Interest rate differentials and exchange rate policies in Austria, The Netherlands, and Belgium

Journalof BANKING &

ELSEVIER F I N A N C E Journal of Banking & Finance 19 (1995) 363-386

Interest rate differentials and exchange rate policies in Austria, The Netherlands, and

Belgium

Klaas Knot, Jakob de Haan * Department of Economics, University of Groningen, P.O. Box 800, 9700 A V Groningen, Netherlands

Received February 1993; accepted September 1993

Abstract

In this paper, the small, but persistent interest rate differentials via-h-vis Germany which have existed in Austria, the Netherlands, and Belgium are analysed. These interest differentials may be thought of to consist of three parts: expected exchange rate movements within the band, expected changes of the central rates and a risk premium. Following a similar test as proposed by Svensson, we examine the credibility of the exchange rate policy in these countries. According to this test the Belgian exchange rate policy clearly lacks credibility for most of the period under consideration. There are, however, serious problems applying this test to Belgium due to the dual exchange rate system. For Austria and the Netherlands we calculate interest differentials which are adjusted for expected exchange rate movements within the band. It appears that the differences between the adjusted and the unadjusted interest differentials can be substantial. The Granger-causal relationship between fundamentals like the rate of inflation, the government budget deficit and the current account is also quite different for the adjusted and the unadjusted interest differential, where the fundamentals have the highest explanatory power for the latter measure.

Keywords: Interest differentials; Credibility; Exchange rate policy; Fundamentals

JEL classification: E43; E52; F31

* Corresponding author.

0378-4266/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0378-4266(94)00091-3

364 K. Knot, J, de Haan /Journal of Banking & Finance 19 (1995) 363-386

1. Introduction

Monetary policy in Austria, the Netherlands, and Belgium is aimed at a stable exchange rate vis-h-vis the German mark. Underlying the choice for this so-called 'hard-currency option' is the importance of Germany as partner in foreign trade for the countries considered and, above all, the pronounced anti-inflation reputa- tion of the German monetary authorities, t Despite almost fixed exchange rates, small but persistent interest rate differentials vis-h-vis Germany have existed in these countries during the last decade. On average, short-term interest rate differentials in Austria, the Netherlands, and Belgium exceeded 0.5 percentage points since 1981, but clearly diminished in the late 1980s. For the Netherlands this positive interest differential has emerged notwithstanding the fact that the average Dutch inflation has been less than German inflation during the period under consideration.

Four possible explanations have been offered for the existence of these interest differentials. First, they may originate from the existence of impediments to international capital movements. In the Netherlands the last minor formal barriers to free capital mobility were removed in July 1983, whereas in Austria similar liberalisation measures did not take place until 1990. 2 Similarly, until July 1990 Belgium had a two-tier exchange rate system which is economically equivalent to capital controls. 3 Second, differential tax treatments of interest income in the various countries can play a role as a potential source of interest differentials. 4 Third, interest differentials may reflect that market participants continuously expected a devaluation in spite of the proclaimed (fixed) exchange rate policy. Finally, the differential may be caused by a risk premium, due to uncertainty with respect to exchange rate policy as perceived by the market. The announced exchange rate policy may not have been completely credible, since differences in economic fundamentals have persisted, e.g. in inflation, unemployment, fiscal policy, and current account positions. The sheer proclamation of a fixed exchange

1 See e.g. Genberg (1990), and Wellink (1989). 2 However, estimated offset coefficients suggest that the Austrian National Bank enjoyed rather

limited autonomy in the 1980s, indicating that capital controls have not been very effective. Egiin (1989) reports for instance an offset coefficient of -0.79 for 1980-1988.

3 The experience with the Belgian two-tier exchange-rate system and its equivalence to capital controls is discussed in Gros (1988). However, as de Grauwe and Vanhaverbeke (1990, p. 152) note with respect to the efficiency of the system, capital flows were mostly free in Belgium during the eighties.

4 For example, according to research of the National Bank of Belgium, the withholding tax change introduced in March 1990 (reduction from 25% to 10%) has led to a substantial reduction of the long-term interest differential vis-h-vis Germany [National Bank of Belgium (1992)].

K. Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386 365

rate policy is not sufficient to remove the devaluation risk since one would not expect a government to announce a devaluation somewhere in the future. 5

In this paper, we will direct our attention to the last two possible explanations of the interest rate differentials. We consider short-term interest rate differentials with Germany for three small open economies: Austria, being a shadow member of the EMS without any realignment during the last decade; the Netherlands, being a full member of the EMS with only one realignment during the period considered; and Belgium, also being a full member of the EMS, but with frequent realignments in the first half of the 1980s. The paper is organised as follows. In Section 2 a model is developed in which the interest rate differential is linked to expected exchange rate movements and uncertainty concerning these changes. We will make a distinction between realignments of central parities and movements of the exchange rate within the band as proposed by Svensson (1991b). In Section 3, we explore whether the market has perceived any risk of a realignment of the central parities during the period considered. In Section 4, the expected exchange rate movements within the band are computed, in order to determine whether these movements can help to explain the existence of interest rate differentials. In Section 5 we try to link the realignment expectations to the economic fundamentals of the countries in question. Finally, Section 6 presents some concluding remarks.

2. A p o r t f o l i o m o d e l o f i n t e r e s t r a t e d e t e r m i n a t i o n

In this section we will focus on the effects of exchange rate risk on the interest rate differential for a small open economy vis-$-vis the rest of the world assuming perfect capital mobility. Following Giovannini and Jorion (1988) and Andersen and S~rensen (1991), we consider a discrete-time two-asset model in which a representative investor has to decide whether to invest in domestic securities or foreign securities. Although the nominal return on both assets is known with certainty, the real rate of return may differ due to the risk arising from the possibility of exchange rate adjustments.

