1. Short-term causality

Table 1 reports the results of the Granger causality test applied to determine the respective influence of the German interest rate on those of France, Italy, Spain, and the United States, and conversely of those rates on the German interest rate. The test is implemented in two steps. First, after taking the first differences of the series, ^6/ each interest rate—excluding the German rate—is regressed on its own lagged values and on the German interest rate lagged values to test that the German rate does not cause the given interest rate, i.e., all coefficients on lagged German interest rates should not be significantly different from zero. Second, the German interest rate is regressed on its own lagged values and lagged values of the given interest rate to test that this rate does not cause the German interest rate, i.e., all coefficients on lagged values of the given interest rate should not be significantly different from zero. The results are presented for the two forms of the Granger causality tests: (i) simple causality in which only enter the lagged values of the exogenous variable, providing evidence of an unidirectional causality from the exogenous to the endogenous variable; and (ii) instantaneous causality in which the contemporaneous value of the exogenous variable is included, providing evidence of simultaneous influence. The most significant causalities emerging from these tests are those linking the variations of the French and italian interest rates to the past (simple causality) or present (instantaneous causality) variations of the German interest rate. Conversely, the variations of the German interest rate appear to have been caused to a significant extent by those of the U.S. interest rate while the variation of the latter are better accounted for by its own lagged values. These results seem to provide support for the German leadership thesis in the ERM. However, evidence of a strong instantaneous causality between the French and German interest rates suggests the existence of reciprocal influence between German and French monetary policies. This interpretation should be taken with caution, however, since the monthly periodicity of the series is not appropriate to disentangle the nature of a decision process which involved daily concertations between the two central banks.

Table 1

Granger Casuality Tests on Short-term Domestic Interest Rates Expressed in First Differences ^1/: Test of Two Regimes Over the period July 1979 to june 1991 ^2/

Regression of ${\mathrm{\Delta }Y}_t=\underset{i=1}{\overset{2}{\mathrm{\Sigma }}}{\alpha }_i{\mathrm{\Delta }Y}_{t-1}+\underset{j=0orj=1}{\overset{2}{\mathrm{\Sigma }}}{\beta }_j{\mathrm{\Delta }X}_{t-j}+{ϵ}_t^r$

^1/The interest rates of the various currencies are represented by the following symbols: FRF, French franc; DEM, Deutsche mark; ITL, lira; PTA, peseta; USD, U.S. dollar.

^2/The breaking points corresponding to changes in regime, as well as their degree of significance are presented in Table 2.

^3/One and two asterisks indicate that X “Granger-causae” Y at levels of significance of 5 and 1 percent, respectively. Numbers in parentheses underlying F-statistics correspond to the degrees of freedom of the relevant test.

Table 1

Granger Casuality Tests on Short-term Domestic Interest Rates Expressed in First Differences ^1/: Test of Two Regimes Over the period July 1979 to june 1991 ^2/

Regression of ${\mathrm{\Delta }Y}_t=\underset{i=1}{\overset{2}{\mathrm{\Sigma }}}{\alpha }_i{\mathrm{\Delta }Y}_{t-1}+\underset{j=0orj=1}{\overset{2}{\mathrm{\Sigma }}}{\beta }_j{\mathrm{\Delta }X}_{t-j}+{ϵ}_t^r$

		F - Statistic on All βS=0 3/
ΔY	ΔX	Simple Causality (j=1)			Instantaneous Causality (j=0)
		OVERALL PERIOD	REGIME 1	REGIME 2	OVERALL PERIOD	REGIME 1	REGIME 2
FRF	DEM	5.46** (2.139)	2.01 (2,33)	5.40** (2,101)	10.29** (2,138)	3.96* (2,32)	8.63** (2,100)
DEM	FRF	1.54 (2,139)	1.58 (2,18)	0.86 (2,116)	6.15** (2,138)	3.67* (2,17)	2.25 (2,115)
ITL	DEM	4.86** (2,139)	7.89** (2,76)	2.12 (2,58)	4.89** (2,138)	8.23** (2,75)	3.73* (2,57)
DEM	ITL	0.19 (2,139)	0.14 (2,18)	0.17 (2,116)	0.25 (2,138)	0.36 (2,17)	0.81 (2,15)
PTA	DEM	3.39* (2,139)	2.23 (2,54)	0.41 (2,80)	3.92* (2,138)	2.47 (2,53)	0.49 (2,79)
DEM	PTA	0.42 (2,139)	0.22 (2,18)	0.22 (2,116)	0.95 (2,138)	0.47 (2,17)	0.29 (2,115)
USD	DEM	0.46 (2,139)	0.12 (2,135)	0.44 (2,99)	1.30 (2,138)	0.36 (2,34)	1.35 (2,98)
DEM	USD	4.75** (2,139)	0.93 (2,18)	3.12* (2,116)	5.61** (2,138)	0.89 (2,17)	4.12* (2,115)

^1/The interest rates of the various currencies are represented by the following symbols: FRF, French franc; DEM, Deutsche mark; ITL, lira; PTA, peseta; USD, U.S. dollar.

