Embed Size (px)
Citation preview
Rational speculative bubblesin MENA stock markets
Jung-Suk YuSchool of Urban Planning & Real Estate Studies, Dankook University,
Gyeonggi-do, South Korea, and
M. Kabir HassanDepartment of Economics and Finance, University of New Orleans,
New Orleans, Louisiana, USA
Abstract
Purpose – The purpose of this paper is to examine the existence of rational speculative bubbles inthe Middle East and North African (MENA) stock markets.
Design/methodology/approach – To complement shortcomings of the traditional bubble tests,such as unit root tests and cointegration tests, mainly relying on expectations of future steams ofdividends, the authors employ fractional integration tests and duration dependence tests.
Findings – Despite recent extreme fluctuations of MENA stock markets, fractional integration testsbuilt on autoregressive fractionally integrated moving average models do not support the possibilityof bubbles in the MENA stock markets. Similarly, duration dependence tests based on nonparametricNelson-Aalen hazard functions not only reject the existence of bubbles but also support equality ofhazard functions between domestic and the US-based investors without regard to the rapid financialliberalization and integration in the MENA stock markets.
Originality/value – The reliable results of bubble tests of the MENA stock markets providedomestic and international investors as well as policy makers with invaluable benchmark to betterunderstand the irregular and highly fluctuating stock market behaviors of the MENA stock marketscompared to other developed and emerging stock markets. For domestic and international investors,the formal analysis of MENA stock markets behavior including rational speculative bubbles will helpthem in their portfolio decisions and hedging purposes. Similarly, the empirical results of bubble testsin the paper will be also helpful to policymakers in MENA countries to take actions to improve thefunctioning of these dynamic markets.
Keywords Economic growth, Stock markets, Middle East, North Africa
Paper type Research paper
1. IntroductionReal economic growth rate across the Middle East and North African (MENA) regionaveraged 5.8 percent in 2008, creating benign prospects for most MENA countries inthe region. The Qatar is expected to be the MENA’s fastest growing economy in 2009,with GDP rising by 7.56 percent following its 9.93 percent expansion in 2008. In March2006, Abu Dhabi Commercial Bank launched the first Swiss franc (Sfr)-denominatedFRN for a Middle Eastern bank, with a Sfrs 300 million five-year deal led by BNP
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1086-7376.htm
This paper is a revised version of a working paper titled in “Rational speculative bubbles: anempirical investigation of the Middle East and North African (MENA) stock markets”co-authored by Jung-Suk Yu and M. Kabir Hassan at the University of New Orleans(www.business.uno.edu/econ/workingpapers/2006WP/12-MENA_Bubbles_UNO2007.pdf).The authors would also like to thank anonymous referees for helpful comments on earlier drafts.
Rationalspeculative
bubbles
247
Studies in Economics and FinanceVol. 27 No. 3, 2010
pp. 247-264q Emerald Group Publishing Limited
1086-7376DOI 10.1108/10867371011060054
Paribas which was placed entirely with Swiss accounts for the purpose of riskdiversification from the US dollar deals (EuroWeek, 2006).
While the current state of the economies of the MENA region suggests thateconomic growth will continue to be solid, one may argue that the 10-79 percentincreases in the monthly stock price index returns for most MENA regions were asymptom of persistent deviations of stock prices from the market fundamentals calledrational speculative bubbles, fads, sunspots, or self-fulfilling prophecies as observed inNASDAQ (between November 1998 and March 2000) and Chinese stock market (fromJuly 1994 till June 2001). However, the no-bubble hypothesis cannot be rejected easily ifnonobservable fundamental variables, such as investor rational expectations andmarket sentiment, are the cause of the rapid and sharp divergence of indexes fromfundamental values in the MENA stock markets.
Therefore, for policy-making decisions and international portfolio diversificationpurposes, it is very important to identify whether rational speculative bubbles exist inthe MENA stock market. For example, Chan et al. (2003) explicate that if rationalbubbles are not present, then it is only necessary to take control of the marketfundamentals in conducting monetary policy. Otherwise, positive policy action will beneeded to control expectations from the bubble path.
However, regardless of capital market growth potentials, sizes and rapid financialliberalization in the MENA countries, information on the MENA stock markets tointernational and domestic investors who is seeking portfolio diversification for hedgingpurposes is generally less available than in other financial markets. In the similar vein,despite the potential benefits of portfolio diversification in emerging markets in generaland MENA countries in particular, there is a lack of research and relatively much lessis known about the existence of rational speculative bubbles of MENA stock markets.
For developed and other emerging markets, most previous studies (Brooks andKatsaris, 2003; Chang et al., 2007; Gurkaynak, 2008, among others) have applied bubbletests for integer orders of integration to the log dividend yield or have tested for integercointegration between stock dividends and prices. However, in this paper, tocomplement and overcome well-known shortcomings of the traditional bubble tests,such as unit root tests and cointegration tests, mainly relying on expectations of futuresteams of dividends, we employ newer approaches – fractional integration tests andduration dependence tests – to investigate the evidence of rational speculative bubblesin the MENA stock markets.
For fractional integration tests relying on autoregressive fractionally integratedmoving average (ARFIMA) models, Cunado et al. (2007) test for the presence of rationalbubbles in the Standard & Poor’s (S&P) 500 stock market index by means of amethodology based on fractional processes. Koustas and Serletis (2005) also indicate thatthe notion of fractional integration allows more flexible modeling of the low frequencydynamics of stock prices, dividends, and their equilibrium relationship, while allowingsignificant deviations from equilibrium in the short run. They yield robust rejections ofthe null hypothesis of rational bubbles based on tests for fractional integration andconclude that a fractionally integrated dividend yield is inconsistent with rationalbubbles in annual SP500 composite stock market index from 1871 through 2000.
