Do Financial Crises Occur in Advanced Economies at Regular Intervals?

Financial series, particularly stock exchange indices, often fluctuate immensely during financial crises. This phenomenon indicates regime changes or structural breaks that cannot be represented by simple linear models or time series. In this study we will use first-order autoregressive Markov switching models in the (MS (2)-AR(1)) to test the hypothesis that international financial crises occur in advanced economies at regular intervals. We have therefore chosen the main stock exchange indices of ten developed OECD countries during the period January 1985-May 2013. Our results allow us, first, to show that there is a strong relation between stock market bear regimes and periods of financial crisis, and second, to validate the hypothesis of recurring periodicity of international financial crises in financial markets, given that these crises happen at regular time intervals: namely, every decade.


Introduction
In the last three decades, the global economy has been marked by a series of international financial crises varying both in type (monetary crises, bank crises, market crashes...) and magnitude, affecting both developed and developing countries.These crises generally occur unpredictably and regularly, and are frequently detrimental to the whole financial and economic system, particularly to the interbank lending and stock markets, on a national, as well as international, scale.An increasing proliferation of these crises, notably the astronomical losses generated in terms of financial and socioeconomic costs by the 2007-2008 international crisis, generated new trends of both theoretical and empirical work, all of it directed towards discerning and understanding the mechanisms that most profoundly contribute to the occurrence of this kind of economic disturbance.The aim of these works is to find ways to address effectively the management and prevention of the phenomenon, before it attains a catastrophic scale.
While closely studying the financial crisis history of the last thirty years, we note that even if each crisis has a unique nature, these crises sometimes display shared causes.According to Rojas-Suarez and Weisbrod (2008), even if each crisis has a unique origin and progression, detailed analysis of all crises reveals the existence of a series of basic mechanisms, which are very similar in nature, even if they differ in intensity and/or occurrence from each other.
In fact, even if, on one hand, the 1929 and 1987 crises, or the 2000 Internet bubble, were due to imbalances on the stock markets (a sharp decline in stock prices or the technology stock market) following speculative bubble bursts, on the other hand, the 1997 Asian crisis and the 2007 subprime crisis derived from dysfunctions in the financial and banking systems (massively unrecoverable debts, excessive risks and depositors' panic...).Nevertheless, detailed analysis of these crises show that these latter two were only results of financial globalization.In effect, financial liberalization has favored the integration of financial markets, the free circulation of capital flows, credit boom, as well as the increased proliferation of financial innovations, which bestows a tremendous power to markets and speculation.This has strongly contributed to the financial and economic system's vulnerability and fragility to various endogenous and exogenous disturbances.Furthermore, not even the countries that had completely sustainable fundamentals were spared by the major   Despite the global magnitude of the 1987 stock market crash, which led some to compare the crash to that of 1929, the 1987 financial crisis did not lead to a global economic crisis.The economic and financial damages of the 1987 financial crisis were limited.The stock market crash affected mainly brokers, such as LF Rothschild in the U.S., whose losses were estimated at 44 million dollars.

The 1997 Asian Crisis
The Asian crisis officially started the 2nd July 1997, when the central bank of Thailand found itself unable to defend its currency and was obliged to let the Baht float.Soon after, in the wake of Thailand's crisis, the Filipino peso, the Indonesian rupiah, and the Malaysian ringgit dropped in value relative to the U.S. dollar in a domino effect; the values of these currencies dropped by over 75 percent.
Corsetti, Paolo and Nouriel (1998), and Goldstein (1998) attribute the cause of the emergence of the 1997 Asian financial crisis to financial liberalization, which led to the appearance of problems in the financial sector.In effect, financial liberalization brought about a credit boom, which was fed by the massive inflow of foreign capital.According to these authors, the rate of credit growth in the Asian countries affected by the crisis became much higher than the rate of GDP growth, and the amount of incoming capital was estimated to be around 75 million dollars from 1993 to 1996.The credit boom led to the deterioration of bank balance sheets.In the countries affected by the Asian crisis, the ratio of non-performing loans grew from 15 to 35% (see for example, Goldstein, 1998).
This crisis also spread beyond Asia.It especially affected the emerging economies of Latin America and Eastern Europe.Investors' fear of a global economic slowdown led to a sharp decrease in the capital flow to developing economies.According to Lozado (1999), the Asian crisis led to a decreased flow of foreign capital to Latin America, which dropped from 100 billion dollars in 1996 and 1997, to 85 billion dollars in 1998.
The 1997 Asian crisis also brought about market capitalization losses on advanced economies' stock markets estimated at 1,700,949 million dollars (see table 1 below).Additionally, the Asian crisis was the source of a global economic slowdown.According to the World Bank (1998), global production dropped by 0.5 percent in 1998, and economic growth in the Middle East, North Africa, Latin America, and the Caribbean dropped by a further 1.0 percent.However, with the exception of Japan, the crisis had less of an impact on the main industrialized countries.