A domestic investor is assumed to maximise a utility function defined over the (conditional) expectation (E) and the (conditional) variance (Var) of end-of-period real wealth (wt+ 1):

Max u[e t [wt+~] ,Var , [w ,+ t]], U~ > 0, U 2 < 0. (1)

5 There is a fifth possible explanation for the interest differential vis-a-vis Germany: the volume of trade in bonds denominated in currencies of the small countries is considerably smaller than that of DM-bonds. In other words, a liquidity premium may explain the interest differentials. See e.g. Cooper (1990). To our knowledge this explanation has never been tested. However, this elucidation can also not explain why the interest differentials have fluctuated that much, since the relative size of the DM-bonds market has hardly changed during the period under consideration.

366 K. Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386

Furthermore, he allocates a fraction A of his initial nominal wealth W, to the domestic security B, and a fraction (1 - A) to the foreign security F, so that:

AW t = B,,

(1 - A)W, = OtFt, ( 2 )

where Ot represents the initial price of foreign currency measured in units of domestic currency. Moreover, we assume that the foreign price level is constant and normalised to one and, imposing some form of relative purchasing power parity, that the domestic price level varies proportionally with the exchange rate. Hence, Pt = Ot and end-of-period real wealth wt+ I equals nominal wealth times 1/0,+ l:

( 1 + i,)AW, ( 1 + i , * ) ( 1 - A)W~ + (3)

Wt+ I ~ Ot+ I Ot '

where I + i t is the gross rate of return during the time to maturity and an asterisk indicates a corresponding foreign variable. As a result of the assumption of a small open economy, the foreign interest rate i: is presumed to be exogenous and constant. Conditions abroad affect the domestic economy, but the economy is too small to have any influence on conditions abroad.

Likewise, a representative foreign investor maximises:

Max U*[E,[w,*+I ] ,Var,[w,+l]LVl* > 0, U 2" < 0, (4)

and allocates a fraction A" of his initial nominal wealth 14:," to the domestic security B, and a fraction (1 - A" ) to the foreign security F:

Bt* X * W , * = - -

o,' (5)

( 1 - A * ) W t" =Ft ' . End-of-period real wealth for foreign investors can thus be written as:

(1 + i t ) a" Wt'O t wt+ 1 = + (1 + it* )(1 -- A* )Wt ' . (6)

Or+ 1

The end-of-period exchange rate is assumed to be determined as: 1 1 + ~

o,+, e, ' ( 7 )

where , is a stochastic variable distributed with Et[¢] and Vart[ ~]. If ~ is positive, the domestic currency is revalued, whereas a negative value of ~ points to a devaluation.

Combining Eqs. (1), (3), and (7), it can readily be shown that the optimal share of initial wealth placed in domestic securities by domestic investors is given by:

i t - i; + (1 + i,)E,[~] = , ( s )

y(1 + i,)2Var,[ ,]


where 3' = -2 (WJO, )U2 /U1 > 0 denotes the coefficient of relative risk aversion for domestic investors which is assumed to be constant. Similarly, foreign investors find it optimal to invest a share A* of initial wealth in the domestic security, which can be expressed as:

i t - it" + (1 + i t ) E t [ , ] A" = , ( 9 )

7 " ( 1 + i , )2Var,[ ,]

where the coefficient of relative risk aversion for foreign investors is , / " = -2Wt*U2"/UI* > 0 , which is also assumed to be constant. Total demand for domestic securities D = B + B" can thus be written as:

i t - i / + (1 + i , ) E t [ , ] D, = ( W , / y + O , W , ' / y * ).

(1 + it)evar,[ e] (10)

The equilibrium condition for the domestic securities market can now be expressed by:

S t = D , ( i , ) , S > O , (11)

where S denotes the supply of domestic securities which is assumed constant. Combining Eqs. (10) and (11) and solving for a stable equilibrium (i.e. 8 D / 8 i > O) yields:

i t )2Vart [ ' ] ,1 + it < S,(1 +

6 - 6 = - ( 1 + i , ) E , [ , ] + W,'--/--r+ O /---v : 2( 1 + it" )

"

(12)

From Eq. (12) we can deduct that above the uncovered interest parity condition i t + (1 + it)Et[~] = i t there exists a (country-specific) risk premium, which is non-linear in the nominal rate of return, the supply of domestic securities relative to the total amount of domestic as well as foreign wealth, and the uncertainty concerning the expected exchange rate movement Vart[E]. Risk-averse investors require a higher premium to invest in a security with uncertain real return, that is the domestic security.

Furthermore, in case of a bilateral exchange rate with a target zone and an explicitly-pronounced central parity, this expected exchange rate change can be split into two parts: the expected realignment, that is a jump in the central parity, and the expected exchange rate movement within the band. To fix ideas, we define the exchange rate within the band ca t as the log percentage deviation from the central parity:

cat - i n O , - ln~/ , (13)

where Ot denotes the central parity. Then, using the familiar lognormal approxi- mation:

---- lnOt -- lnOt+l ---- In~t -- In ' t+1 + tot -- oat+l ---- ¢,I, + e~. (14)


Thusfar we have only considered a maturity of one period, without further specification. For a period (maturity) of ~" years we can combine Eqs. (12) to (14) as follows:

E,[,:] . . . . = - ( 1 + ~'rT) - - (1 + ~'rt~) ~ + p,, (15) r ; r t

T T

- - ¢ o - - - T 9 where e~, -- l n ~ t lnqbt+ ~, e~ --- wt wt+~, PI - r tst(1 + ~-r t ) - [ W J ~ / + O t W t ' / 3 ~ " ] - lVar t [ •], and r ~- - i / ~ is the annualised net rate of return (nominal interest rate) for maturity ~-. From Eq. (15) we can see that nominal interest rate differentials roughly consist of three explanatory pieces: expected rates of revaluation, expected exchange rate movements within the band, and country-specific risk premia. However, Svensson (1992) demonstrates that the incidence of the last component is likely to be negligible in a target zone system, even when there is devaluation risk. 6 Therefore, in the remainder of the paper we will mainly concentrate on the first two components.

