Financial Distress and Early Warning Signals: A Non-Parametric Approach with Application to Egypt

Transcription

1 Financial Distress and Early Warning Signals: A Non-Parametric Approach with Application to Egypt Alaa El-Shazly Department of Economics Cairo University ashazly@cics.feps.eun.eg Paper Prepared for the Ninth Annual Conference of the Economic Research Forum, Emirates, October 2002.

2 Abstract The risks of economic downturn related to business cycle fluctuations and financial distress have raised interest in studying the potential causes and symptoms of banking and currency crises. Policy makers would like to detect those symptoms with sufficient advance so as to adopt preemptive measures. An effective warning system for financial distress should take into account various indicators, as these crises are usually preceded by symptoms that arise in a number of areas. The signals approach to predicting financial crises can serve as the basis for an early warning system. It basically involves monitoring the behavior of a number of indicators as they exceed certain threshold values or critical levels. Since the group of indicators that are issuing signals would be identified, this would provide information about the source and depth of the macroeconomic problems that underlie the probability of a crisis. Based on this information, policy makers would then take appropriate measures to combat these problems in a timely manner. Application of these concepts to the recent financial distress in Egypt shows that, in predicting crises, the signals approach outperforms guesses based on unconditional probabilities. JEL Classification: F31; F41; F47 Keywords: Financial distress; Early warnings; Signals 1

3 Financial Distress and Early Warning Signals: A Non-Parametric Approach with Application to Egypt 1. Introduction The Egyptian economy moved towards a more competitive market-based system in the 1990s. The initial phase of economic reform involved removing the distortions in the price system and impediments to trade and investment. The results of the reforms were positive on the macroeconomic front. The budget deficit was brought down, liquidity was managed, inflation was reduced, exchange rate stability was maintained, external reserves increased, and growth accelerated. The current phase of reform focuses on the microeconomic level by deepening structural reforms to induce a strong and sustainable supply-side response from the private sector. However, there are emerging difficulties in managing the reform process from interrelated factors on the real and the financial side of the economy. In the late 1990s, the Egyptian economy experienced financial distress and a slow down in economic activity. In particular, the pound exchange rate was under pressure and depreciated, foreign reserves declined, the level of non-performing bank loans increased and led to a credit crunch, stock prices fell, investors confidence in public policy declined, and growth prospects deteriorated. These developments were accompanied by deterioration in the trade balance, lower sales-to-inventory ratios, and modest progress on privatization and institutional reforms. The risks of economic downturn related to business cycle fluctuations and financial distress have raised interest in studying the potential causes and symptoms of banking and currency crises. Policy makers would like to detect those symptoms with sufficient advance so as to adopt preemptive measures. While accurately forecasting the timing of financial crises remains a difficult task, governments need to develop and improve upon an early warning system that monitors leading indicators of whether the economy is heading to a crisis situation. Focusing on financial crises, this paper gives a brief review of the theoretical and empirical literature and, on the basis of which, discusses the design of a specific early-warning system for Egypt 1. The discussions will shed light on the main approaches to assessing the usefulness of potential indicators on banking and currency crises and identifying the leading ones. After comparing the relative merits of alternative approaches in designing an early warning system, the paper studies a specific methodology for forecasting the timing of turbulence in financial markets that is appropriate to the case of Egypt. The specific methodology for an early warning of financial distress that is discussed in this paper is based on the so-called signals approach. This approach involves monitoring the evolution of a number of economic indicators that tend to systematically behave differently prior to a crisis. A certain threshold is then determined for each indicator which, when exceeded, issues a warning signal that a crisis may occur within a reasonable period of time. 1 The paper draws on the work of Kaminsky, Lizondo, and Reinhart (1998), Kaminsky and Reinhart (1999), and Kaminsky (1999). See also Berg and Pattillo (1999) and Kaminsky and Reinhart (1998). 2

4 The paper is organized as follows. Section 2 presents an overview of the theoretical and empirical literature on financial distress, including the main methodologies and variables that have been used to assess the probability of a crisis. Section 3 discusses the relative merits of the alternative methodologies and studies a specific procedure to design an early warning system for the Egyptian economy. Section 4 offers an evaluation of the predictive power of the empirical model, based on in-sample and out-of-sample probability forecasts. Section 5 gives conclusions and policy implications. 2. The Literature The main explanations of banking and currency crises that have been presented in the theoretical literature can be broadly classified into two categories, namely, the firstgeneration models and the second-generation models. The first-generation models represent the traditional approach to explaining financial distress, which emphasizes the role played by weak economic fundamentals in inducing a crisis. The second-generation models, on the other hand, hold that economic policies are not predetermined but respond to changes in the economy. As economic agents take this relationship into account in forming expectations about the state of the economy, it is possible to have multiple equilibria and self-fulfilling crises First-Generation Models According to the traditional approach, as developed by Krugman (1979), financial crises are essentially caused by excessive credit expansion, which leads to a gradual but persistent loss of international reserves. Under a virtually fixed exchange-rate regime, economic agents anticipate that the authorities will eventually abandon the parity with the depletion of international reserves. They also understand that even in the absence of a speculative attack on the currency they would still suffer a capital loss on their holdings of domestic money (because of depreciation). Speculative attacks ultimately take place and balance-of-payments crises normally follow. Clearly, to the extent that excessive money creation may result from the public sector borrowing requirements, fiscal imbalances also could serve as indicators of an impending crisis. Extensions of the traditional approach show that a real appreciation of the currency and a deterioration of the trade balance would generally precede speculative attacks. Other variants introduce uncertainty about credit policy or about the level of reserves losses that the authorities are willing to sustain to defend the parity and show that domestic interest rates would increase as a crisis becomes more likely. Thus models of the traditional approach suggest the evolution of domestic credit, particularly to the public sector, international reserves, real exchange rate, the trade balance, and domestic interest rates could be used as leading indicators of crises. As witnessed in the recent Asian crisis, weaknesses in the banking system can contribute to the onset and depth of financial crises. These weaknesses stem largely from excessive credit expansion under inadequate prudential supervision, resulting in a large share of high-risk 2 Surveys of the theoretical literature on currency crises can be found in Agenor, Bhandari, and Flood (1992), Blackburn and Sola (1993), Obstfeld (1994), and Flood and Marion (1998). See also Diaz-Alejandro (1985), Velasco (1987), Sachs, Tornell, and Velasco (1996), and Mishkin (1997) for the links between balance-ofpayments crises and problems in the banking sector. 3

