I. Interest Rate Differentials, Exchange Rate Bands, and Credibility

Under current EMS arrangements, interest rates on financial assets that differ only in their currency of denomination can diverge because of the discounting of two types of exchange rate uncertainty: the day-today fluctuations in exchange rates within the ERM bands and the possibility of a realignment of the centra! rates. It is widely accepted that since the January 1987 realignment the EMS target zones have become much more credible. This has allowed devaluation risk premia to decline and interest rate differentials to narrow considerably. For example, the differential on 12-month Eurofranc and Euromark interest rates (Figure 1) declined from a mean differential of 4.7 percentage points in 1987 to 0.25 percentage points in 1991.

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Parity Deviations of Franc-Mark Exchange Rate and 12-Month Interest Rate Differential

(In percent)

Citation: IMF Staff Papers 1993, 002; 10.5089/9781451973259.024.A004

^a Eurofranc rate minus Euromark rate.^b Percent deviation.

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A simple way to test the credibility of the EMS target zones is tc suppose that investors at time t expect with certainty that there will be no realignment (or change in the width of the exchange rate band) up tc time t + m, the time of maturity of a given asset. Then, at time t + n the spot exchange rate is expected with certainty to be bounded by

where S is the domestic currency price of foreign exchange (franc/mark and S^L and S^U are the lower and upper margins of the exchange rate band Hence, the net profit from a forward safe of one unit of foreign currency is bounded by

where F^m_t is the forward exchange rate at time t for maturity m (measured in years). Further assuming that arbitrage eliminates certain positive minimum profits, it follows that if the forward exchange rate lies outside the exchange rate bands, then the target zone is not credible. If the forward exchange rate lies within the exchange rate band, then the test is inconclusive.³ Alternatively, invoking covered interest parity, the domestic interest rate under full credibility is bounded by

where i_t^*m and i_t^m are the domestic currency (franc) and foreign currency (mark) interest rates on assets of the same default risk and maturity m, expressed as annualized rates of return. If at any time t the domestic interest rate is outside these “credibility bounds,” then agents expect with positive probability that over the time to maturity, t + m, the exchange rate band will shift by way of either a realignment or an increase in the band’s width.

Eurofranc interest rates for 3-, 6-, and 12-month maturities and their corresponding “credibility bounds” are shown in Figure 2. The three-month interest rate was almost always within its credibility bounds; hence, the exchange rate band may or may not have been credible. The one-year interest rate, however, was consistently above the upper bound from January 1987 to March 1990, and thereafter consistently inside the bounds. Thus, it may be inferred that until March 1990 agents expected with positive probability a devaluation of the franc-mark exchange rate. In the case of one-year interest rates, the test is less inconclusive as the credibility bounds are significantly narrower than those for three-month interest rates. The next section outlines a more precise empirical method (from Bertola and Svensson (1991)) for extracting the implicit expected rate of realignment from exchange rates and interest rate differentials.⁴

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Eurofranc Interest Rates and “Credibility Bounds”

(In percent)

Citation: IMF Staff Papers 1993, 002; 10.5089/9781451973259.024.A004

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II. A Model of the Expected Rate of Realignment

Let s, s^L, and s^U denote the natural logarithms of S, S^L, and S^U (the franc-mark spot exchange rate and its lower and upper intervention rates, respectively). By definition, the exchange rate can be decomposed as

where c_t = (S_t^L + S_t^U) /2 is the log of the central parity of the franc-mark exchange rate and s, is the deviation of the franc from the central parity. Taking first differences of equation (4), the total expected rate of change of the franc from time t to t + m, conditional on information available at time t, is equal to the expected rate of realignment (that is, the change in the central parity) plus the expected rate of change of the franc within the band;

Assuming uncovered interest parity (UIP)

it follows that

UIP is an appropriate assumption if the foreign exchange risk premium is small. Theoretical support is provided by Svensson (1990), who argues that the risk premium is likely to be small in exchange rate target zones, even in the presence of devaluation risk. Empirical support of UIP for the franc-mark rate is provided by Rose and Svensson (1991), Andersen and Sorensen (1991), and, indirectly, Frankel and Phillips (1991).

From equation (1) and the definition of s̄_t, it can be shown that the rate of change of the exchange rate within the band is bounded by

which combined with equation (7) gives the following maximal bounds for the expected rate of realignment:

These bounds are shown as the solid lines in Figures 3 and 4. As can be seen, the bounds for the expected parity changes are wider the shorter the maturity. This reflects the fact that the maximal bounds for the expected rate of change of the exchange rate within the band are wider for shorter maturities.