3. Credibi l i ty of the exchange rate pol icy

In Section 2, we showed that interest rate differentials vis-$-vis Germany predominantly consist of two components: expected rates of revaluation and expected exchange rate movements within the band. In this section we will investigate empirically whether nonzero expectations about realignments of central parities against the German mark have existed during the last decade for the countries under consideration. Ever since the foundation of the European Mone- tary System in 1979, its prominent goal has been to bring about greater exchange rate stability among its members. In order to pursue this objective, monetary policy in Belgium and the Netherlands has mainly been aimed at a stable exchange rate vis-a-vis the German mark. Although not a formal member of the EMS, Austrian monetary authorities have followed a similar policy. Despite this proclaimed hard-currency option, market participants may have perceived a devaluation risk at some points in time. In such cases the credibility of the proclaimed exchange rate policy was challenged, which may have been due to persistent differences in economic fundamentals like inflation, fiscal policy, and current account positions.

6 Svensson (1992) shows that the risk premium for an imperfectly credible band consists of two elements: the first originating from uncertainty due to exchange rate movements within the band, and the second arising from uncertainty due to movements of the band. The former element is presumably very small, since exchange rate variability within the band is smaller than variability in a free float, and since empirical studies of risk premia in a free float appear to be fairly small (see e.g. Froot and Thaler, 1990). The latter element is likely to be larger than the former, but still of moderate size in proportion to the total interest differential.


In order to determine whether the exchange rate policy in the countries concerned has been fully credible in the last decade, that is whether Et[ e~ ] has been zero or not, we develop a simple test, similar in spirit to the one that has been proposed by Svensson (1991a). In a fully credible target zone the expected amount of appreciation within the band Et[ e~] must be bounded by the maximum and minimum possible amount of appreciation within the band, that is:

tO t - - 09u < = Et[~r,,] <~ = to t - to t, (16)

where to u and tot denote the upper and lower limits of the exchange rate band. In case of the EMS, for example, tou = _tol = 0.0225 and Et[~] - - 0 , provided the target zone is regarded completely credible. 7 Hence, given foreign interest rates, these limits imply limits on domestic currency rates of return to foreign investment as well as on domestic interest rates, by virtue of Eq. (15). In turn, in the absence of a country-specific risk premium, the latter define a rate-of-return band around the foreign interest rate, where upper (rt ~'~) and lower ( r 7 "t) bounds are given by:

[tou to,] r : , U ~ T, * r, + (1 + "rr7)

T [ t o _ tOt] (17)

r t . I = rtr, . _ (1 + z r T ) T

We assume that for the countries under consideration there is sufficiently free capital mobility, so that no international arbitrage possibilities remain, s Then it definitely follows that, in the absence of a country-specific risk premium, the exchange rate regime can only be completely credible for the horizon implied by the term of the investment if the domestic interest rate for that term is inside the rate-of-return band (17). 9 If it is outside the band, investors must either perceive a risk of a revaluation (shift of the band) before maturity, or the required risk premia are nonzero. In the first case it follows that the target zone is not credible.

Fig. la to lc show the rate-of-return bands around the German interest rate in combination with the domestic interest rates for a time to maturity of one month (~'= 1 /12) for Austria, the Netherlands, and Belgium. The interest rates we use are annualised monthly averages of working days for Euro-market bills, originat-

7 Since the EMS is not a bilateral exchange rate mechanism, the maximum and minimum expected change in the exchange rate within the band relative to the German mark may temporarily be restricted by the bands relative to the other currencies. In practice, the bands relative to the German mark have been the most important, since the German mark has been the strongest currency in the EMS and the onlsY one that has never undergone a bilateral devaluation.

As has been explained in footnotes 2 and 3 there is ample evidence for this assumption even for Austria and Belgium.

9 Note, however, that if the interest rate falls within the rate-of-return bands, it does not necessarily follow that the target zone is credible. A target zone is perfectly credible if and only if Prob[ co t - w u < e~ < oJ t - ~o I ] = 1 for all 1". Since it is not possible to observe the entire probability distribution of e~, we examine the weaker condition Eq. (16).

370 IE Knot, J. de Haan /Journal o[Banking & Finance 19 (1995) 363-386

0.50 .[ (a) / / l \

I ^ / \ ~ , ^ ~ . i *~ J ~ - ~ ' ~ ' - ~ . ~ . ~ , - .~ 0 . 2 5

" -o.~.5 ,t !,,,., i.,i,,,.,,. ....,,...,... ,.. . . . , , . . , - . , - - - , , , .-.,,-,:- . . . . ,.--, - . . . , . . . . , . - - - - - " - . . . . . . . . . . . . ..,- . . . . . .

I -0 .50

80 8 [ 82 83 8 4 85 86 87 88 8g go 9!

- - I n t e r e s t r a t e . . . . . Lower b o u n d - - - - U p p e r b o u n d

o.75 / (b)

I \

0.50 ; ' , ~ ,~ m.~ i i ~ i$

2_ 0.00 " " " " - " - - - - - - ~ -

&=

- 0 . 2 5

-0 .50 .

,' 1 t i ," •

" J i L i t S'%~ ',,," % "',,,, "-,,., . , . . . . . ,,, ,. . . . . . . . . . . . , ,-o--

I I

80 8 [ 82 83 84 85 86 87 88 8g 90 9!

- - I n t e r e s t r a t e . . . . . Lower b o u n d - - - - U p p e r b o u n d

Fig. I . Target Zone Credibili ty: a. Austria. b. The Netherlands. c. Belgium.


I=,

NI t=

0.75

0.50

0.25

0 . 0 0

-0 .25

- 0 . 5 0

-025 .

(c)

J - ' I ~, * ~ I • t \ / iX "

k

. " " . . l ' , l ' , 1% ~ ~,. , ,,,

" i,.., .... ":"-,il ',,,,,.,,/,,..: " " " " ' - . - i / ' - ' " ..... - .... .'".,."' , .

i u

80 8 t 82 83 84 85 86 B7 88 89 90 91

- - I n t e r e s t rite . . . . . Lower bound Fig. 1 (continued).