In addition, many financial researchers have supported duration dependence testsbased on survival analysis in many distinct academic contexts (McQueen and Thorley,1994; Cochran and DeFina, 1996; Chan et al., 1998; Cameron and Hall, 2003; Tudela, 2004;
SEF27,3
248
Buehler et al., 2006; Zhang, 2008; Ali et al., 2009). Traditionally, researchers havepreferred fitting parametric hazard functions such as log-logistic, exponential, Weibull,and Gompertz specifications along with semiparametric tests based on Cox regressionmodel. However, we find that nonparametric hazard functions have much bettersmall-sample properties and are more intuitive to interpret whether hazard functions isdecreasing or increasing. Therefore, we estimate nonparametric Nelson-Aalensmoothed hazard functions together with traditional parametric and semiparametrichazard specifications to investigate duration dependence in runs of positive excessreturns of the MENA stock markets because we have relative small sizes of samples tofit parametric hazard functions. We firmly believe that our approach to plotnonparametric smoothed hazard functions is more reliable to obtain the robustempirical results of duration dependence tests to identify the existence of bubbles in theMENA stock markets.
We summarize the main results as follows. Despite recent extreme fluctuations ofMENA stock markets, we do not find strong evidence of rational speculative bubbles inthe perspective of both domestic and the US-based investors. Fractional integrationtests built on ARFIMA models do not support the possibility of bubbles in the MENAstock markets. Similarly, duration dependence tests derived from nonparametricNelson-Aalen hazard functions strongly reject the existence of bubbles. In addition, itseems that domestic and the US-based investors do not observe rational speculativebubbles in the MENA region, evidenced by the statistically identical hazard functionsacross them, although MENA countries have recently experienced the rapid financialliberalization and integrations with developed countries.
The organization of the paper is the following. In Section 2, provide sample selectioncriteria and descriptive statistics on the MENA stock markets data. Section 3 pointsout empirical challenges of traditional econometric tests to detect rational speculativebubbles. Section 4, describe the newer approaches of rational speculative bubbleidentification. Section 5 analyzes the empirical results. Section 6 concludes the paper.
2. Data and descriptive statistics2.1 Data and sample selection criteriaTo investigate whether rational speculative bubbles exist or not in the MENA region, wecollect monthly S&P/International Finance Corporation Global (IFCG) price indexes ofthe eight MENA stock markets of Bahrain (1999:01-2003:03), Egypt (1996:01-2003:03),Jordan (1979:01-2003:03), Morocco (1996:01-2003:03), Israel (1997:01-2003:03), Oman(1999:01-2003:03), Saudi Arabia (1998:01-2003:03), and Turkey (1987:01-2003:03). Allstock indexes are expressed in local currencies and the US dollar denomination toexamine both domestic and the US-based investors’ perspectives. Then, we computemonthly simple returns rather than continuous compounded returns obtained by logdifferences to perform duration dependence tests to examine the existence of rationalspeculative bubbles in the MENA stock markets.
In addition, reliable dividend yields data are essential to perform formaleconometric bubble tests such as fractional integration tests. Therefore, we considerslightly different sample periods of dividend yields for MENA region from those ofS&P/IFCG price indexes: Bahrain (2000:01-2003:03), Egypt (1996:12-2003:03), Jordan(1984:12-2003:03), Morocco (1996:12-2003:03), Israel (1997:11-2003:03), Oman (2000:01-2003:03), Saudi Arabia (1998:11-2003:03), and Turkey (1987:11-2003:03).
Rationalspeculative
bubbles
249
The source of data is the Emerging Markets Data Base published by S&P’s. Webelieve that S&P/IFCG price indexes are more suitable for our study since they reflectadjusted share price changes and represents stock market performance without takinginto account of restrictions on foreign investors from the domestic investor perspective.According to S&P/IFCG index stock selection guidelines, all of MENA stocks includedin S&P/IFCG indexes must be actively traded and target market share should consist of60-75 percent of total market capitalization. Of course, they should be well-diversifiedacross different industries. Therefore, S&P/IFCG Indexes are intended to representthe performance of the most active stocks in their respective stock markets and to bethe broadest possible indicator of market movements.
2.2 Descriptive statisticsIn Table I, we report descriptive statistics of monthly index returns for eight MENAstock markets. During our sample periods, most of the MENA stock marketsexperienced severe stock markets fluctuations. For the domestic investors’ perspective,Egypt and Turkey are somewhat extreme, evidenced by 7.4 and 19.64 percent ofstandard deviations. Maximum and minimum monthly returns for Egypt and Turkeyare 26.14 percent (79.33 percent) and 211.98 percent (239.27 percent), respectively.Similarly, for the US-based investors’ perspective, Israel and Turkey have the highestuncertainty in their monthly stock market movements among others. Maximum andminimum monthly returns for Israel and Turkey are 14.53 percent (71.29 percent)and 219.07 percent (240.66 percent), respectively.
We also find that except Morocco, Israel, and Saudi Arabia, monthly indexreturns for the MENA stock markets are far from normally distributed with positive ornegative skewness and leptokurtosis as we can see from significant Jarque-Berastatistics. Especially, although Israel suffered the largest fluctuations on marketmovements for the perspective of the US investors, it seems that those volatilities didnot contribute to leptokurtosis, evidenced by the lowest excess kurtosis value (2.7206)and insignificant Jarque-Bera statistics (3.0571). Therefore, maximum and minimumvalues of Israel might be considered outliers since they cannot be representatives ofnormal market movements of Israel.
In Figure 1, we illustrate theoretical quantile-quantile (QQ) plots for the MENA stockmarkets for the perspective of the US-based investors. Although some of countriesinclude significant numbers of outliers in QQ plots, they might result from temporary orspurious shocks not directly related with bubbles, evidenced by insignificant values ofthe Ljung-Box portmanteau test statistics for 12 autocorrelations, Q(12), except Morocco.Therefore, we should be equipped with further formal econometric tests to detect theexistence of bubbles in those rapidly growing MENA stock markets for various practicaland academic reasons such as investments, portfolio diversifications, riskmanagements, and monetary policy and regulation purposes.
3. Empirical challenges of traditional bubble testsAccording to theories of bubbles (Brooks and Katsaris, 2003; Kirman and Teyssiere,2005; Cunado et al., 2007), the actual MENA stock market indexes deviate from thefundamental values if Bubblet . 0. In this case, the markets indexes are called to haverational speculative bubbles:
SEF27,3
250
Bah
rain
Eg
yp
tJo
rdan
Mor
occo
Isra
elO
man
Sau
di
Ara
bia
Tu
rkey
Sam
ple
per
iod
s19
99:0
1-2
003:
0319
96:0
1-2
003:
0319
79:0
1-2
003:
0319
96:0
1-2
003:
0319
97:0
1-2
003:
0319
99:0
1-2
003:
0319
98:0
1-2
003:
0319
87:0
1-2
003:
03P
anel
A:
Dom
esti
cin
vest
ors’
pers
pect
ive
Mea
n2
0.00
362
0.00
250.
