Credit Ratings and Cheap -talk: An ... - University of Miami€¦ · 10-6-2020 · Credit Ratings...
Transcript of Credit Ratings and Cheap -talk: An ... - University of Miami€¦ · 10-6-2020 · Credit Ratings...
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Credit Ratings and Cheap-talk: An Examination of Moody’s 2010 Recalibration*
Pei Li Southwestern University of Finance and Economics - School of Accounting
Phillip C. Stocken†
Dartmouth College - Tuck School of Business
Leo Tang Lehigh University - College of Business and Economics
June 10, 2020
Abstract
We examine whether the cheap-talk framework explains the institutional environment in which rating agencies communicate with investors. When information is unverifiable, we expect that more favorable credit ratings are less informative to investors. Using the standard deviation of yields to measure informativeness, we find that the standard deviation of yields is higher for more favorable rating categories compared to less favorable rating categories. To better identify the informativeness of ratings, we then examine Moody’s 2010 municipal bond recalibration. We posit and find that more favorable Moody’s credit ratings are increasingly less informative to investors in the period after Moody’s recalibration relative to before the recalibration. We also find that retail investors are less likely to comprehend the unverifiable nature of credit ratings. This conclusion has implications for the regulation of credit rating agencies and highlights the importance of aligning interests between rating agencies and investors. Keywords: Cheap-talk model, credit ratings, recalibration, information environment JEL classification: C31, M41
* We thank Stephanie Cheng (discussant), Claire Yan (discussant) and participants at the 2019 American Accounting Association annual meeting, 2020 financial accounting and reporting section meeting, and Lehigh Research Workshop for helpful comments. † Corresponding author: Professor Phillip Stocken, Tuck School of Business at Dartmouth, 204A Tuck Hall, Hanover, NH 03755. Phone: 603-646-2843; Email: [email protected]
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1. Introduction
Credit rating agencies employ a coarse message structure to convey their information about
a debt instrument (e.g., AAA, Aa1, …, Caa3). These letter grades do not convey absolute values
of default risk and are merely ordinal rankings of issuers. The relative ranking of risk conveyed by
credit ratings is also without reference to explicit time horizons (Cantor and Mann, 2003). Despite
the coarse message structure that the credit rating agencies (CRAs) use, investors find these ratings
to be helpful.1 Goel and Thakor (2015) offer a theoretical model to explain this phenomenon. They
assume that a rating is unverifiable; accordingly, a CRA’s opinion can be vague or even
misleading—their “talk is cheap”. This paper examines the information properties of credit ratings
and, by extension, whether it is appropriate to describe credit ratings as being cheap-talk.
Whether credit ratings are indeed cheap-talk has important implications for how to regulate
the rating agencies. If credit ratings are unverifiable opinions, the cheap-talk framework implies
that to enhance the quality of communication, regulation ought to align more fully the interests of
rating agencies and investors. Conversely, if credit ratings convey verifiable information, then full
revelation can result even if it is common knowledge that the interests of rating agencies and
investors are misaligned.
It is prima facie unclear whether viewing rating agencies as engaging in cheap-talk
describes the credit rating environment. On one hand, supporting this view, Coffee (2006) notes
that “the ratings agencies enjoy a virtual immunity from private litigation.” In line with the
adjudication of several courts that rating agencies’ opinions are unverifiable, Deats (2010) argues
that likelihood of rating agencies facing legal liability is remote compared with other information
intermediaries, such as public accountants and security analysts. Moreover, he documents that
1 There is a wide literature which examines the value relevance of credit ratings (e.g., Holthausen and Leftwich, 1986; Hand et al., 1992; Liu et al., 1999; Kliger and Sarig, 2000; Dichev and Piotroski, 2001; Cornaggia et al., 2017).
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courts have often dismissed the legal challenges that CRAs have faced when they have raised the
defense that credit ratings constitute opinions protected as free speech under the First Amendment.
On the other hand, there are several arguments suggesting that rating agencies do face
reporting constraints. For instance, in practice the success of the First Amendment defense that
rating agencies have invoked is not guaranteed. In Abu Dhabi Commercial Bank v. Morgan Stanley
& Co., the Southern District of New York restricted the scope of the First Amendment defense by
pointing out that since in this case credit ratings were disseminated to a “select group of investors”,
they were not afforded the same protections as if they were deemed a matter of public concern.2
In addition, the Credit Rating Reform Act of 2006 authorized the Securities and Exchange
Commission (SEC) to develop and enforce rules regarding the rating quality of the Nationally
Recognized Statistical Rating Organizations (NRSRO). Furthermore, Dimitrov, et al. (2015) argue
that enactment of the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 has
heightened the legal and regulatory penalties that rating agencies face, likely resulting in greater
litigation risk and regulatory scrutiny. Lastly, although it is difficult to assess the accuracy of credit
ratings, because they can be reliably evaluated only over a long period, rating agencies nevertheless
might damage their reporting reputation if they do not opine in a forthright fashion.
The presence of these direct costs of misreporting, therefore, raises the question whether
the cheap-talk framework de facto describes the institutional environment in which rating agencies
communicate with investors. In this light, we develop two primary hypotheses grounded in a
cheap-talk framework.
2 Deats (2010) provides a detailed discussion of the Abu Dhabi case and its implications for rating agencies. He also describes the legal basis for why, under typical conditions, public accountants do not enjoy First Amendment protection for their opinions whereas credit rating agencies do.
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We hypothesize, first, when information is unverifiable, more favorable credit ratings are
less informative to investors. We use the standard deviation of yields and yield spreads to capture
the informativeness of ratings. The standard deviation of yields is calculated using yields in the
secondary market for a given rating level by week. Yield spreads are calculated by adjusting yields
by their corresponding Treasury yields. Using a comprehensive sample of municipal bonds, we
find, consistent with our first hypothesis, that the standard deviation of yields and yield spreads
are greater for higher ratings.
These findings may be confounded by changes in the informational environment that also
influence the standard deviation of yields. For instance, reputational concerns may also decrease
the informativeness of ratings (Dimitrov et al., 2015; deHaan, 2017; Bedendo et al., 2018). To
sharpen our analysis of the informativeness of ratings, we consider Moody’s 2010 municipal bond
recalibration. The 2010 recalibration systematically shifted Moody’s municipal bond ratings
higher to align with its global rating scale, which it uses to rate its sovereign, financial institution,
and corporate obligations. This recalibration provides a setting in which there is a change in the
rating scale that is not motivated by changes in issuer fundamentals or macro-economic factors.
Indeed, Moody’s stressed that “[m]arket participants should not view the recalibration of
municipal ratings as rating upgrades, but rather as a recalibration of the ratings to a different rating
scale” (Moody’s, 2010).
We investigate how investors responded to Moody’s rating scale change and whether the
response is consistent with a cheap-talk framework. We hypothesize, second, that when
information is unverifiable, we expect that more favorable Moody’s credit ratings are increasingly
less informative to investors in the period after Moody’s scale recalibration relative to before the
recalibration.
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We employ a difference-in-differences analysis between Moody’s rated issuers (i.e.,
treatment group) versus Standard & Poor’s (S&P) rated issuers (i.e., control group) around the
recalibration event. Using this setting to test the effect of ratings and has several advantages:
foremost, we are able to examine how the information environment evolved after a change in the
rating scale. Furthermore, given that S&P did not recalibrate their ratings, the subset of S&P rated
bonds serves as a natural control group for comparison with Moody’s rated bonds. Our findings
show that relative to S&P rated bonds, the standard deviation of yields increases as ratings become
more favorable and at an increasing rate for Moody’s rated bonds after Moody’s scale recalibration.
Our study makes several contributions. The cheap-talk framework has been used to
theoretically model firm voluntary disclosure (e.g., Newman and Sansing, 1993; Gigler, 1994;
Fischer and Stocken, 2001), equity analyst communication (e.g., Morgan and Stocken, 2003),
credit ratings (e.g., Goel and Thakor, 2015), polling (e.g., Morgan and Stocken, 2003), and more
generally the presentation of ordinal information (see Chakraborty and Harbaugh, 2007). Despite
the broad theoretical application of the framework, we are unaware of any large sample empirical
research that examines the consequences of the assumption that market participants (such as firm
managers, equity analysts, or rating agencies) provide costless, unverifiable disclosure. This study
is the first to establish empirically that this assumption comports with the observed behavior in a
market setting.
Our findings have important implications for the regulation of the credit rating industry.
Since CRA’s opinions are unverifiable, the cheap-talk framework implies that to enhance the
quality of communication, regulators ought to create an environment in which the interests of
rating agencies and investors are aligned, possibly by revisiting the issuer-pay model and how
CRAs are compensated. Indeed, the SEC formed a committee of bond-market advisers in 2017
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that is currently examining the credit rating industry and the suitability of the “issuer-pay business
model” in which entities that sell bonds pay for the rating (Podkul, 2019a). Our regulatory
prescription differs fundamentally from the prescription that we would propose if rating agencies
communicate verifiable information. When verifiable information is being communicated, the
misalignment of incentives between senders (such as managers or sellers) and receivers (such as
investors or buyers) does not necessarily disrupt communication, even when this misalignment is
common knowledge (see Grossman, 1981; Milgrom, 1981). Accordingly, regulators may be more
tolerant of the misalignment of incentives when information is verifiable.
We examine whether our primary findings differ when our sample is segmented by retail
versus institutional investors. The question of how retail and institutional investors perceive credit
ratings has implications for the regulation of rating agencies. We expect that institutional investors
will have greater expertise pricing bonds independently of credit ratings by using other information
sources relative to retail investors. Further, institutional investors are more likely to recognize the
reporting incentives of a rating agency than are retail investors. Consistent with this view, we find
that for institutional investors, the standard deviation of yields is higher for higher ratings. In
contrast, for retail investors, we do not find that the standard deviation of yields is higher for higher
ratings. These findings suggests that retail investors rely more on credit ratings, reacting to the
ratings as if they convey verifiable information. To protect less sophisticated retail investors, this
finding further emphasizes the need for regulation to better align the interests of rating agencies
and investors.