- - - - - U p p e r b o u n d

ing from the Bank of International Settlements; the exchange rate data also consist of monthly averages, originating from the International Monetary Fund. 10 The period covered is 1981.01 to 1991.12. From Fig. la and lb we can infer that for Austria and the Netherlands, the hard-currency option may have been broadly credible for most of the time during the last decade. On the other hand, the Belgian target zone has definitely lacked credibility even within a one-month horizon at several points in time during the eighties, especially at times right before actual devaluations of the Belgian franc (Fig. lc). Nevertheless, also in Belgium credibility seems to have increased towards the end of the eighties, probably due to the combined effect of a more favourable development of the Belgian fundamentals and the Basle-Nyborg agreement of september 1987. There, the Committee of Central Bank Governors decided to strengthen the Exchange Rate Mechanism of the EMS by adopting a number of measures, including in particular an extension of the facilities to finance intra-marginal interventions, tl EMS countries like Belgium were pushed to commit themselves more f'mnly to the hard-currency option, and the more or less frequent devaluations against the German mark came to a halt. Frankel and Phillips (1992) have shown that with the

10 Exact sources and definitions of the variables are to be found in Appendix 1. n According to Giavazzi and Spaventa (1990), 1987 marked the beginning of a New EMS.


use of survey data on exchange rate expectations instead of expectations implied by interest differentials, similar conclusions can be reached.

There is a rather disturbing problem, however, with the empirical treatment of the Belgian franc, that is normally neglected in the literature. 1_, As already mentioned in the introduction, Belgium has experienced a dual exchange rate system for most of the period under analysis. Underlying Fig. lc are data on the commercial exchange rate, since that rate has been targeted by the Belgian monetary authorities within the Exchange Rate Mechanism (ERM) of the EMS. This official rate, however, only covers current account transactions, so that financial arbitrage cannot have taken place at this rate. If instead we would employ the financial exchange rate, we would introduce an apparent contradiction in the analysis as this rate was not explicitly targeted. The difference between both exchange rates can be seen in Fig. 2a. Furthermore, remaking Fig. lc with the financial exchange rate instead of the official one yielded Fig. 2b.

As can be seen from Fig. 2a and 2b, especially since 1984 the distinction between both rates may not be as pronounced as it seems at first sight. 13 Indeed, the basic conclusion with respect to the credibility of the Belgian exchange rate policy is very similar for both exchange rates. Therefore, the commercial exchange rate is usually employed in the literature, even in combination with interest rates and other financial variables, t4 Only Flood, Rose, and Mathieson (1991) claim to have checked their key results for Belgium with financial rate data but, subse- quently, concluded that their main results remained unaffected [Flood et al. (1991), page 17]. Nevertheless, we do think that this common practice in the literature to employ the official rate for Belgium is a serious and fundamental imperfection in this context. Moreover, in the following section we will show that the time-series properties of both exchange rates are fundamentally different.

4. Es t imat ion o f expected rates o f apprec iat ion wi th in the b a n d

In the last section we saw that within the ERM, the rate of appreciation within the band E,[e~] /T is limited by the band-width of the target zone. We can even go one step further and construct an econometric estimate of the expected rate of appreciation within the band, as the target zone literature has shown on both theoretical and empirical grounds that the band has a stabilising or mean reverting

12 Fortunately, this problem was kindly pointed out to us by one of the referees. 13 The simple correlation between both exchange rates vis-~t-vis the German mark turned out to be

0.93 for the period under consideration. 14 Compare for example Koen (1991), Frankel and Phillips (1992), and Svensson (1991b). Note that

the commercial exchange rate has been targeted by the Belgian monetary authorities, presumably amongst others by manipulating short-term interest rates. In this fashion the relation between the latter and the commercial exchange rate has not been completely absent during the two tier exchange rate regime.

r-~

K. Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386

3 t

20

t9

t8

t7

t6

t5

(a)

i - -7~- . . . . . . . . . . . ! / ::;:--'

U i . L-' I.', I/ I

I I

80 81 82 B3 84- 85 86 87 88 89 90 91

_ _ F i n a n c i a l exchange rate - - - - U p p e r bound ..... Commercial exchan le rate .... Lower bound

373

0.75 {b)

0.50

, . ,,. 0.25 ; ' ; "

i! :'", :'i ,',.

~. o .o0 ,, . . . . - , ,,,,

-0.85 ~ :! /\4 r, /

/ ' i ' 1 l -0.504 -~ [,f#, ~,,,,l ~, "

J ' - 0 . 7 5

- 1 . 0 0 80 81 82 83 84- 85 86 87 B8 89 90 91

Interest rate ..... Upper bound _---Lower bound

Fig. 2. a. The Financial and Commercial Exchange Rate in Belgium. b. Credibility of the Belgian Financial Exchange Rate.

374 If. Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386

effect on to t. However, the exchange rate within the band usually takes a jump at a realignment, which complicates its estimation since the sample distribution of realignments may not be representative (the so-called Peso problem). We therefore estimate the expected rate of appreciation within the band conditional upon no realignment. In order to do so, we model market expectations of realignments in the following way:

Et[ ~ ] = p~Et[ ¢~lRealignment] + (1 - p ; ) 0 , (18)

where p~" is the time-varying probability of a realignment of independent random size during the time to maturity and Et[e~,[Realignment] denotes the expected conditional realignment size. Likewise, the expected rate of appreciation within the band can be subdivided into two components:

Et[ ~ ] -- p tEt[ <lRealignment] + ( 1 - PT ) Et[ ~ lNo Realignment ]

= EI[ ,~INR] + p~[E,[ to,+ ,INR] - E,[ tot+,lR] ]. (19)