^2/The breaking points corresponding to changes in regime, as well as their degree of significance are presented in Table 2.

^3/One and two asterisks indicate that X “Granger-causae” Y at levels of significance of 5 and 1 percent, respectively. Numbers in parentheses underlying F-statistics correspond to the degrees of freedom of the relevant test.

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Table 1

Granger Casuality Tests on Short-term Domestic Interest Rates Expressed in First Differences ^1/: Test of Two Regimes Over the period July 1979 to june 1991 ^2/

Regression of ${\mathrm{\Delta }Y}_t=\underset{i=1}{\overset{2}{\mathrm{\Sigma }}}{\alpha }_i{\mathrm{\Delta }Y}_{t-1}+\underset{j=0orj=1}{\overset{2}{\mathrm{\Sigma }}}{\beta }_j{\mathrm{\Delta }X}_{t-j}+{ϵ}_t^r$

		F - Statistic on All βS=0 3/
ΔY	ΔX	Simple Causality (j=1)			Instantaneous Causality (j=0)
		OVERALL PERIOD	REGIME 1	REGIME 2	OVERALL PERIOD	REGIME 1	REGIME 2
FRF	DEM	5.46** (2.139)	2.01 (2,33)	5.40** (2,101)	10.29** (2,138)	3.96* (2,32)	8.63** (2,100)
DEM	FRF	1.54 (2,139)	1.58 (2,18)	0.86 (2,116)	6.15** (2,138)	3.67* (2,17)	2.25 (2,115)
ITL	DEM	4.86** (2,139)	7.89** (2,76)	2.12 (2,58)	4.89** (2,138)	8.23** (2,75)	3.73* (2,57)
DEM	ITL	0.19 (2,139)	0.14 (2,18)	0.17 (2,116)	0.25 (2,138)	0.36 (2,17)	0.81 (2,15)
PTA	DEM	3.39* (2,139)	2.23 (2,54)	0.41 (2,80)	3.92* (2,138)	2.47 (2,53)	0.49 (2,79)
DEM	PTA	0.42 (2,139)	0.22 (2,18)	0.22 (2,116)	0.95 (2,138)	0.47 (2,17)	0.29 (2,115)
USD	DEM	0.46 (2,139)	0.12 (2,135)	0.44 (2,99)	1.30 (2,138)	0.36 (2,34)	1.35 (2,98)
DEM	USD	4.75** (2,139)	0.93 (2,18)	3.12* (2,116)	5.61** (2,138)	0.89 (2,17)	4.12* (2,115)

^1/The interest rates of the various currencies are represented by the following symbols: FRF, French franc; DEM, Deutsche mark; ITL, lira; PTA, peseta; USD, U.S. dollar.

^2/The breaking points corresponding to changes in regime, as well as their degree of significance are presented in Table 2.

^3/One and two asterisks indicate that X “Granger-causae” Y at levels of significance of 5 and 1 percent, respectively. Numbers in parentheses underlying F-statistics correspond to the degrees of freedom of the relevant test.

Quandt tests for possible changes in regime were carried out for the ERM currencies on Granger simple causality tests. The Quandt Log-likelihood functions are presented in Chart 1 under four panels and the corresponding breaking points determining changes in regime with associated Chow tests ^7/ are reported in Table 2. The first panel concerns the causal relationship characterizing the influence of the French, Italian, and Spanish interest rates on the German rate. For each series, including the U.S. dollar, the maximum of the likelihood functions is reached in May 1981 and the Chow tests confirm the significance of this breaking point. This period marked the end of a phase of a relative weakness of the deutsche mark in the EMS and build-up of inflationary pressures in Germany that were met by important increases in the intervention rate of the Bundesbank at the outset of 1980 and 1981. The second, third, and fourth panels present the Log-likelihood functions of testing for possible change in the causal relationship accounting for the impact of the German interest rate on the French, Italian, and Spanish interest rates, respectively. A perusal of these charts reveals three breaking points: (i) August 1982 for the French rate, (ii) March 1986 for the Italian rate, and (iii) May 1984 for the Spanish rate. Except in the case of the Italian rate, the Chow test does not firmly support these results. Various factors can account for these changes in regime. Some of them are technical and related to changes in the choice of monetary instrument, while others are the expression of changes in the orientation of monetary policy. In the case of the French interest rate, the new regime started after the second realignment of the French franc in the EMS—the central rate of the French franc against deutsche mark was devalued by 10 percent in June 14, 1982—as the French government embarked on more restrictive financial measures and structural reforms in an attempt to counter inflationary pressures and restore the credibility of the stabilization of the French franc in the EMS. The strong increase in the Granger causality test between the two regimes confirms that the central element of the new policy was a greater coordination with German monetary policy. In the case of the lira, the existence of a breaking point in March 1986 appears to coincide with the relaxation of monetary policy as the lira declined in the ERM wide band from the strong position secured after the July 20, 1985 devaluation by 8 percent against all participating currencies. This appears to have been accompanied by a weakening of the influence of the German interest rate on the Italian rate as suggested by the Granger causality test. The participation of the lira in the ERM wide band—up to January 1990—and the implementation of capital controls seem to have been the main factors that allowed Italy to preserve a greater measure of monetary autonomy in the ERM than other members. In the case of the Spanish rate, the change in regime spotted in mid-1984 seems to correspond to the alteration in the implementation of monetary policy as the central bank switched from base money to interest rate control. This finding is consistent with the conclusions of Escriva and Santos (1991) who were unable to find a stable interest rate reaction function for the Bank of Spain before 1984. The Granger causality test does not provide significant evidence of a causal link between the German and Spanish interest rates, in particular after 1984. ^8/ This should not come as a surprise in that the participation of Spain to the EC dates back to January 1986 and the entry of the peseta in the ERM wide band to June 1989. There is, however, recent evidence of the influence of other ERM interest rates, and in particular the German rate, on the Spanish interest rate in 1991–92 following the removal of remaining capital and credit controls. These developments are too recent to be taken into account by the Quandt likelihood test.

