A Debt Risk-Warning Model for Local Government Financing Platforms

EASTERN ACADEMIC FORUM
A Debt Risk-Warning Model for Local Government Financing
Platforms
PENG Wangxian, YE Shujun
Beijing Jiaotong University, Beijing, 100044
[email protected]
Abstract: The scale of debt of local government financing platforms in China has been expanding
rapidly in recent years. The potential risks have caused widespread concern in Chinese society; however,
in academia, there are different concerns about such levels of debt risk related to lack of credibility of
the evaluation system. This study establishes a debt risk-warning model using pattern recognition
methods and collects 158 bonds of local government financing platforms as research samples. Finally,
this study analyzes an example application of this model.
Keywords: Financing platform, Debt risk, Risk-warning model
1 Introduction
Local government financing platforms (LGFPs) are a special kind of state-owned enterprise that
performs investment and financing functions for local government. Since the 1990s, LGFPs in China
have raised huge amounts of money for the construction of urban infrastructure and promoted the
process of urbanization, but they have also produced debt risk. With the surge in debt of LGFPs, the
debt risk of local government has sparked widespread concern in Chinese society. Debt risk warnings
are key measures to control debt risk, and thus, academics have begun substantial and thorough research
into these measures. Liu Yi [1], Wang Xiaoguang & Gao Shudong [2], Chen Guanyou [3], Xie Chunxun [4],
Zhou Qing [5], and other researchers establish debt risk-warning models for local governments or LGFPs
by means of different measurement methods, which provide an important theoretical basis for risk
warning and control. However, these models generally have disadvantages, such as small sample size,
simple methods, and lack of theoretical basis. Based on the abovementioned research, this study collects
158 bonds of LGFPs released in 2012 as research samples, and establishes a new model by using pattern
recognition methods.
2 Debt Risk Evaluation Index
This study summarizes a debt risk evaluation index for local government presented by the mentioned
scholars mentioned in the Introduction. The study establishes a debt risk evaluation index system in
combination with a corporate financial performance evaluation system. The evaluation index includes
five categories, namely, level of economic development, financial strength and structure of government,
government solvency, scale and performance of LGFPs, and LGFP solvency, as well as 12 subindexes,
as shown in Table 1.
Index Categories
Level of economic
development
Financial strength and
structure of government
Government solvency
Table 1 Debt Risk Evaluation Index of LGFPs
Subindexes
Formula
GDP
= GDP
GDP per capita
= GDP / Resident population
Financial strength of government
= Disposable financial resources
= Rigid expenditure / Disposable financial
Rigid income–expenditure ratio
resources
= Government debt balance / Disposable
Financial debt service ratio
financial resources
591
EASTERN ACADEMIC FORUM
Debt burden rate
Land revenue debt service ratio
Scale factor
Return on equity
Asset–liability ratio
Current ratio
Cash flow debt ratio
Scale and performance
of LGFPs
LGFP solvency
= Government debt balance / GDP
= Land revenue / Government debt balance
= Total assets sorting quantile
= Net profit / Average total assets
= Total liabilities / Total assets
= Current assets / Current liabilities
= Net operating cash / Current liabilities
3 Debt Risk Warning Model
This study collects 158 bonds of LGFPs released in 2012 as research samples and sets the bond issuer
credit rating as the risk rating. For construction of the model, refer to the research of Du Zhitao et al. [6]
3.1 The study sample and data processing
The sample comprises the following credit rating levels: 18 AA+ and above, 101 AA, and 39 AA−. To
increase discrimination, the 101 AA samples are divided into 34 AAc, 33 AAb, and 34 AAc sublevels,
according to bond rates. Furthermore, the AA−, AAc, AAb, AAa, and AA+ and above levels are defined
as highest risk, high risk, moderate risk, low risk, and lowest risk, respectively.
The sample data are collected from the prospectus and local government websites. This study calculates
the index values of all samples and standardizes them using a min−max standardized approach.
