Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings [1 ed.] 9783954896561, 9783954891566

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Alex Bergen

Rating Change Probabilities

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An Empirical Analysis of Sovereign Ratings

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Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Bergen, Alex: Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings. Hamburg, Anchor Academic Publishing 2013 Original title of the thesis: Rating change probabilities- An empirical analysis of sovereign ratings Buch-ISBN: 978-3-95489-156-6 PDF-eBook-ISBN: 978-3-95489-656-1 Druck/Herstellung: Anchor Academic Publishing, Hamburg, 2013 Additionally: Mannheim, Universität Mannheim, Germany, Bachelor Thesis Bibliografische Information der Deutschen Nationalbibliothek: Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar Bibliographical Information of the German National Library: The German National Library lists this publication in the German National Bibliography. Detailed bibliographic data can be found at: http://dnb.d-nb.de

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Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlages unzulässig und strafbar. Dies gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Bearbeitung in elektronischen Systemen. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Die Informationen in diesem Werk wurden mit Sorgfalt erarbeitet. Dennoch können Fehler nicht vollständig ausgeschlossen werden und die Diplomica Verlag GmbH, die Autoren oder Übersetzer übernehmen keine juristische Verantwortung oder irgendeine Haftung für evtl. verbliebene fehlerhafte Angaben und deren Folgen. Alle Rechte vorbehalten © Anchor Academic Publishing, ein Imprint der Diplomica® Verlag GmbH http://www.diplom.de, Hamburg 2013 Printed in Germany

Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Contents List of Figures

3

List of Tables

4

1 Introduction

5

2 Previous Literature

7

3 Agencies’ rating assessment 3.1 Rating Definitions and Methodology . . . . . . . . . . . . . . . . . . . . .

9 9

3.2

Rating Transition Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Ordered Probit Model 11 4.1 Mathematical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 4.3

Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Marginal effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Data 5.1 5.2 5.3

15 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Independent Variables and direction of change . . . . . . . . . . . . . . . . 17 Choice of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6 Estimation

22

6.1 6.2

Simple Ordered Probit Model . . . . . . . . . . . . . . . . . . . . . . . . . 23 Random Effects Ordered Probit Model . . . . . . . . . . . . . . . . . . . . 24

6.3

Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7 Predicted Probabilities and Transition matrices 27 7.1 Predicted Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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7.2 7.3

Unconditional Transition Matrices . . . . . . . . . . . . . . . . . . . . . . . 29 Conditional Transition Matrices . . . . . . . . . . . . . . . . . . . . . . . . 29

8 Conclusion

32

Appendix

34

References

46

Statutory Declaration

49

Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

List of Figures Moody’s Credit Rating for Each Country in July 2012 . . . . . . Observation of Ratings per Rating Category . . . . . . . . . . . . Distribution of Coarse Ratings per Year . . . . . . . . . . . . . . Distribution of Coarse Rating Changes per Year . . . . . . . . . . Histogram for Rating Changes and Standard Normal Distribution Dot Plot On Rating Change Probabilities for all Countries . . . .

. . . . . .

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1 2 3 4 5 6

3 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

. . . . . .

. . . . . .

. . . . . .

. . . . . .

34 34 35 35 36 36

List of Tables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

.

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16

Moody’s Credit Rating Definitions . . . . . . . . . . . . . . . . . . . . . Explanation of Independent Variables, considered in the Ordered Probit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequencies of Investment and Speculative Grade Ratings in my Data Set, Rated by Moody’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequencies of Investment and Speculative Grade Ratings in the Data Set of Hu et al. (2002), Rated by S&P . . . . . . . . . . . . . . . . . . . . . Frequencies of Fine and Coarse Rating Changes, Classified by the Change Direction and Notches Moved . . . . . . . . . . . . . . . . . . . . . . . . Regression Table for the Ordered Probit Estimation in the Fine and Coarse Rating Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regression Table for the Random Effects Ordered Probit Model . . . . . Marginal Effects on the Probabilities of Rating Changes, Calculated as Average of Marginal Effects (AME) . . . . . . . . . . . . . . . . . . . . . Marginal Effects on the Probabilities of Rating Changes, Calculated at Means of the Independent Variables (MEM) . . . . . . . . . . . . . . . . Comparison of Probabilities at Mean Values of the Independent Variables and for Average Probabilities . . . . . . . . . . . . . . . . . . . . . . . . Frequencies of Rating Changes in the Fine Rating Category . . . . . . . Frequencies of Rating Changes in the Coarse Rating Category . . . . . . Estimated Transition Matrix for all Countries, Calculated with Average Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimated Transition Matrix for Non-Developing Countries, Calculated with Average Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . Estimated Transition Matrix for Non-Developing Countries in Business Cycle Peak, Calculated with Average Probabilities . . . . . . . . . . . . . . Estimated Transition Matrix for Non-Developing Countries in Business Cycle Trough, Calculated with Average Probabilities . . . . . . . . . . . . .

4 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

. 37 . 38 . 39 . 39 . 39 . 40 . 41 . 42 . 42 . 42 . 43 . 44 . 44 . 45 . 45 . 45

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1 Introduction Sovereign Ratings are in the center of public attention, in times of sovereign debt crisis. They are important for countries as they determine their cost of capital (BissoondoyalBheenick, 2005). And therefore their movements in either direction are observed critically. Whereas an upgrade can cause a decrease in borrowing cost, a downgrade can imply a burden and can cause the dependency of external support in case of default. It is also essential for institutional investors to know the probability of a rating change as it describes the potential gain or loss in their portfolio. After Moody’s recent announcement of changing the outlook from stable to negative on long-term ratings of Germany, the Netherlands and Luxemburg, it seems that even countries which were thought to keep their Aaa credit standing in the sovereign debt crisis are affected of potential rating changes (Moody’s, 2012b). In the same announcement Moody’s affirm that ”Finland’s unique credit standing” assures the country an ongoing stable rating outlook. In this case four countries all belonging to the Euro area and having the same Aaa credit rating, have different exposures to potential rating changes, according to Moody’s. Standard and Poor’s Ratings Services however decided to keep Germany’s long-term rating outlook stable (S & P, 2012). S & P did not change Germany’s rating outlook because they emphasize ”its modern, highly diversified, and competitive economy [...] and expenditure discipline”. They also argue that Germany’s dealing with historic ”economic and financial shocks, such as the reunification of West Germany with East Germany in the 1990s and the global recession in 2009” allow them to have a stable outlook. In the same time, they changed the outlook of the other AAA rated countries Luxemburg, the Netherlands and Finland to negative. Even though S & P and Moody’s have different rating assessments in this case, their general assessment remains similiar. Differences in ratings can appear, depending on the agencies’ priorities and their assessment of risk. The exemplary announcements of changes in rating outlooks raise the question which factors drive a change in the rating outlook or which determinants cause a real credit rating change. A lot of research has been done on the determinants of ratings. Less research has focused on the determinants of credit rating changes and the probabilities of rating transitions. In my Bachelor thesis I will analyze the determinants of rating changes and the variables’ marginal effects on rating change probabilities. Based on my results, I will present transition matrices by computing transition probabilities. Furthermore, I will analyze subsamples of my data set, conditional on the business cycle and the economic strength of a country, by using interaction effects. I thereby verify whether or how the transition matrices change by including interaction effects. I apply a latent variable approach, using an ordered probit model, to calculate the

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effects of different variables on the probabilities of rating changes. I therefore make use of the discreteness of rating changes, classifing them by a number which indicates their change direction and the number of notches moved. I assign an order to the possible rating changes with eight classes, when considering the coarse rating category. This method is proposed by Wooldridge to deal with the underlying ordered nature of the ordered probit model (Wooldridge, 2001, p.506). The non-linearity, assumed by the model, also allows to treat the difference between the rating changes differently. A linear model would not account for the ordinal nature of rating changes, but treat the difference between the rating changes equally (Borooah, 2001, p.5). A further implication of the ordered probit model is the normal distribution of the error term it . This is in contrast to the ordered logit model, where one assumes a logistic distribution of the error term it . Both models are alternatives to each other and only differ in the tails of their graphs (Borooah, 2001, p.9). According to Greene (2012, p.729), one can justify the choice between the ordered probit or logit model with regard to ”mathematical convienience”, but it is difficult to justify it with regard to the distributional assumptions. As the ordered probit model satisfies my mathematical requirements, I choose it for my calculations. My analysis adds value to most prior work on sovereign rating changes because they are dated back ten years or more when sovereign ratings were less available, especially on a global scale. In my Bachelor thesis I account for the increase in availability of sovereign ratings. In my data set I use the maximum amount of countries that are both included in the World Bank data set and rated by Moody’s. This allows for better legitimacy of the ordered probit model as the ”ordered probit asymptotic properties do not generalise for small samples” (Afonso et al., 2011). For example the increase in rated countries since the paper of Hu et al. (2002), who also worked on rating changes, and my paper can be seen in Tables 3 and 4 in the Appendix. Whereas Hu et al. worked with 487 ratings in total, I work with 1,837 ratings in total. In 2011, which is my last year of observation, with a total number of 112 out of 113, nearly every country was rated. In addition to the extended sample, there is also an increase in rating changes due to the bust of the international financial crisis and the following sovereign debt crisis which enables a better estimation of rating changes and therefore allows a better analysis of rating changes. The remainder of my Bachelor thesis is organized as follows. Chapter two presents an overview of the existing literature on rating changes. Chapter three illustrates the definitions of the rating categories and Moody’s approach to rating transitions. Chapter four introduces the ordered probit model. Chapter five explains my data choice and gives an analysis of the data set. Chapter six presents the estimation results of the determinants of rating changes. Chapter seven predicts rating change probabilities and presents the transition matrices with interaction effects. Chapter eight concludes.

