## Abstract

The paper models an adjustable peg exchange rate arrangement as a policy rule with an escape clause under which the timing and magnitudes of realignments are the outcomes of policy optimization decisions. Under the assumptions that market participants are rational, risk averse, and fully informed about the incentives of policymakers, the analysis focuses on the implications for relating realignment expectations, the interest differential, and the risk premium to the state variables that enter the policy objective function, for modeling the bias in using forward exchange rates to predict future spot rates, and for characterizing the effectiveness of sterilized intervention.

This paper draws on recent developments in the theory of monetary policy strategies to address three related issues in the literature on exchange rate behavior. An adjustable peg exchange rate arrangement is viewed as a policy rule with an escape clause, and the timing and magnitudes of realignments are described as the outcomes of policy optimization decisions. Thus, the analysis focuses on the implications of simultaneous optimizing behavior by policymakers and private market participants. Under the assumption that market participants are rational and risk averse, the paper explores the implications (1) for relating realignment expectations—and hence the magnitude of the interest rate differential that is required to stabilize the exchange rate—to the state variables that enter the policy objective function; (2) for modeling the bias in using forward exchange rates to predict future spot rates; and (3) for characterizing the effectiveness of sterilized intervention. Since the main objective of the paper is to illustrate that an explicit focus on the policy optimization problem may be constructive in refocusing the analysis of these issues, the conceptual framework is streamlined: in particular, the model of policy optimization is cast in terms of a one-dimensional problem of output stabilization; home-country output is also modeled in one-dimensional terms as a function of its relative price; and in contrast to the target zone literature, the band around the adjustable peg is assumed to have zero width.

The paper is organized as follows. Section I briefly reviews the three issues in the exchange rate literature. Section II develops the conceptual framework and applies it, first, to a case in which the policy authorities are assumed to control only the exchange rate peg, and second, to a case in which they are also free to vary their stock of foreign exchange reserves through sterilized intervention. Section III concludes.

## I. Some Issues in the Exchange Rate Literature

### Realignment Expectations

The analysis of realignment expectations has become an active area of empirically oriented research associated with the growing literature on target zones.^{1} Among other things, this research has sought to verify that the realignments of exchange rates between European currencies in recent years resulted from pressures that had built up from fundamental macroeconomic imbalances.

The empirical techniques used to obtain measures of realignment expectations have generally been based on the assumption of uncovered interest parity.^{2} Proponents of this approach recognize that its validity depends crucially on whether the foreign exchange risk premium can reasonably be neglected, and have made a serious effort to explore whether the uncovered interest parity assumption can be justified. In particular, Svensson (1992a) has 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 is 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 has 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.^{3} 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.”^{4}

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. Although some recent studies of international interest rate differentials have made progress in relating constructed measures of realignment expectations to macroeconomic fundamentals,^{5} the policy optimization approach provides a less ad hoc approach to hypothesis specification.

### 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 hypothesis, and in many cases observed changes in spot rates are negatively correlated with ex ante forward premiums.^{6}

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.^{7} 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.^{8} The latter models are supported by evidence directly verifying the practice of feedback trading,^{9} along with other suggestive evidence.^{10} 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 behavior 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.”^{11} This strong attraction to the rationality hypothesis has focused attention on the possibility that feedback trading represents rational behavior in an environment of incomplete information.^{12}

The escape-clause framework, as employed in this paper to analyze behavior when the assumption of uncovered interest parity is not imposed, suggests a direction for continuing the effort to reconcile the evidence on forward-rate forecast bias with the rational expectations assumption. In particular, 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.^{13}

### 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.^{14} Surveys of the literature a decade later^{15} 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 channel, it may also have an influence on exchange rate expectations (and the perceived variance of the exchange rate) through a signaling channel.^{16}

