Semiparametric Estimation of a Corporate Bond Rating Model
2. Data and Variable Construction
Measuring Conflicts of Interest
3. Empirical Model
3.1. Model and Motivation for the Estimator
3.2. Estimation Strategy
4.1. Simulation Evidence
4.2. Empirical Illustration: Estimating Moody’s Rating Bias from 2001–2016
4.3. A Placebo Test for Rating Bias
4.4. Bias in Issuer Ratings
Data Availability Statement
Conflicts of Interest
Appendix A. Definitions and Assumptions
Appendix B. Asymptotic Theorems
Extensive literature addresses semiparametric models and the estimation of semiparametric single index models, including Härdle and Stoker (1989); Horowitz and Härdle (1996); Ichimura (1993); Klein and Spady (1993); Manski (1985); Powell et al. (1989). See Stewart (2005), Lewbel (2000), and Klein and Sherman (2002) for applications of a single-index model in the context of an ordered-response model.
Alternatively, one may also use the sieves method to estimate the rating probability. Such methods are more convenient when some prior information and constraints, such as monotonicity, additivity, and nonnegativity, needs to be incorporated in the conditional probabilities (Chen 2007). For instance, Coppejans (2007) estimates an ordered model with a quadratic-spline under the restriction that the distribution functions across all categories are the same. Such a constraint, however, is not appropriate in the current application because Moody’s rating standard can vary with categories.
Macro variables are not included because the model will be estimated separately for each year.
Moody’s was founded as a private company in 1900, acquired by Dun&Bradstreet (D&B) in 1962, and remained one of its divisions until 4 October 2000, when it was spun off and listed on the NYSE. The S&P has been a fully owned division of McGraw-Hill, a publicly traded company, since 1966. Going public makes CRAs more vulnerable to conflicts of interest. For example, Kedia et al. (2017) found that Moody’s assigned favorable ratings toward issuers that Moody’s shareholders have invested in.
From 2001 to 2010, Moody’s had two shareholders, Berkshire Hathaway and Davis Selected Advisors, which collectively own about 23.5% of Moody’s.
The numerical rating matches the seven ordinal rating categories: , and (from the highest credit quality to the lowest).
The vector is assumed to be exogenous throughout. Intuitively, and as one might have expected, some information contained in S, e.g., the manager’s ability, may also drive institutional investors’ investment decisions, implying that is endogenous. The problem of endogeneity can be handled, for example, using the control function approach proposed by Blundell and Powell (2004) provided with a valid exclusion restriction.
Specifically, the rating probability in an ordered-probit model is
Since the functional form of in (6) is not specified, conditioning on the original index and a linear transformation of them deliver the same amount information on ratings. Therefore, without some normalization, the limiting log-likelihood function cannot be uniquely maximized at the true parameters, which is necessary for identification.
More specifically, u is generated from a distribution, standardized to have a mean of zero and unit variance. , and is a standardized .
Confidence Intervals were constructed based on the asymptotic results derived in Appendix B.
The partial effects for MFOI in the ordered-response model are,
The Average Partial Effect, or APE, is computed by evaluating the partial effect for each bond i and averaging the computed effects,
The above calculation can be performed for any category. That is, even for a C-rated bond, one can compute the change in the probability of this bond being rated into AAA. To make the presentation concise and practically relevant, I only report the APE for the category that is one-notch better than the current rating grade. That is, I interpret the APE as the probabilistic change of obtaining a better rating grade if the issuer’s share-ownership relationship with Moody’s strengthens by .
The suggested trimming rule is indeed ad-hoc because the selected threshold may be bad for other DGP. The asymptotic theorems developed later abstracts away from the trimming issue. It is possible to develop a data-dependent optimal trimming rule similar to Ma and Wang (2019), which is left for future work.
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|Small Bandwidth||Large Bandwidth|
|Investment Grade (IG)||High Yield (HY)|
|Year||Aaa||Aa||A||Baa||Ba||B||C||Total||% of IG|
|HARRIS ASSOCIATES L.P.||21||2.42%||5.02%||0.00%|
|CHILDREN’S INV MGMT (UK) LLP||20||2.29%||5.31%||0.01%|
|SANDS CAPITAL MANAGEMENT, INC.||28||3.01%||5.59%||0.40%|
|T. ROWE PRICE ASSOCIATES, INC.||64||1.47%||5.94%||0.18%|
|BARCLAYS BANK PLC||55||2.52%||6.32%||0.03%|
|GOLDMAN SACHS & COMPANY||63||1.94%||7.24%||0.01%|
|VALUEACT CAPITAL MGMT, L.P.||13||5.19%||7.77%||0.93%|
|VANGUARD GROUP, INC.||64||3.79%||7.98%||1.64%|
|MSDW & COMPANY||57||2.20%||8.14%||0.22%|
|DAVIS SELECTED ADVISERS, L.P.||51||5.56%||8.14%||0.10%|
|FIDELITY MANAGEMENT & RESEARCH||64||1.99%||9.08%||0.00%|
|CAPITAL RESEARCH GBL INVESTORS||13||4.80%||11.31%||0.07%|
|CAPITAL WORLD INVESTORS||35||6.07%||12.60%||0.66%|
|BERKSHIRE HATHAWAY INC.||64||14.87%||20.43%||11.33%|
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Jiang, Y. Semiparametric Estimation of a Corporate Bond Rating Model. Econometrics 2021, 9, 23. https://doi.org/10.3390/econometrics9020023
Jiang Y. Semiparametric Estimation of a Corporate Bond Rating Model. Econometrics. 2021; 9(2):23. https://doi.org/10.3390/econometrics9020023Chicago/Turabian Style
Jiang, Yixiao. 2021. "Semiparametric Estimation of a Corporate Bond Rating Model" Econometrics 9, no. 2: 23. https://doi.org/10.3390/econometrics9020023