Selection in Unsolicited Ratings: the Case of the Sovereign Debt Market

Selection in Unsolicited Ratings: the Case of the Sovereign Debt Market Anna Gibert∗ 31 March 2017 Abstract This paper aims at contributing to the debate on whether unsolicited ratings are strategically motivated. I present evidence from the sovereign debt market that strategic motivation is not necessarily behind the patterns that we see in the data and propose a model of credit ratings and ancillary services that abstracts from strategic considerations. In my model, borrowers with different unobservable characteristics select themselves into different solicitation groups. In equilibrium, the model can generate either a negative or a positive selection on unsolicited ratings, depending on the share of unsolicited ratings in a given market. The economic mechanism analyzed in this paper implies a “natural” degree of market selection which is not associated to strategic motivation. JEL Classification: G24; H63; G20. Keywords: Unsolicited ratings; Sovereign debt; Rating Agencies, Ancillary services. ∗German Institute for Economic Research (DIW Berlin). Mohrenstraße 58, 10117 Berlin, Germany. Email: [email protected]. I am grateful to Piero Gottardi, ´ Arp´ad ´ Abrah´am, Vito Polito and the participants at the DIW working group and the 48th Money, Macro and Finance Research Group Annual Conference for their helpful comments. 1 Introduction Unsolicited ratings are opinions about the creditworthiness of the borrower that are not initiated nor paid for by the issuer. Standard and Poor’s (S&P) has been issuing unsolicited ratings since 1996. Moody’s and Fitch - the other two biggest rating agencies - have been doing it as well.1Since the majority of the rating agencies (CRAs) receive compensation from the issuer, one could wonder why the rating agencies would want to issue a rating for which they do not receive fees. Fulghieri et al. (2014) propose a strategic motivation for unsolicited ratings. They argue that unsolicited ratings can be used as threat to pressure issuers towards solicitation. This model implies that unsolicited ratings have to be lower on average than solicited ones and this fact is consistent with the empirical literature.2 Further evidence on the difference between solicited and unsolicited ratings is brought by Bannier et al. (2010). They compare the ex-post default probabilities of similar non-U.S. borrowers with solicited and unsolicited S&P ratings between January 1996 and December 2006 and find that, conditional on a rating, default probabilities are different across the two groups. The unsolicited rating group has lower default rates, which might be an indication that rating agencies choose to rate those borrowers more strictly compared to solicited ones. Understanding whether lower unsolicited ratings are motivated by strategic considerations of the rating agencies is important for policy. For example, the rating agency Moody’s had been subjected to an antitrust investigation in 1996 by America’s Justice Department, which suspected that the agency’s practice of issuing unsolicited ratings on companies might be “a way to force them to pay up for the full service” (The Economist, 2001). In this paper, I argue that lower average unsolicited rating grades and a lower probability of default in unsolicited ratings vis-`a-vis the same solicited ratings do not necessarily imply the strategic use of lower ratings by the rating agencies. Different types of firms might select themselves into soliciting or not soliciting ratings depending on their characteristics. For example, more solvent firms may reasonably expect higher grades on average and thus have more incentives to solicit a rating. Unsolicited ratings are, therefore, more likely to be assigned to lower quality firms. An argument against the strategic motivation of the CRA for giving unsolicited ratings is the fact that, in the sovereign market, unsolicited ratings have higher grades - not lower - than solicited ones. Figure 1 reports the histograms of Moody’s unsolicited and solicited 1At least since 2000 and 2001, respectively, Moody’s and Fitch have recognised issuing unsolicited ratings (Behr and Guettler, 2008) but they were possibly doing it before that. 2Evidence that unsolicited ratings are associated with lower grades is broad in the empirical literature (Poon and Firth, 2005; Poon and Chan, 2010; Van Roy, 2013). 