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Expected Rate of Change of Franc-Mark Exchange Rate Within the Intervention Band

(In percent)

Citation: IMF Staff Papers 1993, 002; 10.5089/9781451973259.024.A004

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Bounds for Expected Rate of Realignment of Franc-Mark Exchange Rate

(In percent)

Citation: IMF Staff Papers 1993, 002; 10.5089/9781451973259.024.A004

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III. Estimation of Expected Exchange Rate Changes Within the Band

To calculate the expected rate of realignment from equation (7), it is necessary to filter out expectations of exchange rate changes within the fluctuation band. As noted earlier, the simplest procedure is to assume that the expected change in the exchange rate within the band is zero—that is, E_t Δs̄_t+m/m = 0—in which case the expected change in the central parity is simply equal to the interest rate differential. This case can be ruled out a priori, however, since the exchange rate within the band cannot follow a random walk. Indeed, an augmented Dickey-Fuller test rejects the hypothesis that s has a unit root.⁵ An alternative procedure, following Bertola and Svensson (1991), Svensson (1990, 1991), and Rose and Svensson (1991), assumes initially that the future exchange rate within the band may be well approximated by the current exchange rate.⁶ The change in the exchange rate within the band, conditional upon no realignment, may thus be estimated from

Estimates of the above equation are presented in Table 1 and plotted in Figure 3.

Table 1.

Estimated Expected Change in the Franc-Mark Exchange Rate Within the Intervention Band, January 1987-December 1991

$({\overline{s}}_{t+m}-{\overline{s}}_t={\beta }_0+{\beta }_1{\overline{s}}_t+{ϵ}_t)$

Note: T-statistics are in parentheses. The franc-mark rate within the band (s) is measured in log deviations from the franc-mark central parity. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

Table 1.

Estimated Expected Change in the Franc-Mark Exchange Rate Within the Intervention Band, January 1987-December 1991

$({\overline{s}}_{t+m}-{\overline{s}}_t={\beta }_0+{\beta }_1{\overline{s}}_t+{ϵ}_t)$

		Maturity (m)
		3 months	6 months	12 months
Coefficient
	β0	0.454	0.768	1.033
		(2.553)	(3.756)	(7.628)
	β1	-0.443	-0.732	-0.943
		(-3.073)	(-3.792)	(-15.541)
Summary statistics
	Standard error	0.577	0.633	0.550
	R-squared	0.269	0.444	0.652
	F-statistic (β1 = 0)	21.34	43.93	91.64
	Number of observations	60	57	51

Note: T-statistics are in parentheses. The franc-mark rate within the band (s) is measured in log deviations from the franc-mark central parity. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

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Table 1.

Estimated Expected Change in the Franc-Mark Exchange Rate Within the Intervention Band, January 1987-December 1991

$({\overline{s}}_{t+m}-{\overline{s}}_t={\beta }_0+{\beta }_1{\overline{s}}_t+{ϵ}_t)$

		Maturity (m)
		3 months	6 months	12 months
Coefficient
	β0	0.454	0.768	1.033
		(2.553)	(3.756)	(7.628)
	β1	-0.443	-0.732	-0.943
		(-3.073)	(-3.792)	(-15.541)
Summary statistics
	Standard error	0.577	0.633	0.550
	R-squared	0.269	0.444	0.652
	F-statistic (β1 = 0)	21.34	43.93	91.64
	Number of observations	60	57	51

Note: T-statistics are in parentheses. The franc-mark rate within the band (s) is measured in log deviations from the franc-mark central parity. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

Two points about the estimation of equation (10) should be noted. One, a consequence of the target zone model is that the conditional distribution of the exchange rate within the band is heteroskedastic. Two, the projection horizons employed (m = 3, 6, and 12 months) are longer than the sampling interval of the data (monthly). The use of overlapping observations implies that the error terms will follow a moving-average process of order m—1. Ordinary least squares will give consistent estimates of the coefficients, but their standard errors will be inappropriate. Consequently, generalized method of moment (GMM) estimates have been used for the standard errors, which are robust to heteroskedasticity and serial correlation as in Newey and West (1987).

