Bond yield and credit rating: evidence of Chinese local government financing vehicles

Abstract

Excessive borrowing of local governments in China sparked concerns that the debt may threaten the financial stability of the economy and ultimately cause economic collapse. It becomes critically important to understand the credit rating of China’s local government financing vehicle (LGFV) bonds and the association between the yields, credit ratings, and bond characteristics under this circumstance. We use a complete pooled data set of 771 LGFV bond issues from 1999 to 2011 and OLS and two-stage-least-squares regressions to examine how credit ratings might affect LGFV bond yields and an ordered probit model to study the determinants of credit ratings. The main findings are: (1) bond characteristic variables, such as duration and guarantee, matter in determining yields though credit rating plays a major role in determining yields of LGFV bond issues; (2) bond issue size and bond type are the main determinants of LGFV bond credit ratings, while the bond issuer characteristics have little explanatory power; (3) at least in Eastern China, smaller credit rating agency tend to give better ratings after controlling for bond issuer and issue characteristics.

Appendix: The ordered probit model for credit rating

Credit ratings are often viewed as important assessments of firms’ underlying credit risk as certified by rating agencies such as Moody’s and Standard & Poor’s. Without such certification, firms who want to borrow from the public debt and loan markets may not be able to do so, and investors would be reluctant to lend money to the firm (Sufi 2007). Credit ratings may also contain information on firms’ credit quality beyond other publicly available information. For instance, firms may be reluctant to release information to the market that would compromise their strategic programs, in particular with regard to competitors. Credit ratings in comparison allow them to incorporate inside information without disclosing specific details to the public at large. Credit ratings can be viewed as resulting from a continuous, unobserved creditworthiness index. Each credit rating corresponds to a specific range of the creditworthiness index, with higher ratings corresponding to a higher range of creditworthiness values. Since the credit rating representation of creditworthiness is a qualitative ordinal variable, the estimation of a model for such a dependent variable necessitates the use of a special technique.

Consider the simple case of a qualitative unordered dichotomous dependent variable, i.e., a variable that can take only two values (such as yes or no, on or off). Assume that this variable, represented as a 0–1 binary variable, is modeled as a linear function of a set of explanatory variables and of an error term. The predicted values from the estimation of this model should fall mainly within the 0–1 interval, suggesting that they could be interpreted as probabilities that the dependent variable takes the value 0 (or 1), given the values of the explanatory variables. However, such estimated probabilities can fall outside the 0–1 range. Various distribution functions are available to constrain the estimated probabilities to lie in the range (0, 1), the most frequently used being the cumulative standard normal probability function and the logistic function. The probit model makes use of the former, while the logit model makes use of the latter. If the qualitative dependent variable can be classified into more than two categories (i.e., if it is a polychotomous variable), estimation can be undertaken by means of the multinomial probit or the multinomial logit models, which are generalizations of the binary probit and logit models. However, the credit rating representation of creditworthiness is not only a polychotomous qualitative variable; it is also an ordinal variable, i.e., a variable with an inherent order (unlike a polychotomous variable representing, say, choices of colors or travel destinations). An ordinal polychotomous dependent variable would usually be coded as 0, 1, 2, 3, and so on. This representation reflects only a ranking; it is not known to what extent going from 0 to 1 is different from (or equivalent to) going from 2 to 3. For such an ordinal dependent variable, using multinomial probit or logit would not be efficient, because these models would misspecify the data-generating process in assuming that there is no order in the different categories that the dependent variable can take.

The ordered multinomial probit (OMP) is used for estimation in the context of an ordinal polychotomous dependent variable (Kao and Wu 1994). While taking into account the existence of a ranking, the OMP also assumes that the size of the difference between any two adjacent ratings is not known but does not matter to the carrying out of the analysis, unlike, for example, the usual regression techniques, where the size of the difference between adjacent elements is known and matters to the carrying out of the analysis.

Assume that the unobserved continuous measure, creditworthiness, is a linear function of a set of explanatory variables ${\text{x}}$, with parameter vector $\beta$, and an error term $\varepsilon$:

$$\widetilde{y} = \beta^{{\prime }} x + \varepsilon$$

(3)

As usual, $\widetilde{y}$ is unobserved. What is observed are the credit ratings assigned to the bonds, which range from AAA to A−.

$$\begin{array}{*{20}l} {y = AAA} & {if\quad \widetilde{y} \le \mu_{1} } \\ {y = AA + } & {if\quad \mu_{1} < \widetilde{y} \le \mu_{2} } \\ { \ldots \ldots } & {} \\ {y = A + } & {if\quad \mu_{5} \le \widetilde{y}} \\ \end{array}$$

(4)

This is a form of censoring. The $\mu$s are unknown partition boundaries (or cut points) that define the ranges of the creditworthiness index (i.e., AAA, AA+, AA, AA−, A+, A, A−); these parameters must be estimated in conjunction with the vector. Estimation proceeds by maximum likelihood.

It is assumed that $\varepsilon$ is normally distributed across observations, and the mean and variance of are normalized to zero and one. With the normal distribution, the following probabilities result (for simplicity, AAA, AA+, AA, AA−, A+, A and A− are denoted as 7, 6, 5, 4, 3, 2 and 1 respectively), where is the cumulative function of a normal distribution:

$$\begin{aligned} prob(y = AAA) = \phi (\mu_{1} - \beta^{{\prime }} x) \hfill \\ prob(y = AA + ) = \phi (\mu_{2} - \beta^{{\prime }} x) - \phi (u_{1} - \beta^{{\prime }} x) \hfill \\ \ldots \ldots \hfill \\ prob(y = A + ) = 1 - \phi (\mu_{5} - \beta^{{\prime }} x) \hfill \\ \end{aligned}$$

(5)

A likelihood function can be formed as follows:

$$L({y \mathord{\left/ {\vphantom {y x}} \right. \kern-0pt} x}) = \sum\limits_{k = 1}^{n} {\left\{ {Y_{1k} \times \ln \phi (\mu_{1} - x_{k}^{{\prime }} \beta ) + \sum\nolimits_{i = 2}^{5} {Y_{ik} \times \ln \left[ {\phi (\mu_{i} - x_{k}^{{\prime }} \beta ) - \phi (\mu_{i - 1} - x_{k}^{{\prime }} \beta )} \right] + Y_{5k} \times \ln \phi (\mu_{4} - x_{k}^{{\prime }} \beta )} } \right\}}$$

(6)

where $Y_{ik}$ is an indicator variable that takes on the value one if the realization of the $k$ th observation $Y_{k}$ is the $i$ th rating, and zero otherwise. Once the likelihood function is formed, the estimation of the unknown parameter μ’s and β’s can be undertaken. The estimated cutoff points, μ’s, along with the estimated β’s, maximize the log-likelihood function stated above.