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... Understanding the risk and reward from investing in emerging equity markets is neces sary for rational flows of equity financing to developing countries Early research claimed that investing in emerging. .. the switching process is largely explained by liberalization periods in many of the emerging markets C hapter 4: I model the volatility of returns in emerging markets using a time-varying probability... whether investing in emerging equity markets was beneficial in a standard portfolio framework that implicitly assumed that emerging markets could be compared directly to the existing markets
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Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BOSTON UNIVERSITY GRADUATE SCHOOL OF ARTS AND SCIENCE Dissertation ABNORMAL RETURNS IN EMERGING EQUITY MARKETS by MARK A. BARNES B.A., The Johns Hopkins University. 1987 M.A.. The University of Texas at Austin. 1991 M.A.. Boston University. 1995 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2003 R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission. UMI Number: 3054524 Copyright 2002 by Barnes, Mark Allan All rights reserved. _ ___ (ft UMI UMI Microform 3054524 Copyright 2002 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. © Copyright by MARK A. BARNES 2002 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. Approved by First Reader Andrew M. Weiss, Ph.D. Professor of Economics Second Readel Jonathan Eaton, Ph.D. Professor of Economics Third Reader Pierre Perron, Ph.D. Professor of Economics R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I will take the rare opportunity to express appreciation publicly for the invaluable help that I received while working on my doctorate. Foremost is Andy Weiss, who has given me unreasonable amounts of support and encouragement over the years. Jonathan Eaton and Pierre Perron kindly agreed to act as readers on my committee and gave many valuable suggestions. I would also like to thank Simon Gilchrist and Jerome Detemple for serving on my committee and putting up with my last minute scheduling. My experience at the economics department was enriched by many professors and staff members, but a few demand special recognition. I would like to thank Uncle Bob Rosenthal for keeping an eye on all of us. and Russ Cooper for somehow making macroeconomics funny. I would not have finished my dissertation without the help of Sam Holmes who always managed to solve my problems. A number of people have given me much needed encouragement at times. They include Joao Ejarque. Melissa Hieger. David Stewart, and of course Lee McKee. Finally. I would like to thank my parents, Emmett and LaNell Barnes, for provided unconditional support from as early as I can remember. iv R e p ro d u c e d with permission of the copyright owner. Further reproduction prohibited without perm ission. ABNORMAL RETURNS IN EMERGING EQUITY MARKETS (Order No. ) MARK A. BARNES Boston University Graduate School of Arts and Sciences. 2003 Major Professor: Andrew M. Weiss, Professor of Economics ABSTRACT Understanding the risk and reward from investing in emerging equity markets is neces sary for rational flows of equity financing to developing countries. Early research claimed that investing in emerging markets significantly improved the performance of global stock portfolios, but this may have been due to misinterpretations of the data. In this dissertation, I analyze the period of financial liberalization of emerging markets, including data up until June 1997. By focusing on possible changes in the return patterns directly associated with the emergence. I suggest that more modest expectations should have been formed. In the first chapter. I present an introduction to the problem and a literature review. In the second chapter. I focus on ten markets th at are found to have abnormally high returns when analyzed using a simple Capital Asset Pricing Model. I find that most of the abnormally high returns came either before the market opened to foreigners, or during the liberalization period when changes in government policy opened the market to foreign investors. In the third chapter, I use a regime-switching model in which the probability of a change in regime varies over the period. This approach provides a better explanation of why the distribution of returns varies over time. I also present evidence that the abnormally high returns are associated with the period around the time when the markets were opened to outside investors. In the fourth chapter, I use a regime-switching autoregressive conditional heteroskedasv R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. ticity (ARCH) framework to model the variance of returns. This approach reduces the effect of extremely large shocks, which are frequently seen in emerging markets. I present evidence that a switching model that conditions the probability of switching on liberaliza tion events provides better forecasts than commonly used models which do not allow for such changes. VI R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. C ontents 1 Introdu ction and L iterature R eview 1 1.1 Introduction................................................................................................................ 1 1.2 Emerging Markets and Portfolio D ecisions............................................................. 2 1.2.1 International in v e stin g ............................................................................... 3 1.2.2 The problem of portfolio th eo ry ............................................................... -I 1.2.3 The problem of time-variation ............................................................... 7 1.2.4 The problem of outliers - an illu stra tio n ................................................ 10 1.2.5 O u tlie rs .......................................................................................................... 12 1.2.6 Robust outlier identification....................................................................... 15 1.2.7 Modeling o u tlie rs .......................................................................................... 25 1.3 Literature re v ie w ...................................................................................................... 28 1.3.1 Static characterization and portfolioc o n se q u e n c e s ............................... 29 1.3.2 Integration and asset p r i c i n g .................................................................... 31 1.3.3 Time-varying integration .......................................................................... 33 1.3.4 Time-varying characteristics....................................................................... 34 1.3.5 Single break in te g ra tio n .............................................................................. 35 1.3.6 Characterization of the emergencep ro cess................................................ 36 1.4 A description of the followingc h a p te rs .................................................................... 38 1.4.1 Time-varying pricing and liberalization episodes ................................... 38 1.4.2 Outliers and liberalization.......................................................................... 39 1.4.3 Switching volatility ....................................................................................... 40 1.4.4 C o n c lu sio n .................................................................................................... 41 vii R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 1.5 2 42 E xp ectation s o f R etu rn s in Em erging E quity M arkets 45 2.1 Introduction.............................................................................................................. 45 2.1.1 Portfolio th e o ry ........................................................................................... 45 2.1.2 Related R ese a rc h ........................................................................................ 47 2.1.3 The problem: perceived m ispricing......................................................... 50 Two approaches to explaining mispricing........................................................... 54 2.2.1 Time varying p a r a m e te r s ........................................................................ 56 2.2.2 Liberalization ep iso d es............................................................................... 62 2.2.3 Results ........................................................................................................ 65 .............................................................................................................. 67 2.2 2.3 3 Appendix: Description of the outlier detection procedure............................... Conclusion O utliers and L iberalization in Em erging M arkets 72 3.1 Introduction.............................................................................................................. 72 3.2 Previous re se a rc h ..................................................................................................... 75 3.3 Discrete changes in policy and asset prices ...................................................... 77 3.4 Models and e s tim a tio n ........................................................................................... 87 3.5 Data and testing p ro c e d u r e .................................................................................. 92 3.5.1 D a t a ............................................................................................................... 92 3.5.2 T e s t i n g ........................................................................................................ 92 R esults........................................................................................................................ 95 3.6.1 S u m m a ry ..................................................................................................... 95 3.6.2 Decomposition into a mixture of n o r m a l s ............................................. 97 3.6.3 Time variation of m o m e n ts ...................................................................... 99 C onclusions............................................................................................................... 107 3.6 3.7 4 A R egim e-Sw itching M o d el o f C onditional Variance in E m erging E quity M arkets 146 4.1 Introduction............................................................................................................... 146 4.1.1 Volatility c l u s t e r i n g .................................................................................. 147 4.1.2 Volatility in emerging markets 148 ................................................................ viii R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission. 4.2 5 A regime-switching ARCH m o d e l........................................................................ 150 4.2.1 A time-varying probability e x ten sio n ...................................................... 155 4.3 Within-sample forecasting re s u lts ........................................................................ 157 4.4 Out-of-sample forecasts ........................................................................................ 160 4.5 Conclusion and ex tensio n s..................................................................................... 163 C onclusion 173 A D a ta D escription 174 B R eturn S tatistics 176 C G raphs o f S ta tistics T im e Series 177 D C urriculum V ita e 192 be R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. List of Tables 1.1 Outlier example 1 .................................................................................................... 11 1.2 Outlier example 2 .................................................................................................... 12 1.3 Jarque-Berra test for n o rm a lity ........................................................................... 13 1.4 Return statistics with and without outliers ..................................................... 18 1.5 Outlier s t a t i s t i c s .................................................................................................... 19 1.6 Identified o u tlie rs.................................................................................................... 24 1.7 Hampel identifier critical v a lu es........................................................................... 44 2.1 Buckberg's b e t a s .................................................................................................... 50 2.2 Estimated a lp h a s .................................................................................................... 52 2.3 Estimated alphas and b e t a s ................................................................................. 53 2.4 Estimated alpha, beta, and d e l t a ........................................................................ 66 2.5 Stacked regression average alpha and post-open d u m m y ................................. 68 2.6 Liberalization episodes used in chapter 2 ............................................................ 71 3.1 Portugal and Colombia liberalization episodes................................................... 80 3.2 Examples of mixture d is tr ib u tio n s ..................................................................... 85 3.3 Model summary 95 3.4 Estimated po (central mean) for the singleand three state models ............... 103 3.5 Liberalization episodes used in chapter 3 ............................................................ 