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TEST OF CHANGE IN REGIME IN GRANGER CAUSALITY TESTS APPLIED INTEREST RATES OF ERM COUNTRIES, JAN 1980-DEC 1990

Citation: IMF Working Papers 1992, 087; 10.5089/9781451850932.001.A001

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Table 2.

Determination of Change in Regime in Granger Causality Tests Using the Quandt Likelihood Test

^1/The breaking points are determined by using the switching regression technique proposed by Quandt (1958), this technique is based on the calculation of a log-likelihood function assuming two regimes with different error variances and choosing the period for which this function is maximized.

^2/One and two asterisks indicate that the existence of two regimes cannot be rejected at a level of significance of 5 and 1 percent, respectively.

Table 2.

Determination of Change in Regime in Granger Causality Tests Using the Quandt Likelihood Test

ΔY	ΔX	Breaking Points 1/	Chow Test 2/
FRF	DEM	AUG 1982	1.89
DEM	FRF	MAY 1981	5.20 (**)
LIT	DEM	MAR 1986	3.98 (**)
DEM	LIT	MAY 1981	2.84 (**)
PTA	DEM	MAY 1984	1.84
DEM	PTA	MAY 1981	2.66 (*)
US	DEM	OCT 1982	0
DEM	US	MAY 1981	2.3 (*)

^1/The breaking points are determined by using the switching regression technique proposed by Quandt (1958), this technique is based on the calculation of a log-likelihood function assuming two regimes with different error variances and choosing the period for which this function is maximized.

^2/One and two asterisks indicate that the existence of two regimes cannot be rejected at a level of significance of 5 and 1 percent, respectively.

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Table 2.

Determination of Change in Regime in Granger Causality Tests Using the Quandt Likelihood Test

ΔY	ΔX	Breaking Points 1/	Chow Test 2/
FRF	DEM	AUG 1982	1.89
DEM	FRF	MAY 1981	5.20 (**)
LIT	DEM	MAR 1986	3.98 (**)
DEM	LIT	MAY 1981	2.84 (**)
PTA	DEM	MAY 1984	1.84
DEM	PTA	MAY 1981	2.66 (*)
US	DEM	OCT 1982	0
DEM	US	MAY 1981	2.3 (*)

^1/The breaking points are determined by using the switching regression technique proposed by Quandt (1958), this technique is based on the calculation of a log-likelihood function assuming two regimes with different error variances and choosing the period for which this function is maximized.

^2/One and two asterisks indicate that the existence of two regimes cannot be rejected at a level of significance of 5 and 1 percent, respectively.

All in all, Granger causality and Quandt tests implemented over the period July 1979 to June 1991 provide evidence of a significant influence of the German interest rate on French and Italian interest rates. After 1982, the tests point to the strengthening of the relationship between German and French interest rates associated with the development of a strong instantaneous causality between the two rates. Conversely, the fluctuations of the German interest rate appear to have been somewhat caused by those of the US interest rate after 1981.

2. Causal relationships in a co-integration framework

This section investigates the long-term causal relationship between the domestic interest rate of a given ERM country and the German interest rate corrected for inflation differentials using co-integration properties as suggested by Granger (1988). Under the German leadership hypothesis, ERM central banks, to establish the credibility of their anti-inflationary stance, would have been expected to secure inflation convergence with Germany by adjusting their domestic interest rates in relation both to variations of the German interest rate and to changes in expected inflation differentials with Germany. In the long run, such policy would translate into the cointegration of the interest rate of the ERM country with that of Germany corrected for inflation differentials. There are some indications that such a procedure was carried out on a regular basis, at least in one central bank, with inflation expectations based in part on recent trends and in part on forecasts issued every semester by international organizations.