5 loans in bank portfolios. They are often magnified in the wake of currency turmoil, as speculative attacks accompanied by bank runs and by a period of high domestic interest rates can push many domestic firms from illiquidity into insolvency. Banking and currency crises have tended to cluster and have come to be known as the twin crises. 2.2 Second-Generation Models Some recent models of financial crises e.g. Ozkan and Sutherland (1995) argue that governments may face a trade-off between maintaining exchange-rate parity and other policy objectives that can pull the economy into an attack. According to this class of models, leading indicators of currency crises include such variables as the stock of public debt, the proportion of non-performing loans, and central bank credit to banks. These indicators reflect fiscal concerns and banking problems. More precisely, an increase in domestic interest rates needed to maintain a fixed exchange rate might result in higher financing costs for the government. Thus, out of concern for the fiscal consequences of their exchange rate policy, the authorities decision to abandon the parity may depend on the stock of public debt. Also, higher interest rates may weaken the banking system through moral hazard and adverse selection problems, and the authorities may prefer to devalue rather than incur the cost of a bailout under implicit or explicit financial safety net. Leading indicators may also include political variables, e.g., change in government and degree of political instability. Recent models also suggest that crises may develop without a significant change in economic fundamentals, as discussed for instance in Obstfeld (1996). These models emphasize that the contingent nature of economic policies may give rise to multiple equilibria and generate selffulfilling crises. Multiple equilibria mean that the economy can move from one state of equilibrium to another without any noticeable change in the fundamentals. Thus, the economy may be initially in a state of equilibrium consistent with a fixed exchange-rate regime but a sudden worsening of growth prospects may lead to changes in policies that result in a collapse of the exchange regime, thereby validating agents expectations. This circularity between the expectations of economic agents and policies generate self-fulfilling crises. As such, this class of models suggests that it may be difficult to find a straight relationship between fundamentals and crises, as sometimes crises may take place without a previous significant change in fundamentals. In general, financial distress is likely to combine elements of both the first- and the secondgeneration models. The traditional approach emphasizes weak fundamentals in the economy and shows the link between banking problems or fiscal imbalances and currency crises. On the other hand, the models of self-fulfilling crises show that a worsening of expectations (e.g. due to external factors or a shift in domestic demand) may trigger changes in economic policy and eventually lead to banking and balance-of-payments problems. Both arguments help to explain the situations of financial distress, which are more common in emergingmarket economies. 2.3 Empirical Methodologies The empirical work on banking and currency crises is mainly concerned with assessing the probability of a crisis. Basically, there are two alternative methodologies that can serve as 4

6 early warning systems of financial distress. 3 First, one may use a multivariate logit or probit model to estimate the one-step (or k-step) ahead probability of banking or currency crises. Second, one may hold a comparison of the behavior of selected variables in the period preceding crises with their behavior in a control group, and identify (using parametric and non-parametric techniques) those variables that are particularly useful in assessing the likelihood of a crisis. A variant of this approach constructs a warning system based on signals issued by those selected variables. It uses a non-parametric approach to evaluate the usefulness of several variables in signaling an impending crisis. The latter approach involves monitoring the evolution of a number of economic variables whose behavior usually departs from normal in the period preceding financial crises. Deviations of these variables from their normal levels beyond a certain threshold value are taken as warning signals of financial distress within a reasonable period of time. Based on the track record of the various indicators, it is possible to assess their individual and combined ability to predict crises. While not restricted to high frequency data, these methodologies mainly use monthly and quarterly data. Also, the definition of a currency crisis employed in the empirical literature varies across studies. Most of the studies focus on devaluation episodes. Some examine large and infrequent devaluation whereas others discuss small and frequent devaluation that may not be described as a currency crisis. A few studies adopt a broader definition of crises by including, in addition to devaluation, episodes of unsuccessful speculative attacks. These are attacks that were averted without devaluation but at the cost of a significant increase in domestic interest rates or a substantial loss of international reserves. Situations of banking crises are mainly identified by the closure, merging, or takeover by the public sector of one or more financial institutions whether there are bank runs or not. A liquidity squeeze is also a sign of banking distress. Leading Indicators Studies on financial crises have used a large variety of indicators, comprising the various sectors of the economy. 4 The indicators that have proven to be most useful in predicting crises, based on formal quantitative assessment, can be identified as leading indicators. The indicators that worked best and were found to be statistically significant include such economic variables as: real exchange rate, M2/international reserves, money growth, banking crises, real interest rates, domestic credit to public sector, international reserves/imports, trade balance, and terms of trade. It is noteworthy that these findings are derived from studies that examine the experience of various countries, and so are suitable for generalization. The case studies of individual countries may exclude some of these variables if found statistically insignificant and include other country-specific indicators. For this reason, when studying the case of Egypt, it will be appropriate to select indicators that take into account the specific characteristics of that economy. 3. Early Warning System The relative merits of the alternative approaches that could serve as the basis for an early warning system of financial distress can help in deciding on the appropriate methodology for 3 See Kaminsky, Lizondo, and Reinhart (1998), and Demirguc-Kunt and Detragiache (1998, 2000), and the references cited therein. 4 Kaminsky et al. (1998) gives a listing of the indicators. 5

