حدس و گمان برای تصمیم رها کردن یک رژیم نرخ ارز ثابت

This paper demonstrates that the implications of first-generation speculative attack models do not hold if there is a rational, forward-looking policy maker. The policy maker will be able to avoid predictable speculative attacks by introducing uncertainty into the decisions of speculators. This changes the sudden attack into a prolonged period of increasing speculation and uncertainty. In addition, the model provides useful insights into the viability of temporary nominal anchor policies, and a theoretical foundation for a useful empirical methodology.

One of the central questions about speculative attacks on fixed exchange rate regimes is the degree to which they are predictable given information on the fundamentals of the economy. Much discussion centers around whether a particular crisis such as the breakdown in the European Monetary System (EMS) in 1992–1993, the Mexican peso in 1994, or the Thai baht in 1997, was the result of predictable deterioration of fundamentals or a sudden switch from one equilibrium to another based on self-fulfilling expectations. The question is theoretically interesting, and of central practical importance. If most attacks are due to predictable movements in fundamentals (first-generation models) then fixed exchange rates may be attractive as long as the monetary authority is willing to subordinate its other goals to the exchange rate policy. On the other hand, if self-fulfilling expectations of crises (second generation models) are common then even if the monetary authority does everything right it may still not be able to avoid a speculative attack. Both types of attacks are supported by extensive theoretical literatures so economists have had to address the very difficult task of trying to differentiate these views empirically.1 This paper reexamines the possibility of predictable speculative attacks. It argues that if monetary authorities are not myopic it is unlikely that predictable movements in fundamentals can create predictable speculative attacks. Once a rational, forward-looking policy maker is incorporated in these models very different, but equally interesting conclusions arise. This literature grew from a framework developed by Krugman (1979) based on a mechanism by Salant and Henderson (1978). This framework posits a central bank with limited resources which is pursuing a fixed exchange rate policy but also has other, higher priority, policies that are fundamentally inconsistent with the exchange rate policy in the long run. Speculators are forward looking. They foresee the eventual abandonment of the fixed rate regime and the potential profit opportunities that might occur. As soon as profit opportunities begin to manifest themselves they attempt to exploit them by buying the central bank’s foreign currency reserves in a sudden attack, forcing the early abandonment of the fixed exchange rate regime. This structure is intuitive, elegant, and empirically tractable. Moreover, many countries which have experienced foreign exchange crises do indeed seem to have been pursuing other policies which appear to have been at odds with the fixed exchange rate system. Therefore the basic structure is quite attractive, and it has fared well empirically. It suffers, however, from an important shortcoming. In these models speculators are rational, forward-looking agents who are able to foresee the inevitable collapse of the fixed exchange rate regime, whereas the monetary authority is not. Even if we assume that the policy maker makes maintaining the fixed exchange rate regime a high priority, it would still realize that indefinite maintenance is impossible given its other objectives. It would therefore take steps to minimize the costs associated with the inevitable collapse of the fixed exchange rate system. It is not clear that the results of these models are robust to the inclusion of an optimizing policy maker. If the structure is extended to allow for a forward-looking, rational policy maker then strategic interaction between speculators and the monetary authority becomes critical to the analysis. Since the policy maker would foresee the speculative attack, it would be tempted to abandon the fixed exchange rate just before the crisis, thereby avoiding large reserve losses. However, if it was optimal for the policy maker to do so, rational speculators would take this into account and change their strategies, potentially altering the date or nature of the attack. I examine this issue, analyzing strategic interaction between speculators and an optimizing policy maker in a linear version of the Krugman model developed by Flood and Garber (1984b). There are five reasons why it may be useful to do so.

