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Application of regression function model based on panel data in financial risk management of bank resource allocation

Pubblicato online: 15 Jul 2022
Volume & Edizione: AHEAD OF PRINT
Pagine: -
Ricevuto: 21 Feb 2022
Accettato: 17 Apr 2022
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
Introduction

The credit rating of the lender is a basic link of the internal rating system of commercial banks, and its accuracy has a direct impact on the effect of the entire internal rating system [1]. The definition and expression of credit rating are different, but the core concept is the same: Banks determine a series of factors that affect credit risk in advance, and use a combination of qualitative and quantitative methods to rate customers' credit, which is to judge the solvency of customers. It is also an important basis for commercial banks to improve their management level, achieve scientific lending, and reduce bank operating risks. Under the “Basel New Capital Accord”, this is the basis for banks to conduct capital supervision and economic capital accounting[2].

Various commercial banks in China have actively invested in the development of internal rating systems, and began to research and implement credit rating models and systems for corporate loan application customers. A mature financial risk management system for bank resource allocation is shown in Figure 1 below [3]. However, the newly established various credit rating systems have many immaturities. It is an important task for Chinese banking industry and banking supervision departments to insist on testing and improving the existing credit rating system and developing a credit rating model that conforms to the characteristics of Chinese economy [4]. This paper will take the credit rating system of a state-controlled commercial bank in China as an example, innovatively use the ranking response panel data model with random effects to test and analyze it, and put forward ideas and suggestions for improving the existing credit rating system.

Figure 1

Bank resource allocation financial risk management system

At present, the bank's rating system contains many subjective judgment components, such as the setting of indicator weights and the analysis and judgment of evaluation indicators, which are all scored by experts, and the results will inevitably lose objectivity and fairness. In order to scientifically and reasonably carry out credit rating of customers, make the rating results more accurate, more conducive to the bank's risk management work, and rationally allocate bank funds, it is very necessary to carry out a scientific measurement test on the existing credit rating system.

One of the spirits of the new Basel agreement is to allow banks to develop and choose their own risk prediction models according to their own circumstances, thus changing the “one-size-fits-all” risk measurement model of the old agreement. To test and adjust the credit rating system to make it more flexible and reasonable to reflect its own market characteristics and operational characteristics, which reflects the core spirit of the New Basel Accord and is an important breakthrough in the field of internal rating [5].

Research Methods
Discrete choice model based on panel data

The benefits of panel data analysis compared to models based on cross-sectional data are clear. First, panel data enriches data information. It can provide information in two dimensions of cross-section and time series, which increases the data information and greatly improves the accuracy of estimation and forecasting. Second, panel data analysis allows the existence of missing values in the calculation process. Therefore, the estimation results of panel data analysis are more effective and have stronger predictive power. Third, panel data analysis reduces the degree of collinearity. Due to the homogeneity of observed objects in credit rating data, it is particularly prone to collinearity[6]. As Tucker pointed out, collinearity is more likely to occur between financial indicators because of the same numerator or denominator. The practice of simply incorporating data from all epochs into the calculation without temporal differentiation is quite detrimental [7]. The panel data model can increase the variability of each variable and effectively reduce the harm of collinearity. Fourth, and most importantly, panel data can effectively capture the heterogeneity of observed objects. Statistical econometric models require that observation samples be independent of each other. However, in general statistical econometric models, observed individuals in the same period are not absolutely independent, and they are simultaneously affected by the same macroeconomic environmental factors. The panel data model comprehensively considers These common factors, and technically distinguish them.

Panel data model makes econometric analysis more comprehensive and specific, so it has been developed rapidly. However, a large number of research works are based on continuous dependent variable models. In comparison, there are few panel data studies on discrete dependent variable models. Ronghua and Hansheng pointed out[8]: Compared with a large number of panel data model studies on continuous response, the research on binary response panel data model is much less; as for the ranked response panel data model, related research is even rarer[9]. In practice, the latter has practical significance.

This paper is an exploration of this field, extending the testing ideas of Wang Heng and Shen Lisheng to the field of panel data analysis, and for the first time introducing a ranking response panel data model with random effects, so as to conduct the evaluation of the bank's existing credit rating system. In-depth analysis and inspection. Rabe-Hesketh and Skrondal[10] combined the adaptive numerical integration method and maximum likelihood estimation, and proposed an estimation and prediction method to solve the discrete response panel data model. The author uses this method for model parameter estimation and prediction work.