3.2 Warning model based on pattern recognition methods
3.2.1 Classification rules
This study sets classification status to w. w1, w2, w3, w4, and w5 stand for highest risk, high risk,
moderate risk, low risk, and lowest risk, respectively. All possible values of risk evaluation indexes
constitute a 12-dimensional eigenvectors space, x=[x1, x2 …, x12] T. A particular vector x is mapped to a
class of w using the Bayesian decision method based on the minimum error rate, that is, the
classification rules of the training sample. The Bayesian formula is as follows:
p ( x | wi ) P ( wi ) , i,j=1,2,3,4,5
(1)
P (w | x) =
i
5
 p( x | w
j
)P(w j )
j =1
Where p(wi) is the a priori probability of risk status and p(wi︱x) is the posterior probability of risk
status. Then, the Bayesian decision condition of x∈wi is p(wi︱x) = p(wj︱x). If a group discriminant
function gi(x),i=1,2,..5 satisfies:
gi(x)= p(wi︱x) or gi(x)= p(x︱wi)P (wi) or gi(x)=Ln[ p(x︱wi)P (wi)]
(2)
then the Bayesian decision condition of x∈wi is converted to gi(x)＞gj(x)(i≠j). First, we calculate the
discriminant function gi(x). Then, we choose the class that corresponds to the maximum value as a result
of the decisions.
3.2.2 Pattern recognition
Assuming that the possible values of all indexes show a normal distribution, the observed values of the
12 indexes x constitute a multivariate normal distribution and the following probability density function
is obtained:
1
 1

P ( x | wi ) =
exp − ( x − μ )T Σ −1 ( x − μ ) 
N
(3)
2


( 2π ) 2 | Σ |
Where μ=E{x} represents the N-dimensional mean vector of each category x and μ=[μ1, μ2, .., μN]; Σ is
an N × N-dimensional covariance matrix, with Σ=E{(x-μ)(x-μ）T}; Σ-1 is the inverse matrix of Σ; and |Σ|
is the determinant of Σ.
592
EASTERN ACADEMIC FORUM
In the multivariate normal distribution, the smallest error rate discriminant is set as:
gi(x)=Ln[ p(x︱wi)P (wi)]
(4)
According to Formulas (3) and (4), under the multivariate normal distribution p(x|wi)~N(μi,
Σi),i=1,2,3,4,5, we obtain the following discriminant function:
g i (x) = −
1
N
1
( x − μ i ) T Σ i−1 ( x − μ i ) −
ln 2 π − ln | Σ i | + ln P ( w i )
2
2
2
(5)
Because (N/2)Ln2π is not related to i, this can be simplified as:
1
1
( x − μ i ) T Σ i−1 ( x − μ i ) − ln | Σ i | + ln P ( w i ) = x T W i x + w iT x + w io
2
2
Where W i = − 1 Σ i−1 (n×n-matrix), w i = Σ i− 1 μ i (n-dimensional column vector), and
2
1
1
w i 0 = − μ iT Σ i−1 μ i − ln | Σ i | + ln P ( w i )
2
2
gi (x) = −
(6)
3.2.3 Establish parameters and discriminant function of training samples
As mentioned in Section 2, the debt risk evaluation system of LGFPs has 12 indexes, that is, n=12. All
sample indicators show the multivariate normal distribution by parameter estimation. We set the a priori
probabilities as: P(w1)=0.2, P(w2)=0.2, P(w3)=0.2, P(w4)=0.2, and P(w5)=0.2. The parameters of the
conditional probability density function (Σ1, Σ2, Σ3, Σ4, and Σ5) are a 12×12-matrix, and μ1, μ2, μ3, μ4,
and μ5 are 12-dimensional column vectors. We input the index value of 158 samples into Formula (6)
and the discriminant function is calculated as follows (a large amount of data are omitted).
x1
x2
g1 ( x ) =
...
T
213.89
...
− 73.60
x12
x1
g 2 ( x) =
T
x2
6.56
6.56
...
...
−3.79
7.14
T
x2
...
−83.42
5.38
x1
x2
g 4 ( x) =
...
x12
T
x1
T
...
− 38.40 ...
...
x12
g5 ( x) =
− 259.54
... − 73.60
... 21.75
...
...
... − 28.66
213.89
− 123.90
...
21.75
x12
x1
g3 ( x) =
− 998.82
5.38
x12
−3.79 x1
7.14 x2
...
...
...
... −21.43 x12
...
1.91
82.31
+
x1
...
1.91
− 4.27
x1
x2
...
...
6.61
x12
64.91
T
x2
− 76.79
...
T
− 15.29
− 8.65
...
− 2.94
x1
7.27
x2
− 8.65
− 51.51 ...
15.02
x2
33.89
x2
...
...
− 2.94
...
15.02
...
9.63
x12
x1
6.61
x2 140.60
+
...
...
x12
19.19
...
...
...
