پویایی بحران ارز با اصطکاک های بازار سرمایه

This paper presents a dynamic model of currency crises with frictions. By construction, a speculative attack is not an instantaneous event but takes a little time to deplete the country's reserves and, in the event of an attack, agents are uncertain about whether they will be able to act before the devaluation comes. The currency will be overvalued (‘ripe for attack’) for a long time before an attack takes place. A discrete and sizable devaluation will occur. Small changes in fundamentals may trigger an attack. The model brings insights about the dynamics of currency crises and the effects of some key policy variables.

The so-called ‘first generation’ models of currency crisis (Krugman, 1979 and Flood and Garber, 1984) show that policies incompatible with a pegged exchange rate regime lead to speculative attacks that produce massive falls in a country's level of reserves and force a government to abandon the peg. Agents attack the currency whenever the “shadow exchange rate” exceeds the current exchange rate,1 a speculative attack instantaneously depletes the country's reserves. The currency is never overvalued before the attack and discrete jumps in the exchange rate are ruled out. However, contrary to what those models imply, currencies seems to stay ripe for attack for long periods of time; attacks that take little time to force the abandonment of a pegged regime take much time to start (and sometimes are triggered without major perceived changes in economic fundamentals), and large discrete devaluations are observed.2 In Flood and Garber (1984), discrete devaluations may occur if the “shadow exchange rate” jumps discretely right before the currency attack, but the currency is never overvalued. Other more recent contributions have generated discrete jumps following the abandonment of a peg. Pastine (2002) includes a maximizing government that cares about reserves and does not like speculative attacks in a first generation setup. It shows that the government randomizes the timing of abandoning the peg instead of passively waiting for the agents to attack the currency. So, crisis cannot be predicted and a discrete devaluation occurs because the abandonment of the peg by the Central Bank is not fully expected. In the model of Broner (2001), there is a ‘secular deterioration of fundamentals’ and agents try to guess when the currency will be ‘ripe for attack’. There may be a discrete devaluation because agents are uncertain about the shadow exchange rate. Chamley (2003) also deals with incomplete information and learning: agents are uncertain about whether the mass of speculators is enough to force the Central Bank to abandon the peg. Broner (2004) shows that a discrete devaluation may also occur if some uninformed agents are included in the model. Abreu and Brunnermeier (2003) show how incomplete information can lead to bubbles and crashes. They show that agents may decide to buy an overvalued asset although they know that the bubble will burst at some point in the future. Rochon (2004) applies their argument to currency crises to show that agents delay their attack to the currency. This paper takes a different approach. Instead of attempting to explain why agents do not perfectly coordinate on attacking the currency whenever it is overvalued, it takes the frictions as its starting point and studies what happens in a dynamic model of currency crises if: (i) an attack does not occurs instantaneously, it takes some (little) time until it forces the abandonment of a peg; and if (ii) agents are uncertain about whether, in the event of an attack, they will be able to escape before the devaluation comes. A simple way to include those features in a model, is to assume that agents get the opportunity of changing position according to a Poisson process, as in Calvo (1983). Due to the Poisson assumption, all agents that are long in the currency at a given point in time face the same probability of being caught by the devaluation. By modelling frictions in this stylized way, this paper is not explaining why a speculative attack lasts for more than a second — that occurs by assumption. But it is showing that an attack that takes a little time (say, 2 or 3 weeks) to deplete the country's reserves and force the currency to float will take much more time (say, several months) to get started if the agents are uncertain about whether they will be able to escape the devaluation or not. The currency will be “ripe for attack” for a long time, a discrete devaluation will occur and small changes in fundamentals may trigger an attack. The advantage of this approach over a formal modelling of limited participation and/or noisy information about others' moves that leads to imperfect coordination is its much greater tractability: the effect of the frictions are numerically evaluated, the dynamics of crises under stochastic fundamentals is analyzed and testable implications are offered. The proposed framework provides some insights on the dynamics of currency crisis and on the impacts of frictions, improving macroeconomic prospects and interest rates. Some features of this model often show up in economic and policy analysis but are rarely incorporated in formal models. The next section presents the non-stochastic model of Flood and Garber (1984). Section 3 adds the Poisson frictions to the model. Section 4 shows that, with uncertainty on the path of shadow exchange rate, the expected devaluation is substantially larger — agents are less aggressive in attacking the peg. A final section concludes. The model shown at Section 4 can also be seen as a dynamic version of Morris and Shin (1998) with Poisson frictions instead of incomplete information. Like in Morris and Shin (1998), agents are deciding about attacking the currency, the fundamentals are given exogenously and the pressure on the peg depends on other agents' choices — so expectations play a key role. The structure of the model is very similar to Frankel and Pauzner (2000) model of sectorial choice and the theoretical contribution of Burdzy et al. (2001). Like in Frankel and Pauzner (2000), agents choose between 2 actions and get the opportunity to revise their decisions according to a Poisson process. Payoffs depend on two state variables: a random economic parameter that follows a Brownian motion and the fraction of agents that had chosen one of the actions. However, the assumption of strategic complementarities, key in Morris and Shin (1998) and Frankel and Pauzner (2000), does not hold in the context of this paper. Section 4 further analyzes this issue.

In a major speculative attack following the Russian crises, in 1998, Brazil lost a third of its foreign reserves in around 3 weeks. For many practical purposes, this is close enough to an instantaneous attack, but this paper shows that new insights arise in a model in which an attack is not an instantaneous event but lasts for a few weeks. Given the complexity of real world problems and the difficulties related to obtaining and analyzing information, it is indeed not surprising that agents do not act exactly at the same time. Without denying that an explicit modelling of informational issues may teach us important lessons, this paper argues that including such frictions in a stylized way in our theoretical models also has important benefits for allowing us to focus on the economic problems we are really interested in.