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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: phillip.c.stocken@dartmouth.edu

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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

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Cer

tain

Rat

ing

Moody's Pre-Period

Moody's Post-Period

43

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

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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.

47

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.

48

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.

50

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.