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2 Previous Literature The research on the determinants of sovereign rating changes is based on the analysis of the determinants of sovereign ratings. As found in the influencial work of Cantor and Packer (1996), using an OLS regression, ratings can be determined mainly on the basis of six variables, which are per capita income, GDP growth, inflation, external debt, level of economic development, and default history. Afonso et al. (2007) modified the analysis of underlying fundamentals of sovereign ratings by using panel estimation and random effects ordered probit approaches in order to account for the ordered nature of ratings. They find that under the ordered probit model there are the following variables that determine ratings: GDP per capita, GDP growth, government debt, government effectiveness indicators, external debt, external reserves, and default history. It seems reasonable to suppose that changes in the above mentioned variables will lead to sovereign rating changes. However not every change in those variables will cause a sovereign rating change, especially not on long-term ratings, as in my case. Sovereign rating changes occur when certain thresholds in the fundamental values are crossed. The aim of my Bachelor thesis is to find out the determining variables which are responsible for the effective rating changes and to estimate those thresholds. The literature of the determinants of sovereign rating changes often deals with different methodologies to assess precise rating change probabilities and the creation of precise transition matrices, given the constraint of low availability of sovereign ratings. Most studies have been made with reference to corporate ratings because they allow to have more data and longer rating histories. Even though corporate ratings differ in their nature from sovereign ratings, some methodologies of their analysis can be helpful and sometimes be applied, in a different manner, to sovereign ratings. The results from corporate rating research can give some insights in the nature of rating changes. Nickell et al. (2000) have estimated transition matrices for 6534 corporate obligors during the time 1970-1997, using an ordered probit approach. They examined how industry, country and stage of the business cycle influence the change in ratings. Nickell et al. (2000) and Bangia et al. (2002) find out that upgrades are more likely in booms and downgrades are more likely in recessions. Altman and Kao (1992) investigated the risk of corporate bonds regarding the aging effect, that is the implication of the length of time since issue. They find that default risk increases in the first three or four years of an issue’s life and disappears afterwards. Hamilton and Cantor (2004) show that obligors that have been downgraded are nearly 11 times more likely to default than those that have been upgraded. Other analysis is based on rating heterogeneity within countries, like serial correlation, which is known as rating drift. According to Altman and Kao (1992), Kavvathas et al. (1993) ratings possess a memory. This means that future changes not only depend on the present credit standing but also on prior rating changes: ”The prob-

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ability of a downgrade following a downgrade within one year significantly exceeds that of an upgrade following a downgrade and vice versa.” (Eisenkopf, 2007). Some studies about rating changes also refer to sovereign rating changes. Hu et al. (2002) search for determinants of rating transitions and find a method to create sovereign transition matrices in the case of a short rating history. They analyze both industrial and emerging market sovereign borrowers, even though the latter category has only few if any ratings available. Therefore they propose a simultaneous ordered probit model of credit ratings and default history. The default history adds to the ratings as a further source of information, in order to prevent biased maximum likelihood estimators. They find that previous year default, debt to GNP, reserves to imports, inflation, economic development, lagged debt service to exports and lagged inflation explain rating changes. Moreover Al-Sakka and ap Gwilym (2009) apply a random effects ordered probit model and show that watchlist status, existing rating and issuers domicile region are useful determinants in modeling sovereign rating changes in emerging economies. Al-Sakka and ap Gwilym (2010) add to their model that the ”estimation of sovereign rating migrations can be improved by considering the sources of heterogeneity, such as rating history, rating duration and Watchlist status, and cross-section error (country-specific heterogeneity)”. The idea is to make use of the random effects ordered probit model because the crosssection error term captures factors for developing countries like ”geopolitical uncertainty, political risk and social tensions” which are mostly time-invariant features and cannot be quantified (Al-Sakka and ap Gwilym, 2010). Also Afonso et al. (2009) find that the random effects ordered probit model slightly outperforms the simple ordered probit model. Even though the approach of random effects ordered probit model by Al-Sakka and ap Gwilym (2010) adds information to the simple ordered probit model, they do not find out the true macroeconomic determinants of rating transitions. The watchlist status and the existing rating are part of the rating agencies’ assessment of rating transitions. Therefore they do not search for the sources of rating changes like Hu et al. (2002) do and like it is part of my research. My analysis will show which variables of Hu et al.’s selection also hold for my data set or which additional variables influence rating changes in the case of longer sovereign rating histories.

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3 Agencies’ rating assessment Rating agencies emphasize that ratings are based on both quantitative and qualitative elements. The qualitative approach is supposed to add additional information which is not incorporated in the quantitative data. Rating agencies have multiple instruments to disclose obligors’ creditworthiness to investors. Besides rating, also outlook and review serve as additional sources of information for investors. The outlook usually precedes rating reviews and serves as an indicator as to the direction of the credit assessment in the medium term. There are four categories ranging from positive, negative, stable and developing (Moody’s, 2012a). ”A review indicates that a rating is under consideration for a change in the near term” ranging from upgrade (UPG), downgrade (DNG) to uncertain direction (UNC). This section explains the basic rating definitions and introduces the agencies’ methodology to construct rating transition matrices.

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3.1 Rating Definitions and Methodology ”Sovereign debt ratings are forward-looking qualitative measures of the probability of default, given in the form of a code” (Afonso et al., 2009). There are both short- and long-term ratings. In this Bachelor thesis I will discuss only long-term ratings because they are better known and because they allow a broader ranking of letter rating categories. There are 9 coarse rating categories and 21 fine rating categories for long-term ratings, whereas there are only four short term ratings which are P-1, P-2, P-3 and not prime. Table 1 in the Appendix shows the order of Moody’s ratings with the respective evaluation of a corresponding country’s credit standing (Moody’s, 2012a). Next to Moody’s credit codes, I also added the codes that I use for my analysis, in order to be able to calculate with them. Moody’s have a three-stage process to determine a sovereign rating (Moody’s, 2008). In the first step, they assess the country’s economic resiliency. In the second step, they assess the government’s financial robustness. Finally, in the third step they determine the rating within the fine rating category. The first step is described by two factors. The first factor is the economic strength, which is given by the quantitative values of GDP per capita and the volatility of GDP. The second factor is the institutional strength of the country, such as ”property right, transparency, the efficiency and predictability of government action, the degree of consensus on the key goals of political action” (Moody’s, 2008). The second step is again described by two factors. The first factor is the financial strength of the government, such as the sort of debt and the government’s ability to ”raise taxes, cut spending, sell assets, obtain foreign currency,...”(Moody’s, 2008). The second factor is the sensibility to event risk. This factor accounts for the country’s ability

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to resist to the ”occurrence of adverse economic, financial or political events” (Moody’s, 2008). Due to the last two mentioned steps, Moody’s have placed the country in one of the nine coarse rating categories. The third step defines the fine category from the 21 ratings by ”adjusting the degree of resiliency to the degree of financial robustness”.

3.2 Rating Transition Matrices

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According to Moody’s, a rating change represents a ”variation in the intrinsic relative position of issuers and their obligations” due to ”alteration in creditworthiness, or that the previous rating did not fully reflect the quality of the bond as now seen” (Moody’s, 2012c). Even though long-term ratings are supposed to reflect the country’s long-term rating standing, there are cases, in which Moody’s change its rating assessment annually or quarterly. This especially happens in times of economic turmoils like the current sovereign debt crisis in Europe. The big three rating agencies S & P, Moody’s and Fitch create one and five year credit transition matrices. Credit transition matrices describe migration probabilities of firms and countries to change from any initial credit standing to any terminal rating in a future time. Moody’s make use of survival or duration modeling, called ”multiple destination proportional hazards model” to calculate the transition probabilities (Moody’s, 2011). Duration models simulate how long the rating stays the same and whether there will be an upgrade, a downgrade or a default. The model uses both macroeconomic and issuer specific variables to determine the transition probabilities. Moody’s have identified two macroeconomic factors to have general predictive power for the creditworthiness of countries, which are the unemployment rate forecast and the forecast of the high yield spread over Treasuries. The unemployment rate is meant to describe the ”macroeconomic health”. The high yield spread over Treasuries is meant to incorporate the ”market’s perception of credit quality and hence credit availability”. Additionally the credit transition matrix takes into account today’s and historic issuer-specific elements: ”the current rating, whether the issuer was upgraded or downgraded into its current rating, how long the issuer has maintained its current rating, how long the issuer has consecutively maintained any credit rating, and the issuers current outlook or watchlist status” (Moody’s, 2011).

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4 Ordered Probit Model My model is similiar to the model of Nickell et al. (2000) and Hu et al. (2002) and is theoretically based on Long and Freese (2001), chapter 5, Greene (2012), chapter 18 and Borooah (2001). As the notations in the ordered probit model differ in Greene and Borooah with regard to the intercept and the first cut-off point, I will try to combine the explanations of both approaches. Moreover using Stata 12.0, this implies different assumptions with regard to the intercept and the cut-off points. I will explain the role of the cut-off points in the following section. According to Long and Freese (2001) the ordered probit model has too ”many free parameters” and cannot estimate both the cutoff points and the constant. Therefore one has to decide for estimating either the constant and assume the first cut-off value to be zero or to omit the constant and to estimate all cut-off points (Long and Freese, 2001, p.187). Stata does not include an intercept term in its output because it is absorbed into the cut-off points, whereas Greene does include it and sets the first cut-off point to zero (Borooah, 2001, p.10). I will stick to the notation of Borooah in order to be congruent with the Stata output. In contrast to Nickell et al. (2000) and Hu et al. (2001), I use credit rating changes as outcomes in the ordered probit model, instead of rating levels. The ordered probit model is useful in the observation of rating changes because I assign an order to the different rating changes by notches moved, where 8 upgrades is the highest outcome and 8 downgrades is the lowest outcome. The ordering is the following: +8, +7, +6, +5, +4, +3, +2, +1, 0, -1, -2, -3, -4, -5, -6, -7, -8, where a plus symbolizes an upgrade and a minus a downgrade. Also negative outcomes are possible in the ordered probit model, as long as ”larger values are assumed to correspond to ”higher outcomes” (Long and Freese, 2001, p.188).

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4.1 Mathematical Framework The sovereign rating from one to another period can be an upgrade, a downgrade or no change. In the coarse rating category, as there are 9 rating levels, there are always 8 possible rating changes. Considering the two extremes Aaa and C, the lowest level of a possible rating change is achieved by a downgrade by eight notches and the highest level of a possible rating change is reached by an upgrade by 8 notches. When also taking into account the possibility of no rating change, like shown above, this gives J =17 possible outcomes of rating changes in total. Suppose that a country i ’s credit rating change in time t is determined by the realization of a linear unobserved latent variable yit∗ . The latent variable is determined by the sum of K (k=1,...,K ) independent variables multiplied with the corresponding estimate for every country in the time horizon 1990-2011 (Borooah, 2001, p.8):

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yit∗

=

K 

βk xkit + it = Zit + it

(4.1)

k=1

, where Zit =

K 

βk xkit

(4.2)

k=1

A country is allocated to a rating change outcome yit , if the latent variable yit∗ falls into the interval [μi−1 , μi ] (Hu et al., 2002). The μ’s are the cut-off points which are unknown parameters that are to be estimated like β’s using maximum likelihood estimation. After the estimation of the parameters, it is possible to assign the fitted values into the intervals between the J-1 = 16 cut-off points: yit = U pgrade by 8 notches, if μ16 ≤ yit∗ yit = U pgrade by 7 notches, if if μ15 < yit∗ ≤ μ16 .. .. .. ... yit = U pgrade by 1 notch, if μ9 < yit∗ ≤ μ10 yit = N o change, if μ8 < yit∗ ≤ μ9

(4.3)

yit = Downgrade by 1 notch, if μ7 < yit∗ ≤ μ8 .. .. .. ... yit = Downgrade by 7 notches, if μ1 < yit∗ ≤ μ2 yit = Downgrade by 8 notches, if yit∗ ≤ μ1 The probability of a rating change is given by the standing of the latent variable in the normal cumulative distribution function. The observed outcome for a given value of yit is the area under the curve between a pair of J-1 cut-off points μ. The cumulative distribution of a standard normal variate X is (Borooah, 2001, p.12): 



x

x

φ(X)dX =

P (X < x) = Φ(x) = 1

(1/2π)exp(−X 2 /2) dX

(4.4)

1

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In the ordered probit model, Φ is the standard normal cumulative distribution function. Moreover Φ follows a standard normal distribution with μ ∼ N (0, σ 2 ) and it ∼ N (0, 1)

(4.5)

If assuming that every possible rating change also occurs, the probabilities for every outcome are given by the following equations (Borooah, 2001, p.10):

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P rob { yit = U pgrade by 8 notches| xit } = 1 − Φ(μ16 − Zˆit ) P rob { yit = U pgrade by 7 notches| xit } = Φ(μ16 − Zˆit ) − Φ(μ15 − Zˆit ) P rob { yit = U pgrade by 6 notches| xit } = Φ(μ15 − Zˆit ) − Φ(μ14 − Zˆit ) .. .. .. ... P rob { yit = Downgrade by 8 notches| xit } = Φ(μ1 − Zˆit )

(4.6)

For the right assignment of the probabilities, we must have an increasing order for the cut-off points μ: μ1 < μ2 < ... < μ16

(4.7)

In my model the cut-off points are extended by negative values because the downgrades are defined to be negative and upgrades are defined to be positive. But as the increasing order is still given, my model satisfies the requirement.