2 sovereign grades between 2010 and 2015. The distribution of unsolicited ratings has more weight to higher grades compared to that of solicited ratings. The unconditional mean of Figure 1: Histogram of solicited versus unsolicited rating grades. Source: Moody’s, 2010 -2015. solicited sovereign ratings is a Baa2 grade while that of unsolicited ratings is on average an A2 grade.3A Wilcoxon-Mann-Whitney test of the difference in means is significantly different from zero as can be seen in table 1. The median values are also statistically different. More generally, equality of the distribution functions is rejected at the 99% confidence using a two-sample Kolmogorov-Smirnov test (K-S statistic: 0.4348). Table 1: Differences between sovereign mean and median grades for solicited and unsolicited ratings. Source: Moody’s, 2010 -2015. difference in value t-statistic p-value Mean −3.89 −5.31 0.0000 Median −8 20.46 0.0000 The fact that unsolicited sovereign ratings are higher on average calls for a model of market self-selection that is able to produce not only a downward bias but also an upward one, like the one I present here. Credit rating agencies provide as well “ancillary services”, a business that has been growing since the late 90s. Ancillary services “comprise market forecasts, estimates of economic 3Moody’s rating scale is, in decreasing order of credit quality: Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C. Moody’s adds numerical modifiers 1, 2, and 3 to each rating grade from Aa through Caa. 3 Figure 2: Moody’s revenues by line of business from 2000 to 2007. Figure 3: Moody’s revenues by line of business from 2006 to 2015. trends, pricing analysis and other general data analysis as well as related distribution services” (ESMA, 2013). Since 2000 the share of revenues from the rating business went from a maximum of 90% (in 2002) to 70% (in 2015) versus an increasing share of ancillary services that reaches up to 30% (see figures 2 and 3). An example of ancillary service consists in providing the borrower with a forecast of the rating. Moody’s Rating Assessment Service was launched in 2000 and charges a company 75.000 euros to know what its credit rating would be if it solicited one (The Economist, 2001). Feedback is provided only to the issuer and assessments are confidential until the issuer decides to announce them publicly. S&P also offers a similar service: the Ratings Evaluation System. Literature. Fulghieri et al. (2014) introduce the first model of strategic motivation for unsolicited ratings. They see unsolicited ratings as an off-equilibrium threat, which is credible because it shows that the CRA fights the temptation to issue inflated ratings. Byoun (2014) presents a model of ratings where the existence of unsolicited ratings in equilibrium is not 4 strategically motivated, it is granted by the assumption that the CRA has to produce a rating for each firm. In my model, rating agencies are interested in issuing unsolicited ratings because it improves visibility, allowing the CRA to charge higher fees on solicited ratings. There is ample empirical evidence regarding the properties of unsolicited ratings (Poon and Firth, 2005; Poon and Chan, 2010; Van Roy, 2013; Bannier et al., 2010; Gan, 2004). None of them studies sovereign unsolicited ratings. As we will see below, descriptive statistics evidence indicate that, contrary to what has been found in other markets, unsolicited sovereign ratings have higher grades and are associated with lower bond yields compared to solicited ones. This contrasts with what has been found in the previous literature for banks, corporations and insurance companies (Behr and Guettler, 2008; Byoun, 2014; Klusak et al., 2015). This paper sheds light on the relationship between different services provided by the rating agency. To the best of my knowledge, this is the first paper that considers the ratings and the ancillary services jointly. The business of ancillary services has received attention from the regulators, who advocated more transparency in order to avoid conflicts of interest.4 Here I focus on their effect in the selection that arises in the market. The paper is organized as follows. In the following section I present some stylised facts about the sovereign unsolicited ratings. In section 3, I set up a model of borrowing under incomplete information where the credit rating agencies may issue ratings, solicited as well as unsolicited, and provide ancillary services. I solve for the equilibrium, characterise the equilibrium outcomes and present the relationship to the empirical facts. Section 4 concludes. 