1. Realignment expectations

The analysis of realignment expectations has become an active area of empirically-oriented research associated with the growing literature on target zones. ^2/ Among other things, this research has sought to verify that the realignments of exchange rates between European currencies in recent years were not the result of random self-fulfilling speculative attacks, but were rather a result of pressures that had built up from fundamental macroeconomic imbalances. ^3/

The empirical techniques used to obtain measures of realignment expectations have generally been based on the assumption of uncovered interest parity. ^4/ Proponents of this approach recognize that “it is crucial whether the foreign exchange risk premium can be neglected or not,” and have made a serious effort to explore whether the uncovered interest parity assumption can be justified. In particular, Svensson (1992a) extended the analysis of real and nominal risk premiums to the target zone framework and derived generous upper bounds on their empirical magnitudes, suggesting that they were “relatively small.” Notably, this result was based on the assumption that the probability distribution of realignments is time invariant and not state contingent—in particular, not contingent on the state variables that tend to generate political pressures for realignments. To provide an alternative perspective, Svensson also calculated the real risk premium associated with a depreciation that is anticipated with probability one, suggesting that even when a realignment is expected with certainty the size of the risk premium is only about one-eighth the size of the expected realignment. ^5/ The literature has thus continued to rely on the uncovered interest parity assumption on the grounds that the empirical results are not significantly affected by a small time-varying risk premium “unless its movements coincide with changing realignment expectations for some mysterious reason.” ^6/

As illustrated below, the analysis of realignment expectations in the context of a policy optimization problem establishes a strong and unmysterious possibility that the co-movements of realignment expectations and the risk premium are indeed highly correlated. This points to the possibility of bias in the existing methodology for constructing measures of realignment expectations, although it does not necessarily imply that the bias has been quantitatively large. The explicit focus on a policy optimization problem also provides an appealing conceptual framework for specifying a testable hypothesis about the nature of the relationship between realignment expectations and fundamental macroeconomic variables. ^7/ In doing so, moreover, it reconciles the view that macroeconomic fundamentals are relevant to realignment decisions and expectations with the finding that constructed measures of realignment expectations for European exchange rates did not begin to widen before the summer of 1992, ^8/ despite the fact that the macroeconomic conditions then prevailing had existed for some time.

2. Forward rate bias

One of the most widely tested propositions about exchange rate behavior is the hypothesis that forward premiums are unbiased predictors of changes in spot exchange rates. The empirical evidence strongly rejects this unbiasedness hypothesis, indicating as well that in many cases observed changes in spot rates are negatively correlated with ex ante forward premiums. ^9/

Efforts to reconcile the evidence of forward rate bias with the hypothesis that market participants form rational expectations have focused on the possible importance of risk premiums, peso problems, rational bubbles, simultaneity bias, and incomplete information with rational learning. ^10/ To date, however, the analysis of these possibilities has not provided a convincing explanation of the observed bias in forward rates, and models of a less than fully rational world with feedback trading have begun to emerge. ^11/ The latter models are supported by evidence directly verifying the practice of feedback trading, ^12/ along with other suggestive evidence. ^13/ Even so, it is difficult for economists to constrain their theories about exchange rates unless they retain the hypothesis that some market participants form rational expectations based on future fundamentals. “If one does not assume rationality…. the behaviour of the exchange market is as much imposed by the theorist as anything else: the magician essentially pulls out of the hat the same rabbit the audience has seen him stuff in a few minutes earlier.” ^14/ This strong attraction to the rationality hypothesis has focussed attention on the possibility that feedback trading represents rational behavior in an environment of incomplete information. ^15/

The escape-clause framework employed in this paper and elsewhere ^16/ suggests a direction for continuing the effort to reconcile the evidence on forward rate forecast bias with the rational expectations assumption. In particular, when the assumption of uncovered interest parity is abandoned, it provides a model of the premium for bearing the risk of a policy decision to adjust the exchange rate peg, which is the type of event on which the peso-problem literature has focused. Thus, the escape-clause framework integrates two of the proposed explanations of forward rate bias that are consistent with rational expectations, emphasizing that risk premiums vary over time with the state variables on which policymakers focus in deciding whether to realign, as well as with the relative asset stock and wealth variables that enter traditional portfolio balance models. ^17/