109 3.6 Number of parameters, log likelihood. AIC. RAISE, and M A E ........................ 124 3.7 J-test 127 3.8 Davies test ..................................................................................................... ....................................................................................................................... .............................................................................................................. x R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 130 3.9 Moment matching s ta t is tic s ................................................................................. 3.10 Transitional probabilities 134 .................................................................................... 137 3.11 Coefficients and standard e rro rs ........................................................................... 145 4.1 Measure of persistence (A) and percent reduction inmean absolute error . . 159 4.2 Out-of-sample forecast percent reduction in mean absolute e r r o r .................. 167 4.3 Liberalization episodes used in chapter 3 ........................................................... 172 B.l Basic statistics on monthly returns. Jan. 1980-June 1997 ............................... 176 xi R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. List o f Figures 2.1 Alphas and betas. 36-month w in d o w .................................................................. 58 2.2 Alphas and betas. 36-month w in d o w ................................................................... 59 2.3 Alphas and betas. 36-month w in d o w ................................................................... 60 2.4 Alphas and betas, 36-month w in d o w ................................................................... 61 3.1 Examples of mixture d is trib u tio n s ....................................................................... 84 3.2 Brazil: histogram of r e tu r n s ................................................................................... 86 3.3 Chile: histogram of r e t u r n s ................................................................................... 97 3.4 Colombia: histogram of r e tu r n s ............................................................................. 98 3.5 Colombia: time series of mixture d e n sity ............................................................. 99 3.6 Portugal: one-step ahead return densities for a three-regime TVP model . . 100 3.7 Portugal. One-step ahead return density for a non-switching m o d e l............... 101 3.8 Time series of mixtures for Argentina and B r a z i l ........................................... 110 3.9 Time series of mixtures for Chile and C o lo m b ia.............................................. Ill 3.10 Time series of mixtures for Greece and India ................................................. 112 3.11 Time series of mixtures for Indonesia and J o r d a n ........................................... 113 3.12 Time series of mixtures for Korea and M alay sia.............................................. 114 3.13 Time series of mixtures for Mexico and N ig e r ia .............................................. 115 3.14 Time series of mixtures for Pakistan and the P h ilip p in es............................... 116 3.15 Time series of mixtures for Portugal and T h a i l a n d ........................................ 117 3.16 Time series of mixtures for Turkey and Venezuela............................................ 118 3.17 Time series of mixtures for Zimbabwe and F ra n c e ............................................ 119 3.18 Time series of mixtures for Germany and J a p a n ............................................... 120 xii R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission. 3.19 Time series of mixtures for UK and US 121 C .l Total return index and total return: Argentina. Brazile. Chile. Colombia. Greece, and I n d ia ..................................................................................................... 178 C.2 Total return index and total return: Indonesia, Jordan. Korea. Malaysia. Mexico, and N ig e r ia ............................................................................................... 179 C.3 Total return index and total return: Pakistan. Philippines. Portugal. Thailand. Turkey, and V enezuela............................ 180 C.4 Total return index and total return: Z im b ab w e ............................................. 181 C.5 1-month statistics, trailing 36-month window: Argentina and Brazil C.6 1-month statistics, trailing 36-inonth window: Chile and Colombia . . . . 183 C.7 1-month statistics, trailing 36-month window: Greece and I n d ia ................ 184 C.8 1-month statistics, trailing 36-month window: Indonesia and Jordan L85 C.9 1-month statistics, trailing 36-inonth window: Korea and Malaysia . . . . C.10 1-month statistics, trailing 36-month window: Mexico and Nigeria . . . . 182 . . . . .... C .ll 1-month statistics, trailing 36-month window: Pakistan and Philippines C.12 1-month statistics, trailing 36-month window: Portugal and Thailand 186 187 . 188 . . . 189 C.13 1-month statistics, trailing 36-month window: Turkey and Venezuela . . . . 190 C.14 1-month statistics, trailing 36-month window: Zim babw e............................. R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 191 List o f A bbreviations A R ............................................................................................................................. Autoregression ARMA ........................................................................................ Autoregressive Moving Average AIC ARCH Akaike Information Criterion Autoregressive Conditional Heteroskedasticity CAPM ...............................................................................................Capital Asset Pricing Model E A F E ......................................................................................Europe. Australasia, and Far East EM ...................................................................................................... Expectations-Maxirnization GARCH Generalized Autoregressive Conditional Heteroskedasticity IFC ......................................................................................... International Finance Corporation IFCG ......................................................................... International Finance Corporation Global MAE ..............................................................................................................Mean Absolute Error MLE Maximum Likelihood Estimation MSCI ................................................................................ Morgan Stanley Capital International RMSE ...................................................................................................Root Mean Squared Error SVVARCH .......................................Switching Autoregressive Conditional Heteroskedasticity TVP ........................................................................................................Time-varying probability xiv R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. C hapter 1 Introduction and Literature R eview 1.1 In trod u ction This dissertation presents a framework for the reevaluation of emerging equity markets. Emerging markets have been presented as an attractive investment from a portfolio stand point in both the academic and practitioner literature because of their distribution of returns, or more specifically their joint distribution of returns with the world market. The framework that I propose indicates that the standard characterization of emerging market returns is an artifact of the process o f emergence of the markets. This is significant because it means that expectations of returns that are based on the period of emergence will be biased unless the peculiarities of the emergence are taken into account. In general, they have not been. In this introductory chapter. I go over the intuition of the problem of including emerging markets in a global portfolio. I review the simplest one-factor asset pricing model that serves as a basis for much of the analysis. I then show how the analysis can be severely affected by outliers that are frequently seen in emerging markets, and I present some evidence that the observed return distributions are dominated by outliers in many emerging markets. I 1 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. review the literature on emerging markets that both shows that this bias was ignored in much of the early research on emerging markets and th at the framework proposed here ties together many of the strands of the later literature. Finally, I briefly introduce the next three chapters of the dissertation: C hapter 2: I show that there are two problems with using the unconditional CAPM to form expectations of excess returns: 1. there is time-variation in the estimated coefficients over the period, and 2. outlier returns associated with liberalization episodes disrupt the CAPM pricing relationship. C hapter 3: Using a time-varying probability switching model, I decompose the uncondi tional univariate distribution of the returns into a mixture of normal distributions. I show that this decomposition explains the time-variation of the moments, and that the switching process is largely explained by liberalization periods in many of the emerging markets. C hapter 4: I model the volatility of returns in emerging markets using a time-varying probability switching ARCH model that accommodates the large outlier returns. This model is shown to outperform the standard GARCH(1,1) model and the fixed switch ing probability model in out-of-sample forecasting simulations. 1.2 E m erging M arkets and P ortfolio D ecision s Portfolio theory plays a major role in the flow of institutional money to emerging markets because it provides an important role for emerging markets in a global portfolio. However, several aspects of how emerging markets fit into a global portfolio have been misunder stood by research on emerging markets. I tie the return distribution directly to the actual emergence of the market, which results in an intuitive explanation for the change of the distribution over time and for the difference between emerging and developed markets. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 3 This framework provides a better explanation for the pattern of returns and points out some possible biases in emerging market data that have been ignored by much of the existing research. Fundamental to this framework is an emphasis on outliers in the return distribution. By associating these large price movements with changes in the underlying investment environment brought on by changes in government policy, I show why we ob served important non-normal and time-varying aspects of the distributions that are likely to occur in all markets that are emerging. This simple understanding of how emerging markets are different from developed markets helps explain why formulaic application of standard mean-variance portfolios techniques is not optimal. Investors invest in emerging markets because of expectations that the emerging market assets will enhance their portfolios. Generally, these expectations are based on historical data for that country and can be based on regression analysis or on simple characterizations of the return distribution. Regression analysis relates the returns to other variables, whereas using the moments of the unconditional distribution is the simplest model that assumes no other variable has information related to returns. In either case, oddities in the return distribution itself will have important effects on the portfolio analysis. For this reason. I focus on the distribution and only make tangential comments on the regression effects. This focus on the return distribution is not too limiting, however. Much portfolio theory uses only the joint distribution of asset returns to make decisions about asset allocation. In this dissertation. I look at univariate distributions of emerging market returns in chapters 3 and 4, and the joint distribution of emerging market returns with the world market returns in chapter 2. 1.2.1 I n te r n a tio n a l in v e stin g The appearance of emerging equity markets as investment opportunities in the late 1980s and early 1990s came at a time when portfolio investing was becoming more international in its orientation. Investors had already broadened their investment horizon from the domestic stock market to include stocks in other developed markets. In this case, the diversification R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 4 away from the domestic markets reduced the risk of portfolios by adding assets with low covariances with the rest of the portfolio. When emerging markets appeared, the typical question asked was. "are these just like the other international stocks or are they fundamentally different?" In other words, did they form a different asset class that could not be compared directly to the developed market, or could they be compared? Did "emerging” just mean "new”or was there something that set them apart from developed markets? These questions were important for both the global investors and the emerging market economies themselves. Some preliminary analysis1 suggested that rebalancing global portfolios should result in the transfer of large amounts of investment capital into emerging markets, with potentially large effects on the developing economies. There was some research in this early period that pointed out some of the differentiating characteristics of emerging markets such as low liquidity, high transaction costs, and restric tions on foreign ownership. However, much of the analysis focused on whether investing in emerging equity markets was beneficial in a standard portfolio framework that implicitly assumed that emerging markets could be compared directly to the existing markets. Given that the appropriateness of portfolio analysis depends on the comparability of the markets, a closer examination is warranted. 