After having stabilized their inflation rates from the three-digit level to a moderate range of between 10 and 30 percent, Mexico and Israel adopted target zones as their exchange rate regime and continued using the exchange rate as the nominal anchor for the economy. This decision came after using fixed or crawling exchange rates for a period of time.
Given the lack of credibility of the exchange rate announcements, the wide swings in expectations of a realignment, and the high degree of capital mobility these countries experienced, a fixed exchange rate made domestic interest rates extremely volatile. The experience with fixed exchange rates led these countries to switch to a target zone on the grounds that such a regime would enable the country to keep some of the benefits of the exchange rate as a nominal anchor and at the same time provide a degree of flexibility to cope with highly variable capital movements.1 An exchange rate band allows for some degree of adjustment of the nominal exchange rate in response to shocks without breaking long-run policy commitments. In contrast to the situation with a fixed exchange rate, the variability of the domestic interest rate will be reduced because exchange rate fluctuations inside the band will help to absorb shocks that are speculative in nature.
After adopting the target zone, Israel changed the width of its band a few times and Mexico continuously widened its target zone. This brings us to the question of what the conditions are under which a target zone reduces the variance of the interest rate differential compared to what would be observed under a fixed exchange rate.
The first part of the paper develops a simple model of a target zone with stochastic realignments and in this framework examines the conditions under which interest rate variability will be reduced. We show that, when the variance of the expected realignment is greater than a linear function of the variance of the fundamentals, the target zone will be useful in reducing the volatility of the interest rate differential.
The second part of the paper looks at the Mexican and Israeli experiences with a target zone. We present evidence supporting the claim that the currency band is a good instrument to reduce the volatility of the interest rate differential. To do this, we construct a measure of the expected realignment by subtracting the expected depreciation inside the band from the interest rate differential (as in Svensson (1991)); then we compare the variance of the expected realignment and the variance of the interest rate differential. The results from this exercise show that the target zone is effective in reducing interest rate variability.
The paper is structured as follows. Section I develops a simple model of the exchange rate in a target zone and looks at the variances of the exchange rate and the interest rate differential. Section II reviews the Mexican and Israeli experiences and Section III concludes.
I. The Model
The exchange rate will be determined, following Bertola and Svensson (1991), in a simple log linear monetary model of the exchange rate. The exchange rate at any point in time will be equal to
where f denotes a measure of fundamentals,2x is the exchange rate, and all variables are measured in logarithms. We assume that when a change in the central parity (realignment) takes place the fundamentals also jump by the size of the realignment and the exchange rate inside the band stays in the same place.3 Given this assumption, the expected depreciation will be the sum of the expected depreciation inside the band plus the expected realignment:
where a bar over a variable denotes deviations from the central parity and g is the expected rate of realignment (that is, the product of the probability of a realignment and the size of it). Using equation (2) we can rewrite equation (1) as
Subtracting the mean of the fundamentals from both sides of equation (3), we finally get
where a bar over a variable denotes deviations from the mean or central parities, as appropriate. The exchange rate deviation from central parity will be a function of the combined fundamental h(t):
We assume that the monetary authority controls the combined fundamental, by controlling f, to stay within the boundaries H and-H. The de-valuation expectation will be modeled as a Weiner process; the fundamentals (f) will also be a Weiner process in the absence of intervention.4 When the combined fundamental reaches H or -H, the government will control f, to maintain h between H and -H. Formally,
With these assumptions and applying Ito’s lemma to equation (4), we get a second-order differential equation for the exchange rate inside the band:
The solution for the exchange rate will be given by the following equation (see Krugman (1991)):
We can write the expression for the exchange rate inside the band as
Next we derive the interest differential. Under the assumption of perfect capital mobility and risk neutrality it will be equal to the expected change in the exchange rate:
where i(t) and i*(f) are the domestic and foreign interest rates, respectively. The interest rate differential is thus the sum of the expected realignment plus the expected change in the exchange rate inside the band (the second term on the right-hand side). These two terms will be negatively correlated because, when the expectations of a realignment increases, this leads to a depreciation of the exchange rate inside the band, which itself creates an expected appreciation inside the band. This is due to the usual mean reversion of exchange rates inside a target zone. This second effect increases with the expected realignment because we are closer to the upper part of the band. This effect will also be stronger the higher the instantaneous variance of the expected realignment, because in such a case the probability of stabilizing intervention is higher.