3. The effectiveness of sterilized intervention

In the early 1980s, a comprehensive study, of exchange market intervention, drawing on a variety of careful research efforts, reached the conclusion that sterilized intervention, unless supported by other policies, has at most a small and short-term effect on exchange rates. ^18/ Surveys of the literature a decade later ^19/ suggest that this conclusion stands largely unchanged, although the analytic framework for assessing the effectiveness of intervention has evolved. In particular, it is now postulated that, in addition to whatever effect sterilized intervention may have through the portfolio-balance or risk-premium channel, it may also have an influence on exchange rate expectations through a signalling channel. ^20/

The discussion of signalling effects has suffered to some extent from the failure of many discussants to focus explicitly on how much market participants are assumed to know about the incentives of the policy authorities. Two cases can be distinguished. When market participants lack full information about the motives of the authorities, sterilized intervention may provide new information, signalling that the authorities intend to resist further exchange rate movement, and thereby leading market participants to revise their assessment of the conditional probability that the authorities will take action stronger than sterilized intervention if the exchange rate movement continues. By contrast, when market participants already have full information about the motives of the authorities and form rational expectations, the signalling effect cannot arise from clarifying the nature of the authorities’ ultimate policy objectives, but rather depends on whether sterilized intervention influences the authorities’ incentives to hold the exchange rate fixed in pursuit of their ultimate objectives. The signalling effect in this context has been characterized as the effect that the authorities can have when they put their money where their mouth is. ^21/ By changing official foreign exchange holdings in a direction that exposes the authorities to the prospect of a greater valuation loss if the exchange rate continues to move, intervention conveys a signal that the authorities’ incentive to resist further exchange rate movement has strengthened endogenously.

The latter effect is illustrated explicitly in the model developed below, which also suggests that the effect of sterilized intervention on the risk premium may be strongly correlated with its effect on exchange rate expectations. Within the context of an adjustable peg regime, sterilized intervention endogenously changes the ex ante probability that the authorities will choose to realign the peg following the realization of a future shock. It is shown, moreover, that the extent to which intervention affects ex ante assessments of realignment prospects depends both on the relative weight attached to foreign exchange valuation losses in the policy objective function and on the state of the macroeconomic variables that enter the objective function. An interesting insight from the policy optimization framework is that the effectiveness of sterilized intervention is directly proportionate to the “costs” that the authorities perceive when their policies lead to foreign exchange valuation losses. Institutional changes that induce the authorities to give greater weight to these costs can make them more reluctant to realign the exchange rate following an increase in their exposure to valuation losses, which in theory can make sterilized intervention more effective in influencing the realignment expectations of rational market participants. Obversely, in the limiting case in which the authorities pay no attention to the prospect of foreign exchange valuation losses, sterilized intervention has no effect on expectations or perceptions of risk and only a minor portfolio-balance effect on the risk premium.

1. Key assumptions and perspectives

The defining characteristic that distinguishes an adjustable peg system from a floating exchange rate regime is the explicit announcement of the policy authorities’ intention to prevent the exchange rate from moving outside a target zone. This announced policy intention, along with the orientation of monetary policy toward stabilizing the exchange rate, provides an anchor for exchange rate expectations—particularly in the short run—that is not present in a floating exchange rate system. Of course, the credibility of announced policy intentions is not always high, and exchange rate pegs are sometimes adjusted. But there is abundant empirical evidence that the variability of nominal exchange rates is substantially lower under adjustable peg regimes than under floating rate systems. ^22/ This obviously suggests that the authorities are motivated to behave differently—and are expected to behave differently—under adjustable peg regimes than under floating rate systems.

An important new direction for exchange rate analysis is to explicitly incorporate the optimization problem of the policy authorities into the set of information that is assumed to be known by market participants when they form their exchange rate expectations. ^23/ In the spirit of recent new perspectives in the discussion of rules versus discretionary strategies for monetary policy, ^24/ the choice of an adjustable exchange rate peg, like any other simple rule for monetary policy that tends to be overridden or modified in extreme circumstances, should be regarded as a strategy for balancing the credibility that can be gained from committing to a rule with the flexibility that is desirable when macroeconomic developments make the social costs of continuing to adhere to the rule very high. Such strategies have become known as “rules with escape clauses.” ^25/ As a proposition in positive economics, the prevalence of simple rules with implicit or explicit escape clauses—such as money supply growth targets and exchange rate pegs—reflects first, the fact that fully state-contingent rules are not a relevant possibility for monetary policy when knowledge about the structure of the economy and the nature of disturbances is incomplete, and second, the fact that partially state-contingent rules and discretion cannot be unambiguously ranked.