2 Stylized facts about sovereign ratings 2.1 Unsolicited sovereign ratings are more frequent than in other markets Unsolicited ratings are not issued homogeneously across market segments nor across regions. In 2000, the proportion of unsolicited ratings with respect to the total number of outstanding ratings varied between 6% and 27% in industrial countries, depending on rating agency and region (Bannier et al., 2010). In the US, unsolicited ratings are rare. In the European Union they are more numerous, especially in the segment of sovereign and public finance. Table 2 reports the number of ratings issued by each rating agency by solicitation status 4Regulation (EC) No 1060/2009 on credit rating agencies, amended by Regulation (EU) No 462/2013 of the European Parliament and of the Council of 21 May 2013. 5 and for each market segment. In 2012, 12.24% of the sovereign and public finance ratings by the three biggest rating agencies in the EU was unsolicited, while only 4.95% of the corporate ratings, 3.33% of the financial and insurance institutions and 0% of the structured finance ratings (ESMA, 2013). The agencies Moody’s and S&P gave in 2012 more unsolicited Fitch Moody’s S&P Corporate Solicited 518 760 951 82.48% 99.48% 99.79% Unsolicited 110 4 2 17.52% 0.52% 0.21% Financials and Insurance Solicited 597 542 1006 97.07% 99.82% 94.82% Unsolicited 18 1 55 2.93% 0.18% 5.18% Sovereign and Public Finance Solicited 296 232 189 83.38% 93.93% 87.91% Unsolicited 59 15 26 16.62% 6.07% 12.09% Structured Finance Solicited 4861 4438 4705 100.00% 100.00% 100.00% Unsolicited 000 0.00% 0.00% 0.00% Table 2: Ratings by solicitation status for different market segments in the EU in 2012. Source: ESMA. rating to sovereigns than to other categories and Fitch to both sovereigns and corporates. The majority of the other smaller rating agencies specialize in issuing only solicited or only unsolicited ratings (ESMA, 2013). For the agency Moody’s, the fraction of sovereigns that receive an unsolicited rating are distributed by grade as follows: 10.9% are high grades (investment grade) and 4.15% are low grades (below investment grade) as can be read from table 3. Table 3: Fraction of sovereigns that receive an unsolicited rating by rating grade (Moody’s, 2010-2015). Unsolicited Observations Grade Baa3 or above 10.9% 412 Grade below Baa3 4.15% 313 6 2.2 Unsolicited sovereign ratings are higher than solicited ones In a sample of all the sovereign ratings issued by Moody’s between 2010 and 2015,5I translated the rating grades into a numerical scale that goes from 1 (grade C) to 21 (grade AAA). If we control for some observable characteristics of the sovereigns (current account, debt over GDP, primary deficit, GDP per capita, inflation, direct investment and a set of regional and year dummies), having an unsolicited rating improves the rating grade by almost one and a half points with respect to a similar country that has paid for its rating. From a rating of Baa2, this would imply an upgrade to A3. The specification is similar to that of Gan (2004) and Van Roy (2013): Ratingi,t =Xi,tβ+δSolicitationi,t +i,t (1) but including time (year) as well as region (country) variation, where Solicitation is a dummy variable for the solicitation status that takes value 0 if the rating is solicited and 1 if it is unsolicited. Table 4 presents the estimated coefficient ˆ δ, which is positive and significant at the 1% level. The first column does not include fixed effects. The estimated positive effect of receiving on unsolicited rating becomes larger and more significant once you include year fixed effects (column 2), country fixed effects (column 3) or both (column 4). The average rating grade is higher for unsolicited sovereign ratings. Is this effect homogeneous along the rating scale? Table 5 reports three quantile regressions. The first column refers to the effect of solicitation on the rating grade for the first quartile (0.25) and its effect is the least significant and the smallest. The higher the rating grades (columns 2 and 3), the more sizeable the positive effect of unsolicited ratings. Let us see which countries are likely to receive unsolicited ratings. The unconditional probability for an individual country of obtaining an unsolicited rating is 7.49% in my sample. It is more likely, though, for countries with a higher rating grade, more outstanding public debt over GDP and a higher GDP per capita. Controlling for other factors, being in the region of Europe or East Asia makes it less likely that a suitable candidate receives an unsolicited rating. This might be due to the fact that there are more countries in those regions that could potentially be candidates. In order to see whether Moody’s changed its criteria for rating countries unsolicitedly over time, I predicted the estimated probability that a country of certain characteristics receives an unsolicited rating for each year between 2010 and 2015.6As expected, countries rated unsolicitedly had a higher predicted probability of receiving an unsolicited rating. But 5The sample is obtained from reading the internal documents published by Moody’s (“Unsolicited Ratings List”) from its earliest release in September, 6 2010 to the latest in December 30, 2015. 6See appendix A. 7 Table 4: OLS with robust standard errors (1) (2) (3) (4) Rating grade Rating grade Rating grade Rating grade Solicitation dummy 0.939* 1.489*** 0.984** 1.469*** (0.498) (0.512) (0.489) (0.506) Current account 0.135*** 0.128*** 0.134*** 0.128*** (0.0140) (0.0140) (0.0139) (0.0139) Debt -0.0177*** -0.0214*** -0.0172*** -0.0207*** (0.00427) (0.00437) (0.00425) (0.00434) Primary deficit -0.211*** -0.196*** -0.209*** -0.194*** (0.0320) (0.0294) (0.0322) (0.0296) GDP per capita 0.000152*** 0.000143*** 0.000151*** 0.000143*** (0.00000924) (0.00000955) (0.00000920) (0.00000956) Inflation -0.151*** -0.145*** -0.156*** -0.150*** (0.0201) (0.0195) (0.0221) (0.0216) Direct investment 0.136*** 0.121*** 0.135*** 0.119*** (0.0199) (0.0215) (0.0197) (0.0214) Region FE no yes no yes Time FE no no yes yes N 669 669 669 669 R-square 0.676 0.690 0.682 0.695 F 126.0 418.5 72.17 198.9 Standard errors in parentheses *p < 0.1, ** p < 0.05, *** p < 0.01 other countries with solicited ratings were just as likely or more to receive an unsolicited rating, for example Austria, Belgium, Norway, Botswana, South Africa and Ghana. You can find the complete list of the sovereign unsolicited ratings in the first column in appendix B. In the second column there is the list of sovereigns with a predicted probability of receiving an unsolicited rating higher than the average predicted probability of the sovereigns in the first column. First, in 2010 and 2011, the profile were top quality sovereign borrowers in Europe. Later on, as the competition across CRAs got increasingly intense and Africa started issuing international debt more frequently, some relatively stable economies in that continent became natural candidates for unsolicited ratings as well. 8 Table 5: Quantile regressions (1) (2) (3) Rating grade Rating grade Rating grade Solicitation dummy 0.775* 1.371*** 1.536*** (0.409) (0.461) (0.451) Current account 0.109*** 0.142*** 0.120*** (0.0134) (0.0161) (0.0157) Debt -0.0177*** -0.0241*** -0.0225*** (0.00331) (0.00370) (0.00415) Primary deficit -0.138*** -0.165*** -0.179*** (0.0271) (0.0302) (0.0245) GDP per capita 0.000127*** 0.000175*** 0.000196*** (0.00000808) (0.00000725) (0.00000620) Inflation -0.202*** -0.134*** -0.134*** (0.0139) (0.0181) (0.0216) Direct investment 0.107*** 0.155*** 0.156*** (0.0212) (0.0208) (0.0215) Region FE yes yes yes Time FE yes yes yes N 669 669 669 Quantile 0.25 0.50 0.75 Residual degree freedom 651 651 651 Standard errors in parentheses *p < 0.1, ** p < 0.05, *** p < 0.01 2.3 Unsolicited sovereign ratings have lower associated debt yields I merged the sample of Moody’s unsolicited ratings between November 2010 and December 2015 with the long-term sovereign yields at the end of the month for the same period. I also have data on the outlook (negative, neutral or positive) at the end of the month. I use the following specification: Sovereign Y ieldsi,t =Xi,tβ+λSolicitationi,t +ui,t (2) 9 3.3 Lenders’ problem Lenders lend the amount qD to the borrower and receive Dat the end of the game if there is no default. In case of default, there is no partial repayment. The lender profit function is: Π = −qD +β[µλAD+ (1 −µ)λBD],(7) where µ=µ(s, g) are the lenders’ beliefs that the borrower is of type A. Beliefs depend on what the lender observes about the borrowers creditworthiness: the solicitation statute and the rating grade. As a result of imposing the zero-profit condition, the price function satisfies: q(µ) = β[µλA+ (1 −µ)λB].