We see that the response of the interest rate differential to a change in the expected realignment will be less than one (the value it has when there is a fixed exchange rate). The value of this response will be
The fact that the interest rate differential is less sensitive to the expectations of a realignment when a band is in place will help reduce the variance of the interest rate differential when a target zone is adopted. On the other hand, the interest rate differential will now be affected by changes in the fundamentals, f (i.e., velocity shocks), that, by affecting the current position of the exchange rate inside the band, generate an expected change in the future position of the exchange rate inside the band. This source of fluctuations in interest rate differentials is not present under a fixed exchange rate. Given that we have these two different forces that affect the variance of the interest rate differential in opposite directions, we would like to know which effect is stronger. We now turn our attention to this problem.
Given that the interest differential is also a Brownian motion, its instantaneous variance will be equal to
Under a fixed exchange rate regime, the variance of the interest rate differential is (σ2g). The next proposition identifies a sufficient condition under which the instantaneous variance of the interest rate differential is reduced when we move from a fixed exchange rate to a target zone.
is a sufficient condition for achieving a reduction in the variance of the interest rate differential when a target zone is adopted instead of a fixed exchange rate.
This equation will be increasing in h and it will be positive at h=H. For some parameter values, equation (17) can be negative when evaluated at h=0. For this reason, equation (15) can achieve its maximum at either h= 0 or h=H. If the maximum is reached at h= 0, then for the variance of the interest rate differential to decrease we need equation (15) evaluated at h+0 to be smaller than the variance of the expected realignment. This requirement gives us
When the maximum is reached at h=H, the condition will give us
Given that when equation (19) holds equation (18) will always hold, then equation (19) is a sufficient condition to achieve a reduction in the interest rate differential variance when a target zone is adopted instead of a fixed exchange rate.
When the condition in equation (19) holds, the introduction of a target zone will increase the volatility of the nominal exchange rate but will reduce the instantaneous volatility of the interest rate differential. To the extent that interest rate hedging is not widespread in the economy and a large proportion of financial transactions are conducted at the nominal interest rate, the existence of a volatile expected realignment will generate volatile ex post real interest rates. This will create an undesirable redistribution of wealth and has the potential to generate a financial crisis. This is why, in our view, the target zone is a useful instrument to partially shift the volatility away from the interest rate differential toward the nominal exchange rate. The arguments made in this section apply to the conditional volatility, but, under some assumptions that make the expected realignment stationary, similar results can be obtained for the case of the asymptotic volatility of the interest rate differential.
Finally, a caveat is in order: we have assumed throughout the paper that the process driving the expected realignment is invariant to the choice of the exchange rate regime (i.e., a band or a target zone). If opting for a fixed exchange rate increases the credibility of the monetary authorities, it is plausible to assume that the volatility of the expected realignment will be lower under a fixed exhange rate than under a target zone. If this is the case, the condition that would make a target zone a better option than a fixed exchange rate will be stronger than condition (19).
II. The Mexican and Israeli Experiences with a Target Zone
An Overview of the Mexican and Israeli Experiences
By the end of 1987 inflation in Mexico had reached 150 percent a year. The authorities then implemented a comprehensive stabilization plan. The important fiscal adjustment was supported by price controls and a fixed exchange rate. After a year with a fixed exchange rate the authorities decided to implement a crawling peg regime. This was done mainly to reduce the rate of appreciation of the real exchange rate. After changing the rate of crawl several times, the Government finally adopted a target zone in November of 1991. The floor of the band was fixed and the ceiling was devalued by 2 cents a day (equivalent to 2.4 percent a year). In October 1992 the pace of crawl of the band’s ceiling was raised to 4 cents a day (or 4.5 percent a year). By the end of 1993 the width of the band was 9.4 percent. Figure 1 shows the evolution of the Mexican exchange rate and target zone.
The experience in Israel was similar. Following the stabilization plan of 1985 the Israeli new sheqel was fixed with respect to the U.S. dollar. This regime persisted with periodic devaluations and a change to pegging the currency to a basket of currencies. In January 1989 the Government adopted a target zone with a fixed central parity and a 3 percent band around it. The width was increased to 5 percent in March 1990. After five realignments the authorities decided to start a daily devaluation of the central parity at a rate of 9 percent a year. Subsequently, there were two minor realignments and a reduction in the rate of crawl of the central parity. Figure 2 shows the evolution of the exchange rate and the target zone for the Israeli case.