We first introduce the basic framework of the ranking response model based on panel data. In this basic framework, random effects in the model are not considered for now. This is actually a “pseudo-panel data” model. In the existing research work on discrete dependent variable models using panel data, this method is mostly used. g{Pr(yit>s|x1it,xkit,xmit)}=logit{Pr(yit>s|x1it,xkit,xmit)}=ln{Pr(yit>s|x1it,xkit,xmit)1Pr(yit>s|x1it,xkit,xmit)}=α+Xitβκs \matrix{ {g\left\{ {{P_r}\left( {{y_{it}} > s|{x_{1it}}, \ldots {x_{kit}}, \ldots {x_{mit}}} \right)} \right\} = \log it\left\{ {{P_r}\left( {{y_{it}} > s|{x_{1it}}, \ldots {x_{kit}}, \ldots {x_{mit}}} \right)} \right\}} \hfill \cr { = \ln \left\{ {{{{P_r}\left( {{y_{it}} > s|{x_{1it}}, \ldots {x_{kit}}, \ldots {x_{mit}}} \right)} \over {1 - {P_r}\left( {{y_{it}} > s|{x_{1it}}, \ldots {x_{kit}}, \ldots {x_{mit}}} \right)}}} \right\} = \alpha + {X_{it}}\beta - {\kappa _s}} \hfill \cr } Where β = (β1it, β2it,…), Xit = (x1it, x2it,…), and category-specific parameter κs. In research work, it is usually expressed in the form of a “latent variable” model, and its model structure is: yit*=α+Xitβ+εityit={1,ifyit*κ12,ifκ1<yit*κ2S,ifκs1<yit* \matrix{ {y_{it}^* = \alpha + {X_{it}}\beta + {\varepsilon _{it}}} \hfill \cr {{y_{it}} = \left\{ {\matrix{ {1,\,if\,y_{it}^* \le {\kappa _1}} \hfill \cr {2,\,if\,{\kappa _1} < y_{it}^* \le {\kappa _2}} \hfill \cr \ldots \hfill \cr {S,\,if\,{\kappa _{s - 1}} < y_{it}^*} \hfill \cr } } \right.} \hfill \cr } In the basic framework we set, it is assumed that α and β do not vary correspondingly across individuals or periods. Xit includes all measurable factors that affect the grade results. ɛit is the random error term of the model, representing those unobservable random factors. ɛit obeys the logit distribution and is independent of each other; ɛit and Xit are also independent of each other. In reality, however, the independence assumption cannot be guaranteed. In terms of business operation, the same factors (such as macroeconomic background) affect each enterprise every year[11].

In the above model, we assume that the slope βk of the independent variable is fixed, and the different residuals ɛit are assumed to be independent of each other. The random effect model established below takes into account the possibility of random coefficients, and relaxes two assumptions according to the actual situation: one is that βk is no longer constant, it will have time effects, and changes in independent variables in different periods will affect the factors. The degree of influence of the variable will no longer remain unchanged; the second is that we divide ɛit into two parts ζt and ζit, ζt represents the randomness of the intercept term of the model, so the intercept term is no longer a fixed value, it is the same It has a time effect and will change with different t, and ζit still represents the unpredictable factors of different individuals in different periods. That is, the model changes to: yit*=α+Zit(β1+λt)+(Xit*)β2+ζt+εityit={1,ifyit*κ12,ifκ1<yit*κ2S,ifκs1<yit* \matrix{ {y_{it}^* = \alpha + {Z_{it}}\left( {{\beta _1} + {\lambda _t}} \right) + \left( {X_{it}^*} \right){\beta _2} + {\zeta _t} + {\varepsilon _{it}}} \hfill \cr {{y_{it}} = \left\{ {\matrix{ {1,\,if\,y_{it}^* \le {\kappa _1}} \hfill \cr {2,\,if\,{\kappa _1} < y_{it}^* \le {\kappa _2}} \hfill \cr \ldots \hfill \cr {S,\,if\,{\kappa _{s - 1}} < y_{it}^*} \hfill \cr } } \right.} \hfill \cr }

The application of the panel data model with random effect sorting response in the field of bank credit rating

There are many financial indicators that can reflect the company's operating conditions. Chen and Shimerda [12]pointed out that there are more than 100 financial ratios used to analyze business performance in a large literature, of which about 50% have been proved to be significant in at least one study. Therefore, careful selection of financial ratios is critical to conducting an effective study of corporate credit ratings. According to the characteristics of financial ratios, this paper divides all financial ratios into four categories: solvency ratio, financial benefit ratio, development capability ratio and asset operation ratio. The specific financial ratios used are shown in Table 1.