7 the case under study. The methodology that estimates the one-step (or k-step) ahead probability of banking or currency crises has the advantage that it summarizes the information about the likelihood of a crisis in one useful number, the probability of financial distress. Also, this approach considers all the variables simultaneously and disregards those variables that do not contribute information that is independent from that provided by other variables already included in the analysis. This methodology, however, has some important limitations. First, it does not provide a way for ranking the indicators according to their ability to predict crises, since a variable either enters the regression significantly or it does not. Also, the nonlinear nature of these models makes it difficult to assess the marginal contribution of an indicator to the probability of a crisis. Second, the method is not transparent on the characteristics of the macroeconomic problems. Within this approach, it is difficult to judge which of the variables is out-of-line, limiting its usefulness for surveillance and preemptive action. In contrast, the signals approach provides information on the source and depth of the macroeconomic problems that determine the probability of a crisis. Also, within this approach it is possible to estimate the probability of a crisis conditional on the signals issued by various indicators. This conditional probability of crisis will depend directly on the reliability of the indicators that are sending the signals. That is, for signals sent from a given number of indicators, the probability of a crisis conditional on those signals will be more accurate if the signals are coming from a reliable group of indicators (leading indicators). Based on these considerations, the signals approach seems to be better suited to serve as the basis for an early warning system. 3.1 The Signals Approach The following definitions help in describing the signals approach at the operational level. Crisis: (a) For the exchange market, a crisis is defined as a situation in which an attack on the currency leads to a sharp depreciation of the currency, a large decline of international reserves, or a combination of both. This includes both successful and unsuccessful attacks on the currency. In Kaminsky et al. (1998), crises are identified (ex-post) by the behavior of an index of exchange market pressure. This index is a weighted-average of monthly percentage changes in the exchange rate and monthly percentage changes in international reserves. The weights are chosen so that the two components of the index have the same conditional variance. As the index increases with depreciation of the currency and with a loss of international reserves, an increase in the index reflects stronger selling pressure on the domestic currency. Periods in which the index is above its mean by more than three standard deviations are defined as crises. Examining developments in foreign exchange markets during the periods identified as crisis checked the appropriateness of this operational definition for a sample of developing and industrialized countries. However, since this operational definition was just appropriate for a particular sample and need not be generalized to all countries, observing the occurrence of events that indicate turbulence in the exchange market may directly identify currency crises for any one country. 5 Examples of such events include the 5 Applying the operational definition of a currency crisis as in Kaminsky et al. (1998) to Egyptian data produced results that were inconsistent with actual developments in the exchange market. This outcome was insensitive to alternative assumptions about the behavior of the index of exchange-market pressure. For this reason, currency crises in Egypt were directly identified from observed events that indicated turbulence in the exchange market as discussed further below in the text. 6