The 2007-2008 Crisis
The global financial crisis of 2007-2008 is the 21st century's first systemic crisis.The crisis started in 2007 following the collapse of the U.S. subprime mortgage market.According to several theorists (Note 6), the 2007-2008 crisis is the result of overly permissive monetary policies, a lack of regulation and supervision of the financial and interbank markets, excessive reliance on the leverage effect, as well as of worldwide macroeconomic imbalances.
The subprime mortgage crisis had negative effects on the entire global economy.The crisis led to the collapse of several stock markets in the early 2008, such as: developing country stock markets (Note 7), which dropped 8%

Stock Markets and Regime Changes
During periods of financial distress, stock indices are frequently subject to dramatic fluctuations.This phenomenon indicates regime changes or structural breaks that cannot be represented by simple linear time-series models.In order to observe the effects of regime changes on stock markets, several studies have made use of Markov switching models introduced by Hamilton (1989).Turner, Startz and Nelson (1989) were the first to use these models to capture stock market regime changes.They emphasized the utility of these models in capturing the behavior of regime changes on the mean and variance.Cheu and al. (1994) studied the relation between stock market returns and stock market volatility by using the autoregressive Markov switching model.Their study highlighted the existence of an asymmetric relationship between market returns and market volatility.Maheu and McCurdy (2000) used the Markov Switching autoregressive Model (MS-AR) to identify different regimes (bull/bear) on the U.S. stock market.
They concluded that MS-AR models were useful for for allowing regime shifts to happen in mean and in variance.Laha (2006) used a Bayesian Markov switching model to capture and predict bull and bear markets on the Indian stock market.Laha concluded that the regime changes regarding themarket were highly correlated to national and international financial events, particularly the 1997 Asian crisis.Similarly, Ismail and Zaidi (2008) used the Markov switching model (MS-AR) in a univariate case to capture the behavior of regime changes of four Main stock indices in Malaysia; namely, the Composite, industrial, financial, and property indices.They emphasized the utility of MS-AR in identifying regime changes in financial time-series.Additionally, Ismail and Zaidi have demonstrated the existence of a strong correlation between bear markets and global economic and financial crises, such as the 1974 spike in gasoline prices, the 1987 stock market crash, and the 1997 financial crisis.

Data
The study is based on monthly frequency data from the period January 1985-May 2013 (341 observations).The data is from the Bloomberg database and relates to the chief stock indices of ten main industrialized countries in the OECD (table 3).All our data sets are analyzed in terms of returns.Thus, for each country, we calculate stock returns.is given by: R it =100* ln ( Where is the stock index of country i during date t. According to the results in our descriptive statistics (table 4), we observe that for the group of countries used in our study, the data set is asymmetrical, has a heavy left tail, and is leptokurtic.Similarly, the results of the Jarque-Bera test require the rejection of the normality hypothesis for the group of our data set.Furthermore, the standard unit root tests show that our ten data sets are stationary (table 5).Note:The regressions of the majority of data sets include only an intercept.The symbol (i) indicates that the data sets include a trend and an intercept.The critical value of 95% for the regressions is -3.44 with trend and -2.88 without trend.

Construction of the Financial Crisis Index
A key element of our study is the construction of binary variables of both national and international financial crises.
To this end, having as principal reference LaevenandValencia's list (2008,2012), we have identified and dated the phases of banking crises (Note 8), currency crises (Note 9), and theSovereign debt crises (Note 10) during the time period of 1985-2013 for each country in our sample (table 6).Let thus be the dummy variable of national financial crises, which will have a unit value when a banking or monetary crisis or debt is observed in a country i at a given time t-and 0 otherwise.
In addition, we have created a binary variable for international financial crises.Let be the dummy variable for international financial crises (See section 2), which has a unit value when an international financial crisis occurs at a given time t, and 0 when it does not.

