## 1 Introduction

^{1}

^{2}The main objective of our paper is to investigate whether an advertisement-based business model may provide sufficient incentives for a CRA to generate accurate ratings when increasing the precision of its ratings is costly.

^{3}Our analysis reveals that the incentive-compatible compensation structure identified by Kashyap and Kovrijnykh (2016) can in fact be implemented by an advertisement-financed business model with state-contingent revenues. Moreover, since revenues are obtained from a third party, namely advertisers, this business model does not suffer from the potential problem of ‘rating shopping’ associated with the issuer-pays model (see, e.g., Skreta and Veldkamp (2009)) or the problem of the investor-pays model that too many investors could ‘free ride’ by obtaining photocopies (see, e.g., White (2010)).

^{4}

## 2 The model

_{t}, which can be good or bad, τ

_{t}∈{g,b}. A good project is successful with probability α and fails with probability 1 − α, while a bad project always fails.

^{5}The project’s type is unknown a priori: All agents believe ex ante that the project is good with probability λ, and bad with probability 1 − λ, where 0 < λ ≤ 1/2. This assumption that good projects are scarce creates a role for the CRA to acquire information in order to find out whether a project is good or bad and facilitates the analysis.

^{6}

_{t}be the CRA’s effort exerted to increase the informativeness of the signal about the project’s type in period t, and let the probability that the signal is favorable, given that the project is good, be

_{t}in the precision of the signal entails a cost of c(s

_{t}), with \(c(0)=c^{\prime }(0)=0,\ c^{\prime }(s_{t})>0\) for s

_{t}> 0 and \(c^{\prime \prime }(s_{t})\geq 0\). We assume that the CRA’s effort is unobserved by firms and investors and unverifiable. Thus, the CRA cannot be directly rewarded for exerting effort to acquire more precise signals. Typically, a CRA’s incentives come from possible reputation cost it incurs when it provides inaccurate information. We address the issue in the following reputation game. In the spirit of Kreps and Wilson (1982) and Milgrom and Roberts (1982), let the CRA be one of two types, 𝜃 ∈{C,O}, i.e., committed to receive a perfectly informative signal \(\left (C\right ) \) or opportunistic (O) in which case it may obtain an imperfect of even completely uninformative signal. Note that one could alternatively assume that the ‘committed type’ faces zero costs of increasing the signal precision. The CRA’s types are private information and investors believe that, at the beginning of period 1, these types are randomly drawn with probability

^{7}That is, the CRA disseminates only correct information. The assumption is made to capture, in a simple way, the fact that, otherwise, the CRA may face potential legal damage. By contrast, Mathis et al. (2009) treat the CRA’s information production technology as exogenous and focus on the CRA’s incentive of misreporting, i.e., giving a good rating when the CRA believes that the project is bad. We will extend our basic framework below to allow for both, shirking and misreporting, as in Kashyap and Kovrijnykh (2016).

_{1}= 1/2, whereas the opportunistic CRA type chooses an effort level of 0 ≤ s

_{1}≤ 1/2. Each CRA type then observes a signal and reports it truthfully on its website in the form of a rating, r

_{1}∈{L,H}. The firm sets R

_{1}, 0 ≤ R

_{1}≤ X, i.e., the return to investors if the project is financed and successful. Investors then choose whether to visit the website or not. Their prior belief at the beginning of period 1 that the CRA is committed to obtain perfectly informative signals is φ

_{1}(see left tree in Fig. 1). This is interpreted as the CRA’s reputation for receiving precise signals at the beginning of period 1. When investors visit the website, they observe the reported rating and update their prior beliefs according to Bayes’ rule. Based on these interim beliefs, they decide whether to invest in the project or not (see right tree in Fig. 1). If the project is financed, investors’ interim beliefs are updated according to Bayes’ rule after the outcome of the firm’s investment project is observed - resulting in final beliefs. If the project is not financed, investors’ interim beliefs are not updated further. Investors’ final beliefs at the end of period 1 determine the prior beliefs of investors at the beginning of period 2, measuring the CRA’s reputation in that period. That is, like e.g. in Mathis et al. (2009), we make the standard underlying assumption that word-of-mouth emerges and evolves over generations within a network of investors.