To test for the presence of co-integration, a two-step procedure is adopted. First, to determine the existence of co-integration, ADF unit root tests are applied to each ERM interest rate and to its estimate, constructed with the German interest rate corrected for the relevant expected interest rate differentials. ^9/ Second, after taking first differences, two regressions are estimated. The ERM interest rate is regressed on its own lagged values and on those of the German interest rate corrected for inflation differentials and vice versa. To the extent that the first step does not lead to a rejection of the assumption of co-integration, an error correction term is included in the regressions to account for the long-term component of the causal relationship. ^10/ The error correction term is the co-integrating vector estimated by regressing the level of the actual interest rate on the estimated rate. The significance of a long-term causal linkage would be recognized if the ADF unit root tests are conclusive and if the regression coefficient on the error correction term is significantly different from zero.

Table 3 reports only the results of the first regression estimating the relationship between the French, Italian, and Spanish interest rates, and the German rate corrected for inflation differentials as the significance of the statistical tests on the opposite relationship were distinctly low. Results are presented both for the overall period and the second regime identified in Table 2 in the case of the deutsche mark. The T-student on the coefficient of the error correction term is generally significant at the 99 percent confidence level while the ADF tests point to the existence of co-integration with a level of significance rather low in the case of the Italian and Spanish rate for the overall period, and much stronger in the case of the French rate after June 1981. The latter result provides additional support for the previous evidence in favor of the German leadership thesis after 1981.

Table 3

Granger Casuality Tests in a Co-integration Framework Applied to ERM Interest Rates

(Tests of Two Regimes Over the period july 1979 to June 1991) ${\mathrm{\Delta }Y}_t=a_0+\underset{i=1}{\overset{3}{\mathrm{\Sigma }}}{b}_1{\mathrm{\Delta }x}_{t-1}+\underset{j=1}{\overset{3}{\mathrm{\Sigma }}}{c}_j{\mathrm{\Delta }Y}_{t-j}+{dz}_{t-1}$ ^1/

^1/Y is the actual interest rate and x the estimated interest rate determined by adding up to the German interest rate, the contemporaneous 12-month inflation differentials between the relevant country and Germany.

^2/One and two asterisks in columns (2), (3), (8) and (9) indicate significance levels of 5 and 1 percent, respectively.

^3/ADF critical values for unit root tests calculated in Engle and Granger (1987) for 100 obversatios are 3.77, 3.17 and 2.84 at a significance level of 1 percent, 5 percent, and 10 percent, respectively, Co-integration at 10 and 5 percent levels of significance is indicated by one and two asterisks, respectively, in columns (6) and (12).

Table 3

Granger Casuality Tests in a Co-integration Framework Applied to ERM Interest Rates

(Tests of Two Regimes Over the period july 1979 to June 1991) ${\mathrm{\Delta }Y}_t=a_0+\underset{i=1}{\overset{3}{\mathrm{\Sigma }}}{b}_1{\mathrm{\Delta }x}_{t-1}+\underset{j=1}{\overset{3}{\mathrm{\Sigma }}}{c}_j{\mathrm{\Delta }Y}_{t-j}+{dz}_{t-1}$ ^1/

		OVERALL PERIOD 2/						REGIME 2 (June 1981 to June 1991) 2/
					ADF Unit Root Test 3/						ADF Unit Root Test 3/
ΔY	ΔX	Theil Adjusted R2	F-Statistic	t-student on z	y	x		Theil Adjusted R2	F-Statistic	t-student on z	y	x
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
FRF	Estimated FRF	0.285	9.14(**)	3.52(**)	1.66	1.06	2.53	0.242	6.31(**)	2.36(*)	1.99	2.85	3.47(**)
ITL	Eetimated ITL	0.219	6.75(**)	3.16(**)	1.47	0.77	2.90(*)	0.209	5.40(**)	2.85(**)	1.16	4.84	2.29
PTA	Estimated PTA	0.285	9.17(**)	3.82(**)	2.97	1.49	3.01(*)	0.253	6.64(**)	3.07(**)	2.71	2.84	2.60

^1/Y is the actual interest rate and x the estimated interest rate determined by adding up to the German interest rate, the contemporaneous 12-month inflation differentials between the relevant country and Germany.

^2/One and two asterisks in columns (2), (3), (8) and (9) indicate significance levels of 5 and 1 percent, respectively.

^3/ADF critical values for unit root tests calculated in Engle and Granger (1987) for 100 obversatios are 3.77, 3.17 and 2.84 at a significance level of 1 percent, 5 percent, and 10 percent, respectively, Co-integration at 10 and 5 percent levels of significance is indicated by one and two asterisks, respectively, in columns (6) and (12).

