RATING MIGRATIONS: THE EFFECT OF HISTORY AND TIME

Huong Dang1 and Graham Partington

University of Sydney

Abstract

We use the Cox proportional hazards model to investigate the probability of rating

transitions using data for the period 1984 to 2005. Variables that capture rating history

and the current rating significantly affect the hazard of a rating transition. Rating history

is at least as important as, or more important than, the current rating in determining the

probability of a rating change. Different models are developed for rating upgrades and

downgrades, but the evidence consistently shows a tendency for rating history to repeat

itself. Longer lagged durations in ratings tend to lead to longer subsequent durations and

rating changes exhibit momentum.

There is also evidence of interactions between the time spent in a rating grade and the

main effect variables. The impact of the rating history variables diminishes as the time

spent in the current rating gets larger. After allowing for the interaction between rating

history and time, the current (start) rating is no longer significant as a main effect, and

only remains as an interaction term in the upgrade model.

JEL classification: C13, C14, C32, C34, C41, G14

Keywords: Survival analysis, proportional hazard, time-varying covariates, rating

migration, rating history, non-Markovian behaviors

1 Corresponding author: Huong Dang. Email: d.huong@econ.usyd.edu.au. Tel.: +61 421523259; Fax: +61 2 93516461. The authors wish to thank Dr. Paul Allison for programming advice and the Capital Markets Cooperative Research Centre (CMCRC) for financial support. We also thank participants at European Financial Management Association Conference (Athens, 2008) and the 2nd European Risk Management Conference (Milan, 2008) for valuable comments on the previous version of this paper.

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1. Introduction

Credit ratings are widely used to assess the risk that a firm will default and the

probability of rating changes is used in pricing debt and in risk management. The use of

credit ratings for credit risk measurement and management is particularly important

under the new capital adequacy framework of the BASEL II Accord. Consequently, the

Accord has stimulated much interest in the modelling of rating migration for both risk

management and capital adequacy purposes.

Modeling rating migration is facilitated by an understanding of the underlying rating

migration dynamics. It has been common to assume that rating migration follows a

Markov process. This is a convenient assumption as the migration probability will only

depend on the current rating and the ending rating, while the history of the rating

changes is irrelevant. However, there is empirical evidence such as Altman (1998) and

Hamilton and Cantor (2004) that rating migrations do depend on rating history. One

objective of this paper, therefore, is to estimate models for the probability of rating

migration based on rating history. The contribution is three-fold, first in extending the

evidence of non-Markovian behaviour in rating dynamics, second in extending the

variables from rating history that are candidates for predictive models, and third in

applying the Cox hazards model with time varying covariates. Cox’s model is the pre-

eminent method for estimating survival models and survival analysis is a natural choice

for estimating the probability that a rating survives in its current state. Cox’s model is

also particularly convenient for estimating models with time-varying covariates. We

also use a more extensive range of rating grades than has been the practice in prior

work.

A second objective of the paper is to examine how the effect of rating history interacts

with time. While the rating continues in its current state the distance in time from the

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historic observations is extending. The impacts of history variables on the migration

probability are thus likely to become increasingly “stale”. Our point here is not just that

more distant variables are likely to be less relevant, but that the impact of the variables

interacts with the duration of the rating. We hypothesize that the variables’ impact

decays over the time for which the current rating persists. We are not aware of any other

work which focuses on this interaction between rating history variables and time.

The study addresses the foregoing issues by examining the probable duration of rating

grades. How probable is it that by time t (in the set t = 1 to n) there will be an upgrade

or a downgrade. It is possible to obtain this probability from a survivor function S(t)

which can be estimated using Cox’s (1972) proportional hazards model. Where S(t) =

P(T>t) and P(T>t) is the probability that the time of the rating transition T will be after

time t.

The results show that several rating history variables and the current rating are

significant predictors of future rating transitions and that there are some aspects of

history repeating itself. Furthermore, for both upgrades and downgrades, the impact of

influential rating transition variables is time-dependent. The impact of rating history

decays the longer a rating continues unchanged. Rating history is at least as important

as, or more important than the current rating in determining the probability of a rating

change. Additionally, the current rating is no longer significant as a main effect once

time interactions are introduced into the rating migration models. It remains as an

interaction term in the model for upgrade migration but it drops out of the downgrade

model completely.

The paper is structured as follows: Section 2 provides an overview of the literature and

discusses the research questions; Section 3 describes the research method; Section 4

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identifies the data; Section 5 presents the results of the analysis; Section 6 discusses the

robustness checks on the results and Section 7 summarizes the main findings.

2. Literature Review and Research Questions

2.1. Literature review

Previous empirical studies have found evidence of non-Markovian behaviour in ratings

migrations, such as serial correlation, momentum, and duration dependence. Evidence

of serial correlation in rating migrations was provided by Altman and Kao (1992) and

Carty and Fons (1994). Hamilton and Cantor (2004) also show that the direction of a

prior rating change impacts on the current migration probability. Figlewski et al (2006)

provide evidence of rating momentum, a downgrade is more likely to be followed by a

downgrade than an upgrade.

The existence of a negative relation between the migration probability and the length of

time a bond stays in a particular rating was suggested by Lando and Skodeberg (2002).

This evidence of duration dependence helps motivate our use of the Cox proportional

hazards model, since an attractive feature of the model is that it controls for underlying

duration dependence, without requiring specification of the functional form of that

dependence.

Newly rated firms, compared with seasoned firms of the same rating class, have a

smaller probability of rating migrations within a few years as suggested by Altman

(1998). While Figlewski et al (2006) show that the longer the time elapsed since a firm

was first rated the more likely it is that the firm will default.

Studies such as Holthausen and Leftwich (1986) have shown that there is a differential

stock price response to upgrades and downgrades, with downgrades having a bigger

effect than upgrades. A possible explanation for this is that downgrades may be more

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difficult to forecast than upgrades and may follow a different stochastic process. This is

one factor that motivated the decision to develop separate models for upgrades and

downgrades.

2.2 Research questions and hypotheses

Taking a Markovian approach to rating history, all of the relevant information about the

impact of history is captured in the firm’s current rating, which we call the start rating

since it defines the beginning of the current rating state.

An important question, therefore, is whether the start rating alone is significant in

explaining rating migrations, or whether additional rating history variables are

significant. If the additional history variables are significant another question is whether

there is an interaction between these variables and time. We hypothesize that the impact

of rating history variables decay as the current rating continues on through time. If so,

interaction variables for history with time should reduce the impact of the main effect

variables for history.