4.2 Model parameters

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In the ordered probit model, the estimated coefficient βˆk corresponds to the predicted probability of the direction of a rating change (Borooah, 2001, p.24). A positive sign of the coefficient indicates for dummy variables that all other variables constant, countries with this feature have a higher probability of being upgraded and a lower probability of being downgraded than countries that do not have this feature (Borooah, 2001, p.24). A negative sign suggests that, ceteris paribus, countries with this feature have a lower probability of being upgraded and a higher probability of being downgraded than countries that do not have this feature. However only the direction of change in the probabilities of the extreme outcomes can be inferred and not of the intermediate ones (Borooah, 2001, p.24). The interpretation of the estimates needs caution. However for interpretation purposes, I will try to interprete the coefficients, as far as this appears reasonable. The additionally estimated cut-off points μ are given underneath the βˆk -coefficients, in contrast to Stata outputs in OLS regressions.

4.3 Marginal effects The marginal effect gives the change in the probability of the outcome if the value of one of the independent variables changes. An important feature of the ordered probit model is that the marginal effects are not given by the estimated βk - coefficients. In the following, I therefore derive the marginal effects.

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Marginal Effects of Continuous Variables: If the independent variable is continuous, the marginal effect can be calculated by the derivative of the probability of an outcome, using the chain rule:

δP rob ( yit = U pgrade by 8 notches| x) = Φ(μ16 − Zˆit )β δx δP rob ( yit = U pgrade by 7 notches| x) = [Φ(μ15 − Zˆit ) − Φ(μ16 − Zˆit )]β δx δP rob ( yit = U pgrade by 6 notches| x) = [Φ(μ14 − Zˆit ) − Φ(μ15 − Zˆit )]β δx .. .. .. ...

(4.8)

δP rob ( yit = Downngrade by 8 notches| x) = −Φ(μ1 − Zˆit )β δx As one can see from the marginal effects, again only the influence on the probabilities from the two extreme outcomes will be unambiguously determined (Greene, 2012, p.829). For the remaining outcomes, marginal effects do not have a clear sign and therefore do not allow a conclusion about the direction of the change. As a practical analysis one could investigate how the probability of a rating transition changes, if GDP growth increases. From the requirement that the probabilities add up to 1, results that the sum of the marginal effects is zero (Greene, 2012, p.830). Marginal Effects of Dummy Variables: If however the independent variable is a dummy variable, then the effect has to be determined differently. In this case, the effect has to be calculated as the difference in probabilities between the two variables which are to be compared. So the difference is calculated between the probabilities of a dummy variable taking the value one and a dummy variable taking the value zero, keeping all other variables at their means (Long and Freese, 2001, p.213):

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ΔP rob(yit |xit ) = P rob(yit |x, xit = 1) − P rob(yit |x, xit = 0) Δxit

(4.9)

Like in the case of continuous variables, the interpretation only holds for the extreme outcomes. A practical example would be the analysis how the probability of a sovereign rating transition changes if the concerning country is a non-developing country.

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5 Data

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5.1 Data summary My dataset contains 113 countries rated by Moody’s in the period 1990 until 2011. I chose all countries that Moody’s rated until 2011. The ratings were observed on the 31st of December of each year. Furthermore I chose the time period because of high data availability at the World Bank. The sovereign ratings refer to the foreign long-term issuer ratings, which means that it deals with maturities of one year or greater. I chose Moody’s sovereign ratings, representatively for all credit rating agencies. Cantor and Packer (1996) also state in their work that there is a high correlation between ratings of Moody’s and S & P with marginal differences: ”Of the forty-nine countries rated by both Moodys and Standard and Poors in September 1995, twenty-eight received the same rating from the two agencies, twelve were rated higher by Standard and Poors, and nine were rated higher by Moodys. When the agencies disagreed, their ratings in most cases differed by one notch on the scale, although for seven countries their ratings differed by two notches.” Furthermore my aim is not to investigate the difference between the rating agencies, but to analyze rating changes, given the agency’s decision on a rating change. I assume that the results do not improve for higher divergencies in opinions about ratings, given the low differences in ratings from different agencies. As far as there are withdrawn ratings, I do not consider them for the period that they are withdrawn. In the following I will present several tables and figures that are supposed to introduce my data set and its structure. I especially want to highlight how rating changes appear in my data set in general and over time. Tables 3 and 5 show that the 113 countries over the 22 years add up to a total number of 1,837 rating observations with 317 rating transitions in the fine rating category and 157 rating transitions in the coarse rating category. I have 1,188 investment grade (Aaa-Baa) rating observations and 649 speculative grade (Ba-C) ratings. Concerning the fine rating category, there were 178 rating changes within investment grade and 140 rating changes within speculative grade. Tabel 4 shows that in the dataset of Hu et al. (2002), there are only 487 sovereign rating observations of which 158 have speculative grade observations over the period 1981-1998. That means that the analysis based on my data set will provide more general results. Figure 1 illustrates the distribution of Moody’s sovereign ratings for July 2012, colored by credit quality (Chartsbin, 2012). Especially it shows the strikingly low availability of sovereign ratings in Africa. Figure 2 shows the distribution of sovereign ratings by rating category in my data set. It reveals the dominance of investment grade ratings (Aaa-Baa). Moreover there is a low presence of Caa and Ca rated countries and no C ratings. Figure 3 additionally shows the

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evolution of the rating distribution along the considered time period. It can be observed that the rating quality has deteriorated constantly. In 1990, at the beginning of the data period around 75% of countries were rated A or better. Until 2011 this share of A or better rated countries decreased to approximately 40%. Figure 4 shows the percentage distributions of rating changes per year, by notches moved. It can be observed that the highest numbers of sovereign rating changes in the form of upgrades occured in 2002 with a share of around 23% of the total of rating actions and no changes. The gradual increase of upgrades since 1999, when the Euro was introduced, can be most probably explained by the ”macroeconomic convergence” within the Eurozone by the efforts of Eurozone member countries to fulfill the Maastricht criteria (Moody’s, 2002), cumulating in 2002 by the introduction of the Euro banknotes and coins (European Central Bank, 2012). The year with the highest number of downgrades was 1998, which was for example the year of the Russian debt default. It can be observed that throughout the data period upgrades dominate downgrades, as this can be also seen in figure 5. Figure 5 shows a histogram with the distribution of the rating changes and the corresponding percentage share of each outcome, including a plot of the probability density function for the standard normal distribution. Table 5 additionally presents the numbers of rating changes by notches moved in both the coarse and fine rating category. In the coarse rating category, the highest downgrade is a change by three notches and the highest upgrade is by one notch. In the fine rating category, the highest downgrade is by nine notches, which is Greece in 2011, and the maximum upgrade is by three notches. Tables 11 and 12 show the basic 1-year transition matrices for my sample, for both the coarse and fine rating category. Each entry pij represents the number of countries Nij which changed from an initial sovereign rating category i to a terminal rating j between 1990-2011, divided by the number of countries Ni that started in the initial rating category (Lando and Skødeberg, 2002):

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pij =

Nij , (j = i) Ni

(5.1)

Accordingly every line adds up to 100%. The tables also present the numbers of absolute frequencies for initial and terminal ratings. As there were no C ratings, I excluded them in both transition matrices. It can be seen from the tables that the volatility of rating changes increases as the credit quality decreases. This implies that countries with high rating standing keep their credit standing with a higher probability than lower rated countries. Aaa, Aa and A rated countries keep their rating with 97.43%, 91.88% and 92.06% respectively, whereas in the case of initially Ca rated countries only 25% keep their rating. However this also results from the decreasing number of absolute frequencies of rating changes in the lower speculative grade categories, so rating changes are subject to weak data existence and therefore cannot be explained precisely. This feature of high volatility in lower rating categories has impact on risk management modelling because it can cause high losses to the portfolio (Nickell et al., 2000).

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5.2 Independent Variables and direction of change My analysis of variables that explain rating changes differs from the analysis of variables that explain rating levels. However to indentify my relevant variables, I partly make use of the findings of the previous literature. As mentioned in the introduction, Cantor and Packer (1996) find out that especially eight factors explain ratings: per capita income, GDP growth, inflation (average annual consumer price inflation rate), fiscal balance (average annual central government budget surplus relative to GDP), external balance (average annual current account surplus relative to GDP), external debt (foreign currency debt relative to exports) and an indicator for economic development. Furthermore Hu et al. (2002) find in their data set that variables that affect rating changes are previous year default, debt to GNP, reserves to imports, inflation, economic development, lagged debt service to exports and lagged inflation. Moreover, I refer to Afonso et al. (2007) and Al-Sakka and ap Gwilym (2009) as sources of inspiration and finally I want to refer to Moody’s and their variables approach for sovereign ratings. In the following I will explain how some of the above mentioned variables and other independent variables can be interpreted in order to lead to a rating change and its direction. I divide the variables in three categories which are macroeconomic variables, external and governmental variables and other variables. Macroeconomic variables: GDP per capita (upgrade): A high GDP per capita can serve as a source of revenues in case of having to repay debt (Cantor and Packer, 1996). Higher GDP per capita increases the probability of an upgrade.

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GDP growth (upgrade): A prospect for higher ability and reliability to repay obligations increases the upgrade probability. Inflation (downgrade): Inflationary monetary policy is the consequence of low fiscal discipline. It results from the unwillingness or inability to pay for ”budgetary expenses through taxes or debt issuance” (Afonso et al., 2011). Inflationary costs can lead to political instability (Cantor and Packer, 1996). It is to be investigated whether changes in inflation differ from the reference point, by including a quadratic inflation specification. Thus, the lower the reference inflation rate, the higher may be the probability of a rating change for an increase in inflation. Unemployment rate (downgrade): Unemployment describes the burden for the government to pay unemployment benefits and may be a danger for the ”macroeconomic health” of a country (Moody’s, 2011). This leads to a higher probability of a downgrade.