In what follows, we study the behavior of the interest rate differential and show that the target zone was a helpful device to reduce the variance of the interest rate differential.
Target Zones and Expected Realignment
One way to detect if the introduction of the target zone reduced the volatility of the interest rate differential is to recover the expected realignment from data on the interest rate differential. If the exchange rate were fixed, the interest rate differential would be equal to the expected realignment. By comparing the variance of the interest rate differential and the expected realignment we can tell whether or not the existence of the band helped decrease the volatility of the interest rate differential.
In a target zone the interest rate differential adjusted by the preannounced devaluation path of the central parity is equal to the sum of the expected realignment plus the expected change of the exchange rate inside the target zone:5
Figure 1.Mexico: Exchange Rate Target Zone Figure 2.Israel: Exchange Rate Target Zone
where δtz is the interest rate differential, g is the expected realignment, and Ed
Next, we need to estimate the expected change of the exchange rate inside the target zone. Following the literature and using weekly data we regress the observed monthly change in the logarithmic deviation of the exchange rate from the central parity (er(i+4) - ert) on a constant and on the logarithmic deviation of the exchange rate from the central parity (ert).6 For the Israeli case, we also included dummies for the different periods between realignments to account for changes in the credibility across regimes. We used weekly data from November 1991 to June 1993 for Mexico and from January 1989 to December 1993 for Israel. The data come from the Banco de Mexico and the Central Bank of Israel. The results for these regressions are shown in Table 1.
The coefficients for the dummy variables for each different band in the case of Israel are not reported, but they are significant for almost all the regimes.7 We see that in both countries the degree of mean reversion inside the band is very significant.
With these estimates we can derive the expected change of the exchange rate inside the band, and subtracting this from the monthly interest differential adjusted by the announced devaluation of the central parity gives us a measure of the expected realignment (see equation (21)).8
In Figures 3 and 4 we plot the estimated expected realignment and the interest rate differential adjusted by the depreciation of the central parity for Mexico and Israel, respectively. Throughout the period, the expected realignment was fairly high and extremely volatile in both countries, although more so in Mexico. The expected realignment was more volatile than the interest rate, and the movements of the exchange rate inside the target zone were very helpful in isolating the domestic short-term interest rates from shocks to the estimated expected realignment. The exchange rate inside the band was not plotted but it goes up every time the expected realignment increases. This is a bit surprising, given the small size of the target zone; however, when we look at the expected rate of change of the exchange rate inside the target zone for the following month, we realize that it is of the same order of magnitude as the interest rate differential. From Table 1 we see that, if the exchange rate is 3 percent higher than the central parity, then the monthly expected appreciation inside the band is 1.5 percent for Mexico and 1.1 percent for Israel. Given that this expected change of the exchange rate has a negative correlation with the expected realignment, the smoothing effect on interest rates is considerable.
|er(1+4)-ert = c + β0ert|
|1991(week 46)-1993(week 26)||(-1.483)||(-4.635)|
|1989(week l)-1993(week 52)||(-3.207)||(-12.334)|
To confirm that the asymptotic and conditional variance of the expected realignment is higher than the interest rate differential variance, we estimated both variances for both countries.9 We used the sample variance to estimate the asymptotic variance of the interest rate differential and the expected realignment (see Hamilton (1994)). To estimate the conditional variance we estimated the process driving the interest rate differential and the expected realignment as an AR(5) for both countries.10Table 2 presents the estimates for the asymptotic and conditional variance and the F-statistic for each of these variances. We see that in both countries the estimated variance for the interest rate differential is much smaller than the expected realignment estimated variance. This is strong evidence in favor of a target zone over a fixed exchange rate regime, because if a fixed exchange rate regime were in place, the interest rate differential would be equal to the expected realignment. For larger maturities this effect will be less because the expected rate of change of the exchange rate in the band is limited by the size of the band. Then as the maturity of the interest rate differential increases the expected change of the exchange rate inside the band per unit time decreases; for this reason, the negative correlation between the expected realignment and the expected change of the exchange rate inside the band also decreases.