Based in part on the research discussed in the literature review, we hypothesise that

there is a tendency for rating history to repeat itself and that recent history has the

strongest effect. If so the direction of the directly prior rating re-grades will positively

affect the probability of a further re-grade in the same direction and negatively affect the

probability of a re-grade in the reverse direction. Additionally, the longer the duration of

the directly prior rating states the longer the likely duration of the current rating state.

Any duration effect may, however, be conditional on the re-grades being in the same

direction. The disruption in continuity created by re-grades in opposite directions could

disrupt persistence in duration. The effect of recent history on duration is expected to

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diminish with the passage of time and if so the penultimate (lag-one) duration will have

a stronger impact on the migration hazard than the antepenultimate (lag-two) duration.

We also hypothesize that a history of frequent rating changes is likely to be repeated.

That is, the higher the rate of prior rating migrations the higher the hazard of future

rating migrations. It is also hypothesized that a rating currently in the investment/

speculative boundary increases the probability of an upgrade. Firms just above the

boundary have strong incentives to avoid a downgrade and firms just below the

boundary have strong incentives to work for an upgrade. We also investigate whether

rating migration is affected by being a fallen angel, rising star, or by a history of

substantial jumps across rating grades.

A natural question to ask is from how far back is the impact of rating history felt? The

answer according to Figlewski et al (2006) is that it extends right back to the firm’s first

rating. Thus the original rating is incorporated in our model and the question is whether

its effect remains in the presence of the additional rating history variables that our

model also includes. The age since first rating is also expected to impact on rating

migrations, as suggested by Altman (1998) and Figlewski et al (2006), and the effect is

expected to be negative.

A period of being unrated creates a break in the rating history of the firm. However, it is

not clear what impact this may have on the probability of rating migrations once the

firm becomes rated again. Some firms may withdraw from being rated because they no

longer carry significant debt, but firms are also likely to withdraw from being rated

when they have poor ratings and/or expect downgrades. Thus firms are likely to become

unrated when they are of poor credit quality. Such firms may subsequently restructure

their business to improve their financial status. These firms may then decide to be re-

rated when they are likely to receive good credit ratings. Alternatively, firms may seek

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re-rating when they need to make a debt issue, even if their rating has not improved. It

is not clear therefore what a period of being unrated signals about current credit quality,

or the probability of rating re-grades. However, if firms use becoming unrated as a

repeat strategy to avoid downgrades, then being downgraded will have a reduced

probability for such firms.

3. Method

3.1. Rating states

A rating state starts from the time the firm enters a rating class (start rating) subsequent

to the commencement date of the study. The state ends at the time the firm either

migrates to another rating class (ending rating), becomes unrated or the study ends. The

time a firm keeps the same rating is the survival time. However, if a firm exits from a

rating class due to a merger, extinction of rated debt, or any reason other than an

upgrade or a downgrade, the survival time is treated as censored. Rating runs

commencing before the start of the model estimation period or finishing after the end of

the model estimation are also treated as censored.2

The duration of each rating state, until transition or censoring, was measured. The

completed transitions were then labelled as upgrades, downgrades, or censored,

according to their ending rating states. These rating transitions were then pooled across

time and across rating states, and as a result, a firm may contribute several rating

transitions to the data-set. The use of multiple observations for the same firm is likely to

introduce dependence among the observations. However, this problem is diminished to

the extent that the covariates in the model control for dependence. To get robust

standard errors in the presence of any residual dependence we use the Wei-Lin-

2 The Cox model uses both completed transitions and censored observations in the estimation process.

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Weissfeld method (Wei, Lin, Weissfeld, 1989). This method, however, does not correct

for any remaining bias in the coefficients.

Two models were developed, one for the probability of upgrades, the other for

downgrades.3 The estimation procedure makes use of risk sets, which are composed of

all the firm ratings that are at risk of a rating change at time t. In the process of

estimating the model a new risk set is formed at each event time t when a rating

transition occurs. Firm ratings leave the risk set once they experience a rating transition,

or when they are censored. In forming the risk sets for the upgrade model, downgrades

are treated as censored and vice versa.

The first set of upgrade and down grade models were estimated without allowing for

any interaction of the variables with time. These models were then extended by adding

the time interaction terms (TVC models). Robustness tests were conducted by

estimating the models over a different time period.

3.2. Lagged macroeconomic factors

Whether the economy is doing well or badly is likely to influence the risk of a rating

migration. Therefore macroeconomic variables are used in the analysis to control for the

different macro economic conditions that prevailed prior to the start of each rating.

Given that macroeconomic conditions are likely to affect ratings with a lag, we follow

Figlewski et. al. (2008) and use an exponentially weighted average of lags for each

macroeconomic variables. The exponentially weighted average value Xt for the monthly

series x for a given macroeconomic variable in month t is calculated as:

3 An all-run model would make no sense since different signs on variables result for upgrade runs and downgrade runs.

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1

1

1

1

Kk

t kk

t Kk

k

xX

δ

δ

−−

=

−

=

=∑

∑ (1)

Where K is the length of the lag window and δ is the decay factor.

Figlewski et. al. (2008) explored windows varying from 12 to 24 months and decay

factors from 0.8 to 1. They found that th.e results were not especially sensitive to these

choices, and settled on the middle of the ranges K=18 months and δ =0.88, which we

also used. However, there was one exception, the monthly Chicago Fed National

Activity Index is published as a three-month moving average and we used this without

further transformation.

After eliminating strongly collinear macroeconomic variables we are left with 6

variables4. The Chicago Fed National Activity Index, the output growth gap, and the

growth in industrial production level capture the general economic activity. The S&P

500 monthly return, and S&P 500 annualized standard deviation represent the

performance of the stock market, while the term structure slope reflects credit condition.

3.3. Estimation and variables

The Cox proportional hazards model works by estimating the hazard rate, which is the

rate of change of the survival probability over an interval, conditional on survival until

the start of that interval. The survival probability can then be derived from the hazard.

The hazard model to be estimated is:

h(Z,t) = h(0,t) expZβ (2)

Where h(Z,t) is the hazard for a rating transition at time t given the covariate vector Z.

h(0,t) is the baseline hazard, which is that hazard with the covariate vector set to zero.

4 Notable omissions due to collinearity are the credit spread and the default rate.

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β is the vector of estimated coefficients

The initial vector of covariates Z contains 16 rating history, 6 macroeconomic

covariates, and 11 sector dummies. The covariate vector includes:

Lag one: The duration (in years) of the rating state that ends with either a down-grade or

an up-grade, and immediately preceding the current rating.

Lag two: The duration (in years) of the rating state that ends with either a down-grade or

an up-grade, and immediately preceding the lag one rating.

Dummy lag1 down: This dummy captures the direction of the lag-one re-grade and takes

the value of one if the lag one rating ends with a downgrade, and zero otherwise.