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External and Governmental variables : Foreign Reserves (upgrade) : They should serve as an instrument to be able to repay foreign currency obligations and therefore be beneficial for an upgrade (Afonso et al., 2011). Higher foreign reserves therefore increases the probability of an upgrade. External debt (downgrade) : Higher external debt causes higher default risk due to increasing interest burden (Afonso et al., 2011). Therefore external debt increases the probability of a downgrade. Fiscal balance (up/ down) : A budget deficit creates a crowding out of private investment and signals a lack in the ability to raise taxes (Cantor and Packer, 1996). This burden can lead to higher probability of a downgrade. Current account balance (up /down) : A high current account deficit can be interpreted as over-consumption or as ”accumulation of investment, which should lead to higher growth” (Afonso et al., 2011). A current account surplus therefore can lead to a higher probability of an upgrade. Other variables: Default History (downgrade) : Past defaults represent a lower tendency to repay obligations or even to accept to reduce debt by default (Afonso et al., 2011). It also reveals the country’ s ability to deal with economic problems. It can either serve as quantitative variable or as qualitative variable, as it was mentioned in the introductory example. If the dummy variable default history takes the value one, there is a higher probability of a downgrade, compared to never defaulted countries.

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Foreign direct investment (upgrade) : This variable stands for political stability and good economic and legal frame. Also it implies expectations of high return on investment because of stable or high productivity and interconnected economy. Higher foreign direct investment should lead to a higher probability of an upgrade. Non-developing Country (Upgrade) : Belonging to either of the two classes, nondeveloping or developing countries can mean a higher or smaller tendency to default. Here the dummy variable for non-developing countries should lower the default tendency (Cantor and Packer, 1996), which is for reasons such as political stability. Non-developing countries should have higher probabilities of an upgrade than developing countries.

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Initial Rating (up/ down) : Belonging to the investment grade rating category increases the probability of keeping the rating. However due to more rating volatility in the speculative grade category, the probability of a rating change increases (Al-Sakka and ap Gwilym, 2009). A low rating means that cost of capital is high which again increases the risk of a rating downgrade. One would expect that higher ratings go along with higher upgrade probabilities.

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5.3 Choice of Variables An appropriate ordered probit model of rating changes should include independent variables that incorporate information to fit the changes. Even though the above mentioned variables are supposed to lead to a rating change, including all of them would not lead to a high goodness of fit. The simple ordered probit model should be built on a comprehensive basis, in order to prevent from multicollinearity or omitted variable bias. Therefore I reject to choose the generel-to-specific specification, but rather build the model step by step. When considering the independent variables, there may occur simultaneous causality between the exogenous variables and the endogenous rating change. The rating changes are not only influenced by the macroeconomic variables, but also the rating changes influence the macroeconomic variables. The result is a biased estimator, which can be illustrated by the example of central government debt: As higher central government debt ceteris paribus would cause a downgrade, by the increased borrowing cost there would also occur higher central government debt. To get consistent estimators, there exists the method of instrumental variables (Greene, 2012, p.292). Even though I point to this problem and provide a theoretical solution, I do not consider it in further detail and exclude the possible causalities from my analysis. A further important question about rating changes is whether to consider 1-year-lagged or unlagged variables. It is obvious that rating changes in long-term ratings do not reflect the simulatanous change in fundamentals, but the assessment in the long-run tendency of a country’ s creditworthiness. The choice about adding lagged or unlagged variables in the regression model however depends especially on the assumptions of rating agencies’ methodology and the role of their expectations on rating changes. Assume a model, where a rating agency assesses a country’s creditworthiness in time t and publishes the rating in the next period t + 1. If rating agencies would only focus on the fundamentals, that is the underlying macroeconomic variables, the rating changes are supposed to be explained by lagged variables. This model would assume that in time t a rating agency assesses a country’s fundamental data and publishes the rating in the next year t + 1. If however rating agencies take into account expectations, like it seems reasonable for long-term ratings, it would rather be appropriate to compare ratings and the unlagged independent variables to explain next year’s ratings. In this way, in time t rating agencies build their expectations about next year’s fundamentals and publish their rating in time t + 1. Also

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hybrid ways can be imagined like in Hu et al. (2002). They find that additionally to some unlagged variables also lagged debt service to exports and lagged inflation influence rating changes. However the hybrid choice of lagged and unlagged variables seems to me more like data mining than a reasoned choice. This impression is amplified due to their short rating history. Therefore I decide to analyze a regression model with either lagged or unlagged variables. I tried to regress some variables, mentioned in section 5.2, and investigated which of them to include in an ordered probit model. My criteria was to choose variables that are statistically significant or also economically important in their impact on rating changes. As it does not seem reasonable for me to include inflation2 in the lagged model, I excluded it in the lagged regression. In the following I explain my choice. Three variables are basic for the understanding of rating changes. First, the initial rating is important as a reference point. When a sovereign rating is settled in the speculative rating category, the rating will be much more volatile than if it is settled in the investment grade category. The initial rating accounts for the stability or resistance against a rating change. A second basic independent variable is the economic development. The variable economic development should take into account political stability and other unobservable variables. It seperates non-developing countries from developing countries, according to World Bank’s calculation on the basis of the gross net income per capita. According to the World Bank, a country is a developing country if the GNI per capita falls into the classification low-income or middle-income (World Bank, 2012). I also want to take into account the emerging countries. Those would be excluded if one would follow the World Bank definition and examine developing versus industrialized countries. According to my opinion, I seperate developing from non-developing countries, by examining developing vs industrialized and emerging countries. I consider as the limit of seperating developing and non-developing countries the GNI per capita at 4,036 US$. This corresponds to the limit between lower and upper middle income at the World Bank in 2012. This split within the middle income group is due to the high heterogeneity within the middle income group, that was recognized by the World Bank since 1989 by setting an ”explicit benchmark between the middle-income and high-income countries [...] at 6,000 US$ per capita in 1987 prices” (World Bank, 2012). I account for this heterogeneity by setting the limit at 4,036 US$ and consider the GNI per capita in the respective year. Any approach remains approximative, but my benchmark seems more reasonable to me than to take the strict GNI per capita at 12,475 US$, which is supposed to seperate middle from high income countries, that is developing from industrialized countries, in 2012. This allocation criterium does not account for the role of the historical evolution of economies since 1990 and would therefore lead to arbitrary belongings of countries in the two groups. The third variable is GDP growth. It is a widely spread indicator for a country’s future development, which is also often mentioned by Moody’s reports as justification of

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a rating action. The remaining variables are chosen based on former research. Default history should emphasize the role of a default on the future rating volatility. Furthermore, as declared above Moody’s take into account the unemployment rate as indicator of the ”macroeconomic health”, so it should be included into the regression. Other macroeconomic and governmental variables like inflation, central government debt, cash deficit and total reserves should add as further information to the government’s (dis)ability to be liquid and fiscally (in)stable. Moreover I add a quadratic specification for inflation to account for the momentum of nonlinearity in the effect of different reference inflation rates. The marginal effect of an increase in inflation on the rating change depends upon the inflation from which the increase takes place. If βInf lation < 0 and βInf lation2 > 0, then increasing a country’s inflation increases the probability of a downgrade, but this effect is smaller the higher the inflation (Borooah, 2001).

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6 Estimation There are theoretically three methods to analyze the determinants of rating change probabilities, using an ordered probit model: ordered probit model with fixed effects, ordered probit model with random effects and simple ordered probit model. The fixed effects and random effects ordered probit models are panel data models with a latent variable (6.1) yit∗ = Zit + it where the error term it is specified as the sum of two components (Greene, 2012, p.838):

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it = ζi + νit

(6.2)

The error term ζi captures the time-invariant country-specific random variable with unobservable country heterogeneity. It is supposed to be unrelated to any independent variable in the random effects model (Al-Sakka and ap Gwilym, 2009). The error term νit is independent both among time and countries (Kaiser and Spitz-Oener, 2000). The fixed effects ordered probit model considers the heterogeneity within countries, which has a practical implication of understanding the impact of historic defaults or rating changes on future rating changes. However Stata does not have a command for fixed effects ordered probit model for panel data, most probably because the estimator suffers from the ”incidental parameters problem” as the fixed effects maximum likelihood estimator is inconsistent when T, the length of the panel is fixed (Neyman and Scott, 1948). The estimation of fixed effects is only possible for linear regression, but not for the non-linear regression like the ordered probit model. Chamberlain (1984) provides an application for the non-linear multinomial logit model, however this cannot be applied to the ordered probit model because of its cut-off points (Kaiser and Spitz-Oener, 2000). The random effects ordered probit model considers the heterogeneity across countries and helps to capture correlation such as the political instability, incorporated in the crosssection error term. ”Because ζi is present in the composite error in each time interval, the it are serially correlated across time” (Al-Sakka and ap Gwilym, 2009). Under the random effects assumptions the variance and correlation are defined as (Al-Sakka and ap Gwilym, 2009): V ar[] = σ2 = σζ2 + σν2

ρ = Corr(it , is ) =

σζ2 , t = s σζ2 + σν2

(6.3)

(6.4)

, where ρ is the proportion of the panel or country-level variance component in relation to the total residual variance (Bonfim, 2009).

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The simple ordered probit model does not account for the additional information, given by the nature of a panel data set. It assumes that the error term it is independent and identically distributed with a mean of zero and variance σ 2 for all countries i and over time t (Kaiser and Spitz-Oener, 2000). Due to the correlation within and across countries, this can lead to inconsistent estimators. Afonso et al. (2009) find out that the random effects ordered probit model slightly outperforms the simple ordered probit model, which results from the ”existence of an additionally distributed cross-section error” (Afonso et al., 2009) In the following I will present the results from the two approaches, simple ordered probit model and random effects ordered probit model.