Several studies examine the effect of the 2010 Moody’s recalibration and focus on its price
effects (Cornaggia, et al., 2017; Tang and Li, 2020) and economic effects (Adelino, et al., 2017).
Beatty et al. (2019) find that the recalibration allowed Moody’s to increase market share while
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Gillette, et al. (2020) and Cheng, et al. (2019) find that recalibration affects disclosure quality.3
The antecedent work also examines the 1982 refinement in credit ratings and finds that investors
reacted to the implementation of this finer partition in ratings (Liu, et al., 1999; Kliger and Sarig,
2000), and that it influenced firm investment policies (Tang, 2009).4 Our paper builds on this prior
work, but it is dissimilar in that we use predictions of the cheap-talk framework to identify the
information properties of credit ratings. We use the recalibration as a setting to better capture
whether investors view credit ratings as unverifiable messages. By enhancing this understanding,
we hope to inform regulators as they deliberate changing the compensation schemes in the credit
rating industry. Indeed, in recent SEC hearings, the head of S&P’s global rating services claimed
that this “business model question is existential for us” (Podkul, 2019a).
The paper proceeds as follows: Section 2 provides the background to Moody’s 2010
municipal bond recalibration, Section 3 grounds the hypotheses about the information properties
of credit ratings within a cheap-talk framework, Section 4 describes our data and variables, Section
5 reports our primary empirical tests and results, Section 6 provides additional analysis and
robustness tests, and Section 7 concludes.
2. Recalibration of Credit Ratings
Credit ratings provide information about an issuer’s default probability and allow investors
to access the risk properties of debt securities through a simple letter grade scale.5 Credit ratings
3 Gillette, et al. (2020) and Cuny, et al. (2020) find that higher rated municipalities reduce financial disclosures. As less information decreases price volatility (Koudijs, 2016), this effect would bias our findings toward our null hypotheses. 4 Tang (2009) finds that precise ratings produce investment efficiencies. These findings are not attributed to the predictions of a cheap-talk model. 5 Research has examined the causes of inflated ratings (Becker and Milbourn, 2011; Jiang et al., 2012; Alissa et al., 2013; Jollineau et al., 2014; Bonsall, 2014; Behr et al., 2016; Flynn and Ghent, 2017) and the various determinants of ratings (Ashbaugh-Skaife et al., 2006; Bonsall and Holzman, 2016; Ham and Koharki, 2016).
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exist for various asset classes including municipalities, corporations and countries. While different
classes of securities all use the same rating scale, not all ratings are useful for relative comparisons
of default risk across asset classes. For instance, prior to the 2010 recalibration, Moody’s municipal
bond ratings were not comparable to corporate bond ratings and were much harsher than corporate
bonds: in comprehensive study of bonds rated from 1970 to 2009, Moody’s found that the five-
year cumulative default rates for investment-grade municipal debt was only 0.03 percent compared
to 0.97 percent for corporate bonds.
Market participants and CRAs have long noted the discrepancy between corporate and
municipal bond default rates. In 2001 and 2006, Moody’s conducted surveys gauging whether
market participants wanted a unified rating scale. While some “cross-over” investors active in both
tax-exempt and taxable markets wanted a single rating scale, Moody’s did not recalibrate its
municipal ratings scale to a global scale until 2010. Part of its hesitancy to recalibrate was that the
recalibrated ratings would make it more difficult for investors to differentiate risk amongst
different municipalities, as Moody’s senior managing director Laura Levenstein noted:
“Investors in corporate or structured securities typically have looked to Moody’s ratings
for an opinion on whether a security or an issuer will meet its payment obligations. Historically,
this type of analysis has not been as helpful to municipal investors. If municipal bonds were rated
using my global ratings system, the great majority of my ratings likely would fall between just two
rating categories: Aaa and Aa. This would eliminate the primary value that municipal investors
have historically sought from ratings—namely, the ability to differentiate among various
municipal securities. I have been told by investors that eliminating that differentiation would make
the market less transparent, more opaque, and presumably, less efficient both for investors and
issuers” (Joffe, 2017).
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During the financial crisis, Moody’s faced greater regulatory pressure to recalibrate
municipal ratings. In July 2008, Congress held a hearing titled “Municipal Bond Turmoil: Impact
on Cities, Towns, and States” during which members of Congress gauged whether municipalities
faced increased interest costs under the dual ratings system (U.S. Congress, 2008). This hearing
led to the Dodd-Frank Act requesting the SEC to study the appropriateness of standardizing credit
rating systems. The subsequent SEC report, published in September 2012 titled, “Report to
Congress: Credit Rating Standardization Study”, indicated that users of credit ratings were
opposed to aligning rating scales. The report noted that “to apply a singular risk analysis to
different asset classes may ignore or downplay asset-specific credit risks and may compromise the
quality and accuracy of credit ratings applicable to an asset class” (SEC, 2012 pg. 37). In reviewing
these comments, the SEC “staff found that credit ratings historically have not been comparable
across asset classes and it may not be feasible to attain this comparability. Consequently, the staff
recommends that the Commission not take any further action at this time with respect to
standardizing credit rating terminology across asset classes, so that named ratings correspond to a
standard range of default probabilities and expected losses independent of asset class and issuing
entity” (SEC, 2012 pg. 38).
Neither the Dodd-Frank Act nor the SEC required Moody’s to shift its municipal ratings
scale. Moreover, many users of credit ratings as well as Moody’s (emphasized earlier) stressed
that shifting municipal ratings higher would make them less meaningful. Additionally, aligning
the ratings of assets classes that are inherently different is also questionable. These issues
notwithstanding, Moody’s decided to recalibrate its municipal ratings for most issuers according
to a pre-announced algorithm.
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Moody’s announced the recalibration algorithm on March 16, 2010, and it implemented
the revised rating scales in stages beginning on April 16, 2010 and ending on May 7, 2010. For
U.S. states and some local governments, the ratings were recalibrated during market hours on April
16, 2010. Certain municipal ratings did not change during recalibration. Notably, the recalibration
did not increase the speculative grade bond ratings because these bond ratings were already aligned
with the global scale (Moody’s, 2010).6 Figure 1 reports the distribution of Moody’s general
obligation bond ratings in the pre-recalibration versus post-recalibration periods. The recalibration
shifted ratings to higher categories.
< Figure 1 >
Moody’s recalibration did not induce S&P to shift its ratings. S&P maintains that their
municipal bond ratings have always been calibrated correctly relative to corporate ratings. Figure
2 illustrates the distribution of general obligation bond ratings for S&P during Moody’s
recalibration. Since S&P did not recalibrate their ratings, we use S&P rated bonds as a natural
control group.
< Figure 2 >
3. Hypothesis Development
The regulation of information intermediaries, such as credit rating agencies, is inextricably
linked to the verifiability of the information being communicated. Information may be viewed as
being verifiable or unverifiable. In models in which information is assumed to be verifiable, the
information sender is restricted to issue a message that cannot be revealed subsequently to have
6 Given the lack of municipal bonds with speculative grade ratings, we do not use these bonds as a control group.
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been false. Conversely, in models in which information is assumed to be unverifiable, the sender
is free to offer vague or even misleading opinions—the “talk is cheap”.
3.1. Unverifiable information setting
The analysis of unverifiable information began with the work of Crawford and Sobel
(1982). Their cheap-talk model features a sender (e.g., an information intermediary) and a receiver
(e.g., an investor) where the sender can costlessly issue an unverifiable message to a receiver who
then takes an action that affects the payoffs of both the sender and receiver. While the sender does
not bear a direct cost from issuing a misleading report, the sender might incur an indirect cost from
misleading the receiver. A distinctive feature of a cheap-talk game is that a partition equilibrium
in which the receiver chooses among a set of finite actions always characterizes the communication
that occurs. Importantly, the equilibrium is characterized by the actions that the sender can induce
the receiver to take and not by the sender’s messages. Indeed, as messages are costless, there are
a continuum of messages that the sender might send that induce the identical receiver action in
equilibrium. Thus, all equilibria that have the same relation between the sender’s privately
observed information and the receiver’s induced action are equivalent regardless of the sender’s
messages that induce the receiver’s equilibrium action.
The prediction of a cheap-talk model that a sender’s messages induce a set of finite actions
is consistent with the behavior of financial intermediaries, as they typically use a coarse message
structure to convey their information about a financial asset. For instance, Goel and Thakor (2015)
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use a cheap-talk model to show that the rating classification systems that credit rating agencies use
to rank bonds (such as Aaa, Aa1, …, Caa3) arise endogenously as equilibria.7
The presence of partition equilibria are consistent with the presence of a cheap-talk game
between a sender and receiver, implying the credit ratings are unverifiable. This observation,
however, is not dispositive. Institutional restrictions, such as the threat of investor legal action and
regulatory oversight by the Securities and Exchange Commission and the Financial Industry
Regulatory Authority, may restrict the number of messages and result in a categorical rating system.
The presence of these constraints and restrictions, therefore, raises an important epistemological
question as to whether, in fact, the cheap-talk framework, which features unverifiable information,
comports with the institutional environment in which CRAs communicate with investors.
Moody’s 2010 municipal bond recalibration provides an ideal setting in which to test
whether the cheap-talk framework de facto describes the institutional environment in which
financial intermediaries communicate with investors. Moody’s recalibration provides a change in
rating scale that was not motivated by changes in issuer fundamentals or macro-economic factors.
As noted earlier, Moody’s claimed that a key driver of the recalibration was the market’s increasing
desire for rating comparability in light of the growing number of investors participating in both
the tax-exempt and taxable markets (Moody’s, 2010). We investigate how investors responded to
this rating scale change and if that response is consistent with a cheap-talk framework.
To develop hypotheses to address whether the cheap-talk framework empirically describes
the environment in which credit rating agencies communicate with investors, we revisit the
7 Relatedly, stock brokerages typically use a categorical equity ranking systems (e.g., buy/hold/sell). Morgan and Stocken (2003) use a cheap-talk model to establish that categorical equity ranking systems that stock brokerages commonly use to rank stocks arise endogenously as equilibria.