1 .2 .2 T h e p r o b le m o f p o r tfo lio th e o r y The portfolio problem is often expressed in a simple form . ,3 _ _ c° v (r i,r rn)_ ri —Pir m — uar(rm) (1-U where r, is the return to asset i and r m is the return to the market, and where both are measured in excess of some risk-free rate of return. The /3 (or beta) notation is used frequently to indicate the covariance risk of a particular asset. If asset i is a "high-beta” asset, then it will be highly correlated with the market and so will be a “risky” asset, requiring a high rate of return to compensate the investor for holding the asset. Conversely, l See section 1.3.1 in the literature review below. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. a low beta asset is a good diversifier and so will have a low expected return in equilibrium. To take into account possible deviations from this equilibrium relationship, an intercept term is often included. (1.2) ri = a ,+ l3 lr m Here a (or alpha) refers to the return to the asset in excess of what is warranted by its beta. If alpha is significantly positive, then the asset is a significant addition to the portfolio because it increases the portfolio return above what is warranted by its effect on the portfolio risk. In other words, an alpha significantly different from zero indicates that the specified equilibrium relationship is not holding. Herein lay the problem presented by emerging markets. The betas of many emerging markets were low. indicating that these markets were not correlated with the world market, and yet their returns were high, generating a high alpha. If this were true, emerging markets would have presented something of a free lunch to international investors. There are probably other explanations for the boom in emerging equity market investment in the early 1990s. but this is the one frequently seen in the academic research on emerging markets. Similarly, there are probably many contributing reasons for the emerging market crash in 1997-1998; however, over-investment probably contributed to the crash and its severity. From this point of view, an explanation of problems in the emerging market analysis may shed light on these contributing factors. Furthermore, an understanding of the first wave of emerging markets may help with interpreting the behavior of markets that emerge in the future. The first part of understanding the emerging market enigma is understanding the stan dard equilibrium relationship given above. I need to make several preliminary caveats: 1. It is important to remember that a test of the relationship is a test of the joint hypothesis of the pricing relationship and a number of assumptions, including that the asset pricing relationship is correct, the market represents the correct portfolio, and that expectations are formed rationally. For that reason, tests of asset pricing R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 6 relationships are rarely conclusive. I am not particularly interested in testing this pricing relationship but rather I am interested in understanding how emerging markets fit into a global portfolio framework. Because the simple portfolio relationship is a reasonable approximation of equilibrium portfolio relationships. I will use it as an indication that we do or do not understand emerging markets rather than conclusive proof. 2. One critique of the simple framework is that it does not sufficiently take into account exposure to other risk factors. A standard extension is a multifactor model written as r; = a , + . . . + PktFk- (1.3) Since a simple one-factor model illustrates my point. I will limit myself to a single factor model. My analysis of the portfolio relationship rests on expectations formation. Because we do not know what the joint distribution of returns will be. we generally write = «< + f t £ t[rmt+1]. (1.4) where Et indicates expectations take at time t. The expected return to the asset is a linear function of the expected market return. However, even this presupposes some knowledge of at and Writing it out in full, we have £ t[rit+i] = E t[ait+l] 4- Et[CaV^ u± oar(rm£+i) ^ [r ^ ]. (1.5) While expectations of the world return characteristics are certainly im portant. I will focus on expectations of the emerging market returns and assume that expectations of the world market are relatively accurate. Making this leap of faith, we can rewrite the equation as R e p ro d u c e d with permission of the copyright owner. Further reproduction prohibited without perm ission. 7 £t[nt+i] = + i?t[/?£+i]rmt+l. (1.6) The key is understanding how investors expect emerging market returns to behave in the future. In a standard framework, unconditional covariance with the world market are used to form expectations. However, if there is something about that historical d ata that we do not expect to see repeated in the future, then expectations using unconditional moments may be biased. A more reasonable approach is to take into account time-variation in the return process. 1.2.3 T he problem o f time>variation Much of the early research that found a high expected alpha simply used the historical mean, standard deviation, and correlations in their calculations. For example in the World Bank Economic Review special issue on emerging markets in 1995. the four papers dealing with asset pricing issues show return statistics for the entire period from 1976 to the present, with two of the four showing statistics on a subperiod beginning in 1985/6. While there is nothing wrong with providing descriptive statistics, most of these papers assume that the return process is stable over this period and so the historical statistics are good approximations of the expected returns at any point in time. While this may seem like an innocuous assumption given our relative ignorance of returns in emerging markets, it is a misleading assumption, as will be explained below. Using the historical statistics in this context implicitly assumes that the return process is stable in the sense that the expected distribution at every point is the same and equal to the unconditional distribution, as is generally assumed in developed markets. Clearly this is a courageous assumption, and I contend that it should be checked. In fact there have been a number of papers that have looked at the time variation of some of these statistics, some of which are discussed in the literature review in section 1.3.1 below. In general, these papers have not, however, attem pted to relate the time variation to expectations of excess return (alpha). Furthermore, these papers generally have assumed R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 8 that there has been some change over the period but have not looked specifically at the process of emergence. There have been a few papers that have looked broadly at the process of emergence but have not gone back to look at the effect that it has on how emerging markets have changed our expectations of excess return. This dissertation looks at this process of emergence. The emergence of emerging equity markets can be described as the process through which investing in the market by global investors becomes possible. For emergence, then, at least two things need to happen: 1. the development of the equity market institutions that allow for the trading of shares. 2. the opening of the market to foreigners, which includes not only permitting the ac quisition of stocks, but the sale and repatriation of returns in the investors’ preferred currency. By and large these things happen as a result of government action. These actions usually have by-products such as changes in macroeconomic conditions, tax rates, and economic growth that also affect the stock market if the financial system becomes more efficient. Some of the results of emergence, then, for which we should look are the following: • The development of the stock market may make the financial system more efficient which should contribute to economic growth. There is some evidence that the emer gence does lower the cost of capital in the countries but the specific topic is beyond the scope of this paper. See Bekaert and Harvey (2000) for a discussion. • The opening of the stock market has been shown by Suret and L'Her (1997) and Henry (2000b) to be directly related to a one time appreciation of stock values as would be expected if the local stocks are more highly valued by international investors than by local investors due to their diversification characteristics. • The effect on the volatility of the market may be mixed. On one hand, the growth of the market should result in the deepening of the market which should reduce the R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 9 volatility often seen in thinly traded markets. On the other hand, the opening of the market to potentially large inflows and outflows of international capital could increase volatility. In fact, in Bekaert and Harvey (1997), the authors find that volatility is lower after liberalization, while in a later paper (Bekaert et al. (1998b)), the authors find that returns are more volatile after integration. • The expected effect on the correlations is also mixed. Related economic liberalization may open up the economy to global shocks which may increase correlations. Fur thermore, to the degree that stock market correlations are driven by the common reaction of global investors to im portant shocks, correlations may increase. However, to the extent that these economies are structurally different from developed market economies, the exposure to shocks should be different and so correlations of emerg ing markets with the world markets should still be lower than the correlation of the developed markets with the world market. The finding has generally been th at while correlations with developed markets have risen, they are still fairly low. See Bekaert and Urias (1999) and Bekaert et al. (1998b) for example. In this dissertation. I look at the last three of these and four points discuss how we may expect the emergence to lead to different mean returns, volatilities, and correlations with the world market. These changes could affect the return process in different ways. If the change is an evolutionary change, it may be that the process changes slowly from a pre emergence pattern to a post-emergence pattern. It could also be that there is a rapid change at the time of emergence which appears as a structural break in the time series. In either case, it could be that the emergence is characterized by large outliers as the market adapts to im portant changes. Because this dissertation emphasizes outliers that appear during the period of emergence, it is worth considering the intuition of outliers in the context of portfolio decisions. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 10 1 .2 .4 T h e p r o b le m o f o u tlie r s - an illu s tr a tio n To appreciate the significance of outliers in the context of portfolio analysis, it is important to understand how outliers affect the measured statistics of returns in a small sample since these statistics can drive asset allocation. In some empirical studies, the tail observations are not very important and can be dropped or winsorized. However, in a return series, as long as the returns are measured correctly, all of the observations are important for the investor's overall return, so the tail observations cannot be ignored. The effect of outliers on investors' portfolio decisions can be seen in the simple CAPM model described above. The effect of a single outlier depends on its magnitude, its direction, and whether it has the same sign as that period's world return. If an outlier is large, positive, and has the same sign as the world return, then it will increase the measured beta of the model, whereas if it has a sign opposite of the world return, it will reduce the measured beta. This effect is largely a small sample effect, but in terms of emerging markets, that is still im portant since emerging markets have only a short history of returns.2 In Table (1.1). I show the results of a simple simulation. Two return series are randomly generated using the covariance structure of the Morgan Stanley Capital International (MSCI) world index and France - as a representative market, using d ata from 1988:1-1993:12. The series are 72 observations long which is six years using monthly returns. I change one of the country's observations by setting it equal to the mean of the series plus or minus some multiple of the standard deviation of the series. I then estimate alpha and beta. As shown in Table (1.1), the beta increases when the shock has the same same sign as the world return, and decreases otherwise. It is interesting to note how much the shock affects the measured beta. W ith a three standard deviation shock, the measured beta varies between 0.489 and 0.659. and with a six standard deviation shock, the measured beta varies between 0.407 and 0.736. 2Actually, the discussion o f outliers probably has wider relevance given that beta is often measured over a m oving window of 5 years or so, which ensures a fairly small sample. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 11 Also, notice that the alpha varies between -0.184 and 0.464. which indicates that the monthly return for the country unexplained by its comovement with the world return ranged from -18.4% to 46.6%. shock crs 0 1 2 3 4 5 6 shock where zq is the q quantile of the N ( 0, 1) distribution. An observation x is an a outlier with respect to N(/ z , ct2) if x € aut(a. [i.cr2). For example, with a standard normal AT(0. 1) distribution, the 0.05 outliers are observations with an absolute value greater than 1.96. When referring to a specific sample .Y.v of size N . we say that the we need to define the outlier region a u t( a tv,£t, cr2). which is complicated by the fact that we generally do not know the mean and standard deviation of the uncontaminated distribution. Detecting multiple outliers consists of examining a sample X , \ of size N and determining a lower bound L ( X , \ . a \ ) and upper bound R(. Y.v.a,v). such that all observations lying outside these bounds are deemed «,v outliers. The set of all these outliers is the identifier outlier region O R { X \ . a \ ) = (-o c .I(.V lV.Q .v)]u[i2(.V ;v . a iV).3c). In order to determine the bounds, we must specify a method of standardizing an outlier identification. Davies and G ather discuss two, but the method I will use here is to require that for a given a.v P ( O R ( X t\ . a x ) C ou t(a y. /j .,a 2)) = 1 —a , where the probability is again calculated under the assumption of an iid sample X , \ . The intuition is that the region generated by the outlier identifier must be a subset of the actual outlier region (out(a^,fx, S \ g ( N , a \ ) to be q .v outliers. The function g{N. a,\) depends on what measures of location and spread are used. In this paper. I use the Hampel statistics defined above. Davies and Gather (1993) present values of g{N. a) for N > 10 for the Hampel statistic in equation 15. These values were derived from simulations and are reproduced here. Q = 0.01 Q.v = 0.0 I Q.v = 0.05 q = 0.05 3.819 -r 2t.09(jV - 7)~ 593B, .V even 3 . 8 1 9 - U .9 l(;V - 6 )~ 56 10. From equation 15 of Davies and G ather (1993). This uses their standardization (3). R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. C hapter 2 E xpectations o f R eturns in Em erging Equity M arkets 2.1 2 .1 .1 Introduction P o r tfo lio th e o r y Asset pricing theory is important for both theoretic and practical reasons. From a purely theoretical perspective, it explains the equilibrium behavior of asset prices in relationship to the asset’s fundamentals or other assets. Research from this perspective has gone in and out of fashion since a test of any asset pricing theory is a test of the joint hypothesis of many different assumptions, and the results are often not very conclusive. Furthermore, because the fundamental value of an asset depends on expectations, it is never actually observed by the econometrician who is sometimes hard-pressed to accept that market par ticipants are rational. If there is a deviation from what seems to be the proper value to the econometrician, it is difficult to tell whether it is due to irrational investors, to investors having more (or less) information than the econometrician, or to the invalidity of any of the assumptions required by the model. A more mundane reason for the importance of asset pricing is that it provides a frame work for investors to understand the markets. Even if the model does not work perfectly 45 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 46 all of the time, a pricing theory allows investors to evaluate their activities in the market. In this case, simpler models that are generally correct are more useful than very complex models that are only marginally better. Arguably the most im portant change in modern applied financial theory is the widespread acceptance of modern portfolio theory, the basic idea of which is that an asset is not priced based only on its own characteristics, but rather based on its contribution to the portfolio's expected return and risk. This paper is concerned with this latter aspect of asset pricing. I am more concerned with how simple, and yet powerful, asset pricing models apply to emerging markets than with the nuances of the asset pricing theory itself. Ultimately, it is the ability of the model to provide a framework for investors that is important. The investors on whom I focus are the large institutional investors whose investments are generally guided by the asset allocation recommendations of portfolio theory. The problem of portfolio theory in emerging markets is that while there was an early burst of enthusiasm for the contribution of emerging markets to global portfolios, research that came out in the early 1990s indicated that the emerging markets did not obey the simple asset pricing models that was the general framework for investors. These papers and subsequent research are reviewed in section 1.3 above. One of the themes that emerged was that it is important to understand how the markets have changed over the period studied. Some of the studies made fairly arbitrary divisions of the data, such as comparing the 1980s to the 1990s and assumed that the behavior was fixed during those periods. Other studies considered very complex models th at attem pted to model the transition process, generally without much success. This paper takes the stance that a proper understanding of asset pricing in emerging markets must look at the process of integration, or the evolution of asset pricing since we believe that the process may be changing over time. Because this process can be both complicated and extend over a period of time. I use a fairly flexible approach that does not impose much structure on the exact dynamics of the transition. While this approach is exploratory in nature, the results have im portant ramifications. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 47 This paper considers two modifications of the standard model to see if they help explain the perceived mispricing. 1. In the first section, I estim ate the model over a moving window to see if there are im portant changes over time. 2. In the second section, I allow the market beta to be conditional on liberalization episodes. I find that there is considerable time variation in the measured alpha, with alpha gener ally being higher before the market was open to foreigners. Also, the betas do rise after the opening for many countries. I also find that conditioning betas on liberalization episodes sig nificantly reduces the perceived mispricing in many countries. This supports the hypothesis that agents have expectations conditional on the liberalization episodes and econometri cians who do not take into account the liberalization history incorrectly infer mispricing when there may be none. Taken together, these results suggest that if investors form their expectations of return patterns based on the period of emergence, their expectations will be unduly optimistic. 2 .1 .2 R e la te d R e se a rc h As emerging equity markets drew attention in the early 1990s, several papers were written on how standard asset pricing models fit the data in these countries. Although there are several different models of asset pricing, they are very similar in spirit to the Capital Asset Pricing Model (CAPM), which is the model that I will use. In a world with multiple assets generating streams of returns, assets exhibiting lower covariances with the aggregate are more valuable because they tend to generate returns when aggregate returns are low. Because they are highly valued, they will be held even if their expected return is low. Of course, in equilibrium, assets that are held in the portfolio have either high expected returns and high covariances with the aggregate, or low expected returns and low covariances, or some combination of the two. This intuition is captured by R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 48 n,l cuv(ri,rw) E ( r t) = — E ( r w) var{rw) x (2.1) ------------------ -— where r, is the return to asset i excess of a risk-free rate and r w is the excess return on the world portfolio. This relationship is often written as (2.2) E i n ) =(3lE ( r w)1 where /?, (in this paper I use "beta") is asset i’s exposure to the world risk factor. An asset with a high beta has high covariance with the world return and so must have a high expected return to remain in the portfolio. Idiosyncratic risk is not priced since it is assumed that there are enough different assets in the potential portfolio that all idiosyncratic risk can be diversified away, leaving only the global risk. Notice that the equation does not have an intercept because it is written in terms of excess returns and is expected to hold exactly. It is useful, however, to include an intercept term: E (r,) = oti + p tE { r w). (2.3) In this equation, alpha can be seen as an indication of an abnormal of the departure of assetpricing from the CAPM. The model return, or equivalently, canbe extended to include multiple risk factors such as exposure to changes in oil prices and interest rate spreads, but the single factor model is sufficient here. The results of tests of asset pricing models in the emerging markets are mixed. Buckberg (1995) reached the conclusion th at the standard CAPM could not be rejected in many of these countries. However, Buckberg assumed that alpha was equal zero and estim ated beta based on the equation r it = Pir wt • (2.4) She used the Generalized Method of Moments to estimate a constant beta that gives a pricing error of R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 49 (2.5) eu = r it - r wt{3i. The orthogonality condition is I (Tit, Pi) = where Z t- \ is a set of instruments available at t — 1. She used instruments proposed by other research, including the lagged world excess stock return; a January dummy; the world dividend yield: the U.S. term structure premium (difference between return to holding a three-month T-bill and the return on a bill thirty days to maturity): the U.S. default risk-yield spread (spread between Moody Baa and Aaa yield): and the lagged local return. GMM imposes the moment restriction £7[cf] = 0 by minimizing the quadratic function T T MP) = [ ^ / ( r u . ^ ' l V U r t i ^ / ^ , / ? ) ] t=i i=i with respect to P. where W r is a weighting matrix. The minimized value of this quadratic form is distributed x~ under the null hypothesis that the model holds. Using this statistic, she could reject the international CAPM for only two countries: Mexico and Zimbabwe. The betas she estimated, shown in Table (2.1) below, include many extreme values. Harvey (1995, p. 31-32) points out that Buckberg;s assumption th at alpha is zero could lead to low power of her tests, and hence her general lack of rejection of the international CAPM. When Harvey tested the null that alpha was indeed zero, he rejected for many countries. To determine if the rejection was due to using only a single factor model, he also used a multifactor model to take into account different risk factors and found that he still rejected the asset pricing model. This conclusion was supported by Korajczyk (1996) who used a principal components technique on stock level data and also found that there was mispricing in many of the countries. Bekaert and Harvey (1995b) used a regime-switching model to attem pt to model the integration process explicitly. They assumed th at returns were priced by covariance with world market if the country was integrated or by variance of returns if the country was segmented. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 50 Country Beta Country Beta Argentina 1.204 Mexico 1.397 Brazil 1.173 Nigeria -1.368 Chile 2.127 Pakistan 0.395 Colombia 0.919 Philippines 2.812 Greece 0.081 Portugal 2.271 India 0.052 Taiwan 1.720 Indonesia 0.276 Thailand 0.624 Jordan 0.280 Turkey -1.859 Korea 1.293 Venezuela 1.156 Malaysia 0.405 Zimbabwe -0.375 Table 2.1: Betas estimated by Buckberg (1995. p. 67) using data from 1985-1991. n,t = The first column of the x matrix is a column of ones. If it is the only column in the x matrix, then the model reverts to the fixed probability model. The more interesting case R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 90 is that in which additional data series are allowed to influence the switching probabilities so 0 is a vector that is estimated along with the other parameters. The first element of the beta vector influences the constant probability of switching. If the other elements are non zero, the probabilities are time-varying and conditional on the other series in x. There is considerable flexibility in this model since different data series can be used to influence the switching probabilities. It also allows me to test the hypothesis that liberalization affects movement to the tails of the distributions. I extend the Diebold. Lee. and Weinbach algorithm to a three-state case. Because of data limitations, I consider only one time-varying probability: the case in which a liberalization event increases the probability of moving from an s = 2 state to an s = 3 state, which corresponds to returns going from "nonnaF to "above-normal." I parameterize the probabilities as follows: p ii 1 _ p i2 _ _______ exp{fin )______ 1 4- e x p (0 u ) + exp(8y2) exp{0l2) 1 + exp {0 n ) + exp((3 12) ___________I___________ Pi13 p2i _ 1 + exp{j3\ i ) + exp(/3l2) expifoi) I + expU hi) + ezp (# m + Xt0232) 1________________ 22 Pi 1 + exp (fo i) + exp {fc3l -I- Xt/%32) p 2 3 _ ^ P (/? 