Econometric Specification
In this study, we will attempt to identify different regimes on the stock markets of 10 main OECD advanced economies during the time period January 1985-May 2013, in order to test the hypothesis of periodic occurrence of international financial crises.
In order to accomplish this, we have chosen Markov switching models, introduced by Hamilton (1989).These models allow us to take into account the asymmetric evolution of the expansion/contraction phases of the cycle, in contrast to the linear models, which require the different phases of the cycle to have identical duration and amplitude.

Hypotheses of the Autoregressive Markov Switching Model
To implement the Markov switching model, the following hypotheses will be needed: H1).The autoregressive order will be assumed to be (p=1).
With the principle of parsimony, we observe that the first-order autoregressive Markov switching model (MS-AR (1)) is the best suited to identify the various regimes in the stock markets of the countries in our work sample.
In this study, we identify the number of states based on a visual examination of the data.From this moment on, we will limit our work to a two-regime Markov switching model.

H3
).The density of the conditional distribution is in this process the general error distribution (GED) law with two different variance for each of the two regimes σ and σ .
The normal density function (iid) could be out of place here, since it does not reflect the thickness characteristic of the distribution tail "fat-tail", which is notably one of the main characteristics of stock returns.By referring to Darrat& al. (2002), we estimate the errors with the law of general error distribution (GED) in order to capture the characteristic too-thick tail distribution (k) and the degree of flatness in our data sets.

H 4 ). Transition probabilities remain constant over time
The classic definition of Hamilton's (1989Hamilton's ( , 1990Hamilton's ( , and 1994) Markov switching model is based on the hypothesis that transition probabilities remain constant over time.

Autoregressive Markov Switching Model
In this study, we will consider a univariate first-order, two-regime Markov switching (MS(2)-AR( 1)).The Hamilton model ( 1989) is defined as follows: We say the process to be an MS(2)-AR(1) process if it satisfies the following equations: S t =j , S t-i =i i,j∈1,2 Where, : is the variable for which we want to determine the evolution in time as a function of past realizations , i =1,…, N.
: follows the law of general error distribution (GED) of variance (Note 11) and parameter .
: is a parameter allowing us to show in our model the fatness of the tail distribution (k being constant in time) For any t, the unobservable variable S t will be 1 when the state is in regime 1, and 2 when it is in regime 2, respectively.In Hamilton's model (1989), S t follows a first-order Markov chain.This means the current regime S t depends solely on the previous (S t-1 .)state's regime.Thus, the S t state follows a first-order Markov chain characterized by the following property: Where , are the transition probabilities.These last ones allow us to measure the probability of transitioning from one regime to another.
Estimating the model is maximizing the log-likelihood (Note 12) function, this allow us to determine the model's parameters ( , , , ,  ,  , , ) and the smoothed and filtered probabilities of the unobserved variable of the MS(2)-AR(1).