A version of the Krugman (1979) balance-of-payments crisis model is developed that explicitly incorporates a rational, forward-looking policy maker. The original feature of the model is that the cost of a speculative attack to the policy maker does not vanish as the duration of the attack goes to zero. This permits an analysis of strategic interaction between the policy maker and speculators in the context of predictably deteriorating fundamentals. In this model the policy maker is able to choose the timing of the move to floating exchange rates while speculators attempt to predict this date and exploit it through their foreign currency purchases. It is shown that the policy maker has an incentive to introduce uncertainty into the decisions of speculators. By doing so it is possible for the policy maker to avoid predictable speculative attacks. This is true even when the only policy instrument available to the policy maker is the decision to abandon or continue maintaining the fixed exchange rate regime. When policy makers have more sophisticated policy instruments at their disposal, avoiding predictable attacks is even easier. Thus, the hypothesis of predictable speculative attacks is inconsistent with rational, forward-looking behavior on the part of the policy maker. The existence of speculators causes the central bank to abandon the fixed exchange rate much earlier than it would have in their absence. This is true in equilibrium even though there are no speculative attacks. With capital mobility and an optimizing policy maker it is the threat of such attacks that causes the policy maker to abandon the fixed exchange rate.15 Even when we do not observe significant speculation, the presence of speculators can have an important effect on the decisions of the monetary authority. In fact, the earliest abandonments of fixed exchange rates will be accompanied by low speculation. But these abandonments are the ones whose timings have been most affected by the presence of speculators. There is an important element of time inconsistency here. Rather than enduring the protracted period of increasing speculation that it must face in equilibrium, the policy maker would prefer the equilibrium of the myopic model. In the myopic model the policy maker had relatively high reserves right up to the attack. While the speculative attack is costly for the policy maker, it is not as costly as the protracted period of increasing speculation.16 The policy maker would like to convince speculators that it will not abandon the fixed exchange rate unless reserves are driven down so far that continued maintenance is impossible. While it would like to be able to commit to this policy, in practice it cannot. Speculators know that the policy maker has an incentive to abandon the fixed exchange rate policy just before they are expected to attack. The policy maker’s announced policy is not credible, and so in equilibrium it must endure a protracted period of increasing speculation. In practice, central banks almost universally claim that they will never, under any circumstances, abandon fixed exchange rate regimes. They are, in effect, claiming to be myopic. In equilibrium it is, in fact, preferable to be myopic, but it is not credible. In the absence of a device which irrevocably commits the central bank to the policy, rational speculators will not believe these claims. It should be noted that this is not an argument in favor of currency boards, in spite of the fact that currency boards cannot legally abandon fixed exchange rate regimes. Since any government with the power to institute a currency board also has the power to abolish it, currency boards do not solve the time inconsistency problem. They simply transfer the problem from the central bank to the government. With a forward-looking monetary authority, there is an incentive to introduce uncertainty into the decisions of speculators. If speculators are certain of the conditions that will cause the policy maker to abandon the fixed exchange rate regime, they will engage in a sudden speculative attack just before the abandonment. In order to avoid such attacks the policy maker must ensure that speculators are not certain of what it will do. This endogenous uncertainty implies that the timing of the move to a floating exchange rate cannot be known with certainty, even in a completely non-stochastic structure. Fundamentals move deterministically but the outcome is stochastic. However, while the date of the abandonment of the fixed exchange rate regime cannot be known with certainty, fundamentals confine the abandonment to a bounded set of dates. The variables that determined the attack date in the traditional analysis also help determine the possible dates of a breakdown with an optimizing policy maker. Thus the model is consistent with the wealth of empirical evidence found using the traditional approach. Moreover, with an optimizing policy maker the probability of abandonment at each date can be completely specified. This derived expression for the probability of abandoning the fixed exchange rate is remarkably similar to that assumed by Cumby and van Wijnbergen in their 1989 empirical work on Argentina’s crawling peg. In order to capture the idea that changing the exchange rate regime is a policy decision they assume that the conditional p.d.f. of the level of reserves at the time of abandonment is distributed uniformly. This assumption implies that the probability of abandonment evolves quite similarly to Eq. (36).17 Hence it is possible to think of this paper as a theoretical foundation for their earlier empirical work, or, conversely, their empirical work as an ex ante empirical application of this type of model.18 The implication of this endogenous probability of abandonment is that the time near an abandonment of a fixed exchange rate is likely to be characterized by a high degree of uncertainty. This uncertainty is not an exogenous feature of fixed exchange rates but rather is introduced endogenously and deliberately by the policy maker in an attempt to move to a floating exchange rate regime before a speculative attack. The seminal work of Harsanyi (1973) provides an additional interpretation of this endogenous uncertainty. If speculators were unsure of the objective function being used by the policy maker, or about the current level of reserves, then the policy maker would use a pure strategy. However, equilibrium uncertainty would be present due to this exogenous uncertainty about the policy maker’s