0076
0.00
710.
0096
0.00
050.
0052
0.06
16M
edia
n2
0.00
312
0.01
222
0.00
110.
0030
0.01
232
0.02
370.
0028
0.02
63M
axim
um
0.10
850.
2614
0.18
190.
1513
0.14
720.
1889
0.10
460.
7933
Min
imu
m2
0.11
242
0.11
982
0.12
882
0.10
732
0.16
772
0.11
842
0.12
592
0.39
27S
D0.
0361
0.07
480.
0446
0.04
800.
0674
0.06
590.
0447
0.19
64S
kew
nes
s0.
1406
1.02
580.
9979
0.54
982
0.41
491.
0975
20.
2123
1.01
56K
urt
osis
5.35
724.
2276
4.97
253.
2317
2.87
754.
1264
3.39
814.
6300
Q(1
2)0.
0810
20.
0140
0.00
400.
2130
0.05
202
0.13
100.
0190
20.
0350
(0.2
960)
(0.5
160)
(0.8
620)
(0.0
050)
(0.8
740)
(0.2
070)
(0.7
640)
(0.5
060)
Jarq
ue-
Ber
a11
.974
920
.721
495
.477
84.
5777
2.19
8912
.934
80.
8890
55.1
115
(0.0
025)
(0.0
000)
(0.0
000)
(0.1
014)
(0.3
331)
(0.0
016)
(0.6
411)
(0.0
000)
Panel
B:
US
-base
din
vest
ors’
pers
pect
ive
Mea
n2
0.00
362
0.00
860.
0046
0.00
540.
0054
0.00
050.
0052
0.02
26M
edia
n2
0.00
342
0.01
832
0.00
140.
0040
0.01
132
0.02
370.
0027
20.
0087
Max
imu
m0.
1087
0.25
880.
1637
0.15
820.
1453
0.18
890.
1052
0.71
29M
inim
um
20.
1121
20.
1262
20.
1288
20.
0980
20.
1907
20.
1184
20.
1260
20.
4066
SD
0.03
600.
0730
0.04
550.
0493
0.07
640.
0659
0.04
470.
1994
Sk
ewn
ess
0.14
771.
0476
0.62
090.
3040
20.
4744
1.09
842
0.21
140.
8369
Ku
rtos
is5.
3561
4.48
094.
4293
2.97
342.
7206
4.12
833.
4014
4.11
87Q
(12)
0.08
102
0.00
900.
0030
0.17
000.
1330
20.
1310
0.01
902
0.04
80(0
.304
0)(0
.287
0)(0
.788
0)(0
.042
0)(0
.870
0)(0
.209
0)(0
.765
0)(0
.491
0)Ja
rqu
e-B
era
11.9
813
23.8
642
43.4
703
1.34
263.
0571
12.9
605
0.89
1932
.932
8(0
.002
5)(0
.000
0)(0
.000
0)(0
.511
0)(0
.216
9)(0
.001
5)(0
.640
2)(0
.000
0)
Notes:
Th
eta
ble
des
crib
esd
escr
ipti
ve
stat
isti
csof
the
eig
ht
ME
NA
stoc
km
ark
etm
onth
lyin
dex
retu
rns;
the
Q(1
2)is
the
Lju
ng
-Box
por
tman
teau
test
stat
isti
cfo
r12
auto
corr
elat
ion
s;th
ep-
val
ues
are
rep
orte
din
par
anth
eses
Table I.Descriptive statistics of
monthly index returns forthe MENA countries
Rationalspeculative
bubbles
251
Figure 1.Theoretical QQ plots forthe MENA stock markets(the US-based investors’perspective)
–4–3–2–101234
–0.1
2–0
.08
–0.0
40.
000.
040.
080.
12
Bah
rain
Normal quantile
–3–2–101234
–0.2
–0.1
0.0
0.1
0.2
0.3
Egy
pt
–4–3–2–101234
–0.1
5–0
.10
–0.0
50.
000.
050.
100.
150.
20
Jord
an
–3–2–101234
–0.1
5–0
.10
–0.0
50.
000.
050.
100.
150.
20
Mor
occo
–3–2–10123
–0.2
0–0
.15
–0.1
0–0
.05
0.00
0.05
0.10
0.15
Isra
el
Normal quantile
–3–2–101234
–0.1
5–0
.10
–0.0
50.
000.
050.
100.
150.
20
Om
an
–3–2–10123
–0.1
5–0
.10
–0.0
50.
000.
050.
100.
15
Saud
i ara
bia
–3–2–101234
–0.6
–0.4
–0.2
0.0
0.2
0.4
0.6
0.8
Tur
key
SEF27,3
252
MENAat ¼ MENAf
t þ Bubblet þ mt
¼X1k¼1
1
ð1 þ i ÞkEtðDivtþkÞ þ
EtðBubbletþ1Þ
ð1 þ i Þþ mt
ð1Þ
where MENAat is the actual index of the MENA stock markets considered in time t, Divt
is the dividend at period t, MENAft is the fundamental value of the index in time t, i is
the market discount rate, Eð · Þ is the mathematical expectation operator, and mt is anidentically and independently distributed (i.i.d.) stochastic process. Bubblet is the valueof the bubble component in time t and it is entirely consistent with rationalexpectations and the time path of expected returns.
However, previous studies on empirical tests to detect rational speculative bubblesconcentrating on developed and emerging stock markets still remain inconclusive.Therefore, many financial economists have tried to explain the main sources of thecontroversy on the tests of bubbles detection. For example, Blanchard (1979) explainsthat speculative bubbles may take all kinds of shapes and their fundamentals may bestochastic. Kaizoji (2000) argues that bubbles and crashes come from the collectivecrowd behavior of many interacting agents. In theory, although an asset’s fundamentalvalue can be obtained by discounting the asset’s future earnings stream, the difficultiesin estimating the earnings stream and in proper discounting make the identification ofbubbles empirically challenging (Chen, 2001). Gurkaynak (2008) surveys the formaleconometric tests of asset price bubbles and concludes that we cannot distinguishbubbles from time-varying or regime-switching fundamentals.