This section develops a simple model of the actual and expected behavior of the exchange rate in a two-country adjustable-peg system in which exchange rate policy is determined by the home country. The model focuses explicitly on the policy optimization problem, abandons the uncovered interest parity assumption, and ignores the band around the central parity. The latter assumption simplifies the task of illustrating how the probability of realignment and the magnitudes of realignment expectations and the risk premium depend on the state variables that enter the policymaker’s loss function. ^26/ The model also formalizes the effects of sterilized intervention in lowering the magnitudes of realignment probabilities and expectations, while emphasizing that, for intervention beyond a certain scale, the “direct benefits” of these effects are outweighed by the “indirect costs” of the greater prospects for overheating or overcooling the economy, given the lower probability that the authorities will choose to realign.

The analysis focuses on the optimizing behavior of the policy authority in the home country, who has two instruments—the logarithm of the exchange rate, s, and the level of foreign exchange reserves, X. The home-country interest rate adjusts endogenously to clear markets, given the settings of s and X. Attention concentrates first on the case in which the level of foreign exchange reserves is exogenously given, emphasizing that variation over time in the state of the economy generates time variation in realignment expectations and the risk premium. It next shifts to the opposite extreme—the case in which the authorities have the ability to vary their foreign exchange reserves without limit through sterilized intervention—emphasizing that optimal policy will then largely mitigate the extent to which time variation in the state of the economy generates time variation in realignment expectations and the risk premium.

To keep the model simple, it is assumed that each country produces a single good. The home-currency price of the home-country good, and the foreign-currency price of the foreign-country good, are assumed to be fixed and normalized to one. The relevant asset portfolios of private market participants are allocated between home-currency-denominated interest-bearing net claims on the home-country government and foreign-currency-denominated interest-bearing net claims on the foreign government. In the tradition of much of the portfolio balance literature, the analysis abstracts completely from the intertemporal budget constraints of the two governments. ^27/

The policy objective of the home-country authorities at time t is to minimize the expected value of a loss function with three components

where: y_t+1 is the deviation of the logarithm of output from its full employment level; s is the logarithm of the exchange rate in home currency per unit foreign exchange; r_t and ${\mathrm{r}}_{\mathrm{t}}^{*}$ are the one-period home and foreign currency interest rates at time t; ${\mathrm{s}}_{\mathrm{t}+1}-{\mathrm{s}}_{\mathrm{t}}+{\mathrm{r}}_{\mathrm{t}}^{*}-{\mathrm{r}}_{\mathrm{t}}$ represents the return on holdings of foreign securities relative to that on holdings of domestic securities; α is the elasticity of home-country output with respect to its relative price, as defined in condition (3) below; a is a parameter of the loss function, where 2aα reflects the weight that society places on avoiding foreign exchange valuation losses relative to the objective of stabilizing output ^28/; and c_t+1 is a fixed cost associated with realignment.

Deviations of home-country output from its full employment level are assumed to be persistent, but to respond positively to a decline in the relative price of home-country output, here equivalent to a depreciation of the home currency ^29/

where u_t+1 is a serially uncorrelated disturbance. ^30/ In this particularly simple case, home-country output changes only in response to changes in its relative price and random shocks. ^31/

The first component of the loss function—the squared deviation of output from its full employment level—has a long tradition. ^32/ The fact that an inflation objective is not included in the loss function may limit the relevance of the example in some contexts, but presumably not for interpreting the pressures that have been imposed on exchange rates between European currencies during the past two years, when many European countries were not concerned about their inflation prospects in the short run.

The second term in the loss function focuses on the one-period valuation gain on holdings of foreign exchange reserves, $\left({\mathrm{s}}_{\mathrm{t}+1}-{\mathrm{s}}_{\mathrm{t}}+{\mathrm{r}}_{\mathrm{t}}^{*}-{\mathrm{r}}_{\mathrm{t}}\right){\mathrm{X}}_{\mathrm{t}}$. The larger the volume of reserves accumulated (spent) to resist appreciation (depreciation), the greater will be the valuation losses associated with a subsequent decision to revalue upward (devalue) the home currency. This component of the loss function isolates a well-defined component of the costs of adjusting an exchange rate peg and plays a central role in making sterilized intervention effective in influencing exchange rate expectations and the risk premium in a rational expectations environment. Here it is implicitly assumed that the home country authorities could issue unlimited amounts of foreign-currency-denominated debt if they desired to do so, and thus—in contrast to much of the literature on speculative attacks ^33/—that the prospect of running out of reserves is not a central factor in precipitating devaluations. ^34/

