انتظارات و اطلاعات درمدلهای بحران ارز نسل دوم

We explore the role of expectations in second generation currency crises models, proving that sudden shifts in speculators’ behavior can trigger currency devaluations, even without any sizable worsening of the fundamentals. Our model shows that ‘small’ (mean-preserving) changes of speculators' beliefs may drive agents to a unique equilibrium with a self-fulfilling attack. Following a recent line of research, we also compare the results of private and public information models, finding the following paradox: releasing public information seems to be more convenient when fundamentals are bad.

The financial turmoil that invested east Asian countries in the summer of 1997 has revealed the limits of theoretical models in explaining actual currency crises episodes. According to many accounts, the event supposed to be the most likely cause of a crisis (a definite worsening of the fundamentals, possibly implied by an unsustainable stance of the economic policy) did not occur, at least in some of the Asian economies struck by speculative attacks.2 Thus, many economists believe that other factors might have a crucial role in determining the dynamics of a crisis. In first generation currency crises models (FGMs), originally developed by Krugman (1979) and Flood and Garber (1984), financial crises follow a deterioration of the fundamentals, typically due to inconsistent economic policies. By contrast, second generation models (SGMs), first developed by Obstfeld, 1986 and Obstfeld, 1994, turned the attention to the costs and benefits of the fixed exchange rate policy, stressing the importance of the trade-off faced by the government between defending a fixed currency peg and other policy targets.3 In these models, a devaluation is the government’s optimal response to the actions of speculators and can take place as a result of self-fulfilling beliefs, without a previous worsening of the fundamentals. Since speculative attacks raise the cost of defending a fixed exchange rate, SGMs may exhibit self-fulfilling multiple equilibria.4 In SGMs the space of fundamentals is usually divided in three parts: when fundamentals are ‘good’, there is a unique equilibrium in which the exchange rate is maintained; when fundamentals are ‘bad’, the currency depreciates; when fundamentals fall in an ‘intermediate’ range (the ‘ripe for attack’ zone), both outcomes are feasible. In a recent paper, Morris and Shin (1998) started a promising strand of analysis, by developing a SGM with incomplete information. They consider speculators having a uniform prior probability distribution over the state of fundamentals that is updated according to the observation of a private signal. Their model, as well as the earliest complete information models, does not allow to examine the role of the distribution of agents’ beliefs about the fundamentals. This issue has been neglected in the literature, presumably because one could think that, in an incomplete information framework, only the mean of speculators’ probability assessment over the fundamentals matters. If this were true, we would have a similar tripartition for the mean of the distribution over the fundamentals. Hence, the incomplete information framework would not enrich the benchmark analysis and would not modify the structure of the equilibria. Nevertheless, agents’ beliefs have often been put forward to explain actual currency crises. For instance, after the Russian crisis, many commentators pointed to an increase in agents’ uncertainty as a possible explanation for the transmission of the speculative pressures to countries (especially in Latin America) that had very limited trade linkages with Russia (see also International Monetary Fund, 1999 and Bank for International Settlements, 1999). Yet, typical SGMs do not explain why uncertainty should influence speculative attacks. In this paper we present two different variants of the incomplete information model studied by Morris and Shin (1998). Our first SGM allows to study the role played by agents’ beliefs about the fundamentals in a standard ‘currency crisis’ game. By explicitly introducing these beliefs, we find that the mean of the distribution over the fundamentals is not the sole relevant parameter. In particular, we show that mean-preserving changes of speculators’ expectations can result in a shift from a model with multiple equilibria to a model with a unique ‘attack’ equilibrium. Hence, currency crises can be triggered by ‘small’ changes in the distribution of agents’ beliefs, even without any underlying deterioration of the fundamentals. Our model differs from Morris and Shin’s because it takes into account a generic prior probability distribution and studies how equilibria change together with it. To focus on the effects of uncertainty of agents’ beliefs, we simplify the model by neglecting private information. Our study supports the thesis that uncertainty matters and offers also some interesting insights about the multiple equilibria zone of the complete information game. When the mean of the distribution over the fundamentals is in this region, we show that if uncertainty is sufficiently large, the incomplete information model has a unique equilibrium that entails a speculative attack. In other words, the ‘good’ equilibrium in the ‘ripe for attack’ zone is not robust to an increase in uncertainty. In the second SGM presented in this paper, we analyze how public information affect the structure of the equilibria. Along the lines of the global games study of Carlsson and van Damme (1993), Morris and Shin (1998) proved that the removal of the hypothesis of common knowledge of agents’ behavior, implicit in their private information framework, determines a unique equilibrium. Here, we develop a model in which agents observe the same public signal (so that the common knowledge of agents’ actions is restored), and we find that multiple equilibria no longer disappear. Interestingly, by comparing the results of private and public information models, the following paradox emerges: providing public information seems to be more convenient when fundamentals are bad! An inspection on the reasons behind this paradox provides some useful insights on the likelihood of the events that determine the equilibria. When the private information model of Morris and Shin (1998) predicts an equilibrium with a currency attack, the equilibrium with no attack in our public information model envisages an implausible (but feasible) situation in which speculators waste a big payoff that could otherwise be obtained with a small coordination effort. Analogously, when the private information model predicts an equilibrium with no attack, the equilibrium with a currency attack in the public information model foresees speculators getting a small payoff and requires very large coordination. Hence, this comparison highlights that the equilibria ruled out by the private information model that re-emerge in the public information framework are hardly plausible. Therefore, the paradox warns that policy conclusions drawn from models with multiple equilibria can be misleading, especially when considerations on the likelihood of the outcomes are neglected. The paper is organized as follows: Section 2 briefly reviews the benchmark model with complete information. In Section 3, we analyzed a basic incomplete information framework where speculators’ expectations over the fundamentals are distributed according to a generic prior probability distribution and we study the consequences of changing its variance. In Section 4, we present the model with public information, and compare our results with those of Morris and Shin. Section 5 concludes.