2 3 1 + X t 0 2 3 2 ) P 31 _ 1 -I- exp(02l) + exp(/323L + Xt0232) exp(/331) 1 +exp(/331) +ezp(/332) P 32 _ exp{032 ) 1 + exp(P3i) +exp{/332) p33 ‘ = _____________ i 1 + exp (fo i) + exp(/332) i=;\ In this notation, x t (in the P f terms) does not contain a column of onesbut is a liberalization dummy series that will be further described below. The intuition is that if liberalization is associated with a move from the “normal” returns associated with state 2 R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission. 91 to "above-normal” returns associated with state 3. @222 will be positive, an easily testable implication. In the two state model, the time-varying probability is again associated with moving from a "normal” return state to an "above-normal” return state. To avoid confusion when reporting results, in the two-state case. I drop state "1” so that state "2” continues to be the normal state and state "3” continues to be the above-normal state. Even with only one time-varying probability series, the three state model thus has thirteen parameters. W ith a maximum of 212 observations for each country, the switch ing model is very difficult to estimate with standard MLE techniques. I use the EM (expectations-maximization) method in which the switching probabilities parameter vector (@ = (,dn, @i2 , @2 1 , ,@2 3 i> @2 3 2 , @3 1 , @3 2 )') and the non-probability parameters (9 = (a, /j i, H2 . P 3 - (p\. fa )') are estimated sequentially in an iterative procedure. In the first (Expecta tions) step of the iteration. 9 is assumed to be known and @ is estimated. Given @ and 9, the smoothed history of the states using the eutire data series is inferred. This smoothed history of the states is then used in the estimation of 9 in the Maximization step. The EM algorithm is stable and moves to the neighborhood of the optimum. After convergence slows. I switch to a standard maximization of all of the parameters simultaneously. The optimization is done using the OPTMUM routine in GAUSS. The estimated parameters of two countries exhibited sensitivity to starting values of (b) JORDAN Figure 3.11: Time series of mixtures for Indonesia and Jordan. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 114 (a) KOREA / (b) MALAYSIA Figure 3.12: Time series of mixtures for Korea and Malaysia. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 115 (a) MEXICO (b) NIGERIA Figure 3.13: Time series of mixtures for Mexico and Nigeria. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 116 (a) PAKISTAN (b) PHILIPPINES Figure 3.14: Time series of mixtures for Pakistan and the Philippines. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 117 (a) PORTUGAL (b) THAILAND Figure 3.15: Time series of mixtures for Portugal and Thailand. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 118 (a) TU R K EY / (b) VENEZUELA Figure 3.16: Time series of mixtures for Turkey and Venezuela. 13-month centered window. R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 119 (a) ZIMBABW E ■v (b) FRANCE Figure 3.17: Time series of mixtures for Zimbabwe and France. 13-month centered window. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 vv. (a) GERM ANY (b) JAPAN Figure 3.18: Time series of mixtures for Germany and Japan. 13-month centered window. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 121 (a) UK (b) US Figure 3.19: Time series of mixtures for UK and US. 13-month centered window. R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 122 Model and 1-step ahead statistics S ta tistic IS 2F 2V 3F 3V 8.000 48.911 -3.483 0.251 0.153 9.000 51.819 -3.473 0.246 0.152 9.000 82.980 -4.127 0.164 0.124 10.000 85.441 -4.103 0.167 0.126 9.000 227.982 -5.864 0.084 0.068 10.000 228.033 -5.852 10.000 194.052 -5.437 0.077 0.057 9.000 195.769 -5.449 0.079 0.058 8.000 213.665 -5.180 0.102 0.069 10.000 215.420 -5.162 0.101 0.068 10.000 217.466 -5.186 0.082 0.062 11.000 222.540 -5.357 0.087 0.065 10.000 94.655 -4.762 0.081 0.064 8.000 94.655 -4.807 0.081 0.062 11.000 358.479 -6.931 0.045 0.034 12.000 358.520 -6.925 0.045 0.03-1 10.000 231.537 -5.540 11.000 233.847 -5.540 Argentina # p a rm s Likelihood A IC R M SE MAE 6.000 22.998 -2.659 0.257 0.151 6.000 15.101 -3.442 0.252 0.152 # p a rm s L ikelihood A IC R M SE MAE 6.000 80.997 -3.135 0.174 0.132 7.000 76.998 -3.938 0.173 0.130 # p a rm s L ikelihood AIC R M SE MAE 6.000 222.218 -4.905 0.084 0.068 7.000 223.555 -4.963 0.080 0.066 # p a rm s L ikelihood A IC RM SE MAE 6.000 176.653 -5.024 0.078 0.058 7.000 190.445 -5.428 0.077 0.056 # p a rm s L ikelihood AIC RM SE MAE 6.000 192.057 -4.474 0.104 0.071 6.000 210.184 -5.099 0.102 0.069 f f p a rm s L ikelihood A IC R M SE MAE 6.000 216.042 -4.746 0.091 0.067 7.000 216.522 -5.206 0.087 0.066 # p a rm s L ikelihood AIC RM SE MAE 6.000 95.087 -4.887 0.081 0.064 6.000 98.630 -5.482 0.075 0.058 # p a rm s L ikelihood A IC RM SE MAE 6.000 340.233 -6.012 0.048 0.035 7.000 351.596 -6.565 0.041 0.032 7.000 47.984 -3.432 0.246 0.150 Brazil 8.000 79.130 -3.904 0.173 0.129 Chile 8.000 224.021 -4.957 0.080 0.065 0.084 0.068 Colombia 8.000 192.198 -5.415 0.077 0.056 Greece 7.000 2 11.864 -5.092 0.101 0.068 India 8.000 216.572 -5.198 0.087 0.066 Indonesia 7.000 101.330 -5.500 0.076 0.060 Jordan 8.000 351.809 -6.570 0.041 0.031 Korea # p a rm s L ikelihood A IC 6.000 222.850 -4.918 7.000 229.668 -5.616 8.000 230.246 -5.599 continued on n ext p a g e R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 123 S ta tistic s - continued from previou s page S ta tistic R M SE MAE IS 0.083 0.066 2F 0.083 0.066 # p a rm s L ikelihood A IC R M SE MAE 6.000 175.4-15 -5.107 0.075 0.058 7.000 174.982 -5.108 0.075 0.057 # p arm s L ikelihood AIC R M SE MAE 6.000 152.706 -4.096 0.125 0.092 7.000 138.195 -4.174 0.126 0.092 # p arm s L ikelihood AIC R M SE MAE 6.000 181.297 -4.730 0.090 0.053 7.000 147.537 -1.994 0.088 0.053 # p arm s L ikelihood AIC R M SE MAE 6.000 210.476 -5.241 0.070 0.047 7.000 203.319 -5.693 0.069 0.048 # p arm s L ikelihood AIC R M SE MAE 6.000 131.981 -4.547 0.099 0.072 7.000 145.899 -5.065 0.098 0.072 # p arm s L ikelihood A IC R M SE MAE 6.000 149.753 -4.292 0.112 0.071 7.000 126.763 -4.927 0.107 0.070 # p a rm s L ikelihood A IC R M SE MAE 6.000 239.651 -5.018 0.079 0.057 7.000 239.733 -5.190 0.079 0.057 2V 3F 0.083 0.066 0.080 0.062 3V 0.081 0.063 8.000 180.672 -5.621 0.074 0.057 11.000 181.743 -5.601 0.072 0.056 10.000 158.273 -4.529 0.125 0.091 11.000 156.337 -4.450 0.125 0.092 9.000 176.663 -5.524 0.089 0.053 10.000 177.279 -5.504 0.089 0.053 12.000 208.218 -6.01-1 11.000 210.365 -6.017 0.070 0.048 0.068 0.049 12.000 150.239 -5.325 0.098 0.071 11.000 150.245 -5.338 0.098 0.071 11.000 139.119 -5.110 0.108 0.071 12.000 142.724 -5.080 0.104 0.067 10.000 249.203 -5.423 0.076 0.057 11.000 247.325 -5.692 0.079 10.000 34.090 -3.797 0.197 0.153 10.000 36.921 -3.762 0.189 0.146 9.000 102.211 10.000 104.111 Malaysia 8.000 175.695 -5.145 0.075 0.058 Mexico 8.000 138.399 -4.167 0.126 0.092 N igeria 8.000 146.453 -4.858 0.089 0.053 Pakistan 8.000 205.23-1 -5.696 0.068 0.048 Philipp ines 8.000 146.032 -4.990 0.099 0.072 Portugal 8.000 130.400 -4.944 0.102 0.066 Thailand 8.000 240.132 -5.186 0.079 0.057 0.058 Turkey r r p a rm s L ikelihood A IC R M SE MAE 6.000 24.946 -3 .1 4 1 0.198 0.153 7.000 34.090 -3.846 0.197 0.153 # p a rm s L ikelihood 6.000 96.524 7.000 96.742 8.000 36.920 -3.788 0.190 0.147 Venezuela 8.000 99.796 continued on n ex t p age R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 124 S ta tistics - continued from previou s page S ta tistic AIC RM SE M AE is -4.003 0.130 0.093 2F -4.202 0.121 0.088 # p a rm s L ikelihood AIC RM SE M AE 6.000 197.252 -4.636 0.096 0.072 6.000 197.581 -4.821 0.095 0.071 # p arm s Likelihood AIC RM SE M AE 6.000 288.790 -5.470 0.063 0.047 7.000 283.019 -5.581 0.060 0.044 # p arm s Likelihood AIC RM SE MAE 6.000 302.113 -5.598 0.059 0.044 7.000 292.701 -5.720 0.059 0.044 # p a rm s Likelihood AIC RM SE M AE 6.000 251.139 -5.191 0.073 0.056 7.000 251.262 -5.250 0.069 0.054 # p arm s L ikelihood AIC RM SE M AE 6.000 303.472 -5.723 0.056 0.042 6.000 307.596 -5.820 0.056 0.042 2V -4.163 0.127 0.094 3F -4.548 0.125 0.090 3V -4.278 0.128 0.095 9.000 203.258 -5.022 0.092 0.069 10.000 204.315 -4.999 0.092 0.070 Zimbabwe 8.000 198.170 -4.807 0.095 0.071 trance 12.000 297.299 -6.003 0.060 0.044 Germany 12.000 302.241 -6.191 0.058 0.044 Japan 11.000 258.115 -5.777 0.066 0.052 UK 10.000 312.532 -6.222 0.051 0.039 USA # p arm s 6.000 7.000 11.000 Likelihood 375.022 385.717 386.152 AIC -6.384 -6.569 -6.577 RM SE 0.040 0.040 0.040 0.029 M AE 0.029 0.029 T able 3.6: N u m b er o f p a ra m e te rs, log likelihood. A IC , R M S E . a n d M A E. All refer to th e reduced m odels a fte r p ro b a b ilities on th e b o u n d a ry have been rem oved from e stim a tio n . R e p ro d u c e d with perm ission of the copyright owner. Furth er reproduction prohibited without permission. 125 J-Test 2F M odel a SE a 3V 3F 2V SE a SE 0.284 1.026 1.068 0.417 1.347 0.233 0.3-15 1.031 1.015 1.166 -0.555 0.246 0.269 0.306 0.663 0.349 0.358 0.365 -0.655 -0.883 4.172 0.642 0.357 0.370 3.658 0.838 0.955 0.670 0.376 0.362 0.069 -0.052 -0.915 0.410 0.416 0. I l l 0.657 1.085 0.116 -0.278 0.403 1.082 0.803 -0.268 1.088 0.338 1.091 0.607 1.611 1.691 1.667 0.220 0.295 0.293 1.595 0.572 0.561 -0.409 0.-149 0.440 0.264 2.310 0.489 0.348 0.596 -0.325 0.090 0.606 0.365 0.361 0.290 0.382 2.075 -0.921 -1.090 0.307 0.281 0.283 2.099 -0.883 -1.066 2.001 0.309 0.279 0.281 5.296 1.965 1.713 1.609 0.387 0.347 1.162 1.086 0.335 1.310 0.025 0.308 0.283 0.335 SE a Argentina is 0.890 0.287 2F 2V 3F 1.031 1.526 0.230 0.449 0.939 0.755 -0.105 0.611 0.373 0.557 0.456 Brazil IS 2F 2V 3F 1.050 0.595 0.803 0.520 1.301 1.378 1.271 0.434 0.622 0.239 0.268 0.252 0.473 Chi le IS 1 .155 0.333 2F 2V 3F 1.617 3.553 0.340 1.865 0.235 -0.641 -0.837 Colombia is 0.618 0.265 2F 2V 3F 0.632 0.984 0.255 1.373 1.272 0.388 1.650 1.533 0.382 1.209 0.796 0.665 Greece is 1.363 0.467 2F 2V 3F 0.659 0.523 1.074 0.6-11 India is 1.6-11 0.382 2F 2V 3F 5.003 0.365 Indonesia is 2.169 0.-169 2F 2V 3F 1.154 0.128 0.339 0.546 0.471 -1.347 -0.191 Jordlan is 1.563 0.169 1.627 4.753 0.169 1.795 0.021 1.215 0.363 0.587 0.789 0.911 2F 2V 3F Korea ts 2F 2V 3F 0.445 Malaysia IS 2F 2V 3F 0.988 IS | 0.103 0.949 0.695 0.479 0.624 0.703 0.224 0.672 0.850 0.810 0.752 0.399 0.433 0.385 1.150 1.120 1.363 1.687 0.348 0.360 0.422 0.621 0.643 0.411 0.470 0.861 Mexico 0.673 continued on next page R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 126 J-l'est - continued from previous page 2F M odel 2F 2V 3F 2V 3F Q SE a 13.448 SE 6.931 1.070 0.384 1.607 0.057 0.879 0.431 0.819 0.460 1.007 1.488 0.377 0.698 3V a 1.306 1.153 SE 0.683 0.669 a 2.197 1.550 0.091 SE 1.422 1.358 0.680 0.864 -2.025 0.643 0 .4 2 1 1.187 0.480 0.853 -0.839 0.653 0.864 0.400 0.910 0.448 1.591 0.456 0.699 0.505 0.952 0.932 0.533 1.648 0.352 0.453 0.636 0.660 0.866 0.684 1.487 1.151 1.241 -4.595 0.660 0.862 0.695 14.307 0.549 0.622 0.259 2.433 1.136 0.060 1.978 0.411 0.406 0.439 0.507 0.352 0.330 0.300 0.620 0.749 0.677 -0.102 0.384 1.519 1.321 0.972 132262.745 -0.067 0.905 129163.804 0.344 1.280 1.132 4.413 1.132 0.370 0.354 4.066 0.354 0.387 0.517 0.463 0.790 -1.060 0.065 -0.266 0.340 0.428 1.481 0.487 1.684 1.710 1.458 0.384 0.455 0.428 1.468 1.516 1.607 0.608 0.345 0.412 0.453 0.856 1.091 0.415 0.224 0.486 N igeria is 2F 2V 3F Pakistan is 2F 2V 3F 0.690 0.211 -0.171 0.649 Philip pines IS 2F 2V 3F 0.908 0.546 0.673 -0.696 0.494 1.355 IS 2F 2V 3F 1.-174 0.392 1.308 0.980 0.247 0.277 IS -0.070 1.100 0.333 0.681 0.744 1.036 0.357 0.344 1.498 1.176 1.231 Portugal 1.889 -0.130 -0.041 Thail and 2F 2V 3F 1.597 0.441 0.399 0.277 Turkey IS 2F 2V 3F 0.972 0.905 1 .190 1.067 IS 2F 2V 3F 1.513 0.301 0.832 -1.002 is 1 1.328 0.640 1.398 1.462 1.202 0.240 1.601 0.677 1.640 0.343 Venezuela 0.349 0.427 1.379 -0.782 1.147 Zimbabwe 2F 2V 3F 0.589 1.319 Prance is 2F Germany is 2F 2.347 1.679 0.555 0.591 1.945 0.259 Japan is continued on next page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 127 J - Lest - continued from previou s page 2F M odel q 2V SE a 3V 3F SE 2F q SE 1.572 0.329 1.658 1.576 0.250 0.240 q UK is 0.139 1.410 0.5-18 0.382 2F USA IS 2F 1.020 0.919 0.544 0.389 T ab le 3.7: J -te s t. L arger m odels are in co lu m n s, s m a lle r in rows. S h ad in g in d ic a te s c a n n o t re je ct t h a t a = I b u t can re je ct a = 0 which indicates th a t th e larg e r m odel is preferred. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. SE 128 Davies Test M odel IS 2V 2F Argentina 2F 2V 3F 3V P[LR > 4-1.21] = P[LR > 49.97] = 2F 2V 3F 3V P[LR > -8 .0 0 ] = P[LR > -3 .7 3 ] = P \ L R > 3.971 = P\ LR > 8.89] = 1.75 1.57 2F 2V 3F 3V P\ LR > P\ LR > P[LR > P[LR > 2.6 li = 3.551 = 11.47] = 11.57] = 0.98 1.22 0.68 0.98 2F 2V 3F 3V P[LR P[LR P[LR P[LR > 27.58] = > 31.09] = > 34.80] = > 38.23] = 0.00 2F 2V 3F 3V P[ I R > 36.25] = P[LR > 39.61] = P[LR > 43.22] = P[LR > 46.73] = 0.00 0.00 0.00 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > 0.96] = 1.06] = 2.85] = 13.00] = 1.21 1.30 1.52 0.71 >F 2V 3F 3V P[LR > 7.09] = P[LR > 12.48] = P[LR > -0 .8 6 ] = P[LR > 14.61] = 0.23 0.07 P [ i f t > 51.83] = P \ L R > 57.641 = 0.00 0.00 0.00 0.00 P[LR > 7.62] = P[LR > 13.44] = 0.75 0.23 P[LR > 1.86] = P[LR > 7.67] = 1.40 0.74 0.20 0.07 P[LR > 7.70] = P[LR > 12.62] = 0.42 0.16 0.53 0.84 P [ L R > 7.92] = P[LR > 8.02] = 0.39 0.67 0.83 0.54 P [ L R > 3.71] = P[LR > 7.14] = 1.19 0.85 0.88 0.57 P[LR > 3.60] = P[LR > 7.11] = 1.21 0.85 1.45 0.36 P[ LR > 1.79] = P[LR > 11.94] = 1.40 0.20 1.14 P\ LR > -1 3 .3 5 ] = P\ LR > 2.12] = 1.49 0.11 0.20 P[LR > 13.34) = PfLR > 13.42} = 0.05 0.12 1.52 0.96 P { L R > 2.58] = P[ LR > 7.20] = 1.37 0.83 0.24 0.23 P[LR > 9.95] = P\ LR > 12.10] = 0.19 0.19 Brazil P[LR > 11.96] = P[LR > 16.88] = Chile P[LR > 8.85] = P[LR > 8.96] = Colombia 0.00 0.00 0.00 P[LR > 7.21] = P[LR > 10.65] = Greece 0.00 P\ LR > 6.96] = P\ LR > 10.47] = India P[LR > 1.89] = P[LR > 12.04] = Indonesia 0.47 3F 3V P[LR > 22.72] = P[LR > 23.15] = P[LR > 36.49] = P[LR > 36.57] := 0.00 0.00 0.00 2F 2V 3F 3V P[LR > 13.64] = P[LR > 14.79] = P[LR > 17.37] = P\ LR > 21.99] = 0.02 0.03 2F 2V 3F 3V P[LR > -0 .9 2 ] = P[LR > 0.50] = P[LR > 10.45] = P[LR > 12.60] = 2F P [L R > -2 9 .0 2 ] = 2F 2V 0.00 P[LR > -7 .9 5 ] = P[LR > 7.52] = Jordan P{LR > 13.77] = P[LR > 13.85] = Korea 0.12 0.05 P[LR > 3.74] = P[LR > 8.36] = Malaysia 1.14 0.87 0.78 P[LR > 11.38] = P[LR > 13.52] = Mexico • 1 continued on n ex t page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 129 Davies te st - continued from previous page M odel IS 2V 2F 2V 3F 3V P[LR > -2 8 .6 1 ] = P[LR > 11.13] = P[LR > 11.56] = 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > -6 7 .5 2 ] -6 9 .6 9 ] -9 .2 7 ! -8 .0 3 ] = = = = 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > -1 4 .3 2 ] -1 0 .4 9 ] -4 .6 2 ] -0 .2 2 ] = = = = 0.74 0.98 P[LR > 40.16] = P[LR > 40.58] = 0.00 0.00 P[LR > 39.75] = P[LR > 40.17] = 0.00 0.00 0.00 0.00 P[LR > 60.42] = P[LR > 61.65] = 0.00 0.00 0.41 0.19 P[LR > 5.87] = P\ LR > 10.26] = 0.72 0.35 0.89 P[LR > .] = P f l.f i > 8.43] = 0.60 Nigeria P[LR > 58.25] = P[LR > 59.48] = Pakistan 2F 2V 3F 3V P[LR > P[LR > P[LR P[LR > 27.84) = 28.10] = > .1 = 36.53] = P[LR > 9.701 = P[LR > 14.09] = 0.00 0.00 0.00 Philippines P\LR > .1 = P[LR > 8.69] = Portugal 2F 2V 3F 3V P[LR > -4 5 .9 8 ] P[LR > -3 8 .7 1 ] P[LR > -2 1 .2 7 ] P[LR > -1 4 .0 6 ] = = = = P[LR > 24.71] = P[LR > 31.92] = P[LR > 17.44] = P[LR > 24.65] = 0.01 0.13 P'LR P'LR 0.01 0.08 1.54 P[LR > —5.66] -P[LR > 0.00] = 1.00 0.28 0.15 P[LR > 4.83] = P[LR > 8.63] = 0.94 0.57 0.24 0.23 P[LR > 10.181 = P[LR > 12.29] = 0.18 0.18 0.00 0.00 P[LR > 28.56] = P[LR > 28.56] = 0.00 0.01 0.03 P[LR > 19.081 = P[LR > 19.08] = 0.01 0.01 0.00 0.00 0.00 Thailand 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > 0.17] = 0.96] = 19.11] = 15.35] = 1.07 1.28 0.07 0.38 2F 2V 3F 3V P[LR > 18.29] = P[LR > 23.95] = P[LR > 18.29] = P[LR > 23.95] = 0.00 P[LR > 18.94] = P[LR > 15.18] = 0.01 > 18.14] = > 14.391 = Turkey 0.00 0.09 0.02 P[LR > - 0 .0 0 ] = P [ L R > 5.66] = Venezuela 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > 0.44] = 6.55] = 11.37] = 15.17] = 1.15 0.59 0.70 0.40 2F 2V 3F 3V P[LR > P[LR > P[LR> P[LR > 0.66] = 1.84] = 12.01] = 14.13] = 1.19 1.40 0.60 0.53 P[LR > 10.94] = P[LR > 14.74] = Zimbabwe P[LR > 11.351 = P[LR > 13.47] = France 2F 2V 3F 3V P[LR > -1 1 .5 4 ] = P[LR > -1 1 .5 4 ] = P[LR > 17.02] = P[LR > 17.02] = 2F 2V 3F 3V P[LR > -1 8 .8 2 ] = P[LR > -1 8 .8 2 ] = P[LR > 0.26] = P[LR > 0.26] = 0.13 0.24 P[LR > 28.56] = P[LR > 28.56j = 0.00 Germany 1.00 1.00 P[LR > 19.08] = P[LR > 19.08] = continued on n e x t page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 130 D avies t e s t - continued from previous page M odel 2F IS 2V ' Japan 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > 0.25j = 0.25] = 13.95] = 13.95] = 1.10 1.06 0.35 0.56 P[LR > 13.71] = P[LR > 13.71] = 0.11 0.21 P\ LR > 13.711 = P\ LR > 13.711 = 0.05 0.11 UK 2F 2V 3F 3V P[LR > P[LR > P[LR > P[LR > 2F 2V 3F 3V P[LR P[LR P{LR P[LR 8.25] = 8.25] = 18.12] = 16.11] = 0.15 0.35 0.09 0.31 P\ LR P[LR > 9.871 = > 7.87] = P' LR P[LR > 9.87! = > 7.87] = 0.20 0.70 > 21.39] = > 21.39] = 0.00 > 22.26] = 0.02 P[LR > 0.87] = 1.17 P[ LR > 0.87] = > 22.26] = 0.04 P[LR > 0.87] = 1.09 P[ LR > 0.87] = T ab le 3.8: D avies te s t. N ote th a t la rg e r m odels are in row s a n d sm a lle r in c o lu m n s. S h a d in g indicates p-value is less th a n 0.05. 1.25 1.17 0.00 0.39 1.07 USA R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 131 Simulated Moment Comparisons D a ta Scat IS Val % D ev Val •F 2V % D ev Val 3F 3V % D ev Val % D ev Val % Dev Argentina Min -0 .6 5 0 -4 .9 5 5 6 .628 -0 .4 7 6 -0.267 -0 .4 7 7 -0 .2 6 6 -0.631 •0 .0 2 8 -0 631 -0.029 Max 1.731 5.134 1.332 1.366 -0 .2 3 3 1.353 -0 .2 3 8 1.343 -0 243 I 351 -0.242 M ean 0-031 0 .0 1 9 •0.380 0 .0 3 0 •0.034 0 .0 3 0 -0 .0 2 1 0 029 -0 074 0 029 0 047 SD 0251 1.045 3.160 0 .2 5 0 •0.006 0 250 •0 .0 0 5 0 248 -0 0 1 1 0 .2 4 9 -0 009 Skew 2 .733 0 .0 4 0 -0.985 2.157 -0.211 2 .1 4 9 -0 213 2.035 -0 .2 5 5 2 .063 -0 245 Kurt 17.367 9 431 -0.469 12.004 -0.328 11 82 6 •0 338 12.064 -0 .3 2 5 12.143 -0.320 Y* \% D ev| 4.995 0 .5 7 7 0.578 0 665 0.622 Brazil Min -0-569 -0 033 -0.942 -0.376 •0.340 -0 .3 7 8 -0 335 •0.472 -0.171 -0.475 Max 0 575 0 135 -0.678 0 .6 1 7 0.072 0 62 7 0 .0 3 9 0 .5 7 9 0 .0 0 7 0 .5 8 8 0.022 Mean 0-029 0 .0 3 6 0.238 0 .0 3 0 0.021 0 .0 3 0 0 .0 1 0 0 030 0 015 0.031 0.046 •0.001 •0.1 6 5 SD 0174 0.011 -0 934 0.174 •0.002 0 .1 7 4 0.001 0 .173 -0 .0 0 7 0.174 Skew 0 426 9 .501 21.310 0 661 0 552 0 .6 6 9 0 .571 0 455 0 .0 6 9 0.461 0.084 Kurt 3 .9 5 9 143 411 35.220 3 .3 1 0 -0.038 3 .3 8 2 -0 .0 2 0 3 367 -0 .0 2 3 3 .916 -0-011 y \%Dev\ 57 702 0 .6 0 2 0 .6 1 3 0 .1 1 5 0.141 Chile Min -0 .2 3 0 -0 .2 2 2 -0.208 -0 .2 1 6 •0.228 -0 .2 1 3 •0 241 •0.241 -0 -1 4 0 •0 241 Max 0 .2 1 3 0 .2 6 3 0.206 0 .2 4 3 0 135 0 253 0 158 0 .2 2 7 0 038 0 227 0 .0 3 7 Mean 0 .0 1 6 0.021 0 336 0 013 0 .150 0 .0 2 2 0 400 0 .0 1 6 0 .0 2 2 0 .0 1 6 0.001 •0.010 -0 141 SD 0 .0 3 6 0 .0 8 4 -0 016 0 .034 -0 021 0 .0 8 4 -0 02 2 0 065 -0 .0 0 8 0 .0 3 5 Skew -0 .1 1 2 -0 .0 1 6 •0 360 -0.035 •0.691 •0 .0 2 3 0 .7 4 7 •0 024 -0 738 -0 021 •0 3 1 1 K urt 3 .0 6 6 3 .164 0.032 2 961 -0 034 2.981 •0 .0 2 8 2-357 •0 068 2.356 •0 069 y I 244 \%Dcv\ 1.197 0 396 0 .8 8 6 0.891 Colombia Min -0 .175 -0 .1 9 5 0 115 -0.160 •0.086 •0 .1 5 9 •0 0 9 0 •0.170 -0 .0 2 7 •0 172 Max 0 .3 7 3 0 .2 4 0 -0 358 0 .3 9 9 0.068 0 .4 0 9 0 .0 9 4 0 .3 3 3 -0 .1 0 9 0 344 -0 080 Mean 0 .0 2 8 0 .0 2 3 -0.207 0 .0 3 3 0.151 0 .0 3 4 0 .1 9 9 0 .0 2 7 -0 .0 6 3 0 .0 2 3 •0 .0 2 0 -0.049 -0.015 SD 0-0 8 7 0 .0 7 3 -0.102 0 .0 9 3 0.071 0 .0 9 5 0 .0 9 3 0.081 -0 .0 6 5 0 .0 6 2 Skew 1.492 0 .0 1 3 -0 991 1.201 -0.195 I 265 -0 .1 5 2 0 .3 0 5 -0 .4 6 0 0 876 •0 413 Kurt 6315 3.271 -0.520 6 .2 7 6 •0.079 6 403 •0.061 5.581 -0 181 5.777 -0 152 y |% £>eu| 1.329 0 .4 9 5 0 505 0 769 0 .633 Greece Min -0 .3 0 8 -0 .3 5 0 0.138 -0 .2 1 9 -0 290 -0 .2 1 9 -0 .2 8 9 •0 293 •0 .0 5 0 -0 292 -0.053 M ax 0 .5 8 6 0 .3 5 2 -0 399 0 483 -0.176 0 .4 8 4 -0 .1 7 3 0-477 -0 .1 8 5 0 .4 3 0 •0.131 M ean 0 .0 1 0 0 .0 0 0 -0 992 0 .0 0 8 -0 133 0 .0 0 9 -0 .1 1 6 9 .0 0 9 -0 051 0 .0 1 0 0.021 SD 0 .1 9 5 0. 16 0 .099 0.103 •0.020 0 103 -0 01 7 0 .1 0 3 -0 .0 1 8 0 .104 -0.013 Skew 1.705 0 .011 -0.994 1.474 *0.136 1.431 -0 .1 3 2 1.315 -0 229 1.335 -0.217 Kurt 9 679 3 .5 3 3 -0.635 7.712 -0.203 7 .7 2 7 -0 202 7.966 -0 .1 7 7 7.962 -0.177 y 2.719 \%Dtv\ 0.492 0 .4 6 7 0 .4 7 4 0-429 India Min -0.244 -0 .2 7 5 0 .128 -0 .1 9 9 •0.183 -0 .1 9 8 0 .1 6 9 -0 .2 0 0 -0 .1 7 8 -0.213 M ax 0 .3 5 3 0 .2 9 4 -0 .166 0 .3 2 6 -0 .0 7 7 0 .3 2 5 -0 .0 7 9 0 .3 2 5 -0 .0 7 9 0 .2 8 9 -0.131 M ean 0 014 0 .0 1 0 -0 .260 0 .0 1 4 0.034 0 .0 1 4 0 029 0.014 0 022 0 014 -0.001 -0 .1 2 5 SD 0 .0 9 0 0 .0 3 9 -0 .007 0-089 -0 .0 0 7 0 .0 8 9 •0.011 0 .0 8 9 -0 .0 1 3 0 .0 3 8 -0 0 1 7 Skew 0 .5 7 2 -0 .0 0 4 -1 .007 0 .6 4 7 0.131 0 .6 5 2 0 139 0 .6 0 8 0 .0 6 2 0 333 •0.330 Kurt 4 .4 2 2 3 .3 0 6 -0 .139 3.951 •0.106 3 .9 6 8 -0 .1 0 3 3.935 -0 .1 1 0 3 .406 -0.230 y 1 414 \%Dev\ 0 .2 8 1 0 .278 0 .2 0 6 0.578 Indonesia Min -0 .2 0 9 -0 .1 9 7 •0.056 -0 .1 7 5 -0.161 -0 .1 7 8 •0 .1 4 6 -0 .2 0 0 -0 .0 4 4 -0 .1 9 9 M ax 0 .2 0 0 0 .2 1 0 0 .0 5 0 0 .2 2 4 0.121 0 .2 2 6 0 .1 3 2 0 .214 0 .0 6 9 0.214 0.063 M ean 0 .0 0 5 0 .0 0 4 -0 .126 0 .0 0 5 -0 .0 6 6 0 .0 0 5 -0.101 0 .0 0 6 0 .2 4 2 0 .0 0 6 0 .1 6 7 SD 0 .0 8 3 0 .0 8 2 -0 .016 0 .0 8 3 0 .0 0 0 Q.Q85 0 .0 1 3 0-084 0.QQ5 0 .0 8 4 0 .0 0 4 Skew 0 .1 3 9 0 .0 7 6 -0 .4 5 6 0 .3 8 3 1.746 0 .3 9 2 1.310 0 .0 5 9 -0 .5 7 5 0 .0 6 2 -0-556 K urt 3 .0 6 4 2 .9 6 3 •0 .0 3 3 2 .932 -0 .0 4 3 2 .9 4 9 -0 .0 3 7 2 .9 3 7 -0 .0 4 1 2 .9 2 9 -0.044 •0.047 continued on n ext page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 132 Simulated moment comparisons - continued from previous pa/xe S ta t D a ta y ' |% £>ee| IS V al 2F % D ev Vat 2V % D ev 1.875 0 .6 3 1 ) 3V 3F % D ev Val Val 1.961 % D ev Val % D ev 0.771 0.864 Jordan M in -0 .1 2 8 -0 .1 5 2 0.184 -0 .1 0 9 -0.151 •0 .1 0 9 -0 .1 5 5 -0 .1 4 5 0.132 -0.145 0.131 M ax 0 .1 6 2 0 .1 5 8 -0 .0 1 9 0 .1 5 8 -0.024 0 .1 5 8 -0 .0 2 4 0 .1 4 2 -0.118 0 .1 4 4 -0.110 -0.056 M ean 0 .0 0 6 0 .0 0 3 -0 .5 4 3 0 .0 0 6 0 .0 1 3 0 .0 0 6 0 .0 1 6 0 .0 0 6 •0.072 0 .0 0 6 SD 0 048 0 .0 4 9 0 .032 0 .0 4 8 0.001 0 .0 4 8 0 .0 0 1 0 047 -o.oia 0 .0 4 7 -0 015 Skew 0 .3 9 4 0 003 -0 .992 0 .4 3 0 0.091 0 437 0 .1 0 9 0 .2 4 7 -0 374 0 .251 •0.363 K urt 3 .9 5 5 3 727 -0 .0 5 8 3 .3 0 0 -0.166 3 .292 -0 .1 6 8 3 822 -0 .0 3 4 3.821 -0.034 / [%Dev{ 1.625 0 .2 7 1 0 .2 9 4 0 .4 9 8 0 .4 6 7 Korea Min -0 .1 9 2 -0.221 0 .1 4 8 -0 1 7 6 •0.087 -0.175 -0 0 9 1 -0.181 •0.057 -0.182 •0 .0 5 3 M ax 0 .3 0 6 0 .2 5 0 •0.184 0-267 -0.127 0.271 -0 1 1 4 0 278 -0.091 0.281 -0.083 M ean 0 .0 1 2 0 .0 1 3 0 .1 3 0 0013 0 097 0 .013 0.L1S 0 .0 1 3 0 .0 8 6 0 01 3 0 .0 5 8 3D 0 .0 8 5 0 .0 8 3 -0 .0 1 6 0 085 0 .004 0 .085 0 00 5 0 085 0 .004 0 085 0 005 Skew 0 .7 3 8 0 038 -0 .9 4 9 0 623 -0 155 0 638 -0 135 0 628 •0.149 0 644 -0.126 K urt 3 .582 3 .1 1 5 -0.130 3 .2 0 8 -0 105 3 265 -0 0 8 9 3 .4 4 2 •0 039 3 .4 8 9 -0 .0 2 6 } \ %Dev\ I 226 0 .3 4 7 0 .3 6 ! 0 278 0 .2 1 6 Malaysia Min -0 .3 0 6 -0 .2 1 6 •0 .2 9 5 •0 .1 8 6 -0.392 •0 1 8 4 -0 40 0 -0 .2 0 7 •0 324 •0.204 -0.332 M ax 0.211 0 .2 5 2 0 .1 9 5 0 .2 1 0 -0.002 0 216 0 025 0 .1 9 5 -0 071 0 .2 0 0 •0.049 M ean 0 .0 1 2 0 .0 1 8 0 .4 8 7 0 .0 1 2 -0 031 0 .012 -0 0 3 9 0 .0 1 3 0 .0 2 6 0 01 3 0 054 SD 0 .0 7 5 0 .0 7 9 0 .057 0 .0 7 4 •0 on 0 .074 -0 0 0 8 0 .0 7 5 0 004 0 07 5 -0 .0 0 2 Skew -0 .4 4 6 -0 .0 0 4 •0.991 0 .0 0 3 -1.007 0 .0 5 0 •1.113 -0.321 •0 .2 8 0 -0.271 -0 393 K urt 4 .6 2 5 3 .6 5 7 -0 .2 0 9 2 .9 7 8 -0.356 3 .024 -0 .3 4 6 3 .1 5 2 -0.319 3 .2 0 3 -0.308 } |% D c u | 1.745 1.405 1.506 0 757 0 .6 2 9 Mexico Min -0 .5 9 3 ♦0 391 -0.341 -0 .3 2 2 ■0.457 -0.323 -0 45 6 -0 .5 0 9 -0.141 -0 495 ♦0 166 M ax 0 .3 9 6 0 .4 2 7 0 .0 7 7 0 465 0.175 0.460 0 .1 6 1 0 430 0 08 6 0 354 •0 106 M ean 0 .0 2 0 0 .0 1 9 -0.072 0 .0 2 2 0 099 0 021 0 071 0 021 0.031 0 021 0 034 SD 0 .1 2 9 0 .1 2 9 -0.001 0 .1 3 0 0 010 0 130 0 009 0 .1 2 9 -0 002 0 126 -0 024 Skew -0 813 •0 .0 0 8 -0.990 0 .2 5 7 -I 316 0 246 -1 30 3 ♦0 61 7 -0.241 •0 701 -0 .1 3 8 K urt 6 584 3 .8 3 4 -0.418 3 .6 0 3 -0.453 3.546 -0 461 6 .0 9 9 -0 .0 7 4 5.241 ♦0.204 y \%Dcv 1.482 I 878 1.844 0 .3 4 8 0 .400 INigeria Min -0 .5 6 0 • I 447 1.581 -0 .1 9 6 -0.650 *0.203 -0 6 3 8 •0 .4 1 8 -0.255 -0 .4 2 0 M ax 0 .3 8 9 1.416 2.642 0.331 -0.149 0 .3 5 0 -0.100 0 .3 2 0 -0 .1 7 7 0 .3 2 2 -0.172 Ntean 0 .0 1 8 0 .0 2 3 0 .2 4 0 0 .0 1 9 0.031 0 01 8 -0 .0 3 7 0 .0 1 8 -0.044 0 .0 1 8 -0 .0 2 4 SD 0 .0 8 9 0 .3 1 0 2 .465 0 .0 9 0 0 .0 0 5 0 .0 8 8 -0 0 1 4 0 .0 8 8 -0.018 0 .0 8 9 -o.on Skew -1 .3 6 ? 0 .0 0 2 -1.001 0 548 ♦1.400 0 .4 4 6 -1 .3 2 6 -0 .6 8 6 •0 .4 9 9 •0.685 -0.499 K urt 1 6.218 10.312 -0.364 4 .1 0 6 -0 747 4.614 •0-716 1 2.836 -0 .2 0 9 12.788 -0.212 y \%Dcv\ 4.071 2.184 2 093 0 .7 6 9 -0 .2 5 0 0 .7 4 5 Pakistan M in -0-161 -13.651 8 3.978 •0 .1 4 5 -0 .0 9 5 -0 1 4 5 -0 0 9 6 -0 .1 8 0 0 .1 2 0 -0 .1 8 0 0 123 M ax 0 .3 5 3 13.192 3 6.405 0 .3 2 2 -0.086 0 .3 2 6 -0 .0 7 6 0 .3 0 3 -0.141 0 .3 0 6 -0.132 M ean 0 .0 1 3 0 .0 3 9 2 .068 0 .0 1 4 0 .095 0.014 0 .1 3 3 0 .0 1 3 0 .0 1 2 0 .0 1 3 0 .0 2 7 SD 0 .0 7 3 2 .9 6 8 3 9.854 0 072 -0.011 0.072 - 0 .0 0 4 0 .0 7 0 -0.043 0 070 -0.039 Skew 1.249 0 .0 1 3 •0 .9 9 0 1.120 •0.104 1.170 - 0 .0 6 3 0 .7 7 6 -0 .3 7 9 0 .8 1 3 -0 .3 4 9 K urt 7 .9 3 8 10.264 0 .2 9 3 6 .5 4 5 -0.176 6 .636 -0 -1 6 4 6 .6 0 6 -0.168 6 .6 4 4 -0 .1 6 3 y |% D e u | 43.205 0385 0 .3 6 4 0 .6 0 2 0 .5 7 8 Phili ppines M in -0 .2 9 3 -0 .2 3 9 •0.184 • 0 .1 9 3 -0.340 -0.201 -0 .3 1 5 -0 .2 4 5 •0 .1 6 3 -0 .2 4 3 M ax 0 .4 2 4 0 .3 0 3 -0.285 0 .4 0 5 -0.044 0 .416 -0 .0 2 0 0 .3 9 0 -0 .0 7 9 0 .3 9 0 -0 .0 8 0 M ean 0 .0 3 0 0 .0 3 1 0 .0 1 8 0 .0 3 0 -0.015 0 .0 3 0 -o.oio 0 .0 3 0 •0.011 0 .0 3 0 -0 .0 0 6 SD 0 .1 0 2 0 .101 -0 .0 0 7 0 .1 0 0 -0.018 0. LOO -0 .0 1 5 0 .1 0 0 -0.021 0 .1 0 0 -0.023 Skew 0 .6 8 2 0 .0 2 0 -0.970 0 .9 0 5 0 .328 0.841 0 .2 3 4 0 .7 2 5 0 .0 6 3 0 .7 3 4 0 .0 7 7 continued on next R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. -0.170 page 133 Simulated moment comparisons - continued from previous page S ta t D a ta K urt % 5 .753 IS 2F V 3F 3V Val % D ev Val % D ev Val % D ev Val % D ev Val % D ev 3 .0 1 7 -0 476 4 .9 3 2 -0.143 5 .012 -0 1 2 9 5-375 •0.066 5 389 •0 .0 6 3 |% D ev( 1.470 0.504 0 .3 8 8 0 169 0 .1 6 0 Fort;ugal M in -0.293 -0 455 0 .552 -0 .2 0 9 •0.288 -0.210 -0 .2 8 2 -0 .2 5 7 -0 .1 2 3 -0 .2 4 6 -0.160 M ax 0 .708 0 474 -0.331 0 .4 5 0 -0.265 0 .4 2 0 -0 .4 0 7 0 .4 2 7 -0 .3 9 7 0 .4 1 7 -0.411 M ean 0 .0 2 3 0.011 -0.513 0 .0 2 5 0 .0 8 9 0 021 -0 .1 1 4 0 .0 2 3 0 .0 0 6 0 .0 2 0 ■0.128 SD 0 .115 0.121 0 .0 5 3 0 .1 1 4 -0.005 0 .1 0 9 -0 .0 4 8 0 .1 1 0 -0.044 0 103 -0 107 Skew 1.979 -0 .0 1 6 -1.008 1 .134 -0 .4 2 7 1.014 -0 .4 8 7 0 .9 5 0 -0 520 0 924 -0 533 K urt 12.503 7 .620 -0.391 5 .3 4 7 -0 572 4.967 -0 .6 0 3 5 .7 6 5 -0 .5 3 9 6 .0 0 2 -0.520 y \%Dtv\ 1.965 1.093 1 253 1.109 1.288 Thailand M in -0 J3S -0 22 1 -0 339 •0 303 -0 104 •0 307 •0 .0 9 2 -0 .2 8 8 -0 148 -0 271 -0 200 M ax 0 .322 0 .2 4 8 •0 230 0 220 -0.318 0 .2 1 9 -0 322 0 315 -0 .0 2 3 0 232 -0.281 M ean 0 .013 0012 -0. I l l 0 012 •0.081 0 012 -0 124 0 013 -0 .0 3 9 0 012 •0 072 SD 0 .0 8 0 0 .0 8 0 0 .0 0 0 0 .0 8 0 0 001 0.081 0014 0 079 -0.003 0 .0 7 9 -0.009 Skew -0.0-10 0 .0 1 5 -1.443 •0.461 10 435 ■0.508 11.591 -0 .0 1 7 -0 .5 7 8 -0 .0 8 2 1.029 K urt 5 625 3 .352 •0 404 4 .511 -0 198 4.559 -0 .1 8 9 5.641 0 .0 0 3 4 058 -0.279 } |% D eu | I 958 10.715 I 1.918 1.389 0 .6 2 3 Turkey M in -0.315 -0 475 0.511 •0 .3 8 2 0.216 -0.382 0 216 -0 .3 8 2 0 .2 1 3 -0.381 0 .2 1 0 M ax 0 693 0 540 -0.221 0 63 4 •0 085 0 624 -0 100 0 637 •0.081 0 620 -0.106 0 048 M ean 0.03-1 0 .0 3 4 -0.011 0 .0 3 5 0 020 0 036 0 .0 4 3 0 .0 3 6 0 05 0 0 036 SD 0 .2 0 0 0 .195 -0 .026 0 .1 9 7 -0 016 0.198 • 0 .0 1 0 0 .1 9 7 -0 015 0 198 0 011 Skew 0 .962 -0 010 -1 .0 1 1 0 .6 7 2 -0.302 0.642 -0 332 0 673 -0.301 0 638 ■0 338 K urt 1 021 2 .960 -0.264 3 .5 0 8 -0.128 3 339 -0 170 3 505 ■0 128 3 .335 } J% Dev| 1 311 0 .4 6 5 0 554 0 171 0 568 0 495 Venezuela M in -0.198 •I 232 1.475 -0 .2 9 6 -0 405 ■0 .293 ♦0 412 -0 .4 2 6 •0 .1 4 4 -0 420 -0 157 M ax 0 .185 1.248 1.571 0 .4 0 8 -0.160 0.472 • 0 .0 2 9 0 399 •0 179 0 459 -0.054 M ean 0 .0 2 7 0 .0 0 7 -0.735 0 .0 3 3 0 .198 0 029 0 07 7 0 02 9 0 .0 6 3 0 029 0 .068 SD 0.131 0 .2 8 0 1.132 0 .1 3 1 0.001 0 129 -0 014 0130 0 128 -0.027 S kew 0 .1 3 0 -0 018 -1.137 0 203 0 .568 0.374 1 886 0 00 6 -0.952 0 029 •0 779 K urt 5.360 11.632 I 170 3 .0 8 5 -0 424 3 .832 -0 .2 8 5 4 .424 -0.175 5.061 •0 .0 5 6 > ' \%Dzv\ 4.171 1.191 2.261 -0.011 I 201 0.931 Zimbabwe M in -0.279 -0 .2 4 9 -0 .1 0 7 •0 .2 4 4 -0 124 •0 243 -0 .1 3 0 -0 .2 7 5 -0 .0 1 4 -0 .2 7 3 -0.023 M ax 0 .1 6 0 0 .2 9 2 -0.366 0 .3 7 3 -0 .1 8 9 0 .3 7 2 -0 .1 9 2 0 .3 2 8 -0 .2 8 7 0 332 -0 277 -0 .0 3 2 M ean 0 .0 1 3 0.021 0 .533 0 .0 1 2 -0.143 0 .012 -0 .1 1 0 0 .0 1 3 -0.068 0 .0 1 3 SD 0 .0 9 9 0 .0 9 5 -0.041 0 .0 9 8 •0 .0 0 5 0 098 -0 .0 0 9 0 .0 9 7 -0 .0 1 7 0 .0 9 6 -0 022 Skew 0 .2 7 0 0 .0 1 0 -0.965 0 .3 8 0 0 .404 0 388 0 .4 3 4 0182 -0.326 0 .1 9 4 -0.281 K urt 5.121 3 .1 6 0 -0.383 3 .9 6 4 •0.226 3 .964 •0 .2 2 6 3 .731 -0.271 3 776 -0 263 > ' |% D evi 0 .7 7 8 1.921 0 778 0 682 0 .5 9 7 France M in ♦0.269 -0 .1 9 2 -0.286 -0 162 -0.398 -0 237 •0 .1 1 8 M ax 0 .205 0 .2 1 0 0.011 0.024 0 .2 1 5 0 .048 0 .1 8 5 0 .0 1 6 0 .403 0.011 -0 .0 9 9 -0.021 M ean 0.011 SD 0 .0 6 3 0 064 0 .0 1 2 0 .0 6 6 0 .0 3 8 0 .0 6 5 S kew -0.4*18 -0.019 -0 .9 5 7 0 .1 9 3 -1.431 -0 .6 0 9 0 .3 6 0 K urt 5.033 3 .5 7 8 •0.289 3 .1 0 5 -0.383 4 .9 0 9 -0 .0 2 5 / |% D ev{ 1.278 2.256 0 .0 0 1 0 .031 0 .4 1 6 Germany M in -0 .1 9 4 -0 .1 8 9 -0 .0 2 7 -0 .1 8 6 -0 043 -0 .1 8 0 M ax 0 .1 9 0 0.201 0 .0 5 8 0 .1 7 2 -0.096 0 .2 1 6 0 135 0 .0 1 4 0 .202 0 .0 1 1 -0 .0 2 2 -0 .0 1 7 M ean 0.011 0 .011 0.000 SD 0 .0 5 9 0 .0 6 3 0053 0 .0 5 9 -0 .0 0 5 0 .0 5 8 S kew 0 .042 -0 .0 2 0 -1 .4 6 4 -0 .2 5 3 -6.952 0 .2 0 8 -0.074 3.901 continued on next page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 134 Simulated moment comparisons - continued from previous page D a ta S ta t IS 2F V % D ev Val Val % D ev Val % D ev Val I K urt \ 4 .125 3.931 \%Dev\ -0 .0 4 7 3 .540 1.565 -0 .1 4 2 4 .5 0 3 7 301 3V 3F % D ev 1 4 032 1 M in ♦0.245 -0.194 -0.206 •0.192 -0.215 -0 233 •0 .0 5 0 M ax 0 .2 1 6 0 .2 3 7 0.095 0 .222 0 .0 2 6 0 .2 1 3 -0 .0 1 6 M ean 0 .0 1 3 0 .0 1 5 0 .175 0 .015 0 .1 3 0 0 01 3 -0 .0 4 6 3D 0 073 0 .0 7 3 -0 .0 0 2 0.074 0.011 0 .0 7 5 0 .0 2 9 S kew 0 .0 8 6 0 .0 4 6 -0 .4 7 8 0 .0 0 0 -1 .00 0 -0.264 •3 .9 8 8 K urt 3 .7 2 7 3 .254 -0 .1 2 7 3 .003 -0.194 3 .572 •0 .0 4 2 \%Dev\ 0.781 1.334 4 .105 UK M in -0.224 •0.138 -0.384 -0-194 •0 .1 3 4 -0 .1 4 9 M ax 0.171 0 .1 6 7 •0.024 0 162 •0.051 0.181 0 .0 6 2 M ean 0 O il 0011 •0 .0 1 3 0 013 0145 0 .0 1 0 -0 063 •0 .3 3 3 3D 0 .0 5 6 0 055 •0.015 0 055 •0 .0 2 3 0 05 5 -0 .0 0 9 Skew -0 .089 0 045 -1 .5 0 0 •0.321 2.604 0. 14 -2 .2 8 0 Kurt 4.351 2 .910 -0.331 4.100 -0 .0 5 8 3 .469 •0 198 y \%Dcv\ 1.860 2 829 3.550 USA Min ♦0.216 ■0.113 ♦0.475 -0 159 -0 264 -0.184 •0 .1 4 8 M ax 0 .1 4 0 0 .1 3 3 •0 047 0 .1 0 9 -0 221 0 .1 3 3 -0 .0 4 5 -0 .0 0 4 M ean 0.011 0 .0 1 0 •0.117 0 01 1 •0 02 7 0.011 3D 0 .0 4 0 0 .044 0 096 0.041 0 024 0 04 0 0 .0 0 7 Skew -0 .8 6 0 0 .004 -I 005 •0.632 -0 .2 6 5 •0 621 -0 .2 7 8 K urt 7 701 3 .132 •0.593 4.885 •0 .3 6 6 7 100 -0 .0 7 8 >_ !% D eu | % Dev 0 .0 9 2 Jaipan Y Val 1.811 0 682 0 .3 6 7 T a b le 3.9: M om en t m atch in g s t a tis tic s M ean s t a t is t ic s from 2000 ran d om ite r a tio n s of th e m o d els. S h a d in g in d ica te s lea st % d e v ia tio n . T h e su m lin e su m s a b so lu te % d e v ia tio n s o f first fou r m om en ts. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 135 M odel Lser pn Transitional probabilit ies p i- p ij p -1 pa p -j p si P J- 0.20 0.20 0.20 1.00 1.00 1.00 0.80 0.80 0.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.74 0.73 0.73 0.77 0.77 0.77 0.26 0.27 0.27 0.23 0.23 0.23 0.04 0.04 0.04 0.01 0.01 0.01 0.45 0.45 0.45 0.99 0.99 0.99 0.51 0.51 0.51 0.25 0.25 0.25 0.26 0.25 0.25 0.00 0.00 0.00 0.74 0.75 0.75 0.75 0.75 0.75 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.63 0.63 0.63 0.00 0.00 0.00 0.37 0.37 0.37 0.36 0.55 0.55 1.00 1.00 1.00 0.49 1.00 1.00 0.00 0.00 0.00 0.18 0.00 0.00 0.42 0.44 0.58 0.56 Argentina 2F 2V 2V 3F 3V 3V 0 1 0 1 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.98 0.99 0.90 0.98 0.99 0.89 0.02 0 .0 1 0.10 0.02 0.01 0.11 0.92 0.95 0.80 0.90 0.93 0.73 0.08 0.05 0.20 0.08 0.05 0.25 0.98 0.98 0.00 0.70 0.71 0.66 0.02 0.02 1.00 0.30 0.29 0.34 Brazil 2F 2V 2V 3F 3V 3V 0 1 0 I 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 0.02 0.02 0.02 Chile 2F 2V 2V 3F 3V 3V 0 I 0 1 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 Colombia 2F 2V 2V 3F 3V 3V 0 L 0 L 0.22 0.00 0.00 0.78 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.99 1.00 0.96 0.99 1.00 0.96 0 .0 1 0.00 0.04 0.01 0.00 0.04 0.96 0.98 0.90 0.96 0.97 0.89 0.04 0.02 0.10 0.04 0.02 0.11 0.95 0.94 0.96 0.78 0.96 0.89 0.05 0.06 0.04 0.22 0.04 0.64 0.45 0.11 0.45 Greece 2F 2V 2V 3F 3V 3V 0 1 0 I 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.01 0.01 0.01 India 2F 2V 2V 3F 3V 0 3V I 0 I 0.95 0.51 0.51 0.03 0.39 0.39 0.03 0.10 0.10 0.00 0.00 0.00 Indonesia 2F 2V 2V 3F 3V 3V 0 1 0 1 1.00 0.29 0.29 0.00 0.71 0.71 0.00 0.00 0.00 0.65 0.07 0.10 0.73 0.67 1.00 0.30 0.59 0.90 0.27 0.33 0.00 0.05 0.35 0.00 0.93 0.92 0.07 0.08 0.33 0.00 0.00 Jordan 2F 2V 0 continued on next page R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission. 136 Transitional orobabilities - continued from previous p age M odel 2V 3F 3V 3V Lser I 0 I P ii 0.00 0.00 0.00 p 12 0.80 0.80 0.80 p 13 0.20 0.20 0.20 p ll p ii 0.01 0.01 0.01 0.96 0.89 0.89 0.91 0.04 0.10 0.11 0.09 0.82 0.85 0.72 0.78 0.83 0.61 0.18 0.15 0.28 0.03 0.02 0.28 p j i p 0.10 0.10 0.10 P J0.44 0.45 0.45 0.45 0.56 0.45 0.45 0.45 0.84 0.87 0.87 0.82 0.84 0.84 0.00 0.00 0.00 0.18 0.16 0.16 0.16 0.13 0.13 0.00 0.00 0.00 0.94 0.94 0.94 1.00 1.00 1.00 0.06 0.06 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.56 0.56 0.54 0.55 0.55 0.46 0.44 0.44 0.46 0.45 0.45 0.00 0.00 0.00 0.54 1.00 1.00 0.63 0.62 0.62 0.46 0.00 0.00 0.37 0.38 0.38 0.26 0.22 0 22 0.22 0.74 0.75 0.75 0.53 0.53 0.53 0.00 0.00 0.84 0.89 0.89 0.83 0.83 0.83 0.16 0.11 Q .lt 0.17 0.17 0.17 0.24 0.25 0.50 0.56 0.56 0.26 0.21 0.50 0.44 0.44 0.50 0.50 Korea 2F 2V 2V 3F 3V 3V 0 1 0 I 0.00 0.00 0.00 0.61 0.63 0.63 0.39 0.37 0.37 0.19 0.15 0.11 Malaysia 2F 2V 2V 3F 3V 3V 0 1 0 I 0.59 0.60 0.60 0.00 0.13 0.13 0 .1 1 0.27 0.27 0.08 0.08 0.05 0.95 1.00 0.73 0.92 0.92 0.65 0.05 0.00 0.27 0.00 0.00 0.30 0.99 0.99 1.00 0.98 0.98 0.98 0.01 0.01 0.00 0.01 0.01 0.98 0.99 1.00 0.97 0.97 0.91 0.02 0.01 0.00 0.03 0.02 0.08 Mexico 2F 2V 2V 3F 3V 3V 0 1 0 1 0.43 0.43 0.13 0.57 0.57 0.57 0.00 0.00 0.00 0.02 0.02 0.02 0.00 N igeria 2F 2V 2V 3F 3V 3V 0 L 0 L 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.01 0.01 0.01 Pakistan 2F 2V 2V 3F 3V 3V 0 1 0 I 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.05 0.05 0.04 0.98 0.99 0.90 0.93 0.94 0.85 0.02 0.01 0.10 0.02 0.01 0.10 0.25 0.25 0.25 0.25 0.25 Philippines 2F 2V 2V 3F 3V 3V 0 L 0 L 0.38 0.38 0.38 0.62 0.62 0.62 0.00 0.00 0.00 0.03 0.03 0.03 0.95 0.96 1.00 0.91 0.91 0.92 0.05 0.04 0.00 0.05 0.05 0.05 0.00 Portugal 2F 2V 2V 3F 3V 0 I 0 0.50 0.50 0.27 0.26 0.23 0.25 0.00 0.00 0.97 0.98 0.53 0.98 0.99 0.03 0.02 0.47 0.02 0.01 continued on next page R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 137 Transitional M odel 3V orobabilities - continued fromprevious page Lser P ii p ii p !3 P -1 p i 2— p23 p j i P J- pSJ I 0.50 0.26 0.25 0.00 0.78 0.22 0.25 0.24 0.50 0.01 0.01 0.01 0.99 0.99 0.99 Thailand 2F 2V 2V 3F 3V 3V 0 1 0 1 0.26 0.31 0.31 0.74 0.69 0.69 0.00 0.00 0.00 0.01 0.00 0.00 Turkey 2F 2V 2V 3F 3V 3V 0 1 0 1 0.00 0.00 0.00 0.98 1.00 1.00 0.02 0.00 0.00 0.00 0.04 0.02 0.25 0.43 0.75 0.57 0.00 0.88 1.00 0.02 0.12 0.55 0.45 0.86 0.14 0.07 0.47 0.14 0.08 0.48 0.97 0.93 0.53 0.86 0.89 0.50 0.00 0.30 0.05 0.05 0.70 0.56 0.56 0.11 0.00 0.00 0.00 0.89 0.69 0.69 0.89 0.69 0.69 0.00 0.00 0.00 0.19 0.67 0.67 0.42 0.70 0.70 0.81 0.33 0.33 0.58 0.30 0.30 1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.21 0.79 0.62 0.38 0.38 0.31 0.31 0.11 0.31 0.31 Venezuela 2F 2V 2V 3F 3V 3V 0 1 0 I 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.01 0.01 0.01 0.97 0.03 1.00 0.00 0.85 0.91 0.99 0.84 0.15 0.08 Zimbabwe 2F 2V 2V 3F 3V 3V 0 I 0.14 0 I 0.1-1 0.14 0.00 0.00 0.00 0.86 0.86 0.86 0.02 0.02 0.02 0.15 0.69 0.16 0.03 0.15 0.98 0.99 0.02 0.01 0.92 0.95 0.96 0.84 0.08 0.03 0.14 0.00 0.00 0.00 0.99 0.95 0.01 0.01 0.00 0.38 0.33 0.92 0.67 0.06 0.08 0.69 0.98 0.23 0.99 0.89 0.01 0.00 0.08 0.48 0.92 0.52 0.01 0.99 0.25 trance 2F 3F 0.00 0.01 Germany 2F 3F 0.26 0.61 0.13 0.02 Japan 2F 3F 0.28 0.10 0.62 0.04 UK 2F 3F 0.14 0.00 0.86 0.06 0.07 0.00 1.00 0.91 0.03 0.02 0.00 0.75 USA 2F 3F 0.46 0.54 0.01 0.99 0.01 0.00 1.00 T able 3.10: T ra n s itio n a l p ro b a b ilities. T h e L Ser colum n in d ic a te s th e value of th e lib e ra liz a tio n in te rv en tio n series. P ro b a b ilitie s affected by tim e -v a ry in g p a ra m e te rs a re sh a d e d . 0.00 1.00 0.00 0.00 R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 0.99 0.00 138 Coefficients and standard errors Argentina 2F is C oef SE 2V 3V 3F C oef SE C oef SE C oef SE C oef SE -3.674 0.453 -4.448 2.300 0.711 0.942 -3.668 0.453 -1.39-1 1.119 -4.145 2.306 -1.402 0.711 0.939 1.120 0.169 -0.675 0.006 1.168 0.026 -0.022 0.008 0.191 0.012 0.079 0.081 0.068 0.169 -0.675 0.006 1.163 0.026 -0.024 0.008 0.192 0.012 0.083 0.082 0.069 C oef SE C oef SE -3.592 -2.459 1.080 0.172 -3.710 -2.926 1.839 0.929 0.568 0.830 1.227 0.122 -0.340 -0.003 0.346 0.132 0.053 0.587 0.009 0.123 0.013 0.041 0.135 0.092 1.227 0.122 -0.356 -0.003 0.350 0.171 0.049 0.589 0.009 0.104 0.013 0.043 0.145 0.091 J ii ^12 ^21 *^231 J-232 ^ 31 ^32 •> 2 t (I* * ) = 9st *(ao + a [ -r a> H aq L). g^[-l = •) 1) forecasts, current shocks can have very long lasting effects if the persistence parameter is close to 1. 4.2.1 A tim e-varying probability extension There is a fundamental problem in that the standard Markov switching model estimates fixed switching probabilities over the entire period. This is problematic because with only a few switches, the switching probability is estimated very inaccurately and is subject to considerable revision as each new switch is reached. This is a small sample problem, but the sample size for the switching process is really the number of switches and not the total number of data points. This means that even if higher frequency data were collected, this would continue to be a problem. Another fundamental problem is that the switching process may not be stationary. If the periods of volatility are related to the process of integration, we would expect that high volatility periods would become less frequent as the emerging markets developed and stabilized. By using the integration period to estimate transitional probabilities, we would bias the probability of moving from a low to a high variance regime upward, and bias the probability of staying in a low variance state downward. Conversely, a country that is moving into a period of integration may have biases in the opposite direction. If this R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 156 is a problem, we would expect that the fixed switching probability model would fit well in-sample but not forecast well out-of-sample. There is some evidence of this presented below. To alleviate this problem. I extend the SWARCH model by using time-varying switching probabilities. I allow the probability of switching to a high variance state to depend on whether the country is undergoing a liberalization policy shock, since we would expect liberalization to result in higher probability of having an extreme shock. Not only should this increase the accuracy of the estimation, but it allows for the probability of switching to a high volatility state to change through the time period, which is not possible in the standard Markov framework. An extension to Hamilton's fixed probability model is presented in Filardo (1994) and Diebold et al. (1994) in which the switching probabilities are endogenous. The switching probabilities are estimated as a logistic function although other functions could be used. In a two state model, this can be written as pu _ plJ = exp{xt- n i ) 1 + exp(ar£_ i7 ,) exp(xt_i7i) \ + e x p { x t- a ,) for lj = i2 (412) The first column of the x matrix is a row of ones. If it is the only column in the x matrix. then the model reverts to the fixed probability model. The more interesting case is that in which additional data series are allowed to influence the switching probabilities so 7 is a vector that is estimated along with the other parameters. The first element of the 7 vector influences the constant probability of switching. If the other elements are non-zero, the probabilities are time-varying and conditional on the other series. There is considerable flexibility in this model since different data series can be used to influence the switching probabilities. Here. I use a single intervention series that indicates whether the market was experiencing a policy shock .3 5 For a recent paper that allows the duration of the state to affect the switching probabilities, see Maheu and McCurdy (2000). R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 157 The shocks used in this series are given in a table at the end of this paper. The intervention series is formed by taking a value of • It = 0.8 in the month of the "direct" policy change and I t = 0.8l+T. for r = 1........ 