objective function. Harsanyi’s insight is that as this exogenous uncertainty goes to zero, the equilibrium uncertainty does not. In fact, the probability of abandoning the fixed exchange rate at each time approaches the probabilities found in the model. This remarkable fact implies that even arbitrarily small uncertainty about the policy maker’s objective function or foreign currency reserves will lead to very large uncertainty about the conditions under which the policy maker will abandon the fixed exchange rate regime. Hence, it is not realistic to presume that if speculators have reasonably good information about the policy maker’s objective function and about central bank foreign currency holdings, that they will be able to deduce good estimates of the conditions under which the policy maker will abandon the fixed exchange rate regime. This endogenous uncertainty means that prior to the switch in exchange rate regimes there are increasing domestic interest rates, and increasing forward exchange rate premia over the fixed exchange rate. In addition, the exchange rate may jump during the move to the floating rate, yielding ex post profits to foreign currency speculators. These empirical implications are attractive features of this model that have previously been generated in the traditional model by incorporating uncertainty via exogenous shocks. However, the magnitude of the uncertainty introduced to the fixed exchange rate period relative to the flexible rate period is different in each approach, which leads to differences in the magnitude of the empirical implications. These empirical implications of this paper which are different from those generated by the exogenous shock approach include the following. • Interest differentials leading up to the breakdown in the fixed exchange rate are greater than the interest differentials in the flexible exchange rate period. • The forward exchange rate premium leading up to the breakdown in the fixed exchange rate is greater than the forward exchange rate premium in the flexible exchange rate period. • The size of the devaluation at the breakdown in the fixed exchange rate is not dependent on the size of the last shock. The exogenous shock approach implies that the length of the period of increasing interest rates and forward exchange rate premia is related to the size of the expected shocks. The size of a jump in the exchange rate is directly related to the size of the last shock. In fact the magnitude of the jump must be less than the jump that would occur if the same shock hit in a flexible exchange rate environment. Likewise the interest differentials and forward premia must be less than what they would have been in a flexible exchange rate environment. With an optimizing policy maker, however, these empirically observed phenomena are no longer the result of exogenous shocks. They arise in equilibrium even in this non-stochastic framework due to the endogenous uncertainty introduced by the policy maker. This endogenous uncertainly is confined to the period leading up to the breakdown in the fixed exchange rate regime and hence is greater than the uncertainty in the flexible exchange rate period. The results are encouraging for the viability of temporary nominal anchor policies to combat runaway expectations-driven inflation. These implications are more speculative, but nevertheless worth considering. By introducing uncertainty into speculators’ decisions, it is in fact possible for a central bank to leave a fixed exchange rate regime gracefully, even when the abandonment is anticipated by rational speculators. Nevertheless, the results of the model also suggest that these policies are likely to be very dangerous. During the time leading up to the abandonment of the fixed rate regime, the existence of rational speculators ensures that the policy maker is indifferent between maintaining and abandoning the fixed exchange rate. This means that the central bank will be very vulnerable to shifts in peoples’ perceptions of its commitment to the announced policy. Any perceived weakness, or any negative shock could cause a sudden crash.19 Seen in this light, it is not surprising that while we do see several successful implementations of nominal anchor policies (most notably Poland and Israel), the list of dramatic failures is much longer. However, the reader should be aware that the model used here is very stylized and does not incorporate many of the features that are important to the success of nominal anchor policies. Work still needs to be done in more fully specified models to see how the policy maker’s incentive to introduce uncertainty into speculators’ decisions affects the adjustment of inflationary expectations, and how this incentive interacts with the possibility of rational and self-fulfilling expectations of attacks. One significant implication of introducing an optimizing monetary authority is that it implies that speculative attacks cannot be precipitated by predictable movements in fundamentals. If speculative attacks were predictable, the policy maker would avoid them by abandoning the fixed exchange rate system just before they occurred. However, this would mean that the breakdown of the fixed rate regime was predictable and rational speculators would exploit this, resulting in an earlier attack. But the same logic would apply to that attack as well. Therefore, in equilibrium, speculative attacks cannot be predictable in a world with an optimizing policy maker.20 Speculative pressure, however, may be entirely predictable. This does not imply that speculative attacks do not depend on fundamentals. Many models of speculative attacks with optimizing monetary authorities imply that the existence of multiple equilibria depends on fundamentals. See Cole and Kehoe, 1996a and Cole and Kehoe, 1996b, Davies and Vines (1995), Obstfeld, 1994 and Obstfeld, 1996, Ozkan and Sutherland (1998), and Velasco (1997). The point is that while the conditions for a speculative attack may depend on predictable fundamentals, the precise time of a speculative attack cannot. By extension one could speculate that in models with multiple equilibria the coordination of speculator expectations on a particular equilibrium cannot depend on predictable variables, since otherwise the policy maker could predict the attack, and therefore avoid it. The coordination of speculator expectations could, however, depend on the unpredictable components of predictable variables, including the unpredictable components of fundamentals.