Financial ratios used in the model

Solvency ratio Financial benefit ratio Development capacity ratio Asset Operating Conditions Ratio
Assets and liabilities (alr) 、 Earned interest multiple (ei) 、 Current ratio (qr) 、 Total debt ratio/EBITDA (le) 、Total capitalization ratio (ba) 、Net cash flow from operating activities/total debt (ncfl) Roe (nra) 、Roa (rota) 、OPE (nri) 、Cost profit margin (roce) 、 Main business cash ratio (cfi) Sales (Operating) Growth Rate (sgr) 、Total asset growth rate (assetsgr) 、 Capital accumulation rate (agr) 、Three-year average profit growth rate (pgr) Total asset turnover (tat) 、 Inventory turnover (it) 、Current asset turnover (cat) 、 Accounts Receivable Turnover (ar)

We established a “pseudo-panel data” model (Model 1) and a panel data model with random effects (Model 2). Through the comparison of the two models, it is judged which model can better test the existing rating system. In the two models, the asset-liability ratio, the current ratio, the main business profit ratio, the current asset turnover ratio, the capital accumulation ratio, the total capitalization ratio, the net cash flow/total debt from operating activities, and the cost and expense profit ratio are 8 Financial ratios are all statistically significant. In the second model, the coefficients of the five financial ratios of asset-liability ratio, current ratio, main business profit ratio, current asset turnover ratio, and capital accumulation ratio show randomness. After model adjustment, the estimated results are shown in Table 2.

Estimated results of the ordinal response panel data model with/without random effects

Model 2 Model 1

exp(b) Std. Err [95% Conf. Interval] exp(b) Std. Err [95% Conf. Interval]
alr 11.837 (0.000) 8.021 3.136, 44.675 10.734 (0.000) 7.283 2.839,40.57
cr 0.987 (0.398) 0.112 0.892,1.333 0.902 (0.301) 0.090 0.741,1.097
nri 0.055 (0.000) 0.040 0.013,0.231 0.034 (0.000) 0.025 0.008,0.146
cat 0.724 (0.000) 0.048 0.636,0.824 0.760 (0.000) 0.044 0.680,0.851
agr 0.844 (0.010) 0.056 0.741,0.961 0.838 (0.007) 0.055 0.737,0.954
ba 2.901 (0.048) 1.563 1.009,8.338 2.817 (0.052) 1.500 0.992,8.000
ncfl 0.404 (0.001) 0.113 0.234,0.698 0.566 (0.027) 0.146 0.342,0.937
roce 0.001 (0.003) 0.000 0.000,0.001 0.002 (0.000) 0.000 0.000,0.001
Variances and covariances of random effects
level 2 (year) var(1):0.072var(2):0.005var(3):0.079var(4):18.070var(5):0.041var(6):0.010

We use these two models for prediction and estimation, and obtain the probability value pr(i) of each loan application customer obtaining different grades. The expected rating is the predicted expected value of each loan application customer's credit rating, and its calculation formula is: i=110i×pr(i) \sum\limits_{i = 1}^{10} {i \times {p_r}\left( i \right)} The prediction error of the model can be obtained by subtracting the expected level from the original level. Since some observations contain missing values of some financial indicators, these observations need to be eliminated during model prediction. Finally, we get 1229 qualified prediction objects, and the statistical results are shown in Table 3.

Model prediction error statistics

Model 1 Model 2

Prediction error Number of prediction objects Percentage Cumulative percentage Prediction error Number of prediction objects Percentage Cumulative percentage
0 100 8.14 8.14 0 545 48.27 48.27
−1 105 8.45 16.68 −1 110 9.74 58.02
1 103 8.38 25.06 1 119 10.54 68.56
−2 127 10.33 35.39 −2 105 9.30 77.86
2 97 7.89 43.29 2 101 8.95 86.80
−3 106 8.62 51.91 −3 58 5.14 91.94
3 76 6.18 58.10 3 56 4.96 96.90
−4 89 7.24 65.34 −4 18 1.59 98.49
4 73 5.94 71.28 4 17 1.51 100
−5 68 5.53 76.81
5 61 4.96 81.77
−6 34 2.77 84.54
6 63 5.13 89.67
−7 24 1.95 91.62
7 25 2.03 93.65
8 37 3.01 96.66
9 41 3.34 100
Total 1229 100 100 Total 1129 100 100
Experiment result

For a clearer comparison of the predictive power of the two models, a plot of the prediction error distribution is presented (Figure 2). In Figure 2, the two line graphs represent the prediction error distributions of Model 1 and Model 2, respectively. The abscissa represents the error between the expected level predicted by the model and the grading result obtained by the original bank rating system, and the ordinate represents the number of observation objects falling into each error level.