8 introduction of exchange controls, a change in the exchange rate regime, a significant devaluation beyond the established rules of a prevailing crawling peg regime or exchange rate band, a significant devaluation under a fixed exchange-rate regime, and/or a substantial loss of international reserves. (b) For the banking sector, a crisis is defined as a situation characterized by the closure, merging, or takeover by the public sector of one or more financial institutions. Banking distress can be also directly identified from observed signs of a liquidity squeeze, such as significant increases in inter-bank rates. Indicators: Theoretical priors, country-specific experience, and the availability of high frequency data, such as monthly observations, determine the choice of indicators. Signaling horizon: This is the period within which the indicators would be expected to have ability for predicting crises. A signal that is followed by a crisis within a reasonable period of time is called a good signal while a signal not followed by a crisis within that interval of time is called a false signal or noise. In this regard, however, there is no general accepted criterion of selection of a reasonable period of time. For all practical purposes, the signaling horizon may range from 6 12 months depending on the data sample and country-specific factors. Signals and threshold: An indicator is said to issue a signal whenever it exceeds a given threshold level. Threshold levels are chosen so as to strike a balance between the risk of missing many crises and the risks of having many false signals. These risk situations would happen, respectively, if the signal is issued only when the evidence is overwhelming, and if a signal is issued at the slightest possibility of a crisis. If the threshold is too tight to reduce the number of false signals, the type I error (rejecting the null hypothesis of crisis when in fact there is a crisis) is large. In contrast, if the threshold is too slack, i.e. too close to normal behavior, it is likely to catch all the crises but it is also likely to announce many crises that never happened. In this case, the type II error (accepting the null hypothesis of a crisis when in fact there is none) will be large. For each of the indicators, the following two-step procedure is used to obtain the optimal set of thresholds that will be employed in the empirical application. First, thresholds are defined in relation to percentiles (10 percent) of the distribution of observations of the indicator. Second, a grid of reference percentiles is considered and the optimal set of thresholds is defined as the one that minimizes the noise-to-signal ratio, i.e. the ratio of false signals to good signals. Application to Egypt The Egyptian economy implemented economic reform and structural adjustment programs in the first half of the 1990s. During that period, economic variables were in a transitory state before evolving around new normal levels as an outcome of the reform effort. The various macroeconomic indicators started to respond to the new policy environment by the mid- 1990s and the economy was generally in a good normal condition through late Emerging difficulties in the economy and symptoms of financial distress started to surface in 1999 with turbulence in the exchange market related to a deteriorating trade balance, and a liquidity squeeze related to increases in non-performing loans. The liquidity crisis was manifest in the significant increase of inter-bank rates from 9 percent to 16 percent. Two major crises can be identified for the 1999 early 2001 period. (1) In March 1999, the central bank introduced administrative measures that essentially rationalized the demand for foreign currency and domestic credit to restore exchange-market stability and ease liquidity 7

9 especially that inter-bank rates increased significantly. (2) In January 2001, the authorities introduced new arrangements in the exchange market that effectively allowed a crawling peg and devalued the currency to avoid an attack on the pound. While there is one other event which may qualify as a sign of financial distress according to the above definition of a banking crisis, it can be overlooked as being more of a banking sector restructuring (in tranquil period) than a banking crisis per se. That event is the merger of two real-estate specialized banks in mid-1999 and will not be considered in the present analysis. It should also be mentioned that further exchange-rate adjustments took place in August 2001 that would qualify for the definition of a currency crisis. In particular, the authorities allowed a wider band for exchange rate movements (within 3 percent compared to an earlier one percent of the market-based rate of the central bank) and further devalued the domestic currency. This incident of financial distress will be used, however, for out-of-sample assessment of the usefulness of the empirical model in predicting crises as discussed below in Section 4. Taking into account these factors, we may consider the period January 1995 December 2000 as a relevant time span for studying the signals approach to banking and currency crises. In the case of Egypt, this period comprises both normal conditions of the economy ( ) and recent financial distress. Before 1995, the economy was in a state of transition and observations on various macro indicators may not be helpful in forecasting crises under normal conditions of tranquil times (the control group). Similarly, going beyond December 2000 will not add to the in-sample forecasting ability of economic indicators, as there is only one major symptom of financial distress immediately after that date as mentioned above. The indicators used in the analysis are determined in light of the availability of monthly information for closer monitoring of economic developments, and of the country-specific factors that are consistent with theoretical priors as possible explanation of the recent financial distress. The list of potential indicators includes: (1) Exports (2) Imports (3) Trade balance (4) Net international reserves (NIR) (5) M2/NIR (6) Interest rate differential (7) Real exchange rate (RER) (8) Domestic credit/gdp (9) Stock price index The source of data for indicators (1) - (3) is the International Monetary Fund s International Financial Statistics; for indicators (4) - (8) is the Central Bank of Egypt; and for the stock price index is the Capital Market Authority. The data for exports, imports, trade balance, and NIR is in US dollars. The ratio of broad money (M2, converted into US dollars) to NIR reflects stock imbalances and is used to define whether reserves are low or high. The interest rate differential is calculated as the difference between the return on 3-month pound deposits and the return on 3-month US dollar deposits, adjusted for exchange rate appreciation. The exchange rate indicator is measured as deviation of the real pound-dollar exchange rate index from trend (in percentage terms). The ratio of 8