(8) The value µ(0,0) represents the lenders’ beliefs when they see no rating for some borrower, µ(0, H) and µ(0, L) the lenders see an unsolicited rating of Hor L, respectively. 3.4 Borrower’s problem The borrower faces two problems: whether to buy ancillary services at t= 0 and whether to solicit a rating at t= 2. The borrower’s payoff, depending on its rating, is the following: •If the borrower buys ancillary services and it also solicits a rating: q(µ)D+λi(R− D) + (1 −λi)r−φ(D, γ)−χ, where the first term is the amount of borrowing at price q(µ) = q(1, g), the second and third terms are the net revenues weighted by the repayment probabilities and the last two terms are the fee for solicitation and ancillary services, respectively. •If the borrower solicits a rating but does not buy ancillary services, it saves on the amount of ancillary fees: q(1, g)D+λi(R−D) + (1 −λi)r−φ(D, γ). •A borrower that does not buy ancillary services may receive an unsolicited rating with an associated payoff of q(0, g)D+λi(R−D) + (1 −λi)r, where the price of debt is q(0, g) and the borrower does not incur in any fees. •Finally, if the borrower is unrated the payoff equals q(0,0)D+λi(R−D) + (1 −λi)r if it did not buy ancillary services or q(0,0)D+λi(R−D) + (1 −λi)r−χif it did. 3.5 Equilibrium I solve using the Perfect Bayesian Equilibrium. 16 Definition 3.1. Given the CRA rule of g∗(a, u, s, σ), a symmetric equilibrium is a γ∗, a strategy for the borrower: {a∗, s∗}:{A, B}→{0,1}×{0,1},(9) where a∗(i)is the choice of ancillary services and s∗(i, a(i)) is the rating solicitation, a strategy for the lender about the debt price q∗(s, g) : {0,1}×{H, L, 0} → R+and a system of beliefs µ∗(s, g) : {0,1}×{H, L, 0} → [0,1] about the borrower being type A, such that: •γ∗maximises the CRA profit function (6) and f∗(γ)is consistent with the borrower’s strategy. •The strategy profile is sequentially rational given the beliefs and γ∗. •The beliefs are consistent with Bayes’ rule whenever possible. 3.6 Model without ancillary services Let us first solve the model without ancillary services as a benchmark. The game starts at t= 1. All the other modeling assumptions stay the same. Proposition 3.1. A rule of g∗(u, s, σ):g∗(0,1, σ) = σ,g∗(1,0, σ) = σand g∗(0,0, σ) = 0, the strategies s∗(A) = 1, s∗(B) = 0,q∗(µ) = µλA+ (1 −µ)λBand γ∗=(1−θ)c+θα1 −2θα2D+1 2 constitute an equilibrium of the model without ancillary services given the following beliefs µ(s, g):µ(s, L)=0∀s, µ(1, H) = 1, µ(0, H) =    1w. prob. θ θ+(1−θ)p 0w. prob. (1−θ)p θ+(1−θ)p and µ(0,0) =    1w. prob. θξ θξ+(1−θ)(1+γ(ξ−1)) 0w. prob. (1−θ)(1+γ(ξ−1)) θξ+(1−θ)(1+γ(ξ−1)) . The CRA assigns a proportion γ∗of unsolicited ratings to both type Aand type B borrowers in order to maximise its profit function (6) in t= 1: max γ−γc + (1 −γ)θ[φ(D, γ)−c]. 17 Substituting the functional form of φ(D, γ) and solving the maximization problem, we obtain the first order condition: −c−θ(α1+α2γD) + θ(1 −γ)α2D+θc = 0. Rearranging we find an expression for the optimal fraction of unsolicited ratings that the CRA issues: γ∗=(1 −θ)c+θα1 −2θα2D+1 2.(10) Since γ0(D)>0 if α1> c,γ∗is increasing in the amount of debt. For condition φ > φ > ¯ ¯ φ11 type Aprefers to solicit a rating rather than remaining unrated, if they are not given an unsolicited one, while type Bdoes not. Conditions state that φin equilibrium has to stay within some upper and lower bounds: the bounds depend on D, γ∗, θ, λAand λB. A fee too high would discourage even the best borrowers to ask for a rating. Type A can have either a solicited or unsolicited Hrating and a fraction ξis unrated by assumption. If type A were allowed to solicit a rating after an unsolicited one they may choose to do so. The reason is the price of debt is better for solicited ratings for the same Hgrade. We simplify away from this possibility but this behaviour is something