Combining Eqs. (15), (18), and (19), and rearranging yields:

r ~ - rt r ' ' + (1 + ~'rt)

p~[E,[ to,+. I R] - E,[ to,+¢ I NR] - E,[ e$lR]] = (1 + ~'r;)

T

+ . , . (20)

We shall refer to the first term of the right-hand side of Eq. (20) as the product of the gross rate of return and the expected rate of revaluation. The latter is again the product of the probability of a realignment divided by the term (p~'/~'), and the expected conditional revaluation size between double brackets, that is the sum of the negative of the expected conditional realignment size and the difference between the expected exchange rate within the band at maturity conditional upon a realignment and the expected exchange rate within the band at maturity conditional upon no realignment. The left-hand side of Eq. (20) represents the interest rate differential adjusted for the expected rate of appreciation within the band. For sufficiently long maturities the latter will approximately be zero, since the maximum amount is bounded by the width of the band and then divided by a high r. Moreover, a longer 1" allows more mean-reversion of tot, regardless of whether a realignment occurs during the time to maturity. Then, the expected conditional revaluation size (E,[tot+~IR]-Et[to,+TINR]-Et[~IR]) will be close to the expected conditional size of the realignment ( - E t [ ¢~,IR]), and the expected rate of revaluation is likely to equal the expected rate of realignment. If r approaches zero, the expected conditional revaluation size is the expected jump in the actual exchange rate/9 at a realignment, which differs from the jump in central parity by


the expected change in the exchange rate within the band. For short maturities, the latter may be sizable. Hence, for sufficiently long maturities the unadjusted interest rate differential is an adequate measure of the expected rate of revaluation whereas for shorter maturities it could make sense to adjust the differential according to Eq. (20).

So in what follows we present estimates of Et[e~INR]/ I"= Et[to t - t o t + TINo Realignment] /r for Austria, the Netherlands, and Belgium, conditional upon information available at time t, for a time to maturity of one month (1 /12 year). Following Svensson (1991b), and Frankel and Phillips (1992), we use a simple linear regression where the single determinant of the future exchange rate within the band is the current exchange rate within the band tot. ,5 Consequently, the expected rates of appreciation can be estimated by a linear regression of the equation:

1 2 ( t o t - tot+,) = Zj°t0/dj + a, to, + ~',+t. (21)

The variable dj is a dummy for each period between two realignments, in order to allow the intercepts to vary across realignments. Estimating the expected future exchange rate appreciation within the band is equivalent to estimating the expected future exchange rate within the band, that is Eq. (21) can be rewritten as:

to,+1 = Ej[3oja/ + ~,tot + tit+l, (22)

where 13o/= - ot0j/12, 131 = 1 - oq/12, and r/,+ 1 -- - ~',+ 1/12. In case of the occurrence of mean reversion in the data on to, 131 will be less than one. Table 1 shows the regression results of OLS estimation of Eq. (22) for four exchange rates on a monthly base: (3S/DM, N G / D M , B F / D M (commercial rate), and B F / D M (financial rate).

It follows from the first column of Table 1 that the O S / D M exchange rate has been pegged firmly without a single realignment during the period considered. The intercept does not differ significantly from zero, while the slope turns out to be 0.851. The critical level for a standard Dickey-Fuller test on a 5 percent significance level is - 2 . 8 8 for this sample size [MacKinnon (1991, Table 1, p. 275)], so this test indicates mean-reversion in the exchange rate within the band for Austria. t6

For the Netherlands we can distinguish between two regimes: before and after the March 1983 realignment. Because of this realignment, the number of observa-

t5 Although in principle the relation between the actual and expected exchange rate within the band is non-linear, "...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" [Svensson, (1991b)].

16 Because of the rather disturbing values of the Durbin Watson statistic for Austria and the Netherlands, we also tried to correct these regressions for serial correlation by means of the Cochrane Orcutt procedure. Nevertheless, in all cases our estimate of rho turned out to be insignificant.

376 K. Knot, J. de Haan /Journal of Banla'ng & Finance 19 (1995) 363-386

Table 1 Expected future exchange rates within the band (22)

(1) OS/DM (2) NG/DM (3) BF/DM (er) (4) BF/DM fir)

Intercepts: 80.01-81.09

81.11-82.01

82.03-82.05

82.07-83.02

83.04-86.03

86.05-86.12

87.02-92.01

Slope:

DF N R e DW

0.001 (0.1)

0.851 (31.3) - 5.52 145 0.89 2.3

- O. 105 O. 125 0.539 (2.2) (1.2) (1.8)

0.571 1.818 (6.4) (2.3) 0.049 0.464 (0.1) (0.5) 0.445 0.324 (4.0) (0.6)

- 0.007 0.185 0.236 (0.3) (2.7) (1.4)

] 0.364 0.351 I (3.2) (1.8) I 0.069 0.032 I (1.8) (0.4) 0.813 0.891 0.931 (17.3) (28.9) (14.0) - 3.98 - 3.52 - 1.04 144 139 139 0.75 0.82 0.91 1.4 2.1 1.6

Note: t-statistics in parentheses. Method: OLS with heteroskedasticity-consistent covariance matrix. Regressand: tot+ 1(%). Regressor: ~ot(%). A vertical bar indicates no change in the intercept. DF: Standard Dickey-Fuller test. Critical value (5%, N = + 140) is -2.88. N: Number of observations. R2: Adjusted R-squared. DW: Durbin Watson.

tions is lower for the Netherlands than for Austria. Since the estimation is conditional upon no realignment, each observation enclosing a realignment is excluded in order not to include the jump in the exchange rate within the band that normally occurs at a realignment. The last intercept is approximately zero, and the slope is estimated at 0.813. Again, mean reversion in the exchange rate within the band is indicated (column (2)).