10 domestic credit to GDP reflects monetary and banking sector stability. This indicator is measured in real terms, where domestic credit in current pounds is deflated by the consumer price index (CPI), and the monthly data for real GDP is interpolated from annual observations using a cubic spline function. 6 Lastly, the stock price indicator is the general index of the Capital Market Authority. For the listed variables other than the exchange rate and the interest rate differential, the indicator on a given month is defined as the percentage change in the level of the variable with respect to its level a year earlier. Filtering the data by using the annual percentage change ensures that the transformed variables are stationary and free from seasonal effects. As will be discussed in the next subsection, the listed variables will be ranked according to their forecasting ability and the low scoring indicators will be removed from the list if they are not helpful in predicting crises. 3.2 Non-Parametric Techniques The effectiveness of the signals approach can be examined at the level of individual indicators and at the level of a set of indicators. That is, we can examine the extent to which an individual indicator is useful in anticipating crises, and the extent to which a given group of indicators taken together is useful in anticipating crises. The empirical analysis normally focuses on ranking the various indicators according to their forecasting ability and examining the lead time and persistence of their signals. The information on the various indicators can then be combined to estimate the probability of a crisis conditional on simultaneous signals from any set of indicators as in Kaminsky (1999). In the present analysis, the signaling horizon for financial distress will be defined as 6 months. This is determined in light of the number of observations and crises, and the grid search for optimal percentiles. With two major crises identified for the period under study, the signaling horizon of 6 months would require the grid search to allow at least 12 months for testing the forecasting ability of the various indicators. Given 72 monthly observations for each indicator over the period , one may then consider a grid of reference percentiles between 20 percent and 30 percent. As already noted, the optimal set of thresholds is the one that minimizes the noise-to-signal ratio. For variables such as exports, trade balance, international reserves, RER, and stock price index, for which a decline in the indicator increases the probability of a crisis, the threshold is below the mean of the indicator. For other variables, such as imports, interest rate differential, M2/NIR, and domestic credit/gdp, for which an increase in the indicator raises the probability of a crisis, the threshold is above the mean of the indicator. To examine the effectiveness of individual indicators, it is useful to consider the performance of each indicator in terms of the following matrix due to Kaminsky et al. (1998): Table 1: Signals and Crises Crisis (within 6 months) No Crisis (within 6 months) Signal was issued A B No signal was issued C D 6 See, for example, Judge et al. (1985). 9

11 In this matrix, cell A is the number of months in which the indicator issued a good signal. Cell B is the number of months in which the indicator issued a bad signal or noise. Cell C is the number of months in which the indicator failed to issue a signal that would have been a good signal. Finally, Cell D is the number of months in which the indicator did not issue a signal that would have been a bad signal. A perfect indicator would only produce observations that belong to cell A and cell D of the matrix. It would issue a signal in every month that is to be followed by a crisis (within the next 6 months), so that A > 0 and C = 0. It would also refrain from issuing a signal in every month that is not to be followed by a crisis (within the next 6 months), so that B = 0 and D > 0. In practice, it is difficult to have perfect indicators in this sense. Nevertheless, the above matrix will be a useful reference to assess the performance of each indicator. Information on the performance of individual indicators is presented in Table 2. The first column of the table shows a measure of the tendency of individual indicators to issue good signals (their forecasting ability). It shows the number of good signals issued by the indicator as a share of possible good signals (A/(A+C) in Table 1). To have a score of 100 percent, a signal must be issued every month during the 6 months prior to each crisis. The second column of Table 2 measures the performance of individual indicators with regard to sending bad signals. It shows the number of bad signals issued by the indicator as a share of possible bad signals (B/(B+D) in Table 1). The lower the number in this column the better is the indicator ceteris paribus. The third column of Table 2 combines the information about the indicators ability to issue good signals and to avoid bad signals into a measure of the noisiness of the indicators, namely the noise-to-signal ratio. This ratio is obtained by dividing the number of bad signals issued by the indicator as a share of possible bad signals, by the number of good signals issued by the indicator as a share of possible good signals ([B/(B+D)]/[A/(A+C)] in Table 1). The lower is the number in this column the better is the indicator ceteris paribus. The noise-to-signal ratio can be used as a criterion for deciding which indicators to remove from the list of potential indicators. A signaling device that issues signals at random times would obtain a noise-to-signal ratio equal to unity. Therefore, those indicators with a noiseto-signal ratio equal or higher than unity would introduce excessive noise, and so could be dropped from the analysis. An alternative way to measure the noisiness of the indicators is to compare the probability of a crisis conditional on a signal from the indicator with the unconditional probability of a crisis, respectively, A/(A+B) and (A+C)/(A+B+C+D) in terms of Table 1. This is shown in columns 4 and 5 of Table 2. If the indicator has useful information, the conditional probability will be higher than the unconditional one. The two criteria for deciding on the predictive power of the indicators, namely, the noise-to-signal ratio and the difference between the conditional and unconditional probabilities of a crisis, are equivalent. Based on these criteria, the following variables lacked predictive power and were removed from the list of potential indicators: exports, interest rate differential and domestic credit/gdp. As can be seen from Table 2, the remaining indicators differ significantly with respect to their noise-to-signal ratio. While this ratio is 0.27 for the real exchange rate, it is 0.73 for imports. Based on this criterion for ranking the indicators according to their ability to 10