we might observe. Type Bcan have an Hunsolicited rating, Lunsolicited rating or no rating. There are no grade Lsolicited ratings. Thus, unsolicited ratings have lower grades on average. Type A knows that it is more likely to receive an Hrating, so it has an incentive to pay the fee for a solicited rating. Type B, on the contrary, has a lower probability pto receive an Hrating and a high probability to receive an Lrating, which bears a higher risk premium than an absence of rating. The fact that higher quality borrowers are more inclined to get rated is a well-known result in the literature (Lizzeri, 1999; Mathis et al., 2009; Fulghieri et al., 2014). 3.7 Introducing ancillary services Proposition 3.2. For g∗(a, u, s, σ)given by equations (3)-(5), the strategies a∗(A) = 0, a∗(B) = 1, s∗(A, 0) = 1, s∗(B, 0) = 0, s∗(A, 1) = 1,s∗(B, 1) = 1 if m=hand 0if m=l, q∗(µ) = µλA+ (1 −µ)λBand γ∗that solves problem (6) constitute an equilibrium of the 11See Appendix C for a proof. 18 model given the following beliefs: µ(0, H) = 1, µ(0, L) = 0, µ(1, L)=0, µ(1, H) =    1w. prob. 2θ(1−γ) 2θ(1−γ)+(1−θ)(p+) 0w. prob. (1−θ)(p+) 2θ(1−γ)+(1−θ)(p+) and µ(0,0) =    1w. prob. 2θξ 2θξ+(1−θ)(ξ+1) 0w. prob. (1−θ)(ξ+1) 2θξ+(1−θ)(ξ+1) if γ > ¯γ. The CRA assigns a proportion γ∗of unsolicited Hratings to type A borrowers. Type B borrowers enter a contract of ancillary services and avoid receiving unsolicited ratings. They can either have a solicited Hor Lrating, after having observed the assessment m=h, or no rating, after having observed the assessment m=l. A fraction ξof borrowers is unrated by assumption. Type A borrowers who are neither unrated nor received an unsolicited rating, solicit and receive an Hrating. There are no grade Lunsolicited ratings, as the type B borrowers that would be subject to receiving one prefer to pay for ancillary services and veto that possibility. Hence, unsolicited ratings have higher grades on average. There are two thresholds values ¯ φand φ12 such that: for φ > φ and φ < ¯ φ,s∗(A, a) = 1 ∀aand s∗(B, 0) = 0, s∗(B, 1) = 1 if m=hand 0 if m=l. Type A prefers to solicit a rating whenever φ < ¯ φ, whether they are clients of ancillary services or not. Their incentives to solicit are high, because the probability of getting a high rating is large, as long as the price of ratings is sufficiently low. Type B, on the contrary, prefers not to solicit a rating unless they are given a strong signal, a positive assessment, that the rating will be high. That is, if the fees are high enough with respect to the probability pof being given an H rating. The CRA problem (6) can be rewritten in the following way: max γ−γc + (1 −γ)θ[φ(D, γ)−c] + 1 2(1 −θ) [φ(D, γ)−c].(11) Plugging in the functional form of φ(D, γ) and solving for γ: γ∗=(1 −θ)c+θα1 −2θα2D+1 21 2+1 2θ,(12) 12The thresholds depend on the parameters of the model and a formal derivation can be found in appendix D. 19 where the first two terms coincide with the expression for the optimal fraction of unsolicited ratings in the model without ancillary services and the term in parenthesis, which is >1 for 0> θ > 1, represents the additional incentive to issue unsolicited ratings due to the gains coming from the clients of ancillary services. For a∗(B) = 1, Proposition 3.3. Provided γis high enough, type B prefers to buy ancillary services for a fee χand obtain a rating Hwith probability p and no rating g= 0 with probability 1−pthan risk getting an unsolicited Hrating with probability γp and Lwith probability γ(1 −p). The existence of this equilibrium depends on the value of γ: γ > ¯γ:= βG(θ, ξ, λA, λB) + α1 2+χ 2βG(θ, ξ, λA, λB)−α2D.(13) where G(θ, ξ, λA, λB) = 2θξλA+(1−θ)(ξ+1)λB 2θξ+(1−θ)(ξ+1) . Note that a∗(A) = 0 is always true13. If type A does not ask for ancillary services it might get an unsolicited Hrating or a solicited H rating. With ancillary services the outcome is always a solicited Hrating but at the extra cost of having to pay the fee χ. In this set-up, unsolicited Hratings are assigned only to Atypes, therefore they are fully revealing of the high quality type. This confirms equilibrium beliefs in proposition 3.2. Off-equilibrium beliefs µ(0, L) are set equal to 0. Since unsolicited Hratings are assigned only to Atypes but solicited Hratings can be assigned to Aand Btypes, we expect to see a market premium