Empirical Results
We recall that the goal of this study is to identify, by means of the Ms(2)-AR(1), the different regimes on the stock markets of ten main advanced OECD economies during the period January 1985-May 2013, in order to test the hypothesis that international financial crises occur periodically.The results of estimations for each of our data sets are given by table 7.According to the results of table 7, we note that for the majority of our data sets, the coefficients AR(1) et k aresignificant.Similarly, expected averages of regime 1 are greater than the expected averages of regime 2 .Thus, regime 1 allows us to capture the behavior of stock markets during their growth or bull phases, and conversely, regime 2 allows us to capture the fluctuations of stock markets during their recession or bear phases.
For the majority of our data sets, recession phases are characterized by significant volatility and expected mild average growth in stock returns.In effect, we note that the volatility of the bullish regime 1 ( ) is less than thevolatility of the bearish regime 2 , except for the S&P/TSX index, where the volatility of the bull regime ( 14.58) exceeds that of the bear regime (σ 2 2 =9.38).
Similarly, for most of our data sets, the conditional averages of the bear regime ( are characteristically negatives, except for the IBGM index (μ 2 =0.19).This indicates that for most of the countries in our sample, the average monthly stock returns during recession phases (regime 2) tend to decrease at around 0.08 and 1.54.Reciprocally, the average monthly stock returns during growth phases (regime 1) tend to increase at around 0.10 and 2.94.
Moreover, the probability of staying in the bullish regime 1 is higher than that of staying in the bearish regime 2 for the majority of our data sets, except for the HEX, DAX, TOPIX, and IBGM indices, which are less likely to stay in the bullish regime than in the bearish regime.For the other data sets, the values are between 0.90 and 0.98, while is around 80 and 95.Thus, the duration expectancy of the bullish regime is around 9.87 and 40.49months, and the duration expectancy of the bearish regime is around 5.07 and 28.07 months.This means that the majority of our data sets remains in a bullish regime longer than in a bearish regime.We can thus come to the conclusion that only an extreme event or a shock can shift stock markets from a bullish to a bearish regime.
In addition to the expected average, volatility, and duration of each regime (Bull/Bear), Ms(2)-AR(1) has the advantage of being able to provide smoothed and filtered values of the unobserved variable associated with each of the two regimes (high or low regimes) at a given time t.This also allows us to identify and date the tipping points from one regime to another in our data sets, i.e. the peaks and troughs.
With the aim of testing the hypothesis of international financial crises' periodicity, in this study we will focus solely on bear markets (regime 2) in stock markets of the countries in our sample.Therefore, we have, on one hand, illustrated on the same graph the probabilities curve-smoothed to be in regime 2-and the national (NCI) and international (ICI) financial crisis indices during the time period of January 1985 to May 2013 (figure 2); on the other hand, we have identified and dated the different turning points and the duration of regime 2 (Note

Conclusion
During the last four decades, the global economy has been punctuated by a series of financial crises varying in type and intensity.Some of these crises had global impact and caused enormous losses in terms of financial, economic, and socioeconomic costs.
Starting from the premise that, during the last three decades, major international financial crises that undermin the global economy (i.e., the crises in 1987, 1997, and 2007), seem to occur periodically, we have attempted in this study to provide a framework for the understanding of market behavior dynamics in different regimes (bear/bull).More specifically, on one hand, to emphasize the harmony between bear market peaks and periods of financial crisis, and, on the other hand, to test the hypothesis of the periodicity of international financial crises in financial markets.
Stock market returns are often subject to large fluctuations during financial crises.These fluctuations indicate regime changes or structural breaks that cannot be represented by simple linear models or time series, which is why we have used Markov switching models.These models allow us, moreover, to observe the evolution of stock markets during their bull and bear phases.
We have thus analyzed the monthly behaviors of ten advanced economies in the OECD, monitored during the interval between January 1985 to May 2013; we relied on first order autoregressive Markov switching models in theunivariatecase MS (2)-AR(1).
Our results allowed us, first, to demonstrate, the existence of a strong correlation linking the peaks of the bear regime to the periods of financial crises occurring at a national level; this observation is consistent with the hypothesis of efficient markets exempt from regulatory distortions (Fama, 1970).Second, we were able to conclude that the main economic events that were happening around the world heavily impacted stock market behavior.In fact, the vast majority of the stock markets in our sample database share the same downturns.These downturns match the international crises of 1987, 1997-1998 and 2007-2008, allowing us to a certain extent, to validate the concept of regular cyclic recurrence of financial crises in the world's economically advanced markets.
So will we see a financial crisis in 2017? it is recommended that the used of GARCH Markov switching models -MS-GARCH-on a larger sample, comprising both advanced and emerging economies, in order to make the generalization of our results possible. Figur
on average; the London stock market registered a 5.48% stock index decline; the Australian stock market index (SPI 200) dropped by 41.8%; the Parisian stock market index (CAC 40) dropped by 15.5%; the U.S. stock index (Dow Jones) dropped by 4.02% and the Nasdaq dropped 4.10%; the Hong Kong and Chinese stock indices dropped by 6.20% and 5.55%, respectively.Similarly, the 2007-2008 crisis caused significant production losses, a high tax cost, as well as a sharp increase in public debt in several countries, notably in the large industrialized economies (see table 2 below) and the Asian ones.The International Monetary Fund (2010) has estimated the bank losses at around 2300 billion dollars, almost 16% of the United States' GDP.

Table 8a .
Identification of the bear regime periods