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6.1 Simple Ordered Probit Model Table 6 presents the regression table from the simple ordered probit model for both the lagged and unlagged variables, in both the coarse and fine rating category. The three variables initial rating, GDP growth and economic development remain highly significant for all four ordered probit regressions. The regression with the most significant results is the unlagged category, suggesting that rating agencies have good anticipation or good expectations about changing the sovereign rating according to the fundamental value of the respective period. A positive sign of the coefficient means that countries, ceteris paribus, have a higher probability to be upgraded than to be downgraded if the independent continuous variable changes. A negative sign of the coefficient means that countries, ceteris paribus, have a higher probability to be downgraded than to be upgraded if the independent continuous variable changes. The signs of the estimates are always equal in both the fine and coarse rating category. The signs of the estimates are also as expected, apart from the initial rating. For the initial rating, it can be understood that a higher rating implicates a lower probability to be upgraded because a higher level in creditworthiness is less possible as one increases in creditworthiness. Furthermore, as results from prior observations suggest, there is less volatility in the higher rating categories which means also less upgrades. Another annotation for the deficit per GDP may also be helpful. As the deficit per GDP is defined to be negative, it is obvious that a higher value of deficit is considered to increase the probability of an upgrade. Though, one has to be careful with the interpretation of the coefficients, as mentioned above, as only the extreme outcomes allow a definite interpretation. Comparing the coarse and fine rating category, there are no clear differences in significance of the variables. In most cases the estimates are very similiar to each other, if comparing the lagged and unlagged variables in both coarse and fine rating category. This leads to the conclusion that the fine and coarse rating category both lead to almost equally good results. Nickell et al. (2000) already say that transition matrices ”are not

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that reliable for finer ratings and the added complexity of having three times as many categories is probably not worthwhile”. This can be confirmed in my regression as the results of both coarse and fine categories are very similiar. Especially it is important to check whether the existing differences in the coarse and fine rating category are due to more complexity or to more preciseness. If finer ratings do not provide more precise results, then coarse ratings should be preferred. However a deeper analysis will not be subject of this Bachelor thesis. For the same reasons, given by Nickell et al. (2000), I will stick to the coarse ratings in my further analysis. It is striking that the unemployment rate is not significant in the unlagged fine rating regression, whereas it is significant at the 5% level in the unlagged coarse rating category or at the 10% level in the lagged coarse rating category. This is important because, as mentioned above Moody’s take into account the unemployment rate for transition matrices. However only in the lagged and unlagged coarse rating category it is weakly significant, whereas not significant in the fine rating category. Central government debt has no effect and is statistically insignificant. However I add it to the regression model because it seems to be economically important. In my opinion it would lead to an omitted variable bias because of the simultaneously causal relationship between borrowing cost and rating change if it would be ignored. The cut-off points are almost all highly significant and correctly increasing in order. The statistics state that all coefficients in the four models are commonly significantly different than zero. So the zero hypothesis can be refused. The Bayesian information criterion which accounts for the trade-off between model explanation and number of regressors is smallest for the unlagged coarse rating regression. That means that this model is to be prefered from all four models. Additionally, the unlagged coarse rating model has a pseudo R2 of 0.24. This is a good value, as values between 0.2 and 0.4 indicate good explanation of the model. Greene (2012, p.574) points to the problem that the pseudo R2 is usually provided by the literature as measure of explanation for ordered probit models, but according to him it is not completely satisfying. He therefore suggests a better measure of goodness of fit, which is the correlation between predicted outcome and actual outcome. An exemplary measure is the in average rightly predicted probability, given by Ben-Akiva and Lerman and Kay and Little for balanced samples (Greene, 2012, p.574). However I will accept the pseudo R2 =0.24 as a good result of goodness of fit and continue to work with the unlagged model in the coarse rating category.

6.2 Random Effects Ordered Probit Model In this section I examine if the random effects ordered probit model produces more precise results than the simple unlagged ordered probit model in the coarse rating category. Wooldridge (2002) suggests two possibilities to estimate the random effects ordered probit

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model (Afonso et al., 2009). On the one hand one can assume a single ”error term that is serially correlated within countries” (Afonso et al., 2009). This way one would assume a simple ordered probit model, using a robust variance-covariance matrix estimator to account for the serial correlation. On the other hand one can estimate a random effects ordered probit model with the composite error term consisting of ζi and νit . Table 7 presents the results from the robust variance-covariance estimation (clustered ordered probit) compared with the simple ordered probit regression from table 6. I do not display the second possibility to estimate a random effects ordered probit model with a composite error term because the results are identical to my simple ordered probit model. One would perform the random effects ordered probit model using the -gllamm-, generalized linear latent and mixed models, command in Stata (Zheng and Rabe-Hesketh, 2007). There only exist slight differences between the -gllamm- or simple ordered probit model and the robust variance-covariance estimation. Some standard deviations differ and there occur differences in the significance levels for inflation, deficit per GDP and total reserves. Finally, the regressions of the two models are so similiar that we cannot derive conclusions about a better performance of the random effects ordered probit model compared to the simple ordered probit model, like Afonso et al. (2009) found out. Apparently there is no additional information that can be captured across countries. It can only be stated that the results from the robust variance-covariance estimation are more precise as they account for the correlation within the countries. Therefore I will continue to use the random effects ordered probit model, using the robust variance-covariance estimation, in my further analysis of rating change probabilities, when computing marginal effects and transition probabilities.

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6.3 Marginal Effects To obtain the effect of a change in an independent variable on the probability of a rating change, it is necessary to calculate the marginal effects. As described in chapter 4.3 the marginal effects are calculated as the derivative of the probability of an outcome for continuous variables and as a difference between two probabilities, taking the value 1 and 0, for dummy variables. There are two possibilities to calculate the marginal effect. Either one takes the average of marginal effects, refered to as average marginal effects (AME), or one takes the independent variables at means, refered to as marginal effects at the mean (MEM) (Bartus, 2005). According to Bartus (2005), the literature does not provide a clear opinion about which marginal effect to prefer, but the ”demand for realism” calls for the AME because ”the calculation of MEM might refer to either nonexistent or inherently nonsensical observations”. Tables 8 and 9 show the marginal effects for the AME and MEM respectively. The marginal effects are calculated for the various rating changes, using the robust variance-covariance matrix estimation with the variables of the above section. The

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marginal effect of every independent variable is calculated, holding all other independent variables constant at their means. There are some differences between the tables of AME and MEM in the values of marginal effects for initial rating and economic development and some slight differences in significance for some other variables. However the differences remain small most of the time. To account for the concerns of more realism, I will interprete the marginal effects, refering to Table 8, which are the marginal effects calculated as AME. The signs of the marginal effects are as expected, apart from the initial rating, which was already mentioned in chapter 6.1. However not every variable is significantly influencing the outcome and sometimes the marginal effect is very weak. The lack in significance in the categories ”no change” and ”downgrades by 2 or 3 notches” is especially due to the low availability of rating changes, when seperating them in the various outcomes. For significance, one needs at least around 30 observations. Table 5 reveals that there are only nine observations of rating downgrades by two notches and only two observations of rating downgrades by three notches. However as the number of outcomes of the other rating changes allows to judge significance, some conclusions can be drawn from the marginal effects, especially for up and downgrades by one notch. As an example of a continous variable, an increase in GDP growth ceteris paribus increases the probability of an upgrade by one notch by 0.6 percentage points and lowers the probability of a downgrade by one notch by 0.3 percentage points. This is consistent with the expectations from chapter 5.2. The sign of the variable initial rating seems to be unexpected. The probability of an upgrade decreases by 4.2 percentage points if the initial rating level is higher by one notch. This implicates that a higher starting rating level bears more risk for a downgrade because there is not much possibility to increase any further in the creditworthiness. Analogously for downgrades the probability of a downgrade by one notch increases by 2.6 percentage points if the initial rating increases by one notch. This may be possible because the downside risk increases as the starting rating level is higher. However, in a further regression I found that this result differs if one includes the initial belonging to the investment grade category in the model instead of the initial rating. Then one gets a positive effect on the probability of an upgrade if the country starts from the investment grade category, as it would be expected. The following marginal effects hold for dummy variables. The probability of an upgrade by one notch increases ceteris paribus by 12.6 percentage points for a non-developing country, compared to developing countries. At the same time a non-developing country is around 8 percentage points less likely to be downgraded by one notch, compared to developing countries. Furthermore, if a country already defaulted on its bonds, this decreases the probability of being upgraded by 9.3 percentage points.

26 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

7 Predicted Probabilities and Transition matrices The ordered probit model allows to determine rating transition matrices as it calculates probabilities for the various outcomes. After having found the determinants of rating changes, it is now possible to compute the transition probabilities. For transition matrices, the predicted probabilities are computed to reach a terminal rating level in t + 1, given an initial rating level in t.

7.1 Predicted Probabilities Again there are two ways to calculate the predicted probabilities of the rating changes. One possibility is to calculate the mean of the individual probabilities for each outcome. The mean of the estimated probabilities in the coarse rating level pˆi1 , pˆi2 , pˆi3 ,..., pˆi17 is refered to as p¯1 , p¯2 , p¯3 ,..., p¯17 (Borooah, 2001, p.25). Another possibility is to estimate the probability at the mean of the independent variables which is refered to as pˆ1 , pˆ2 , pˆ3 ,..., pˆ17 (Borooah, 2001, p.25). Again it can be reasoned that the mean of the predicted probabilities provides more realistic results than the prediction at the mean of the independent variable. Mean of individual probabilities The possibility to calculate the probabilities of rating changes is based on the idea that the estimates from the simple or clustered ordered probit regression in tables 6 or 7 are multiplied with the corresponding variables, as introduced in chapter 4.1: Zˆit =

K 

βˆk xkit

(7.1)

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k=1

The probabilities of the various outcomes are calculated as in equation 4.6. Afterwards the percentage share of every outcome is calculated, representing the probability of a rating change. Figure 6 presents an overview of predicted rating change probabilities for the whole data set in a dot plot. It shows the distribution of plotted probabilities for every country and year for the various outcomes. It can be observed that the figure fits the shape of the standard normal distribution of the probability function Φ, even though it is cut to the right side. In the coarse rating category there are only five possible outcomes. According to figure 6, only the probability of no change can be often predicted with a probability near to 1. However the probabilities of rating changes are not high. Only for the probability of ”1 notch upgrades” the highest value is around 0.7, but this can be

27 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

identified as an outlier. Also it can be observed that the probabilities of rating changes decrease as the number of notches moved increases, resulting in a lot of predicted zero probabilities of downgrades by 2 or 3 notches changed. The means of the estimated probabilities of rating changes, given in the right column of table 10, are p¯1 = 0.18% for a 3 notches downgrade, p¯2 = 0.44% for a 2 notches downgrade, p¯3 = 2.99% for a 1 notch downgrade, p¯4 = 91.53% for no change, p¯5 = 4.86% for a 1 notch upgrade. The sum of the mean probabilities add up to 100%. The results do not change for the clustered and for the simple ordered probit model. Estimation at the mean In this approach, the probabilities of rating changes are calculated different to the just mentioned method. We take the estimation at the mean of the independent variables, which changes the value of Z :

Z¯ =

N  K  ( βˆk xkit )

N  Zˆit

i=1

N

=

i=1 k=1

ˆ  βk xkit =

N

k

i

N

=



βˆk x¯k

(7.2)

k

As there are only five different rating changes in the coarse rating category, I compute the probabilities for the five outcomes as follows (Borooah, 2001, p.31):

¯ pˆ1 = P rob { yit = U pgrade by 1 notch| xit } = 1 − Φ(μ4 − Z) ¯ − Φ(μ3 − Z) ¯ pˆ2 = P rob { yit = N o change| xit } = Φ(μ4 − Z)

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¯ − Φ(μ2 − Z) ¯ pˆ3 = P rob { yit = Downgrade by 1 notch| xit } = Φ(μ3 − Z) ¯ − Φ(μ1 − Z) ¯ pˆ4 = P rob { yit = Downgrade by 2 notches| xit } = Φ(μ2 − Z) ¯ pˆ5 = P rob { yit = Downgrade by 3 notches| xit } = Φ(μ1 − Z)

(7.3)

The results for the new predicted rating change probabilities for every outcome are given in the left column of table 10, where they are contrasted to the average probabilities calculated above. It can be seen that the probabilities of rating changes are smaller at mean values. The estimation at the mean of the independent variables appears to be lower than the mean of the predicted probabilities, because high outliers in the independent variables are less weighted. In the following I will continue to calculate with the average probabilities instead of the probabilities at mean values, to maintain more realistic results, as discussed above.

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7.2 Unconditional Transition Matrices

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Table 13 shows an estimated transition matrix, consisting of all countries. The approach to create this transition matrix is to estimate the clustered ordered probit model and to predict rating change probabilities for every rating change. With the respective probabilities of rating changes I am able to allocate a probability to reach a specific terminal rating for every initial rating. However in the estimated model, there were no rating change observations, if the initial rating was C or Ca and only three observations if the initial rating was Caa. Therefore I merged the rating categories B, Caa, Ca and C, to obtain at least 27 rating change observations in one category. Again, the table shows a higher rating change volatility for lower rated countries, compared to higher rated countries. The results from the table do not exactly correspond to the expected transition probabilities because the probabilities to stay in the same rating in the low rating categories is too high. The estimated transition probability to stay in the initial rating category B/Caa/Ca/C is 89.04%. On page 44, the transition matrix of rating change frequencies is contrasted to the estimated transition matrix. The results from the estimated rating change probabilities are contrary to the rating change frequencies in table 12 in the low rating categories. I expected rating change probabilities that are more similiar to the values in table 12 as here the rating volatility in lower classes is more evident than in the estimated transition matrix. This is probably due to the fact that in the estimated model there are too few ratings in the lower rating category and therefore the probabilities cannot be estimated precisely. Comparing the rest of the table 12 with table 13, it turns out that the predicted probabilities do not differ much, but the model of course shows a tendancy to reduce the influence of outliers. Furthermore, in the estimated model there are now positive estimated probabilities, where there used to be no rating change observations in the transition matrix of frequencies. To conclude, the high similiarities between the two transition matrices show that the regression model has a high goodness of fit, if one refers to Greene (2012, p.574), as he prefers the correlation of predicted and actual outcomes, as measure of fit, instead of the pseudo R2 . In fact, it can be observed that many probabilities resemble each other.

7.3 Conditional Transition Matrices Until now I have considered the unconditional overall transition matrix. However it would be interesting to consider transition matrices for subsamples, conditional on variables like the economic strength of a country or the business cycle. Nickell et al. (2000) created transition matrices for firms in the bank and industry sector, both in economic trough and peak, using an ordered probit model. They verified the hypothesis that the volatility of rating changes is higher for the bank sector than for the industry sector. As shown above, in the ordered probit regression, economic development has a sig-

29 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

nificant coefficient and a significant marginal effect on rating changes. This legitimates to calculate transition matrices for the subsample non-developing countries and contrast them to the overall transition matrix. One would suppose that non-developing countries have lower exposure to downgrades and higher tendancy of upgrades, than average performing countries. It would be also possible that non-developing countries have less volatility in the high rating categories than in the overall sample. If one wants to compute the transition matrices, one has to add an interaction variable for each variable, that is the original explanatory variable multiplied by the dummy variable ”Non-developing Country (ND)” (Borooah, 2001, p.36). The latent variable is then described by the following equation:

yit∗ = β1 + γ1 ∗ N Dit + β2 ∗ Initial Rating + γ2 ∗ N Dit ∗ Initial Rating + β3 ∗ GDP Growth + γ3 ∗ N Dit ∗ GDP Growth + β4 ∗ Def ault History + γ4 ∗ N Dit ∗ Def ault History + β5 ∗ Inf lation + γ5 ∗ N Dit ∗ Inf lation + β6 ∗ Inf lation2 + γ6 ∗ N Dit ∗ Inf lation2 + β7 ∗ U nemployment rate

(7.4)

+ γ7 ∗ N Dit ∗ U nemployment rate + β8 ∗ CG Debt + γ8 ∗ N Dit ∗ CG Debt + β9 ∗ Def icit + γ9 ∗ N Dit ∗ Def icit + β10 ∗ T otal Reserves + γ10 ∗ N Dit ∗ T otal Reserves + it

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= Zit + ZitN D + it I create interaction variables with every independent variable and the results are significant for most of the variables. It would be possible to exclude variables that are statistically insignificant, but I will not do it because I reasoned the importance of the variables beforehand (Borooah, 2001, p.40). The transition probabilities from the equation given above are computed in table 14. They differ from the overall transition probabilities in table 13 in that most of the downgrade probabilities are lower for non-developing countries and the upgrade probabilities are mostly higher than the average. A very striking feature of the new transition matrix is that non-developing countries have a 11.17% upgrade probability if they were initially rated B/Caa/Ca/C, compared to 6.16% upgrade probability in the overall sample. Moreover non-developing countries have a higher probability to remain in the same rating category, than the overall sample, if they are rated Aaa, Aa or A, that is 94,57% vs 93,58%, 96,38% vs 95,97% and 92,23% vs 90,82% respectively. Further transition matrices can be constructed that represent the transition probabilities of non-developing countries conditional on the business cycle, as a peak or a trough. This implies the construction of a new interaction variable that is the product of the dummy variable for the business cycle (BC), either peak or trough, and the explanatory variable. This means that in total there are three kinds of variables. The latent variable is then described by:

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yit∗ = Zit + ZitN D + ZitBC + it

(7.5)

Zit accounts for the original independent variables, ZitN D accounts for the additional effect of non-developing countries and ZitBC adds for the effect of the business cycle, either peak or trough. I constructed the dummy variable peak, based on the highest third per year of the sample GDP growth and the dummy variable trough on the lowest third per year of the sample GDP growth. I assumed GDP growth as a proxy for the business cycle peak or trough of a country. However when including the business cycle in the regression model, a business cycle peak or trough does not have a significant impact on rating changes. I do not display the regression, accounting for the business cycle and its insignificant results, for the sake of brevity. The insignificant values for the business cycle are probably due to two reasons. First, one can suppose that non-developing countries are less sensitive to rating changes as they have built a reputation of staying in the same rating category, for example by managing economic turmoils. Second, it can be due to the nature of choosing long-term ratings, that are less sensitive to short-term changes in fundamentals, like GDP growth. Maybe the results would be different, when choosing short-term rating changes as dependent variable. The second possibility appears more probable, because the business cycle was also insignificant when I added the interaction variable with business cycle trough and peak for the overall sample. Tables 15 and 16 show transition matrices for non-developing countries, conditional on a business cycle peak and trough. As can be seen, the transition probabilities only differ slightly from table 14. Nevertheless, some conclusions can be drawn. Whereas for a business cycle trough downgrade probabilities are often higher than in an average business cycle, the effect of lower downgrade probabilities in a business cycle peak cannot be observed. Accordingly, in a business cycle trough upgrade probabilities are lower in higher rating categories than in an average business cycle, but for business cycle peaks the effect of higher upgrade probabilities does not occur. Also the probabilities to stay in the same rating is approximately equal for the three estimated transition matrices for non-developing countries. It can be concluded that whereas a business cycle peak has only a weak effect on the rating change probabilities, compared to the average business cycle for non-developing countries, a business cycle trough involves slightly higher effects on the rating change probabilities of non-developing countries in an average business cycle. However both influences seem to be small. I could have calculated lots of conditional transition matrices. However the aim was to show that transition matrices can differ in subsamples, compared to the overall sample. This is not always the case. Non-Developing countries have different transition probabilities than the average sample, like one would expect. However one would usually guess that the business cycle has an influence on the rating change probabilities, which is not the case in my investigation.

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8 Conclusion The aim of my Bachelor thesis was to provide the determinants of rating change probabilities and to use the results in order to analyze which effects they have on the probability of rating changes. My analysis was based on a latent variable approach, using the ordered probit model. The model allowed me to calculate probabilities of rating transitions in the form of conditional and unconditional transition matrices, as they are used as a tool for risk management at rating agencies. In the ordered probit model, the variables initial rating, GDP growth, economic development, default history, inflation, unemployment rate and deficit mainly explain rating change probabilities. Furthermore I found that unlagged variables have higher significance levels than lagged variables. This leads to the conclusion that named macroeconomic variables explain the rating changes when the change occurs and therefore rating agencies well anticipate the long-term macroeconomic situation of the countries correctly. My estimated model explains the transition probabilities well and allows to compute a realistic unconditional transition matrix. I was also able to calculate conditional transition probabilities for subsamples if the considered independent variable significantly influenced the rating change probabilities, as this was the case for non-developing countries. The results differed considerably from the overall transition matrix for all countries. However modeling non-developing countries in a business cycle only influenced the rating transition probabilities weakly. It turned out that, in the subsample of non-developing countries, a business cycle trough has a slightly higher impact on rating changes than a business cycle peak. My Bachelor thesis shows that the findings of Afonso et al. (2007) and Cantor and Packer (1996) concerning the determinants of sovereign rating levels can be also transferred to sovereign rating changes, like also Hu et al. (2002) found out. Sovereign rating changes can be explained by publically available macroeconomic variables. Even though rating agencies claim to imply qualitative elements in their rating assessment, they do not have much private information at their disposial to do so, like this is the case for corporate ratings. They can just make use of their experience concerning priorities of some variables that have higher influence than others, like Moody’s do it with the unemployment rate and the high yield spread over Treasuries for transition matrices. However, their assessment of priorities does not have to be correct. Sometimes it can turn out that like in the case of the unemployment rate, its influence is not highly significant for rating changes. For econometric analysis, the qualitative assessments of rating agencies definitely make it more complex to find out the determinants of rating changes (Nickell et al., 2000). However, even though it is questionable whether expert knowledge improves sovereign ratings, it could be verified in fut research how big the share of unobservable factors is that explains rating changes. This is especially important as there is only a low availability of

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sovereign ratings. This could also provide an impression of the potential added value of rating agencies. One disadvantage of my data set is that for some rating categories there were just too few rating transitions. Therefore the transition matrix did not give the expected probabilities for the low rating categories. When longer rating histories will exist, the models will better fit the traditional maximum likelihood estimators which are less biased in big samples. A practical implication for further research is the consideration of correlation and spillover effects between countries in subsamples. If one takes the Eurozone as an example, there is the correlation within the Euro member countries which leads to upgrades as in the beginning of the European Monetary Union, due to the obligations to the Maastricht criteria and there occur downgrades as to account for the sovereign debt crisis which has an impact on even highly rated countries, like I illustrated in the introductory example of the negative outlook of Germany, the Netherlands, Finland and Luxembourg. It should be subject of further investigation whether rating changes occur more frequently due to the own contribution of a country or more due to the ”unobservable” economic and financial interconnectedness between countries, like through currency unions. Al-Sakka and ap Gdwilym (2010) already tried to head in this direction by adding issuers domicile as a proxy in their regression. The regional influence can be understood as the possibility to trade with each other and therefore have higher correlation of rating changes. However further research is needed in the analysis of correlation among countries to improve the detection of determinants of rating changes and the prediction of rating change probabilities.