in the price of debt of high unsolicited ratings with respect to solicited. Note that γis a choice of the rating agency that is described by the expression (12). When γis low, type B does not choose ancillary services and the equilibrium outcome is similar to the one described in the solution to the model without ancillary services. Proposition 3.4. For g∗(a, u, s, σ)given by equations (3)-(5), the strategies a∗(A) = 0, a∗(B) = 0, s∗(A, 0) = 1, s∗(B, 0) = 0, s∗(A, 1) = 1,s∗(B, 1) = 1 if m=hand 0if m=l, q∗(µ) = µλA+ (1 −µ)λBand γ∗that solves problem (6) constitute an equilibrium of the model given the following beliefs: µ(s, g):µ(s, L)=0∀s, µ(1, H) = 1, µ(0, H) =    1w. prob. θ θ+(1−θ)p 0w. prob. (1−θ)p θ+(1−θ)p 13For a∗(A) = 0: γq(0, H)D+(1−γ) [q(1, H)D−φ(γ, D)] >1 2q(1, H)D+1 2q(1, H)D−φ(γ, D)−χ. Since q(0, H)> q(1, H), the statement is always true. 20 and µ(0,0) =    1w. prob. θξ θξ+(1−θ)(1+γ(ξ−1)) 0w. prob. (1−θ)(1+γ(ξ−1)) θξ+(1−θ)(1+γ(ξ−1)) if γ≤¯γ. Thus, all grade Hsolicited ratings are assigned to type A borrowers whereas grade Hunsolicited ratings can be given to type A or B with different probabilities. Grade L unsolicited ratings are assigned to type B borrowers. Finally, unrated borrowers can be either type A or B. This confirms equilibrium beliefs in proposition 3.4. Off-equilibrium beliefs µ(1, L) are free to be [0,1], in this case, they are equal to 0. 3.8 Comparative statics Some parameters affect the determination of the equilibrium. •The amount of debt issued by a given borrower category or in a given market segment (D). Daffects the fraction of borrowers susceptible to receive an unsolicited rating: since γ0(D)>0, the higher the amount of debt in a given market or whenever the borrowers issue more debt, the more incentives the CRA has to assign unsolicited ratings. This is because the benefits from increased fees in the future - due to the high debt - more than compensate for the costs of issuing unsolicitedly. The CRA has incentives to increase their revenues when those are the largest, as it is the case when there is a lot of debt to intermediate. Suppose there are two equilibrium probabilities of issuing an unsolicited rating, γ∗ 1and γ∗ 2, where γ∗ 1<¯γ < γ∗ 2. Recall that ¯γis the threshold of γthat makes type B want to buy ancillary services as defined in equation (13). An increase from γ∗ 1to γ∗ 2makes type B willing to buy ancillary services in order to avoid a more likely unsolicited rating. Therefore, the equilibrium changes from one without equilibrium ancillary services and lower grades unsolicited ratings to one with equilibrium ancillary services and higher grades unsolicited ratings. •The ex-ante market perception about the creditworthiness of a borrower (θ). θaffects the conditions on the maximum and minimum levels of φthat allow to sustain a given equilibrium. A higher θprovides more incentives for B to ask for ancillary services but also more incentives for A to solicit a rating since both q(0,0) and q(1, H) increase but q(0, H) does not change. Hence, it favours the equilibrium with ancillary services. On 21 the contrary, a lower θfavours the equilibrium without ancillary services because the worsening of the unrated pool makes it less attractive to be a part of it. •The parameters governing the fixed part (α1) and the variable part (α2) of the CRA’s rating fees. γ0(α2)>0, hence, an increase in α2makes γhigher and it is more likely that there is an equilibrium with ancillary services. α2captures the steepness in which unsolicited ratings allow you to charge more fees per unit of debt. Hence, it works very similarly to an increase in γ: φ(α1, α2, D, γ) = α1+α2γD. (14) α2can be interpreted as the bargaining power or the market share of the CRA. If they are in a better position to extract more fees per unit of debt in one market; it is reasonable that they want to take advantage of that by increasing their presence and maximising revenues. α1is the fixed part of the CRA compensation, irrespective of debt and market position. You can think of it as the minimum amount they require to rate a borrower no matter what the circumstances. It might not compensate the CRA to issue a rating if they are paid below a certain compensation. Condition (10) tells us that α1has to be higher than the cost of issuing a rating for γ0(D)>0. I.e. the fixed part of the rating fees has to compensate for the fixed costs of issuing a rating. 