Figure 2

Model prediction error distribution

The full-sample prediction estimation for the model is actually a test of the fitness of the model. Comparing the results of the two models shows that even though the model parameter estimates are not very different, their predictions are quite different. For the second model, the model prediction was completely correct in 48.27% of the time, and the percentage of the prediction level error within two levels reached 86.8%. The prediction accuracy rate of multivariate classification is much lower than that of binary classification model. This paper uses a 10-category ranking response model, so the prediction effect of model two is quite ideal, which also shows that model two is not effective for real situations. The fit is quite high.

The prediction effect of model one is significantly weaker than that of model two. First, the prediction accuracy of Model 1 is much lower than that of Model 2. From Table 5, it can be seen that the prediction accuracy rate of Model 1 is only 8.14%, and the prediction error rate within two levels is only 43.29%. Such a low prediction accuracy indicates that the model cannot fit the original bank rating system ideally, so it cannot test the original system. Secondly, Figure 2 shows that the prediction error distribution of Model 2 is similar to a normal distribution, symmetrical to the left and right, but it exhibits the characteristics of “spiky peaks and thick tails”, and its maximum error level is controlled within four levels. This shows that when random effects are included, the prediction error of the model can be effectively controlled, and the error distribution is uniform and symmetrical. Without random effects, the model prediction errors are scattered, and the maximum grade error reaches as many as nine grades, and the error distribution is left-biased. twenty one].

We can confirm that due to the consideration of the time effect of the data, the random effect is added to the model, and the prediction ability has been greatly improved, so the second model is suitable for further testing and analysis of the existing credit rating system.

According to the obtained data results, the analysis is as follows:

First, according to the estimation results of Model 2, even if the financial ratios for credit rating are reduced to 8, the model can still fit the original credit rating results well. This shows that there are redundant indicators in the original credit rating system. These redundant indicators cause multicollinearity, which directly affects the estimation results and predictive ability of the credit rating model.

Second, we found that the OR value corresponding to the two indicators of the asset-liability ratio and the total capitalization ratio in the estimation results exceeded 1. The OR value corresponding to the asset-liability ratio was 11.837, and the OR value corresponding to the total capitalization ratio was 2.901. The OR values corresponding to other financial indicators are all less than 1. This shows that the asset-liability ratio and the total capitalization ratio have a positive effect on the credit rating. The higher the asset-liability ratio, the higher the corresponding credit rating of the enterprise, and the worse the credit quality. The same goes for the overall capitalization ratio.

Third, we further found that the OR value corresponding to the cost-to-expense margin is quite small, only 0.001. This shows that although the cost profit margin is statistically significant, the model analysis results show that its impact on the credit rating is quite small. At the same time, in the existing rating system, the weight setting corresponding to the financial ratio is also quite small, only 0.02, which indicates that the financial ratio is not regarded as a particularly important indicator in the existing rating system; on the other hand, from From the original data, for each observation object, the fluctuation of the financial ratio is very small, indicating that the ratio cannot distinguish the credit rating of each observation object well. Therefore, we can judge that the cost-to-expense margin, although statistically significant, is indeed a redundant indicator that can be excluded from the existing rating system.

Fourth, according to the provisions of the bank's credit rating method, in the original credit rating system, the order of the weights corresponding to each financial ratio is: asset-liability ratio, main business profit margin, current asset turnover ratio, current ratio, Capital accumulation rate, net cash flow/total debt from operating activities, total capitalization rate, cost expense profit margin. Through the model, we can see that in fact, the order of the absolute value of the impact of each financial ratio on the credit rating is not completely consistent with the pre-set, and the order is: asset-liability ratio, total capitalization ratio, current ratio, Capital accumulation rate, current asset turnover rate, net cash flow/total debt from operating activities, main business profit rate, cost and expense profit rate. Therefore, according to the model test results, on the premise of ensuring the relative importance order of the original indicators, we can modify the weight settings of the original rating system accordingly, so as to conduct credit rating work more scientifically and reasonably. For example, in the existing rating system, the profit margin of the main business is regarded as the second most important financial ratio, but the model results show that its influence is far from enough, which means that the weight originally set by the system is not enough to reflect its importance In order to enhance its influence, its corresponding weight setting should be increased.

