Modelling Currency Crises in Nigeria: An Application of Logit Model

Currency crises inflict significant social and economic costs on economies that have suffered its occurrence. Thus, statistical models have been developed over the years to construct reliable early warning systems as part of strategies for preventing or reducing the devastating effects of such crises. To the knowledge of this study, no recent work has been done in this regard with respect to Nigeria, especially following the 2008/09 global financial crisis. Using a logit model, this paper estimates the probabilities of currency crises in Nigeria as a logistic function of selected macroeconomic variables. Particularly, it provides answer to the question of whether real exchange rate misalignment propels currency crises. The empirical investigation used quarterly data for the period 2000Q1 to 2012Q4. Model results show that the likelihood of currency crisis in Nigeria increases when the real exchange rate is misaligned; the exchange rate is volatile; oil price declines; debt/GDP ratio increases; and the current account balance to GDP ratio declines. Real exchange rate misalignment has overarching influence on the tendency for currency crash during the estimation period. The paper therefore recommends regular assessments of the value of the Naira exchange rate vis-à-vis its equilibrium level with a view to implementing appropriate policy responses to arrest or avoid prolonged and substantial misalignment. Since all the variables entered the equation in their one period lag, the estimated model constitutes a reliable early warning system to policy makers on the likelihood of impending currency crisis in the country.


Introduction
Following the collapse of the Bretton Woods system of fixed exchange rates in March 1973, the frequency and costs of currency crises have increased substantially. This unfortunate collapse led many developed countries to adopt the flexible exchange rate system while most developing countries responded by attempting to sustain their fixed exchange rate parities. Eventually, some of these developing countries abolished the fixed exchange rate system and embraced intermittent adjustments by implementing regimes such as the crawling pegs or the managed float. Their strategy is to avoid current account problems and currency crises via exchange rate policies.
Consequently, exchange rate setting in those countries became the role and concern of monetary authorities rather than that of the market forces.
In Nigeria, exchange rate policies are implemented by the Central Bank of Nigeria (CBN) and consistently targeted at avoiding substantial misalignments as well as achieving a realistic Naira exchange rate that is capable of addressing the basic problems of the country's external sector. These ranged from a fixed exchange rate regime prior to 1986 to various forms of floating exchange rate system, following the liberalization of the foreign exchange market in 1986. Consequent upon the adoption of Social Adjustment Programme (SAP) in 1986, the Second-tier Foreign Exchange Market (SFEM) was introduced as a market-driven mechanism for foreign exchange allocation. Currently, foreign exchange transactions are guided by the Wholesale Dutch Auction System (WDAS), which was introduced on the 20th of February, 2006.
Historically, many currencies of the world have suffered crashes. These include the  Hutchison and Noy (2002) found a 5-8 per cent currency-crises-caused output reduction in emerging market economies while Bordo et al. (2001) estimated currency crisis cost amounting to 5-10 per cent of GDP. There is also evidence that currency crises can result to banking crises (i.e. the twin crises), especially when the banking sector holds substantial unhedged foreign liabilities during periods of sharp exchange rate depreciation (Glick and Hutchison, 2001). In this regard, the balance sheets of banks are negatively affected as the domestic currency value of their foreign liabilities become bloated. These historical perspectives as well as the experiences of the 2008-09 financial crisis underscores the pervasiveness as well as the spread of currency crises via contagion.
Reinforced by the recent global financial crises is the need for early warning systems, as most of the past crises episodes were largely unpredicted and preemptive policies could not be taken to avoid their impending costs. To the knowledge of this study, no work has been done to model currency crises in Nigeria, especially after the 2008/09 global financial crisis which led the government to substantially intervene in the foreign exchange market (using foreign exchange reserves) in order avoid large changes in exchange rate. This paper seeks to bridge this gap by modeling the probabilities of currency crises in Nigeria as a function of selected macroeconomic variables, using a logistic function.
The rest of the paper is structured as follows. The next section reviews related empirical literature, with particular attention to variable selection and estimation methods.
Section 3 focuses on the methodology for the study. The results are presented and discussed in section 4 while the final section concludes.