More importantly, many researchers have also reported that it is very difficult todetect rational speculative bubbles precisely using traditional econometric tests, suchas unit root tests and cointegration tests, mainly relying on expectations of futuresteams of dividends especially in small samples. For example, Taylor and Peel (1998)point out that although rational speculative bubbles imply noncointegration of index orstock prices and dividends, the traditional cointegration tests are subject to sizedistortion or specification error especially in small samples. Owing to these undesirableproperties of cointegration tests, they apply the robust noncointegration test withmuch smaller size distortion and good power characteristics to a long run of the US realstock price and dividend data, then reject the bubbles hypothesis on the US data. Morerecently, using SP 500 log dividend yields, Koustas and Serletis (2005) show thataugmented Dickey-Fuller and Phillips-Perron unit-root tests are unable to reject a unitroot in the price-dividend ratios (dividend yields), which suggests the lack of acointegrating relationship between stock prices and dividends. Therefore, in thefollowing section, we briefly summarize the general idea of newer approaches toidentify rational speculative bubbles in the MENA stock markets.
4. Newer econometric tests to identify rational speculative bubbles4.1 Fractional integration testsTo be consistent with recent study (Cunado et al., 2005; Koustas and Serletis, 2005), weemploy ARFIMA model for bubble detections of a univariate time series of log(dividend yields). With a fractional integration parameter d, the ARFIMA ( p, d, q) iswritten as:
Rationalspeculative
bubbles
253
FðLÞð1 2 LÞdð yt 2 mtÞ ¼ QðLÞ1t ð2Þ
and the fractional differencing operator, ð1 2 LÞd , is defined by:
ð1 2 LÞd ¼ 1 2 dL 2dð1 2 d Þ
2!L 2 2
dð1 2 d Þð2 2 d Þ
3!L 3 2 . . . ð3Þ
where, yt is log (dividend yields), mt is the mean of dividend yields and L is the lagoperator, Lkyt ¼ yt2k:
FðLÞ ¼ 1 2Xp
i¼1
fiLi andQðLÞ ¼ 1 þ
Xq
i¼1
uiLi
represent stationary AR and MA polynomial in the lag operation L. The p and q areintegers, but d is real values, respectively. Furthermore, we assume 1t , N ð0;s 2Þ.The ARFIMA ( p, d, q) models nests the more familiar autoregressive movingaverage (ARMA) (or “Box-Jenkins”) (when d ¼ 0) or autoregressive integrated movingaverage (when d is a positive integer) models as special cases. The ARMA part of themodel is also assumed invertible and stationary, which means that all roots ofFðLÞ ¼ 0 and QðLÞ ¼ 0 are outside the unit circle.
We check the log dividend yield for a fractional exponent in the differencing processusing the exact maximum likelihood (EML) since the unit-root and cointegration testsallow for only integer orders of integration. We also calculate the standard errors by theinverse of the Hessian, estimated by Broyden, Fletcher, Goldfarb, and Shanno algorithmto judge the significance of estimated parameter values. Fractionally integrated longmemory processes are different from both stationary, I ð0Þ, and unit-root processes, I ð1Þ,in that they are persistent but are also mean reverting. In addition, if rational speculativebubbles are present in the MENA stock markets, the fractional integrating parameter oflog dividend yields, d, should not be statistically equal to zero.
4.2 Duration dependence testsAs Cochran and DeFina (1996) point out, hazard functions are appropriate to examineduration dependence since they specify the probability that a particular state will endconditional on the time, which has been spent in the state. On the other hand,traditional time series approaches, such as cointegration tests and unit root testsprovide no information concerning the probability that a run will end or that deviationsfrom the mean will be completely dissipated although they can be useful in identifyingmean-reverting components in monthly returns of the MENA stock markets.
Therefore, first, we parameterize hazard functions to be consistent with traditionalapproaches (McQueen and Thorley, 1994; Chan et al., 1998, among others) along withsemiparametric Cox regression model for bubble identification. Then, second, we alsoperform bubble tests by plotting nonparametric Nelson-Aalen smoothed hazardfunctions, rather than by directly estimating parameterized hazard functions to considerthe relative small sample sizes of the MENA stock markets (For more technical details,Cleves et al., 2004).
4.2.1 Bubble tests based on semiparametric Cox proportional and parametric hazardsmodels. We estimate the following semiparametric Cox proportional hazards toidentify rational speculative bubbles in the perspective of domestic and the US-basedinvestors:
SEF27,3
254
Cox hiðtjCurrencyÞ ¼ h0ðtÞexp{b · Currency} ð4Þ
where h0ðtÞ is the base-line hazard at time t and b is a unknown parameter to estimate.The variable Currency is a dummy variable with values 1 or 0; it equals 1 in the case oflocal currency denomination and 0 otherwise. By definition, exp{b · Currency}is calledthe hazard ratio. In the semiparametric Cox proportional hazards models, the baselinehazard, h0ðtÞ, is given no particular parameterization and, in fact, is left unestimated.
We can also think of a variety of parametric hazard functions specificationsdepending on the expected shapes of hazard functions by making reasonableassumptions about the shape of the baseline hazard, h0ðtÞ. For example, theexponential model is the simplest of parametric hazard models because it assumes thatthe baseline hazard is constant:
Exponential hiðtjCurrencyÞ ¼ expðb0 þ b1 · CurrencyÞ ð5Þ
Similarly, the Weibull regression in the proportional hazard model can provide avariety of monotonically increasing or decreasing shapes of the hazard function, andtheir shape is determined by the estimated parameter p:
Weibull hiðtjCurrencyÞ ¼ pt p21expðb0 þ b1 · CurrencyÞ ð6Þ
Note that when p ¼ 1, the hazard is constant, and thus, the Weibull model reduces tothe exponential model. For other values of p, the Weibull hazard is not constant; it ismonotone decreasing when p , 1 and monotone increasing when p . 1. The Weibullis suitable for modeling data that exhibits monotone hazard rates.
The Gompertz distribution is an old distribution that has been extensively usedby medical researchers and biologists modeling mortality data. This distribution issuitable for modeling data with monotone hazard rates that either increase or decreaseexponentially with time, and the ancillary parameter g controls the shape of thebaseline hazard:
Gompertz hiðtjCurrencyÞ ¼ expðgtÞ expðb0 þ b1 · CurrencyÞ ð7Þ
If g is positive, the hazard function increases with time; if g is negative, the hazarddecreases with time; if g ¼ 0, the hazard function is expðb0Þ for all t, which is to saythat it reduces to the hazard from the exponential model. As such, we estimateparameter values and hazard ratios in each semiparametric and parametric hazardspecification to decide whether different currency denominations make shifts on thebubble identifications between domestic and the US-based investors.
4.2.2 Bubble tests based on the nonparametric Nelson-Aalen hazard functions. Wealso perform bubble tests by plotting an estimate of the hazard function, hðtÞ, by takingthe steps of the Nelson-Aalen cumulative hazard and smoothing them with a Gaussiankernel smoother, rather than by directly estimating parameterized hazard functions toconsider the relative small sample sizes of the MENA stock markets. The estimatednonparametric Nelson-Aalen hazard is calculated as a kernel smooth of the estimatedhazard contributions as obtained by sample hazard rates. The sample hazard rates,hi ¼ ðNiÞ=ðMi þ NiÞ, represents the conditional probability that a run ends at i, giventhat it lasts until i, where Ni is the count of runs of length i and Mi is the count of runswith a length greater than i.
Rationalspeculative
bubbles
255
The cumulative Nelson-Aalen estimator is defined as:
H ðtÞ ¼
Z t
0
hðuÞdu ð8Þ
where hð · Þ is the hazard function. The following nonparametric Nelson-Aalenestimator of cumulative hazard function, HðtÞ, has much better small-sampleproperties than corresponding parameterized ones:
HðtÞ ¼jjtj#t
X dj
nj
ð9Þ
where nj is the number at risk at time tj, dj is the number of failures at time tj, and thesum is over all distinct failure times less than or equal to t. For each observed run endstime tj, the estimated hazard contribution, DHðtjÞ, can be obtained by:
DHðtjÞ ¼ HðtjÞ2 Hðtj21Þ ð10Þ
Therefore, we can estimate the hazard functions with:
hðtÞ ¼ b21XD
j¼1
Kt 2 tj
b
� �DHðtjÞ ð11Þ
for some symmetric Gaussian density function (the kernel) and bandwidth b, thesummation is over the D times at which run ends occur.
In any case, the null hypothesis (H0) of no duration dependence implies that theprobability of a run ending is independent of the prior returns or that positive andnegative abnormal returns are random. The alternative hypothesis (H1) of durationdependence suggests that the probability of a positive run ending should have adecreasing function of the run length. Therefore, if bubbles are detected, the samplehazard rates should decrease as the run length increases (see McQueen and Thorley(1994) and Chan et al. (1998) for further detailed explanations on duration dependencetests to detect rational speculative bubbles).
5. ResultsSince rational speculative bubbles must be persistent to survive several months oryears until market crashes, we should observe statistically significant positiveautocorrelations, skewness, and leptokurtosis due to excess returns during bubbleperiods if bubbles exist in the MENA stock markets. In our study, although summarystatistics show excess kurtosis and positive or negative skewness evidenced bysignificant Jarque-Bera statistics for Morocco, Israel, and Saudi Arabia, many otherfactors not directly related with bubbles can affect market returns. Therefore, the muchcare should be taken to associate higher moments of market returns with thepossibility of rational speculative bubbles. However, unlike Jarque-Bera normalitytests, most MENA stock markets do not show significant positive autocorrelationsexcept Morocco based on the Ljung-Box Portmanteau tests statistics for12 autocorrelations, Q(12), supporting no bubbles to some degree in the MENAstock markets.
SEF27,3
256
The results of these autocorrelation tests question whether the MENA stockmarkets really experienced rational speculative bubbles during our sample periodseven though they suffered a lot of extreme positive or negative monthly returns. AsKoustas and Serletis (2005) insightfully points out, rational speculative bubbles mustbe continually expanding and persistent in order to survive since stock buyers will paya price higher than that suggested by the fundamentals if they believe that someoneelse will subsequently pay an even higher price. Therefore, statistically significantpositive autocorrelations among monthly returns are prerequisite for rationalspeculative bubbles to be present in the MENA stock markets.
The estimation results of fractional integration tests via EML methods in Panel A ofTable II for log dividend yields of the MENA stock markets strongly support theresults of the Ljung-Box autocorrelations tests statistics shown in Table I. We also testwhether fractional integrating parameter ðdÞ is statistically 0 (no unit root) or 1 (unitroot) by performing linear restriction tests in Panel B of Table II. Unlike previousstudies (e.g. Brooks and Katsaris, 2003; Gurkaynak, 2008, among others) that havetested for integer orders of integration, we are able to obtain robust rejections of a unitroot in the log dividend yield from the linear restriction tests. Therefore, we confirmthat fractional integrating parameters of log dividend yields, d, are not statisticallydifferent from zero and reveal no bubbles based on ARFIMA approaches, implyingstationarity of log dividend yields.
In recent study, Koustas and Serletis (2005) also report similar empirical findings asours using SP500 log dividend yields in that they also find the possibility of bubblesbased on unit root tests, but they reject null hypothesis of bubbles based on ARFIMAmethods. They clarify that fractional integration tests are robust to the choice ofparametric estimator of the fractional differencing parameter and data frequency, andbootstrap inference fully supports the estimation results. Therefore, our results of thefractional integration tests are inconsistent with rational speculative bubbles in theMENA stock markets.
In Panel A of Table II, the parameters, f and u, are the estimators of the first orderAR(1), and MA(1), processes in ARFIMA (1, d, 1) models, respectively. To check modeladequacy, we also tabulate residual tests for normality, autoregressive conditionalheteroskedasticity (ARCH) effects, and serial correlations (Portmanteau tests) in PanelC of Table II along with the p-values in parantheses.
For the MENA markets, we can reject the null hypothesis of normality of residualsexcept Morocco and Israel even after the ARFIMA fitting, which suggests usingalternative fatter-tailed distributions such as skewed t-distribution and generalizederror distribution rather than simply assuming normal distributions. For ARCH tests,it appears that ARFIMA settings are well-suited to fit residuals in all of the MENAstock markets even though we assume constant volatility rather than time-varyinggeneralized autoregressive conditional heteroskedasticity-families for the convenience.For Portmanteau tests, it is likely that our ARFIMA (1, d, 1) model successfullycaptures the serial correlations of residuals except Israel. However, although furthercomplexity of model setups considering alternative fatter-tailed distributions andhigher orders of AR or MA processes might improve the overall fits of our ARFIMAmodels, we do not believe that these additional computational efforts will change ourmain results of fractional cointegration tests to detect bubbles in the MENA stockmarkets.
Rationalspeculative
bubbles
257
Bah
rain
Eg
yp
tJo
rdan
Mor
occo
Isra
elO
man
Sau
di
Ara
bia
Tu
rkey
Sam
ple
per
iod
s20
00M
01-2
003M
0319
96M
12-2
003M
0319
84M
12-2
003M
0319
96M
12-2
003M
0319
97M
11-2
003M
0320
00M
01-2
003M
0319
98M
11-2
003M
0319
87M
11-2
003M
03P
anel
A:
Para
met
eres
tim
ate
sd
20.
9975
20.
0624
0.06
932
0.08
082
0.18
992
0.05
472
0.16
072
0.31
02(0
.202
0)(0
.848
0)(0
.829
0)(0
.853
0)(0
.382
0)(0
.879
0)(0
.695
0)(0
.448
0)A
R1(f
)0.
8368
0.84
490.
8084
0.81
040.
9724
0.83
880.
8967
0.86
37(0
.042
0)(0
.000
0)(0
.000
0)(0
.002
0)(0
.000
0)(0
.000
0)(0
.000
0)(0
.000
0)M
A1(u
)0.
1094
0.39
352
0.00
890.
3353
0.18
502
0.04
310.
0446
0.07
79(0
.777
0)(0
.063
0)(0
.974
0)(0
.168
0)(0
.550
0)(0
.883
0)(0
.901
0)(0
.814
0)P
anel
B:
Tes
tsfo
rlin
ear
rest
rict
ion
d¼
01.
6873
0.03
700.
0475
0.03
490.
7831
0.02
340.
1560
0.58
80(0
.194
0)(0
.847
4)(0
.827
3)(0
.851
6)(0
.376
2)(0
.878
3)(0
.692
8)(0
.443
2)d¼
16.
7659
10.7
321
8.57
206.
2570
30.7
339
8.69
358.
1384
10.4
895
(0.0
093)
(0.0
011)
(0.0
034)
(0.0
124)
(0.0
000)
(0.0
032)
(0.0
043)
(0.0
012)
Panel
C:
Res
idualte
sts
for
mod
eladeq
uacy
Nor
mal
ity
17.3
540
47.2
560
38.2
540
4.19
132.
6637
7.47
1133
.522
012
.653
0(0
.000
2)(0
.000
0)(0
.000
0)(0
.123
0)(0
.264
0)(0
.023
9)(0
.000
0)(0
.001
8)A
RC
H0.
0458
0.05
630.
2528
0.22
750.
4366
3.14
170.
0149
1.74
92(0
.831
7)(0
.813
8)(0
.618
3)(0
.636
4)(0
.513
2)(0
.085
3)(0
.903
3)(0
.194
8)P
ortm
ante
au0.
6899
2.63
762.
5505
0.94
408.
4031
1.49
011.
8141
0.82
78(0
.875
6)(0
.450
9)(0
.466
2)(0
.814
8)(0
.038
4)(0
.684
6)(0
.611
9)(0
.842
8)
Notes:
Th
eta
ble
rep
orts
the
esti
mat
ion
resu
lts
offr
acti
onal
inte
gra
tion
test
sv
iaE
ML
met
hod
s;w
eal
sote
stif
frac
tion
alin
teg
rati
ng
par
amet
er(d
)is
stat
isti
call
y0
(no
un
itro
ot)
or1
(un
itro
ot)
by
per
form
ing
lin
ear
rest
rict
ion
test
s;th
ep
aram
eter
s,f
andu
,are
the
esti
mat
ors
ofth
efi
rst
ord
erA
R(1
)an
dM
A(1
)pro
cess
esin
AR
FIM
A(1
,d,1
)mod
els;
toch
eck
mod
elad
equ
acy
,we
also
tab
ula
tere
sid
ual
test
sfo
rn
orm
alit
y,A
RC
Hef
fect
s,an
dse
rial
corr
elat
ion
s(P
ortm
ante
aute
sts)
;th
ep-
val
ues
are
rep
orte
din
par
anth
eses
Table II.Fractional integrationbubble tests in the MENAstock markets
SEF27,3
258
In Table III, to perform duration dependence tests, we compute the actual number ofpositive runs (sequences of excess returns of the same sign) for monthly positive excessindex returns during our sample periods for the perspectives of both domestic and theUS-based investors. We find the longest positive runs (ten months) in Egypt (sampleperiod: 1996:01-2003:03), next 8 months for Bahrain (sample period: 1999:01-2003:03). Allof the MENA countries experience at least five-month positive runs for monthly positiveexcess index returns during our sample periods. However, it seems that those numbersof positive runs are too short, transient, and spurious to be considered as bubbles.
For example, before the worst market crash like Black Thursday (October 24, 1929),the bull markets lasted about 63 months. The presence of a positive and increasingbubble premium continued about 18 months before the crash of Black Monday(October 19, 1987). When the NASDAQ index of technology stocks in the US peaked,the market tripled in value between November 1998 and March 2000 (17 months). Morerecently, the Chinese stock market index had risen 700 percent, propelled by china’sdouble-digit growth rates and surging corporate profitability from July 1994 till June2001 (84 months).
As we can also find from Figure 2, none of the nonparametric smoothed hazardfunctions is monotonically decreasing, implying no bubbles in the MENA stockmarkets. Even though the nonparametric Nelson-Aalen smoothed hazard functionshave different values of hazard rates except Bahrain, Oman, and Saudi Arabia,depending on the types of currency denominations, we observe that Jordan, Morocco,Israel, Saudi Arabia, and Turkey generally show increasing hazard functions, which arenot acceptable if bubbles exist in those markets. Bahrain, Egypt, and Oman also showdistinct patterns, which are not completely consistent with bubbles. Nonparametricsmoothed hazard functions initially increase then decrease.
In Table IV, we provide the comprehensive test results for equality of hazardfunctions between domestic and the US-based investors. Panel A and B of Table IVshows the estimation results of hazard ratios, expðbÞ, of semiparametric Cox andparametric proportional hazards models, respectively, when the currencies are US dollardenominated. It seems that the hazard ratios are insensitive to model specifications,such as Cox, Exponential, Weibull, and Gompertz models. In addition, all of hazard ratesare not only very close to 1 but also statistically insignificant, implying that currencydenominations do not make any difference for bubble identification for the MENA stockmarkets. We also obtain nonparametric statistical test results supporting the equality ofhazard functions between domestic and the US-based investors from log-rank,Wilcoxon, Tarone-Ware, and Peto-Peto tests in Panel C of Table IV. Therefore, we do notfind any statistically significant evidence of bubbles from both fractional integrationtests and duration dependence tests for all of the eight MENA stock markets.
6. ConclusionsWhen we consider sizable market capitalizations and the degree of liberalization in theMENA countries, we believe that the reliable results of bubble tests of the MENA stockmarkets could provide domestic and international investors as well as policy makerswith invaluable benchmark to better understand the irregular and highly fluctuatingstock market behaviors of the MENA stock markets compared to other developed andemerging stock markets. For domestic and international investors, the formal analysisof MENA stock markets behavior including rational speculative bubbles will help
Rationalspeculative
bubbles
259
Bah
rain
Eg
yp
tJo
rdan
Mor
occo
Isra
elO
man
Sau
di
Ara
bia
Tu
rkey
Pos
itiv
eru
ns
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Len
gth
Cou
nt
Panel
A:
Dom
esti
cin
vest
ors’
pers
pect
ive
16
18
139
111
110
17
16
129
23
25
216
21
27
22
24
211
31
31
33
34
32
31
41
38
41
51
43
41
41
51
51
51
81
101
51
52
51
71
62
Tot
al12
1664
1921
1113
49P
anel
B:
US
-base
din
vest
ors’
pers
pect
ive
16
110
138
112
110
17
16
127
23
25
217
22
29
22
24
211
31
31
38
32
31
31
41
37
41
41
43
42
41
51
51
42
81
101
52
51
51
71
51
61
71
Tot
al12
1869
2022
1113
48
Notes:
Th
eta
ble
rep
orts
the
resu
lts
ofd
ura
tion
dep
end
ence
test
sto
det
ect
the
pos
sib
ilit
yof
rati
onal
spec
ula
tiv
eb
ub
ble
s;fo
rth
isp
urp
ose,
we
com
pu
teth
eac
tual
nu
mb
erof
pos
itiv
eru
ns
for
mon
thly
pos
itiv
eex
cess
ind
exre
turn
sfo
rth
ep
ersp
ecti
ves
ofd
omes
tic
(Pan
elA
)an
dth
eU
S-b
ased
(Pan
elB
)in
ves
tors
;a
run
isd
efin
edas
ase
qu
ence
ofex
cess
retu
rns
ofth
esa
me
sig
n
Table III.Duration dependencebubbles tests in theMENA stock markets
SEF27,3
260
Figure 2.Nonparametric
Nelson-Aalen smoothedhazard functions
0.1
0.2
0.3
0.4
0.5
Haz
ard
rate
s
0.1
0.2
0.3
0.4
Haz
ard
rate
s
0 2 4 6 8
Run length
Bahrain
0 2 4 6 8 10
Run length
Egypt
0.3
0.4
0.5
0.6
0.7
Haz
ard
rate
s
1 2 3 4 5 6
Run length
Jordan
0.3
0.35
0.4
0.45
0.5
0.55
Haz
ard
rate
s
0 2 4 6 8
Run Length
Morocco
US-based investors
Local investors
0.35
0.4
0.45
0.5
0.55
0.6
Haz
ard
rate
s
1 2 3 4 5
Run length
Israel
0.38
0.4
0.42
0.44
0.46
Haz
ard
rate
s
1 2 3 4 5
Run length
Oman
0.26
0.28
0.3
0.32
0.34
0.36
Haz
ard
rate
s
0 2 4 6 8Run length
Saudi arabia
0.4
0.5
0.6
0.7
Haz
ard
rate
s
1 2 3 4 5Run length
Turkey
US-based investors
Local Investors
Rationalspeculative
bubbles
261
them in their portfolio decisions and hedging purposes. Similarly, the empirical resultsof bubble tests in this paper will be also helpful to policymakers in MENA countries totake actions to improve the functioning of these dynamic markets.
For this purpose, we extended the speculative bubble literature to the MENA stockmarkets in the perspectives of domestic and the US-based investors. This paper hasemployed fractional integration techniques and duration dependence tests based on theARFIMA models and nonparametric Nelson-Aalen smoothed hazard functions in theMENA stock markets. In this study, we do not find any strong evidence of rationalspeculative bubbles in the MENA stock markets without regard to local currency andthe US dollar denominations. Fractional integration tests do not support the possibilityof rational speculative bubbles in the MENA stock markets, evidenced by thestatistically zero fractional integrating parameter values of log dividend yields.Similarly, duration dependence tests strongly reject the existence of bubbles as well,supported by nondecreasing nonparametric Nelson-Aalen smoothed hazard functions.These test results to identify rational speculative bubbles in MENA region do not differbetween domestic and the US-based investors.
References
Ali, N., Nassir, A., Hassan, T. and Abidin, S. (2009), “Stock overreaction and financial bubbles:evidence from Malaysia”, Journal of Money, Investment and Banking, Vol. 11, pp. 90-101.
Blanchard, O.J. (1979), “Speculative bubbles, crashes and rational expectations”, EconomicsLetters, Vol. 3, pp. 387-9.