The results indicate that the exchange rate within the band is mean reverting: within the band, the expected exchange rate is closer to the long-run mean of the exchange rate at longer time horizons. The estimated slopes are negative for all maturities, as implied by mean reversion, and are targe relative to their standard errors. Moreover, the longer is the maturity, the larger is the estimated slope in absolute value. The estimates also show that the expected change of the franc-mark exchange rate within the band has narrowed over the January 1987 to March 1992 period and has gradually turned from an expected depreciation to an expected appreciation by the end of the period (Figure 3).

An attempt was made to refine the estimates in Table 1 by the inclusion of additional explanatory variables in equation (9). First, s² and s³ were included so as to capture possible nonlinearities in the relationship. They were found to be insignificant. Second, the mark-dollar interest rate differential for the corresponding maturity was included on the assumption that its movements may affect the franc-mark exchange rate (Artus and others (1991)). This, too, proved insignificant. The estimates in Table 1 are thus used to calculate the expected rate of realignment of the franc-mark exchange rate. It is shown in Figure 4 for different maturities.

IV. Explaining the Expected Rate of Realignment

This section examines whether the calculated expected rate of realignment can be explained by generally observed macroeconomic variables.⁷ It is assumed that in forming expectations of a currency’s possible realignment, agents consider a number of factors, at home and abroad, that may cause a change in the central parity. These include inflation differentials, changes in foreign exchange reserves, fiscal developments, unemployment rates, relative money supply growth, and other macro-economic variables. They may also include other factors that influence market sentiment, such as the authorities’ perceived policy behavior or commitment.

The results of regressing the calculated expected rates of realignment on a selected set of macroeconomic variables that are believed to enter agents’ information sets are shown in Table 2.⁸ For all three maturities the results are quite similar. More than 70 percent of the variation in the expected rate of devaluation is explained by the change in foreign exchange reserves, the government financing requirement (as a ratio to GDP) of France relative to Germany, the inflation differential, France’s export price competitiveness relative to Germany’s, the unemployment rate, and the position of the franc-mark rate within the fluctuation band. Relative money supply growth rates and the trade balance were also included, but they were found to have no additional explanatory power.

Table 2.

Determinants of the Expected Rate of Realignment Based on Filtered Euromarket Interest Rate Differentials, February 1987-November 1991^a

Note: T-statistics are in parentheses.

^aThe expected rate of realignment is defined as the French-German Euromarket interest rate differential minus the estimated expected rate of depreciation within the band. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

^bAll variables enter the estimated equations with a one-period lag, except the government borrowing requirement variable, which enters with a two-period lag. The regression equations also include a constant term, which is not reported.

^cThe percent ratio of the government borrowing requirement to GDP in France relative to Germany.

^dDifferential in the annual rates of change of consumer prices.

^eAnnual rate of change of real exchange rate in terms of export prices. An increase represents an improvement in France’s competitiveness relative to Germany’s.

Table 2.

Determinants of the Expected Rate of Realignment Based on Filtered Euromarket Interest Rate Differentials, February 1987-November 1991^a

		Maturity (m)
Variableb		3 months	6 months	12 months
Change in foreign exchange		-0.118	-0.097	-0.088
	reserves	(1.42)	(-1.29)	(-1.23)
Government financing		0.939	0.853	0.733
	requirementc	(2.86)	(2.38)	(2.18)
Inflation differentiald		0.744	0.794	0.842
		(5.36)	(7.70)	(10.21)
Export price competitivenesse		-0,245	-0.249	-0.243
		(-5.10)	(-5.58)	(-7.79)
Unemployment rate		1.284	1.376	1.400
		(4.31)	(5.34)	(6.75)
Deviation of franc-mark		1.502	1.256	0.800
	rate from upper edge of band	(6.63)	(6.41)	(4.61)
Summary statistics
	Standard error	0.91	0.83	0.71
	R-squared	0.73	0.76	0.81
	F-statistic (6,51)	22.75	26.32	36.41
	Number of observations	58	58	58

Note: T-statistics are in parentheses.

^aThe expected rate of realignment is defined as the French-German Euromarket interest rate differential minus the estimated expected rate of depreciation within the band. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

^bAll variables enter the estimated equations with a one-period lag, except the government borrowing requirement variable, which enters with a two-period lag. The regression equations also include a constant term, which is not reported.

^cThe percent ratio of the government borrowing requirement to GDP in France relative to Germany.

^dDifferential in the annual rates of change of consumer prices.

^eAnnual rate of change of real exchange rate in terms of export prices. An increase represents an improvement in France’s competitiveness relative to Germany’s.

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Table 2.