Dummy lag2 down: This variable captures the direction of the lag-two re-grade and

takes the value of one if the lag two rating ends with a downgrade, and zero otherwise.

Rate prior change: This indicates the average number of rating changes per year over

the firm’s rating history. It is calculated as the number of rating changes observed

between the entry of the firm to the study and the beginning of the current rating state

divided by the period the firm has been in the study.

Rate prior down: This equals the average number of down-grades per year over the

firm’s rating history. It is estimated as the number of down-grades observed between

the entry of the firm to the study and the beginning of the current state divided by the

period the firm has been in the study.

Age since first rated: The rating age of the firm, which is equal to the length in years

from the time the firm was first rated until the beginning of the current state.

Original rating: The numerically coded rating of the firm when it was first rated.

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Start rating: The numerically coded rating at the beginning of the state analyzed.

Dummy investment (inv) boundary: The dummy takes the value of one if the start rating

falls within the investment boundary BBB-, BBB, BBB+, and zero otherwise.

Dummy speculative ( junk) boundary: This dummy takes the value of one if the start

rating falls within the speculative (junk) boundary BB-, BB, BB+, and zero otherwise.

Number of Not rated (NR) status: This indicates the number of times a firm underwent a

break in rating history from the entry of the firm to the study until the beginning of the

current rating state5.

Number of Fallen Angels (FA) events: This indicates the number of times a firm

experienced a fallen angel event (a down-grade from investment state to speculative

state) from the entry of the firm to the study until the beginning of the current rating

state.

Number of Rising Star (RS) events: This indicates the number of times a firm

experienced a rising star event (an up-grade from speculative state to investment state)

from the entry of the firm to the study until the beginning of the current rating state.

Number of big down jumps: This indicates the number of times a firm experienced a big

down-grade jump, defined as a jump of at least three rating notches6, from the entry of

the firm to the study until the beginning of the current rating state.

5 The occurrence of an unrated history is infrequent. No firm experienced more than two periods of being unrated. The firms with two unrated periods represented less than 0.5 percent and those experienced one period of being unrated account for only 6.5 percent of the estimation sample. Becoming unrated might substitute for being downgraded in which case censoring by being unrated could lead to informative censoring. In this paper, we present the estimation results obtained on the sample that excludes censored rating cases ending with a NR status. Including such censored cases does not qualitatively change the results. 6 A study by Mood’s (July, 1997), indicated that the period 1920-1996 observed very infrequent substantial change in credit rating, and change of more than one rating category (three rating notches) represented only 11 percent of all rating changes. In this research, firms that experienced a down-grade of at least three rating notches account for 13.4 percent of the estimation sample and 17 percent of the robustness test sample

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Number of big up jumps: This variable indicates the number of times a firm experienced

a big up-grade jump, defined as a jump of at least two rating notches7, from the entry of

the firm to the study until the beginning of the current rating state.

Chicago Fed National Activity Index (CFNAI): This composite index is a weighted

average of 85 monthly economic series that cover four broad groups including (1)

production and income, (2) employment, unemployment and hours, (3) personal

consumption and housing expenditure, (4) sales, orders and inventories8. This monthly

index was used in its published form of a three-month moving average.

Actual real GDP growth minus potential real GDP growth: This output growth gap

measures the deviation of the actual real GDP growth from the potential real GDP

growth. Unlike the CFNAI, which reflects the “absolute strength” of the economy, the

output growth gap indicates the relative strength of the current economy state in relation

to its sustainable state.

Industrial production change: The industrial production change represents the strength

of the corporate sector.

S&P 500 monthly return: The monthly index return represents the overall performance

of the stock market.

S&P 500 annualized standard deviation: The stock market volatility is measured as

S&P 500 annualized standard deviation derived from daily returns for each month. The

exponential weighted average is then based on the monthly annualized standard

deviation.

7 Firms that experienced an up-grade of at least two rating notches account for 8.3 percent of the estimation sample and 5.2 percent of the robustness test sample 8 http://www.chicagofed.org/economic_research_and_data/cfnai.cfm

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Term structure slope: The term structure slope is measured as the spread between US

Treasury Constant Maturity 3-month and 10-year rates. The slope is considered a

predictor of future change in short term rates. A positively sloped yield curve tends to

go with stronger economic activities, which are associated with firms’ higher growth

rates and lower default exposures.

Industry Dummies: Firm’s industry sectors, as identified by Standard & Poors, were

used to control for any sector effects. The industry dummy took a value of one if the firm

was in an industry sector and zero otherwise. Due to their unique business nature and

credit risk exposure, firms in the financial institution sector were excluded from the study,

which left twelve sectors in the study. The twelve industry sectors resulted in eleven

dummy variables with the insurance sector left un-coded.

Time varying rating history covariates: These are created through multiplication of each

rating history variable by the event time t, where the event time t is updated as each risk

set is formed. Consequently, the interaction terms are time varying and the covariate

vector becomes, Zt. As rating age (Age since first rated) and rating volatility (Rate of

prior change, and Rate of prior down) are functions of time, we do not examine the

interactions between these variables and time. The interaction terms are:

Lag one time = Lag one * Event time

Lag two time = Lag two * Event time

Lag1 down time = Dummy lag1 down * Event time

Lag2 down time = Dummy lag2 down * Event time

Original rating time = Original Rating* Event time

Start rating time = Start rating * Event time

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Investment boundary time = Dummy investment boundary * Event time

Junk boundary time = Dummy junk boundary * Event time

Not rated (NR) time = Number NR * Event time

Fallen Angel (FA) time = Number FA * Event time

Rising Star (RS) time = Number RS * Event time

Big down time = Number big down * Event time

Big up time = Number big up * Event time

Because the interactions are time varying covariates, the proportionality property of the

Cox model no longer holds. This poses no problem for the estimation of coefficients on

the covariates in the model, but precludes the use of the model for forecasts of the rating

migration hazard9.

Unlike most studies on rating dynamics, which focus on coarser rating categories, such

as AAA, AA, or investment and speculative grades, we employ the full rating sub-

categories such as AAA, AAA-, AA+. The rating scales are coded from 0 to 26 with 0

indicating the default state (D) and 26 indicating the AAA state. Details of the rating

codes are provided in Table 1.

A similar coding technique was employed by Kim, and Wu (2006) to examine the impact

of sovereign credit ratings history on international capital inflows to emerging economies,

and on the development of the financial sectors in these economies. The numeric

conversion maintains the rank order of the rating and assumes that the difference between

any two consecutive rating states is the same. For instance, it is assumed that the “rating

gap” between BB+ (15) and BBB- (16) is the same as “rating gap” between C- (1) and C

9 This is because it is not possible to extract the baseline hazard from the Cox’s regression result when there are time-varying covariates.