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Appendix Figure 1: Moody’s Credit Rating for Each Country in July 2012 Source: chartsbin.com

Figure 2: Observation of Ratings per Rating Category

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Source: Own figure

34 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Figure 3: Distribution of Coarse Ratings per Year Source: Own figure

Figure 4: Distribution of Coarse Rating Changes per Year

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Source: Own figure

35 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Figure 5: Histogram for Rating Changes and Standard Normal Distribution Source: Own figure

Figure 6: Dot Plot On Rating Change Probabilities for all Countries

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Source: Own figure

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Table 1: Moody’s Credit Rating Definitions Coarse letter rating

Coarse Rating Code

Fine letter Rating

Fine Rating Code

Aaa

9

Aaa

21

Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 Caa2 Caa3

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3

Aa

8

A

7

Baa

6

Ba

5

B

4

Caa

3

Ca

2

Ca

2

C

1

C

1

Source: Moody’s Explanation

Obligations rated Aaa are judged to be of the highest quality, subject to the lowest level of credit risk Obligations rated Aa are judged to be of high quality and are subject to very low credit risk. Obligations rated A are judged to be upper-medium grade and are subject to low credit risk. Obligations rated Baa are judged to be medium-grade and subject to moderate credit risk and as such may possess certain speculative characteristics. Obligations rated Ba are judged to be speculative and are subject to substantial credit risk. Obligations rated B are considered speculative and are subject to high credit risk. Obligations rated Caa are judged to be speculative of poor standing and are subject to very high credit risk. Obligations rated Ca are highly speculative and are likely in, or very near, default, with some prospect of recovery of principal and interest. Obligations rated C are the lowest rated and are typically in default, with little prospect for recovery of principal or interest

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Table 2: Explanation of Independent Variables, considered in the Ordered Probit Model Source: Own Table with World Bank Definitions Variable Initial Rating GDP growth Indicator for Economic Development

Unit/ Measure Rating Scale % Dummy variable

Source

1-year-lagged Rating

Moody’s

Annual percentage growth rate of GDP at market prices based on constant local currency. Classification in developing and non-developing countries, based on the GNI per capita; nondeveloping country=1 if belonging to upper middle income and high income; developing country=0 if GNI below upper middle income

World Bank Data World Bank Data; with slightly modified interpretation

Indicator for Default History Inflation, consumer prices

Dummy variable

Default on long-term foreign currency debt since 1990

%

Annual Inflation as measured by the consumer price index

Inflation2

%

Squared Inflation

Unemploy ment, total

%

Central % of Government GDP Debt

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Explanation

Cash deficit % of GDP Total reserves, includes gold

current US$

Unemployment refers to the share of the labor force that is without work but available for and seeking employment. Debt is the entire stock of direct government fixed-term contractual obligations to others outstanding on a particular date. It includes domestic and foreign liabilities such as currency and money deposits, securities other than shares, and loans. It is the gross amount of government liabilities reduced by the amount of equity and financial derivatives held by the government. Cash deficit is revenue (including grants) minus expense, minus net acquisition of nonfinancial assets Total reserves comprise holdings of monetary gold, special drawing rights, reserves of IMF members held by the IMF, and holdings of foreign exchange under the control of monetary authorities.

38 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Moody’s World Bank Data Own Generation World Bank Data World Bank Data

World Bank Data World Bank Data

39

Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

30 6 36

Investment grade Speculative grade Total

29 7 36

’91

30 7 37

’92 31 11 42

’93 36 13 49

’94 41 13 54

’95 50 20 70

’96 57 29 86

’97 55 37 92

’98 55 41 96

’99 59 37 96

’00 61 36 97

’01 63 35 98

’02 63 35 98

’03 64 36 100

’04 64 37 101

’05 66 37 103

’06 66 41 107

’07 66 42 108

’08

67 41 108

’09

68 43 111

’10

12 0 12

’81

12 0 12

’82

11 1 12

’83 12 1 13

’84 12 1 13

’85 12 1 13

’86 12 1 13

’87 12 1 13

’88 23 2 25

’89 23 2 25

’90 23 3 26

’91 23 6 29

’92 23 11 34

’93 23 15 38

’94

23 19 42

’95

25 22 47

’96

25 33 58

’97

23 39 62

’98

329 158 487

Total

Fine Rating Coarse Rating

3 up 9

2 up 40

67 45 112

’11

1,188 649 1,837

Total

Source: Own table 1 up unchanged 1 down 2 down 3 down 4 down 5 down 6 down 7 down 8 down 9 down Total changes 161 1406 56 23 11 6 3 5 2 0 1 317 93 1567 53 9 2 157

Table 5: Frequencies of Fine and Coarse Rating Changes, Classified by the Change Direction and Notches Moved

Investment grade Speculative grade Total

Time

Source: Hu et al. (2002)

Table 4: Frequencies of Investment and Speculative Grade Ratings in the Data Set of Hu et al. (2002), Rated by S&P

’90

Time

Source: Own table

Table 3: Frequencies of Investment and Speculative Grade Ratings in my Data Set, Rated by Moody’s

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Table 6: Regression Table for the Ordered Probit Estimation in the Fine and Coarse Rating Categories Source: Own table Rating Change Initial Rating GDP Growth Economic Development Default History Lagged Inflation Lagged Unemploymentrate Lagged Central Government Debt Lagged Deficit Lagged Total Reserves

Coarse Lagged -0.295*** (0.09) 0.097*** (0.02) 1.131*** (0.30) -0.464 (0.43) -0.021 (0.01) -0.036* (0.02) 0.003 (0.00) 0.147*** (0.04) 0.000 (0.00)

Inflation Inflation2 Unemployment rate Central Government Debt Deficit Total Reserves Cut-Off point 1 Cut-Off point 2 Cut-Off point 3

-4.558*** (0.75) -3.570*** (0.70) 0.354 (0.65)

Cut-Off point 4 Cut-Off point 5 Cut-Off point 6

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Cut-Off point 7 Cut-Off point 8 Cut-Off point 9 Cut-Off point 10 Number of Observations Pseudo R2 LR test Log Likelihood BIC * p < 0.1, ** p < 0.05, *** p < 0.01,

393 0.1584 47.58 -126.42 318.5424 Standard

Rating Fine Rating Unlagged Lagged Unlagged -0.551*** -0.098*** -0.180*** (0.10) (0.03) (0.03) 0.083*** 0.105*** 0.097*** (0.03) (0.02) (0.02) 1.662*** 1.015*** 1.458*** (0.34) (0.23) (0.25) -1.231** -0.398 -1.101*** (0.52) (0.36) (0.42) -0.020* (0.01) -0.003 (0.02) 0.001 (0.00) 0.137*** (0.03) 0.000 (0.00) -0.093*** -0.088*** (0.03) (0.03) 0.001* 0.001* (0.00) (0.00) -0.050** -0.027 (0.02) (0.02) 0.000 0.000 (0.00) (0.00) 0.117*** 0.104*** (0.04) (0.03) 0.000* 0.000* (0.00) (0.00) -7.184*** -4.100*** -6.062*** (0.99) (0.55) (0.73) -6.639*** -3.903*** -5.732*** (0.90) (0.53) (0.66) -5.708*** -3.527*** -5.516*** (0.85) (0.50) (0.63) -1.359* -3.089*** -5.348*** (0.74) (0.48) (0.61) -2.616*** -5.217*** (0.47) (0.60) 0.434 -4.855*** (0.44) (0.58) 1.237*** -4.259*** (0.45) (0.56) 1.756*** -0.905* (0.48) (0.51) 0.001 (0.52) 0.62 (0.55) 389 393 389 0.2423 0.1155 0.1686 70.33 71.05 96.66 -109.96 -271.99 -238.29 297.4512 639.5548 589.8854 errors in parantheses

40 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Table 7: Regression Table for the Random Effects Ordered Probit Model Source: Own table Coarse Rating Change Initial Rating GDP Growth Economic Development Default History Inflation Inflation2 Unemployment rate Central Government Debt Deficit Total Reserves Cut-Off point 1 Cut-Off point 2 Cut-Off point 3

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Cut-Off point 4 Number of Observations Pseudo R2 LR test Log Likelihood BIC * p < 0.10, ** p < 0.05, *** p < 0.01,

Simple ordered probit Clustered ordered probit -0.551*** -0.551*** (0.10) (0.09) 0.083*** 0.083*** (0.03) (0.02) 1.662*** 1.662*** (0.34) (0.29) -1.231** -1.231*** (0.52) (0.41) -0.093*** -0.093** (0.03) (0.04) 0.001* 0.001* (0.00) (0.00) -0.050** -0.050** (0.02) (0.02) 0.000 0.000 (0.00) (0.00) 0.117*** 0.117** (0.04) (0.05) 0.000* 0.000*** (0.00) (0.00) -7.184*** -7.184*** (0.99) (0.94) -6.639*** -6.639*** (0.90) (0.89) -5.708*** -5.708*** (0.85) (0.90) -1.359* -1.359* (0.74) (0.80) 389 389 0.2423 0.2423 70.33 -109.96 -109.96 297.4512 297.4512 Standard errors in parantheses

41 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Table 8: Marginal Effects on the Probabilities of Rating Changes, Calculated as Average of Marginal Effects (AME) Source: Own table 1 up

No Change

Initial Rating -0.04166*** GDP Growth 0.00624*** Economic Development 0.12577*** Default History -0.09318** Inflation -0.00704** Inflation2 0.00009** Unemployment rate -0.00377** Central Government Debt -0.00002 Deficit 0.00887** Total Reserves 0.00000***

1 down

2 down

3 down

0.00809 0.02639*** 0.00477 0.00240 -0.0012 -0.00396** -0.00071 -0.00036* -0.02444 -0.07969*** -0.01439 -0.00725 0.01810 0.05903** 0.01066* 0.00537 0.00137 0.00446** 0.00081 0.0004 -0.00002 -0.00006** -0.00001 0.00000 0.00073 0.00239** 0.00043 0.00022 0.00000 0.00001 0.00000 0.00000 -0.00172 -0.00562** -0.00102 -0.00051 0.00000 0.00000** 0.00000 0.00000

Table 9: Marginal Effects on the Probabilities of Rating Changes, Calculated at Means of the Independent Variables (MEM) Source: Own table 1 up

No Change

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Initial Rating -0.02413*** GDP Growth 0.00362** Economic Development 0.07285*** Default History -0.05397** Inflation -0.00408** 0.00005** Inflation2 Unemployment rate -0.00218** Central Government Debt -0.00001 Deficit 0.00514** Total Reserves 0.00000**

1 down

0.00655 0.01617*** -0.00098 -0.00242** -0.01979 -0.04883*** 0.01466 0.03618** 0.00111 0.00273** -0.00001 -0.00004** 0.00059 0.00146** 0.00000 0.00000 -0.00140 -0.00344** 0.00000 0.00000**

2 down

3 down

0.00119 0.00021 -0.00018 -0.00003 -0.00360 -0.00065 0.00267 0.00048 0.00020 0.00004 0 .00000 0.00000 0.00011 0.00002 0 .00000 0.00000 -0.00026 -0.00005 0.00000 0.00000

Table 10: Comparison of Probabilities at Mean Values of the Independent Variables and for Average Probabilities Source: Own table Rating Change Probabilities at means pˆ Average probability p¯ Downgrade by 3 notches 0.0000982 0.0018249 Downgrade by 2 notches 0.0006423 0.0043713 Downgrade by 1 notch 0.0115686 0.0298669 No Change 0.9699007 0.9152932 Upgrade by 1 notch 0.0177902 0.0486438

42 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

43

Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 Caa2 Caa3 Ca Obs.

