بحران ارز: تکامل باورها و آزمایشهای سیاست

We study a model of currency crisis where agents’ beliefs are the only source of volatility containing the potential for currency devaluation. Using the basic framework of Arifovic and Masson (2003), we simulate the model for a large number of parameter specifications. The learning dynamics of our agent-based computational model, based on imitation of successful expectational rules and occasional experimentation, result in recurrent currency crises. Recurrent crises are a robust feature of the dynamics regardless of the model's parameter specifications. We discuss both the impact of imitation and experimentation on the model's dynamics, as well as the impact of the parameter values on the duration of episodes of devaluation and periods of no-devaluation. In addition, we compare the first difference in interest rate spread statistics of the data generated in our simulations and real world data. Finally, we conduct policy experiments in our agent-based type environment designed to examine the power of the interest rate policy changes in decreasing the number as well as the duration of the episodes of currency crisis. Our results indicate that the policy of decreasing, rather than increasing, the emerging market interest rate proves more effective at reducing the likelihood of devaluation.

Models based on rational expectations hypothesis have had a difficult time capturing and explaining the features of the actual financial time series such as volatility clustering, fat tails of the time series of returns, etc. On the other hand, agent-based computational (ACE) approaches have had much more success in matching the features of the observed time series.1 Arifovic and Masson (2003) study an agent-based, dynamic model of currency crisis in which heterogenous expectations of boundedly rational agents change through an evolutionary algorithm that involves imitation and experimentation. Their model generates recurrent crises that result from investors’ changes in expectations; periods of excessive optimism are followed by periods of excessive pessimism. Currency crises are characterized by recurrent episodes of devaluations that are purely expectationally driven. We base the work presented in this paper on a version of their ACE model of currency crisis. The model is based on the idea of social learning where a population of beliefs of a large number of agents evolves together over time. This concept captures well the fact that a large number of investors participate in trading in real markets. Investors in real markets can also observe the behavior of some of the other investors which is captured well by imitation. They can also occasionally try out new, different rules which is captured well by experimentation. We refer to this setup as a model of social evolutionary learning (SEL). SEL has been widely used in the ACE literature to model the evolution of agents’ beliefs and decision rules. 2 The economic environment is a simple model of portfolio balance in which agents (investors) make a decision of whether to invest their wealth into an emerging market with a risky rate of return, or a domestic market with a safe rate of return. This environment, when endowed with rational agents and stochastic behavior of the trade balance, can result in multiple rational expectations equilibria. If an exogenously specified sunspot process is added to it, it can also result in sunspot equilibria with recurrent currency crisis.3 We simplify the model by setting the trade balance to a constant value. This way, we have a model in which sunspot equilibria cannot exist. We endow the model with boundedly rational agents and focus on the evolution of their beliefs as the only source of potential currency crisis. Agents’ beliefs, or expectational rules, are modeled as agents’ assessments of probability of devaluation. The central bank of the emerging market economy sets the rate of return on the investment that reflects agents’ average sentiment about the probability of devaluation. Using their expectational rules and the announced rate of return in the emerging market, agents make their portfolio decisions. These decisions determine the total amount of deposits invested in the emerging market in a given period. The total amount of deposits invested in this period, together with the amount that the emerging market economy has to pay out in terms of principal and interest earned for the past investments, determines the level of reserves. If it is above an exogenously given threshold, there is no devaluation. Otherwise, there is currency devaluation in the percentage sufficient to bring the reserves back to the threshold level. We simulate our model of social learning for a large number of different parameter values. The results are characterized by recurrent currency crises (which is consistent with Arifovic and Masson's results). This feature is robust across different parameter specifications. However, the duration of episodes of devaluation, as well as periods of no devaluation depend on the number of investors, as well as on the rate of experimentation. We analyze the impact of the interaction between the number of agents and the imitation process on the durations of periods of devaluation and no-devaluation. Our analysis of the effects of imitation on the dynamics suggests that periods of no-devaluation last longer than periods of devaluation due to a weaker selection effect associated with the former. The imitation process affects the evolution of the distribution of expectational rules, and thus, the distribution of the emerging market interest rate and the distribution of the first difference in interest rate spreads. We compare the time series properties of the differences in interest rate spreads of the data generated in our simulations with the real world data on the emerging market interest rate spreads.4 There has been an on-going debate about the appropriate policy response in face of a possible speculative attack on a currency. Increase in interest rates should prevent excessive capital outflow, and thus prevent currency devaluation as well. However, there is always concern that high interest rates would worsen the financial conditions of highly indebted financial institutions (which is often the case in these circumstances) and corporations, and could also lead to a slowdown in output growth. Bankruptcies and decreased output growth would then lead to further contraction of credit, further bankruptcies and so on. The alternative policy of loose credit and low interest rate would help prevent bankruptcies and credit squeeze, would stimulate growth in output and would thus help restore the confidence in the country's financial and economic conditions, and defend its currency from an attack (see, for example, Corsetti et al., 1998 for a discussion of the policy debate regarding the Asian currency crisis). In our simple, balance-of-payment model, we do not explicitly model financial or real sector of the economy. However, we can still examine the consequences of the central bank's intervention on the emerging market interest rates. We design and conduct simulations of policy experiments which are aimed at preventing the occurrence of currency crisis. The policy may be stated in the following way: when the reserve/deposit ratio reaches a predefined ‘threshold’, set the interest rate to the level that is lower (higher) by a given percentage from what the market interest rate would have otherwise been. We set up a computer testbed for policy analysis using a number of different ‘threshold’ values of currency reserve ratios and varying policy responses in terms of different percentage increases, or decreases, in the emerging market interest rate. Our results show that decreasing the interest rate in the wake of a possible currency attack is much more successful in defending the currency. Furthermore, we provide an explanation based on the evolutionary dynamics (the effects and interaction of imitation and experimentation) of why this policy is more effective in our type of the ACE environment. The design of our policy experiments and the analysis of the resulting outcomes and underlying dynamics demonstrate the way, both in terms of methodology and implementation, in which the ACE approach can be used to evaluate various policy scenarios. We proceed as follows. In Section 2, we outline a model of currency crisis that has been used in the literature to study the existence of sunspot equilibria. This is followed by a presentation of a simplified representative agent version in which there are no exogenous stochastic shocks to the economic fundamentals. We incorporate heterogenous agents with different expectational rules, and describe the evolution of these rules in Section 3. In Section 4, we discuss the results of our simulations and features of the observed dynamics. In Section 5, we describe our policy experiments. We provide concluding remarks in Section 6.