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(2). While this might not be the case, the alternative of coding each rating class through

dummy variables would consume a substantial number of degrees of freedom. Adding an

extra twenty-five dummy variables to the model would also preclude compact

presentation of the results and make interpretation rather difficult, particularly in the case

of the models where we introduce interaction terms.

TABLE 1 HERE

4. Data

4.1. Rating history data

Rating data was obtained from Standard & Poors CreditPro 2005. The whole dataset

includes the rating history of 11,605 firms (of which 63.2% are American) over the period

1981-2005. The estimation sample covering the period 1984-2000 was formed from 3841

available rating states with non-censored measurements of all rating history variables.

This sample was used to estimate the base and time-varying covariate models for

downgrades and upgrades. The robustness test sample included 1728 available rating

states with non-censored measurements of all rating history variables. It was constructed

to test the robustness of the model for the period 2001-2005.

The year 1984 was used as the starting point of our study for several reasons. First,

macro-economic variables entered the models in the form of 18 month distribution lags

and 1982 is as far back as all data are available. Thus, the earliest starting point of our

estimation period could be July, 1983. Second, rating migrations are more common

events in the high yield bond sector, and the high yield bond market in the US was

being substantially established in the first half of the 1980’s. Migrations from 1984,

consequent to the establishment of the high yield bond market, were expected to

constitute a significant source of events for the study.

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This estimation time span of 16 years (1984-2000) is long enough to cover different

phases of business cycles in the US, and captures major market downturns and

international crises. The estimation period witnessed the US stock market crash in 1987,

the Mexican currency crisis in 1994, the Thai financial crisis in 1997, the Russian

sovereign bond default in 1998, and the collapse of Long Term Capital Market (LTCM)

hedge fund in 1998.

Histograms of rating durations for estimation and robustness firms are depicted in

Figure 1 and Figure 2 respectively. Both upgrades and down grades have positively

skewed distributions. The range of the distributions is similar, but it is clear that

durations for downgrades tend to be shorter than for upgrades. There is a noticeable

concentration of downgrades in durations shorter than one year.

FIGURE 1 AND 2 HERE

Table 2 – Panel A provides descriptive statistics for the durations of rating states in the

estimation period 1984-2000. In the down-grade model, 1,698 states (44.2%)

experience migrations (down-grades), and 2173 states (56.8%) are censored (including

upgrades). Downgrade durations vary from 1 day to 11.35 years, have a mean length of

1.66 years, and a median length of 0.99 years. In the upgrade model, 1175 states

(30.6%) experience migrations (upgrades) and 2666 states (69.4%) are censored

(including downgrades). Upgrade durations vary from 6 days to 11.44 years, have a

mean length of 2.25 years, and a median length of 1.72 years.

TABLE 2 – PANEL A HERE

Descriptive statistics of start rating for the 1698 down-grade states and the 1175 up-

grade states in the estimation sample are depicted in Table 2 - Panel B. Further analysis

(not reported) show that start ratings for up-grades are heavily concentrated at the range

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11 to 20 which predominantly consists of B grades. The majority of start ratings for up-

grades (60.24%) lie in the investment / speculative boundary region, whereas only

37.51% of down-grades start ratings reside in this region.

TABLE 2 – PANEL B HERE

4.2. Macroeconomic data

The monthly CFNAI Index was obtained from the Chicago Federal Reserve. The

potential real GDP growth rates came from the St. Louis Federal Reserve while the

actual real GDP growth rates were collected from the Bureau of Economic Analysis.

The industrial production series, and 3-month and 10-year US Constant Treasury

Maturity rates were obtained from the US Federal Reserve Board. The return on the

S&P 500 index was collected from Datastream.

5. Estimation Results

The model given by equation 2 was estimated for the upgrades and downgrades. There

are a large number of potential covariates to include in the model, thirty three in all. In

the interest of a parsimonious model and compact presentation of the results, we employ

a backward stepwise estimation procedure. Variables were retained in the models

according to the likelihood ratio test. All the selected variables were significant at the

5% level or better.

The estimation results of the base models, and the models extended by the time

interaction variables, are given for downgrades and upgrades in Panel A - Table 4. Panel

B – Table 4 is appended to Panel A and provides statistics on the fit of the models.

The discussion that follows focuses on the effects of the rating history variables as their

analysis is the purpose of this study. Consequently, there is no discussion of the macro-

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economic or industry sector control variables, except to note that changes in industrial

production and term structure slope were significant across all the models estimated.

PANEL A - TABLE 4 HERE

In interpreting Panel A - Table 4, a negative coefficient reduces the hazard and therefore

reduces the probability of a rating migration. The reported hazard ratios represent the

relative change in the hazard for a one unit change in the independent variable. For

example, in the base model for downgrades, an increase in the length of the lag one

rating run by one year reduces the chance of a downgrade by (1- 0.931) or 6.9%.

The results in Panel A - Tables 4 are generally as hypothesized. The hazard of a rating

change depends significantly upon several aspects of rating history as well as the

current rating. The better the current (start) rating the more likely the current rating state

continues. However, the impact of the current (start) rating is modest relative to the

combined impact of the rating history variables. Indeed, it is modest in relation to some

of the rating history variables considered individually. For example, in the base model

for down-grades a one unit (one notch) increase in the current rating reduces the

downgrade hazards by 11.2 percent but a rating downgrade at lag one increases the

hazard of a further downgrade by 143 percent.

There is some tendency for history to repeat itself. For example, longer lagged durations

increase the probability of the current rating continuing while lagged downgrade

increase the probability of a further downgrade and reduce the probability of an

upgrade.

It is also clear from Panel A- Table 4 that there are significant interactions with time for

most rating history variables. The interaction effects are generally consistent with decay

in the impact of rating history the longer a rating remains unchanged. Notably, the main

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effect of the current (start) rating disappears after allowing for the interaction between

rating history and time.

Comparison of the log-likelihood statistics in Panel B- Table 4 shows that adding the

time interaction terms significantly improves upon the base models for both down-

grades and up-grades. The likelihood ratio test shows that this improvement is

significant at better than the one percent level.

PANEL B - TABLE 4 HERE

While the foregoing provides a general picture of the results, there are some differences

between the upgrade and downgrade models.

5.1. Comparison of upgrade and downgrade models, 1984-2000

The base models for upgrades and downgrades (Panel A - Table 4) have many rating

history variables in common, but often their signs are reversed. A downgrade at lag one,

makes a downgrade more likely and an upgrade less likely. The incidence of being not

rated, the number of fallen angel events, and whether the rating is just above or just

below the investment/junk boundary, reduce the probability of a downgrade and

increase the probability of an upgrade.

The effects of longer durations at lag one, and a higher (better) start rating are the same

for upgrades and downgrades, the probability of a change in the current rating is

reduced. However, the impact of lagged rating durations is much smaller than the

impact of lagged rating changes. Extending duration by a year at lags one and two

reduces the chance of a downgrade by 6.9 percent and 5.2 percent respectively. In

contrast downgrades at lags one and two increase the hazard of a further downgrade by

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143 percent and 21.5 percent respectively, which is consistent with momentum in rating

migrations.10

Additional variables in the downgrade model include, the rate of prior downgrades, the

incidence of being a rising star, at lag two the direction of the rating change and the

duration of the rating, and the age since first rated. Consistent with Altman (1998) and

Figlewski et al (2006) a greater age since first rating makes a subsequent downgrade

more likely.

There is only one rating history variable in the upgrade model that is not shared with the

downgrade model and that is the original rating. The higher the original rating the

higher the probability of an upgrade, but the effect is the smallest of all the variables in

the upgrade model.

5.2. The impact of the time interactions

As Panel A – Table 4 shows, most of the variables from the base models appear as main

effects in the time varying covariate models and with one exception they retain the same

sign. The exception is the age since first rated. An increase in age since first rated now

reduces the probability of a downgrade. Age since first rated now also appears in the

upgrade model, where it reduces the probability of an upgrade. Thus an increase in the

age since first rated increases the probability of staying in the same rating grade.

A particularly notable change is that the start rating is no longer significant as a main

effect. The start rating only appears as a time interaction term in the upgrade model.

This result is a striking contrast to the Markovian assumption that all the effect of rating

history is captured in the start rating.

10 For upgrades a one year increase in duration at lag one reduces the probability of an upgrade by 7.2%. Given a downgrade at lag one, the hazard of an upgrade is 62 percent of the hazard of cases where there was an upgrade at lag one. Therefore, an upgrade at lag one makes a further upgrade (1/0.62)-1 or 61 percent more likely.

20

Another notable change is the very large increase in the main effect of a downgrade at

lag one on the risk of future down grades. A downgrade at lag one raises the risk of a

further downgrade by 545.6 percent. However as time passes in the current rating, the

time interaction for the lag one downgrade kicks in and the risk drops by 41.1 percent

for every year the current rating remains unchanged.

A few new main effects become significant. For downgrades the incidence of a big

down jump in ratings is added and this variable increases the risk of a further

downgrade by 41.7 percent. For upgrades, additional main effects are age since first

rated (as discussed above), the duration of the rating at lag two and the rate of prior

downgrades. A higher rate of prior downgrades reduces the probability of an upgrade

and a longer duration at lag two increases the probability of an upgrade. This latter

result differs from the usual effect of longer lagged durations, which is to make a rating

transition less likely. However, the interaction term for the lag two duration has a

negative sign. Consequently, a longer duration at lag two will make a rating transition

less likely conditional on a sufficiently long duration in the current rating state.

Most of the significant interaction terms selected arise from main effects in the time

varying covariate models. However a few interaction variables arise not from main

effects, but from variables in one or other of the base models. Where a variable is

significant as a main effect in the time varying covariate model, the time interaction

term has the opposite sign to the main effect. Consequently, the impact of the main

effect decays as the duration of the current rating gets longer.

6. Robustness Check

6.1. The robustness sample

The robustness tests were designed to address the question, do the effects of rating history

and time interactions remain significant in a different time frame? The robustness tests

21

were conducted for the period covering 2001 to 2005. This period was markedly

different from the estimation period 1984-2000, and had a quite different rating history

profile and current (start) rating distribution.

Descriptive statistics of the macroeconomic variables for estimation and robustness states

are presented in Table 3- Panel A. The independent sample t-tests and the Wilcoxon/

Mann – Whitney tests show that macroeconomic variables in the estimation period have

significantly different means and medians from the macroeconomic variables in the

robustness test period.

TABLE 3 – PANEL A HERE

The 2001-2005 period saw the Internet bubble burst and the 9/11 terrorist attack. The

bursting of the Internet bubble was followed by an economic slowdown and falling

business investment in the US, with negative stock returns for three consecutive years

2000 to 2002. The year 2002 was considered the worst year for the corporate bond

market in over 20 years. This year saw unprecedented credit deterioration and the

dramatic bankruptcies of fallen angels like WorldCom. Of the ten biggest bankruptcies

in US history, seven worth about $335 billion of assets, occurred in 2001-2002.

Corporate rating volatility intensified and the default rate escalated.

The robustness sample includes 1728 available rating states. Downgrades represent

46.4% and upgrades are 14.2% of the samples. Further tests (not reported) indicate that

there was no statistically significant difference between the proportion of down-grades

in the robustness sample and the proportion of down-grades in the estimation sample.

On the other hand, the proportion of up-grades in the robustness sample was

significantly different from the proportion of up-grades in the estimation sample.

22

Descriptive statistics of duration (run length) for the robustness down states and up

states are presented in Table 2 - Panel C. The durations of robustness test downgrades

have higher skewness and kurtosis whereas the durations of robustness upgrades have

smaller skewness and kurtosis than the durations of the respective estimation regrades.

TABLE 2 – PANEL C HERE

Descriptive statistics of rating history variables and start ratings for estimation states

and robustness states are presented in Table 3 – Panel B.

TABLE 3 – PANEL B HERE

Start rating states for the estimation sample have negative skewness, an investment

grade median rating (BBB), with distribution concentrated in investment boundary

BBB-, BBB, BBB+ while for the robustness test, start rating states have positive

skewness, a speculative grade median rating (B+), with distribution concentrated in

speculative rating categories B-, B, B+.

Further analysis (not reported) shows that rating states in the 2001-2005 sample had

higher percentage of fallen angel events, and big down jumps, and lower percentage of

rising star events, and big up jumps than the estimation rating states. Besides, rating

momentum evidence was observed more often for robustness states than estimation

states.

The two independent sample t tests indicate that there is a statistically significant

difference (at 1% or better) between the mean of the start rating / the means of rating

history variables, except dummy junk boundary and the number of FA, for estimation

and robustness states. The Wilcoxon – Mann – Whitney tests suggest that there is

statistically significance (at 5% or better) between the underlying distributions of the

23

start rating / rating history variables, except dummy junk boundary, for estimation and

robustness test

6.2. Results of the robustness check

Given the different conditions in the estimation period and the subsequent period used

for the robustness check, it is not surprising to observe some changes in the models (see

Panel A - Table 5.) However, the main conclusions remain unchanged, rating history

variables are significant predictors of rating changes. Including time interactions

significantly improves the log-likelihood statistic and the main effects for the start

rating drop out of the model once the time interaction terms are included. The time

interactions have the opposite sign to the main effects in the time varying covariate

model. However, it is a noticeable feature of the robustness check that a majority of the

interaction terms are not accompanied by a significant main effect.

Examining the results in more detail it is apparent that the majority of rating history

variable significant in the robustness check models are also significant in the

corresponding models for the estimation sample, but there are a minority of these

variables where the sign reverses. The effect of being a rising star is no longer

significant and variables for lagged duration, the incidence of being a fallen angel, and

being on the invest/junk boundary are less frequently significant.

Past rating volatility, irrespective of the direction of the rating changes, increases the

probability of both upgrades and downgrades. The incidence of big jumps to lower

rating grades only feature in the estimation results for the TVC down-grade model, but

is significant in all models in the robustness check. This variable increases the

probability of both upgrades and down grades, that is to say it diminishes the probability

of staying in the current rating state.

24

The effect of the direction of the rating change at lag one remains very strong for

downgrades. In the time varying covariate model for downgrades, a downgrade at lag

one increases the risk of a further downgrade by 1000 percent. However, for the

upgrade model, the effect of a downgrade at lag one is only significant as an interaction

term.

7. Conclusion

A Cox regression model is used to estimate dynamic models for the hazard of rating

migration. The purpose of this modeling is to investigate whether a set of rating history

variables, in addition to the current (start) rating, are significant determinants of the

probability of a rating migration. That is to say we test for non-Markovian behaviour in

rating migrations. The study also investigates whether the effect of the predictor

variables is constant, or whether it interacts with the time elapsed in the current rating

state.

Using a sample from Standard & Poor’s CreditPro 2005 dataset, hazard models were

estimated for rating upgrades and downgrades for the period 1984-2000. Robustness

checks of the models were conducted over the period subsequent to the estimation

period, 2001-2005. These robustness checks confirm the main findings discussed below.

Overall, the results are consistent with our hypothesis. Rating history is at least as

important as, or more important than the current (start) rating in determining the hazard

of a rating change. The models differ between upgrades and down grades, but they

consistently show that history has a tendency to repeat itself. Longer lagged durations,

tend to increase subsequent durations by reducing the probability of a current re-grade.

If the lagged rating change was a downgrade, the probability of a current downgrade is

increased and if the lagged rating change was an upgrade the probability of a current

25

upgrade is increased. The impact of these lagged rating changes has a particularly large

effect on the hazard of the subsequent rating change. Thus, there appears to be

substantial momentum in rating changes. It is evident that an unrated period tends to

make a further up-grade more likely and a subsequent down-grade less likely.

However, there is variation across time in the significance and magnitude of some of the

estimated coefficients. Changes in significance are particularly evident for the

investment / speculative rating boundary, the number of fallen angels, rising star events,

the number of substantial jumps to lower / upper rating grades, the frequency of prior

rating changes/ prior down-grades, and the period since the firm was first rated. The

variation is sufficient to suggest that there is some dependence on the conditions

prevailing in each period.

There is consistent evidence of an interaction between time and the main effect

variables, although not for all variables in all periods. The nature of the interaction is

such that the impacts of the rating history variables diminish as the time spent in the

current run gets larger. Notably the the start rating only appears as a time interaction

term in the upgrade model and its main effect disappears after allowing for the

interaction between rating history and time. This is striking contrast to the Markovian

assumption that all the effect of rating history is captured in the start rating.

26

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29

30

Figure 1: Histogram of duration, down states vs. up states, 1984-2000 Figure 2: Histogram of duration, down states vs. up states, 2001-2005

TABLE 1: RATING CODES

S&P rating Numeric code S&P rating Numeric code S&P rating Numeric codeInvestment grade Speculative (Junk) grade Speculative (Junk) grade (Continue)

AAA 26 BB+ 15 CC+ 6AAA- 25 BB 14 CC 5AA+ 24 BB- 13 CC- 4AA 23 B+ 12 C+ 3AA- 22 B 11 C 2A+ 21 B- 10 C- 1A 20 CCC+ 9 D (default) 0A- 19 CCC 8

BBB+ 18 CCC- 7BBB 17BBB- 16

TABLE 2: DESCRIPTIVE STATISTICS

Panel A Descriptive statistics of duration (run length), 1984-2000 * sample size includes 4487 runs

Non-censored runs/ Mean Median Standard Min Maxsample size* (years) (years) Deviation (days) (years)

Down-runs 2344 52.24% 1.658 0.997 1.957 2.365 7.547 1 day 15.345Up-runs 1821 40.58% 2.247 1.715 1.837 1.837 4.22 6 days 11.436

Panel B Descriptive statistics of run start rating, 1984 - 2000

Sample Mean Median Standard Skewness Kurtosis Min MaxDeviation

Down runs 14.7 16(BBB-) 4.96 -0.21 -0.96 2 ( C ) 26 (AAA)Up runs 15.57 16 (BBB-) 3.4 -0.26 -0.027 2 ( C ) 24 (AA+)

Panel C Descriptive statistics of duration (run length), 2001-2005 ** sample size includes 1872 runs

Non-censored runs/ Mean Median Standard Min Maxsample size** (years) (years) Deviation (days) (years)

Down-runs 801 42.79% 0.514 0.296 0.596 2.378 8.074 1 day 4.337Up-runs 245 13.09% 1.2 1.189 0.84 0.75 0.599 1 day 4.69

Run types Number of non-censored runs

Skewness Kurtosis

Run types Number of non-censored runs

Skewness Kurtosis

TABLE 3: DESCRIPTIVE STATISTICS

Sample Mean Standard Min Max Median Skewness KurtosisDeviation

Panel A: Macroeconomic

CFNAI 2001-2005 -0.126 0.496 -1.430 0.740 -0.08 -0.737 0.0671984-2000 0.005 0.511 -1.890 0.900 0.13 -1.399 2.667

RealGDPg actual minus potential 2001-2005 -0.116 0.308 -0.795 0.320 0.00387 -0.393 -1.0251984-2000 0.065 0.273 -0.927 1.123 0.1452 -1.444 2.812

Industrial production change 2001-2005 0.097 0.187 -0.437 0.381 0.122 -1.277 1.3541984-2000 0.293 0.205 -0.329 0.767 0.3299 -0.617 0.284

SP500 monthly return 2001-2005 -0.176 1.351 -3.324 2.036 0.416 -0.515 -0.7471984-2000 1.247 0.945 -2.177 3.351 1.277 -0.383 -0.006