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Table 3

Granger Casuality Tests in a Co-integration Framework Applied to ERM Interest Rates

(Tests of Two Regimes Over the period july 1979 to June 1991) ${\mathrm{\Delta }Y}_t=a_0+\underset{i=1}{\overset{3}{\mathrm{\Sigma }}}{b}_1{\mathrm{\Delta }x}_{t-1}+\underset{j=1}{\overset{3}{\mathrm{\Sigma }}}{c}_j{\mathrm{\Delta }Y}_{t-j}+{dz}_{t-1}$ ^1/

		OVERALL PERIOD 2/						REGIME 2 (June 1981 to June 1991) 2/
					ADF Unit Root Test 3/						ADF Unit Root Test 3/
ΔY	ΔX	Theil Adjusted R2	F-Statistic	t-student on z	y	x		Theil Adjusted R2	F-Statistic	t-student on z	y	x
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
FRF	Estimated FRF	0.285	9.14(**)	3.52(**)	1.66	1.06	2.53	0.242	6.31(**)	2.36(*)	1.99	2.85	3.47(**)
ITL	Eetimated ITL	0.219	6.75(**)	3.16(**)	1.47	0.77	2.90(*)	0.209	5.40(**)	2.85(**)	1.16	4.84	2.29
PTA	Estimated PTA	0.285	9.17(**)	3.82(**)	2.97	1.49	3.01(*)	0.253	6.64(**)	3.07(**)	2.71	2.84	2.60

^1/Y is the actual interest rate and x the estimated interest rate determined by adding up to the German interest rate, the contemporaneous 12-month inflation differentials between the relevant country and Germany.

^2/One and two asterisks in columns (2), (3), (8) and (9) indicate significance levels of 5 and 1 percent, respectively.

^3/ADF critical values for unit root tests calculated in Engle and Granger (1987) for 100 obversatios are 3.77, 3.17 and 2.84 at a significance level of 1 percent, 5 percent, and 10 percent, respectively, Co-integration at 10 and 5 percent levels of significance is indicated by one and two asterisks, respectively, in columns (6) and (12).

3. Reaction functions

A reaction function was estimated for each currency, except the peseta. To take into account the short- and long-term relationships observed in the causality tests, the reaction function was estimated as an error correction model including both the levels, lagged by one period, and changes of the explanatory variables identified in the previous tests. Other relevant explanatory variables were included in the reaction function on the basis of further empirical evidence and results of previous studies (Galy (1985), Artus and alii (1987), Artus and alii (1991)). The following explanatory variables were added: (i) the ratio of foreign reserves to imports; (ii) the deviations of the exchange rates of the French franc and Italian lira from their ERM central rates against the deutsche mark; (iii) the exchange rate of the deutsche mark against the U.S. dollar.

Table 4 presents the reaction functions while the long-term elasticities implied by the correction terms are reported in Table 5. The Quandt test was also applied to the reaction functions and the conclusions provided on the breaking points confirmed broadly the results provided by the causality tests, except for the Italian rate for which the maximum of the likelihood function is now reached in June 1981. This apparent change in regime follows the first devaluation of the lira in the ERM on March 23, 1981 (Chart 3, Table 6). It seems that after the two first years of the ERM, the Italian authorities paid greater attention to the constraints imposed on domestic monetary policy through participation in the ERM. This is suggested by the greater significance acquired by the German interest rate in the reaction function after June 1981.

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ACTUAL AND ESTIMATTED MONEY MARKET INTEREST RATES IMPLIED BY THE PPP AND UIP PARADIGMS, JAN 1980-AUG 1991

Citation: IMF Working Papers 1992, 087; 10.5089/9781451850932.001.A001

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TESTS OF CHANGE IN REGIME IN THE INTEREST RATE REACTION FUNCTION OF ERM COUNTRIES, JUN 1980-DEC 1990

Citation: IMF Working Papers 1992, 087; 10.5089/9781451850932.001.A001

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Table 4.

Estimation of the Reaction Functions for Short-term ERM Interests Rates ^1/

${\mathrm{\Delta }i}_t={\alpha }_i{\mathrm{\Delta }i}_t*+{\alpha }_2\mathrm{\Delta }{(p-p*)}_t+{\alpha }_3\mathrm{\Delta }{(s-\overline{s})}_t+{\alpha }_4{\mathrm{\Delta }sus}_t+{\alpha }_5\mathrm{\Delta }r+\delta [i_{t-1}-{\beta }_{1}i{*}_{t-1}-{\beta }_2{(p-p*)}_{t-1}-{\beta }_3{(s-\overline{s})}_{t-1}-{\beta }_4{sus}_{t-1}-{\beta }_5{r}_{t-1}]$

^1/The breaking points and their degree of significance are presented in Table 6.

^2/All variables are expressed in natural logarithms, except interest rates and inflation rates. The inflation differential is the 12-month inflation differential between France (Italy) and Germany for the French (Italian) reaction function, and between Germany and France for the German reaction function. The deviation from central rates is the ratio of the exchange rate of the French franc in terms of one unit of deutsche mark to its ERM central rates. The exchange rate of the deutsche mark is expressed per unit of U.S. dollar. Coefficients in parentheses are t-ratios. One and two asterisks point to level of significance of 5 and 1 percent, respectively. F, R², DW, and SEE denote the F, test, the coefficient of determination, the Durbin-Matson statistic and the standard error.

^3/The β’s coefficients are long-term elasticities. They are estimated by dividing the coefficient estimated on the variable in level (part II of the table) by the error correction term of the relevant endogenous interest rate. The long-term elasticities are presented in Table 5.