4 in the four months after the policy change. • It = 0-4 in the month of the "indirect” policy change and It = 0.41_rr. for r = 1........ 4 in the four months after the policy change. • If there is any overlap, the highest value is used. • It = 0 otherwise. This intervention series is similar to that used in chapter 2. See page 63 for a more complete explanation of the rationale. Two important differences are that this paper does not use any lead information, and does use more types of shocks, including political shocks. For a description of the episodes used in this paper, see page 168. The intervention series allows the probability of switching to a high volatility state to be influenced by the policy shock, with some residual effect in the four months after the policy shock. It may be that the policies are anticipated so that the affect of the policy was anticipated before the policy date, but that was not considered here. 4.3 W ith in -sam p le forecasting results In Table (4.1). I show in-sample results. These results are in-sample in the sense that the estimation is done using data from the entire period. The estimated coefficients are then used to forecast variance 1-month ahead using pre-determined data. For each country and each model, I show the estimated measure of persistence (A) and the percentage reduction in mean absolute forecasting error (MAE) from the constant variance model. For example, the 19.92 for SWARCH in Argentina indicates that the SWARCH model had a mean absolute forecasting error that was 19.92 percent lower than the constant variance model. The results of the model that had the largest reduction in forecasting error are shaded. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 158 Two im portant results stand out: • the persistence parameter for the GARCH model is frequently very large and close to one .6 • the SWARCH models tend to have the most accurate volatility forecast, with the two flavors of SWARCH having the highest reduction in mean absolute error in 21 of the 24 countries. Interestingly, the SWARCH model performed well in four of the five developed countries, with only the U.S. getting better fit from the GARCH model. Notice that if the TVPSWARCH model were not in the comparison, the SW'ARCH model would have the highest reduction in mean absolute error in 19 of of the 24 countries, including 15 of the 19 emerging market countries. Still at issue is whether the fixed switching probability SWARCH model is overfitting the data. 6One interesting note is that Lamoureux and Lastrapes (1993) find that the persistence problem is m ainly seen in high frequency data and tends to lessen as data is aggregated. Here, it is a problem even using monthly data. R e p ro d u c e d with permission of the copyright owner. Further reproduction prohibited without perm ission. 159 A rg e n tin a B razil C h ile C o lo m b ia G reece In d ia In d o n esia J o rd a n K orea M alay sia M exico N igeria P a k ista n P h ilip p in e s P o rtu g a l T h a ila n d T urkey V enezuela Z im babw e F rance G e rm an y Japan UK USA A PRM AE A PRM AE A PRM AE A PRM A E A PRM A E A PRM A E A PRM A E A PRM AE A PRM AE A PRM AE A PRM A E A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE A PRM AE ARCH 0.90 -10.64 0.34 1.10 0.48 4.25 0.45 19.44 0.47 4.41 0.52 3.08 0.00 1.11 0.33 -0.36 0.41 1.00 0.58 -4.34 0.62 6.97 1.13 -9.45 1.56 -46.59 0.12 3.73 1.02 21.10 0.43 2.13 0.39 0.00 0.67 -14.78 0.54 0.77 0.37 1.91 0.37 0.03 0.43 2.91 0.26 2.03 0.03 0.92 GARCH 1.0-1 -8.51 1.00 1.85 0.96 0.55 0.55 12.06 0.96 -2.15 0.62 1.76 1.00 0.18 0.33 -0.24 0.88 1.87 0.90 -0.03 0.89 5.20 1.13 -1.24 1.10 6.15 0.66 1.55 0.96 22.69 0.7-1 -0.08 0.00 1.04 0.67 -14.78 0.96 0.77 0.67 2.03 1.00 1.09 0.50 1.40 1.00 0.77 0.03 0.92 SVVARCH 0.74 19.92 0.02 5.70 0.48 5.08 0.35 24.76 0.00 10.03 0.-15 7.73 0.00 1.25 0.13 0.13 0.00 6.80 0.63 -8.31 0.34 14.89 0.50 16.84 0.95 5.80 0.00 3.24 0.39 28.91 0.24 10.26 0.40 -7.98 0.40 -10.60 0.00 5.32 0.45 11.10 0.00 8.46 0.36 T V P -S W A R C H 0.76 22.62 0.16 6.34 0.47 4.30 0.35 22.30 0.00 7.63 0.42 4.56 0.00 0.67 0.46 2.29 0 .0 1 5.19 0.79 3.0-1 0.35 13.48 0.44 13.97 1.11 7.34 0.00 2.32 0.38 28.72 0.24 8.05 0.42 -3.06 0.74 0.80 0.56 10.93 5.49 0.37 8.23 0.13 0.24 Table 4.1: Measure of persistence (A) and percent reduction in mean absolute error (PRMAE) from the constant variance model. 1-month ahead forecasts. R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission. 160 4.4 O ut-of-sam ple forecasts The in-sample results of the previous section show that the standard switching ARCH model does a relatively good job of fitting the data for many countries. Although this is interesting in itself, it is important to check out-of-sample results for several reasons. For one, more flexible models have a natural advantage in fitting d ata in-sample even if they do not model the process better. This over-fitting is generally not possible to see without looking at out-of-sample results. The regime-switching model is particularly susceptible to this kind of problem due to problems discussed below. Another reason for looking out-ofsample is because practitioners are interested only in out-of-sample forecasting and must be convinced of a model's usefulness. The out-of-sample forecasts discussed in this section are based on re-estimating the model each period. It is in this sense that they are out-of-sample. I am also considering forecasts up to fifteen months ahead. Two potential problems with the SWARCH forecasts come to mind. First, the SVVARCH estimation is difficult with the short data series used here and the reduction of data points by 36 for the out-of-sample estimation may have had a significant impact on the estimation of the parameters. Secondly, while the in-sample forecast errors were measured across the entire sample, the results in this section only deal with the last 36-month period. If this period did not have changes in regimes, the SWARCH model forecasts would benefit from better estimates of the parameters, but the differences would not be as dramatic as during a period of changes in regime. For example, while Argentina had considerable changes in variance early in the full sample, the last 36 months displayed relatively constant and moderate variance. In the notation used below, r is the period in which the forecasts were made and was moved from January 1994 through May 1997. The forecast variances were then compared with the actual variances. The m-step ahead forecasts are calculated in the following ways. For the constant variance (CV) model, the forecast is simply the measured variance at time r using data available at the time. Note that because this is recalculated each period, the measured variance can change over time, and so the expected volatility can change with R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. 161 each new re-estimation. The ARCH(2) forecasts were calculated by ^ r + m l r ^ 0 4 " ■+■ O t o ^ x - r m — 2 ( 4 - 1 3 ) where u i and u"_L are known but all others use forecast values calculated by iterating on equation ( 4 . 1 3 ) . The GA RCH (l.l) forecasts were similarly calculated by ^ T-rrn\r flo "i"® l^ T T in -L ® 2 ^ r + m - l (T 1 A ) where u i and h i are known but all other u* and k 2 terms use forecast values calculated by iterating on equation ( 4 . 1 4 ) . Notice that the forecast of the variance is the same as the forecast of the forecast of the variance for t > r and so equation ( 4 . 1 4 ) collapses to a r x m | r = a 0 + ( « 1 4- (4 -1 5 ) which is why aq + a-j is taken to be the persistence parameter in the G A R C H (l.l) model in the results reported above. The forecast of the SVVARCH(2.‘2) model is slightly more complicated. All of the pa rameters are calculated using time r information. The intuition is that the "smoothed’' variance series u 2 is calculated based on the smoothed values of the states in periods r and r — 1. The "smoothed" (or scaled) variance forecast h.2+m is calculated based on the smoothed variance series. Finally the actual variance forecast ov-rm is derived by scaling up the ^smoothed” variance forecast by the scale factor gSr^ m where the value of g is the weighted value given by the probability of being in the various states at time r -f- m. ^ x + m | r 9sT-i.m{&0 4 “ C t i U T _j_r T l _ i 4 - Q 2 ^ r x - m — 2) ’ ( 4 - 1 6 ) The probabilities of being in particular states are calculated by iterating on the tran sition matrix, since the m-step ahead transition m atrix is obtained by multiplying the transition matrix by itself. The 1x2 vector of probabilities is given by R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without perm ission. _ P ( S r ^ m = 2) _ 3 P ( s T+m = 1) II 162 P(Sr = 1) _ P{ * T = 2) _ To compare the models in terms of accuracy of variance forecast. I compare the variance forecast ([...]... non-normal and time-varying aspects of the distributions that are likely to occur in all markets that are emerging This simple understanding of how emerging markets are different from developed markets helps explain why formulaic application of standard mean-variance portfolios techniques is not optimal Investors invest in emerging markets because of expectations that the emerging market assets will... limiting, however Much portfolio theory uses only the joint distribution of asset returns to make decisions about asset allocation In this dissertation I look at univariate distributions of emerging market returns in chapters 3 and 4, and the joint distribution of emerging market returns with the world market returns in chapter 2 1.2.1 I n te r n a tio n a l in v e stin g The appearance of emerging equity. .. developing economies There was some research in this early period that pointed out some of the differentiating characteristics of emerging markets such as low liquidity, high transaction costs, and restric tions on foreign ownership However, much of the analysis focused on whether investing in emerging equity markets was beneficial in a standard portfolio framework that implicitly assumed that emerging markets. .. portfolio risk In other words, an alpha significantly different from zero indicates that the specified equilibrium relationship is not holding Herein lay the problem presented by emerging markets The betas of many emerging markets were low indicating that these markets were not correlated with the world market, and yet their returns were high, generating a high alpha If this were true, emerging markets would... would have presented something of a free lunch to international investors There are probably other explanations for the boom in emerging equity market investment in the early 1990s but this is the one frequently seen in the academic research on emerging markets Similarly, there are probably many contributing reasons for the emerging market crash in 1997-1998; however, over-investment probably contributed... switching model, I decompose the uncondi tional univariate distribution of the returns into a mixture of normal distributions I show that this decomposition explains the time-variation of the moments, and that the switching process is largely explained by liberalization periods in many of the emerging markets C hapter 4: I model the volatility of returns in emerging markets using a time-varying probability... reevaluation of emerging equity markets Emerging markets have been presented as an attractive investment from a portfolio stand point in both the academic and practitioner literature because of their distribution of returns, or more specifically their joint distribution of returns with the world market The framework that I propose indicates that the standard characterization of emerging market returns is... crash and its severity From this point of view, an explanation of problems in the emerging market analysis may shed light on these contributing factors Furthermore, an understanding of the first wave of emerging markets may help with interpreting the behavior of markets that emerge in the future The first part of understanding the emerging market enigma is understanding the stan dard equilibrium relationship... Capital International Tests of normality show that emerging market returns are not normally distributed The results for percent returns and log returns are show in Table (1.3) Normality is rejected even when using log returns, although less so because it reduces the influence of the large positive returns that are seen in the emerging market data I will use percentage returns rather than log returns in. .. statistics, trailing 36-month window: Argentina and Brazil C.6 1-month statistics, trailing 36-inonth window: Chile and Colombia 183 C.7 1-month statistics, trailing 36-month window: Greece and I n d ia 184 C.8 1-month statistics, trailing 36-month window: Indonesia and Jordan L85 C.9 1-month statistics, trailing 36-inonth window: Korea and Malaysia C.10 1-month statistics, trailing 36-month window: