Can alternative business models discipline credit
rating agencies?∗
Dion Bongaerts†
February 11, 2013
Abstract
Could other business models for credit rating agencies (CRAs) than the
current issuer-paid oligopoly lead to better social outcomes and if so, could
those arise naturally? To answer these questions, I set up a theory model
where all agents are rational and opportunistic. Due to a friction on the
issuers’ side, CRAs misbehave and inefficient outcomes arise. I show that
systems of investor-paid CRAs, issuer-produced ratings or mandatory coinvestments can all improve social welfare, but each in a different way. Moreover, I show that high to very high degrees of regulatory intervention are
needed to make these alternative business models take hold. The model explains several empirical regularities such as profitability spikes and ratings
failure leading up to the sub-prime crisis, the regulatory inability to punish
inaccurate ratings and the failure of investor-paid CRAs to capture a meaningful market share.
∗
I would like to thank Mark Van Achter, Andrei Dubovik, Joost Driessen, Andrea Gamba,
Frank de Jong, Volker Lieffering, Arjen Mulder, Frederik Schlingemann, Joel Shapiro, Marti Subrahmanyam, Dragon Tang, conference participants at the EFA 2012 annual meeting, the ESSFM
Gerzensee 2012 and seminar participants at Erasmus University Rotterdam and The University
of Hong Kong for useful discussions and helpful comments. This paper has been prepared by the
author under the Lamfalussy Fellowship Program sponsored by the ECB. Any views expressed are
only those of the author and do not necessarily represent the views of the ECB or the Eurosystem.
All remaining errors are my own.
†
Rotterdam School of Management, Erasmus University, Burgemeester Oudlaan 50, 3062PA,
Rotterdam, The Netherlands. e-mail: dbongaerts@rsm.nl
1
1
Introduction
After the financial crisis of 2007-2009, CRAs, like Moody’s, S&P and Fitch, have
come under increased public scrutiny. Globally, estimated losses on structured products such as sub-prime residential mortgage-backed securities (RMBSs) average $4
trillion,1 about 10 times the face value of the Greek sovereign debt. Arguably, a substantial part of those losses could have been avoided if credit ratings had reflected
the risks of these products more accurately. The fact that the peak in CRA profits
was driven by the very same products that lay at the base of the sub-prime crisis,
gives rise to suspicions of opportunistic behavior on the CRAs’ side.2 Indeed, several
recent articles show that ratings on structured products were inflated (Griffin and
Tang (2011) and Rösch and Scheule (2010)).
In essence, the failure of ratings for structured products follows from (a slightly
modified version of) a classical principal-agent model. One can see a CRA as an
agent that on behalf of the principal, the investor, conducts a credit assessment by
exerting costly effort. So far, the setting is comparable to an executive compensation
problem (e.g. Jensen and Meckeling (1976)). Yet in contrast, the CRA is selected
and paid by the debt issuer, which creates an additional possible friction, because
the issuer may have a preference for high rather than accurate ratings. The fact that
it is not the investor that compensates the CRA for its services, is in an idealized
world not an issue because in a steady state equilibrium with rational investors, any
expected losses are charged to the debt issuer in the form of high interest rates.
Interestingly, the investor may even be indifferent about ratings quality as long as
a minimum standard is met and more importantly, the ratings quality is according
to expectation. However, in reality, the issuer-pays-model can create another layer
of incentive distortions through frictions on the side of the investor (e.g. naive
investors as in Bolton, Freixas and Shapiro (2012)) or the side of the debt issuer
(private benefits of undertaking negative NPV projects, this paper). Hence, there is
a high need for incentive alignment between investors and CRAs in order to obtain
socially optimal allocations of (debt) capital.
In the paper I explore alternative business models for CRAs that have the potential to improve the incentive alignment of CRAs. As such, I contribute to the growing
literature on the role and functional design of CRAs in three ways. First, I analyze
1
IMF estimation. See http://www.imf.org/external/pubs/ft/weo/2009/01/
For example, anecdotal evidence reports rating fees of 2 to 4 bps on corporate bonds compared
to fees of 13 to 16 bps on structured products. For Moody’s, these products had a profit margin
of around 50% and generated about 50% of total profit by the end of 2006.
2
2
the economics of investor-paid ratings, investor-produced ratings and mandatory
co-investments for CRAs. All alternative business models improve on the status
quo, but each in a different way. For example, investor-paid CRAs create a winner’s
curse for non-subscribers, while mandatory co-investments directly align incentives
of investors and CRAs. Second, I show that none of the welfare improving market
structures would get hold without additional regulatory intervention. The degree
of required intervention does differ however. Co-investments simply need to be
imposed, whereas the possibility of investor-produced ratings in combination with
the presence of a strong regulator can improve the behavior of issuer-paid CRAs.
Third, the paper provides a number of novel results with respect to the effects of
competition and reputation among CRAs on economic outcomes, particularly with
respect to which equilibrium outcomes can arise, which underlying frictions drive
the equilibrium outcomes, and how stable the equilibria are.
As said, one of the contributions of this paper is to analyze the economics of
market structures for CRAs that have the potential to better link CRA pay-off to
CRA performance. A natural way to achieve this is by requiring co-investments from
CRAs upon issuing high ratings. The idea of co-investments for CRAs stems from
the desire to make CRAs more accountable for their actions. CRAs are commercial
entities that express their opinions on the creditworthiness of debt issuers for a fee,
to be paid by the issuer. The CRAs themselves claim that their ratings reflect ”mere
opinions”, because of which, at least in the U.S., freedom of speech legislation waives
them of any legal liability concerning the accuracy of their ratings. Yet, unlike other
opinions in financial markets such as stock analyst recommendations, these opinions
have an institutionalized regulatory function (see for example Bongaerts, Cremers
and Goetzmann (2012)). Therefore, exemptions from legal liability may impose
excessively large negative externalities on other market participants. Earlier work by
Listokin and Taibleson (2010) has hinted at a solution by suggesting rating fees to be
paid in kind (that is, the rating fee is paid by granting the bonds rated to the CRA).
In this paper I extend their idea by allowing the size of the co-investment to exceed
the rating fee. More precisely, I show analytically that the value of the co-investment
must exceed the size of the rating fee in order to be effective. My analysis shows that
co-investments are very strong commitment devices that are even guaranteed to lead
to first-best outcomes if the required co-investments are sufficiently large and the
market for credit ratings is characterized by a monopoly. For a competitive CRA
market with mandatory co-investments, achieving an equilibrium with the first-best
outcome is also possible, but not guaranteed, because captive equilibria may arise.
3
In addition, I show that the equilibria with mandatory co-investments are more
resilient to information shocks on the CRAs’ behalf than equilibria without. As
a consequence, co-investments would considerably reduce the risk of bubbles and
consequent bursts, as witnessed at the onset of the sub-prime crisis.
Despite the attractive features of the co-investments system, there may be practical hurdles or unmodeled frictions that prevent its practical implementation. For
example, CRAs may argue that because of funding constraints, they would have
to cut back on the number of issues to be rated, leading to inefficiencies due to
market-wide under-investment. Therefore, I also explore the possibility that parties
that naturally have skin-in-the-game (like banks3 and credit insurers), can start to
offer credit ratings. Investor-produced ratings will be accurate if production costs of
are low enough compared to the amount of skin-in-the-game. While this mechanism
may sound appealing, it will be ineffective by itself in my model as debt issuers prefer high over accurate ratings. Rating producing investors may simply be ignored by
debt issuers, while investors can endogenize the expectation of low rating accuracy
by charging higher interest. However, in the presence of a regulator with the authority to revoke licenses of under-performing CRAs, the rating-producing investors can
function as backups (i.e., raters of last resort) for the regulator (which is relatively
powerless without these alternatives). Therefore, the regulator has a more credible
threat to revoke CRA licenses and equilibria are possible in which CRAs conduct
the ratings, but exert high effort. Banks or credit insurers are natural candidates to
produce ratings in issues that they also have a stake in. Especially larger banks have
proper rating technology available, because they have to comply with the Basel II
advanced IRB approach. A concrete example of investor-produced rating-initiative
is the French credit insurer Coface. On July 29th 2010, announced its ambition to
become the first European Union based CRA. Interestingly, for this new entrant,
selling ratings is not the core business. Rather, it sells the ratings that it uses itself
for its own risk management. As the ratings producer is also an end-user, Coface
states that4, 5
3
Of course, banks may have their own frictions that may induce rating biases, especially when
leverage is high and the effective skin-in-the-game is limited. Yet the recent regulatory push
towards increased capital buffers in for example Basel III, reduces these concerns substantially.
Modeling these effects is a potential future extension of the model.
4
See
http://www.coface.com/CofacePortal/ShowBinary/BEA%20Repository/HK/en_EN/
documents/wwa_news_events/20100729CofaceCESR-HK_en
5
When contacted to give more information on this initiative, Coface responded that this initiative has been withdrawn for the time being. Unfortunately, Coface was unwilling to motivate this
decision.
4
”Coface only rates companies on which it has a significant credit risk
exposure: credit insurance is the first customer for Coface ratings. This
assures a strict alignment of Coface, and of Coface ratings’ users interests”.
An even more indirect way of aligning incentives of CRAs and investors is to
allow for investor-paid CRAs. This is a system that many academics as well as policy
makers have been striving for (e.g. Pagano and Volpin (2010)). The intuition behind
this thought is that if investors pay for ratings, investors will punish CRAs displaying
low accuracy. The only credible punishment threat is going to a competitor. So for
this system to work, at least two investor-paid CRAs are required. However, in
order for investor-paid CRAs to have a reasonable chance to compete with issuerpaid CRAs, issuers should also prefer high over accurate ratings, otherwise they
could only apply for funding at non-subscriber banks and force issuer-paid CRAs on
their financiers. At first glance, it looks like investor-paid CRAs have a mechanism to
overcome this problem. Given misbehaving issuer-paid CRAs, investor-paid CRAs
could capture the whole market by creating a winner’s curse for the non-subscribing
investors, thereby capturing the whole market. As subscriber-banks will only make
offers to highly rated issuers, those issuers learn about their own type and will be
unwilling to pool with low quality issuers.
However, issuer-paid CRAs can also condition their behavior on the presence of
investor-paid CRAs and increase their effort, consistent with the empirical results
in Xia (2012). As a consequence, issuers and investors will at best be indifferent
between issuer- and investor-paid ratings. The reason why issuer-paid CRAs will in
the end dominate is that issuer-paid CRAs can be more competitive as they never
generate a rating that will not be used, which in general is not true for investorpaid CRAs. Moreover, as issuers have higher utility in an equilibrium without
investor-paid CRAs, they will most likely push investor-paid CRAs out. The only
option is then to ban issuer-paid CRAs, which is a measure that goes very far.
If issuer-paid CRAs are banned and at least two investor-paid CRAs are present,
the aforementioned winner’s curse will induce all CRAs to exert maximum effort in
equilibrium. However, this outcome is socially sub-optimal as at least twice as many
resources are spent on producing ratings compared to the first best case. Moreover,
this option is only feasible if free-riding problems are relatively small.6
Working out these alternative business models, I report several novel results
6
The maximum tolerable degree of free-riding problems is derived in the paper.
5
on the effects of competition and reputation among CRAs on economic outcomes.
These results relate to 1.) which equilibrium outcomes arise, 2.) which underlying
frictions drive the equilibrium outcomes and 3.) to how stable equilibria are. A
popular proposal to fix the CRAs’ problem is to introduce more competition among
rating agencies.7 However, recent theoretical literature has shown that competition
among CRAs is likely to reduce social welfare, primarily because of rating shopping
(e.g. Skreta and Veldkamp (2009) and Bolton et al. (2012)). A notable exception is Hirth (2011), who shows that a new entrant can discipline the incumbent
CRAs. Empirically, Becker and Milbourn (2011) show that more intense competition in the corporate bond market reduces rating accuracy. In my baseline model,
increased competition fails to discipline CRAs, but I do not need irrational investors
as Bolton et al. (2012) do. On this aspect, my approach has more similarities with
the setting of Winton and Yerramilli (2011) who study the originate-to-distribute
market. This fundamental difference in underlying friction generates a need for different solutions. Additionally, I show that if competing CRAs receive a very small
private information shock about reduced future issuance volumes or lower average
credit quality, they will inflate ratings and trigger a bubble and a consequent burst
as recently observed in the sub-prime crisis. My model also predicts that during
such a bubble, issuance volumes peak as do CRA profit margins, which is again consistent with recent observations. The size of the private information shock required
for a monopolistic CRA to engage in similar behavior is much larger. The reason
for these different degrees of fragility is that in competitive equilibria, the incentive
compatibility constraint binds, which means that future rents are just enough to
enforce at least the minimum required effort to prevent markets from collapsing.
An infinitely small shock about the relative value of exerting some effort compared
to slacking altogether can immediately tip the balance to the wrong side. A monopolist on the other hand has higher future rents at stake and is therefore less easily
tempted to misbehave.
Interestingly, the fragility described above results from the fact that CRAs need
reputation as a disciplining device in order to exert any effort at all. Hereby I provide
additional evidence that, contrary to what CRAs claim, reputation is insufficient to
enforce accurate ratings in line with Mathis, McAndrews and Rochet (2009) and BarIsaac and Shapiro (2010). The fragility largely disappears with the introduction of
7
See, for example, the testimony by SEC deputy director John Ramsay: ”The Commission’s
efforts in this area have been designed to [...] and promote competition among rating agencies that
are involved in this business.” (http://www.sec.gov/news/testimony/2011/ts072711jr.htm)
6
mandatory co-investments, because correct behavior in that setting is not enforced
by reputation but by contemporaneously well aligned incentives. Finally, in my
basic model, effort is perfectly ex-post observable. Yet, in the base case, the social
welfare contribution of having CRAs falls short of the theoretical optimum by a
large amount and is even negative. This indicates that measures beyond improving
transparency (e.g. Partnoy (2009), Pagano and Volpin (2010)) are needed.
A recent body of literature, inspired by the recent financial crises has linked the
incentive problems of CRAs and their low ex-post accuracy to frictions induced by
regulation. On the theoretical side, Opp, Opp and Harris (2011) investigate under
which conditions regulatory importance of credit ratings leads to ratings arbitrage.
Their model shares certain features with the model used in this paper, but has
notable differences. These differences include the fact that competition in their
paper is only modeled in a reduced form way, while their model allows the degree of
regulatory importance and the degree of asset complexity to vary. On the empirical
side, Bongaerts et al. (2012) show that only certification can explain the demand
for an extra Fitch rating in the corporate bond market and that the extra Fitch
rating at the margin only lowers credit spreads if it is pivotal from a regulatory
perspective. Consistent with those findings, Kisgen and Strahan (2009) show that
bond prices react to the qualification of Dominion as an NRSRO in the direction of
the Dominion ratings relative to the others. Ellul, Jotikasthira and Lundblad (2011)
indeed show that the interaction of regulation and rating downgrades can trigger
fire sales with massive losses on the investor’s side.
Yet, this paper shows that taking measures to remove regulatory importance
will not guarantee efficient and accurate credit assessments. Instead, this paper
shows that if anything additional regulation is required. The additional regulation
can come in the form of explicit and stringent prescriptions of how CRAs should
be structured. However, such measures can kill innovation and can easily go too
far, thereby imposing high compliance costs and potentially unwarranted effects
on an industry. A lighter form of regulation would be to instate a regulator as
suggested by Partnoy (2009) that can condition a license going forward on past
performance. Yet, my model shows that such a regulator by itself resorts little effect.
The source of this limited regulatory power stems from the importance of financial
intermediaries in an economy and the high barriers to entry. Restricting financial
intermediaries too much can hamper credit supply, which immediately leads to real
economic losses. This gives financial intermediaries a strong bargaining position
against regulators. Accepting a limited amount of moral hazard may from a social
7
welfare perspective be preferable over a severely reduced credit supply. This model
outcome is also consistent with patterns observed during the sub-prime crisis. For
example, the SEC proposed to remove all references to NRSROs from a large number
of regulatory rules, in response to the poor rating performance of RMBS ratings.8
Yet, most investors disapproved of the idea because of the lack of alternatives and
the high costs if every investor were to conduct a credit assessment himself.9 Thus,
such a regulator is only an option in the presence of a decent alternative such as
accurate investor-produced ratings.
The remainder of the paper is structured as follows. Section 2 describes the
players in my model and derives the first-best solution as a benchmark for model
outcomes with respect to social welfare. Section 3 analyzes base case equilibrium
outcomes. Section 3.3 analyzes the stability of the base case equilibria. Section 4
derives equilibria when co-investments or competition from bank-produced ratings
are introduced. Section 6 analyzes model outcomes with three different forms of
investor-paid ratings. Finally, section 7 concludes.
2
Model setup and socially optimal outcomes
The baseline model consists of an infinitely repeated game that has three player
types, namely firms, CRAs and banks. All players in this economy, also in later extensions are risk-neutral and all model parameters are known by all players. Moreover, at time t, the complete history of all actions and realizations, denoted by Ft−1
is observed by all players. Below I describe the players and their actions, a time line
of each iteration of the game as well as a more detailed description of each stage of
the game.
As mentioned before, the game has three player types, issuers, banks and CRAs
. First, there are infinitely many issuers. Each issuer j lives for one period, has an
initial endowment β0 < 1 and has a project for which an investment of 2 units of
capital is needed in order to be undertaken. The project has a quality qj ∈ {G, B},
where P (qj = G) = θ. Hence, θ measures market-wide average credit quality. If
qj = G the project has a payoff R > 2, while if qj = B, it has a payoff of zero.
Unconditionally, the project has a negative NPV, that is θR < 2. As in Mathis
et al. (2009), the issuer does not know the quality of its own project. Moreover,
8
See http://www.sec.gov/comments/s7-17-08/s71708-26.pdf
See, for example, the response by the Securities Industry and Financial Markets Association
(SIFMA) on http://www.sec.gov/comments/s7-17-08/s71708-26.pdf
9
8
the CEO of the issuer makes decisions, owns a fraction of the issuer and has a
private benefit γ ≥ (2 + β0 ) of operating the issuer. This setup is equivalent to a
more tractable one where the issuer has a private benefit β > 2 + β0 of undertaking
the project and β = γ . For tractability reasons, I assume that the magnitude of and γ are negligibly small in the decision making processes for each type of player,
except for the CEO of each issuer. After rating fees have been paid, the residual
endowment is paid out to the shareholders as a dividend, such that it cannot be
seized in case a issuer defaults. Each CEO maximizes his own utility.
Second, there are N identical infinitely lived CRAs. Each CRA c can exert effort
ec to obtain a signal sj,c ∈ {G, B} about issuer j, such that P (sj,c = G|qj = G) = 1
and P (sj,c = B|qj = B) = ec . That is, a good project is always correctly identified,
but a bad project is only identified correctly with probability ec . Hereafter the CRA
can issue a rating rj,c ∈ {G, B}. The CRAs have a marginal effort cost cc > 0. Each
CRA discounts future payoffs with a discount factor δ ∈ (0, 1) and maximizes the
present value of its contemporaneous and future expected cash flows.
Finally, there are infinitely many banks that each live for one period. Each bank
b has one unit of investable capital that can only be invested in one project. The
amount of bank funds available for lending exceeds the amount needed to fund all
projects such that banks compete and there is no shortage of capital. Each bank
maximizes its own expected profit.
Each stage t of the game then proceeds as follows.
1. Short-lived players are added and everyone observes Ft−1
2. Each CRA c quotes a rating fee fc and determines effort plans ec
3. All banks make a blacklist Zb and quote interest rates ιxb conditional on a
rating rc = G from a CRA not on the blacklist
4. issuers select raters and banks conditional on G ratings.
5. Ratings are produced and issued, rating fees are paid and residual endowment
is paid out, loans are granted and investments are made
6. Projects are realized, interest is paid, performance is observed
7. Start period t + 1
In stage 2 CRAs, publicly quote rating fees fc conditional on their information
set FtC = {Ft−1 , ē}. As in for example Bolton et al. (2012), a CRA c is only paid
9
a fee upon issuing a public rating rj,c = G. Each CRA also plans to exert effort ec
to obtain a signal sj,c and given this signal issue a rating rj,c for each issuer j that
selects CRA c.
In stage 3, conditional on the information set FtB = {FtC , fc ∀ c} each bank
selects and announces the set Zb of CRAs it bans and quotes an interest rate ιcb at
which it commits to fund one project with a rating rc = G, where c ∈
/ Zb .
In stage 4, each issuer selects one single CRA and two banks conditional on the
C
information set FtF = {FtB , ιcb , Zb ∀ b, c}. That is, each issuer j chooses Ij,c
, ∈ {0, 1}
P
P
P
B
B
C
B
= 0 ∀ (j, b).
= 2 and c∈Zb Ij,c,b
= 1, c,b Ij,c,b
∈ {0, 1} such that c Ij,c
and Ij,c,b
2.1
First best outcome
In this section, I derive the first best outcome, that is, the outcome that a social
planner would choose if he could control actions of all market participants perfectly.
In the model, social welfare is created by implementing projects of quality G. Social
welfare is destroyed by defaults and rating effort exerted. Naturally, the first best
outcome is dependent on parameter values. Typically, if rating costs are relatively
low, producing the ratings causes little social welfare loss and the social planner
would let the most efficient party (the CRA) produce ratings with the highest possible accuracy, and thereafter will mandate (riskless) investment in all G rated projects
as is shown below.
Proposition 1. If cc ≤ 2(1 − θ) and cc ≤ θ(R − 2), the first best outcome generates
a social welfare of θ(R − 2) − cc and is attained by letting CRAs rate all debt with
effort ec = 1 and invest in all projects with rj,c = G, irrespective of whether banks
can perform ratings or not. If those conditions are not satisfied, ”no action” is
socially optimal.
Proof. See Appendix.
Typically, only situations in which investment has the potential to generate value
are worthwhile analyzing. Therefore, for the rest of the paper, I assume that cc ≤
2(1 − θ) and cc ≤ θ(R − 2), such that social welfare can possibly be improved upon
by public credit assessment.
10
3
Baseline model equilibria
In the rest of the paper, I will explore equilibria under different market organizations.
However, before doing so, I will first define the type of equilibria I will look at.
3.1
Equilibrium definition
Because the game is strategic in nature, I will look at Nash equilibria. More specifically, I will look for equilibria that do not differ from one period to the other, in other
words, that are steady state, that are sub-game perfect and that are sequentially
rational. The requirement for sequential rationality is similar to assuming rational
investors in asset pricing studies. More concretely, I start with a belief set ζ for all
players in the market. To simplify notation, I define êc as the belief about ec under
the belief set ζ. Given this belief set and the respective information sets, I derive
optimal strategies for each player. If these strategies generate the belief set I started
with, I have a sequentially rational equilibrium. As I study an infinitely repeated
game, I search for steady state equilibrium strategies, such that the equilibria can be
characterized by a set of strategies and beliefs over one stage game. The sub-game
perfect requirement is to avoid equilibria involving threats that are not credible.
In the process of exploring equilibria, I will as much as possible try to derive
general results that hold broadly and build towards more specific equilibria.
To establish a benchmark to compare the alternative business models to, I first
explore a base case equilibrium.
3.2
Base case
In this section, I derive a strategic equilibrium in which banks, issuers and CRAs
optimize their value over their possible strategies and show that in this case, social
welfare is negative. In other words, if issuers want the ’wrong things’, financial
intermediation destroys more value than it creates. Throughout the paper, I will
try to give the intuition before stating the formal result.
Given the belief set beliefs ζ, banks need to set interest rates ιcb and decide which
CRAs to distrust (i.e., put on the blacklist Zb ). Because banks have a short-term
horizon, are identical and operate in a market without transaction costs and entry
barriers, they compete and employ identical strategies.
Proposition 2. In any sequentially rational steady state equilibrium with investment
11
and a given a common belief set ζ, banks set identical blacklists and set interest rates
ιcb =
(1 − θ)(1 − êc )
.
θ
(1)
Proof. See appendix.
Banks will set interest rates and distrust CRAs in such a way that they at least
expect to break even. That is, given êc and conditional on a rating rj,c = G their
expected interest payments should at least compensate their expected losses:
ιcb ≥
(1 − θ)(1 − êc )
.
θ
(2)
In equilibrium, the actions should generate the belief set. Banks will only invest
if there is enough pledgable income from projects with qj = G to make up for
losses incurred on projects with qj = B. This pledgeability constraint leads to a
minimum sustainable rating effort level in any equilibrium with investment (also in
later extensions of the model):
Proposition 3. In any sequentially rational steady state equilibrium with invest, which is
ment, the minimum equilibrium effort level e∗ is given by e∗ = 1−0.5Rθ
1−θ
strictly between zero and one.
Proof. See appendix.
Banks need to take a stand on how to handle CRAs not living up to their
expectations. In principle, for banks the effort level exerted by a CRA does not
matter as long as it exceeds e∗ and is expected ex-ante. Banks will adjust their
quoted interest rates and break even. Thus, banks take the equilibrium effort ec
that results from bargaining between the CRA and the issuers as the expected effort
level. However, it is very likely that issuers and CRAs would prefer ec < e∗ . In this
case, investment for banks would not be profitable as pledgable income would not
be high enough to compensate expected default losses. However, as the CRA is long
lived and ec is ex-post verifiable, a breakdown of credit markets can be prevented.
Banks can take the strategy to boycott a CRA if it ever exerted ec < e∗ , leading
to a reputational concern for the CRA10 . This punishment threat can overcome the
In principle, any punishment-trigger larger or equal than e∗ would yield the desired type of
equilibria, but those may be fragile, as conditional on many banks boycotting, a small fraction of
10
12
commitment problem on the CRA’s side as will be described below.11
CRAs are long-lived and identical. As such, they compete for business and are
sensitive to losing future business. In particular, they optimize their total value:
Vc,u (FtC , ζ) =
X
Ij,c ((θ + (1 − θ)(1 − ec ))fc − cc ec ) + δE(Vc (FtC , ζ)).
(3)
j
Equivalently, we can divide this expression by the total size of the debt market to
get
Vc (FtC , ζ) = M Sc ((θ + (1 − θ)(1 − ec ))fc − cc ec ) + δE(Vc (FtC , ζ)).
(4)
where Vc (FtC , ζ) is the scaled version of Vc,u (FtC , ζ) and M Sc is the market share
of CRA c. As CRAs, banks and issuers are homogeneous, there are no scale
(dis)advantages and CRAs have infinite capacity, preferences of CRAs over actions
are uniform and thus optimal CRA strategies are identical and we have that in equilibrium M Sc = N1 . Moreover, if N > 1, competition among CRAs makes sure that
{ec , fc } are chosen such that Vj (FtF , ζ) is maximized while satisfying the pledgability
and incentive-compatilbility (described below) constraints.
issuers maximize the expected payoff after interest payments and redemptions,
corrected for the rating fees spent and their private benefit. Thus, under a belief of
effort levels êc exerted by the CRAs, the value of issuer j is given by
Vj (FtF , ζ) = (β −
X
C
fx Ij,x
)(θ + (1 − êc )(1 − θ)) + θ(R − 2 −
x
X
B
ιxb Ij,x,b
),
(5)
(x,b)
where
X
B
C
Ij,x,b
= 2Ij,x
∀x
(6)
(b)
X
C
Ij,x
= 1.
(7)
x
The first part of (5) gives the expected value of private benefits and fees due, i.e.
banks (at least two) may find it profitable to accept ratings with a lower punishment trigger. With
the punishment-trigger equal to e∗ , this is not possible anymore. Moreover, the issuers’ preferences
for high rather than accurate ratings lead to additional pressure towards e∗ .
11
Note that there are either infinitely many ways to punish the CRA effectively or none, by
varying the time period over which the boycott is implemented. I only look at the permanent
”grimm-trigger” version of this strategy as this maximizes the incentive for the CRA to deliver at
least the minimum required effort level e∗ .
13
the probability of rj,x = G, multiplied with the payoff (private benefit minus the
rating fee due). The second part consists of the the expected value of net profits,
i.e. the probability of undertaking a project of quality qj = G multiplied with the
payoff of that scenario (gross profit minus interest payments). Each issuer optimizes
B
C
. Substituting (1) into (5) and using the fact that CRAs
and Ij,x,b
Vj (FtF , ζ) over Ij,x
have identical optimal strategies, the issuer’s value function in equilibrium can be
written as
(1 − θ)(1 − êc )
F
Vj (Ft , ζ) = (β − fc )(θ + (1 − êc )(1 − θ)) − fc + θ R − 2 − 2
.
θ
(8)
Given fc , this value function is again linear in êc with a negative coefficient on êc ,
as β > 2 + β0 . Thus, issuers will prefer uninformative (but high) ratings.12 Now we
know the demand of the issuers and the value function of the CRAs, we can fully
characterize an equilibrium.
Proposition 4. The following strategies and the belief set generated by those constitute an equilibrium:
1. CRA c is added to the blacklist Zb by every bank b if it ever exerted an effort
level ec lower than e∗ or has quoted an incentive incompatible fee this stage
game
2. Every bank b is willing to fund issuer j with a rating rj,c = G from any CRA
c not the the blacklist Zb with an interest rate
ιcb = ι∗ =
(1 − θ)(1 − e∗ )
θ
(9)
3. Every issuer j selects the CRA c and two banks b1 , b2 such that c ∈
/ Zb1 ∪ Zb2
and it minimizes the combined interest and fee costs
(θ + (1 − e∗ )(1 − θ))fc + θ(ιcb1 + ιcb2 )
(10)
4. Every CRA c exerts effort ec = 0 for a fee fc = β0 if it has ever exerted effort
12
Typically, in equilibrium fc < β0 , such that the bound on β can be tighter. Moreover, as will
be shown later, fc is typically increasing in ec , leading to an even stronger pressure to demand
(low-quality) ratings that always equal G.
14
ec < e∗ and otherwise exerts effort ec = e∗ for a fee

1
f ∗ = c e∗ (1 + A)
if N > 1
c
(1−(1−θ)e∗ (1+A))
fc =
β if N = 1
(11)
0
where A =
(δ −1 −1)
.
δ
The equilibrium with investment is only feasible if f ∗ ≤ β0 .
Proof. See appendix.
In order to commit to exert effort, the incentive compatibility constraint
(θ + (1 − θ)(1 − e∗ ))fc − cc e∗
((1 − θ)fc + cc )e ≤ δ
δ −1 − 1
∗
(12)
for CRAs should be satisfied. As can be seen from this constraint, effort will only
be exerted if fc is high enough, in other words, if there are future rents to the CRA
that can be lost. The equilibrium rating fees depend on the competitive setting.
Under competition, each CRAs gets the minimum rents that still ensure incentive
compatibility, while a monopolistic CRA will capture the full initial endowment.
From Proposition (4), we see that the minimum incentive compatible rating fee
is equal to its production cost plus a markup (1 + A) that is required to achieve
1
to
incentive compatibility from the cost-side and another markup (1−(1−θ)e
∗ (1+A))
achieve incentive compatibility from the revenue side. These markups are increasing
in discount rate, break-even effort level, unconditional failure probability and ratings
production cost.
The social welfare in these equilibria is easily calculated and is independent of
the competitive structure of the market. As all surplus of good projects is used by
the issuer to pay interest to the banks and the banks only use interest payments
to break even on their default losses, the social gains of the projects with qj =
G are exactly offset by the default losses on projects with qj = B that are still
undertaken. Additionally, there is the effort cost for producing ratings which is
equal to cc e∗ . Thus, in this case, total social welfare is reduced by cc e∗ and even
having no investments would be better from a social welfare point of view.
15
3.3
Stability of base case equilibria
The previous analysis shows that competition is an ineffective device to enhance
reputation effects in the base case. In this section, I show that competition in
interaction with reputation makes equilibria vulnerable to the types of bubbles we
have seen in the sub-prime crisis. I also show that a monopolistic setting is much
more resilient to such bubbles and bursts.
The social welfare in the base case is negative, but anticipated. Yet, the setting
with only rational investors prevents the model from generating bubbles and bursts
such as seen in the sub-prime crisis. However, it turns out that a minor modification
to the model can generate bubbles very easily. To this end, we need to introduce an
unanticipated information shock to the CRAs in the model that is not observable
by other market participants. In my model, I consider two types of information
shocks, namely information about declining future issuance volumes and information on increasing (fundamental) default rates (lower θ). As the main business of
CRAs is to do research about default rates and CRAs have a long-term view, it is
plausible that CRAs at times have an informational advantage over investors. Both
types of information shocks lead to bubbles but the two types differ in resistance to
proposed solutions in section 4. The result of either type of friction is that the IC
constraint will be violated, resulting in zero effort13 . Interestingly, this problem creates extreme instability under perfect competition, while a monopoly provides some
resilience. The reason is that competition makes the IC bind while a monopoly does
not (necessarily) do so. I work out the effect of both types of information asymmetry
shocks below.
Let us work out asymmetric information shocks on future issuance volumes first.
We start from beliefs consistent with the base case equilibrium. However, CRAs
know that from next period onwards, issuance volume will only be a factor g < 1 of
current issuance volume.
Proposition 5. Consider the equilibrium described in proposition 4. For N > 1,
any private information shock g < 1 to every CRA c will lead to effort ec = 0 with
13
I am assuming that CRAs are unaware of each other having this information. Otherwise, the
possibility of becoming a monopolist will give the equilibrium some resistance against this behavior.
Yet, because of symmetry of CRAs, the probability of becoming a monopolist will typically be less
or equal to 50%. Therefore, the temptation to misbehave will be larger for a competing CRA
than for a monopolistic CRA. Therefore, even if CRAs are aware of each other’s informational
advantage, bubbles are triggered more easily than in a monopolistic setting.
16
fee fc = f ∗ . For N = 1, ec = 0 with fee fc = β0 will only happen when
β0 <cc e∗ (1 + A/g)
1
.
(1 − (1 − θ)e∗ (1 + A/g))
(13)
Proof. See appendix.
For the banks the perceived IC is (12), while in practice, CRAs experience it as
((1 − θ)fc + cc )e∗ ≤ gδ
1 (θ + (1 − θ)(1 − e∗ ))fc − cc e∗
.
N
δ −1 − 1
(14)
As (12) is violated, CRAs either slack or restore incentive compatibility by increasing
fees. As increasing fees gives them a competitive disadvantage, they slack. Interestingly enough, conditional on slacking, CRAs cannot compete further on fees, as
that would drive down fees below the incentive compatible level prescribed by (11)
and deny investment.14 Thus, we see more high ratings. Since a higher fraction
of applications gets a good rating, issuance volume goes up and profit margins for
CRAs are unprecedentedly high 15 , as costs are extremely low (due to zero effort)
and fees are high. After this period, higher downgrade/default frequencies are observed. Loss rates are higher than foreseen by investors, leading to severe losses on
their investments. This is exactly the pattern described by Griffin and Tang (2011)
and Rösch and Scheule (2010).
Proposition 5 also shows that the only industry setup with CRAs that could
have prevented this collapse from happening is a CRA monopoly and only for a
sufficiently large initial endowment level β0 . In case N = 1, the CRA will not face
any competitive pressure, so fc = β0 . Therefore, the perceived IC (12) does not
bind. As long as
β0 ≥ cc e∗ (1 + A/g)
1
,
(1 − (1 − θ)e∗ (1 + A/g))
(15)
(12) is still satisfied and effort ec = e∗ is still exerted. Thus, more competition
among CRAs would leads to worse rather than to better outcomes. Note that this
result corroborates other findings in earlier literature (e.g. Bolton et al. (2012) and
14
In other words, financiers would not believe incentive compatibility anymore.
For example, Moody’s reported quarterly net profit margins rose sharply from below 25% in
December 2003 to 47.2% in December 2006 and still a handsome 40% in June 2007. By December
2007, it had fallen to 25% and continued to do so to 20.1% by the end of 2009.
15
17
Becker and Milbourn (2011)) and invalidates recent calls from politicians for more
competition among CRAs.
Besides private information shocks about future issuance volumes, also private
information shocks about average credit quality in the market can cause instability
of (competitive) equilibria. Let us now assume that CRAs receive a the private
information shock that the fraction of type G issuers is kθ instead of θ, with k ∈
(0, 1). This leads again to a violation of the IC constraint. The IC perceived by the
banks is again (12), while in practice, CRAs experience it as
((1 − kθ)fc + cc )e∗ ≤ δ
1 (kθ + (1 − kθ)(1 − e∗ ))fc − cc e∗
.
N
δ −1 − 1
(16)
By the same logic as before, competition among CRAs leads to a bubble, while a
monopolistic CRA will maintain accuracy and effort e∗ as long as
β0 ≥ cc e∗ (1 + A)
1
.
(1 − (1 − kθ)e∗ (1 + A))
(17)
Thus, the rating patterns observed recently in the market are consistent with
CRAs abusing private information on market-wide trends. The analysis above shows
that equilibria in a competitive setting are extremely fragile and can experience
bubbles even with small informational advantages of CRAs, while a monopolistic
setting has some resiliency.
4
Equilibria under mandatory co-investments
The low accuracy levels in the base case equilibria result from a combination of
perverse incentives for both CRAs and debt-issuers. The fact that only reputational
concerns are used to discipline CRAs, leads to the fragility described in the previous
section, in particular in competitive settings. While it may be hard to fix incentive
problems on the issuers’ side, several suggestions have come up to fix the incentive
problems on the CRAs’ side. One suggestion is to to give CRAs more skin-in-thegame, for example by having their fees paid in bonds they rated themselves. In
the remainder of this section, I will explore the equilibrium implications for these
suggested solutions and quantify the expected welfare improvements.
18
4.1
CRA co-investments
The first suggested solution I will explore is requiring co-investments from CRAs.
While the first amendment is a strong argument for CRAs against any litigation
concerning liability for ratings they issued, a required co-investment for high (say
investment grade) ratings will have a similar effect on CRA incentives, as in both
cases low ratings accuracy leads to losses for the CRA. In this subsection, I show in a
monopolistic setting, the first best outcome can be attained with certainty, while it
is only one of the possible outcomes in a competitive setting. The reason for this is
that in a competitive setting, issuers can enforce low effort by rating shopping, while
the threat of boycotting the CRA in case of a monopoly is not credible. Moreover,
I show that mandatory co-investments can make equilibria robust against private
information on future issuance volumes, as it can render reputational concerns irrelevant. On the other hand, sensitivity to asymmetric information on aggregate
default rates is still there, but cannot lead to bubbles anymore.
In this section, I force long-lived CRAs to take on some co-investment in an
attempt to discipline CRAs. In particular, I assume that a co-investment of ψj,c ≤ 1
must be made upon issuing a rating rj,c = G. An effort level ec = 1, corresponding
to the first best outcome, can only be achieved if a CRA has a sufficiently large
co-investment that leads to contemporaneously well aligned incentives. If we have
a monopolistic CRA, it cannot commit to slack, even with high fees and will always
exert the highest possible effort for a sufficiently high ψj,c . As issuers have no
alternative for the CRA, there is no credible disciplining strategy possible from the
issuer’s side.
Proposition 6. In an economy with a monopolistic CRA c that is required to make
a co-investment ψj,c in issuer j upon issuing a rating rj,c = G, any equilibrium with
cc
+ β0 and β0 > cθc .
investment must have ec = 1 if ψj,c > 1−θ
Proof. See appendix.
In a monopolistic setting with co-investment, reputational concerns play no role,
cc
which makes the condition ψj,c > 1−θ
+ β0 a sufficient condition to have ec = 1 in
equilibrium (besides some regularity conditions that have been mentioned before).
This is not necessarily the case in a competitive setting. Absent any pressure from
issuers on the CRAs, the co-investments align CRA incentives with social welfare.
Competition among CRAs then drives the rating fee down to expected production
costs, as no rents are required to induce proper behavior. However, issuers prefer low
19
effort on the CRA’s behalf and can engage in a (grim-)trigger strategies to punish
CRA that previously exerted high effort. This mechanism may even be at work when
(1−θ)(ψj,c −fc ) > cc , which at first glance may be surprising. Crucial to realize here
is that in the current period, we condition on ιcb , such that in the value function,
current period profits are increasing in the long term effort level ec chosen, while
for future periods, a low expected effort level translates into a higher interest rate.
This prevents losses from showing up in the future cash flow part of the CRA value
function. Moreover, future excess profits may even cross-subsidize contemporaneous
losses for CRAs, leading to captive equilibria. However, in a captive equilibrium,
CRAs that have co-investments need future rents in order to be willing to suffer
contemporaneous losses. This leads to higher rating fees than in the equilibrium
without ’pushy’ issuers. Additionally, lower effort induces higher interest rates,
because banks still need to break even. Therefore, issuers trade off higher private
benefits against higher interest rates and rating fees. As a consequence, certain
conditions need to be satisfied for a captive equilibrium to exist. Below, I will give
an example of such an equilibrium. The equilibrium described here is not the only
possible captive equilibrium. The purpose is merely to show that captive equilibria
can exist.
Proposition 7. Given N ≥ 4, a required co-investment ψj,c upon issuing a rating
rj,c = G, and the existence of a pair (f˜, ẽ) satisfying the following conditions
ẽ = arg max
(1 − θ)(1 − e)β −
∗
e [e ,1]
cc
(1 − θ)(1 − e)
− f˜ +
θ
θ
(18)
subject to
ẽ < 1,
(19)
cc
Vj (ẽ, f˜) ≥ Vj (1, ),
θ
((1 + A−1 + 1)cc − ψj,c (1 − θ))ẽ + (1 − θ)ψj,c − cc
f˜ =
(A−1 + 1)(1 − (1 − θ)ẽ) − θ
cc ẽ
f˜ ≥
θ + (1 − θ)(1 − ẽ)
cc
f˜ ≤ min(β0 , ψj,c
),
1−θ
(20)
(21)
(22)
(23)
at each iteration t, the following set of strategies with the beliefs ζ̃ they generate
constitute an equilibrium:
20
1. Each bank b offers a loan to each issuer j with rj,c = G, with interest rate
(
ιcb
=
(1−θ)(1−ẽ)
θ
0
if CRA c has always exerted effort ec = ẽ and Mt ≥ 2,
otherwise,
(24)
and offers no funding otherwise.
2. Each CRA c exerts effort ec = ẽ for a fee fc = f˜ if it has always exerted effort
ec = ẽ and Mt ≥ 2, and exerts ec = 1 for a fee fc = cθc otherwise,
3. Every issuer j selects the CRA c that quotes the lowest fee fc > f˜ that
has only exerted effort ec ≤ ẽ in the past if Mt ≥ 2 and Vj (FtF , ζ̃, ẽ, fc ) ≥
Vj (FtF , ζ̃, 1, fs )∀s ∈
/ Yt , and selects the CRA c that quotes the lowest fee fc
otherwise, where any CRA c ∈ Yτ −1 is avoided if possible.
where Yt denotes the set of Mt CRAs that have always exerted effort ẽ till iteration
t and τ is the first iteration in which Mt < 2.
Proof. See appendix.
Thus, competition combined with reputational effects and rating shopping behavior can still induce CRAs to slack, even if they have aligned incentives due to
co-investments. The prospect of the rents that are required for incentive compatibility will induce CRAs to accommodate such an outcome as much as possible.16
Concluding, with required co-investments that are sufficiently large, the first
best outcome can be guaranteed in a monopolistic setting. In a competitive setting,
captive equilibria may be possible that lead to socially sub-optimal outcomes.
4.2
Equilibrium stability with co-investments
In subsection 3.3, I showed how the dependence on reputation to achieve incentive
compatibility can lead fragility of equilibria, in particular with competing CRAs. In
this sub-section, I explore whether and to which extent mandatory co-investments
can reduce this fragility or mitigate the negative effects of it.
Co-investments can increase stability because they reduce the contemporaneous
benefits of low effort. For example, for a monopolistic CRA with co-investments,
E.g., CRAs may signal they plan to end up in this type of equilibrium by quoting a fee f˜c and
thereby facilitate coordination on such an equilibrium.
16
21
an information shock about future issuance volumes will be completely irrelevant as
contemporaneous incentives make sure that maximal effort will be exerted. With
respect to information shocks about θ, depending on the size of the co-investment,
a monopolistic CRA c can be induced to deviate from ec = 1. However, it will most
likely have some rents to be captured in the future and therefore exert effort e∗ to
ensure future business.
With mandatory co-investments, a competing CRA c in a first-best equilibrium
will, after a private information shock about θ, be even less likely to exert effort
ec < 1 compared to a monopolistic CRA. The reason is that fc for a competing
CRA c is lower. Therefore, the benefit of getting fc in case of shirking is lower.
However, in case of a sufficiently large information shock to θ, a competing CRA c
has no or hardly any future rents to capture (due to the low fc ) and will most likely
exert effort ec = 0.
In case of a captive equilibrium in a setting with co-investments, a similar type
of fragility as described in section 3.3 plays up. However, this time, fragility reduces
the probability of socially sub-optimal outcomes. Because of this fragility, a small
information shock can induce a deviation from perverse incentive compatibility and
thereby trigger CRAs to exert ec = 1. So in case of a captive equilibrium, there
is fragility such that information shocks can push CRAs from a captive towards a
first-best equilibrium.
5
Investor-produced ratings
Politicians have repeatedly made statements that CRAs have become too powerful
and that the world needs to get used to living without CRAs. Yet, anecdotal evidence such as the aforementioned opposition to the SEC proposal to remove regulatory references to CRAs indicate that such measures may lead to under-investment.
Yet, the previous analysis on the effects of co-investments indicates that the idea of
letting end-users should also produce the credit assessments is not unreasonable as it
aligns incentives much better. Therefore, in this subsection, I analyze what happens
if banks are allowed to issue ratings for the loans that they fund. As banks have
the technology available to perform ratings, this idea is not unrealistic. If banks are
efficient enough in producing credit assessments, they may even crowd out CRAs.
Moreover, in the presence of a regulator, they can serve as an alternative to CRAs
and thereby overcome limits to regulatory power.
22
5.1
Without a regulator
Now we add banks that can also produce a rating for a fee fb using the same
technology as a CRA. As for CRAs, a bank b is only paid a rating fee fb conditional
on producing a rating rj,b = G. 17 However, they are less efficient in producing
ratings as is indicated by their higher marginal effort cost cb > cc . Additionally,
they are required to make a co-investment of 1 unit of capital if they issue a rating
rj,b = G. If rating production costs for banks are sufficiently low, the skin-in-thegame leads to bank ratings that are always fully accurate when they are observed.
Banks offer quotes for rating fees and make effort plans at the same time as CRAs
and produce ratings at the same time too.
Proposition 8. In any equilibrium in which banks issue ratings, every bank b that
conducts a rating exert effort eb = 1. These equilibria can only arise when cb ≤
θ(1 − θ)(R − 1). For every bank b that conducts a rating, the rating fee fb and
interest rate ιbb on the co-investment satisfy θ(ιbb + fb ) = cb in equilibrium.
Proof. See appendix.
Note that in an equilibrium with bank ratings, issuers only care about θ(ιb + fb )
and not about the individual components. Therefore, without loss of generality, I
can continue my equilibrium analysis for the other players under the assumption
that for any bank b that conducts a rating, ιbb = 0 and fb = cθb if eb = 1.
Looking at competitive outcomes, issuers will prefer CRA ratings when
Vf (FtF , ζ, e∗ , f ∗ ) ≥ Vf (FtF , ζ, 1, cb /θ)
(β − f ∗ )(θ + (1 − e∗ )(1 − θ)) + θ(R − 2 − 2ι∗ ) ≥ βθ − cb /θ + θ(R − 2 − 2 × 0)
β(1 − e∗ )(1 − θ)) − (θ + (1 − θ)(1 − e∗ ))fc − θ2ι∗ ≥ −cb /θ,
Acc e∗
∗
− (β − 2)(1 − θ)(1 − e ) ≤ cb .
θ
1 − (1 − θ)e∗ (1 + A)
(25)
Thus, competition from banks may drive CRAs out of business. The reason is that
the efficiency advantage of CRAs over banks and the private benefits of lower effort
for issuers may not be able to compensate the required fee premium to enforce
incentive compatibility from CRAs. Aggregate welfare can then be improved by
allowing banks to conduct ratings if in equilibrium, rating production costs for banks
17
If the fee is paid irrespective of the rating issued and not only upon issuing rj,b = G, banks
would not exert any effort, always give a rating B and pocket the fee. This behavior results from
their short horizons and lack of reputational capital.
23
are lower than the combination of rating production costs for CRAs and expected
default losses. This is the case when
cb ≤ cc e∗ + 2(1 − θ)(1 − e∗ ).
(26)
So if the probability of a bad project (1 − θ) is relatively large compared to the CRA
rating production cost cc , private benefits for issuers are relatively small, discount
rates for CRAs are relatively large and bank rating production costs are relatively
small, the mere addition of banks as raters will improve social welfare. It is straightforward to see that social welfare in this setting will equal θ(R − 2) − cb , which may
still be negative.
5.2
With a regulator
In the previous subsection, we saw that only for a very limited range of parameter
values, investor-produced ratings would generate natural demand in the presence
of the traditional CRAs. One solution to force investor-produced ratings on the
market would be to ban issuer-paid CRAs altogether. This measure however is very
drastic and may suffer from other problems beyond the scope of this model, for
example relating to independency of ratings. Therefore, one may want to impose
a lighter form of regulation, in which traditional CRAs are only banned in case
they misbehave. To this end, we need to extend the model setup with an active
regulator. Below, I first show that such an active regulator has little power on its
own. Thereafter, I will show that the availability of investor-produced ratings as
an alternative for CRA ratings can substantially increase regulatory power. As a
result, at least the same level of social welfare as with only investor-paid ratings can
be achieved, while interfering less with the market. As a result, CRAs will, under a
certain range of parameter values, continue to conduct all ratings, but at a higher
effort level.
5.2.1
Base case with a regulator
In this section, I introduce a regulator that can set a regulatory hurdle and revoke
rating licenses in case of CRA misbehavior. We will see that this instrument has
only limited usability.
The regulator I consider here can revoke CRA licenses if the number of realized
defaults exceeds a threshold, which is pre-specified by the regulator himself. The
24
regulator maximizes social welfare. More specifically, the regulator sets sets a hurdle
ē ∈ [0, 1] every stage game in between phases 1 and 2. Between stages 6 and 7, the
regulator compares the observed ec and eb to ē and decides whether or not to revoke
the license of any rater x with ex < ē .
The base case equilibrium is worse for the regulator than no investment at all, as
social welfare in this equilibrium is negative. A regulator can try to enforce a higher
effort level ē > e∗ by punishing a CRA c if it exerts effort ec < ē. It would however
be irrational for the regulator to use this tool to shut down all CRAs in case they
create social welfare. It would also be irrational for the regulator to put its future
threat of revoking licences at risk to achieve a minimal improvement in CRA effort.
Thus, because of limited credibility of this threat, sub-game perfect equilibria are
required. Using these insights, one can show that only sub-game perfect steady state
equilibria are possible that yield zero social welfare. Because in these equilibria the
regulator is always indifferent between revoking all licenses and allowing all CRAs
to continue, these equilibria are weak form.
Proposition 9. Let us assume that
1
,
(1 − (1 − θ)e∗∗ (1 + A))
(27)
2 − θR
.
2(1 − θ) − cc
(28)
β0 ≥ cc e∗∗ (1 + A)
where
e∗∗ =
For any N , there is a sub-game perfect (weak form) steady state equilibrium characterized by the following strategies and the belief set those strategies generate:
1. CRA c is added to the blacklist Zb by every bank b if it ever exerted an effort
level ec lower than e∗ or has quoted an incentive incompatible fee this stage
game
2. Every bank b is willing to fund issuer j with a rating rj,c = G from any CRA
c not the the blacklist Zb with an interest rate
ιcb
∗∗
=ι
(1 − θ)(1 − e∗∗ )
=
θ
(29)
3. Every issuer j selects the CRA c and two banks b1 , b2 such that c ∈
/ Zb1 ∪ Zb2
25
and it minimizes the combined interest and fee costs
(θ + (1 − e∗∗ )(1 − θ))fc + θ(ιcb1 + ιcb2 )
(30)
4. Every CRA c exerts effort ec = 0 for a fee fc = β0 if it has ever exerted effort
ec < e∗ and otherwise exerts effort ec = e∗∗ for a fee

1
c e∗∗ (1 + A)
if N > 1
c
(1−(1−θ)e∗∗ (1+A))
fc =
β if N = 1
(31)
0
5. Every period, the regulator sets the regulatory threshold ē = e∗∗ and always
enforces that.
These equilibria yield zero social welfare irrespective of N . Any out-of-equilibrium
behavior by a single CRA in a single period is followed by a similar steady state
equilibrium in the next period, possibly with a lower N .
Proof. See appendix.
Proposition 9 quantifies the welfare that a regulator can enforce in equilibria
that are long-run consistent. While results from such equilibria typically provide
guidance for fundamental economic structures, they may be limiting in a sense that
using non-steady state strategies may be able to enforce strictly higher social welfare.
For example, if N = 1, the maximum effort a regulator can achieve in equilibrium
is ec = 1 in exactly one period and e∗∗ in all others.18 However, equilibria in which
every sub-game is a steady state equilibrium yield in zero social welfare.
5.2.2
Investor-produced ratings as an alternative
When banks can issue ratings, the regulator may have a more credible threat to
revoke CRA licenses. Now the welfare losses in case all CRA licenses are revoked
merely boil down to the production costs cb for bank ratings instead of losing θ(R−2)
due to under-investment.
18
An effort level ē > e∗∗ cannot be achievable in more than one period as the value that will
be created in the last compliant period makes the threat to revoke a license in any earlier period
not credible. Exploring the maximum achievable welfare when N > 1 requires the specification of
a discount factor for the regulator, as not only steady state strategies will be involved. Such an
exploration will be included in a future version of this paper.
26
Thus, with the threat to leave all the rating business to the banks, the regulator
can enforce an effort level e∗∗∗ ≥ e∗∗ from the CRAs.
Proposition 10. If banks can issue ratings, a regulator can enforce a minimum
2(1−θ)−cb
in any equilibrium with investment.
effort level e∗∗∗ = 2(1−θ)−c
c
Proof. See appendix.
To see whether CRAs will get perform all ratings in equilibrium or whether banks
will take over, we have to fill in (11) to get the incentive compatible rating fee and
see whether issuers prefer CRAs or banks.
5.3
Stability
Competition from bank-produced ratings19 will naturally remove any equilibrium
fragility if banks completely take over the rating business. If banks conduct the
ratings in equilibrium, there are no conflicts of interest and maximal effort is always
exerted. This scenario is however unlikely, as banks will crowd out CRAs only for a
very limited range of parameter values.
When CRAs produce the ratings in equilibrium, competition from bank-produced
ratings will also reduce fragility problems when the number of CRAs compete, i.e.
when N > 1. In this case, the incentive compatibility constraint for CRAs still binds
and bubbles and burst may arise. Yet, without bank-produced ratings, no investment takes place anymore after a bubble. With the availability of bank-produced
ratings, continued credit availability is ensured, which after a burst prevents bad
social outcomes due to underinvestment.
The story is more subtle when N = 1. As with N > 1, bank-produced ratings still
ensure the continuation of credit availability. Yet, at the same time, the competition
from bank-produced ratings will put downward pressure on fees and upward pressure
(through the regulator) on effort to be exerted by the CRA. Therefore, future rents
are reduced and the incentive compatibility constraint tightens, thereby increasing
fragility.
6
The Use of Investor-Paid Ratings
One often proposed solution to poorly performing CRAs is to instate more investorpaid CRAs. Interestingly, this was the general business model before the ’70s,
19
or rather the threat of entry
27
basically until copiers became too cheap. Indeed, after the sub-prime crisis, there
have been investor-paid CRAs entering the market (e.g. Rapid Ratings) and some
of them even obtained an NRSRO qualification (Kroll, Egan-Jones). The fact that
those CRAs are investor-paid is often used as an argument why their ratings should
be more independent and more accurate than issuer-paid ratings. Yet, as I show
below, both issuers and existing issuer-paid CRAs may put up barriers that prevent
investor-paid CRAs from entering the market and make it impossible for investorpaid CRAs to survive in the long run.
To assess the competitive strength of investor-paid CRAs within the framework
of this paper, I investigate two extensions of the model in which investor-paid CRAs
compete head-on with issuer-paid CRAs.
Under mechanism 1, there are M ≥ 1 investor-paid CRAs in addition to N issuer
paid CRAs that function exactly the same way as issuer-paid CRAs, except for the
fact that they are selected by the banks rather than the issuers (the issuer will still
pay for the rating). More concretely, in phase 4 of each stage game, each investor j
can choose not to select a CRA and instead make an application with a bank that
will select a CRA. The issuer is obliged pay the rating fee of the selected CRA.
Under mechanism 2, there are also M ≥ 1 investor-paid CRAs in addition to N
issuer paid CRAs that have access to the same technology at the same cost as the
other CRAs. In phase 2 of every stage game, every investor-paid CRA m rates all
issues with effort em and makes offers to sell ratings to investors for a fee fm /MˆS(m)
before interest rate quotes rate issued, where MˆS(m) is the expected market share
of CRA m. Banks can decide between phases 2 and 3 to purchase investor-paid
ratings and become a subscriber-bank. Subscriber-banks pass through the rating
fees paid with a transaction fee that is paid from the initial endowment β0 . This
transaction fee is quoted along with the interest rates in phase 3.
Under mechanism 3, only investor-paid CRAs are allowed, but there is a freeriding problem. Basically, the model-setup is as under mechanism 2, but N is set
to zero. Moreover, for each issuer, all non-subscriber banks learn the rating without
paying for it, with probability φ.
I work out the equilibria under those three mechanisms below. However, before doing so, I need to make one change to the basic setup to prevent spurious
conclusions about business models. This change is motivated first.
28
6.1
Payment schedules for CRAs
The assumption of payment conditional on a rating rx,j = G has been maintained
throughout the paper, to level the playing-field for issuer-paid CRAs and ratingproducing investors. Investors that only live for one period would otherwise have
no incentive to ever give out a low rating. However, for investor-paid CRAs, the
assumption of receiving a fee conditional on a high rating may be less realistic.
Therefore, in this section I will impose a payment system such that investor- and
issuer-paid CRAs get paid for a rating irrespective of the outcome. This change is
rather innocent as it only changes the exact numbers of the incentive compatibility
constraint, but does not make it redundant. In other words, the base case results
are qualitatively similar to those obtained without conditional fee payments. The
main reason for imposing this change in structure is that flat fees are more realistic
for investor-paid CRAs and I want to prevent attributing the effect of different fee
structures to different business models.
6.2
Equilibria with investor-paid CRAs
Under mechanism 1, issuers still prefer high over accurate ratings and banks can
commit to not use investor-paid CRAs, for example by quoting negative interest
rates.20 Therefore, issuers can push banks to avoid investor-paid CRAs if the expectation is that investor-paid CRAs exert more effort than issuer-paid ones. Banks
would not select investor-paid CRAs if they believe those CRAs would exert lower
effort than e∗ because of the pledgability constraint. Therefore, the only way in
which investor-paid CRAs would get any business is to behave exactly the same
way as issuer-paid CRAs.
Proposition 11. Under mechanism 1 and N > 1, an investor-paid CRA m will in
equilibrium act exactly the same as an issuer-paid CRA in a setting with N + M
competing issuer-paid CRAs or have no business at all.
Proof. See appendix.
Mechanism 1 shows that the mere fact that the investor is the one hiring an
investor-paid CRA is insufficient to make it behave well. Yet, the simple structure
sketched here is far away from reality. Investor-paid CRAs typically rate all, or at
20
Banks could commit to a negative interest rate for a G rating from an investor-paid CRA.
This would clearly make it sub-optimal for the bank to use that CRA’s ratings.
29
least very many securities without specifically being asked to do so. Mechanism 2
models that situation and is therefor a lot more realistic (it conforms to the business
model of for example Kroll bond ratings). On first glance, it looks like a business
model that could survive and even drive traditional CRAs out of business. However,
we will see that in the long run, it will be hard to sustain such a business model
and except for very specific parameter values, one would not expect such a CRA
to survive in a long-term steady state equilibrium. The intuition for this is as
follows. Under mechanism 2, subscribers could signal to issuers that they have a
positive signal about the issue by their quote setting, thereby triggering positive
selection. As a result, any of the non-subscribers would suffer from a winner’s curse
and be presented with a negative selection of low quality firms. However, an issuerpaid monopolistic CRA would react by increasing effort for solicited ratings and
match the effort level of the investor-paid rating, while lowering the fee below the
investor-paid fee. This would drive the investor-paid CRA out of business. In the
case of competing CRAs this is also possible, but only to the extent that higher
effort than e∗ can be committed to. If competing CRAs cannot deter entry, then
one possibility is that all but one of them should go out of business leading to the
situation where N = 1 and the investor-paid CRA would be unable to survive. One
might suspect that under some conditions, equilibria can be found in which both
issuer-paid and investor-paid CRAs have some market share. Below, I show that
such conditions cannot be satisfied. The simple reason is that if such an equilibrium
existed, under the equilibrium beliefs, for each of the issuer-paid CRAs, it would be
optimal to try and capture the whole market by lowering fees. This attempt would be
incentive compatible, because in the next period the aggressive CRA would become
a monopolist. Finally, in addition to the equilibria described above, there are also
the ’trivial’ equilibria where there is no confidence at all in investor-paid (issuerpaid) without any strategic behavior of the issuer-paid (investor-paid) CRAs and
that therefore, for investor-paid (issuer-paid) CRAs it is optimal to never exert any
effort.
Proposition 12. If N = 1, the issuer-paid CRA can perfectly prevent entry from
investor-paid CRAs.
Proof. See appendix.
Proposition13. If N > 1, issuer-paid
CRAs can
prevent the entry of an investorcc A(1+A−1 )
β0
paid CRA if 1 − 2(1−θ)
min cc A(1+A−1 ) , 1 < e∗ .
30
Proof. See appendix.
Proposition 14. An equilibrium with both types of CRAs cannot be sustained.
Proof. See appendix.
Proposition 14 crucially depends on the ability of a CRA to ’strike’ before any
of the other CRAs can react. If rating purchase decisions are sticky, for example
due to switching costs (which conforms better to reality), issuer-paid CRAs will
prevent each other from attempts to capture the whole market by the implicit threat
of cut-throat competition in which no issuer-paid CRA will survive. Therefore,
if switching costs are high enough, it may not be credible to make an attempt
to capture the whole market and an equilibrium with both investor-paid CRAs
and issuer-paid CRAs may arise, satisfying the conditions outlined in the proof
of proposition 14. Issuer-paid CRAs in such an equilibrium will also need to exert
higher effort than in an equilibrium without investor-paid CRAs, but this effort level
will be lower than the effort level employed by investor-paid CRAs. Such equilibria
are in accordance with the empirical results in Xia (2012). An additional problem
for the investor-paid CRAs in such an equilibrium is that they need to charge a fee
that is disproportionately high compared to effort exerted, because many ratings
they produce are not used in the end. These high fees in the end create a strong
incentive for free-riding. The effects of free-riding will be incorporate in the analysis
of mechanism 3.
Thus, even without taking information-leakage of investor-paid ratings and the
resulting free-riding into consideration, issuer-paid CRAs can successfully deter
investor-paid CRAs from entering the market or at least obtain significant market share. Policy makers could prevent this from happening by banning issuer-paid
CRAs altogether. As also investor-paid CRAs are disciplined by reputation (effort is
costly), this mechanism will only work when there are multiple investor-paid CRAs.
This is what mechanism 3 aims to achieve. Under mechanism 3, high accuracy could
be enforced, but only when leakage and free-riding is sufficiently low. The leakage
decreases the ex-ante expected profitability of purchasing ratings by investors. This
has to be compensated for with a higher transaction fee in order to make purchasing these ratings worthwhile. If the required transaction fee exceeds the initial
endowment β0 , then no ratings are purchased. Thus, at some point competition and
accuracy would decrease as the leakage probability relative to the initial endowment
β0 decreases, up to the point that the business model is not sustainable anymore.
31
Proposition 15. Under mechanism 3 when M > 2, equilibrium rating effort equals
−1
∗
β0
em = min( A(1+A−1 )M
, 1) when φ ≤ 1 − A(1−A β0 )M cc e and no competitive
cc (1−φ)−1
equilibrium materializes when φ ≥ 1 −
A(1−A−1 )2cc e∗
.
β0
Proof. See appendix.
In addition to the setting under mechanism 3, there could be situations (outside
of the model) such as segmentation under which investor-paid CRAs could attract
business, but would not become dominant and most likely would not induce materially higher effort from issuer-paid CRAs. For example, there could be a situation
in which investors can be hit by random liquidity shocks inducing them to trade in
the secondary market. Because issuers will have less or no influence on the selection
of secondary market buyers, there is room for investor-paid ratings. This setting
would be consistent with the market segmentation findings reported by Cornaggia
and Cornaggia (2011).
7
Conclusion
In this paper, I have explored the potential of different business models for CRAs
to improve on the status quo with respect to social welfare maximization. Systems
of co-investments, investor-produced ratings and investor-paid ratings all have the
potential to improve social welfare and equilibrium stability, but each in its own
way. The system of mandatory co-investments to be made by CRAs upon issuing
high ratings can even lead to first best outcomes in equilibrium. Interestingly, for all
of these business models to take hold, a substantial amount of regulatory ’push’ is
required. These business models are unlikely to take hold by themselves as if there
were an invisible hand leading all agents to socially optimal outcomes.
While the model predictions are largely in line with recent observations in the
markets for credit ratings and credit risky debt, some concessions in the model have
been made, which provides avenues for further research. For example, one could
verify how results change if debt issuers have (noisy) information about their own
quality, when exerted effort is not perfectly verifiable and when perfect accuracy is
not achievable. Finally, one could criticize the lack of internal frictions that banks
experience, especially in view of recent events. Therefore, in order to assess whether
private party ratings are viable, more theoretical research needs to be done on the
incentives banks experience and more empirical research on how these incentives
influence internal rating systems.
32
References
Bar-Isaac, H. and Shapiro, J. D.: 2010, Ratings quality over the business cycle.
Working Paper.
Becker, B. and Milbourn, T. T.: 2011, How did increased competition affect credit
ratings?, Journal of Financial Economics Forthcoming.
Bolton, P., Freixas, X. and Shapiro, J.: 2012, The credit ratings game, Journal of
Finance 67(1), 85–111.
Bongaerts, D., Cremers, K. and Goetzmann, W.: 2012, Tiebreaker: Certification
and multiple credit ratings, Journal of Finance 67(1), 113–152.
Cornaggia, J. and Cornaggia, K. J.: 2011, Does the bond market want informative
credit ratings? Working Paper.
Ellul, A., Jotikasthira, P. and Lundblad, C. T.: 2011, Regulatory pressure and
fire sales in the corporate bond market, Journal of Financial Economics
101(3), 596–620.
Griffin, J. M. and Tang, D. Y.: 2011, Did subjectivity play a role in cdo credit
ratings?, Journal of Finance Forthcoming.
Hirth, S.: 2011, The credit ratings game - revisited. Working Paper.
Jensen, M. C. and Meckeling, W. H.: 1976, Theory of the firm: Managerial behavior, agency costs and ownership structure, Journal of Financial Economics
3(4), 305–360.
Kisgen, D. J. and Strahan, P. E.: 2009, Do regulations based on credit ratings affect
a firm’s cost of capital? Working Paper.
Listokin, Y. and Taibleson, B.: 2010, If you misrate, then you lose: Improving credit
rating accuracy through incentive compensation, Yale Journal on Regulation
27(1), 91–113.
Mathis, J., McAndrews, J. and Rochet, J.-C.: 2009, Rating theraters:are reputation
concerns powerful enough to discipline rating agencies?, Journal of Monetary
Economics 56, 657–674.
33
Opp, C. C., Opp, M. M. and Harris, M.: 2011, Rating agencies in the face of
regulation. Working Paper.
Pagano, M. and Volpin, P.: 2010, Credit ratings failures and policy options, Economic Policy 25(62), 401–431.
Partnoy, F.: 2009, Rethinking regulation of credit rating agencies: An institutional
investor perspective. Working Paper.
Rösch, D. and Scheule, H.: 2010, Securitization rating performance and agency
incentives. Working Paper.
Skreta, V. and Veldkamp, L.: 2009, Ratings shopping and asset complexity: A
theory of ratings inflation, Journal of Monetary Economics 56(5), 678–695.
Winton, A. and Yerramilli, V.: 2011, Lender moral hazard and reputation in
originate-to-distribute markets. Working Paper.
Xia, H.: 2012, Can competition improve the information quality of credit ratings?
Working Paper.
34
A
A.1
Appendix: proofs
Proof of proposition 1
We need to show that when satisfying the parameter restrictions (i) investment will
be undertaken and (ii) that ec = 1 is socially optimal.
As cb > cc , it is never socially optimal for a social planner to let banks conduct
the ratings. Moreover, as projects with rj,c = B always have qj = B, investment
in projects with rj,c = B are also never optimal. As projects have unconditionally
negative NPV, investing in projects without a rating is socially suboptimal too.
If investments are made in projects with a rating rj,c = G, the increase in social
welfare (compared to no investment) is given by
∆SW = θ(R − 2) − 2(1 − θ)(1 − ec ) − cc ec .
(32)
(32) is linear and increasing in ec if 2(1−θ)−cc > 0, in which case it is maximized
when ec = 1. Producing ratings and investing in projects with rj,c = G is only
socially optimal if this produces positive social welfare, i.e. ∆SW > 0. This is
exactly the case when θ(R − 2) − cc .
A.2
Proof of proposition 2
Because of the over-supply of capital (which is equivalent to completely free entry),
the absence of scale (dis)advantages for any player type, the uniformity of beliefs and
the fact that all banks are identical, all issuers are identical and all CRAs are identical, the preference ordering of actions is uniform across banks and across issuers.
Therefore, their optimal actions are identical. Moreover, because banks maximize
profits, they compete perfectly, which means that they set expected marginal costs
equal to marginal benefits. In this setting, expected marginal costs are given by
c)
and marginal benefits are given by ιcb . This, in
expected default losses (1−θ)(1−ê
θ
combination with ec = êc implied by sequential rationality, leads to 1.
A.3
Proof of proposition 3
Assume we are in an equilibrium with investment. From proposition proposition
2, we know that banks compete with each other for investment opportunities and
break even, making (2) bind. A loan with an interest rate ιxb will only be offered
35
when conditional on qj = G, ιxb is pledgable. That is, a loan offer is only made when
expected profits from a project of quality qj = G are sufficient to pay ιxb :
(R − 2) ≥ 2ιb ,
0.5θ(R − 2) ≥ (1 − θ)(1 − êc ),
1 − 0.5Rθ
ec = êc ≥ e∗ =
,
1−θ
(33)
(34)
(35)
where the last equality is due to sequential rationality. Because θR < 2 and R > 2,
e∗ is always strictly between zero and one.
A.4
Proof of proposition 4
Let us start with the belief set ζ generated by the strategies described.
Given ζ, every bank b expects a CRA c that has ever exerted effort ec < e∗ to
exert effort ec = 0 and therefore, it is optimal to add c to Zb . Given ζ, êc = e∗ for
every CRA c that has always exerted effort ec ≥ e∗ and therefore, by proposition 2
∗)
.
every bank b quotes ιcb = ι∗ == (1−θ)(1−e
θ
Given ζ, applying for a combination of banks b1 , b2 and a CRA c such that the
CRA is on the blacklist of one of the banks gives a payoff of −fc to issuer j, which
is always worse than not applying at all. As êc = e∗ ∀c, the only dimension issuer
j can optimize on are the expected costs of the CRA/bank combination. Those are
given by
(θ + (1 − e∗ )(1 − θ))fc + θ(ιcb1 + ιcb2 ).
(36)
Given ζ, it is pointless for a CRA c to exert any effort if it has ever exerted
effortec < e∗ , as it would be costly and will not affect current income and current or
future market share. It is then optimal to quote the maximum possible fee such that
profits are maximized if any firm j deviates form the equilibrium strategy. Even if
CRA c has always exerted effort ec ≥ e∗ , it is suboptimal to exert effort ec > e∗ , as
it is costly and does not affect future or current market share, nor the fee level that
will be paid.
For a CRA that is boycotted, exerting zero effort for a rating application is
optimal as that minimizes contemporary gains while it has no effect on future cash
flows under the belief that it will be boycotted for ever. If the CRA has never exerted
effort below e∗ , it will not exert more than e∗ as its value and investor demand are
decreasing in ec as long as it exceeds e∗ . If exerted effort is lower than e∗ , then the
36
value of future cash flows is equal to zero and it is optimal to set ec = 0 as that
maximizes contemporaneous gains. Given the strategy to exert effort e∗ at every
period in the future, the CRA contemporaneously exerts ec = e∗ if that is more
valuable than exerting ec = 0:
Vc (ec = 0) ≤ Vc (ec = e∗ ),
((1 − θ)fc + cc )e∗ ≤ δ
A.5
(θ + (1 − θ)(1 − e∗ ))fc − cc e∗
.
δ −1 − 1
(37)
(38)
Proof of proposition 5
Consider the equilibrium belief set ζ from proposition 4 and an information shock
g < 1 for all CRAs without being aware that the others also have this information.
For the CRAs, the incentive compatibility constraint changes to (14), while under
ζ the CRA beliefs that the other players consider it to be given by (12).
If N = 1, slacking will not happen as long as (14) is satisfied. In that case, it
is still optimal to quote fc = β and exert effort ec = e∗ . Because β is finite, (14)
cannot be satisfied if (13) is violated as too little resources on the issuers’ behalf are
available for future CRA rents. Therefore, it is optimal in that case for the CRA to
quote fc = β and exert effort ec = 0.
If N > 1, each CRA expects under ζ that next period when g has been revealed
and is public knowledge, the equilibrium rating fee fc = f ∗ as before, as both sides
of the IC will be multiplied with g, such that the effect neutralizes. As before,
competition makes the IC bind going forward. One possibility to restore incentive
compatibility would be to lower fc in the current period. However, under ζ banks
will not fund an application with a rating from a CRA that does not quote an
incentive compatible fee, such that in the current period, sales and profits will
be zero. Moreover, as the IC is violated, the present value of future income is
by definition lower than the profit from having regular market share and exerting
zero effort. Thus, reducing fees to restore incentive compatibility is suboptimal.
Therefore, the optimal CRA strategy in this case is to quote fc = f ∗ and exert
effort ec = e∗ .
A.6
Proof of proposition 6
The proof consists of showing that i) the value of the CRA increases in ec , irrespective
of ιb , ii) that for banks, given the belief ec = 1, investment will be undertaken, iii)
37
that given the belief ec = 1 and the associated interest rate, it is optimal for firms
to apply for a rating and funding, and (iv that it is optimal for the CRA to conduct
any ratings at all.
With the co-investment ψj,c , the value function of the monopolistic CRA changes
to
Vc = ((θ + (1 − θ)(1 − ec ))fc − cc ec − ψj,c (1 − θ)(1 − ec ) + (1 − θ)ψj,c ιb ) + δE(Vc ),
(39)
where I is the interest paid on the co-investment and will be set such that in equilibrium the co-investment yields zero profit. As ιb is committed to ex-ante and the
effort decision is only made after a rating application, ιb can be conditioned upon.
Differentiating (39) with respect to ec , yields
∂V
= (1 − θ)(ψj,c − fc ) − cc .
∂ec
(40)
cc
Because the CRA is a monopolist, fc = β0 . If ψj,c > 1−θ
+ β0 , then substituting
∂V
gives that ∂ec > 0, such that it is optimal for the CRA to have ec = 1. So, the
co-investment aligns contemporaneous interests of investors and the CRA better,
reducing the incentive to slack and reducing the need for an excess profit to achieve
incentive compatibility.
Because we assumed a sequentially rational steady state equilibrium, banks have
the belief that ec = 1. As 1 ≥ e∗ , such an equilibrium is feasible for the banks and
by competition they will charge an interest rate ιb = 0.
The firms would prefer ec = e∗ < 1 in equilibrium. However, the project can not
lead to losses for the firm, only the rating fee fc can. But we have that β > β0 ≥ fc ,
such that the private benefit of undertaking the project is always larger than the
rating fee and under the belief that a firm with a rating of type G is funded, it is
always optimal to apply for a rating and funding.
The only thing required for this to happen is that for the CRA it is optimal
to do any rating business at all. This is only the case if every period profits are
positive, i.e., if (θ + (1 − θ)(1 − ec ))fc − cc ec − ψj,c (1 − θ)(1 − ec ) + (1 − θ)ψj,c ιb ≥ 0.
Substituting fc = β0 , ec = 1 and ιb = 0 and rewriting gives β0 ≥ cθc .
A.7
Proof of proposition 7
In order to have a captive equilibrium, we need to have the following:
38
1. Firms find it worthwhile to pay for lower ratings, i.e., they should prefer some
low effort level equal to or exceeding e∗ over high effort, incorporating the
required fee markup and the higher interest due
2. Low CRA effort now should be rewarded with high future profits, in other
words, ”perverse” incentive compatibility for the CRA should be satisfied
3. Conducting the rating should be profitable for the CRA in each period as we
look at a steady state equilibrium
4. The rating fee should be affordable and therefore bounded from above by the
initial endowment
The existence of a solution to the optimization problem (18) to (23) ensures the
preference of firms for some low effort level, which should exceed e∗ as otherwise
no equilibrium with investment is possible (by proposition 3). Given the belief that
any CRA that has never exerted other effort than ẽ again exerts ẽ, choosing the
cheapest among those is optimal for the firm. For the banks, given those beliefs and
competition among banks, interest is set such that all banks break even given their
beliefs.
In order for reputation to work, we need to have that the benefits from exerting
high effort are more than offset by the loss of future business due to the boycott. In
other words, we need to have that given f˜c
Vc (ec = 1) ≤ Vc (ec = ẽ)
((1 − θ)(ψj,c − f¯c (ẽ)) − cc )(1 − ẽ) ≤ δ
(θ + (1 − θ)(1 − ẽ))f˜c − cc ẽ
.
δ −1 − 1
(41)
(42)
Rewriting this expression and substituting in A gives
((1 + A−1 + 1)cc − ψj,c (1 − θ))ẽ + (1 − θ)ψj,c − cc
˜
fc ≥
(A−1 + 1)(1 − (1 − θ)ẽ) − θ
(43)
Due to competition among CRAs, this constraint will bind, such that incentive
compatibility is enforced by condition (21).
Moreover, it could be that incentive compatibility is satisfied, but that rating
fees are lower than expected rating production costs, in which case it is better for
the CRA to do no rating at all. Condition (22) rules out those cases. Note that
unconditionally, the co-investment does not lead to losses even with low effort as
the interest rate will exactly compensate for expected losses.
39
Finally, the rating fee cannot be more than the initial endowment, which is
ensured by (23).
A.8
Proof of proposition 8
Any equilibrium for which bank ratings are observed have positive investment, otherwise for the firm it would not be optimal to apply for a rating and pay a rating
fee. As the bank lives for only one period, it has no reputation to worry about and
optimizes, conditional on a rating application w.r.t. eb . Since conditional on the
quoted interest rate, its marginal utility w.r.t. eb is given by (1 − θ)(1 − fb ) − cb ,
which is linear. Therefore, either eb = 0 or eb = 1. Since for the other investing bank
an effort of at least e∗ is required, eb = 0 cannot occur in a sequentially rational
equilibrium. eb = 1 if marginal utility is positive, i.e. if
(1 − θ)(1 − fb ) − cb >0,
(44)
(note that fc can be negative which will be compensated with a higher interest rate
in the future). As banks are short-lived and compete, they make zero profit in
equilibrium, such that conditional on eb = 1, the other bank will set a zero interest
rate and for the rating bank we have
cb = θ(ιb + fb ) ≤ θ(R − 2 + fb ).
(45)
Combining (45) with (44) and realizing that θ (0, 1) gives
cb
1
1−θ
= cb 1 +
θ
1−θ
< cb +
θ
(1 − fb ) ≤ θ(R − 1).
1−θ
(46)
Rewriting gives
cb < θ(1 − θ)(R − 1).
A.9
(47)
Proof of proposition 9
I will first prove existence of such equilibria. The proof for arbitrary N is done by
induction. Thereafter, I will prove uniqueness.
Let us assume N = 1 and the belief set that the monopolistic CRA every period
exerts effort e∗∗ , that the regulator shuts down the CRA after it ever exerts effort
40
∗∗
)
ec < e∗∗ , that banks fund upon a rating rj,c = G at interest rate ι∗∗ = (1−θ)(1−e
θ
and firms always apply for a rating.
Given this belief set, it is optimal for the CRA to at least exert effort e∗∗ every
period, as an incentive compatible fee is charged. As its utility is decreasing in effort
level, the optimal effort is given by ec = e∗∗ . For the regulator, its strategy is weakly
optimal given the belief set, as given the belief set the maximum achievable social
welfare is zero. If the CRA adopts a steady state strategy in which it exerts effort
ec > e∗∗ , setting a threshold ē > ec and enforcing that is sub-optimal and hence
this threat is not credible. Therefore, such a strategy cannot be part of a sub-game
perfect equilibrium. If the CRA adopts a steady state strategy in which it exerts
effort ec < e∗∗ , revoking its license is optimal, as social welfare will be negative.
In any given period, conditional on the belief that the CRA will in all future exert
ec = e∗∗ , both revoking and not revoking the CRA license are weakly optimal for
the regulator, irrespective of the CRA action in the current period.
Now consider the case for N > 1. Let us assume that for any number of CRAs
less than N there is a weak steady state equilibrium with equilibrium strategies
as described above. Moreover, let us assume the belief set that each CRA every
period exerts effort e∗∗ , that the regulator shuts down a CRA after it ever exerts
effort ec < e∗∗ , that banks fund upon a rating rj,c = G at interest rate ι∗∗ and firms
always apply for a rating. For the regulator, its strategy is weakly optimal given
the belief set, as given the belief set the maximum achievable social welfare is zero.
If one of the CRAs adopts a steady state strategy in which it exerts effort ec > e∗∗ ,
setting a threshold ē > ec and enforcing that is sub-optimal and hence this threat
is not credible. Therefore, such a strategy cannot be part of a sub-game perfect
equilibrium. If one of the CRAs adopts a steady state strategy in which it exerts
effort ec < e∗∗ , revoking its license is optimal, as social welfare will be negative and
at least zero welfare is achievable. In any given period, conditional on the belief that
all CRAs will in the future exert ec = e∗∗ , it is weakly optimal to revoke a license
of any CRA that contemporaneously exerts effort ec < e∗∗ , as under these beliefs
and by the assumption made at the start of the induction step, for any number of
CRAs smaller than N social welfare in all future periods will be zero, which is not
lower than the status quo and therefore weakly optimal. The proof of existence for
any N then follows by induction.
Next, we prove uniqueness of the sub-game perfect steady state equilibrium. In
any steady state equilibrium, the number of CRAs in equilibrium should remain
constant, in other words, in equilibrium, no licenses are revoked. For the regulator,
41
it is only optimal to continue licenses from period to period if each period at least
zero social welfare is produced. Therefore, it is optimal for the regulator to revoke
the license of any CRA employing a steady state strategy involving an effort level
ec < e∗∗ . Suppose now that for a given N there is a steady state sub-game perfect
equilibrium in which at least one CRA exerts effort ē > e∗∗ every period and a
regulator revokes a license of any CRA exerting effort lower than ē (clearly, exerting
effort more than the regulatory threshold is suboptimal for the CRA, so such a case
can never be an equilibrium and need not be considered). The rest of the proof is
again by induction.
If N = 1 and the threat of the regulator to revoke the CRA license if the CRA
in a single period exerts effort e∗∗ < ec < ē is not credible and hence, for N = 1,
such an equilibrium is not sub-game perfect. Thus, for N = 1, uniqueness is proved.
Now suppose that N > 1 and that for any number of CRAs smaller than N ,
the only sub-game perfect steady state equilibrium yields zero social welfare. If
one of the compliant CRAs in any given period exerts effort ec < ē, revoking that
CRA’s license yields zero welfare in all future periods, which is strictly sub-optimal
to keeping the compliant CRA under the belief that it will exert effort ec > e∗∗ in at
least one future period. Therefore, the threat of the regulator is not credible and the
equilibrium is not sub-game perfect. If the regulator sets a regulatory level ē ≥ e∗∗ ,
but does not enforce it for the compliant CRA, compliance is sub optimal for that
CRA. The proof is then completed by the induction.
A.10
Proof of proposition 10
Suppose we are in an equilibrium with positive investment. This means that either
the banks or the CRAs issue ratings. If banks issue ratings in equilibrium, eb =
2(1−θ)−cb
and social welfare is given by θ(R − 2) − cb . Now suppose that
1 ≥ 2(1−θ)−c
c
CRAs issue ratings and exert effort ec . The associated social welfare is given by
θ(R − 2) − 2(1 − θ)(1 − ec ) − cc ec . The increase in social welfare that a regulator
can achieve if all CRA licenses are revoked is given by
∆SW = 2(1 − θ)(1 − ec ) + cc ec − cb ,
(48)
which is linear and decreasing in ec . If ∆SW < 0, for a regulator, revoking all rating
licenses is always better than taking no regulatory action. If in equilibrium CRAs
conduct the ratings, ∆SW has to be positive and setting (48) to zero and solving
42
gives
ec ≥ e∗∗∗ =
A.11
2(1 − θ) − cb
.
2(1 − θ) − cc
(49)
Proof of proposition 11
Take the equilibrium from proposition 4 with N > 1. If M > 0 investor-paid CRAs
are added, utility in equilibrium for issuers will not increase. Under the belief that
em < e∗ , banks will not select m. Under the belief êm > e∗ , utility for issuers
only increases if fm << f ∗ . However, this in equilibrium will not happen as m
is subject to the same incentive compatibility constraint as every issuer-paid CRA
c. Therefore, it is sub-optimal for an issuer j to select a bank b that does not
exclude m. Under the belief generated by this issuer strategy, it is optimal for a
bank b to put m on the blacklist Zb . Hence, issuer j will only consider selecting
bank b when êm = e∗ , ∀m ∈
/ Zb . As fm = f ∗ by competition and the incentive
compatibility constraint, m completely mimicks an issuer-paid CRA in equilibrium
or has no business at all (in an equilibrium where issuers never select banks that do
business with investor-paid CRAs).
A.12
Proof of proposition 12
It is sufficient to show that there is no equilibrium in which m has a strictly positive
market share. Suppose there is some equilibrium belief level êm ≥ e∗ for effort
from m, in which m has strictly positive market share. For c is it always strictly
optimal to exclude m from the market as in the presence of m, future fees will be
lower, future volume will be at least 50% lower and current volume will be at least
50% lower. Now assume (i) c can commit to always match the êm upon observing
presence of m and when doing so charges a fee fc infinitesimally smaller than fm
and (ii) incentive compatible fees are quoted by m, (iii) c and m have never exerted
effort below e∗ and (iv) given that eˆc = eˆm issuers have a preference for the CRA
with the lowest fee and (v) investors only purchase ratings from m if they expect to
use them and recover the rating fee from a transaction fee. Conditions (ii) to (v)
need to hold for any equilibrium set of strategies to be optimal and the equilibrium
to exist. Under these conditions, c can conditionally on observing the presence of
m match by setting ec = êm and fc infinitesimally smaller than fm . Because of (i)
it can commit to do so. Because of (iv) all investors will apply for ratings from c
and êc = êm because c can commit to set ec = eˆm . As a result, (v) dictates that
43
no investor will buy ratings from m, because of which the equilibrium cannot exist.
The only thing left to show is that assumption (i) is valid. Letting m enter would
cost c at least half of its value due to lost business. Because incentive compatibility
of c is satisfied in the setting without m, this means that the loss in value would
exceed one period of monopoly profits. Playing the strategy outlined above would
in the current period yield more than a profit of zero, such that the strategy can be
committed to.
A.13
Proof of proposition 13
The proof runs along the same lines as the proof of proposition 12. Assumption (iv)
needs to be sharpened however. Instead we need that (iv.a) issuers choose any CRA
that has always maximized issuer value in the past according to the equilibrium
beliefs if there is at least one of those. The only thing left to show then is that the
strategy of matching effort of m is committable. This is only true if the present
value of the equilibrium profit without m is high enough. The issuer indifferent
if fm + 2(1 − em )(1 − θ) = fc + 2(1 − ec )(1 − θ). fm is incentive compatible if
fm ≥ M cc em A(1+A−1 ). As more than 1 investor-paid CRA entering the market will
make it even harder for an investor paid CRA to gain any market share, it is sufficient
to show when under which conditions one investor-paid CRA can be prevented to
enter the market. Therefore, I only consider the case M = 1. m will maximize em
and minimize fm in order to make it as hard as possible for
issuer-paid CRAs to
β0
outbid it. The maximum affordable em is given by em = min cc A(1+A
−1 ) , 1 . Issuerpaid CRAs can only credibly outbid m if they can match effort, while satisfying
the IC for the situation without m, i.e. cc ec ≤ A(fc∗ − cc e∗ ), which implies that
ec ≤ e∗ . They can set the instantaneous fee fc = 0 as that one will not influence
the IC and satisfying the IC ensures that this strategy over-all has a positive payoff.
Working everything out, we get that investor-paid CRAs can be prevented to enter
by competing issuer-paid CRAs if
fm − 2em (1 − θ) > fc − 2ec (1 − θ),
β0
−1
, 1 ) > −2(1 − θ)ec ,
(cc A(1 + A ) − 2(1 − θ))(1 − min
cc A(1 + A−1 )
cc A(1 + A−1 )
β0
1−
min
, 1 < ec ≤ e∗ .
−1
2(1 − θ)
cc A(1 + A )
(50)
44
(51)
(52)
A.14
Proof of proposition 14
For such an equilibrium to exist, specific conditions need to be met. First, conditions
(ii), (iii), (iv.a) and (v) need to be satisfied, but as before, in any equilibrium
these conditions are trivial. Moreover, for such an equilibrium to exist, equilibrium
effort from each CRA needs to be optimal, committable and such that the issuer
is indifferent between using investor-paid and issuer-paid ratings in equilibrium.
Condition (iv.a) means that for each issuer that has received an interest quote from
a subscriber bank (i.e. when the private benefit β is secured)
fm − 2êm (1 − θ) = fc − 2êc (1 − θ).
(53)
Moreover, incentive compatibility and competition imply that
fm = (N + M )cc êm A(1 + A−1 ),
fc = cc êc A(1 + A−1 ).
(54)
(55)
As profits (rents) of all CRAs are increasing in the equilibrium effort levels, m will
exert maximum effort, thereby by invoking
a winner’s curse
and push all c to also
β0
exert higher effort. Setting ēm = min 1, (N +M )cc A(1+A−1 ) implied by the budget
constraint, we have that f¯m = (N +M )cc ēm A(1+A−1 ). Substituting everything into
+M −1)(1−θ)
. One necessary condition for a co-existing
(53), we get ēc = N +M + cc2(N
A(1+A−1 )−2(1−θ)
equilibrium to exist is that the calculated ēc ∈ [e∗ , 1] as in other cases, issuer-paid
CRAs strictly dominate investor-paid CRAs. Another necessary condition is that
ēc is committable. This is never the case because given the equilibrium belief êc , it
is optimal for an issuer-paid CRA to set a fee that is infinitesimally smaller than
cc ēc A(1 − A−1 ). This strategy is committable, because with this strategy this CRA
would become a monopolist next period.
A.15
Proof of proposition 15
Investor-paid CRAs are identical and will therefore obtain identical market shares,
everything else equal. Banks again compete and break even. If a non-subscriber
banks get access to ratings, they quote break-even interest rate quotes and quote no
transaction fee. For the issuer it is optimal to take the offer with the lowest expected
cost. As banks need to at least break even in equilibrium, issuers will typically end
up with a break-even interest rate and zero transaction fee, conditional on leakage.
45
To compensate for the fact that a fraction φ of the purchased ratings turns out to be
of no added value to a subscriber bank, it needs to ask a transaction fee of fm (1 −
φ)−1 M in order to make purchasing ratings worthwhile for the subscriber bank.
Competition will make this inequality bind. When investor-paid CRAs compete,
their incentive compatibility constraint binds as before. Therefore, in equilibrium
fm = A(1 + A−1 )M cc em . Subscriber banks will offer competitive interest rates to
issuers. For issuers it is optimal to choose the bank offering the lowest rate 21 and
therefore negative selection happens for the subscribers of the less reputable investorpaid CRA. As a consequence, the CRAs will exert maximal effort, which is equal
to one, unless the budget constraint of the issuer is violated, in which case an effort
level is chosen that matches a fee level such that the budget constraint binds. Of
course, the pledgability constraint need to be satisfied, such that it is only possible
−1
∗
to have competing investor-paid CRAs in equilibrium if φ ≤ 1 − A(1−A β0 )M cc e . If
the budget constraint is violated, but M > 2, the it is possible to reduce the number
of CRAs (reduce the amount of double work) in the economy such that the budget
constraint is satisfied again. Maintaining a competitive equilibrium when M = 2
and the budget constraint is violated is impossible, so in such a case a monopolistic
equilibrium will arise in which em = e∗ as before and fm = β0 if the incentive
compatibility constraint can be satisfied that way.
21
as long as θ(1 − θ) ≥ A(1 + A−1 )M cc
46