The discussion of signaling 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 policy authorities’ incentives. Two cases can be distinguished. When market participants lack full information about the authorities’ motives, sterilized intervention may provide new information, signaling that the authorities intend to resist further exchange rate movement, and thereby leading market participants to revise their assessments 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 signaling 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 signaling effect in this context has been characterized as the effect that the authorities can have when they put their money where their mouth is.^{17} 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 is realigned, intervention conveys a signal that the authorities’ incentive to resist 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. To the extent that foreign exchange valuation losses require higher tax rates to meet the government’s budget constraint, other things equal, the relative weight attached to foreign exchange valuation losses can be interpreted in terms of the marginal disutility of taxes. 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. Although the relative weights of foreign exchange valuation losses (higher taxes) and deviations from full employment in the “true social loss function” cannot be regarded as parameters to be manipulated, the weights implicit in the behavior of the policy authorities are rarely, if ever, defined by an explicit social loss function and in that sense may differ from the socially desirable weights. Accordingly, when appropriate, institutional changes that induced the authorities to give greater weight to the costs of foreign exchange valuation losses would make them more reluctant to realign the exchange rate following an increase in their exposure to valuation losses, which in theory would make sterilized intervention more effective in influencing the realignment expectations of rational market participants. Obversely, in the limiting case in which the authorities paid no attention to the prospect of foreign exchange valuation losses, sterilized intervention, in theory, would have no effect on realignment expectations or perceptions of risk.

## II. An Illustrative Model

### 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.^{18} 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 explicitly to 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. The literature already includes a number of studies that follow this approach in exploring the links between realignment expectations and macroeconomic fundamentals. These studies focus on several different issues. Obstfeld (1991) is mainly concerned with the possibility of multiple equilibria and its implications for policy rules with escape clauses. De Kock and Grilli (1993) analyze the choice between three exchange rate regimes (monetary union, free floating, and an adjustable peg) in a multiperiod context with a government budget constraint. Cukierman, Kiguel, and Leiderman (1994) focus to a large extent on the determinants of credibility in the context of private sector uncertainty about the nature of the policymaker. Drazen and Masson (1993) and Masson (1994) explore the relationship between credibility and macroeconomic fundamentals in a multiperiod context with uncertainty about the nature of the policymaker. Obstfeld (1994) and Ozkan and Sutherland (1994) are primarily interested in formulating new models of speculative attacks in which the prospect of running out of reserves does not play a central role in precipitating devaluations. All of these studies, unlike this paper, retain the uncovered interest parity assumption; none of them focuses on the risk premium or addresses the effectiveness of sterilized intervention and its influence on realignment expectations.

In the spirit of recent new perspectives in the discussion of rules versus discretionary strategies for monetary policy,^{19} 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, can 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.”^{20} 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 non-state-contingent rules can be difficult to sustain, and therefore lack credibility, in a world subject to occasional large unanticipated disturbances; second, the fact that fully state-contingent rules are not possible when knowledge about the structure of the economy and the nature of disturbances is incomplete; and third, the fact that partially state-contingent rules and discretion cannot be unambiguously ranked.^{21}

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.^{22} 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, which 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, the interest rate differential required to stabilize the exchange rate, and the risk premium. The analysis then 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 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.

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 *t*; *2a*α reflects the weight that society places on avoiding foreign exchange valuation losses relative to the objective of stabilizing output;^{23} 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^{24}

where u_{t +1} is a serially uncorrelated disturbance.^{25} In this particularly simple case, home-country output changes only in response to changes in its relative price and random shocks. It would be interesting to extend the model by adding a direct link between home-currency output and the home (real) interest rate, which is determined endogenously, but such an extension is beyond the scope of this paper.^{26}

The first component of the loss function—the squared deviation of output from its full employment level—has a long tradition.^{27} The fact that an inflation objective is not included in the loss function may limit the relevance of the example in some contexts. ^{28}

The second term in the loss function focuses on the one-period valuation gain on holdings of foreign exchange reserves, ^{29}

The third component of the loss function—which amounts to a fixed cost that is incurred whenever the escape clause is exercised—is intended to capture the social costs of exercising discretion in the context of time consistency problems.^{30} 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,^{31} the model of real output determination introduces a temptation to override the announced exchange rate peg. This temptation is mitigated by the 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 discretion inappropriately.

### 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, the stock of foreign exchange reserves

*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*. 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

_{t+1}*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.^{32} 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.^{33} 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}.