3.9 Relationship with the data Higher average debt and high α2give incentives to the CRA to assign more unsolicited ratings. In the equilibrium with ancillary services, the proportion of unsolicited ratings, γ∗, is higher, hence, the percentage of type A borrowers that get an unsolicited rating is higher. Moreover, the percentage of unsolicited ratings over total ratings, θγ θ+(1−θ1 2)is higher than in the equilibrium with unsolicited ratings, γ θ+(1−θ)γ, as long as there is not a large number of type B firms: γ < θ(1−θ) 2(1−θ−θ2). We have seen that unsolicited ratings are frequent among sovereign ratings and they are mostly high rating grades (stylised facts 2.1 and 2.2). The equilibrium with a higher probability of unsolicited ratings features higher unsolicited rating grades thanks to the opt out option provided by ancillary services (see figure 6). In the equilibrium without ancillary services (low probability of unsolicited ratings γ∗), unsolicited ratings are g=Hand g=L(shaded areas) while in the equilibrium with ancillary services (with high probability of unsolicited ratings γ∗) they are g=H. Hence, in the latter equilibrium unsolicited ratings are higher on average than solicited ones. But this is not 22 Figure 6: Percentage of solicited and unsolicited ratings. necessarily true for the other equilibrium. This explains δ > 0 in the regression of sovereign rating grades on solicitation status (table 4).14 Conditional on the rating, unsolicited ratings are associated with higher or lower yields depending on the equilibrium. In the equilibrium with ancillary services, q(0, H)−q(1, H)> 0 and q(0, L)−q(1, L) = 0, hence, unsolicited ratings are associated with lower yields whereas in the equilibrium without, q(0, H)−q(1, H)<0 and q(0, L)−q(1, L) = 0, they are associated with higher yields. High unsolicited ratings are associated with a higher q(0, H) because they reveal a type A perfectly (type B chooses to buy ancillary services). This result is in line with δ < 0 in the regression of sovereign yields on solicitation status (table 6). 4 Conclusion To what extent rating agencies strategically downgrade their unsolicited ratings? The answer to this question is relevant for policy because it matters to determine if the rating agencies may have misbehaved. In this paper I propose a model that assumes away strategic motivations for unsolicited ratings by assuming true-telling on the part of the CRA. The degree of market selection in equilibrium depends on the market size and other market characteristics. The model is, hence, able to explain both the downward bias in unsolicited ratings for certain categories of borrowers (banks, insurance, corporates) as well as the upward bias for sovereign borrowers. The equilibrium with positive selection on unsolicited ratings is generated thanks to the possibility to enter a private contract with the CRA with a confidentiality clause (e.g. ancillary services). This also allows us to explore in which circumstances the value of opacity 14This effect would disappear if we could control perfectly for the type, which we assume we cannot do here since it is private information. 23 for some borrowers can be marketed by the CRAs. When the rating agencies cater to both the borrowers that have incentives to be transparent as well as those that prefer opacity, they still provide the market with valuable information but the amount of information might be biased towards a particular group of borrowers. An extended version of the model presented in this paper, properly calibrated, could be able to deliver a useful benchmark for the downward natural bias as a function of the characteristics of the market under study. Identifying the “natural size” of the market selection bias would help to detect the presence of strategic motivation and, hence, inform policy intervention. 24 References Bannier, C., Behr, P., and Guettler, A. Rating opaque borrowers: Why are unsolicited ratings lower? Review of Finance, 14:263–294, 2010. Behr, P. and Guettler, A. The informational content of unsolicited ratings. Journal of Banking & Finance, 32:587–599, 2008. Bolger, A. and Wigglesworth, R. Dash for trash lifts unrated debt sales. 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