12 predict crises while producing few false alarms, the real exchange rate is the top-ranked indicator. [Insert Table 2 here] It should be mentioned that the noise-to-signal ratios reported in Table 2 correspond to the optimal set of thresholds for the individual indicators. Precisely, for each indicator, a grid search was performed for threshold values corresponding to percentiles between 20 and 30 percent of the distribution of observations of the indicator. The optimal set of thresholds or critical levels was then defined as the one that minimized the noise-to-signal ratio. Table 3 lists the optimal set of threshold values for the selected indicators of the recent financial distress in Egypt. [Insert Table 3 here] From such a grid search, the indicator value that can cast worrying concerns about the fragility of the economy, though not yet reaching a critical level for signaling an impending crisis may be also determined. For example, one can consider the indicator value corresponding to 5 percent less than the percentile of the optimal threshold value on the grid search scale. Such indicator values (issuing mild signals) are worth monitoring by the authorities as appropriate policy measures at an early time may prevent the economic indicators from even crossing their threshold values of predicting a crisis. Lead Time of the Signals In focusing on the 6-month window prior to the onset of the crisis, the criteria for ranking the indicators presented in Table 2 does not distinguish between a signal given 6 months prior to the crisis and one given one month prior to the crisis. Policy makers who want to implement preemptive measures will not be indifferent between an indicator that send signals well before the crisis occurs and one that signals only when the crisis is imminent. To examine the lead time of a signal, we observe for each of the indicators considered the number of months in advance of the crisis when the first signal occurs. The selected indicators in the present analysis send the first signal 6 months before the crisis erupts and so they offer a reasonable lead time. Hence, on this basis, the indicators are leading rather than coincident, which is consistent with the idea of an early warning system. It should be noted, however, that the lead time may well vary among the indicators depending on the sample data. Persistence of the Signals Another desirable feature in a potential leading indicator is that signals be more persistent prior to crises (i.e. during the 6-month window) than at other times. To assess the behavior of the indicators in this regard, Table 4 presents a summary measure of the persistence of the signals (measured as the average number of signals per period) during the pre-crisis period relative to tranquil times. This concept of persistence is just another way of looking at the noisiness of the indicators; the measure in Table 4 is just the inverse of the noise-to-signal ratio. 11

13 As in Table 2, the indicators are ranked according to their performance. For instance, for the real exchange rate, signals are roughly four times more persistent prior to crises than in tranquil times. For the top-tier indicators, signals tend to be at least twice as persistent in precrisis periods relative to tranquil times. [Insert Table 4 here] Likelihood of Financial Distress The information provided by all the indicators can be combined to assess the likelihood of an upcoming crisis. One way of capturing the fragility of the economy at the onset of crisis is to keep track of the number of signals being issued in the economy. The larger the number of signals, the higher is the probability of a financial distress. Let X denote the vector of n indicators. In any period, there may be anywhere between zero and n signals. Thus, a composite indicator may be defined as n I t = S t j= 1 j (1) j j where S t is equal to one if variable j ( X t ) crosses the threshold in period t and zero otherwise. This composite indicator, however, does not account for the different forecasting accuracy of each variable. To correct for this, the signals of different variables may be weighted by the inverse of their noise-to-signal ratio (or, equivalently, by the persistence of the signals). Thus, a more accurate composite indicator may be defined as I * t = n j= 1 S ω j t j (2) where ω j is the noise-to-signal ratio of variable j. It is noteworthy that, as with the individual indicators, a critical value can be chosen for the adjusted or weighted composite indicator (2) so that when I * t crosses the threshold, a crisis is deemed to be imminent. This methodology is equivalent to deciding the optimal stoppingtime. That is, at each point of time the decision-maker faces the choice of whether to signal an upcoming crisis or not to signal one and wait for more observations. Figure 1 shows the performance of the weighted composite index for the period July 1998 December 2000 of financial distress. The index reflects the degree of fragility of the economy. It is an index of vulnerabilities in the banking sector and the balance of payments to assess the likelihood of an upcoming crisis. The index is relatively high for the 6 months window before the first crisis of March It then declines and fluctuates through Mid-2000, before recording significant levels for the 6 12

14 months window prior to the second crisis of early So the fragility index captures to a reasonable extent the turbulence in markets and the onset of crises. [Insert Fig. 1 here] Using the sample distribution of the fragility index and the distribution of crises, time-series probabilities of crisis can be calculated. These are conditional probabilities of banking and currency crises as follows: Months with I * t = k and a crisis within h months P( C I * t, t+ h t = k) = (3) Months with I * = k where P denotes probability, ( C I * k) t t + h t = t, is the occurrence of a crisis in the time interval [t, t + h], given that the fragility index at time t is equal to k, and h = 6 in the present analysis (the 6 months window). Note that the fragility index is just a weighted sum of indicators signaling a crisis (the weighted composite index). Figure 2 displays the probabilities given by equation (3) and shows significant scores for the probability of crisis during the 6 months preceding each of the two crises identified for the period 1999 early 2001 in Egypt. (Note that the figure is somewhat choppy because probability takes a limited number of values in the present analysis.) The conditional probability of crisis is especially high for the 6 months window prior to the crisis of March This is consistent with the performance of the fragility index as depicted in Figure 1. [Insert Fig. 2 here] 4. Model Evaluation The signals approach to forecasting the probability of crisis does not lend itself to hypothesis testing; it gives no indication of when results are statistically significant. Nonetheless, the forecasting ability of the signals approach can be evaluated in terms of accuracy and calibration. The probability forecasts are evaluated with an analog of a mean squared error measure, namely, the quadratic probability score (QPS), and with the log probability score (LPS), that evaluate the accuracy of probability forecasts. In addition, overall forecast calibration is measured by the global squared bias (GSB). 7 Goodness-of-fit of the probability forecasts, regarding the fraction of observations that are correctly-called whether for crisis or tranquil periods, can also be measured. 8 The two tests that are implemented to evaluate the probability forecasts in terms of accuracy examine the average closeness of predicted probabilities and observed realizations, as measured by a zero-one dummy variable. Let { P } T t t = 1 denote T probability forecasts, where P t is the probability of crisis in [t, t + h] conditional on information provided by the fragility 7 See Diebold and Rudebusch (1989), and Diebold and Lopez (1996). 8 Berg and Pattillo (1999). 13

15 R 1 index I * in period t. Similarly, let { } T t be the corresponding time series of realizations; t = i.e. the actual time series of observations on C t, t + h, where Rt = 1if a crisis occurs between t and t + h and equals zero otherwise. As above, h = 6 months in the present analysis. The quadratic probability score for the forecasts is 1 QPS = T T t= 1 ( ) 2 P t R t 2 (4) The QPS ranges from 0 to 2, with a score of 0 corresponding to perfect accuracy. The second accuracy-scoring rule is the log probability score, given by 1 LPS = T T [ ( 1 Rt ) ln( 1 Pt ) + Rt ln( Pt )] t= 1 (5) The LPS ranges from 0 to, with a score of 0 corresponding to perfect accuracy. The LPS depends exclusively on the probability forecast of the event that actually occurred, assigning as a score the log of the assessed probability. The loss function associated with LPS differs from that corresponding to QPS, as large errors are penalized more heavily under LPS. The analogy of QPS to mean squared error for probability forecasts is rough, however, because P t is not the forecast of the event (which is a zero-one dummy variable) but the probability of the event. The calibration of a probability forecast refers to closeness of forecast probabilities and observed relative frequencies. Calibration compares the mean forecasted probability to the average realization. Overall forecast calibration is measured by the global squared bias ( P ) 2 GSB = 2 R (6) T T 1 1 where P = P t, and R = R t. The GSB ranges from 0 to 2, with GSB = 0 T t = 1 T t= 1 corresponding to perfect global calibration, which occurs when the average probability forecast equals the average realization. Table 5 shows the accuracy and calibration scores for the in-sample probability forecasts, covering the period July 1998 December 2000 of financial distress. All measures indicate a high predictive power. The table also displays goodness-of-fit for the probability forecasts. Two cut-off levels for the estimated probability of crisis are considered: 50 percent and 25 percent. A crisis period is correctly called when the estimated probability of crisis is above the cut-off level and a crisis ensues within h months. On the other hand, a tranquil period is correctly called when the estimated probability of crisis is below the cut-off probability and no crisis ensues within h months. The model correctly calls a reasonable percentage of observations at the 50 percent cut-off level. The greater part of the crisis and the tranquil periods are correctly called (50 percent and 75 percent, respectively). For the 25 percent cut-off level, the probability forecasts show higher predictive power. The model correctly calls most observations through correct 14

16 prediction of both crisis and tranquil periods (83 percent and 90 percent, respectively). The lower cut-off level reflects a situation in which analysts are more interested in predicting crises than predicting tranquil periods even though they may end up calling too many crises with a higher percent of false alarms, in that no crisis actually occurs within h months. Thus they may want to consider an alarm to be issued when the estimated probability of crisis is just above 25 percent. [Insert Table 5 here] These predictions are better than the unconditional probability of crisis, estimated as the ratio of months in the crisis window (6 months number of crises) over the total number of months for the period July 1998 December The unconditional probability of crisis is 40 percent. Thus, in predicting crises, the signals approach outperforms guesses based on unconditional probabilities. Out-of-Sample Probability Forecasts As mentioned earlier in Section 3.1, the exchange-rate adjustments of August 2001 account for a currency crisis. Thus, the post-december 2000 period can be used to assess the predictive power of the empirical model in forecasting this crisis. Precisely, the out-of-sample probability forecasts for 2001 can provide further evidence on the usefulness of the signals approach for predicting financial distress, as applied to the case of Egypt. There are different ways to forecast 2001 outcomes using the signals approach. One possibility is to apply the optimal thresholds of the leading indicators and the noise-to-signal ratios that we have already calculated to the out-of-sample values of the predictive variables and determine whether the different indicators are issuing signals or not. Alternatively, we can combine the information from the different variables to estimate the probability of crisis on the bases of the weighted composite indicator. The second alternative is more interesting for assessing future fragility and monitoring purposes. Table 6 shows the performance of the out-of-sample probability forecasts. The accuracy and calibration measures of crisis probabilities indicate a high predictive power. The goodness-of-fit scores also indicate that most observations of the crisis and tranquil periods are correctly called at the 50 percent cut-off probability level. These results reinforce the in-sample assessment of the forecasting ability of the empirical model. [Insert Table 6 here] 5. Conclusions and Policy Implications The temporal connections between banking and currency crises as well as their similar roots indicate that it is important to monitor fragility in the exchange market and the banking sector. An effective warning system for financial distress should take into account various indicators, as these crises are usually preceded by symptoms that arise in a number of areas. This paper shows that the signals approach to predicting banking and currency crises can 15

17 serve as the basis for an early warning system. It basically involves monitoring the behavior of a number of indicators as they exceed certain threshold values or critical levels. Indicators with a noise-to-signal ratio less than unity are helpful in anticipating crises and the signaling usually occurs sufficiently early to allow for preemptive policy actions. On any given month, the system would estimate the probability of default within a reasonable period of time (e.g. 6 months) conditional on the indicators issuing signals at that date. Since the group of indicators that are issuing signals would be identified, this would provide information about the source and depth of the macroeconomic problems that underlie the probability of a crisis. Based on this information, policy makers would then take appropriate measures to combat these problems in a timely manner. The usefulness of predicting financial crises depends essentially on the government s incentive to take the necessary steps for correcting the course of the economy without delay. Governments are often reluctant to consider corrective measures that may cause a slowdown in business activity out of concern for popularity issues and on the hope that the underlying macroeconomic imbalances are temporary. However, the risks of deepening crises remain high and may eventually call for more costly reforms. To mitigate this risk, it is helpful that central banks enjoy greater independence in conducting monetary policy with the aim of emphasizing currency and banking stability for the longer-term good of the economy. Also, the availability of high frequency data (with reasonable time lags) that are compiled on sound statistical bases is crucial for close monitoring of the economy. If the data quality is doubtful or the availability of information is subject to significant delays, both businesses and policy makers run the risk of taking wrong and time-inconsistent decisions that can be detrimental to macroeconomic and financial stability. The design of effective early-warning systems necessitates efficient dissemination of information on the real and financial sides of the economy. 16

18 References Agenor, P., Bhandari, J., and Flood, R. (1992), Speculative Attacks and Models of Balance of Payments Crises, IMF Staff Papers, Vol. 39, pp Berg, A., and Pattillo, C. (1999), Are Currency Crises Predictable? A Test, IMF Staff Papers, Vol. 46, pp Blackburn, K., and Sola, M. (1993), Speculative Currency Attacks and the Balance of Payments Crises, Journal of Economic Surveys, Vol. 7, pp Demigruc-Kunt, A., and Detragiache, E. (1998), The Determinants of Banking Crises in Developed and Developing Countries, IMF Staff Papers, Vol. 45, pp Demigruc-Kunt, A., and Detragiache, E. (2000), Monitoring Banking Sector Fragility: A Multivariate Logit Approach, World Bank Economic Review, Vol. 14, pp Diaz-Alejandro, C. (1985), Good-Bye Financial Repression, Hello Financial Crash, Journal of Development Economics, Vol. 19, pp Diebold, F. and Lopez, J. (1996), Forecast Evaluation and Combination, in Maddala, G. and Rao, C., eds., Handbook of Statistics (Amsterdam: North-Holland). Diebold, F. and Rudebusch, G. (1989), Scoring the Leading Indicator, Journal of Business, Vol. 62, pp Flood, R., and Marion, N. (1998), Perspectives on the Recent Currency Crisis Literature, IMF Working Paper No Judge, G., Griffiths, W., Hill, R., Lutkepohl, H., and Lee, T. (1985), The Theory and Practice of Econometrics, New York: John Wiley. Kaminsky, G. (1999), Currency and Banking Crises: The Early Warnings of Distress, IMF Working Paper No Kaminsky, G., Lizondo, S., and Reinhart, C. (1998), Leading Indicators of Currency Crises, IMF Staff Papers, Vol. 45, pp Kaminsky, G. and Reinhart, C. (1998), Financial Crises in Asia and Latin America: Then and Now, American Economic Review, Vol. 88, pp Kaminsky, G., and Reinhart, C. (1999), The Twin Crises: The Causes of Banking and Balance-of-Payments Problems, American Economic Review, Vol. 89, pp Krugman, P. (1979), A Model of Balance of Payments Crises, Journal of Money, Credit and Banking, Vol. 11, pp Mishkin, F. (1997), Understanding Financial Crises: A Developing Country Perspective, in Bruno, M., and Pleskovic, B., Annual World Bank Conference on Development Economics 1996 (Washington, D.C.: The World Bank). 17

19 Obstfeld, M. (1994), The Logic of Currency Crises, Banque De France Cahiers Economiques et Monetaires, No. 43, pp Obstfeld, M. (1996), Models of Currency Crises with Self-fulfilling Features, European Economic Review, Vol. 40, pp Ozkan, F., and Sutherland, A. (1995), Policy Measures to Avoid a Currency Crisis, Economic Journal, Vol. 105, pp Sachs, J., Tornell, A., and Velasco, A. (1996), Financial Crises in Emerging Markets: The Lessons from 1995, Brookings Papers on Economic Activity, No. 1, pp Velasco, A. (1987), Financial and Balance of Payments Crises: A Simple Model of the Southern Cone Experience, Journal of Development Economics, Vol. 27, pp

20 In terms of the matrix of Table 1 A/(A+C) B/(B+D) [B/(B+D)]/[A/(A+C)] A/(A+B) [A/(A+B)] - [(A+C)/(A+B+C+D)] RER International Reserves M2/NIR Trade Balance Stock Price Index Imports Notes: 1. Good signals as percentage of possible good signals. 2. Bad signals as percentage of possible bad signals. Table 2: Performance of Leading Indicators, Signals Approach 3. Noise-to-signal ratio: Ratio of bad signals (measured as a proportion of months in which bad signals could have been issued ) to good signals (measured as a proportion of months in which good signals could have been issued ). 4. Percentage of the signals issued by the indicator that were followed by at least one crisis within the subsequent 6 months. This yields the conditional probability of a crisis given the signals issued. 5. The term yields the conditional probability of a crisis (as in 4) less the unconditional probability of a crisis, [(A+C)/(A+B+C+D)] in terms of the matrix of Table 1. 19