We study the dynamics of a model of currency crisis where the only source of volatility that contains potential for speculative attacks and devaluation of currency is agents’ expectational rules. These expectational rules are heterogenous and evolve over time. The model combines the elements of the ‘herd’ behavior captured by imitation and ‘surprises’ that experimentation brings in. As part of our methodology, we conduct a large number of simulations for different parameter values to check for the robustness of the results of our ACE model. All of the simulations resulted in recurrent currency crisis. We discuss the differential impact of the imitation's selective pressure in the periods of devaluation and no-devaluation. The impact is much stronger during devaluation periods, as the rules, characterized by lower values of probability of devaluation, that are investing in the emerging market get punished with zero fitness. This makes them ‘invisible’ to the other investors as their probability of imitation equals zero. The whole distribution of π is pushed towards ‘high’ probability of devaluation values increasing the average View the MathML sourceπt¯ at the same time. As a result, there is also relatively large increase in the emerging market interest rate. High interest rates continue as long as devaluations occur. Once they are over, agents who invest in the emerging market receive higher fitness than those who invest in the domestic market. Thus, they will be imitated with higher probability. As these are the rules with ‘low’ probability of devaluation, they will move the distribution of the mean to lower values, and thus bring down the emerging market interest rate as well. However, the rules with ‘high’ probability of devaluation do not become ‘invisible’, as they have non-zero fitness value, and thus positive probability of imitation. This weakens the selective pressure in periods of no-devaluation compared to the devaluation episodes, and has consequences for the behavior of the changes in interest rate and in differences in spread. The interest rate falls, but the change is smaller, in absolute terms, than the change during the periods of devaluation. The prediction of our analysis is that the selection pressure has the following impact on the distribution of differences in spreads. Weaker selection pressure results in periods of no-devaluation longer than periods of devaluation. It also pushes the mass of the distribution of differences in spreads into a very small range, as there are extended periods during which the interest rate moves slowly downward, with occasional small upward surges as a result of experimentation. In addition, changes in differences in spreads that occur when the devaluation starts, and once again when it stops are big relative to the rest of the changes during no-devaluation periods. However, on average, positive changes are bigger in absolute terms than negative changes. Overall, the distributions are characterized by fat tails, with most of the mass of distribution lying in a very small range, and observations, for the periods when devaluation episodes begin, and stop, at the far end of the tails of the distribution. This results in high, positive values of kurtosis. The distributions are also skewed. The sign of the skewness depends on the magnitude and frequency of positive and negative changes. If positive changes are larger in absolute magnitude and frequency than the negative changes, the distribution will be positively skewed. Otherwise, it will be negatively skewed. From the above discussion, it follows that due to the selection pressure, positive changes are larger, in absolute terms, and the resulting distributions will sometimes be positively skewed. Finally, we use our model to perform a set of policy experiments that are designed to mimic what real world policy responses would be in face of currency crisis. We investigate the policy of lowering and increasing the emerging economy interest rate from what it would otherwise be. Our findings show that both policies can result in decreases of the occurrence of devaluations for certain parameter values. However, the policy of reduction of interest rate is much more successful. All of our policy experiments where interest rate reduction was implemented resulted in a decrease in the number of devaluations compared to the baseline simulation. Our analysis of the evolutionary dynamics show that, during the periods leading up to devaluations, the distribution of investors’ rules is not tight enough (around the geometric mean) in order that an increase in the interest rate captures any significant number of investors. Instead, it only serves to increase the amount of interest paid on the emerging market debt, and therefore the amount of money leaving the emerging market economy. Likewise, a decrease in the interest rate does not result in a big increase in the outflow of funds. However, it does reduce the amount of interest that is paid out, and thus relieves some pressure on the reserves and decreases the likelihood of devaluation.