Figure 3.Mexico: Interest Rates and Expected Realignment Figure 4.Israel: Interest Rates and Expected Realignment
|(1) Asymptotic variance Interest differential||3.03E-06||1 3E-05|
|(2) Asymptotic variance Expected realignment||1.27E-05||2.13E-04|
|(3) Conditional variance Interest differential||2.55E-07||1.55E-06|
|(4) Conditional variance Expected realignment||2.68E-06||5.41E-05|
|F-Statistic for difference between (2) and (I)||4.19*||16.17*|
|F-Statistic for difference between (4) and (3)||10.5*||34.87*|
We first studied a model of exchange rate determination under a target zone with stochastic realignments, to find the conditions under which the introduction of the target zone is helpful in reducing the variance of the interest rate differential. The main conclusion from this exercise is that, if the volatility of the expected realignment is sufficiently large, then the target zone will reduce the variance of the interest rate differential.
The second part of the paper looks at the Mexican and Israeli experiences with a target zone. The principal result from the empirical study is that the target zone regime helped to reduce interest rate variability by absorbing part of the shocks to the expected realignment through movements of the exchange rate inside the band. We conclude that the target zone is a useful exchange rate regime to reduce the variance of the interest rate differential.
Bertola, Giuseppe, and LarsSvensson, “Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models,”NBER Working Paper No. 3576 (Cambridge, Massachusetts: National Bureau of Economic Research, January1991); also published in Review of Economic Studies,Vol. 60 (July1993), pp. 689-712.
Caramazza, Francesco, “French-German Interest Rates Differentials and Time Varying Realignment Risk,”Staff Papers, International Monetary Fund, Vol. 40 (September1993), pp. 567-83.
Hamilton, James D., Time Series Analysis (Princeton, New Jersey: Princeton University Press, 1994).
Helpman, Elhanan, and LeonardoLeiderman“Israel’s Exchange Rate Band,”Tel Aviv Foerder Institute for Economic Research Working Paper No. 17-19 ((Tel Aviv: Tel Aviv University, 1992).
Krugman, Paul, “Target Zones and Exchange Rate Dynamics,”Quarterly Journal of Economics,Vol. 106 (August1991), pp. 669-82.
Svensson, Lars, “Target Zones and Interest Rate Variability,”Journal of International Economics,Vol. 31 (August1991), pp. 27-53.
Svensson, Lars, “Assessing Target Zone Credibility: Mean Reversion and Devaluation Expectations in the ERM, 1979-1992,” European Economic Review,Vol. 37 (May1993), pp. 763-93.
Alejandro M. Werner, an Economist in the Western Hemisphere Department, was in the Research Department when this paper was written. He holds a Ph.D. from MIT and was a Visiting Assistant Professor at Yale University. The author would like to acknowledge the comments and suggestions of Ricardo Caballero, Gustavo Canonero, Martina Copelman, Rudiger Dornbusch, Stanley Fischer, Luis Herrera, Leonardo Leiderman, and Peter Wickham. This research was partly supported by a grant from the World Economy Laboratory at MIT.
If we think in terms of a monetary model, f is the sum of the nominal money stock and a velocity shock. Starting with a money demand, m— p= v + y — an and assuming purchasing power parity, we can arrive at equation (1).
The model will not change if we alternatively assume that a realignment implies a jump of fixed size in the exchange rate independent of the position in the band, and that this level of the exchange rate will be the new central parity. Thus, the central parity is adjusted by different amounts depending on the position of the exchange rate inside the band. At the time of a realignment the money supply will be adjusted to achieve this result.
We assume that these two stochastic processes are uncorrelated. Assuming that these two processes are correlated would add an extra term to equation (7), but it would not change any of the qualitative results of the paper.
We ignore the effect that other variables have on the expected realigment. In particular, several studies have documented the significant effect that the position of the exchange rate inside the band has on the expected realigment. (See Caramazza (1993).) Including this assumption in the model would not change the results derived in this paper, but the interested reader is referred to Werner (1995) for the implications of this assumption on target zone models.
Although the previous section’s model did not include a deterministic trend for the devaluation of the central parity, this will not substantively change any of the paper’s results but merely shift them by a constant.
The estimation of the expected change of the exchange rate inside the band is done under the assumption that no realignment takes place. For this reason, in the case of Israel we drop the observations from the months before and after each realignment.
Several specifications were tried with no effect on the results presented here.
The estimation procedure does not incorporate the possibility that the expected future deviations of the exchange rate from the central parity cannot be greater than the width of the band. A logistic transformation that took this into account was tried and the results were similar to those reported here. Another drawback is the lack of offshore interest rates denominated in Mexican pesos and new sheqels.
We rejected the null hypothesis of a unit root at 20 percent for the expected realignment and the interest rate differential for both countries.
Where a lower order process was appropriate we estimated that one instead. These results are available from the author upon request.