... − 29.56 x12
(8)
(9)
x12
16.05
− 115.34
...
11.77
x12
− 9.80
x1
−40.19
16.05
...
4.61
+
(7)
x12
T
19.07
−4.27 x2
57.48
+
...
...
...
...
... − 23.92 x12 55.46
...
4.61
... 11.77
...
...
... − 22.60
x1
x2
− 29.08
...
37.02
−33.06 ...
...
T
x1 106.48
x2
15.77
+
...
...
T
x1
x2
− 68.16
...
x12
x1
...
− 69.50
(10)
(11)
4 An Example
This study analyzes the debt risk of a LGFP in 2012. First, we collect the relevant data of this LGFP and
the local government. Then, we calculate and standardize the LGFP’s index values, as shown in Table 2.
593
EASTERN ACADEMIC FORUM
Table 2 Debt risk evaluation index value of a LGFP
Index Categories
Subindexes
Index Values
Standardization
Level of economic
development
GDP
391.70 hundred million
0.03
GDP per capita
7.94 ten thousand
0.50
Financial strength of government
294.88 hundred million
0.21
Rigid income–expenditure ratio
34.37%
0.00
Financial debt service ratio
71.03%
0.50
Government solvency
Debt burden rate
Land revenue debt service ratio
53.47%
0.86
1.00
0.70
Scale and performance of
LGFPs
Scale factor
0.80
0.80
Financial strength and
structure of government
LGFP solvency
Return on equity
6.63%
0.11
Asset–liability ratio
66.27%
0.74
Current ratio
Cash flow debt ratio
3.40
−0.25
0.29
0.25
By inputting standardization to Formulas (7)–(11), this study obtains the debt risk state of this LGFP in
2012 as follows: g1(x)=−18, g2(x)=−15, g3(x)=−23, g4(x)=−129, and g5(x)=−7. As g5(x) is the
maximum, the debt risk of this LGFP is the lowest risk status and its bond credit rating should be at the
level of AA+ and above. This may be related to the high level of economic development of the region,
good financial flexibility, a large-scale LGFP, and high land revenue.
5 Conclusion
This study established a debt risk evaluation index system for LGFPs. On this basis, it established an
early warning model by pattern recognition methods and collected 158 bonds of LGFPs as research
samples. Through case studies, the model provides analytical tools of risk management and
decision-making for financial institutions. These can be used to assess the credit risk of LGFPs. In
addition, the model provides theoretical references for local governments and regulatory authorities
establishing debt risk-warning systems. The model has the following disadvantages. First, the model
samples are of more efficient LGFPs, which are identified by regulatory authorities to comply with
conditions for issuing bonds. This means that the model has good value for operation specifications and
larger LGFPs, but not others. Second, the measure of risk in the model is based on historical data, but in
reality, the debt risk of LGFPs is dynamic under the influence of the macroeconomic environment,
regulatory systems, industrial policy, financial operations, and other factors. The warning of debt risk for
LGFPs is a complex scientific issues and this study provides only a preliminary exploration. Further
study is required.
Acknowledgements:
We thank the financial supports from the National Nature Science Foundation of China (71072028).
References
[1]. Liu Yi, Liu Xing, Ma Qianzhen, Liu Yuanchun. A Study on Monitor System and Empirical
Analysis for Local Fiscal Risk. Journal of Central University of Finance & Economics. 2004, 7:
1-5 (in Chinese)
[2]. Wang Xiaoguang, Gao Shudong. Early Warning Evaluation and Control of Local Government
Debt Risk. Contemporary Economic Research. 2005, 4: 53-55 (in Chinese)
594
EASTERN ACADEMIC FORUM
[3]. Chen Guanyou. A Tentative Discussion of the Evaluation and Control of the Debt Risk of Local
Governments. Journal of Xiangnan University. 2007, 8: 32-36 (in Chinese)
[4]. Xie Chunxun, Lei Chunhai. Research on Debt Risk Early Warning System of Local Government.
Modern Management. 2007, 5: 40-42 (in Chinese)
[5]. Zhou Qing. Study on the Risk Management and Measurement of Investment and Financing
Platform of Local Government. Hongqing University. 2011: 60-62 (in Chinese)
[6]. Du Zhitao, Li Lingjuan, LI Fan. Research on Operation Risk Forecasting and Early Warning of
Enterprise Intellectual Capital. Statistics and Decision. 2011, 7: 59-63 (in Chinese)
595