The third component of the loss function is intended to capture the social costs of exercising discretion in the context of time consistency problems. ^35/ Although the present example, by not including inflation in the policy loss function, departs from the traditional way of illustrating the time consistency problem for monetary policy, ^36/ the model of real output determination introduces a temptation to override the announced exchange rate peg. This temptation is mitigated by the third component of the loss function—characterized as a fixed cost of exercising the escape clause—which can be viewed from the perspectives of both positive and normative economics. From a positive perspective, unless one assumes that the policy authorities perceive it to be costly to override announced policy rules, it is difficult to explain why exchange rates exhibit much lower short-term variability under fixed rate regimes than under floating rate regimes. And from both normative and positive perspectives, society can and does design institutional mechanisms—involving both accountability procedures and reward/penalty structures—for insuring that individual policy authorities do not exercise excessive discretion.

2. Optimal behavior and market-clearing conditions

The description of optimal behavior and market clearing conditions reflects the following sequence of actions and events, starting just after the determination of s_t and continuing through the determination of s_t+1. First, X_t is set (at an exogenous level in the first instance and an optimal level in a second case) and the private sector forms its expectations and chooses its asset portfolio, given information about X_t and the ex ante probability distribution of u_t+1. These actions generate the market clearing levels of the unobserved risk premium and the observed home-currency interest rate, given the fixed foreign-currency interest rate. Second, the realization of u_t+1 occurs. Third, the authorities set s_t+1 at the level that minimizes the policy loss L_t+1, conditional on u_t+1.

The private sector’s portfolio choice problem involves allocating wealth between claims on the home government bearing the home-currency interest rate, and claims on the foreign government bearing the foreign-currency interest rate. The literature reflects several approaches to modeling this problem. One approach assumes that residents of the two countries have identical consumption preferences, often specified as Cobb Douglas functions of the amounts of each of the two goods consumed. ^37/ Another approach assumes that home-country (foreign-country) residents have relatively strong preferences for the home (foreign) good, sometimes specifying each group’s utility as a function of the mean and variance of its consumption. ^38/ In addition to requiring a decision on how to represent consumer preferences, model specification requires a choice between ignoring non-portfolio income or specifying a model of the income earned from goods production.

With regard to these various modeling choices, the approach taken in this paper ignores non-portfolio income, assumes that residents of the two countries hold portfolios of both assets but have different consumption preferences, with each group consuming only the good produced in its own country, and postulates a mean-variance utility function, such that market clearing conditions depend in a simple approximate way on the perceived mean and variance of the one-period-ahead exchange rate. The objective of home-country (foreign-country) residents at time t is to maximize a function of the mean and variance of their one-period-ahead normalized wealth as valued in the home (foreign) currency after the realization of s_t+1.

It is convenient to let W describe the portfolio wealth of home country residents and B and B* their holdings of home and foreign bonds, with ${\tilde{\mathrm{W}}}^{*}$, $\tilde{\mathrm{B}}$, and ${\tilde{\mathrm{B}}}^{*}$ describing analogously the aggregate portfolio of foreign residents. Variables superscripted (not superscripted) with * are measured in foreign-currency (home-currency) units. Accordingly, for home-country residents at time t, the levels of initial wealth and one-period-ahead wealth can be expressed as

where S denotes the level (and s the logarithm) of the exchange rate. To simplify the notation, let

where E_t and Var_t denote expected values and variances perceived at time t. Note that if the covered interest parity condition is approximately valid, conditions (6) and (7) can be re-expressed as

where ${\mathrm{f}}_{\mathrm{t}}={\mathrm{s}}_{\mathrm{t}}+{\mathrm{r}}_{\mathrm{t}}-{\mathrm{r}}_{\mathrm{t}}^{*}$ is the logarithm of the forward exchange rate. The term, γ_t+1, represents the ex post measure of the forward rate forecast error. The risk premium, ϕ_t, can be viewed as the expected excess yield on home-country securities that is required ex ante to compensate market participants for the risk of realignment. It also measures the forward-rate forecast bias, or more precisely, the expected value ex ante of the forward rate forecast error.

