation (and of the expected rate of realignment, since these are close for sufficiently long maturities), and no adjustment of the interest rate differential is necessary. This reasoning is confirmed by the empirical results of Lindberg, Svensson and Söderlind (1991). They estimate the expected rates of depreciation within the band for the Swedish krona for maturities between 1 and 12 months. The expected rate of depreciation with the band for 12 month maturity is rarely above 1 percent per year in magnitude, whereas the expected rate of depreciation with the band for 6 month maturity and shorter is sometimes above 4 percent per year. A tentative conclusion from the Lindberg, Svensson and Söderlind (1991) study is that for the narrow Swedish band (±1.5 percent) it is necessary to adjust the interest rate differential for the expected rate of depreciation within the band for maturities below one year, whereas it is probably not necessary for maturities above one year. 15/

Several extensions of the method to estimate expected rates of devaluation, and several potentially fruitful uses of the estimates are obvious. It would clearly be very interesting, although it is beyond the scope of this paper, to analyze and compare the estimated expected rates of devaluation for the EMS currencies with other information about devaluation expectations. It would also be very interesting to correlate the estimated expected rates of devaluation with potential fundamental determinants of realignments, like inflation differentials, real exchange rates, reserve levels, unemployment, etc.

The estimates of the expected rates of devaluation given here are point estimates. As demonstrated in Lindberg, Svensson and Söderlind (1991) a confidence interval can be constructed for the expected rates of depreciation within the band, given the estimated covariance matrix for the intercepts and slopes of the expected rate of depreciation within the band. 16/ This results in a confidence interval for the expected rates of devaluation that can be conveniently plotted as a complement to Figures 5a-f.

The expected rates of devaluation have been estimated under the maintained hypothesis of uncovered interest parity and a negligible foreign exchange risk premium. Although I believe there are sound arguments why the foreign exchange risk premium can be neglected in narrow exchange rate bands, it is in principle possible to compute the expected rates of devaluation with nonzero foreign exchange risk premia. Given an estimate of the foreign exchange risk premium, the interest rate differential is then simply adjusted by both the foreign exchange risk premium and the expected rate of depreciation within the band. For instance, suppose the foreign exchange risk premium was not negligible during 1989 for the DK/DM exchange rate discussed above, and suppose that it has, one way or another, been estimated to be as high as +1 percent per year. Then the expected rate of devaluation for the DK/DM exchange rate during 1989 was not around 5 percent per year but around 4 percent per year. With an expected conditional devaluation size of 2.5 percent, the frequency of realignment was 1.6 per year, the expected time to a realignment was 7.5 months, and the probability of a realignment within one month was about 13 percent.

It is beyond the scope of this paper to independently test and evaluate the validity of the reported estimates of the expected rates of devaluation. Such tests can be done in a number of ways. One way is to compare the estimates with other information about devaluation expectations, for instance rumors reported in newspapers, surveys of expectations, and anecdotal evidence. Another way is to test whether the estimated expected rates of devaluation can predict actual devaluations and realignments. Under the maintained hypothesis of rational expectations by market agents, such a test can be seen as a test of the overall model of expected rates of devaluation. Under the maintained hypothesis that the model of expected rates of devaluation is true, the test can be seen as a test of how good market agents were in predicting actual devaluations and realignments. Rose and Svensson (1991) conduct a test of the predictive power of the expected rate of devaluation for the FF/DM exchange rate. They find that the estimated expected rate of devaluation indeed has some predictive power.

Although the method of extracting expected rates of devaluation that is used here is independent of the validity of the Bertola-Svensson (1990) model (or any other target zone model), the estimated expected rates of devaluation can of course be used to test that model (and other models of devaluation in exchange rate target zones). Rose and Svensson (1991) report some results along this line, for instance plots of the inferred exchange rate function and unit–root tests of the expected rate of devaluation. The results lend some empirical support for the Bertola–Svensson model. A more systematic study of that model can however be done by using the techniques of Flood, Rose and Mathieson (1990).

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1/

The author is Professor of International Economics at the Institute for International Economic Studies, Stockholm University. He thanks Bernard Dumas, Robert Flood, Lazaros Molho, William Perraudin, Paul Söderlind and, in particular, Andrew Rose for discussions and comments. Andrew Rose has also generously provided the data. The research for this paper was initiated while the author was a visiting scholar at the Research Department of the International Monetary Fund; he thanks the Research Department for its hospitality.

2/

For alternative empirical approaches to target zone credibility see for instance Bartolini and Bodnar (1991), Bertola and Caballero (1990), Bodnar (1991), Collins (1986), Edin and Vredin (1991), Fratianni and von Hagen (1990), Giovannini (1990), Svensson (1991) and Weber (1991).

Frankel and Phillips (1991) have independently applied the Bertola-Svensson (1990) and Rose-Svensson (1991) methodology to evaluate the credibility of EMS exchange rates. They examine the period 1987-1991 and use a survey of exchange rate forecasts rather than interest rate differentials to measure exchange rate expectations.