Determinants of the Expected Rate of Realignment Based on Filtered Euromarket Interest Rate Differentials, February 1987-November 1991^a

		Maturity (m)
Variableb		3 months	6 months	12 months
Change in foreign exchange		-0.118	-0.097	-0.088
	reserves	(1.42)	(-1.29)	(-1.23)
Government financing		0.939	0.853	0.733
	requirementc	(2.86)	(2.38)	(2.18)
Inflation differentiald		0.744	0.794	0.842
		(5.36)	(7.70)	(10.21)
Export price competitivenesse		-0,245	-0.249	-0.243
		(-5.10)	(-5.58)	(-7.79)
Unemployment rate		1.284	1.376	1.400
		(4.31)	(5.34)	(6.75)
Deviation of franc-mark		1.502	1.256	0.800
	rate from upper edge of band	(6.63)	(6.41)	(4.61)
Summary statistics
	Standard error	0.91	0.83	0.71
	R-squared	0.73	0.76	0.81
	F-statistic (6,51)	22.75	26.32	36.41
	Number of observations	58	58	58

Note: T-statistics are in parentheses.

^aThe expected rate of realignment is defined as the French-German Euromarket interest rate differential minus the estimated expected rate of depreciation within the band. The standard errors of the coefficients are GMM estimates allowing for heteroskedastic and serially correlated error terms using the method of Newey and West (1987).

^bAll variables enter the estimated equations with a one-period lag, except the government borrowing requirement variable, which enters with a two-period lag. The regression equations also include a constant term, which is not reported.

^cThe percent ratio of the government borrowing requirement to GDP in France relative to Germany.

^dDifferential in the annual rates of change of consumer prices.

^eAnnual rate of change of real exchange rate in terms of export prices. An increase represents an improvement in France’s competitiveness relative to Germany’s.

The government financing requirement and inflation variables are found to be positively related, and the competitiveness variable negatively related, to the expected rate of realignment. Thus, decreases in France’s government financing requirement and in its inflation rate relative to Germany’s lower the expected rate of devaluation of the franc, as does an improvement in France’s export price competitiveness relative to Germany’s. Moreover, the null hypothesis that the coefficient on the inflation differential is equal to one cannot be rejected at the 5 percent significance level. The change in foreign exchange reserves enters the equations for the expected rate of realignment with the expected negative sign: an increase in reserves decreases the expected rate of devaluation. Its statistical significance, however, depends on the specification of the equation. In particular, when the unemployment rate is also included its statistical significance declines considerably. The unemployment rate itself, however, is highly significant.⁹ This raises an interesting point. In a recent paper, Drazen and Masson (1992) extend the notion of policy credibility to encompass not only the role of government policies in signaling the “type” of government (how “tough” it is, to use their terminology) but also the situation in which a government finds itself—since in very adverse circumstances even a policymaker with a reputation for being “tough” may renege on a commitment. Applied to the EMS, this suggests that the increased credibility of the EMS reflects the dominance of the signaling motive for setting policies as governments maintain their commitment not to realign. However, under the Drazen-Masson notion of credibility, expectations of realignment also reflect pressures to increase employment and growth after a period of restrictive policies. The expected rate of devaluation will, therefore, be positively correlated with the rate of unemployment.

The position of the exchange rate within the fluctuation band—expressed as the deviation of the franc-mark rate from the upper (weak) edge of the band—may be interpreted as capturing intangible market sentiment about the credibility of the target zone. Its statistical significance suggests that when the franc trades close to the upper intervention margin, market expectations of a realignment intensify and a devaluation risk premium is built into franc interest rates. As an alternative way of capturing market sentiment, the deviation of the franc-mark rate from the upper band was replaced in the regression equations by a dummy variable that takes increasing values as the exchange rate approaches the upper intervention margin.¹⁰ The results were not qualitatively different.¹¹ The statistical significance of these variables suggests that the recent policy of allowing the franc to strengthen in the ERM may pay off by way of reducing the devaluation risk premia on French short-term interest rates. One interpretation of these results is that agents may consider it more difficult to defend a currency that is close to the weak edge of the band by sales of reserves (since reserves are limited) than it is to sterilize capital inflows when a currency is at the strong edge of the intervention margin. In the event of a shock, therefore, a country whose currency is in the weak part of the band may have to raise interest rates in order to maintain its currency within the band. If this is seen as introducing a conflict between the domestic and the exchange rate objectives of monetary policy, the credibility of the central parity may suffer.