As additional notation, let *W* describe the portfolio wealth of home-country residents and *B* and *B ^{*}* their holdings of home and foreign bonds, 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 _{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 *U _{1}* > 0 and

*U*< 0 are the first derivatives of

_{2}*U*with respect to its two arguments and θ =

*–2U*/U

_{2}_{1}> 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 *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

*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 *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 *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 distribution, 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.^{34} 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.^{35} 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},^{36}

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 distribution of given 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 _{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 ^{37}

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

*m =*0 and

*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}, it can be seen from condition (19) that *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, the interest rate differential required to stabilize the exchange rate, 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 with the magnitude of the risk premium.^{38} 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, the magnitude of realignment expectations, and the perceived risk of realignment. Indeed, by keeping *m* = 0, the authorities could maintain a zero ex ante probability of realignment in this particular example, thereby also maintaining the magnitudes of realignment expectations and the risk premium at zero. Recourse to sterilized intervention on such a scale would not be optimal, however, since the costs of large deviations from full employment output make it important for the authorities to retain some willingness to realign in response to large shocks.

## III. Concluding Remarks

This paper has argued that, for fixed but adjustable exchange rate arrangements, the analysis of exchange market pressures and interest differentials can usefully be extended by focusing explicitly on the policy optimization problem. In developing a simple illustrative model of exchange market pressures, it follows several other recent papers by characterizing the policy decision as a choice between adhering to a simple rule or exercising an escape clause. It departs from other studies of the relationship between realignment expectations and macroeconomic state variables, however, by relinquishing the assumption of uncovered interest parity and exploring the implications of the policy optimization approach for analyzing the behavior of the risk premium, the sources of forward-rate bias, and the effectiveness of sterilized intervention in influencing exchange rate expectations and the perceived risk of realignment.

The example developed in the paper has emphasized that if market participants are rational, their realignment expectations—and hence the magnitude of the interest rate differential that is required to stabilize the exchange rate—will depend on the fundamental macroeconomic state variables that enter the policy objective function, and quite likely in a nonlinear way. Moreover, the co-movements of realignment expectations and the risk premium may be strongly correlated, thus pointing to a possible bias in the existing methodology for constructing measures of realignment expectations, although not necessarily a bias that is quantitatively large. The example also has emphasized that the relationship between realignment expectations and macroeconomic fundamentals may depend critically on the extent to which the authorities have political independence to conduct sterilized intervention operations, which expose taxpayers to the risk of foreign exchange valuation losses.

The escape-clause framework with policy optimization integrates two lines of thinking about the possible causes of forward-rate prediction bias in a rational-expectations environment. An important perspective in this regard is that the incentives of the policy authorities create a peso problem for market participants: in each period the ex ante probability of a realignment is generally positive, even though realignments occur infrequently; and persistence in the fundamental macroeconomic state variables that influence the realignment decision leads, during intervals of no realignment, to positive serial correlation in realignment expectations and prediction errors. Related to this, when the uncovered interest parity assumption is abandoned, the escape-clause framework provides a model of the risk premium that integrates traditional concepts based on portfolio stocks and wealth variables with insights about the determinants of time variation in the risk of realignment within a peso-problem environment. Such an integrated model may be quite relevant for understanding forward-rate prediction bias in adjustable-peg regimes. It is not clear, however, whether the policy optimization framework can appropriately be extended to provide parallel perspectives on forward-rate bias in floating exchange rate systems.

The policy optimization framework also provides useful perspectives on the effectiveness of sterilized intervention, including the perspective that the effects of intervention on the risk premium and on expectations about future exchange rates are not independent of each other. In analyzing these effects, it is important to specify whether market participants are assumed to have complete information about the incentives of the policy authorities. Under the assumptions of complete information and rational expectations, sterilized intervention cannot signal new information about the authorities’ ultimate policy objectives, but it can signal that the authorities have taken on a larger exposure to foreign exchange valuation losses and, in doing so, can rationally be regarded to have strengthened endogenously their incentives to resist a realignment.