3/

See for instance Ungerer, Hauvonen, Lopez- Claros and Mayer (1990) for details on the operation of the ERM.

4/

We use the approximation ln(1 + i1τ)≈i1r, etc.

5/

Svensson (1990) shows that the foreign exchange risk premium for an imperfectly credible exchange rate band with devaluation risk has two components: one arising from exchange rate uncertainty due to exchange rate movements within the band, and the other arising from exchange rate uncertainty due to realignments of the band. The first component is likely to be very small, since conditional exchange rate variability inside the band is smaller than conditional exchange rate variability in a free float, and since foreign exchange risk premia even in a free float appear in empirical estimates to be fairly small. The second component is likely to be much larger than the first, but still of moderate size: Even with a coefficient of relative risk aversion of 8 and an expected conditional devaluation size of 10 percent, the foreign exchange risk premium is no more than 1/5 of the total interest rate differential. Hence at least 4/5 of the interest rate differential remains to be explained by something else than the foreign exchange risk premium.

6/

We disregard the possibility of more than one realignment occurring during the period from time t to t+τ. This is not restrictive since in this paper we will only consider the short period and maturity of one month. For longer maturities the possibility of two or more realignments should be taken into account (see Lindberg, Svensson and Söderlind (1991)).

7/

In the literature on stochastic processes the variable vtτ is usually called the (average) intensity (of a jump process). The variable is called the frequency of realignment here because that terminology is perhaps more intuitive. The variable has the interpretation (if it does not vary much with the maturity τ) that the probability of a jump during a short period of duration Δt is equal to vtτΔt,and the expected time to the next realignment is 1/vtτ.

8/

This is true also when proper account is taken of the possibility that several realignments can occur within long maturities.

9/

Data and programs are available from the author upon receipt of a formatted 3. 5-inch high -density diskette.

10/

The different cases examined include as explanatory variables the exchange rate within the band, its square and its cube; lagged exchange rates within the band; other ERM cross exchange rates; interest rate differentials. Also GARCH regressions, locally weighted regressions, and recursive regressions have been used.

11/

The number of observations is also less than the number of days in Table 1 because some observations are missing.

12/

Inclusion of lags and the square and cube of the exchange rate within the band might reduce standard errors and increase the magnitude of the t-statistics somewhat, increasing the possibility that a unit root is rejected also for the IL/DM exchange rate. Serially correlated error terms because of overlapping data does not invalidate the Dickey-Fuller test as long as the standard errors are consistently estimated (see Phillips (1987)). However, intercepts that are allowed to differ across regimes motivate variants of the Dickey-Fuller test that are likely to have critical values somewhat larger in magnitude than the standard test (see Perron (1989)). The margins to the critical t-value seem large enough that a unit root will still be soundly rejected at a 5 percent significance level, except possibly for the IL/DM exchange rate.

13/

Equations (3.1) and (3.2) have also been estimated without the restriction that the slopes are the same across regimes (the detailed results are not reported here). For FF/DM and NG/DM the hypothesis that the slopes are the same across regimes cannot be rejected, so for those two exchange rates the restriction to identical slopes across regimes is not binding. For the other exchange rates the hypotheses of identical slopes across regimes are rejected. Typically the slopes for some of the short regimes are outliers. In a couple of instances for short regimes the slope in equation (3.2) is above unity (indicating mean dispersion), although not significantly so. As discussed in Rose and Svensson (1991), imposing restrictions across regimes may alleviate small-sample problems arising with short regimes.

The hypothesis that intercepts for each exchange rate are identical across regimes is rejected, and there is no reason not to allow different intercepts for each regime.

14/

As discussed in Rose and Svensson (1991), this small-sample problem can arise when the length of the regime is sufficiently short compared to the expected time for the exchange rate within the band to hit one of the edges of the band when starting at the center. This small-sample problem can hence arise also with a high frequency of data and many observations.

15/

The maximum magnitude of the expected rate of depreciation within the band depends on both the maturity and the width of the band. For the standard EMS exchange rate band of ±2.25 percent the maximum magnitude of the rate of depreciation within one year is 4.5 percent per year if the exchange rate is expected to drift from one edge to the other in one year, and 2.25 percent per year if the exchange rate is expected to drift to the middle of the band. For the wide EMS bands of ±6 percent, the corresponding maximum magnitudes are 12 and 6 percent per year, respectively. Clearly, the expected rate of depreciation within the band within one year can be seizable, and the safe way is of course to estimate the expected rate of depreciation rather than to assume that it is negligible.

16/

In addition to the standard errors reported in Table 3, the covariance estimates between the intercept and slope estimates are needed.

Assessing Target Zone Credibility: Mean Reversion and Devaluation Expectations in the EMS
Author: Mr. Lars E. O. Svensson