Table 4.

Estimation of the Reaction Functions for Short-term ERM Interests Rates ^1/

${\mathrm{\Delta }i}_t={\alpha }_i{\mathrm{\Delta }i}_t*+{\alpha }_2\mathrm{\Delta }{(p-p*)}_t+{\alpha }_3\mathrm{\Delta }{(s-\overline{s})}_t+{\alpha }_4{\mathrm{\Delta }sus}_t+{\alpha }_5\mathrm{\Delta }r+\delta [i_{t-1}-{\beta }_{1}i{*}_{t-1}-{\beta }_2{(p-p*)}_{t-1}-{\beta }_3{(s-\overline{s})}_{t-1}-{\beta }_4{sus}_{t-1}-{\beta }_5{r}_{t-1}]$

			Change in French interest rate (Δi) 1/		Change in German interest rate (Δi) 1/		Change in Italian interest rate (Δi)
	Exogenous Variables / Endogenous Variables		Regime 1 7–1979 7–1981	Regime 2 8–1981 10–1991	Regime 1 7–1979 3–1981	Regime 2 4–1981 10–1991	Regime 1 7–1979 5–1981	Regime 2 6–1981 10–1991
I. First differences (in t-1) 2/
	Δi* - italian interest rate		—	—	0.13 (0.53)	0.11* (2.39)	0.09 (0.44)	0.41** (4.89)	(in t-1)
	Δi* - French interest rate		—	—	0.51 (1.43)	0.17** (3.41)	—	—
	Δi* - German interest rate		0.23 (1.38)	0.23* (2.47)	—	—	0.12 (0.72)	0.27 (1.94)
	Δ(p-p*) - Inflation differential		0.01 (0.04)	0.24** (2.99)	0.08 (0.21)	0.05 (0.74)	0.13 (0.73)	0.11 (1.11)
	Δ(s-Ṡ) - Deviation from central rates		-0.09 (0.52)	0.11** (3.33)	—	—	—
	Δ(sus) - U.S. dollar (in t-1)		—	—	-0.057 (0.85)	(0.023** (3.49)	—	—
	Δr - Foreign reserves/import ratio		-0.04** (4.31)	-0.005** (3.81)	-0.019 (0.48)	-0.017** (3.55)	-0.02 (1.32)	-0.013*
II. Error correction term: variables in level in t-1 3/
	i, i* -Italian interest rate		—	—	—	—	0.53**(3.55)	-0.06*
	i, i* - French interest rate		-0.26* (2.13)	-0.15** (3.65)	0.41 (1.71)	0.06* (2.47)	—	—
	i, i* - German interest rate		0.21 (1.75)	0.08* (2.57)	-0.36 (1.16)	-0.07** (3.14)	0.42** (3.12)	0.04 (2.00)
	(p-p*) - Inflation differential		-0.05 (0.16)	0.12** (3.73)	0.37 (1.50)	0.07** (4.40)	0.44** (2.94)	0.08* (2.02)
	(s-Ṡ) - Deviation from central rates		0.21 (0.98)	0.11** (3.49)	—	—	—	—
	sus - U.S. dollar		—	—	0.11* (2.47)	0.003 (1.95)	—	—
	r - Foreign reserves/import ratio		-0.003 (1.19)	-0.001** (3.36)	-0.048* (2.32)	-0.002 (1.77)	-0.01 (1.51)	-0.001 (0.62)
III. Statistical parameters
		- F-statistic	7.10	10.35	2.99	7.91	4.39	5.287
		- R2 (adjusted)	0.66	0.39	0.42	0.35	0.54	0.21
		- DW (or H statistic for Italian lira)	1.95	1.80	1.73	1.83	-5.70	0.15
		- SEE	0.006	0.003	0.003	0.003	0.006	0.004
		- Number of observations	25	123	21	127	23	148

^1/The breaking points and their degree of significance are presented in Table 6.

^2/All variables are expressed in natural logarithms, except interest rates and inflation rates. The inflation differential is the 12-month inflation differential between France (Italy) and Germany for the French (Italian) reaction function, and between Germany and France for the German reaction function. The deviation from central rates is the ratio of the exchange rate of the French franc in terms of one unit of deutsche mark to its ERM central rates. The exchange rate of the deutsche mark is expressed per unit of U.S. dollar. Coefficients in parentheses are t-ratios. One and two asterisks point to level of significance of 5 and 1 percent, respectively. F, R², DW, and SEE denote the F, test, the coefficient of determination, the Durbin-Matson statistic and the standard error.

^3/The β’s coefficients are long-term elasticities. They are estimated by dividing the coefficient estimated on the variable in level (part II of the table) by the error correction term of the relevant endogenous interest rate. The long-term elasticities are presented in Table 5.

View Table

Table 4.

