بحران ارز با تهدید دفاعی نرخ بهره

While virtually all currency crisis models recognise that the decision to abandon a peg depends on how tenaciously policy makers defend it, this is seldom modelled explicitly. We add the threat of an interest rate defence to the global game model of Morris and Shin (American Economic Review 88, 1998). With an endogenous defence, actions of speculators may become strategic substitutes instead of the usual complements. Nevertheless, our generalised model remains tractable and has a unique threshold equilibrium. It provides additional insights. For instance, the threat of an interest rate defence makes speculation riskier and this may be sufficient to keep speculators out when fundamentals are still relatively strong.

Virtually all modern currency crisis models recognise that the decision to abandon a currency peg depends on how tenaciously the policy maker is willing to defend it. Yet this is seldom modelled explicitly. In the model in this paper, the policy maker is willing to increase the interest rate to offset the buildup of speculative pressure on exchange markets. This increases the financing costs of speculators, and makes speculation riskier. We add this threat of an interest rate defence to Morris and Shin's (1998) global game model of the onset of a speculative attack, which has proved fruitful to investigate a wide variety of topics on crises (see e.g. Heinemann and Illing, 2002, Corsetti et al., 2004, Cukierman et al., 2004, Goldstein, 2005, Corsetti et al., 2006, Guimaraes and Morris, 2007 and Cornand and Heinemann, 2009). Including the threat of an interest rate defence leads to a crucial difference with standard global game models. There, a speculator's payoff from attacking a currency weakly increases when more speculators attack, no matter whether the attack is successful or not. Hence, the actions of speculators are strategic complements. In our model, a larger amount of speculators attacking the peg may lead to a harsher defence by the policy maker, which means that the costs of speculation are higher. In case the attack is unsuccessful, actions are strategic substitutes instead of complements. Our model has a unique equilibrium in threshold strategies, as familiar from global games, but the threat of a policy response affects the equilibrium. As in standard models, strategic uncertainty about the odds of a successful attack plays an important role in our model. Yet the threat of an interest rate defence makes speculation even riskier and may be sufficient to keep speculators out when fundamentals are still relatively strong, even without actually setting a high interest rate. A relatively large deterioration of fundamentals is necessary to trigger a speculative attack, which may be accompanied by a spike in the interest rate due to the interest rate defence. This outcome of our model appears to be broadly consistent with a stylised fact about past currency crises, which suggests that a currency can remain overvalued during a protracted and by and large tranquil period before its peg finally collapses. The robustness of global games to the inclusion of more realistic elements such as an interest rate defence has sometimes been questioned. For instance, Chamley (2003) challenges several aspects of global games, one of them being the role of small and fixed transaction costs. Indeed, although it is common in the global game literature to assume the costs of an unsuccessful speculative attack are fixed and known in advance, this is actually not the most realistic setting. Consider the following strategy that is widely used in reality. A speculator believes the weak currency will depreciate and instructs her broker to sell weak for strong currency spot.1 Spot traded currency is due for delivery in two business days, yet the speculator has no interest in actual delivery. Therefore, each night the broker will automatically roll-over the speculator's position via a so called tomorrow-next procedure, closing it out at the end of the day on her behalf and re-opening it the next day. The roll-over costs are determined by the prevailing overnight interest rate differential, and are debited from (or credited into) the speculator's margin account. Hence, for as long as the position remains open (typically a few weeks, and the exact time span is unknown to speculators when they start), the speculator is exposed to interest rate risk—besides exchange rate risk. Our model shows how global games can account for this. Its setup is close to that of Morris and Shin (1998). But rather than assuming that the costs of speculation are known ex-ante, it emphasises the additional uncertainty stemming from interest rate risk that results from the policy maker's readiness to defend the weak currency. We thus contribute to a closely related literature that incorporates interest rates in global game models. This literature typically models the interplay between interest rates and the behaviour of speculators using a general equilibrium approach. Angeletos and Werning, 2006, Hellwig et al., 2006 and Tarashev, 2007 study global game models in which speculators can take positions in the weak currency conditional on the behaviour of the interest rate during the attack, and a Walrasian auctioneer then clears the market by setting the interest rate. Essentially, agents are able to condition their decision on the market clearing interest rate that is, in fact, the result of their joint behaviour. It is as if agents can observe the interest rate that will result from the attack before they commit to their decision. The Walrasian approach is fine for many economic applications, but less obviously so in the context of speculative attack models. First, in these models, the market clearing interest rate necessarily reflects the outcome of the speculative attack. If agents can predict the outcome using the interest rate, the element of strategic uncertainty associated with the speculation decision is substantially reduced. In reality, it is doubtful that the interest rate is informative enough as to substantially reduce strategic uncertainty. Second, in this approach there may be multiple market clearing interest rates, in each of which speculators conditionally demand the amount of weak currency consistent with the model's outcome. Multiple equilibria may reduce the predictive power of the model. In our paper, we adopt an opposite approach and model the interest rate as an uncertain policy response at the onset of the attack. The key difference between the models above and our own, discussed in detail in subsection 4.5, is the inability of speculators to condition decisions on the market clearing interest rate. Our approach abstracts from the informational role of the interest rate during the attack, and allows us to focus on the effect of interest rate risk on equilibrium instead. As we have indicated above, interest rate risk during the attack is a real-life phenomenon that affects the value of positions of speculators. Another advantage of our model is its unique threshold equilibrium. Because of our endogenous interest rate, none of the usual equilibrium results for global games apply directly to our model. We extend the class of global game models for which a unique threshold equilibrium is known to exist. Our model's payoff structure is most closely related to a global game bank run model of Goldstein and Pauzner (2005) (and relatedly, Dasgupta, 2004), which also deals with strategic substitutes. Yet the threat of an interest rate defence makes the impact of changes in fundamentals on payoffs non-monotonic, which is not the case in their model. Under the additional assumption that information in the global game is characterised by a uniform noise distribution—the original assumption in Morris and Shin's (1998) article—the threshold equilibrium is the unique equilibrium of our model among all possible types of equilibria. There are other studies about how an interest rate may help defend during a speculative attack. Some focus on how the interest rate affects the sustainability of government policies, in particular fiscal policy. Examples are Flood and Jeanne, 2005, Lahir and Végh, 2003 and Lahiri and Végh, 2007. This perspective suggests that a policy maker will be able and willing to go to greater lengths to defend the peg under stronger fundamentals. This trade-off is also captured in our model, where fundamentals affect the effectiveness of the interest rate defence. Another strand of literature is based on the signalling model of Drazen (2000), in which the central bank sets the interest rate before speculators move. Speculators interpret the interest rate as a signal that transmits information about a policy maker's intentions, and this may lead to multiple equilibria. Global game variants of this model have been studied by Angeletos et al., 2006 and Angeletos et al., 2007. The question of signalling intentions in earlier stages is distinct from the issue considered in our paper. An important reason for governments to manipulate the interest rate in reality is to try to stabilise the spot exchange market. As an attack unfolds, the optimal level of the interest rate is determined endogenously by attempts to calm the market. It is no longer set just to signal intentions. The rest of the text is structured as follows. Section 2 explains how a defence policy affects the payoffs of speculators, and why this may lead to strategic substitutes. Section 3 develops a model that incorporates this feature in a global game model. We solve for the model's equilibrium and discuss its properties in Section 4. In Section 5 we conclude. Proofs are found in the Appendix A

