افراط، سطح بازده و شناسایی بحران ارز

Recent literature has attempted to apply Extreme Value Theory (EVT) in the identification of currency crises. However, these approaches seem to have confused the thresholds in extreme modeling with the cutoffs of currency crises. Our paper proposes a Return Level Identification Approach, also based on EVT but overcoming this pitfall. Besides, it includes the conventional identification approach in the most literature as a special case, but relaxes the embedded normality assumption. A detailed procedure is outlined to demonstrate the implementation of the new approach, further illustrated by an empirical study on identifying the currency crises of China. Results are compared and evaluated by different approaches, and reveal remarkable improvement of our approach. We further combine our method with Early Warning Systems and the second-generation crisis models. Results demonstrate better performance of models with crises identified by our approach than those by conventional approach and also the necessity to include market-expectation variables in the prediction.

Ever since the seminal work of the Nobel laureate Krugman (Krugman, 1979), literature on currency crises has been flourished by the three generations of theories (typically, Flood and Garber, 1984, Obstfeld, 1994 and Kaminsky et al., 1998). Although there have been such successful models as the Early Warning Systems (EWS, e.g., Kaminsky et al., 1998), our viewpoint is that two fundamental questions must be answered first: how to define a currency crisis and under what conditions a currency crisis occurs. The disputes upon the first question mainly concentrate on whether currency crises should merely contain the sharp changes of exchange rates: One definition states that currency crises only consist of the speculative attacks that successfully make the currency of a country depreciate (Frankel and Rose, 1996 and Roy and Tudela, 2000); Another popular definition defined a currency crisis as one ‘necessarily entails a speculative attack which causes the exchange rate to depreciate or forces the authorities to defend it by radically raising interest rates or expending reserves’ ( Eichengreen et al., 1995 and Eichengreen et al., 1996). We believe that the latter definition is more accurate, as it takes into account not only the exchange rate risk but also a smart government or central bank that exhibits their ability to ward the currency by either adjusting monetary policies or intervening in the foreign exchange markets, which has become more and more realistic (Eichengreen, 2003). Besides, for countries like China and several other Asian countries, fixed exchange rate regime has been conducted for quite a long period; therefore, this definition combines exchange rate changes with interest rate and international reserves changes to measure the overall pressure on currency (van Horen et al., 2006). As to the second question on identifying currency crises, following the second definition, the standard practice is first to construct a composite index, i.e., the Exchange Market Pressure index (EMPI, henceforth), as a weighted average of exchange rate, foreign reserve and interest rate, then to decide a critical value of this index, and finally to categorize those periods with a higher EMPI than this cutoff as currency crises. Therefore, the main question to identify crises becomes to determine an appropriate critical value of the EMPI. The traditional approach sets the mean plus k times the standard deviation of the EMPI to be the cutoff, with diversified ks in different studies (see, e.g., Eichengreen et al., 1995, Eichengreen et al., 1996, Kaminsky and Reinhart, 1999 and Sachs et al., 1996) and assumes a normal distribution of the EMPI to justify this selection. This method is intuitive and moreover easy to carry out, and thus has a huge group of adherents. It can be naturally interpreted as finding a high quantile of the EMPI distribution, however, with a strong parametric assumption of normality. Several researchers have admitted its arbitrariness nevertheless adopting it at the same time ( Abiad, 2003). Furthermore, conflicting identification results are often obtained for the same periods and same countries under this method if different researchers use different crisis models and EMPIs ( Berg et al., 2003). However, the literature seems not to have identified better alternatives. In recent studies, some researchers started to derive more quantitative identification approaches by the use of Extreme Value Theory, which becomes an acceptable tool in the financial research.1 They abandoned the conventional approach and applied the threshold selection method of plotting the estimates of the tail index in EVT to decide the critical values of currency crises (Pozo and Dorantes, 2003, PAD henceforth; Haile and Pozo, 2006, Pontines and Siregar, 2004 and Pontines and Siregar, 2007). The only difference in these papers are the use of different estimates to the tail index, with the classical Hill estimator (Hill, 1975) in the first two papers and the estimator suitable for small samples (Huisman et al., 2001) in the latter. Applying EVT in the crisis modeling is an inspiring albeit intuitive thought, as currency crises are by principle extreme events in the foreign exchange markets. However, by going deeper into the statistical logic behind EVT, an inherent problem we feel about their approach might be that, the major target to which extreme value statistics develops various methods to decide an appropriate threshold is to obtain a stable distribution for the exceedances, but this threshold is not necessarily equivalent to the cutoff value that triggers currency crises. In other words, currency crisis is an extreme outcome in the foreign exchange market, but the converse is not always true. Besides, the Hill plot method applied in PAD may lead to very poor and misleading estimates of the tail index, if data do not belong to a distribution with a positive tail index or formally a regularly varying tail (Embrechts et al., 1997 and McNeil et al., 2005). These drawbacks of existing approaches give impetus to a new method, which is the main goal of this paper. We also adopt EVT due to its excellence in not imposing strong parametric assumption on the EMPI, and thus overcome this major limitation of the traditional approach. However, our approach completely differs from PAD and their followers', and thus is not exposed to the hazard of disobeying the statistical meaning embedded in EVT. Meanwhile, as we also aim to choose a high quantile of EMPI as the cutoffs of currency crises, the merits of the traditional approach are inherited in our study. The new method is named the Return Level Identification Approach, as this new cutoff corresponds to the return level originated from hydrology.2 To test the practical performance of this new approach, an empirical study on China is conducted which is usually viewed not to have experienced any currency crisis. Another advantage of our approach is that it has more consistency among different pairs of reference or anchor currencies and EMPIs pairs, compared with others. The rest of this paper is structured as follows. Section 2 examines the three well-know EMPIs in the current literature which is the basis of all current identification methods. Section 3 proposes the new approach to identify currency crisis based on EVT and lays out a clear procedure to implement the techniques. Section 4 explores an empirical study on China and compares the results under different approaches. Section 5 proposes the framework to combine the new identification approach with Early Warning Systems and the second-generation crisis models, and provides comparison among various model specifications. Section 6 summarizes the findings and draws some implications for future work.