SP500 annual SD 2001-2005 3.726 1.148 2.107 5.454 4 -0.071 -1.4971984-2000 3.038 0.955 1.638 5.788 2.8925 0.533 -0.524

Term structure slope 2001-2005 2.468 0.697 -0.070 3.239 2.774 -1.487 1.7321984-2000 1.528 0.958 0.075 3.429 1.2998 0.399 -1.133

Panel B: Rating history

Age since first rated (year) 2001-2005 10.257 7.331 0.203 24.992 7.3932 0.724 -0.8981984-2000 8.578 4.892 0.134 20.008 7.7342 0.548 -0.600

Original rating 2001-2005 16.026 4.236 7 (CCC-) 26 (AAA) 15 (BB+) 0.507 -0.7601984-2000 17.254 4.385 7 (CCC-) 26 (AAA) 17 (BBB) 0.054 -0.954

start rating 2001-2005 12.723 4.151 2 ( C ) 26 (AAA) 12 (B+) 0.216 -0.4571984-2000 15.610 4.351 2 ( C ) 26 (AAA) 16 (BBB-) -0.333 -0.416

Dummy inv boundary 2001-2005 0.182 0.386 0 1 0 1.648 0.7181984-2000 0.279 0.449 0 1 0 0.986 -1.029

Dummy junk boundary 2001-2005 0.206 0.405 0 1 0 1.454 0.1131984-2000 0.195 0.396 0 1 0 1.544 0.383

Lag one (year) 2001-2005 0.966 0.917 0.003 4.690 0.6822 1.396 1.6991984-2000 2.131 2.059 0.003 16.126 1.5343 2.206 6.664

Dummy lag1 down 2001-2005 0.773 0.419 0 1 1 -1.304 -0.2991984-2000 0.600 0.490 0 1 1 -0.409 -1.833

Lag two (year) 2001-2005 0.981 0.830 0.003 4.718 0.7795 1.252 1.6141984-2000 2.183 2.025 0.003 16.833 1.6274 2.387 8.298

Dummy lag2 down 2001-2005 0.823 0.382 0 1 1 -1.691 0.8601984-2000 0.600 0.490 0 1 1 -0.406 -1.836

Rate prior change (p.a.) 2001-2005 1.473 2.351 0.216 48.667 1.0965 15.048 277.0811984-2000 0.640 0.536 0.061 14.898 0.5143 7.316 132.613

Rate prior down (p.a.) 2001-2005 1.250 2.007 0 48.667 0.9395 15.758 344.3441984-2000 0.413 0.539 0 14.898 0.2841 7.601 139.228

Number NR 2001-2005 0.017 0.134 0 2 0 8.118 69.8901984-2000 0.077 0.283 0 2 0 3.785 14.608

Number FA 2001-2005 0.274 0.456 0 2 0 1.149 -0.3081984-2000 0.262 0.485 0 2 0 1.627 1.728

Number RS 2001-2005 0.058 0.238 0 2 0 4.034 15.5321984-2000 0.199 0.431 0 2 0 1.989 3.114

Number big down 2001-2005 0.342 0.598 0 4 0 1.735 2.7971984-2000 0.301 0.565 0 4 0 2.037 4.874

Number big up 2001-2005 0.139 0.388 0 3 0 2.960 9.3951984-2000 0.394 0.668 0 4 0 1.824 3.564

TABLE 4PANEL A: COEFFICIENT ESTIMATES (BACKWARD SELECTION), 1984-2000

Variables

Rating historyAge_since_first_rated 0.03014*** 0.00837 1.031 0.58437*** 0.09823 1.794 -0.26528*** 0.08013 0.767Original_rating 0.02256** 0.0106 1.023Start_rating -0.1138*** 0.00834 0.892 -0.12163*** 0.00954 0.885 -0.13507*** 0.01222 0.874 -0.09549*** 0.01218 0.909Dummy_inv_boundary -0.36558*** 0.07183 0.694 -0.44762*** 0.08537 0.639 0.24131*** 0.07317 1.273 0.18255** 0.0771 1.2Dummy_junk_boundary -0.3188*** 0.08527 0.727 -0.53877*** 0.106 0.583 0.52349*** 0.08219 1.688 0.47966*** 0.08632 1.616Lag_one -0.06578*** 0.01687 0.936 -0.12634*** 0.0221 0.881 -0.0786*** 0.01825 0.924 -0.15612*** 0.02861 0.855Dummy_lag1_down 0.91392*** 0.06416 2.494 1.27037*** 0.09662 3.562 -0.41133*** 0.06237 0.663 -0.55445*** 0.08345 0.574Lag_two -0.05105*** 0.01705 0.95 -0.05084*** 0.01609 0.95Dummy_lag2_down 0.20504*** 0.06415 1.228Rate_prior_changeRate_prior_down 0.11336 0.07347 1.12Number_NR -0.46009*** 0.11862 0.631 -0.72592*** 0.15098 0.484Number_FA -0.44473*** 0.09138 0.641 -0.43387*** 0.09032 0.648 0.19397*** 0.06356 1.214 0.23242*** 0.0577 1.262Number_RS 0.33203*** 0.09199 1.394 0.28892*** 0.10348 1.335Number_big_down 0.13258** 0.06385 1.142Number_big_up 0.10816** 0.05315 1.114Original_rating_timeStart_rating_time 0.02843*** 0.00455 1.029 -0.01774*** 0.00435 0.982Inv_boundary_time 0.1327*** 0.03189 1.142Junk_boundary_time 0.28226*** 0.05529 1.326Lag_one_time 0.03077*** 0.00786 1.031 0.03777*** 0.00883 1.038Lag1_down_time -0.21693*** 0.03005 0.805 0.08513*** 0.02795 1.089Lag_two_timeLag2_down_timeNR_time 0.20552*** 0.07727 1.228FA_timeRS_timeBig_down_time -0.09504*** 0.03128 0.909Big_up_timeAge_time -0.56226*** 0.09813 0.57 0.27087*** 0.07934 1.311Rate_change_time -0.8716*** 0.23837 0.418Rate_down_time 1.06524*** 0.22905 2.902

*** P ≤ 1%, ** 1%< P ≤ 5%, * 5%< P ≤ 10% based on Wald chi-square tests

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Downgrade base model Downgrade TVC model Upgrade base model Upgrade TVC model

TABLE 4PANEL A: COEFFICIENT ESTIMATES (BACKWARD SELECTION), 1984-2000

Variables Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Downgrade base model Downgrade TVC model Upgrade base model Upgrade TVC model