Estimation of the Reaction Functions for Short-term ERM Interests Rates ^1/

${\mathrm{\Delta }i}_t={\alpha }_i{\mathrm{\Delta }i}_t*+{\alpha }_2\mathrm{\Delta }{(p-p*)}_t+{\alpha }_3\mathrm{\Delta }{(s-\overline{s})}_t+{\alpha }_4{\mathrm{\Delta }sus}_t+{\alpha }_5\mathrm{\Delta }r+\delta [i_{t-1}-{\beta }_{1}i{*}_{t-1}-{\beta }_2{(p-p*)}_{t-1}-{\beta }_3{(s-\overline{s})}_{t-1}-{\beta }_4{sus}_{t-1}-{\beta }_5{r}_{t-1}]$

			Change in French interest rate (Δi) 1/		Change in German interest rate (Δi) 1/		Change in Italian interest rate (Δi)
	Exogenous Variables / Endogenous Variables		Regime 1 7–1979 7–1981	Regime 2 8–1981 10–1991	Regime 1 7–1979 3–1981	Regime 2 4–1981 10–1991	Regime 1 7–1979 5–1981	Regime 2 6–1981 10–1991
I. First differences (in t-1) 2/
	Δi* - italian interest rate		—	—	0.13 (0.53)	0.11* (2.39)	0.09 (0.44)	0.41** (4.89)	(in t-1)
	Δi* - French interest rate		—	—	0.51 (1.43)	0.17** (3.41)	—	—
	Δi* - German interest rate		0.23 (1.38)	0.23* (2.47)	—	—	0.12 (0.72)	0.27 (1.94)
	Δ(p-p*) - Inflation differential		0.01 (0.04)	0.24** (2.99)	0.08 (0.21)	0.05 (0.74)	0.13 (0.73)	0.11 (1.11)
	Δ(s-Ṡ) - Deviation from central rates		-0.09 (0.52)	0.11** (3.33)	—	—	—
	Δ(sus) - U.S. dollar (in t-1)		—	—	-0.057 (0.85)	(0.023** (3.49)	—	—
	Δr - Foreign reserves/import ratio		-0.04** (4.31)	-0.005** (3.81)	-0.019 (0.48)	-0.017** (3.55)	-0.02 (1.32)	-0.013*
II. Error correction term: variables in level in t-1 3/
	i, i* -Italian interest rate		—	—	—	—	0.53**(3.55)	-0.06*
	i, i* - French interest rate		-0.26* (2.13)	-0.15** (3.65)	0.41 (1.71)	0.06* (2.47)	—	—
	i, i* - German interest rate		0.21 (1.75)	0.08* (2.57)	-0.36 (1.16)	-0.07** (3.14)	0.42** (3.12)	0.04 (2.00)
	(p-p*) - Inflation differential		-0.05 (0.16)	0.12** (3.73)	0.37 (1.50)	0.07** (4.40)	0.44** (2.94)	0.08* (2.02)
	(s-Ṡ) - Deviation from central rates		0.21 (0.98)	0.11** (3.49)	—	—	—	—
	sus - U.S. dollar		—	—	0.11* (2.47)	0.003 (1.95)	—	—
	r - Foreign reserves/import ratio		-0.003 (1.19)	-0.001** (3.36)	-0.048* (2.32)	-0.002 (1.77)	-0.01 (1.51)	-0.001 (0.62)
III. Statistical parameters
		- F-statistic	7.10	10.35	2.99	7.91	4.39	5.287
		- R2 (adjusted)	0.66	0.39	0.42	0.35	0.54	0.21
		- DW (or H statistic for Italian lira)	1.95	1.80	1.73	1.83	-5.70	0.15
		- SEE	0.006	0.003	0.003	0.003	0.006	0.004
		- Number of observations	25	123	21	127	23	148

^1/The breaking points and their degree of significance are presented in Table 6.

^2/All variables are expressed in natural logarithms, except interest rates and inflation rates. The inflation differential is the 12-month inflation differential between France (Italy) and Germany for the French (Italian) reaction function, and between Germany and France for the German reaction function. The deviation from central rates is the ratio of the exchange rate of the French franc in terms of one unit of deutsche mark to its ERM central rates. The exchange rate of the deutsche mark is expressed per unit of U.S. dollar. Coefficients in parentheses are t-ratios. One and two asterisks point to level of significance of 5 and 1 percent, respectively. F, R², DW, and SEE denote the F, test, the coefficient of determination, the Durbin-Matson statistic and the standard error.

^3/The β’s coefficients are long-term elasticities. They are estimated by dividing the coefficient estimated on the variable in level (part II of the table) by the error correction term of the relevant endogenous interest rate. The long-term elasticities are presented in Table 5.

Table 5.

Long-Term Elasticities in the Reaction Functions with Error Correction Terms ^1/

^1/Long-term elasticities are determined on the basis of the error correction terms in Table 4.

Table 5.

Long-Term Elasticities in the Reaction Functions with Error Correction Terms ^1/

		French interest rate	German interest rate	Italian interest rate
		8/1981 to 10/1991	4/1981 to 10/1991	6/1981 to 10/1991
Explanatory variables
	- French interest rate		0.86
	- German interest rate	0.53		0.67
	- Inflation differential	0.80	1.00	1.33
	- Deviation from central rates	0.73
	- U.S. dollar		0.04
	- Foreign reserves/import ratio	-0.007	-0.03	NS

^1/Long-term elasticities are determined on the basis of the error correction terms in Table 4.