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analysis in Crawford and Sobel (1982), which much of extant theoretical cheap-talk literature has
applied in various settings.8
Consider a setting featuring a CRA, which ranks a municipality’s bond issuance, and an
investor. In line with the adjudication of several courts that a CRA opinions are unverifiable, and
thus they enjoy robust First Amendment protection (see Deats, 2010), we assume that a CRA bears
no direct cost from reporting. Further, we suppose the interests of the CRA and investor are not
perfectly aligned. The CRA’s objective when rating bonds is to balance the divergent interests of
the issuing municipality and the investor purchasing the bonds. A municipality wants a high rating
to minimize the cost of external financing, whereas the investor seeks to accurately rate the bond
(e.g., Deats, 2010; Goel and Thakor, 2015).
CRA offer a forward-looking opinion about credit risk whereby they rank issuers and
obligations in an ordinal and not a cardinal fashion.9 As the primary value that investors have
sought from ratings is to obtain a relative ranking among the issuers, we assume that the relative
ranking of an issuer is a uniformly distributed random variable, denoted 𝜃𝜃�, on the unit interval.10
The CRA privately observes a signal of the actual ranking of the issuer’s bond 𝜃𝜃. It then chooses
a rating 𝑟𝑟𝑖𝑖 from a set of feasible ratings 𝑅𝑅 = {𝑟𝑟1, … , 𝑟𝑟𝑖𝑖, … , 𝑟𝑟𝑁𝑁}. As the CRA’s signal is unverifiable,
its rating may be vague or misleading. Given the CRA’s rating 𝑟𝑟𝑖𝑖, the investor prices the bond,
denoted 𝑃𝑃, at its expected value; that is, 𝑃𝑃(𝑟𝑟𝑖𝑖) = 𝐸𝐸�𝜃𝜃�|𝑟𝑟𝑖𝑖�. The CRA’s payoff is given by
8 Model of unverifiable information in the accounting disclosure literature, include, for instance, Newman and Sansing (1993), Gigler (1994), and Fischer and Stocken (2001). 9 The largest CRAs view their credit ratings in this manner: Moody’s notes that “our rating system is a relative (or ordinal), rather than an absolute (or cardinal) ranking system” (Zarin, 2011). Likewise, S&P contends that its “credit ratings are designed primarily to provide relative rankings among issuers and obligations of overall creditworthiness; the ratings are not measures of absolute default probability” (S&P RatingsDirect, 2018). Similarly, Fitch indicates that “credit ratings express relative risk in relative rank order, which is to say they are ordinal measures of credit risk and are not predictive of a specific frequency of default or loss” (Fitch Ratings, 2019). 10 In the context of an equity analyst setting in which analysts rank stocks, Morgan and Stocken (2003) adopt an analogous assumption.
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𝑏𝑏𝑃𝑃(𝑟𝑟𝑖𝑖) − �𝑃𝑃(𝑟𝑟𝑖𝑖) − 𝜃𝜃��2, (1)
where the parameter 𝑏𝑏 > 0 is increasing in the misalignment of CRA’s and investor’s interests.
The first term in the brackets of the CRA’s objective function in (1) captures the extent to which
the CRA seeks to promote the interests of the issuing municipality, and the second term reflects
the objective of the investor to accurately price the bond. The CRA balances these divergent
interests while aiming to influence the investor’s rating. As talk is cheap, the CRA’s rating does
not enter directly into the CRA’s payoff in (1) but only affect the CTRA’s payoff through the
ratings effect on the investor’s beliefs.
The equilibrium to this game follows readily from Crawford and Sobel (1982, 1440-1442).
They establish that all equilibria are partition equilibria in which the unit interval support of the
CRA’s private information is partitioned into 𝑁𝑁 elements {𝑎𝑎0(𝑁𝑁) = 0, … ,𝑎𝑎𝑖𝑖(𝑁𝑁), … ,𝑎𝑎𝑁𝑁(𝑁𝑁) = 1},
where
𝑎𝑎𝑖𝑖 = 𝑖𝑖/𝑁𝑁 + 𝑖𝑖(𝑖𝑖 − 𝑁𝑁)𝑏𝑏 for 𝑖𝑖 = 0,1, … ,𝑁𝑁, (2)
and 1 ≤ 𝑁𝑁 ≤ 𝑁𝑁(𝑏𝑏) = �−1/2 + �(1 + 4/𝑏𝑏)/2�, which is a positive integer.11 We interpret 𝑁𝑁 as
the number of ratings in the CRA’s classification system (e.g., Aaa, Aa1, ..., Caa3). Therefore, the
number of distinct investor actions that the CRA can induce is given by 𝑁𝑁. The CRA that privately
observes 𝜃𝜃 ∈ (𝑎𝑎𝑖𝑖−1(𝑁𝑁),𝑎𝑎𝑖𝑖(𝑁𝑁)] issues the rating 𝑟𝑟𝑖𝑖 ∈ 𝑅𝑅 that induces the investor to price the bond
at 𝑃𝑃(𝑟𝑟𝑖𝑖) = �𝑎𝑎𝑖𝑖−1(𝑁𝑁) + 𝑎𝑎𝑖𝑖(𝑁𝑁)�/2. The maximum number of ratings is 𝑁𝑁(b), which decreases in
the misalignment between the CRA’s and investor’s interests.12
11 ⌊𝑥𝑥⌋denotes the smallest integer greater than or equal to 𝑥𝑥 12 We assume the misalignment of interests between the CRA and investor is common knowledge. Institutionally, however, the incentive misalignment may be uncertain. Morgan and Stocken (2003) study a cheap-talk model when there is uncertainty about an equity analyst’s incentives in a stock recommendation setting. They continue to find the presence of a partition equilibrium even when the sender’s interests are uncertain.
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A feature of a partition equilibrium is that the form of the CRA’s rating system (e.g., Aaa,
Aa1, …, or AAA, AA+, …) and the CRA’s rating 𝑟𝑟𝑖𝑖, say 𝑟𝑟𝑖𝑖 = Aa1, has no intrinsic meaning except
to the extent that the CRA rating induces a particular investor evaluation of the issuer’s ordinal
ranking among the set of issuers. Further, the CRA’s rating is noisy as it only reveals the element
of the partition containing the CRA’s private signal about the issuer’s ranking rather than the
CRA’s actual signal 𝜃𝜃. Importantly, even though the bond rating is noisy, it does not induce the
investor to hold biased beliefs: for instance, when the CRA knows the actual ranking of the bond
is 𝜃𝜃 , where 𝜃𝜃 ∈ (𝑎𝑎𝑖𝑖−1,𝑎𝑎𝑖𝑖], the investor will correctly infer from the CRA’s rating 𝑟𝑟𝑖𝑖 that 𝜃𝜃 ∈
(𝑎𝑎𝑖𝑖−1,𝑎𝑎𝑖𝑖) , and consequently, the investor will price the bond at the conditional expectation
𝑃𝑃(𝑟𝑟𝑖𝑖) = 𝐸𝐸[𝜃𝜃|𝑟𝑟𝑖𝑖] = (𝑎𝑎𝑖𝑖−1 + 𝑎𝑎𝑖𝑖)/2.
To develop our hypotheses, we now turn to consider the relation between the CRA’s rating
system and the quality of the investor’s information. Define the quality of the investor’s
information as the expected precision of the investor’s beliefs about the bond conditional on the
CRA’s ranking; formally, the quality of the investor’s information equals
(𝐸𝐸[𝑣𝑣𝑎𝑎𝑟𝑟(𝜃𝜃|𝑟𝑟𝑖𝑖)])−1 = �∑ ∫ �𝐸𝐸[𝜃𝜃|𝑟𝑟𝑖𝑖]− 𝜃𝜃��2 𝑑𝑑𝜃𝜃�𝑎𝑎𝑖𝑖𝑎𝑎𝑖𝑖−1
𝑁𝑁𝑖𝑖=1 �
−1= � 1
12∑ (𝑎𝑎𝑖𝑖 − 𝑎𝑎𝑖𝑖−1)3𝑁𝑁𝑖𝑖=1 �
−1. (3)
It then follows from Theorem 3 in Crawford and Sobel (1982) that the quality of the investor’s
information is increasing in the cardinality 𝑁𝑁 of the rating system and attains a maximum at 𝑁𝑁(𝑏𝑏).
Intuitively, we expect that reducing the cardinality of the rating classification system will heighten
the difficulty investors experience differentiating between issuers. Institutionally, this decline in
the quality of investor information will manifest in more dispersion of municipal bond yields and
yield spreads in the secondary market.13
13 This claim is consistent with the literature examining information and stock price volatility. For instance, West (1988) finds that more information about future dividends decreases idiosyncratic volatility. In a similar vein, Kelly
16
To measure the information that a CRA’s rating conveys, we define dispersion conditional
on rating report 𝑟𝑟𝑖𝑖 as
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖 ≡ 𝑣𝑣𝑎𝑎𝑟𝑟(𝜃𝜃|𝑟𝑟𝑖𝑖) = ∫ �𝐸𝐸[𝜃𝜃|𝑟𝑟𝑖𝑖] − 𝜃𝜃��2 1𝑎𝑎𝑖𝑖−𝑎𝑎𝑖𝑖−1
𝑑𝑑𝜃𝜃�𝑎𝑎𝑖𝑖𝑎𝑎𝑖𝑖−1
for 𝑖𝑖 = 1, … ,𝑁𝑁. (4)
We can show that 𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖 is increasing in the favorableness of the rating 𝑟𝑟𝑖𝑖 ; formally,
𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖 > 0 for 𝑖𝑖 = 1, … ,𝑁𝑁.14 To develop loose intuition for this relation, observe that
the probability the CRA will induce the bond price 𝑃𝑃(𝑟𝑟𝑖𝑖), which is given by
𝑎𝑎𝑖𝑖 − 𝑎𝑎𝑖𝑖−1 = 1𝑁𝑁
+ (2𝑖𝑖 − 1 − 𝑁𝑁)𝑏𝑏, (5)
is increasing in 𝑖𝑖 for 𝑖𝑖 = 1, … ,𝑁𝑁. Thus, ratings that are more favorable are less informative to
investors about the CRA’s underlying ranking of the bond. It follows that a more favorable rating
(e.g., Aaa) will induce greater dispersion than a less favorable rating (e.g., Baa1). This analysis
leads to our first hypothesis, stated in the alternative form:
Hypothesis H1: Ceteris paribus, for a given rating classification system 𝑁𝑁, the dispersion
in yields associated with a rating increase as the rating becomes increasingly favorable.
This relation should prevail for any CRA for a given rating classification system 𝑁𝑁
(provided 𝑁𝑁 > 1). This relation, however, is a function of the cardinality of the rating system and
the alignment between the CRA’s and investors’ interests. Thus, this relation will be confounded
in a pooled sample of ratings from different CRAs and that have different rating systems. Indeed,
Figure 1 and 2 evidence the different frequencies of ratings that Moody’s and S&P issue before
and after Moody’s recalibration.
(2014) documents that firms with better information environments are associated with smaller idiosyncratic return volatility. 14 The proof establishing that 𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖 > 0 for 𝑖𝑖 = 1, … ,𝑁𝑁 is available on request. The proof follows from substituting expression (2) into expression (4) and differentiating with respect to 𝑖𝑖.
17
In this light, to sharpen our empirical tests, we focus on Moody’s 2010 municipal bond
recalibration, which it implemented in stages beginning on April 16, 2010 and ending on May 7,
2010. While the alignment of interests between the CRA and investors’ is unlikely to vary much
during this short period, the cardinality of Moody’s rating system decreased. We can establish that
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖 is increasing and at a higher rate as the favorableness of a rating 𝑟𝑟𝑖𝑖 increases when
the cardinality of the rating classification system 𝑁𝑁 decreases; formally, 𝜕𝜕(𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖)/
𝜕𝜕𝑁𝑁 < 0 for 𝑖𝑖 = 1, … ,𝑁𝑁.15 Moody’s rating scale recalibration reduced the number of ratings that
Moody’s actually uses to rate its general obligation municipal bonds (see Figure 1), which we
interpret as a reduction in the cardinality of the rating system 𝑁𝑁. Thus, we expect dispersion to be
more positively associated with an increase in the favorableness of a rating after Moody’s
recalibration. This analysis leads to our second hypothesis, stated in the alternate form:
Hypothesis H2: Ceteris paribus, after Moody’s recalibration reduced the cardinality of
the rating system 𝑁𝑁, the dispersion in yields associated with a Moody’s rating increase and at a
higher rate as the favorableness of the Moody’s rating increases.
The proposition that more favorable ratings are less informative to investors is a distinctive
feature of a setting in which information is unverifiable. This relation is expected to be more
pronounced after Moody’s recalibration. To establish that there is a credible null hypothesis, we
pause and consider investor beliefs about a bond conditional on a CRA ranking when information
is verifiable.
15 The proof establishing that 𝜕𝜕(𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖)/𝜕𝜕𝑁𝑁 < 0 for 𝑖𝑖 = 1, … ,𝑁𝑁 is available on request.
18
3.2. Verifiable information setting
The analysis of verifiable information began with the work of Grossman (1981) and
Milgrom (1981). In their models, they assumed that the sender is free to withhold information, but
if the sender sends a message, then the message must be truthful. They established that even though
the interests of the sender and receiver are misaligned in that the sender seeks to induce the receiver
to have the highest possible valuation, full revelation of the sender’s information occurs in
equilibrium. This equilibrium arises because the receiver assumes that a sender that does not
disclose must have observed the worst possible information realization. Given these receiver
beliefs, every sender that has anything but the worst information will prefer to disclose and thereby
avoid been pooled with senders that are believed to have the worst information. Models of
verifiable information have been widely studied in the accounting literature; see Verrecchia (1983),
Dye (1985), and Jung and Kwon (1988).
To develop the null hypothesis, return to the setting considered in Section 3.1, but instead
of assuming that the CRA’s information is unverifiable, assume that it is verifiable. In this case,
the CRA can withhold information, but any disclosure must be truthful. Hence, the CRA’s
expected payoff becomes 𝑏𝑏𝑃𝑃(𝑟𝑟𝑖𝑖). If the CRA is free to offer any rating 𝑟𝑟𝑖𝑖 ∈ 𝑅𝑅, provided it is not
falsifiable, then it follows immediately from Grossman (1981) and Milgrom (1981) that the unique
equilibrium is characterized by full revelation.16
Now suppose that the rating classification system is fixed to have 𝑁𝑁 categories for
exogenous institutional reasons (unlike the unverifiable information case in Section 3.2 where the
cardinality of the rating system was determined endogenously). In this case, the CRA cannot fully
16 Alternatively, suppose the CRA’s information is unverifiable, but the CAR incurs a direct cost when misreporting. In the unique equilibrium of this costly signaling model, investors again can infer perfectly the CRA’s privately observed information (see Stein, 1989).
19
reveal its information. If investors or regulators wish to maximize the expected precision of the
investor’s beliefs given the CRA’s ranking system has a cardinality of 𝑁𝑁, then it is optimal to
choose the 𝑁𝑁 elements {𝑎𝑎0(𝑁𝑁) = 0, … ,𝑎𝑎𝑖𝑖(𝑁𝑁), … ,𝑎𝑎𝑁𝑁(𝑁𝑁) = 1} such that at
𝑎𝑎𝑖𝑖 = 𝑖𝑖/𝑁𝑁 for 𝑖𝑖 = 1, … ,𝑁𝑁. (6)
In the equilibrium, the CRA sends the rating 𝑟𝑟𝑖𝑖 when 𝜃𝜃 ∈ (𝑎𝑎𝑖𝑖−1(𝑁𝑁),𝑎𝑎𝑖𝑖(𝑁𝑁)] and the
investor prices the bond at the conditional expectation 𝑃𝑃(𝑟𝑟𝑖𝑖) = 𝐸𝐸[𝜃𝜃|𝑟𝑟𝑖𝑖] = (𝑎𝑎𝑖𝑖−1 + 𝑎𝑎𝑖𝑖)/2 for 𝑖𝑖 =
1, … ,𝑁𝑁.17 The distinctive feature of this verifiable information equilibrium is that each rating is
equally informative about a bond’s actual ranking. Indeed, notice that the probability the CRA will
induce the bond price 𝑃𝑃(𝑟𝑟𝑖𝑖) is given by
𝑎𝑎𝑖𝑖 − 𝑎𝑎𝑖𝑖−1 = 1𝑁𝑁
(7)
for all 𝑖𝑖 = 1, … ,𝑁𝑁 . Thus, each rating is equally informative. When each rating is equally
informative, a more favorable rating will induce the same dispersion in yields; formally,
𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖 = 0 for 𝑖𝑖 = 1, … ,𝑁𝑁. This observation stands in contrast to the relation posited
in H1.
When the CRA’s information is verifiable and the cardinality 𝑁𝑁 of the rating classification
system is reduced, the dispersion in yields will increase. Importantly, however, while each rating
is less informative than it was before the cardinality 𝑁𝑁 was reduced, each rating is still equally
informative in that a more favorable rating induces the same dispersion in yields as a less favorable
rating. Thus, the strength of the relation between dispersion and rating favorableness does not vary
with the cardinality of the rating classification system when information is verifiable; formally,
𝜕𝜕(𝜕𝜕𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝑖𝑖/𝜕𝜕𝑟𝑟𝑖𝑖)/𝜕𝜕𝑁𝑁 = 0 for 𝑖𝑖 = 1, … ,𝑁𝑁. This observation stands in contrast to the relation
hypothesized in H2.
17 The formal proofs for the claims in Section 3.2 are available on request.
20
In summary, when CRA’s information is unverifiable, more favorable ratings induce
higher dispersion in yields than less favorable ones and this relation is more pronounced as the
rating system becomes increasingly coarse. In contrast, when the CRA’s information is verifiable,
more favorable ratings induce the identical dispersion in yields as less favorable ones and this
relation does not vary in the cardinality of the rating system.
4. Sample Selection and Variable Measurement
This study extracts the bond trading information in the secondary market from the
Municipal Securities Rulemaking Board (MSRB) Database for the period from year 2009 through
year 2011, and bond information from the Mergent Municipal Bond Securities Database (Mergent).
MSRB provides yields of the trade, trade price, CUSIP number, security description, trade date,
maturity date, an indicator showing whether the trade was initiated as a purchase from a customer,
a sale from a customer, or an interdealer transaction. From Mergent, we collect the issue-specific
information: bond offering date, bond insurance, historical credit rating change (Moody, Standard
and Poor’s, and Fitch), bond type, maturity date. We merge the trade data from MSRB with issue-
specific information from Mergent by CUSIP.
The sample selection procedures are summarized in Table 1. All tests employ a difference-
in-differences analysis between Moody’s rated bonds (treatment group) versus S&P rated bonds
(control group). The samples are limited to municipal bonds without any insurance or any credit
enhancement, as otherwise, the insured municipal bonds assume the credit worthiness of insurers
instead of the issuers themselves. To avoid the confounding influence of multiple ratings, we limit
bonds with only Moody’s or only S&P rated bonds before calculating dispersion in yield. To better
isolate the effects of recalibration, we exclude any new issuances during the test period and limit
21
the sample to bonds without any rating changes except for changes due to Moody’s recalibration.
The bonds outstanding during this period are merged with the trade data from MSRB by CUSIP.
To meaningfully measure the standard deviation in yields, we require that there must be at least
four observations for each rating level by week for a maturity category to be included in sample.
Table 1 presents 3,654 observations for the Moody’s sample and 3,602 observations for the S&P
sample, which generates the final sample with 7,256 observations.
<Table 1>
We examine the informativeness of ratings by using standard deviation of yields, which
are calculated as follows: we first collect yields of the trade in the secondary market from MSRB.
Then, we calculate standard deviation of yields for a given rating level by week by maturity level.
There are four maturity levels: bonds with maturity of less than 5 years, bonds with maturity of
more than 5 years but less than 15 years, bonds with maturity of more than 15 years but less than
25 years, and bonds with maturity of more than 25 years. The dependent and independent variables
are defined in Appendix B.
To control for market risk, we include 10-year Treasury yields. Following Nanda and Singh
(2004), we transform the bond ratings into a numeric scale for regression analysis. The detailed
classification scheme for the numerical score is provided in Appendix C. The Maturity Category
variable indicates one of four maturity levels: bonds with maturity of less than 5 years, bonds with
maturity of more than 5 years but less than 15 years, bonds with maturity of more than 15 years
but less than 25 years, and bonds with maturity of more than 25 years.
Table 2 presents summary statistics. Panel A contains the sample with only Moody’s rated
bonds, and Panel B contains the sample with only S&P rated bonds. The univariate results indicate
that Rating variable has a bigger mean in the post-recalibration period than in the pre-recalibration
22
period. The means of Rating are not statistically different from each other. The univariate results
of the S&P sample indicate that the post-recalibration period has a smaller mean of Standard
Deviation of Yields than the pre-recalibration period. The T-test indicates that the mean of
Standard Deviation of Yields in the post-recalibration period is different from the mean in the pre-
recalibration period at the 1-percent level.
<Table 2>
Table 3 reports the Pearson correlation matrix. Significance at the 5-percent level or greater
is starred. The negative correlation between the Standard Deviation of Yields variable and Moody
dummy variable indicates that bonds only with Moody’s ratings have smaller average Standard
Deviation of Yields than bonds only with S&P ratings. The positive correlation between the
Standard Deviation of Yields variable and Rating variable indicate that higher ratings have larger
standard deviation of yields.
<Table 3>
5. Empirical Research Design and Results
To recognize differences between the rating system that Moody’s and S&P use and the
effect of the recalibration event, we use a difference-in-differences design specification. The
difference-in-differences estimator is based on the idea that when only a portion of a population is
exposed to a treatment, an untreated control group can be used to identify temporal variation in
the outcome that is not due to treatment exposure. A key assumption of the difference-in-
differences design is that in the absence of the treatment, the difference between the treatment and
control group is constant over time (i.e., the parallel trend assumption). In our setting, recalibration
only affected Moody’s rated bonds and not S&P rated bonds; we assume that S&P and Moody’s
23
ratings are comparable otherwise.18 Using S&P rated bonds as a control group, we examine the
relation between yield dispersion and rating favorableness. This research design should mitigate
concerns that our results are attributable to other changes during the period, such as changes in
general economic conditions or changes in regulation, including the effect of the financial crisis
or the Dodd-Frank Act.
Against this background, we turn to examine the two primary hypotheses. Hypothesis H1
posits that the dispersion in yields associated with a rating increases as the rating becomes
increasingly favorable. To test this hypothesis, we use the following pooled cross-section ordinary
least squares (OLS) specification to see how dispersion in yields varies with ratings before and
after Moody’s recalibration:
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷 = 𝛽𝛽0 + 𝛽𝛽1𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 × 𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 + 𝛽𝛽2𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 + 𝛽𝛽3𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷
+ 𝛽𝛽4𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽5𝑀𝑀𝑎𝑎𝑅𝑅𝑀𝑀𝑟𝑟𝑖𝑖𝑅𝑅𝑀𝑀 𝐶𝐶𝑎𝑎𝑅𝑅𝐷𝐷𝑅𝑅𝐷𝐷𝑟𝑟𝑀𝑀 + 𝛽𝛽6 10-𝑀𝑀𝐷𝐷𝑎𝑎𝑟𝑟 𝑇𝑇𝑟𝑟𝐷𝐷𝑎𝑎𝐷𝐷𝑀𝑀𝑟𝑟𝑀𝑀 𝑌𝑌𝑖𝑖𝐷𝐷𝑅𝑅𝑑𝑑 + 𝜀𝜀. (8)
Moody is an indicator variable that takes a value of one for bonds only with Moody’s ratings, and
zero for bonds only with S&P ratings. Recalibration is an indicator variable that takes a value of
one for observations in the post-recalibration period and zero for observations in the pre-
recalibration period. Rating is an ordered ranking from one to ten of the numerical categorization
of the bond’s credit rating assigned by the rating agencies. Since H1 predicts that the dispersion in
yields increases as the rating becomes increasingly favorable, we expect that the sign of the sum
of the coefficients 𝛽𝛽1 + 𝛽𝛽4 to be positive. Alternatively, a coefficient that is not significantly
different from zero would be consistent with ratings conveying verifiable information. The 10-
year treasury yield is used to control for market risk. Standard errors are clustered at the rating
level.
18 In additional analysis, we examine pre-period trends.
24
Model 1 of Table 4 reports the results of estimating equation (8). The sum of the coefficient
𝛽𝛽1 + 𝛽𝛽4 is 0.063, which is significantly positive (Prob > F = 0.088). This finding shows that for
bonds that Moody’s and S&P rate the dispersion of yields is associated increases as the rating
becomes increasingly favorable across the entire sample period, which is consistent with H1. Also
consistent with H1, the coefficient of the interaction between Recalibration and Rating in the
regressions is significantly positive at the 1-percent level, with a magnitude of 0.018. This finding
indicates that for bonds that Moody’s and S&P rate the dispersion of yields increases with the
favorableness of ratings in the post-recalibration period. These findings in Model 1 suggest,
however, that it is important to control for the recalibration event when examining the
informational properties of the ratings.
To further examine how dispersion in yields varies with ratings that Moody’s and S&P
issue, we use the following pooled cross-section OLS specification:
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷 = 𝛽𝛽0 + 𝛽𝛽1𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 × 𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽2𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 + 𝛽𝛽3𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 + 𝛽𝛽4𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅
+ 𝛽𝛽5𝑀𝑀𝑎𝑎𝑅𝑅𝑀𝑀𝑟𝑟𝑖𝑖𝑅𝑅𝑀𝑀 𝐶𝐶𝑎𝑎𝑅𝑅𝐷𝐷𝑅𝑅𝐷𝐷𝑟𝑟𝑀𝑀 + 𝛽𝛽610-𝑀𝑀𝐷𝐷𝑎𝑎𝑟𝑟 𝑇𝑇𝑟𝑟𝐷𝐷𝑎𝑎𝐷𝐷𝑀𝑀𝑟𝑟𝑀𝑀 𝑌𝑌𝑖𝑖𝐷𝐷𝑅𝑅𝑑𝑑 + 𝜀𝜀. (9)
Model 2 of Table 4 reports the results of estimating equation (9). The coefficient on rating
main effect, 𝛽𝛽4, is significantly positive, indicating dispersion is increasing in the favorableness of
S&P rated bonds over the entire sample period. This finding is consistent with H1. Interestingly,
the coefficient on the interactive effect between Moody and Rating, 𝛽𝛽1, is significantly negative,
suggesting that the relation between dispersion and the favorableness of the bonds is more muted
for Moody’s rated bonds than S&P rated bonds that were issued over the entire sample period.
Indeed, the relation between dispersion and the ratings for Moody’s rated bonds, given by the sum
of the coefficient 𝛽𝛽1 + 𝛽𝛽4 = -0.004, is not statistically significant different from zero. While the
lack of a relation between dispersion and the favorableness of the Moody’s ratings is consistent
25
with the prediction of a model of verifiable information, Model 1 highlights the need to recognize
the recalibration event when examining the information that Moody’s ratings convey.
To examine the effect of the recalibration on the informativeness of Moody’s ratings, we
use the following pooled cross-section OLS specification:
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷 = 𝛽𝛽0 + 𝛽𝛽1𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 × 𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 + 𝛽𝛽2𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 + 𝛽𝛽3𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷
+ 𝛽𝛽4𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽5𝑀𝑀𝑎𝑎𝑅𝑅𝑀𝑀𝑟𝑟𝑖𝑖𝑅𝑅𝑀𝑀 𝐶𝐶𝑎𝑎𝑅𝑅𝐷𝐷𝑅𝑅𝐷𝐷𝑟𝑟𝑀𝑀 + 𝛽𝛽610-𝑀𝑀𝐷𝐷𝑎𝑎𝑟𝑟 𝑇𝑇𝑟𝑟𝐷𝐷𝑎𝑎𝐷𝐷𝑀𝑀𝑟𝑟𝑀𝑀 𝑌𝑌𝑖𝑖𝐷𝐷𝑅𝑅𝑑𝑑 + 𝜀𝜀. (10)
Model 3 of Table 4 reports the results of estimating equation (10). It focuses on the impact
of recalibration on Moody’s rated bonds without differentiating by rating level. The coefficient of
the interaction between Moody and Recalibration is significantly positive at the 10-percent level,
with a magnitude of 0.147. Thus, we find that the variation of yields increases for Moody’s rated
bonds relative to S&P rated bonds after Moody’s recalibration. Consistent with Moody’s
motivation for using a finer municipal rating scale rather than the global rating scale for municipal
bonds, Moody’s ratings became less informative after its scale recalibration.
Models 1 and 2 provide evidence consistent with H1. The results reported in Models 1, 2
and 3, however, highlight the need to recognize differences between the rating system that
Moody’s and S&P use and the effect of the recalibration event.
We now turn to examine H2, which predicts that the dispersion is more positively
associated with an increase in the favorableness of a rating after Moody’s recalibration. To
examine whether dispersions increase in the favorableness of a rating at an increasing rate after
Moody’s recalibration, we use the following pooled cross-section OLS specification:
26
𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷𝑖𝑖𝐷𝐷𝐷𝐷 = 𝛽𝛽0 + 𝛽𝛽1𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 × 𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 × 𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽2𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 × 𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷
+𝛽𝛽3𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀 × 𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽4𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 × 𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 + 𝛽𝛽5𝑀𝑀𝐷𝐷𝐷𝐷𝑑𝑑𝑀𝑀
+𝛽𝛽6𝑅𝑅𝐷𝐷𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝑏𝑏𝑟𝑟𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝐷𝐷 + 𝛽𝛽7𝑅𝑅𝑎𝑎𝑅𝑅𝑖𝑖𝐷𝐷𝑅𝑅 + 𝛽𝛽8𝑀𝑀𝑎𝑎𝑅𝑅𝑀𝑀𝑟𝑟𝑖𝑖𝑅𝑅𝑀𝑀 𝐶𝐶𝑎𝑎𝑅𝑅𝐷𝐷𝑅𝑅𝐷𝐷𝑟𝑟𝑀𝑀
+𝛽𝛽9 10-𝑀𝑀𝐷𝐷𝑎𝑎𝑟𝑟 𝑇𝑇𝑟𝑟𝐷𝐷𝑎𝑎𝐷𝐷𝑀𝑀𝑟𝑟𝑀𝑀 𝑌𝑌𝑖𝑖𝐷𝐷𝑅𝑅𝑑𝑑 + 𝜀𝜀. (11)
Model 4 of Table 4 reports the results of estimating equation (11). We focus on the interaction
between Moody and Rating and Recalibration. Given H2, we expect the sign of the coefficients
on this three-way interaction 𝛽𝛽1 to be positive. This coefficient is significantly positive at the 5-
percent level. Thus, after Moody’s recalibration, the informativeness of Moody’s ratings decline
as they become more favorable, and they decline at an increasing rate.
Further, consistent with the finding for Model 3, the coefficient of the interaction between
Moody and Rating, 𝛽𝛽3, is significantly negative at the 5-percent level. Hence, the dispersion of
yields is lower for higher rated Moody’s bonds relative to higher rated S&P bonds in the pre-
recalibration period. Also similar to our earlier findings, the coefficient on the Rating main effect
𝛽𝛽7 is significantly positive at the 10-percent level. This result for the S&P rated bonds is consistent
with H1 that the dispersion of yields increases with the favorableness of ratings over the sample
period. Collectively, these findings are consistent with the predictions of a cheap-talk model that
assumes CRAs communicate unverifiable information.
<Table 4>
6. Robustness test
In this section, we perform a battery of robustness tests.
6.1. Dispersion of Yield Spreads
As a robustness test, we examine the yield spread as an alternative way to capture the risk
component in the pricing of municipal bonds. Schwert (2017) estimates that default risk accounts
27
for as much as 84 percent of the municipal bond spread. Yield spreads contain the expected risk
premiums for taking default risk. To measure dispersion in yield spreads, we first calculate the
yield spread by subtracting its corresponding Treasury yield from yields of the trade in the
secondary market matched by duration. Then, the standard deviation of yield spreads is calculated
for a given rating level by week for the four maturity levels. We use the same specification as
testing for dispersion of yields to see how dispersion in yield spreads varies with ratings that
Moody’s and S&P issue and how the recalibration influenced dispersion in yield spreads varies
with ratings.
We examine the same specification as in equation (8) and (9). In untabulated results, we
observe similar results. The results examining equation (8) show that the sum of the coefficient
𝛽𝛽1 + 𝛽𝛽4 is 0.047, which is significantly positive (Prob > F = 0.088). The coefficient of the
interaction between Recalibration and Rating in the regression is significantly positive at the 10-
percent level, with a magnitude of 0.013. The results examining equation (9) show the coefficient
of Rating is 0.101, which is significantly positive (Prob > F = 0.050). These findings are consistent
with H1.
We examine the same specification as in equation (11). In untabulated results, we find that
the coefficient of the interaction between Moody, Recalibration, and Rating is significantly
positive at the 10-percent level, with a magnitude of 0.031. Similar to the results for standard
deviation of yields, the results indicate that, relative to S&P, higher rated Moody’s bonds have
greater variance of yield spreads in the post-recalibration period. This finding is consistent with
H2 that the dispersion in yield spreads is more positively associated with an increase in the
favorableness of a Moody’s rating after Moody’s recalibration.
28
6.2. Dispersion of Yields for Institutional and Retail Investors
The question of how institutional and retail investors perceive credit ratings adds an
important dynamic to policy recommendations regarding how CRAs should be regulated. We
examine whether our main results differ when our sample is segmented by retail versus
institutional investors. We expect that institutional investors are more sophisticated and have
superior ability to assess bond risk (Green et al., 2007; Cuny, 2018). Further, institutional investors
are more likely to recognize the reporting incentives of a rating agency than are retail investors.
For institutional investors, therefore, we expect that the dispersion of yields will increase as the
favorableness of the rating increases. Conversely, for retail investors, who are less capable of
conducting their own analysis and will rely more on credit ratings. Accordingly, we expect that
the positive association between dispersion and the favorableness of the rating will be weaker for
retail relative to institutional investors.
The proxy for retail held bonds comes from a comprehensive report conducted by the
United States Government Accountability Office (GAO) in 2012 that examines the municipal bond
market. In this report, the GAO interviewed broker-dealers, investors and other market participants
and concluded that retail investors typically trade in amounts of less than $100,000 (GAO, 2012
pg. 5). Accordingly, bonds held by retail investors are restricted to issues that only trade in amounts
less than $100,000.
Tables 5 and 6 report the results using standard deviation of yields as a measure of
dispersion for institutional and retail investors, respectively. Model 1 of Table 5 shows that the
sum of the coefficient 𝛽𝛽1 + 𝛽𝛽4 is 0.057, which is statistically different from zero (Prob > F = 0.004).
Consistent with the main findings, for bonds that Moody’s and S&P rate, the dispersion of yields
increases as the rating becomes increasingly favorable across the entire sample period. This result
29
for institutional investors is consistent with H1. However, in Model 1 of Table 6, the sum of the
coefficient 𝛽𝛽1 + 𝛽𝛽4 is not statistically different from zero. Thus, for retail investors, the dispersion
of yields does not increase as the ratings become increasingly favorable.
Model 2 of Table 5 and Table 6 reports that the coefficient of Rating variable is positive
and statistically significant, which indicates that the dispersion of yields increases with the increase
of ratings for S&P rated bonds.
Model 4 of Table 5 reports that the coefficient of the interaction between Moody,
Recalibration, and Rating is significantly positive, which indicates that for institutional investors,
higher Moody’s ratings become less informative in the post-recalibration period relative to the pre-
recalibration period. In Model 4 of Table 6, where the sample is limited to retail investors, this
relation is not significant. These findings suggest that retail investors respond to credit ratings as
if they convey verifiable information, which is inconsistent with the response of the more
sophisticated institutional investors.
<Table 5>
<Table 6>
6.3. Rating Coarseness and Favorable Information
Model 3 in Table 4 examined equation (10) and established that in the post-recalibration
period the variation of yields are greater for Moody’s rated bonds relative to S&P rated bonds. The
analysis examined the impact of recalibration on Moody’s rated bonds without differentiating by
rating level. Thus, it does not address the research question of whether the cheap-talk framework
explains the institutional environment in which rating agencies communicate with investors.
30
To address this question, we consider whether the dispersion in yields associated with a
Moody’s rating are increasing and at increasing rate after Moody’s recalibration, as hypothesized
in H2. We reexamine expression (10) within five sub-samples: bonds with ratings Aaa and Aa1,
bonds with ratings Aa2 and Aa3, bonds with ratings A1 and A2, bonds with ratings A3 and Baa1,
and bonds with ratings Baa2 and Baa3.
Table 7 Panel A shows that the interaction between Moody and Recalibration are
significantly positive at the 5-percent level for Model 1 (bonds with ratings Aaa and Aa1), Model
2 (bonds with ratings Aa2 and Aa3). The coefficient of the interaction between Moody and
Recalibration in Model 3 (bonds with rating A1 and A2) and Model 4 (bonds with A3 and Baa1)
is positive but not statistically significant. The coefficient of the interaction variable for Model 5
(bonds with ratings Baa2 and Baa3) is significantly negative at the 10-percent level.
More importantly, as a test of the cheap-talk framework for modeling the bond rating
environment, we consider that the coefficients of the interaction between Moody and Recalibration
increase as ratings become more favorable. The coefficient of the interaction between Moody and
Recalibration of Model 1 is larger than the coefficients of other four models. Specifically, Panel B
shows that the difference between the coefficients of Model 1 and Model 4 is statistically
significant at the 1-percent level, as indicated by a Wald chi-square test (Prob > chi2 = 0.000). The
difference between the coefficients of Model 1 and Model 5 is statistically significant at 5-percent
level, as indicated by the Wald chi-square test (Prob > chi2 = 0.035). Meanwhile, we also observe
that the coefficient of the interaction between Moody and Recalibration of Model 2 is larger than
the coefficients of Model 3, Model 4 and Model 5. Specifically, Panel B shows that the difference
between the coefficients of Model 2 and Model 4 is statistically significant at the 5-percent level,
as indicated by the Wald test (Prob > chi2 = 0.013). This indicates that in the post-recalibration
31
period, the standard deviation of yields (and hence, information uncertainty) increase as Moody’s
ratings become more favorable, which is consistent with H2.
<Table 7>
6.4. Placebo Test
Moody’s recalibration took place several years after the 2008 financial crisis. While we
believe that business cycle effects are unlikely to explain our results, we perform a placebo test to
examine if our results are a product of time trends prior to the recalibration. We focus on the period
from 2007 to 2009, as data availability is limited prior to 2007. We define the pre-period as the
beginning of 2007 to the first half of 2008 and the post-period as the second half of 2008 to the
end of 2009. In untabulated results, we find no evidence that our results are explained by the trends
prior to recalibration.
7. Conclusion
Credit rating agencies are an important source of information to investors. They use a rating
classification system (e.g., AAA, Aa1, Aa2, …) to rank bonds. Goel and Thakor (2015) used a
cheap-talk model to explain the presence of these credit rating systems. The primary assumption
underlying the cheap-talk framework is that the rating agencies’ messages are unverifiable. The
courts have ruled that rating agencies receive robust First Amendment protection under typical
circumstances because their ratings are predictive opinions. Despite this protection, however, there
are reputation and regulatory constraints that might impose directs costs on the ratings agencies if
they misrepresent their privately observed information. Accordingly, it is an empirical question
whether credit ratings are unverifiable, as the cheap-talk framework assumes.
32
We compare the municipal bonds that Moody’s or S&P rated over the period from April
15, 2009 to April 16, 2011,covering when Moody’s recalibrated municipal bonds beginning on
April 16, 2010 and ending on May 7, 2010. Moody’s 2010 recalibration systematically shifted
municipal bond ratings to a global scale resulting in coarser rating system.
We developed two primary hypotheses grounded in an analysis of the cheap-talk
framework. First, when information is unverifiable, we predicted that the dispersion in yields
associated with a rating increases as the rating becomes more favorable, for a given credit rating
scale. Consistent with this hypothesis, we document that the informativeness of ratings decline as
they became increasingly favorable for S&P rated bonds over the entire sample period and for
Moody’s rated bonds after its municipal rating scale recalibration.
Second, when information is unverifiable, we posited that the dispersion in yields
associated with a Moody’s rating increase and at a higher rate as the Moody’s rating becomes
increasingly favorable after Moody’s recalibration relative to before it. Consistent with this
hypothesis, we document that more favorable Moody’s credit ratings are increasingly less
informative in the period after Moody’s recalibration relative to before the recalibration.
Collectively, these findings are consistent with the predictions of the cheap-talk framework, which
implies rating agencies communicate unverifiable information. These findings contrast those we
would expect if information were verifiable.
In conclusion, our empirical results establish that credit ratings of bonds are de facto cheap-
talk in the sense that the information content of the ratings is consistent with that expected when
rating agencies do not bear any direct cost from offering their unverifiable opinions on bond issues.
Establishing the properties of information that intermediaries communicate to investors has
important implications for how the SEC decides to regulate these intermediaries, such as the
33
Nationally Recognized Statistical Rating Organizations—Fitch, Moody’s, and S&P. In a cheap-
talk setting, the extent of information communicated in equilibrium depends crucially on the
interest alignment of the rating agencies and investors. To improve information transmission,
particularly for investors, a regulator must seek to enhance the alignment of interests of the rating
agency and investors. Their interests might be aligned, possibly by revisiting the appropriateness
of the issuer-pay model, disallowing rating agencies to advise issuers how they might obtain more
favorable ratings, and disallowing issuers to shop for the most favorable ratings (Deats, 2010;
Podkul, 2019a, b). Indeed, the Dodd-Frank Act, recognizing this misalignment problem, requires
studies of alternative means for compensating rating agencies (see Rhee, 2014).
In contrast to our prescription for this cheap-talk setting in which information is
unverifiable, in an alternative environment in which information intermediaries’ reports are
verifiable, our prescription would fundamentally differ. When information is verifiable, as is often
the case in financial reporting settings, a regulator’s focus needs to be on ensuring that the well-
known “unravelling argument” in Grossman (1981) and Migrom (1981) operates, such as reducing
disclosure costs as in Verrecchia (1983). The “unravelling argument” maintains that when
intermediaries’ reports are verifiable, even though it is common knowledge that the interests of the
intermediaries and investors are misaligned, full revelation occurs in equilibrium. This is not the
communication equilibrium that prevails for credit ratings, which are unverifiable.
34
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market structure, pricing, and regulation.
38
Zarin, F. 2011. Credit Rating Standardization Study – Release No. 34-63573; File No. 4-622 (the “Request for Comment”). Moody’s Investor Service. February 18, 2011.
39
Appendix A Moody’s Recalibration Details
Municipal Scale Rating
General Obligation; Water & Sewer;
Distribution-Only Utilities; Municipal
Utility Districts
Special Tax; Mass Transit; Non-Utility
Enterprises; Tax Increment
Financing Districts; Grant Anticipation
Revenue Bonds
Public Universities and Public University
Foundations
Health Care; Housing; Private K-12 & Charter
Schools; Private Universities and Other
Not-For-Profits; Transportation & Other
Infrastructure Enterprises; Power
Generating Utilities; State Revolving Funds; Bond Banks; Federal
Leases Aaa 0 0 0 0 Aa1 0-1 1 0-1 0 Aa2 1 1 1 0 Aa3 1 1 1 0 A1 2 1 1 0 A2 2 1 1 0 A3 2 1 1 0
Baa1 3 1 1 0 Baa2 3 0 1 0 Baa3 2-3 0 1 0 Ba1 0 0 0 0 Ba2 0 0 0 0 Ba3 0 0 0 0 B1 0 0 0 0 B2 0 0 0 0 B3 0 0 0 0
Caa1 0 0 0 0 Caa2 0 0 0 0 Caa3 0 0 0 0
This Appendix shows Moody’s recalibration algorithm. For each rating level, the numbers represent the amount of upward shift in terms of rating notches for each corresponding sector.
40
Appendix B Variable Measurement
Variables Name Description and Measurement Main Dependent Variable:
Standard Deviation of Yields The dispersion of yields in the secondary market for a given rating level by month for four different maturity categories.
Standard Deviation of Yield Spread
The dispersion of yield spread in the secondary market for a given rating level by month for four different maturity categories. We calculate the yield spread by subtracting its corresponding Treasury yield from the bond’s yield in the secondary market matched by duration.
Main Independent Variable:
Moody An indicator variable that takes a value of one for bonds only with Moody's underlying ratings, and zero for bonds only with S&P underlying ratings.
Recalibration An indicator variable that takes a value of one for observations in the post-recalibration period, and zero for observations in the pre-recalibration period.
Rating A numerical categorization of the bond’s credit rating assigned by the rating agencies. Appendix C shows the numerical classification.
Maturity Category
An ordinal variable with values of 1, 2, 3, and 4. If the maturity of a bond is less than or equal to 5 years, this variable takes a value of 1. If the maturity of a bond is more than 5 years and less than or equal to 15 years, this variable takes a value of 2. If the maturity of a bond is more than 15 years and less than or equal to 25 years, this variable takes a value of 3. If the maturity of a bond is more than 25 years, this variable takes a value of 4.
10-Year Treasury Yield The yield of the debt issued by the United States government with a maturity of 10 years upon initial issuance.
41
Appendix C Classification of Bond Ratings
Moody’s Rating S&P Rating Numerical Code
Aaa AAA 10 Aa1 AA+ 9 Aa2 AA 8 Aa3 AA- 7 A1 A+ 6 A2 A 5 A3 A- 4
Baa1 BBB+ 3 Baa2 BBB 2 Baa3 BBB- 1
This table lists the numerical codes associated with the ratings assigned by Moody's and S&P.
42
Figure 1
Moody’s General Obligation Bond Ratings for Moody’s Pre- versus Post-Recalibration Periods
Figure 1 compares the percentage of bonds with a certain rating level in the pre-period with the percentage of bonds with a certain rating level in the post-period for all Moody’s rated bonds
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
Baa3 Baa2 Baa1 A3 A2 A1 Aa3 Aa2 Aa1 Aaa
Perc
enta
ge o
f Bon
ds w
ith a
Cer
tain
Rat
ing
Moody's Pre-Period
Moody's Post-Period
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Figure 2
S&P General Obligation Bond Ratings for Moody’s Pre-Recalibration versus Post-Recalibration Periods
Figure 2 compares the percentage of bonds with a certain rating level in the pre-period with the percentage of bonds with a certain rating level in the post-period for all S&P rated bonds
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
BBB- BBB BBB+ A- A A+ AA- AA AA+ AAA
Perc
enta
ge o
f Bon
ds w
ith a
Cer
tain
Rat
ing
Moody's Pre-Period
Moody's Post-Period
44
Table 1 Sample Selection and Data Requirements
Moody’s Sample S&P Sample Outstanding Bonds 1,060,731 802,323 Less: Bonds with insurance or credit enhancement 723,938 532,280 Bonds with multiple ratings 183,164 174,683 New issuances during test period 46,914 41,949 Bonds with rating changes 1,972 2,391 Bonds included in tests 104,743 51,020 Bonds merged with MSRB trade by CUSIP 372,671 160,737 Less: Group by week 222,898 92,909 Group by rating level and maturity level 145,959 64,091 Observation with less than 4 trades 160 135
Sample for testing hypotheses 3,654 3,602
This table reports sample selection procedures. All tests employ a difference-in-differences analysis between Moody’s rated bonds (treatment group) versus S&P rated bonds (control group). The Moody's Sample contains the sample selection procedure for only Moody’s rated bonds, while the S&P Sample contains the sample selection procedure for only S&P rated bonds.
45
Table 2 Summary Statistics
Panel A: Sample with only Moody’s ratings
Variable Pre-Recalibration Post-Recalibration
Sample Size Mean Std.
Dev. Min Max Sample Size Mean Std.
Dev. Min Max
Standard Deviation of Yields 1,840 1.246 0.513 0.174 3.966 1,814 1.220 0.522 0.029 4.885 Rating 1,840 5.719 2.854 1 10 1,814 5.824 2.877 1 10 Maturity Category 1,840 2.624 1.075 1 4 1,814 2.747 1.016 1 4 10-year Treasury Yield 1,840 3.510 0.244 2.520 3.850 1,814 3.144 0.382 2.540 3.850 Panel B: Sample with only S&P ratings
Variable Pre-Recalibration Post-Recalibration
Sample Size Mean Std.
Dev. Min Max Sample Size Mean Std.
Dev. Min Max
Standard Deviation of Yields 1,790 1.734 1.534 0.023 12.333 1,812 1.534 1.363 0.019 19.027 Rating 1,790 5.680 2.849 1 10 1,812 5.724 2.833 1 10 Maturity Category 1,790 2.645 1.057 1 4 1,812 2.698 1.033 1 4 10-year Treasury Yield 1,790 3.508 0.244 2.520 3.850 1,812 3.149 0.381 2.540 3.800 This table reports descriptive statistics for key variables. Panel A contains the samples with only Moody’s rated bonds, and Panel B contains samples with only S&P rated bonds. Each panel reports the descriptive statistics for the pre-recalibration period and the post-recalibration period. See Appendix B for variable definitions. Mean is the average value, min is the minimum, and max is the maximum value.
46
Table 3 Pearson Correlation Matrix
Variable Standard
Deviation of Yield
Standard Deviation of
Yield Spreads Moody Recalibration Rating Maturity
Category
10-year Treasury
Yield Standard Deviation of Yield 1 Standard Deviation of Yield Spreads 0.9276* 1 Moody -0.1809* -0.1732* 1 Recalibration -0.0495* -0.0524* -0.0066 1 Rating 0.0887* 0.0539* 0.0121 0.0129 1 Maturity Category 0.2893* 0.2520* 0.0065 0.0421* -0.1522* 1 10-year Treasury Yield 0.0177 0.0254* 0.0014 -0.4929* -0.0037 -0.0202 1 This table reports Pearson correlation matrix for key variables. Significance at the 5% level or lower is starred. See Appendix B for variable definitions.
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Table 4 Dispersion of Yields
Model 1 Model 2 Model 3 Model 4 Coef. t-stat Coef. t-stat Coef. t-stat Coef. t-stat
Moody × Recalibration × Rating 0.049** 2.48 Moody × Recalibration 0.147* 1.94 -0.124 -0.78 Moody × Rating -0.119** -2.33 -0.144** -3.08 Rating × Recalibration 0.018*** 3.48 -0.007 -0.67 Moody -0.410** -2.37 0.272 1.00 -0.483** -2.60 0.335 1.52 Recalibration -0.261*** -5.10 -0.156*** -6.71 -0.230*** -5.01 -0.196** -2.30 Rating 0.045 1.41 0.115* 2.10 0.054 1.67 0.118* 2.21 Maturity Category 0.333*** 4.59 0.333*** 4.65 0.332*** 4.59 0.334*** 4.64 10-year Treasury Yield -0.030 -0.63 -0.034 -0.70 -0.030 -0.62 -0.033 -0.67 Intercept 0.666 2.82 0.280 0.76 0.653 2.86 0.295 0.84 Sample Size 7,256 7,256 7,256 7,256 R-squared 14.07% 16.37% 14.13% 16.64% This table shows the regression results for the dispersion of yields for all municipal bonds in the secondary market. The dependent variable is the standard deviation of yields. The sample ranges from year April 15, 2009 to April 16, 2011. This test employs a difference-in-differences analysis between Moody’s rated issuers (treatment group) versus S&P rated issuers (control group) around the recalibration event. The test sample is constructed by combining samples from Moody’s sample (3,654 observations) and S&P sample (3,602 observations). The sample size of the tests is 7,256 (7,256=3,654+3,602). The standard errors are clustered at the rating level. Trade data are winsorized at 0.2% to avoid extreme values before calculating dispersion of yields. See Appendix B for variable descriptions. R-squared represents a goodness-of-fit measure. ***, **, * denote statistical significance (two-sided) at the 1%, 5% and 10% levels, respectively.
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Table 5 Dispersion of Yields for Institutional Investors
Model 1 Model 2 Model 3 Model 4 Coef. t-stat Coef. t-stat Coef. t-stat Coef. t-stat
Moody × Recalibration × Rating 0.050* 2.09 Moody × Recalibration 0.110 1.62 -0.197 -1.04 Moody × Rating -0.049 -1.13 -0.074 -1.72 Rating × Recalibration 0.009 0.66 -0.018 -1.41 Moody -0.277* -2.22 0.032 0.11 -0.328** -2.35 0.126 0.44 Recalibration -0.144 -1.32 -0.082 -1.73 -0.144** -2.33 -0.040 -0.40 Rating 0.048** 2.56 0.078* 2.17 0.052*** 3.34 0.087** 2.29 Maturity Category 0.370*** 6.15 0.372*** 6.27 0.369*** 6.09 0.373*** 6.24 10-year Treasury Yield 0.088* 2.13 0.089* 2.08 0.089* 2.14 0.089* 2.09 Intercept -0.053 -0.20 -0.241 -0.74 -0.051 -0.20 -0.266 -0.81 Sample Size 5,036 5,036 5,036 5,036 R-squared 12.44% 12.79% 12.48% 12.96% This table shows the regression results for the dispersion of yields in the secondary market for institutional investors. The dependent variable is the standard deviation of yields. The sample ranges from year April 15, 2009 to April 16, 2011. The test sample is constructed by combining samples from Moody’s sample (2,697 observations) and S&P sample (2,339 observations). The sample size of the tests is 5,036 (5,036 = 2,697 + 2,339). The standard errors are clustered at the rating level. Trade data are winsorized at 0.2% to avoid extreme values before calculating dispersion of yields. See Appendix B for variable descriptions. R-squared represents a goodness-of-fit measure. ***, **, * denote statistical significance (two-sided) at the 1%, 5% and 10% levels, respectively.
49
Table 6 Dispersion of Yields for Retail Investors
Model 1 Model 2 Model 3 Model 4 Coef. t-stat Coef. t-stat Coef. t-stat Coef. t-stat
Moody × Recalibration × Rating 0.033 1.31 Moody × Recalibration 0.127 1.61 -0.059 -0.33 Moody × Rating -0.136** -2.31 -0.153** -2.96 Rating × Recalibration 0.017*** 3.51 0.001 0.08 Moody -0.395* -2.04 0.384 1.36 -0.458** -2.34 0.415* 1.85 Recalibration -0.258*** -5.83 -0.156*** -7.96 -0.222*** -5.34 -0.230** -2.59 Rating 0.040 1.08 0.118* 1.84 0.049 1.31 0.118* 1.91 Maturity Category 0.283*** 3.71 0.282*** 3.79 0.282*** 3.70 0.282*** 3.78 10-year Treasury Yield -0.035 -0.74 -0.038 -0.78 -0.035 -0.73 -0.038 -0.77 Intercept 0.770 2.75 0.338 0.77 0.754 2.76 0.372 0.88 Sample Size 7,033 7,033 7,033 7,033 R-squared 9.54% 12.23% 9.57% 12.40% This table shows the regression results for the dispersion of yields in the secondary market for retail investors. The dependent variable is the standard deviation of yields. The sample ranges from year April 15, 2009 to April 16, 2011. The test sample is constructed by combining samples from Moody’s sample (3,555 observations) and S&P sample (3,478 observations). The sample size of the tests is 7,122 (7,122 = 3,555 + 3,478). The standard errors are clustered at the rating level. Trade data are winsorized at 0.2% to avoid extreme values before calculating dispersion of yields. See Appendix B for variable descriptions. R-squared represents a goodness-of-fit measure. ***, **, * denote statistical significance (two-sided) at the 1%, 5% and 10% levels, respectively.
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Table 7 Dispersion of Yields for All Bonds for Different Rating Levels
Panel A: Standard Deviation of Yield for Different Rating Levels
Model 1 Model 2 Model 3 Model 4 Model 5 Aaa,Aa1 Aa2, Aa3 A1, A2 A3, Baa1 Baa2, Baa3
Coef. t-stat Coef. t-stat Coef. t-stat Coef. t-stat Coef. t-stat Moody×Recalibration 0.290** 2.44 0.250** 2.67 0.159 1.40 0.157 1.59 -0.142* -1.78 Moody -1.047*** -12.38 -0.496*** -7.47 -0.695*** -8.72 -0.0511 -0.74 -0.010 -0.18 Recalibration -0.269*** -2.94 -0.265*** -3.75 -0.236*** -2.73 -0.215*** -2.86 -0.125** -2.05 Rating 0.667*** 11.23 0.233*** 4.99 0.237*** 4.20 0.056 1.13 -0.006 -0.15 Maturity Category 0.532*** 19.85 0.290*** 13.73 0.336*** 12.41 0.198*** 7.53 0.152*** 6.91 10-year Treasury Yield -0.196** -2.12 -0.051 -0.71 0.077 0.87 0.023 0.30 0.009 0.14 Intercept -4.752 -7.19 -0.703 -1.60 -0.604 -1.35 0.685 2.05 0.965 4.02 N 1,564 1,608 1,467 1,328 1,289 R-squared 33.35% 14.96% 17.12% 4.76% 5.45% Panel B: Wald test of comparing the coefficients of the interaction between Moody and Recalibration among different models Model 1 Model 2 Model 3 Model 4 Chi2 p-value Chi2 p-value Chi2 p-value Chi2 p-value
Model 1 Model 2 1.42 0.23 Model 3 0.22 0.64 0.11 0.74 Model 4 12.98*** 0.00 6.17** 0.01 0.00 1.00 Model 5 4.42** 0.04 3.64* 0.06 0.76 0.38 2.12 0.15 This table shows the regression results when standard deviation of yields is used to measure dispersion in yields. Panel A shows the regression results for the standard deviation of yields for different rating levels in the secondary market. The sample is split into five categories. Model 1 includes bonds with ratings Aaa and Aa1. Model 2 includes bonds with ratings Aa2 and Aa3. Model 3 includes bonds with ratings A1 and A2. Model 4 includes bonds with ratings A3 and Baa1. Model 5 includes bonds with ratings Baa2 and Baa3. The main variable of interest is the interaction between Moody and Recalibration. Panel B shows the Wald test results of comparing the coefficients of the interaction between Moody and Recalibration among different models. It shows both the Chi2 and P-value. The standard deviation of yields is calculated using yields in the secondary market for a given rating level by week for a certain maturity category. This test employs a difference-in-differences analysis between Moody’s rated issuers (treatment group) versus S&P rated issuers (control group) around the recalibration event. The sample ranges from April 15, 2009 to April 16, 2011. Trade data are winsorized at 0.2% to avoid extreme values. See Appendix B for variable descriptions. ***, **, * denote statistical significance (two-sided) at the 1%, 5% and 10% levels, respectively. R-squared represents a goodness-of-fit measure.