MacroeconomicCFNAIRealGDPg_actual_minus_potentialIndustrial_production_change 0.33692* 0.17999 1.401 0.38499** 0.17665 1.47 -0.66101*** 0.17168 0.516SP500_Monthly_returnSP500_annual_SD 0.12024*** 0.03905 1.128 0.08134** 0.03757 1.085 -0.10606** 0.04188 0.899Term_structure_slope -0.12142*** 0.04085 0.886 -0.08461** 0.04103 0.919 0.1284*** 0.03754 1.137

IndustryAerospace / automotive / capital goods / metal -0.19058** 0.07849 0.826 -0.53015*** 0.11304 0.589 -0.61943*** 0.11892 0.538Consumer / service sector 0.23122*** 0.06908 1.26 -0.6916*** 0.1178 0.501 -0.71961*** 0.12093 0.487Energy and natural resources -0.49573*** 0.12562 0.609 -0.34828*** 0.11644 0.706 -0.49653*** 0.12826 0.609 -0.53917*** 0.13513 0.583TelecommunicationsInsuranceLeisure time / media -0.46953*** 0.13674 0.625 -0.52306*** 0.13746 0.593Real Estate -2.61416*** 0.89875 0.073 -2.57211*** 0.87365 0.076Utility -0.30619*** 0.07799 0.736 -0.17693** 0.07563 0.838 -0.39449*** 0.09745 0.674 -0.44137*** 0.10109 0.643Forest and building products / homebuilders -0.81441*** 0.14557 0.443 -0.89185*** 0.15425 0.41Health care / chemicals -0.23268* 0.12723 0.792 -0.90075*** 0.14733 0.406 -1.01999*** 0.16485 0.361Transportation -0.26093** 0.1258 0.77 -0.73163*** 0.1472 0.481 -0.81614*** 0.1623 0.442High technology / computers / office equipment -0.29663** 0.14517 0.743 -0.39467*** 0.14612 0.674 -0.43078*** 0.15163 0.65

PANEL B: MODEL FIT STATISTICS, 1984-2000 Panel A: *** P ≤ 1%, ** 1%< P ≤ 5%, * 5%< P ≤ 10% based on Wald chi-square testsPanel B: ^ P-value is based on chi-square test

-2LogL DF P-value^Downgrade modelLikelihood base model 19694.22 21 <.0001Likelihood TVC model 19430.051 28 <.0001Likelihood difference 264.169 7 <.0001

Upgrade modelLikelihood base model 14079.14 19 <.0001Likelihood TVC model 14025.291 22 <.0001Likelihood difference 53.849 3 <.0001

TABLE 5PANEL A: COEFFICIENT ESTIMATES (BACKWARD SELECTION), 2001- 2005

Variables

Rating historyAge_since_first_ratedOriginal_rating 0.07942*** 0.02058 1.083 0.0869*** 0.02277 1.091Start_rating -0.10899*** 0.01081 0.897 -0.07436*** 0.01072 0.928 -0.21525*** 0.02472 0.806 -0.24027*** 0.02873 0.786Dummy_inv_boundary Dummy_junk_boundaryLag_one -0.34034*** 0.07698 0.712 -0.65955*** 0.10482 0.517 -0.32243** 0.14791 0.724Dummy_lag1_down 1.38115*** 0.15464 3.979 2.22449*** 0.19819 9.249 -0.41432*** 0.14873 0.661Lag_twoDummy_lag2_down 0.40285** 0.1583 1.496 0.41936*** 0.15275 1.521Rate_prior_change 0.07891** 0.03084 1.082 0.10008*** 0.01924 1.105 0.0922*** 0.03487 1.097Rate_prior_down -0.20348*** 0.05929 0.816 -0.13778*** 0.03607 0.871 0.07796*** 0.02824 1.081Number_NR -2.04404*** 0.68294 0.13 -2.06845*** 0.64709 0.126 0.64195*** 0.2103 1.9 0.67416*** 0.1457 1.962Number_FA -0.35429** 0.16202 0.702Number_RSNumber_big_down 0.34779*** 0.08097 1.416 0.41463*** 0.12347 1.514 0.31391*** 0.11599 1.369Number_big_upOriginal_rating_timeStart_rating_timeInv_boundary_timeJunk_boundary_timeLag_one_time 0.52506*** 0.09654 1.691 0.35957*** 0.1072 1.433Lag1_down_time -1.15307*** 0.11868 0.316Lag_two_timeLag2_down_timeNR_timeFA_timeRS_timeBig_down_time -0.42147*** 0.15566 0.656Big_up_timeAge_timeRate_change_time 1.09423*** 0.29617 2.987Rate_down_time -1.29836*** 0.30033 0.273

*** P ≤ 1%, ** 1%< P ≤ 5%, * 5%< P ≤ 10% based on Wald chi-square tests

Downgrade base model Downgrade TVC model Upgrade base model Upgrade TVC modelParameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

TABLE 5PANEL A: COEFFICIENT ESTIMATES (BACKWARD SELECTION), 2001- 2005

VariablesDowngrade base model Downgrade TVC model Upgrade base model Upgrade TVC model

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

Parameter estimate

Standard error

Hazard ratio

MacroeconomicCFNAIRealGDPg_actual_minus_potential 0.82885*** 0.24336 2.291Industrial_production_change 1.31625*** 0.40707 3.729 -3.83461*** 0.64259 0.022 -2.49213*** 0.75507 0.083SP500_Monthly_return -0.09767** 0.04077 0.907SP500_annual_SDTerm_structure_slope 0.79244*** 0.21247 2.209 0.59224*** 0.21962 1.808

IndustryAerospace / automotive / capital goods / metal 0.22035** 0.10981 1.247Consumer / service sector 0.2793*** 0.10767 1.322Energy and natural resources Telecommunications 0.36176** 0.14274 1.436InsuranceLeisure time / media -0.49055*** 0.17843 0.612 -0.70162*** 0.26755 0.496 -0.72485*** 0.26503 0.484Real Estate Utility Forest and building products / homebuildersHealth care / chemicals 0.39082*** 0.14485 1.478Transportation 0.46701** 0.1828 1.595 -1.11099*** 0.38463 0.329 -1.13865*** 0.39431 0.32High technology / computers / office equipment

PANEL B: MODEL FIT STATISTICS, 2001-2005 Panel A: *** P ≤ 1%, ** 1%< P ≤ 5%, * 5%< P ≤ 10% based on Wald chi-square testsPanel B: ^ P-value is based on chi-square test

-2LogL DF P-value^Downgrade modelLikelihood base model 8228.686 10 <.0001Likelihood TVC model 8110.769 17 <.0001Likelihood difference 117.917 7 <.0001

Upgrade modelLikelihood base model 2683.638 11 <.0001Likelihood TVC model 2666.318 13 <.0001Likelihood difference 17.32 2 0.0001