Bahrain Egypt Jordan Morocco Israel Oman Saudi Arabia Turkey
Panel A: Semiparametric tests based on Cox regression modelCox 1.0000 0.9544 1.0437 1.0298 0.9875 1.0000 1.0000 1.0586
(1.0000) (0.8910) (0.8060) (0.9280) (0.9670) (1.0000) (1.0000) (0.7800)Panel B: Parametric tests for proportional hazards modelsExponential 1.0000 0.9356 1.0551 1.0230 0.9790 1.0000 1.0000 1.0591
(1.0000) (0.8450) (0.7570) (0.9430) (0.9450) (1.0000) (1.0000) (0.2800)Weibull 1.0000 0.9166 1.0626 1.0772 0.9482 1.0000 1.0000 1.1404
(1.0000) (0.7980) (0.7260) (0.8170) (0.8620) (1.0000) (1.0000) (0.5180)Gompertz 1.0000 0.9356 1.0406 1.0928 0.9572 1.0000 1.0000 1.1276
(1.0000) (0.8450) (0.8190) (0.7840) (0.8860) (1.0000) (1.0000) (0.5550)Panel C: Nonparametric tests for equality of hazard functionsLog-rank 0.0000 0.0400 0.1400 0.0200 0.0000 0.0000 0.0000 0.2000
(1.0000) (0.8394) (0.7087) (0.8976) (0.9514) (1.0000) (1.0000) (0.6585)Wilcoxon 0.0000 0.0400 0.5700 0.0100 0.0000 0.0000 0.0000 0.1500
(1.0000) (0.8422) (0.4518) (0.9246) (0.9685) (1.0000) (1.0000) (0.7004)Tarone-Ware 0.0000 0.0400 0.4500 0.0000 0.0000 0.0000 0.0000 0.1900
(1.0000) (0.8347) (0.5009) (0.9809) (0.9452) (1.0000) (1.0000) (0.6613)Peto-Peto 0.0000 0.0400 0.5200 0.300 0.0000 0.0000 0.0000 0.1300
(1.0000) (0.8488) (0.4701) (0.8736) (0.9650) (1.0000) (1.0000) (0.7229)
Notes: This table provides hazard ratios in each of semiparametric (Panel A) and parametric (Panel B)hazard specifications to decide whether different currency denominations make shifts on the bubbleidentifications between domestic and the US-based investors; we also provide test results for equalityof hazard functions (Panel C) between domestic and the US-based investors; the p-values are reportedin parantheses
Table IV.Tests for equality ofhazard functions betweendomestic and theUS-based investors
SEF27,3
262
Brooks, C. and Katsaris, A. (2003), “Rational speculative bubbles: an empirical investigation ofthe London stock exchange”, Bulletin of Economic Research, Vol. 55, pp. 319-46.
Buehler, S., Kaiser, C. and Jaeger, F. (2006), “Merge or fail? The determinants of mergers andbankruptcies in Switzerland, 1995-2000”, Economics Letters, Vol. 90, pp. 88-95.
Cameron, A.C. and Hall, A.D. (2003), “A survival analysis of Australian equity mutual funds”,Australian Journal of Management, Vol. 28, pp. 209-26.
Chan, H.L., Lee, S.K. and Woo, K.Y. (2003), “An empirical investigation of price and exchangerate bubbles during the interwar European hyperinflations”, International Review ofEconomics and Finance, Vol. 12, pp. 327-44.
Chan, K., McQueen, G. and Thorley, S. (1998), “Are there rational speculative bubbles in Asianstock markets?”, Pacific-Basin Finance Journal, Vol. 6, pp. 125-51.
Chang, T., Chiu, C. and Nieh, C. (2007), “Rational bubbles in the US stock market? Furtherevidence from a nonparametric cointegration test”, Applied Economics Letters, Vol. 14,pp. 517-21.
Chen, N.K. (2001), “Asset price fluctuations in Taiwan: evidence from stock and real estate prices1973 to 1992”, Journal of Asian Economics, Vol. 12, pp. 215-32.
Cleves, M.A., Gould, W.W. and Gutierrez, R.G. (2004), An Introduction to Survival Analysis UsingSTATA, Revised ed., Stata Press, College Station, TX.
Cochran, S.J. and DeFina, R.H. (1996), “Predictability in real exchange rates: evidence fromparametric hazard models”, International Review of Economics and Finance, Vol. 5,pp. 125-47.
Cunado, J., Gil-Alana, L.A. and Gracia, F.P. (2005), “A test for rational bubbles in the NASDAQstock index: a fractionally integrated approach”, Journal of Banking & Finance, Vol. 29,pp. 2633-54.
Cunado, J., Gil-Alana, L.A. and Gracia, F.P. (2007), “Testing for stock market bubbles usingnonlinear models and fractional integration”, Applied Financial Economics, Vol. 17,pp. 1313-21.
Gurkaynak, R.S. (2008), “Econometric tests of asset price bubbles: taking stock”, Journal ofEconomic Surveys, Vol. 22, pp. 166-86.
Kaizoji, T. (2000), “Speculative bubbles and crashes in stock markets: an interacting-agent modelof speculative activity”, Physica A: Statistical Mechanics and its Applications, Vol. 287,pp. 493-506.
Kirman, A. and Teyssiere, G. (2005), “Testing for bubbles and change-points”, Journal ofEconomic Dynamics and Control, Vol. 29, pp. 765-99.
Koustas, Z. and Serletis, A. (2005), “Rational bubbles or persistent deviations from marketfundamentals?”, Journal of Banking & Finance, Vol. 29, pp. 2523-39.
McQueen, G. and Thorley, S. (1994), “Bubbles, stock returns, and duration dependence”, Journalof Financial and Quantitative Analysis, Vol. 29, pp. 379-401.
Taylor, M.P. and Peel, D.A. (1998), “Periodically collapsing stock price bubbles: a robust test”,Economics Letters, Vol. 61, pp. 221-8.
Tudela, M. (2004), “Explaining currency crises: a duration model approach”, Journal ofInternational Money and Finance, Vol. 23, pp. 799-816.
Zhang, B. (2008), “Duration dependence test for rational bubbles in Chinese stock market”,Applied Economics Letters, Vol. 15, pp. 635-9.
Rationalspeculative
bubbles
263
Further reading
Moore, P. (2006), “Middle eastern capital markets”, Euroweek, pp. 45-50.
Yu, Jung-Suk and Kabir Hassan, M. (2006), “Rational speculative bubbles: an empiricalinvestigation of the Middle East and North African (MENA) stock markets”, Working PaperNo. 388, Economic Research Forum, Dokki.
Corresponding authorM. Kabir Hassan can be contacted at: [email protected]
SEF27,3
264
To purchase reprints of this article please e-mail: [email protected] visit our web site for further details: www.emeraldinsight.com/reprints