Assume that the utility function to be maximized is

Note that the arguments of U can be expressed as

Thus, for home-country residents the optimal choice of the portfolio share b_t must satisfy the first order condition

where U₁>0 and U₂<0 are the first derivatives of U with respect to its two arguments and θ=-2U₂/U₁>0 reflects the degree of risk aversion.

The portfolio choice problem for foreign-country residents can be specified and solved analogously. The analogs of (5), (9), (11), (12), and (13) are

Accordingly, the market clearing condition for claims on the foreign public sector can be written as

where ${\overline{\mathrm{B}}}^{*}$ is the stock of such claims that would be pushed into private portfolios in the absence of any official holdings of foreign exchange reserves by the home-country authorities and ${\overline{\mathrm{W}}}_{\mathrm{t}}^{*}=\left({\mathrm{W}}_{\mathrm{t}}/{\mathrm{S}}_{\mathrm{t}}\right)+{\tilde{\mathrm{W}}}_{\mathrm{t}}^{*}$ is the initial level of aggregate private wealth valued in foreign currency. Note that the stock of non-interest-bearing monetary assets does not enter the analysis explicitly and thus is implicitly assumed to remain constant in this example; hence, all official intervention is sterilized. The analysis concentrates on the case in which market participants have full knowledge of X_t at time t; intervention operations are not kept secret.

The next steps in solving the model are to derive the expected exchange rate and the market clearing domestic interest rate and risk premium that would emerge at any level of X_t. Note that, whenever it is optimal to change the exchange rate peg, the optimal value at which to set the new peg, ${\mathrm{s}}_{\mathrm{t}+1}^0$—after observing the realization of u_t+1—is determined by the first-order condition ∂L_t+1/∂s_t+1 = 0; in particular, from (1) and (3)

whether or not a realignment to ${\mathrm{s}}_{\mathrm{t}+1}^0$ dominates a decision to maintain the peg at s_t depends on whether ${\mathrm{L}}_{\mathrm{t}+1}\left({\mathrm{s}}_{\mathrm{t}+1}^0\right)<{\mathrm{L}}_{\mathrm{t}+1}\left({\mathrm{s}}_{\mathrm{t}}\right)$. From (1) and (3) it is straightforward to demonstrate that maintaining the peg at s_t is optimal if and only if -c ≤ y_t-aX_t+u_t+1 ≤ c. This condition provides the basis for characterizing the market clearing conditions that would emerge under rational expectations prior to the realization of u_t+1, given information about y_t, X_t, a, c, and the ex ante probability distribution of u_t+1.

To illustrate, consider a relatively simple example in which u_t+1 is uniformly distributed on the interval [-U,U]. For this example, the set of possible combinations of initial conditions (in period t) and parameter values gives rise to four cases:

In case 1 there is no incentive to realign under any feasible realization of the shock. ^39/ In case 4 there are incentives to depreciate the domestic currency under large positive realizations of u_t+1 and to appreciate under large negative realizations. In cases 2 and 3 the incentives to realign are one-sided.

Consider case 3, in which a sufficiently large positive shock would overheat the home-country economy and provide an incentive to appreciate the home currency. ^40/ In such a setting, market participants—with an understanding of this incentive and knowledge of the ex ante probability distribution of the shock—will rationally form expectations about s_t+1 such that, from (15) and (16), using the notation z = y_t−aX_t+u_t+1 ^41/

Similarly, the probability of realignment can be expressed as

where

Note that (17) gives a nonlinear (in this case, quadratic) expression for the magnitude of the expected realignment as a function of y_t+U, which can be seen from (3) to represent the maximum degree to which the economy could be left overheated (i.e., the upper bound on y_t+1) in the absence of realignment. The level of X_t does not affect the conditional probability of y_t+1 in the event of no realignment, but (when a>0) it does affect the authorities’ incentives to realign and thereby influences the ex ante assessments of realignment probabilities and expectations by rational market participants.