Initial Rating

Aaa 97.43 9.76 3.13 1.79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 315

Aa1 1.93 79.27 7.29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 78

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Aa2 0.32 6.1 84.38 17.86 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97

Aa3 0 2.44 2.08 76.79 12.09 2.04 0 0 0 0 0 0 0 0 0 0 0 0 0 0 60

A1 0 1.22 2.08 1.79 80.22 13.27 3.41 3.41 0 0 0 0 0 0 0 0 0 0 0 0 96

A2 0 0 1.04 0 5.49 76.53 12.5 5.68 1.33 0 0 0 0 0 0 0 0 0 0 0 98

A3 0 0 0 0 0 4.08 80.68 7.95 4 0.74 0 0 0 0 0 0 0 0 0 0 86

Baa1 0.32 1.22 0 0 0 1.02 2.27 77.27 10.67 3.68 0.81 0 0 0 0 0 0 0 0 0 87

Baa2 0 0 0 0 0 0 0 0 81.33 8.09 1.63 0 0 0 0 0 0 0 0 0 74

Baa3 0 0 0 1.79 0 1.02 1.14 3.41 2.67 80.88 13.01 3.23 0 0 0 0 0 0 0 0 137

Ba1 0 0 0 0 1.1 2.04 0 1.14 0 2.94 78.86 13.98 5.36 0 0 0 0 0 0 0 121

Ba2 0 0 0 0 1.1 0 0 1.14 0 1.47 3.25 74.19 14.29 2.54 0 0 0 0 0 0 88

Terminal Rating

Source: Own table

Ba3 0 0 0 0 0 0 0 0 0 0.74 0 2.15 66.07 7.63 2.22 0 0 0 0 0 51

B1 0 0 0 0 0 0 0 0 0 0.74 0 2.15 10.71 80.51 12.22 4.84 0 0 0 0 118

B2 0 0 0 0 0 0 0 0 0 0 0.81 3.23 1.79 4.24 76.67 14.52 4.26 0 0 0 90

Table 11: Frequencies of Rating Changes in the Fine Rating Category

B3 0 0 0 0 0 0 0 0 0 0.74 0.81 1.08 1.79 3.39 4.44 74.19 14.89 0 0 0 65

Caa1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.85 3.33 4.84 76.6 16.67 25 50 47

Caa2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.61 2.13 66.67 25 0 7

Caa3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.11 0 0 0 50 25 4

Ca 0 0 0 0 0 0 0 0 0 0 0.81 0 0 0.85 0 0 2.13 16.67 0 25 5

Obs. 311 82 96 56 91 98 88 88 75 136 123 93 56 118 90 62 47 6 4 4 1724

Table 12: Frequencies of Rating Changes in the Coarse Rating Category Source: Own table Initial Rating Aaa Aa A Baa Ba B Caa Ca Obs.

Terminal Rating Aaa 97.43 5.13 0 0 0 0 0 0 315

Aa A Baa 2.25 0 0.32 91.88 2.14 0.85 4.69 92.06 1.81 0 6.69 89.63 0 0 8.09 0 0 0 0 0 0 0 0 0 235 280 298

Ba B Caa Ca 0 0 0 0 0 0 0 0 1.44 0 0 0 3.01 0.67 0 0 85.66 5.88 0 0.37 5.19 91.11 3.33 0.37 0 15.79 80.7 3.51 0 0 75 25 260 273 58 5

Obs. 311 234 277 299 272 270 57 4 1724

Table 13: Estimated Transition Matrix for all Countries, Calculated with Average Probabilities Source: Own table Initial Rating

Terminal Rating Ba B/Caa/Ca/C 0.03 0.33 0.16 3.09 0.35 86.53 2.90 6.16 89.04

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Aaa Aa A Baa Aaa 93.58 4.30 0.67 0.32 Aa 2.19 95.97 1.68 0.00 A 6.76 90.82 1.93 Baa 5.60 90.86 Ba 9.91 B/Caa/Ca/C -

44 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

Table 14: Estimated Transition Matrix for Non-Developing Countries, Calculated with Average Probabilities Source: Own table Initial Rating

Terminal Rating

Aaa Aa A Baa Aaa 94.57 3.89 0.51 0.20 Aa 2.20 96.38 1.31 0.09 A 5.72 92.23 1.70 Baa 5.02 90.02 Ba 10.43 B/Caa/Ca/C -

Ba B/Caa/Ca/C 0.02 0.25 0.11 4.17 0.57 86.23 2.74 11.17 81.96

Table 15: Estimated Transition Matrix for Non-Developing Countries in Business Cycle Peak, Calculated with Average Probabilities Source: Own table Initial Rating

Terminal Rating

Aaa Aa A Baa Aaa 94.99 3.50 0.44 0.18 Aa 1.99 96.71 1.20 0.08 A 4.54 92.74 2.16 Baa 5.11 89.96 Ba 11.97 B/Caa/Ca/C -

Ba B/Caa/Ca/C 0.02 0.36 0.20 4.13 0.56 84.71 2.79 10.47 82.15

Table 16: Estimated Transition Matrix for Non-Developing Countries in Business Cycle Trough, Calculated with Average Probabilities

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Source: Own table Initial Rating

Terminal Rating

Aaa Aa A Baa Aaa 94.87 3.43 0.46 0.20 Aa 1.86 96.65 1.35 0.11 A 4.76 92.45 2.01 Baa 5.46 89.62 Ba 10.52 B/Caa/Ca/C -

Ba B/Caa/Ca/C 0.03 0.45 0.33 4.18 0.53 85.82 3.04 11.44 82.02

45 Bergen, Alex. Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings : An Empirical Analysis of Sovereign Ratings, Diplomica Verlag, 2013. ProQuest Ebook

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Bonfim, D. (2009); ”Credit risk drivers: evaluating the contribution of firm level information and of macroeconomic dynamics”; Journal of Banking and Finance 33, p. 281-299 Borooah, V.K. (2001); ”Logit and Probit: Ordered and Multinomial Models (2001)”; Sage University Paper Series on Quantitative Applications in the Social Sciences, 07-138. Thousand Oaks, CA: Sage Cantor, Richard, Packer, Frank (1996); ”Determinants and Impact of Sovereign Credit Ratings (1996)”; FRBNY Economic Policy Review, vol. 6, p. 76-91 Chamberlain, G. (1984); ”Panel Data”. In: Griliches, Z., Intriligator, M. D. (Eds.), Handbook of Econometrics 18, 5-46, vol II. North - Holland, Amsterdam

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Chartsbin.com (2012); ”Moody’s Credit Rating for each country”; http:// chartsbin.com/view/1175; accessed August 16, 2012 Eisenkopf, Axel (2007); ”The real nature of credit rating transitions”; Goethe University Frankfurt, Finance Department European Central Bank (2012); ”Use of the Euro”; http://www.ecb.int/euro/ intro/html/index.en.html; accessed August 18, 2012 Greene, William H. (2012); ”Econometric Analysis”, International Edition, Seventh Edition Hamilton, D., Cantor R. (2004); ”Rating Transitions and Defaults Conditional on Watchlist, Outlook and Rating History”; Moodys Investor Service, Special Comment, February Hu, Yen-Ting, Kiesel, Rudiger, Perraudin, William (2002); ”The estimation of transition matrices for sovereign credit ratings”; Journal of Banking & Finance, vol. 26 (2002), July 2002, p. 1383-1406 Kaiser, Ulrich, Spitz-Oener, Alexandra (2000); ”Quantification of Qualitative Data Using Ordered Probit Models with an Application to a Business Survey in the German Service Sector”; ZEW Discussion Paper No. 00-58, Mannheim Lando, David, Skødeberg, Torben M. (2002); ”Analyzing rating transitions and rating drift with continuous observations”; Journal of Banking and Finance; vol. 26 2002, p. 423-444 Long, J. Scott, Freese, Jeremy (2001); ”Regression Models for categorial dependent variables using Stata”; College Station, Texas : Stata Press 2001 Moody’s (2002); ”Moody’s upgrades Greece to A1 from A2”; http://www.moodys. com/research/MOODYS-UPGRADES-GREECE-TO-A1-FROM-A2--PR_61154; accessed August 18, 2012

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Moody’s (2012b); ”Announcement: Moody’s changes the outlook to negative on Germany, Netherlands, Luxembourg and affirms Finland’s Aaa stable rating”; http://www.moodys.com/research/ Moodys-changes-the-outlook-to-negative-on-Germany-Netherlands-Luxembourg-% 20-PR_251214; accessed July 27, 2012 Moody’s (2012c); ”Ratings Definitions, Changes in Ratings”; http://www.moodys. com/Pages/amr002002.aspx; accessed July 20, 2012 Neyman, J., Scott, E. L. (1948); ”Consistent Estimates based on Partially Consistent Observations”; Econometrica 16, p. 1-32. Nickell, Pamela, Perraudin, William, Varotto, Simone (2000); ”The stability of ratings transition”; Journal of Banking & Finance, vol. 24(2000), p. 203-227 Standard & Poor’s Ratings Services (2012); ”Germany ’AAA/A-1+’ Ratings Affirmed On Strong Economic Fundamentals; Outlook Remains Stable”; http://www.standardandpoors.com/ratings/articles/en/us/?articleType= HTML&assetID=1245337921785 ; accessed August 5, 2012 Wooldridge, Jeffrey M. (2001); ”Econometric analysis of cross section and panel data”; Second Edition, October 2001 Wooldridge, Jeffrey M. (2002); ”Introductory Econometrics: A modern approach”; Second Edition World Bank (2012); ”How we Classify Countries, A Short History”; http://data. worldbank.org/about/country-classifications/a-short-history; accessed July 13, 2012

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Zheng, X. and Rabe-Hesketh, S. (2007); ”Estimating parameters of dichotomous and ordinal item response models using gllamm”; The Stata Journal 7 (3), p. 313-333

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