As a corollary to the latter point, the signaling effect of intervention on exchange rate expectations, and the associated effect on the perceived risk of realignment, depend critically on the costs of foreign exchange valuation losses (or higher tax rates, other things equal) relative to the costs of deviations from full employment output, as reflected in the coefficients of the policy objective function. The appropriate interpretation of this theoretical result, however, requires care in distinguishing between the relative welfare costs perceived by society and the relative costs perceived by policymakers. If society—perhaps acting against its own best interests—wanted to make sterilized intervention very effective (whenever conducted) in influencing market assessments of realignment prospects, it could simply design accountability procedures and reward/penalty structures that made it very costly for the authorities to incur valuation losses, thereby making them very reluctant to realign the exchange rate following an increase in their exposure to valuation losses. By the same token, if the authorities perceived that valuation losses had no costs, sterilized intervention would have no effect on realignment expectations in an environment in which market participants had complete information about the authorities’ incentives and formed their expectations rationally.

Alternatively, the policy authorities may be motivated to minimize a loss function that reflects the relative welfare costs actually perceived by society. In this case, the coefficients of the policy objective function are not parameters to be manipulated, but rather reflect the inherent preferences of society. Thus, in the context of a government budget constraint through which valuation losses on foreign exchange reserves translated directly into higher tax rates, the coefficients of the policy objective function could be interpreted in terms of the relative social welfare costs of deviations from full employment and variations in tax rates.

When valuation losses are perceived to be costly and sterilized intervention is effective in influencing market assessments of realignment prospects, the time variation of realignment expectations and the risk premium may depend importantly on the extent to which there are explicit or implicit quantitative constraints on the use of sterilized intervention as a policy instrument. In the unrealistic hypothetical case in which there were no quantitative restrictions on the scale of sterilized intervention, the authorities would have the potential to prevent time variation in the state of the economy from having any effect on realignment expectations or the risk premium.^{39}

The hypothetical case illustrates an important point for empirical research: namely, that success in relating realignment expectations or the risk premium to macroeconomic state variables may depend critically on efforts to take account of institutional considerations governing the use of sterilized intervention. This, unfortunately, poses a difficult challenge. In reality, countries generally do not set explicit quantitative limits ex ante on the scale of sterilized intervention. Experience suggests, however, that beyond some point, the monetary authorities—or the elected officials to whom they are accountable—inevitably find continuing intervention intolerable.^{40}

### APPENDIX Derivation of Condition (23)

Define:

Then using (15) and (17),

So

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^{}*

Peter Isard is an Advisor in the Research Department. He holds degrees from the Massachusetts Institute of Technology and Stanford University. He is particularly grateful to Peter B. Clark and Lars Svensson for helpful comments on an earlier draft.

^{}1

See Svensson (1992b) for perspectives on the target zone literature.

^{}2

For example, Bertola and Svensson (1993) and Lindberg, Söderlind, and Svensson (1993).

^{}3

Svensson (1992a), pp. 35–6. The calculation focuses on exchange rate jumps within the band but is also relevant to realignments anticipated with probability one.

^{}4

Rose and Svensson (1993), p. 34.

^{}5

For example, Caramazza (1993), Halikias (1994), Bartolini (1993), and Thomas (1994).

^{}6

Hansen and Hodrick (1980), Bilson (1981), Hodrick (1987), Meese (1989), Froot and Thaler (1990).

^{}7

Obstfeld (1989) and Isard (1995) provide summary perspectives on several of these possibilities. See also Meese (1986), Borensztein (1987), Lewis (1988, 1989), Froot and Frankel (1989), Edison (1993), Kaminsky (1993), and McCallum (1994).

^{}9

Taylor and Allen (1992), Group of Ten Deputies (1993). Feedback trading means trading motivated by analysis of the recent history of transactions prices, trading volumes, or other technical information about market trading.

^{}11

Krugman (1993), p. 8.

^{}13

See Dooley and Isard (1983) for a traditional model of the risk premium.

^{}16

Mussa (1981) was one of the first to draw attention to the signaling effects of intervention. See Dominguez and Frankel (1993) for a recent relatively favorable assessment of the effectiveness of intervention.

^{}17

Mussa (1981), Obstfeld (1990).