From (6), (7) and (17), the risk premium—or equivalently, the expected error in using the forward rate as a predictor of the future spot rate—can be expressed as

whereas (14) implies

Thus,

In general, as can be seen from (21), the sign of the risk premium depends on the sign of $\left({\overline{\mathrm{B}}}_{\mathrm{t}}^{*}-{\mathrm{X}}_{\mathrm{t}}-{\tilde{\mathrm{W}}}_{\mathrm{t}}^{*}\right)$. If the foreign country is an international creditor and the home country has positive net holdings of foreign exchange reserves, ${\overline{\mathrm{B}}}_{\mathrm{t}}^{*}-{\mathrm{X}}_{\mathrm{t}}-{\tilde{\mathrm{W}}}_{\mathrm{t}}^{*}<0$ and ϕ_t>0.

Condition (21) indicates that time variation in the risk premium has two main sources: variation in portfolio stock variables and time variation in ${\mathrm{\sigma }}_{\mathrm{t}}^2$, which in this particular example has the nonlinear form ^42/

For case 3, as defined in condition (16), m ranges from 0 when y_t and X_t are such that y_t-aX_t+U=c, to 2U at y_t-aX_t-U=c; and it is easily seen from (23) that ${\mathrm{\sigma }}_{\mathrm{t}}^2=0$ at m=0 and ${\mathrm{\sigma }}_{\mathrm{t}}^2={\mathrm{U}}^2/3{\mathrm{\alpha }}^2$ at m=2U. As can also be seen from (18), the ex ante probability of realignment increases monotonically from 0 to 1 as m increases from 0 to 2U.

These results require careful interpretation. If, as one extreme case, the authorities had no freedom to vary X_t, m would vary directly with y_t (given the parameter c and the probability distribution of the shock), and variation over time in the state of the economy would lead to time variation in the probability of realignment and the magnitudes of realignment expectations and the risk premium. There is a clear possibility, moreover, that the magnitude of realignment expectations would be strongly correlated with the perceived risk of realignment and hence the magnitude of the risk premium. ^43/ At the other extreme, as evident from conditions (17)-(19) and (23), with complete freedom to vary X_t through sterilized intervention, the authorities—if they chose to do so—could prevent time variation in the state of the economy (y_t) from generating time variation in the ex ante probability of realignment and the magnitude of realignment expectations, while largely mitigating the time variation in the risk premium. ^44/

The analysis now shifts to the case in which X_t is a policy choice variable. Before solving for the optimal level of foreign exchange reserves, consider the effects of sterilized intervention on the probability and expected magnitude of realignment. By differentiation of (17) and (18)

Thus, since y_t-aX_t+U is unambiguously positive in case 3, sterilized intervention purchases of foreign exchange (sales of home-currency securities) unambiguously reduce the expected magnitude and probability of an appreciation of the home currency when a>0, but have no effect on either unless the policy objective function attaches non-zero costs to foreign exchange valuation losses. Sterilized intervention is effective in influencing exchange rate expectations and the perceived risk of realignment if and only if a≠0, and the effectiveness of intervention on the expected magnitude and probability of appreciation is directly proportionate to a.

The next step is to derive the level of X_t that the policy authorities regard as optimal ex ante, before observing the realization of u_t+1. This requires solving the first-order condition ∂(E_tL_t+1)/∂X_t = 0 which, from (1), requires

Using (2), (3), (15), (18), and (19), it is straightforward to establish that

Substituting these expressions into (26), and simplifying, implies that the optimal stock of foreign exchange reserves must satisfy

where η = (X_t/ϕ_t)∂ϕ_t/∂X_t and

Note that H corresponds to the sum of the expressions in (27) and (28), divided by the positive parameter a. Thus, H>0 corresponds to a situation in which an increase in X_t reduces the expected loss associated with the fixed costs of realignment by less than it increases the expected loss associated with the possibility of an overheated economy, given that it reduces the probability of a realignment to cool the economy. Note also, from (19), that at m=2U, X_t=(y_t-U-c)/a and H=-c; while at m=0, X_t=(y_t+U-c)/a and H=c. Accordingly, for cases in which the term 2αϕ_t(1+η) in (29), and hence H, is smaller than c in absolute value, the optimal level of X_t must be such that 0<m<2U. Such cases provide an example in which it is optimal for the authorities not to accumulate so large a quantity of foreign exchange reserves that they would be conditionally motivated to refrain from adjusting the exchange rate peg under even the largest possible realization of the shock (that is, not to increase X_t to the point at which m=0). Rather, under the welfare parameters embodied in the policy objective function, the costs associated with an overheated economy make it important for the authorities to retain some willingness to exercise the escape clause (that is, to adjust the exchange rate peg) in response to large realizations of the shock.