From column (3) of Table 1 we can infer that the commercial B F / D M exchange rate has had 6 realignments; the intercepts vary between 0.049 and 0.571. The slope is high (0.891), but estimated sufficiently precise (standard error is 0.031). Therefore, /31 differs significantly from unity, indicating the absence of a unit root also for the Belgian commercial exchange rate. However, the difference between the commercial and the financial exchange rate in Belgium is confirmed once more in column (4). For the latter, we cannot reject the hypothesis of a unit root instead of mean reversion. This comes hardly as a surprise, since the unit root property represents one of the stylised facts of ' f reely ' floating exchange rates [de Vries (1992)] and the Belgian financial exchange rate has not been subject to the EMS rules.


Finally, for the Netherlands as well as for the Belgian commercial rate, there is a lot of similarity between our results and those obtained by Svensson (1991b), despite our use of monthly instead of daily data. With the estimates of Table 1 we can adjust short-term nominal interest rate differentials according to Eq. (20). Fig. 3a and 3b show the one-month adjusted and non-adjusted interest rate differentials with Germany for Austria and the Netherlands. ~7 Fig. 3c shows the one-month unadjusted interest differential for Belgium. Given the aforementioned problems with the dual exchange rate system it does not make much sense to calculate adjusted interest differentials for Belgium.

It follows from Fig. 3a and 3b that the differences between the adjusted and unadjusted interest rate differentials in Austria and the Netherlands can be substantial, in magnitude as well as in sign. Fig. 3c shows that especially in Belgium, times of uncertainty about the aims of monetary policy and subsequent uneasiness at financial markets at the beginning of the eighties have led to large (unadjusted) interest rate differentials. On average these differentials have been much more moderate in Austria and the Netherlands. Towards the end of our sample exchange rate uncertainty diminished and, consequently, interest rate differentials narrowed in all three countries. Especially for the Netherlands and, to a lesser extent, also for Austria, filtering out the movements of the exchange rate within the band increases the volatility of the interest differentials, is Apparently, the monetary authorities have employed the exchange rate within the band as a buffer for possibly undesirable interest rate adjustments.

5. C a u s e s o f in teres t rate d i f f erent ia l s : f u n d a m e n t a l s

Economic theory teaches that expected exchange rate changes and interest differentials can be linked to the underlying economic fundamentals of the country in question. Moreover, for a narrow target zone system like the EMS, Svensson (1991c) has demonstrated that this relationship appears to be approximately linear. It is well known, however, that the available theoretical models are inconclusive as to what constitute these fundamentals, so they can be suggestive at best. 19 The empirical objective then is to find proxies that capture the essence of expected exchange rate changes, for example proxies that might signal central bank behaviour in an escape-clause model like in Giovannini (1990). Such possible

17 The blank in Figure 3b is caused by the exclusion of the March 1983 observation. ts The standard deviation of the Austrian interest differential increases from 0.85% to 1.12% after the

adjustment; for the Netherlands these figures amount to 0.78% and 1.21%, respectively. t9 Compare for example OECD (1989), and Dornbusch 0989).

378 IC Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386

o.o5 ] (a)

~ 0.02 i ~ 0.01

~ 0.00

-0.01

-0.02

-0.03

/

, t

i

I , I

80 81 8?. 83 84 85 86 87 88 89 90 91

- - U n a d j u s t e d . . . . . A d j u s t e d

0.05

0.04

0.03

0.02.

t, o.ol.

=" 0.00.

'~ -O.Ot.

-0.02

-0.03.

-0 .04

(b)

;\

= et t t ¢~ s ¢ , i I e i = = •

• ~ ~ ~ t et t t I t J=°t= ==l | =l=" i = • ~ 1 = , t ~sI s, t t • ,

II t;

80 81 82 83 84 85 86 87 88 89 90 91

- - U n a d j u s t e d . . . . . A d j u s t e d

Fig. 3. Interest differentials with Germany: a. Austria. b. The Netherlands. c. Belg/um.


o.135 ] Ic) 0'00 0.075

0.050

80 8t 82 83 8¢ 85 86 87 88 89 90 91

Unadjusted Fig. 3 (continued).

indicators are the rate of inflation zr, the government budget deficit GD, and the current account CA:

r - r ° = f ( r r , G D , CA ... . . ) . (23)

Thus, we expect to find an empirical causal relation between those fundamentals and the interest rate differential. An interesting issue here is whether it makes any difference if the adjusted or unadjusted differential is being used, and, whether we can find support for the observation made by Svensson (1991b) that adjusting interest differentials in this manner represents a step forward in the measurement of realignment expectations. Therefore, we have estimated an empirical model encompassing Eq. (23) in order to reveal any potential form of causality between three country-specific fundamentals (rr, G D , C A ) and the interest rate differentials for the countries under consideration.

Before estimating the model, each variable is converted into a stationary proces using the proper degree of differencing. It was found that the first-difference operator is adequate to induce stationarity for all variables in the analysis. To allow for possible feedback mechanisms among the various variables considered, a 4 x 4 vector autoregressive (VAR) system is specified and estimated. This VAR modelling technique has been recommended by Sims (1980) among others, because the procedure takes into account the potential endogeneity of the explana-

380 K. Knot, J. de Haan /Journa l o f Banking & Finance 19 (1995) 363-386

Table 2 A: System specification and F-tests of multivariate Granger-causality hypotheses for Austria

Unadjusted differentials Adjusted differentials Sample: 1982 .Ql -1991 .Q4 Sample: 1982 .QI -1991 .Q4

Specification of A(L): Specification of A(L):

0 d62(L) d~3(L) d~(~.) 0 d,~2(L) d~3(L) d~4(~.) a,',(L) a,3~(L) o a~,(L) a,',(L) a~2(L) o a,34(L) o o a~fL) o o o a~3(L) o a~,(£) a62(L) o ,~4(£) a~,(L) a~2(~.) o a~4(L) Goodness of fit R 2 Goodness of fit R 2

Equation (24.1) 0.88 Equation (24. I) 0.80 Equation (24.2) 0.57 Equation (24.2) 0.57 Equation (24.3) 0.78 Equation (24.3) 0.78 Equation (24.4) 0.81 Equation (24.4) 0.80