Literature Review
The first step in the measurement of currency crisis relates to crisis definition. A narrow definition includes successful attack on the currency that results in a substantial depreciation of the exchange rate. Based on this definition, studies such as Frankel and Rose (1996) defined currency crisis as a nominal depreciation of 25 per cent or greater, which is at least 10 per cent greater than the depreciation in the preceding year. Raising the threshold a little, Leaven and Fabian (2008) defined currency crisis as a nominal depreciation of the currency of at least 30 per cent that is also at least 10 per cent increase in the rate of depreciation compared to the year before.
In a broader sense, currency crisis is defined as a speculative attack on a country's currency that can result in a sharp depreciation or the need for the government to intervene in the market by selling foreign exchange reserves. This definition includes episodes of unsuccessful attacks as captured by large changes in the index of while Kaminsky and Reinhart (1999) used a three standard deviation cutoff.
In terms of models of currency crisis, there are two popular methodologies in literature.
These have been extensively used in the generation of early warning signals for currency crisis. These are the Signals approach, which is a non-parametric approach, and the limited dependent variable regression (Probit/Logit), which is a parametric approach to the anticipation of a currency crisis. The signal approach was introduced by Kaminsky et al. (1998), and further developed by Edison (2003). Kaminsky et al. (1998) monitored the evolution of several indicators with a view to assessing their relevance, individually in predicting currency crisis. Thus, if any of the macro-financial variables of a specific country tends to exceed a given threshold during the period preceding a crisis; it is interpreted as a warning signal indicating that a currency crisis in that specific country may take place soon.
On the other hand, the limited dependent variable regression models estimate the probability of a currency crisis as a function of selected factors. The two popular ones are probit and logit models. Within this framework, the currency crisis indicator is modeled as a binary response based on relevant input variables and the model predictions are interpreted as the probability of a crisis (Singh, 2010). The use of nonlinear methods such as probit/logit derives from the nonlinearity in the nature of relationship between economic fundamentals and currency crisis. Examples of empirical works that have used the probit model to predict currency crisis include Eichengreen et al. (1995Eichengreen et al. ( , 1996 and Frankel and Rose (1996). Recently, Berg and Pattillo (1999), Komulainen and Lukkarila (2003) and Kumar et al. (2003) have also analyzed the predictability of emerging market currency crises using probit/logit models, whereas Bussière and Fratzscher (2002) used a more sophisticated multinomial logit model.
The variables often used in logit/probit models of currency crisis include money or domestic credit growth, the fiscal deficit, current account balance, real exchange rate misalignment, and output gap; as well as variables that gauge a country's vulnerability to attacks, such as measures of the adequacy of international reserves relative to possible short-run liabilities of foreign and domestic origin, foreign financing needs, and the overall soundness of the financial sector. Other variables include indicators of market expectations or investors' risk appetite, such as interest rate differentials, and exposure to contagion from crises in other countries. Trade and financial openness may also affect the likelihood of currency crisis (Frankel and Rose, 1996;Kaminsky et al., 1998;Kaminsky and Reinhart, 1998).

Methodology
In this study, currency crisis is defined using the concept of Exchange Market Pressure (EMP) developed by Girton and Roper (1977). They measured the EMP in country 'i' at time 't' as: where ei,t denotes the price of a U.S. Dollar in the country i's currency at the time 't'; ri,t denotes the foreign reserves (excluding gold) of country 'i' at the time 't' and α and β are the weights that equalize the variances of these two components. The first term, have ranged between 1.5 to 3 standard deviations above the mean of the EMP. We decided to use a threshold of 2.0 for this study, similar to Hutchison (2001, 2005) and Glick, et. al. (2006).
Having constructed a currency crisis dummy as outlined above, we estimate a binomial logistic regression that models the probability of a crisis as a function of carefully selected explanatory variables based on the equation below: Electronic copy available at: https://ssrn.com/abstract=3464559 where Pt is the probability that there is currency crisis (i.e.

Results
The computed exchange market pressure based on equation (1)  In terms of magnitude, the coefficient of real exchange rate misalignment is large (0.5761) underscoring its influence on the likelihood of a crash incidence in Nigeria.
The fact that the included explanatory variables enter the model in their one period Electronic copy available at: https://ssrn.com/abstract=3464559 lag implies that they constitute early warning signals for currency crises in Nigeria. In view of the role of oil prices in external reserves accumulation and exchange rate determination in the country, a lag two of the oil price variable was also included in the model. The variable retained its sign as in its lag one but was significant at the 10 per cent level.

Conclusion
The purpose of this study was to examine the predictability of currency crisis in Nigeria during the last two decades based on the logit model. This paper is one of the first applications of the logit model to currency crisis modeling in Nigeria. Factors affecting currency crises were evaluated with special focus on the macroeconomic fundamentals derived from the currency crises theories.
Electronic copy available at: https://ssrn.com/abstract=3464559 The analysis showed that the included macroeconomic variables have statistically significant impact on the probability of currency crises in the country. Particularly, we found that higher real exchange rate misalignment increases the probability of currency crisis in the country. This finding suggests the need for continuous and credible assessment of the naira exchange rate relative to its long run equilibrium value. A widening real exchange rate misalignment indicates the need for a policy shift. Thus, this paper recommends the continued use of market-based exchange rate determination arrangement (such as the current Wholesale Dutch Auction System -wDAS) that is capable of preventing real exchange rate misalignment as a strategy for reducing the probability of currency crisis in the country.