Fifth, an important feature of the rank-response panel data model with random effects is that the model not only considers the financial status of different companies at a certain point in time, but more importantly, it also comprehensively considers the financial status of the same company at different points in time. Financial changes and changes in credit rating. After considering the time effects of macroeconomic factors that act on each enterprise at different time points, the model can more completely describe the statistical measurement characteristics of the bank credit rating system from two aspects: cross-section and time series, so as to more reasonably evaluate the existing The rating system is checked for plausibility.

Conclusion

This paper combines the panel data model and the ranking response model, and establishes a random effect model considering the time effect, which is used in the inspection of the bank credit rating system. This model can make a preliminary assessment of the credit rating changes of loan applicants in the following years, and provide more scientific and objective evidence for the bank's credit extension work. This method overcomes the shortcomings of the existing evaluation methods, and at the same time retains the advantages of the logit model, which is easy to operate and easy to carry out economic interpretation, and is convenient for the test and use of the model, so it has strong theoretical and practical significance. The results of the empirical analysis show that this method can scientifically and reasonably test the existing rating system of the bank, provide an important basis for the bank to revise the rating system, and can perform preliminary rating on loan applications and provide more objective credit rating results, thereby Improve the quality of bank loans and improve the efficiency of commercial banks in managing and distributing funds.

Figure 1

Bank resource allocation financial risk management system
Bank resource allocation financial risk management system

Figure 2

Model prediction error distribution
Model prediction error distribution

Financial ratios used in the model

Solvency ratio Financial benefit ratio Development capacity ratio Asset Operating Conditions Ratio
Assets and liabilities (alr) 、 Earned interest multiple (ei) 、 Current ratio (qr) 、 Total debt ratio/EBITDA (le) 、Total capitalization ratio (ba) 、Net cash flow from operating activities/total debt (ncfl) Roe (nra) 、Roa (rota) 、OPE (nri) 、Cost profit margin (roce) 、 Main business cash ratio (cfi) Sales (Operating) Growth Rate (sgr) 、Total asset growth rate (assetsgr) 、 Capital accumulation rate (agr) 、Three-year average profit growth rate (pgr) Total asset turnover (tat) 、 Inventory turnover (it) 、Current asset turnover (cat) 、 Accounts Receivable Turnover (ar)

Estimated results of the ordinal response panel data model with/without random effects

Model 2 Model 1

exp(b) Std. Err [95% Conf. Interval] exp(b) Std. Err [95% Conf. Interval]
alr 11.837 (0.000) 8.021 3.136, 44.675 10.734 (0.000) 7.283 2.839,40.57
cr 0.987 (0.398) 0.112 0.892,1.333 0.902 (0.301) 0.090 0.741,1.097
nri 0.055 (0.000) 0.040 0.013,0.231 0.034 (0.000) 0.025 0.008,0.146
cat 0.724 (0.000) 0.048 0.636,0.824 0.760 (0.000) 0.044 0.680,0.851
agr 0.844 (0.010) 0.056 0.741,0.961 0.838 (0.007) 0.055 0.737,0.954
ba 2.901 (0.048) 1.563 1.009,8.338 2.817 (0.052) 1.500 0.992,8.000
ncfl 0.404 (0.001) 0.113 0.234,0.698 0.566 (0.027) 0.146 0.342,0.937
roce 0.001 (0.003) 0.000 0.000,0.001 0.002 (0.000) 0.000 0.000,0.001
Variances and covariances of random effects
level 2 (year) var(1):0.072var(2):0.005var(3):0.079var(4):18.070var(5):0.041var(6):0.010

Model prediction error statistics

Model 1 Model 2

Prediction error Number of prediction objects Percentage Cumulative percentage Prediction error Number of prediction objects Percentage Cumulative percentage
0 100 8.14 8.14 0 545 48.27 48.27
−1 105 8.45 16.68 −1 110 9.74 58.02
1 103 8.38 25.06 1 119 10.54 68.56
−2 127 10.33 35.39 −2 105 9.30 77.86
2 97 7.89 43.29 2 101 8.95 86.80
−3 106 8.62 51.91 −3 58 5.14 91.94
3 76 6.18 58.10 3 56 4.96 96.90
−4 89 7.24 65.34 −4 18 1.59 98.49
4 73 5.94 71.28 4 17 1.51 100
−5 68 5.53 76.81
5 61 4.96 81.77
−6 34 2.77 84.54
6 63 5.13 89.67
−7 24 1.95 91.62
7 25 2.03 93.65
8 37 3.01 96.66
9 41 3.34 100
Total 1229 100 100 Total 1129 100 100

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