^{}21

Obviously, it is important to establish rules with escape clauses that limit the scope for discretion to be used inappropriately. In general, the effectiveness of rules with escape clauses in balancing credibility and flexibility depends critically on the nature of the institutional mechanisms through which society holds policymakers accountable for exercising discretion excessively or too infrequently.

^{}22

It seems reasonable to conjecture that, if the analysis were extended to a target zone with non-zero width, realignment probabilities and expectations would also depend on the position of the exchange rate within the zone. Cukierman, Kiguel, and Leiderman (1994) provide insights into the case with non-zero bands.

^{}23

There is no loss of generality, and a significant gain in subsequent notational simplicity, from writing this weight as the product of *a* and 2α.

^{}24

The home-currency price of home output and the foreign-currency price of foreign output are fixed and normalized to unity.

^{}25

Given that deviations from full employment output are persistent, it would be desirable to extend the example to the case in which policymakers minimize the expected value of a multi-period loss function. Drazen and Masson (1993) and Masson (1994) consider multi-period frameworks, emphasizing that persistence in the process driving unemployment implies that adhering to a no-realignment pledge in the first period may reduce the credibility of the pledge in subsequent periods.

^{}26

Efforts to extend the model might also consider reducing the unit coefficient on lagged output or making output responsive only to the unexpected component of changes in its relative price. In general, these revisions would complicate the nature of the link between realignment expectations and deviations of output from its full employment level, but such a link—which essentially generates the relationship between realignment expectations and macroeconomic state variables—would be present for all cases in which output deviations were at least partially persistent.

^{}27

Early applications include Gray (1976) and Flood and Marion (1982). Aizenman and Frenkel (1985) derive this component as the optimal specification of the objective function for a world with sticky nominal wages when social welfare depends positively on consumption and negatively on labor. See Aizenman (1994), however, for a recent reconsideration based on an argument that the expected level of full-employment output is sensitive to the nature of the exchange rate regime. Barro and Gordon (1983) and others have added squared changes in the price level to the loss function, while noting the difficulty of justifying such an extension.

^{}28

Presumably, this is not a significant issue for interpreting the pressures that were imposed on exchange rates between European currencies during 1992–93, when many European countries were not very concerned about their inflation prospects in the short run.

^{}29

The literature on speculative attacks, emanating from the pathbreaking paper by Krugman (1979), was inspired by the literature on government price-fixing schemes in markets for exhaustible resources, including the analysis of gold prices by Salant and Henderson (1978); see Agénor, Bhandari, and Flood *(1992)* and Blackburn and Sola (1993) for survey articles. As argued by Obstfeld (1994) and Ozkan and Sutherland (1994), however, it has become difficult to defend the notion that countries with access to world capital markets have an exhaustible supply of foreign exchange reserves.

^{}30

This treatment follows Flood and Isard (1989).

^{}31

See, for example, Barro and Gordon (1983) and Rogoff (1985).

^{}32

See, for example, Svensson (1992a).

^{}33

See, for example, Dornbusch (1983).

^{}34

It is easily shown in this case that ϕ _{t} = 0 and

^{}35

A large positive shock would create the same type of incentive in an extended model in which home-country output was a negative function of the domestic interest rate as well as a negative function of the relative price of home-country output.

^{}38

It can be seen from (17) that the magnitude of realignment expectations is a monotonically decreasing function of *y*_{t} (given *X*_{t}*)* in case 3, independently of the parameters *c* and *U*. By contrast, the nature of the relationship between realignment risk and the state of the economy depends on the relative magnitudes of these parameters. Computer solutions of (23) show, for example, that the magnitude of realignment risk is a (near)-monotonically increasing function of y, for *c* ≤ *U*, whereas a plot of *y*_{t} has an approximately inverted-U shape for *c = 10U*.

^{}39

As noted above, however, full use of that potential would leave the authorities unwilling to realign in response to large shocks to the economy, which would not be optimal.

^{}40

For example, the events of September 1992 revealed that even the “unlimited” facilities for providing short-term credit to support intervention within the European Monetary System were curtailed when the scale of intervention was perceived to be a threat to price stability in Germany; see Eichengreen and Wyplosz (1993), pp. 109–13.