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Bodnar, Gordon M., “Target Zones and Euro-Rates: A Model of Eurocurrency Interest Rate Differentials in the European Monetary System,” Working Paper (unpublished, University of Rochester, 1991).
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Edin, Per-Anders, and Anders Vredin, “Devaluation Risk: Evidence from the Nordic Countries,” Working Paper (unpublished, Trade Union Institute for Economic Research, Stockholm, and Uppsala University, 1991).
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The author is Professor of International Economics at the Institute for International Economic Studies, Stockholm University. He thanks Bernard Dumas, Robert Flood, Lazaros Molho, William Perraudin, Paul Söderlind and, in particular, Andrew Rose for discussions and comments. Andrew Rose has also generously provided the data. The research for this paper was initiated while the author was a visiting scholar at the Research Department of the International Monetary Fund; he thanks the Research Department for its hospitality.
For alternative empirical approaches to target zone credibility see for instance Bartolini and Bodnar (1991), Bertola and Caballero (1990), Bodnar (1991), Collins (1986), Edin and Vredin (1991), Fratianni and von Hagen (1990), Giovannini (1990), Svensson (1991) and Weber (1991).
Frankel and Phillips (1991) have independently applied the Bertola-Svensson (1990) and Rose-Svensson (1991) methodology to evaluate the credibility of EMS exchange rates. They examine the period 1987-1991 and use a survey of exchange rate forecasts rather than interest rate differentials to measure exchange rate expectations.
See for instance Ungerer, Hauvonen, Lopez- Claros and Mayer (1990) for details on the operation of the ERM.
We use the approximation ln(1 + i1τ)≈i1r, etc.
Svensson (1990) shows that the foreign exchange risk premium for an imperfectly credible exchange rate band with devaluation risk has two components: one arising from exchange rate uncertainty due to exchange rate movements within the band, and the other arising from exchange rate uncertainty due to realignments of the band. The first component is likely to be very small, since conditional exchange rate variability inside the band is smaller than conditional exchange rate variability in a free float, and since foreign exchange risk premia even in a free float appear in empirical estimates to be fairly small. The second component is likely to be much larger than the first, but still of moderate size: Even with a coefficient of relative risk aversion of 8 and an expected conditional devaluation size of 10 percent, the foreign exchange risk premium is no more than 1/5 of the total interest rate differential. Hence at least 4/5 of the interest rate differential remains to be explained by something else than the foreign exchange risk premium.
We disregard the possibility of more than one realignment occurring during the period from time t to t+τ. This is not restrictive since in this paper we will only consider the short period and maturity of one month. For longer maturities the possibility of two or more realignments should be taken into account (see Lindberg, Svensson and Söderlind (1991)).
In the literature on stochastic processes the variable
This is true also when proper account is taken of the possibility that several realignments can occur within long maturities.
Data and programs are available from the author upon receipt of a formatted 3. 5-inch high -density diskette.
The different cases examined include as explanatory variables the exchange rate within the band, its square and its cube; lagged exchange rates within the band; other ERM cross exchange rates; interest rate differentials. Also GARCH regressions, locally weighted regressions, and recursive regressions have been used.
The number of observations is also less than the number of days in Table 1 because some observations are missing.
Inclusion of lags and the square and cube of the exchange rate within the band might reduce standard errors and increase the magnitude of the t-statistics somewhat, increasing the possibility that a unit root is rejected also for the IL/DM exchange rate. Serially correlated error terms because of overlapping data does not invalidate the Dickey-Fuller test as long as the standard errors are consistently estimated (see Phillips (1987)). However, intercepts that are allowed to differ across regimes motivate variants of the Dickey-Fuller test that are likely to have critical values somewhat larger in magnitude than the standard test (see Perron (1989)). The margins to the critical t-value seem large enough that a unit root will still be soundly rejected at a 5 percent significance level, except possibly for the IL/DM exchange rate.
Equations (3.1) and (3.2) have also been estimated without the restriction that the slopes are the same across regimes (the detailed results are not reported here). For FF/DM and NG/DM the hypothesis that the slopes are the same across regimes cannot be rejected, so for those two exchange rates the restriction to identical slopes across regimes is not binding. For the other exchange rates the hypotheses of identical slopes across regimes are rejected. Typically the slopes for some of the short regimes are outliers. In a couple of instances for short regimes the slope in equation (3.2) is above unity (indicating mean dispersion), although not significantly so. As discussed in Rose and Svensson (1991), imposing restrictions across regimes may alleviate small-sample problems arising with short regimes.
The hypothesis that intercepts for each exchange rate are identical across regimes is rejected, and there is no reason not to allow different intercepts for each regime.
As discussed in Rose and Svensson (1991), this small-sample problem can arise when the length of the regime is sufficiently short compared to the expected time for the exchange rate within the band to hit one of the edges of the band when starting at the center. This small-sample problem can hence arise also with a high frequency of data and many observations.
The maximum magnitude of the expected rate of depreciation within the band depends on both the maturity and the width of the band. For the standard EMS exchange rate band of ±2.25 percent the maximum magnitude of the rate of depreciation within one year is 4.5 percent per year if the exchange rate is expected to drift from one edge to the other in one year, and 2.25 percent per year if the exchange rate is expected to drift to the middle of the band. For the wide EMS bands of ±6 percent, the corresponding maximum magnitudes are 12 and 6 percent per year, respectively. Clearly, the expected rate of depreciation within the band within one year can be seizable, and the safe way is of course to estimate the expected rate of depreciation rather than to assume that it is negligible.