The game-theoretic approach of SGMs has proven to be an important line of research for the investigation of the role of speculators’ expectations and information in the onset of a currency crisis. A promising strand of analysis is offered by the study of global games, initiated by Carlsson and van Damme (1993), applied to speculative attacks by Fukao (1994), and to second generation currency crises models by Morris and Shin (1998). On the theoretical ground, global games show the importance of the hypothesis of common knowledge of agents’ actions for the result of multiple equilibria and also give some insights about the likelihood of the equilibria of complete and public information games. The results achieved in the paper are consistent with this theory. In fact, with public information, the reintroduction of the common knowledge of agents’ actions (still maintaining some uncertainty over the states of fundamentals), leads us to determine the existence of a multiple equilibria zone. Moreover, the comparison between the results of the public and the private information models highlights an interesting paradox: the government has more convenience in providing public information when fundamentals are ‘bad’ than when fundamentals are ‘good’! However, one realizes that this occurs because the equilibria of the public information model that are eliminated in the private information game rely on the occurrence of implausible events: e.g. getting a small payoff with a large amount of coordination or giving up a big payoff that could have been achieved with a small amount of coordination. Our example shows that it is easy to draw deceptive conclusions from models with multiple equilibria, especially when any consideration about the likelihood of the outcomes is neglected. Hence, the paradox calls for some equilibrium selection procedure since, with multiple equilibria, not only game theory can be a ‘weak and uninformative theory’ (Harsany and Selten, 1988), but it can also can lead to wrong policies. Global games, that lead to a unique equilibrium in a wide class of models, can be a very powerful tool in this perspective. By focusing on speculators’ expectations, we also prove that mean preserving changes of speculators' probability assessments over the state of fundamentals may be sufficient to drive agents to a unique ‘bad’ equilibrium with a self-fulfilling currency attack. Hence, the model suggests an explanation for sudden shifts in speculators' behavior that trigger currency devaluations and that do not seem to be justified by the fundamentals of the economy. In fact, modifications of agents’ beliefs that induce speculative attacks can occur even without a worsening of the expected state of fundamentals. Moreover, the model highlights that a crisis can be triggered by an increase of the uncertainty over the state of the fundamentals (measured, say, by the variance of the distribution) or, in general, by an increase of the subjective probability of an ‘unforced’ currency devaluation. Finally, we prove that an increase of the uncertainty over the fundamentals that induces a shift to a unique equilibrium with a currency crisis may occur when the mean of the distribution is in the ‘ripe for attack’ zone. Therefore, the model shows that, even with unbiased expectations, an economy whose fundamentals are in that zone is not robust to changes in agents’ beliefs due to, say, an increase in the uncertainty. Note that such an economy would be considered vulnerable to a currency attack in a complete information model because speculators can trigger a crisis, but this outcome might not occur. The suggestion coming from the incomplete information model is, instead, that such an economy should be regarded as fragile as it is in the ‘unstable’ zone, because for some unbiased agents’ expectations there can be a unique ‘bad’ equilibrium with a speculative attack and a devaluation of the currency.