Hypothesis F-statistic Hypothesis F-statistic

d l2(L) = 0 F[6,27] = 5.55 a' d t2(L) = 0 F[6,27] = 2.83 * dl3(L) = 0 F[2,27] = 4.52 # dt3(L) = 0 Fl2,27] = 3.05 dl4(L) = 0 F[4,271 = 5.28 ~ dl4(L) = 0 F[4,27] = 2.33 d21(L) = 0 FD.3, ] = 4.13 dzl(L) = 0 F[1.321 = 3.55 d3t(L) = 0 - d31(L) = 0 - d41(L) = 0 ]:'[4,26] = 5.92 '¢ d41(L) = 0 F[4.29] = 6.91 #

B: System specification and F-tests of multivariate vat Granger-causality hypotheses for The Netherlands

Unadjusted differentials Adjusted differentials Sample: 1982 .Ql -1991 .Q4 Sample: 1982 .Q1-1991 .04

Specification of A(L): Specification of A(L):

a2~fL) a52(L) a~3(~.) o a2~(L) 0 a23(L) o

0 d3(L) d223(L) 0 0 d32(L) d223(L) 0 0 d~2(L) d33(L) d~4fL) 0 d42(L) d33(L) d /4(L) 0 d22(L) d23(L) d34(L) all(L) d422(L) d23(L) d3(L)

Goodness of fit R 2 Goodness of fit R 2

Equation (24.1) 0.81 Equation (24.1) 0.53 Equation (24.2) 0.45 Equation (24.2) 0.45 Equation (24.3) 0.65 Equation (24.3) 0.65 Equation (24.4) 0.64 Equation (24.4) 0.66


d l2(L) = 0 F[5.311 = 2.33 d12(L) = 0 - d l3(L) = 0 F[1,31] = 4.74 # d13(L) = 0 F[2.35! = 2.75 d14(L) = 0 - d14(L) = 0 - d2t(L) = 0 - d21(L) = 0 - d31(L) = 0 - d31(L) = 0 - d , l ( L ) ~ 0 - d , l ( L ) = 0 F[I.31I = 2.29

K. Knot, J. de Haan /Journal of Banking & Finance 19 (1995) 363-386

Table 2 (continued)

381

C: System specification and F-tests of multivariate Granger-causality hypotheses for Belgium

Unadjusted differentials Sample: 1982.Ql-1991.Q4

Specification of A(L): Goodness of fit R e

d~l(L) d~z(L) dt33(L) d~4(L) Equation (24.1) 0.92 d61(L) daze(L) 0 d~4(L) Equation (24.2) 0.82 0 0 d~3(L) d324(L) Equation (24.3) 0.92 d~t(L) d432(L) d433(L) d434(L) Equation (24.4) 0.81


die(L) = 0 F[3.261 = 1.25 d21(L) = 0 F[6.28] = 2.78 # d13(L) = 0 ]7[3,26] = 3.19 # d31(L) = 0 -

d l a ( L ) = 0 F[4.261 = 3.41 ¢~ d41(L) = 0 F[5,251 = 3.26 '~

Notes: A(L) is the matrix of estimated coefficients of the system (24), employing full information maximum likelihood. X = [ D(r - r * ), D(Ir ), D(GD), D(CA)] r. dij ~ 0 means that the hypothesis is tested whether it is allowed statistically to omit the lags on variable j included in the specification of variable i if inclusion has been decided upon according to the FPE criterion. An (~) indicates rejection of the hypothesis at the 5% level of significance.

tory variables, thereby imposing no restrictions on the dynamic linkages among all variables in the model. Although it may be difficult to interpret individual coefficient estimates due to the reduced-form nature of VAR-models, more general Granger-causality inferences may be derived from the joint significance of a group of coefficients in the system. The general form of our vector autoregressive model can be represented by the following reduced-form system:

x , = c + A(L)X, + u,, (24)

where C is a 4 × 1 vector of constants, and u t is a 4 × 1 vector of white-noise disturbance terms. X t is a 4 × 1 column vector of the four endogeneous variables, in which we can substitute the unadjusted interest differential as well as the adjusted measure according to Eq. (20):

X - [ D ( r - r * ) , D ( z r ) , D ( G D ) , D ( C A ) ] r , D = 1 - L . (25)

Finally, in Eq. (24) A ( L ) is a 4 × 4 matrix of lagged polynomial coefficients. The (i,j)th element of A ( L ) is defined in terms of the lag operator L such that

~ijk(L) = (¢~/jl L + 602 L2 + ... + 8#kL~). The number of lags on each variable in each equation is determined by

Akaike 's Final Prediction Error criterion (FPE) whilst the maximum number of lags is set at six. After first having determined the number of autoregressive lags per equation, we picked that combination of the number of lags of the various exogeneous variables that yielded the global minimum FPE over all possible


combinations (73- - 343 per equation). 20 Under fairly general conditions, Hsiao (1981) has shown that the inclusion of a variable in an equation based on the FPE criterion is evidence that a weak Granger-causal ordening exists. If it further proves to exert a statistically significant effect, then the Granger-causal impact can be identified as strong form [Kawai (1980)]. Once specified, the system is then estimated by means of a full information maximum likelihood (FIML) procedure, thereby also incorporating the contemporaneous relationship among the variables.

We have used quarterly data for inflation, government deficits, and current account positions originating from the International Financial Statistics of the IMF. 2t Data on government deficits and current account positions are measured as ratios to (quarterly) GNP. The model specifications with system F-tests of multivariate strong Granger-causality hypotheses to match are reported in Tables 2a to 2c for Austria, the Netherlands, and Belgium.