View Table

Table 5.

Long-Term Elasticities in the Reaction Functions with Error Correction Terms ^1/

		French interest rate	German interest rate	Italian interest rate
		8/1981 to 10/1991	4/1981 to 10/1991	6/1981 to 10/1991
Explanatory variables
	- French interest rate		0.86
	- German interest rate	0.53		0.67
	- Inflation differential	0.80	1.00	1.33
	- Deviation from central rates	0.73
	- U.S. dollar		0.04
	- Foreign reserves/import ratio	-0.007	-0.03	NS

^1/Long-term elasticities are determined on the basis of the error correction terms in Table 4.

Table 6.

Determination of Change in Regime in the Interest Rate Reaction Functions using the Quandt Likelihood Test

^1/See Table 2.

^2/See Table 2.

Table 6.

Determination of Change in Regime in the Interest Rate Reaction Functions using the Quandt Likelihood Test

Interest Rate Reaction Function	Breaking Points 1/	Chow Test 2/
France	August 1981	13.77 (**)
Germany	April 1981	10.40 (**)
Italy	June 1981	3.13 (**)

^1/See Table 2.

^2/See Table 2.

View Table

Table 6.

Determination of Change in Regime in the Interest Rate Reaction Functions using the Quandt Likelihood Test

Interest Rate Reaction Function	Breaking Points 1/	Chow Test 2/
France	August 1981	13.77 (**)
Germany	April 1981	10.40 (**)
Italy	June 1981	3.13 (**)

^1/See Table 2.

^2/See Table 2.

The perusal of the reaction functions estimated over the two regimes suggests the following observations:

- In the French interest rate equation, only foreign reserves stand out as a strong explanatory factor during the first regime. By contrast, after July 1981, all exogenous variables, including the error correction terms become highly significant. The German interest rate and the inflation differentials have a notable influence both in the short-term dynamics and in the long-term components of the reaction function. The long-term elasticities emerging from the error correction terms (Table 6) point to the important role played by the inflation differentials with Germany and to a lesser degree by the German interest rate in the long-run orientation of the French monetary policy. Also, the intensity of the reaction of the French central bank increased significantly over the second regime with respect to deviations of the French franc from its central rate against the deutsche mark but weakened with respect to changes in foreign reserves. This suggests that, during this period, the authorities relied more on monetary policy than on exchange rate policy to stabilize the exchange rate. This outcome is consistent with the decline of the effectiveness of sterilized foreign exchange intervention that was prompted by greater capital mobility and substitutability as capital controls were progressively phased out. While the coefficient of the German interest rate remained stable over the two regimes, suggesting the absence of changes in the behavior of the central bank in this regard, the fact that the coefficient of the deviations of the French franc from its deutsche mark central rate increased strikingly during the second regime, could be interpreted as a relative tightening of the constraint imposed by German monetary policy on French monetary policy.

- In the German interest rate equation, as in the French one, most of the explanatory variables are hardly significant or possess signs that disagree with a priori expectations during the first regime. Over the second period, most of the coefficients turn out to be highly significant. The short-term dynamics of the German interest rate are explained by the reaction of the Bundesbank to changes in: (i) the French and Italian interest rates; (ii) the exchange rate of the deutsche mark against the U.S. dollar; (iii) and foreign reserves. The long-term trend of the German interest rate is significantly influenced by the French interest rate and inflation differentials, mirroring in part the results obtained in the French interest rate reaction function.

- In the Italian reaction function, short-term explanatory variables are not significant during the first regime. Over the second regime, only the lagged changes of the Italian interest rate and foreign reserves appear to drive the short-term dynamics of the Italian rate. The level of significance of the German interest rate, while improving substantially compared to the first regime, remains weak and deviations from central rates are not significant at all. Also, the error correction elements exhibit a modest degree of significance. These results seem to illustrate the relative independence enjoyed by the Italian central bank during the 1980s, thanks to capital controls and to the relatively limited constraint imposed by the participation of the lira in the ERM broad band.

V. Conclusion

Econometric evidence presented in this paper provides some support to the German leadership thesis but points also to an increased interdependence between French and German monetary policies after 1981–82 while results in the Italian and Spanish case suggest the persistence of a significant monetary autonomy. Changes in regime appear to be concentrated in the first years of the ERM and are related to technical changes in the implementation of monetary policy, and to the introduction of adjustment programs to strengthen the credibility of the exchange rate commitment, generally following a major realignment. There is no doubt that the total removal of capital controls in 1990–91 has reduced further monetary autonomy among ERM participants, including Germany, requiring a rapid implementation of the concerted approach proposed in the Maastricht Agreement. However, the consecutive possible changes in ERM central banks’ behavior are too recent to be identified by the tests presented in this paper.