The analysis thus far has been conducted using short-term Euromarket deposit rates. Euromarket rates have the advantage over domestic money market rates of not being affected by the existence of capital controls. Since capital controls were being phased out over the sample period, it seemed preferable to use Euromarket rates.¹² Euromarket rates are not available for long maturities, however, and the latter have an advantage in that the expected rate of mean reversion of the exchange rate within the band becomes very small at long horizons.¹³ Since E, Δs is bounded, the term E_t Δs_t+m/m in equation (7) becomes progressively smaller as the forecast horizon lengthens, so that the expected rate of devaluation is well approximated by the interest differential.

Table 3 reports the results of regressing the differential in the yield on long-term government bonds on the same set of macroeconomic variables used in the equation for the expected rate of realignment derived from Euromarket rates. The results are broadly similar. The inflation rate, competitiveness, and the unemployment rate are again the major factors influencing devaluation expectations.¹⁴ The relative government financing requirement, however, is not as significant as in the regression equations based on short-term rates, and the market sentiment variables are insignificant. This last result is not surprising, as the current position of the franc in the intervention band should be of little relevance in forming expectations of exchange rates several years hence: views of the long-term viability of the central rate are shaped by the unfolding of more fundamental economic factors.

Table 3.

Determinants of the Expected Rate of Realignment Based on Long-Term Interest Rate Differential, February 1987-November 1991

Note: T-statistics are in parentheses. Interest rates are yields on 7-10 year government bonds. The method of estimation is OLS; robust standard errors are estimated using a spectra! density kernel. The coefficient for the constant term is omitted. Variables are defined as in Table 2.

Table 3.

Determinants of the Expected Rate of Realignment Based on Long-Term Interest Rate Differential, February 1987-November 1991

		Regression
Variable		(1)	(2)
Change in foreign exchange reserves		-0.123	-0.055
		(-2.21)	(-1.37)
Government financing requirement		0.562	0.179
		(1.73)	(1.25)
Inflation differential		0.967	0,538
		(8.17)	(9.55)
Export price competitiveness		-0.150	-0.169
		(-2.90)	(-8.44)
Unemployment rate		…	1.065
			(8.52)
Deviation of franc-mark		0.086	…
	rate from upper edge of band	(0.61)
Summary statistics
	Standard error	0.52	0.34
	R -squared	0.80	0.92
	F-statistic (5,52)	41.49	116.41
	Number of observations	58	58

Note: T-statistics are in parentheses. Interest rates are yields on 7-10 year government bonds. The method of estimation is OLS; robust standard errors are estimated using a spectra! density kernel. The coefficient for the constant term is omitted. Variables are defined as in Table 2.

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Table 3.

Determinants of the Expected Rate of Realignment Based on Long-Term Interest Rate Differential, February 1987-November 1991

		Regression
Variable		(1)	(2)
Change in foreign exchange reserves		-0.123	-0.055
		(-2.21)	(-1.37)
Government financing requirement		0.562	0.179
		(1.73)	(1.25)
Inflation differential		0.967	0,538
		(8.17)	(9.55)
Export price competitiveness		-0.150	-0.169
		(-2.90)	(-8.44)
Unemployment rate		…	1.065
			(8.52)
Deviation of franc-mark		0.086	…
	rate from upper edge of band	(0.61)
Summary statistics
	Standard error	0.52	0.34
	R -squared	0.80	0.92
	F-statistic (5,52)	41.49	116.41
	Number of observations	58	58

Note: T-statistics are in parentheses. Interest rates are yields on 7-10 year government bonds. The method of estimation is OLS; robust standard errors are estimated using a spectra! density kernel. The coefficient for the constant term is omitted. Variables are defined as in Table 2.

V. Conclusions

The differentials between French and German interest rates have narrowed considerably since the EMS realignment in January 1987 as the franc-mark exchange rate band has become increasingly credible. Expectations of realignments of the central parity have been found to be influenced by the evolution of fundamental economic factors such as inflation differentials, competitiveness, unemployment, government financing requirements, and foreign reserves. France’s favorable economic performance, especially with regard to inflation, the external position, and its fiscal situation, has allowed the implicit expected rate of devaluation to decrease considerably. The results further suggest that the devaluation risk premium on franc interest rates could be reduced further and differentials with respect to Germany additionally narrowed by an improved labor market performance and, in the case of short-term rates, by a strengthened position of the franc in the ERM band.