It follows from Table 2a that in Austria interest differentials vis-a-vis Germany were markedly influenced by all three fundamentals in question. Furthermore, it does appear to make a difference whether we employ unadjusted or adjusted interest rate differentials. Only inflation does exert a statistically significant effect on the adjusted measure, whereas all three fundamentals turn out to be important for the development of the unadjusted differential in a strong Granger-causal sense. So our evidence suggests that the somewhat disfavourable development of the Austrian government deficit as well as the current account has mainly affected the position of the schilling within the band, a component that is excluded from the adjusted differential. As was already indicated in the previous section, presumably this component was welcomed by the Austrian monetary authorities because it enabled them to avoid potentially undesirable short-term interest rate adjustments.

For the Netherlands, the correlations investigated in Table 2b are much weaker. But also here, the relation between the Dutch fundamentals under consideration and the interest differentials is more pronounced for the unadjusted differential, albeit mainly in a weak Granger-causal sense. In case of the Netherlands only government deficits help explain unadjusted interest differentials vis-a-vis Ger- many, while at the same time this variable is the single one included in the

20 The FPE procedure as recommended by Thornton and Batten (1985), has been extensively applied in various empirical studies. For computational simplicity this procedure is often supplemented by the "specific gravity" criterion of Caines, Keng, and Sethi Caines et al. (1981), by which the variables are ranked for inclusion in each equation. A useful discussion of this procedure can be found in Darrat (1988, p. 882), and Faclder (1985, p. 30). Here we abstain from this ranking, since in a number of occasions this criterion yielded a merely local minimum that was too far apart from the global one. The main conclusions were unaffected by the use of this criterion.

2! The quarterly data for the interest rate differentials were obtained by taking the three-monthly averages of our monthly data set. For the first quarter of 1983 only two observations were available for the adjusted differential in the Netherlands, since 1983.Q1 contained a realignment of the guilder against the mark (section 3). Hence, we took the average of the available (2) months.


specification of the adjusted differential. The almost complete absence of explanatory power of this set of fundamentals in case of the adjusted differential can be reconciled with the outcomes of the credibility test of section 3, as the adjusted differential represents the expected revaluation plus a risk premium. Once we recall that these expectations must have been fairly close to zero during most of the period under consideration, the evidence for Austria as well as for the Netherlands would suggest that netting out the movements of the exchange rate inside the band indeed yields an improved measure of realignment expectations as compared to unadjusted interest differentials.

Table 2c demonstrates that Eq. (23) is also broadly supported by the data for Belgium. From our collection of fundamentals, government deficits and current account positions in Belgium do explain a significant part of the development of the unadjusted interest differential with Germany in a strong Granger-causal sense, as opposed to past inflation. In turn, two out of the three fundamentals are also markedly influenced by the interest differential itself. Unfortunately, the existence of the dual exchange rate system in Belgium did not allow us to further investigate whether these correlations could be traced back to the effect of the fundamentals on expected exchange rate movements within the band, or to their effect on expected movements of the band.

6. Concluding remarks

In this paper we investigated interest rate differentials with Germany for Austria, the Netherlands, and Belgium. It followed from our theoretical model that these differentials consist of three parts: expectations about currency realignments, expected exchange rate movements within the band, and a country-specific risk premium. Since the maximum and minimum amount of appreciation within the band is limited by the band-width of a target zone, we were able to derive a simple test of target zone credibility. According to this test Austrian and Dutch exchange rate policies were credible over the period under consideration, whereas Belgian exchange rate policy would seem to lack credibility at several points in time. However, due to the dual exchange rate system in Belgium there are some fundamental problems applying this test which are largely ignored in the literature on the credibility of the Belgian exchange rate policy.

We computed the expected exchange rate movements within the band by means of a straightforward lineair regression. We found that the commercial and financial exchange rate of Belgium exhibit different time-series characteristics, thereby furthering the objectives raised against the credibility and similar tests as usually applied. For Austria and the Netherlands the adjusted interest differential --i .e. taking into account the movement within the band-- and the unadjusted differential vis-~t-vis Germany were small but persistent, notwithstanding the observation that the exchange rate policy pursued has been considered fairly credible during


the eighties. There was only limited evidence for a Granger-causal relationship between a set of economic fundamentals of both countries and the adjusted interest rate differentials vis-h-vis Germany, whereas there was more evidence that these fundamentals affect the unadjusted interest differentials. Apparently, the fundamentals considered here mainly affected the movement within the band without causing realignment expectations. The unadjusted interest differential of Belgium is influenced by government deficit and current account positions.

Acknowledgements

The authors would like to thank Geert Almekinders, Bas Bakker, Willem Buiter, Jan Jacobs, Elmer Sterken, and two anonymous referees for their stimulat- ing comments on an earlier version of this paper. The usual disclaimer applies.

Appendix 1: sources and definitions of the variables used

f 1-Month Euro-market interest rate, period averages of working days, rom the Bank of International Settlements (BIS), kindly provided by De Neder- landsche Bank.

67 Spot exchange rate against the German mark, period averages, computed from International Financial Statistics (IFS), line rf. For Belgium we also employed the financial exchange rate, being series BE94QBBA from BIS. Central parities against the German mark. For Belgium and the Netherlands this series was taken from De Nederlandsche Bank, Quarterly Bulletin, various editions. For Austria it was taken from t3sterreichische Nationalbank (1991), Erneuerung durch Integration: 175 Jahre Osterreichische National- bank.

7r CPI-inflation,IFS, line 64. GD Government Deficit, IFS, line 80. For Belgium these data were kindly

provided by Mrs. Frieda de Wit from The National Bank of Belgium. CA CurrentAccount, IFS, line 77ad. GNP Gross National Product, IFS, line 99a for Austria and Belgium. This variable

was used as a scaling variable for GD and CA. For Belgium this series was not available on a quarterly base. We therefore converted the annual series, using quarterly index numbers on total industrial production for each year from OECD, Main Economic Indicators. For the Netherlands we used data from the Central Bureau of Statistics, Kwartaalrekeningen.

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Interest rate differentials and exchange rate policies in Austria, The Netherlands, and Belgium

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