During currency crises, the policy maker undertakes defensive actions aimed at increasing the financing costs of speculators, such as raising the interest rate. Any approach that abstracts from these actions, and solely focuses on the policy maker's decision whether or not to devalue under speculative pressure, gives a partial picture of the strategic interaction. In particular, it only focuses on the strategic complementarities in the speculators' decisions, whereas the policy maker's defence can also easily generate strategic substitutes. We have incorporated the threat of an interest rate defence into the well-known global game speculative attack model of Morris and Shin (1998). In our model, the policy maker's interest rate defence is endogenous and the payoff function varies non-monotonically both with respect to the fraction of attackers and the fundamentals. We have proved that the model still has a unique threshold equilibrium, just like the usual global game models. Thus global games are robust to this more realistic specification of the payoff function. While we have focused on currency crises, our results rely only on the payoff structure, so that they also apply in other settings. Our focus on currency crises leads to a number of observations that are broadly consistent with how crises develop in reality. A relatively large deterioration of fundamentals is necessary to trigger a speculative attack, which may be accompanied by a spike in the interest rate, while much less stress on markets (in terms of an elevated interest rate) will be observed for smaller misalignments of fundamentals. A successful speculative attack will lead to a substantial jump of the exchange rate following the attack. As a policy implication, we find that a defence of the peg not based on the interest rate instrument, but consisting, say, of interventions in the foreign exchange spot market is less effective insofar as the costs of speculation are not increased