The identification issue is the building block of all models built for currency crises, including the well-known Early Warning Systems. Current approaches are found to have several drawbacks. This paper develops a new approach to identify currency crises in terms of the Return Level derived from Extreme Value Theory. Our method inherits the nice property of the traditional approach in also selecting a critical value of EMPI using quantile method, but is capable of overcoming the limitation on the strong distributional assumption in the traditional approach. Our approach also comes through the pitfalls that recent literature applying EVT in this area create confusion between the thresholds in extreme modeling and the critical values of currency crises. By exploring an empirical study on China and comparing the results generated by Return Level Identification Approach with the existing approaches, we reveal much more invariance with respect to the distributions of EMPIs and significant consistency over various choices of Exchange Market Pressure indices and anchor currencies under our approach, whereas no such nice consistency but conflicting results are derived from other approaches. In total, three incidences are detected to be currency crises since 1994, which seems to be an unexpected outcome. Another interesting finding is that no currency crises are identified during the recent two years after July 2005 when China built a managed floating exchange rate regime, which at least partly shows the successfulness of this reform from this perspective. Besides, the traditional approach with US dollar the anchor currency, a standard procedure followed by most studies, seems to fail at least in China's case, whichever type of EMPI is used. Throughout, no assumption is imposed on the distribution of the EMPIs. Our new identification approach surpasses the traditional and the recent PAD approach in both theory and practice. Although one can always test the distributional assumption of the data before applying any models, a more general approach would be more useful. In case that the test suggests the existence of normality, our approach covers the traditional approach as a special case. In case of non-normality, the adoption of traditional approaches can be irrelevant and even dangerous sometimes.23 It may report much fewer crises than there actually are. From this perspective, being distributional-free is indeed a remarkable advantage of all EVT-based methods, including ours. We also propose the framework to combine our method with Early Warning Systems and to incorporate the ideas of the second-generation crisis models by including variables which reflects the market expectation. Based on comparisons among various model specifications, we find that the probit models with crises identified by the RLIA approach significantly outperform those with crises identified by traditional approach. The probit model with market expectation and RLIA identified crises exhibit the smallest forecasting error. However, the difference between this model and the MRS model is only slightly significant. Moreover, results show that the introduction of forward-looking variables improves the forecasting properties of the EWS. This confirms the role of market expectation and the adequacy of the second-generation crisis models in explaining the occurrence of currency crises. Nevertheless, according to Frankel and Saravelos (2012), models and indicators found to be useful in one round of crises and certain countries may not be useful to predict the next round and other countries. Therefore, it would be helpful to investigate more countries and longer period in the future study. Moreover, our method may be combined with the signaling approach and extended to determine the critical values of indicators in predicting crises, and this is also left for future study.