^{8}This information structure ensures that all relevant information for the second-period decisions is summarized in the CRA’s reputation parameter φ

_{2}. Based on φ

_{2}, all stages of period 1, except nature’s initial choice of the CRA’s type, are then repeated in period 2.

## 3 Equilibrium analysis

_{t}and effort choice \(\tilde {s}_{t}\) in period t, investors will find it optimal to finance the project after observing an H-rating whenever

_{t}. For \(\hat {R}_{t}>X\), the firm cannot induce any investment, and we assume, without loss of generality, that R

_{t}= X in such a case. Furthermore, note that the firm cannot induce any investment when the investor observes an L-rating or when investors will not visit the website.

_{t}≤ X. That is, \(\hat {\varphi }_{t}\left (\tilde {s}_{t}\right ) \) the lowest CRA’s reputation at the beginning of period t such that (10) still holds.

^{9}and is an indicator function that yields 1 if \(\varphi _{2}\geq \hat {\varphi }_{2}\left (\tilde {s}_{2}\right ) \) and 0 otherwise. It is straightforward to show that the maximum of (12) is attained at s

_{2}= 0. To understand this, note that whether advertisement revenue is generated or not is determined solely by the market conditions, as captured by α, λ, and X, and by the investors’ beliefs φ

_{2}and \(\tilde {s}_{2}\), which cannot be influenced by the CRA in that period, whereas the marginal cost are \( c^{\prime }(s_{2})>0\) for all s

_{2}> 0. The second-period equilibrium play is summarized in the next proposition. The proof is placed in the Appendix.

_{2}= 0. Furthermore, investment takes place whenever the rating is good and \(\varphi _{2}\geq \hat {\varphi }_{2}\left (0\right ) \), where \(\hat {\varphi }_{2}\) is defined above, and no investment takes place otherwise.

_{2}, measuring the CRA’s reputation in that period. As a consequence, the opportunistic CRA may have an incentive to improve the precision of the signal in period 1. Note also that the main insights of this paper are not driven by the finiteness of the game. The reason is that the payoff in period 2 would be proportional to the net present value of future payoffs to the CRA in an extended version of the model with an infinite horizon. We start our analysis by identifying the opportunistic CRA’s optimal effort choice in period 1 for arbitrary investors’ beliefs \(\tilde {s}_{1}\). For this, note that the marginal expected revenue of a slightly higher informativeness of the signal is zero in two cases: first, when the CRA’s initial reputation φ

_{1}is so high such that \(\varphi _{2}\geq \hat {\varphi }_{2}\left (0\right ) \), independent of the project success in period 1, the CRA obtains positive advertisement revenue π > 0 in period 2 for sure. Second, when the CRA’s initial reputation φ

_{1}is so low that \(\varphi _{2}<\hat {\varphi }_{2}\left (0\right ) \), independent of the project success in period 1, the advertisement revenue is 0 in period 2. In both cases the CRA gains from reducing the precision of the signal in period 1 whenever \(c^{\prime }(s_{1})>0\), which is the case for all s

_{1}> 0. Nevertheless, we find that there is a range of reputation levels φ

_{1}, such that the CRA’s marginal expected revenue of increasing s

_{1}is positive, given arbitrary investors’ beliefs. The reason is that ratings produced with higher signal precision reduce the probability that the CRA is revealed to be opportunistic.

## 4 Misreporting

_{1}) > 0 for s

_{1}> 0, it is easy to see that constraint (15) cannot be fulfilled. Thus, in the Reputation building equilibria in which investors turn away whenever the CRA announces an L-rating, the CRA always has an incentive to inflate ratings. Furthermore, constraint (14) implies that the cost of improving the signal precision \(c\left (s_{1}^{\ast }\right ) \) has to be sufficiently small. Assuming that this cost is close to zero at s

_{1}= 1/2, we provide sufficient conditions for the existence of equilibria involving positive efforts and truth-telling under the advertisement-financed business model.