Credit Scoring Model Based On Bayesian Methods For Small Businesses

In small business credit scoring, sample selection bias is commonly referred to as "reject inference", where partial observations of delinquent variables are missing due to a credit screening process of the bank.Sample selection bias may lead to biased parameter estimation, tehreby affects the accuracy of model prediction and the effectiveness of credit decision. Therefore, to imporve the sample selection bias is the crucial content of current credit scoring model studies.A literature review leads to the conclusion that most solutions currently proposed for reject inference are not fully validated. In this paper we propose a new reject inference technique based on Bayesian inference using bound and collapse firstly suggested by Sebastiani and Ramoni(2000). The intuition of this method is that it is possible to set a bound for possible estimates of missing data within an interval defined by some extreme distribution, no matter what the missing data mechanism is. The complete set of data will provide constrains on the interval. When information about the missing data mechanism is available, it is encoded in a probabilistic model of non-response and used to select a single estimate. The second step of BC collapses the interval to a single value of missing data. By this method a randomly imputed datum will be generated to replace the missing datum so that samples with complete data can be prepared for the evolution of small business credit scoring model.Based on the2003National Surveys of Small Business Finances (NSSBF) datasets we design an experiment to test the power and efficiency of the proposed model. Firstly, we develop a credit scoring model to predict the probability of credit delinquency based on logistic regression by use of the first sample. Applying this credit scoring model to the second sample, we simulate a credit granting policy. A selected sample is obtained by applying a credit cutoff policy. Secondly, we simulate the process of how the small business credit scoring model loses its classification power during its evolution based on those incomplete samples. And then we apply two sources of data to estimate the missingness function. The missingness mechanism is computed as a weighted average of both external and internal information. Finally, a value for each missing datum is simulated and imputed to generate a complete sample. Based on this new sample we establish three new models.The proposed reject inference technique is compared against an ideal model where the missing outcome data for the second sample are known and against the case named censored model where no adjustments are made for the missing data. To investigate the robustness of the model we simulate two credit granting policies by applying two cutoff scores, so that the degree of missingness is different across two selected samples and the degree of bias is also different. By comparing these three models’performances through K-S test, Brier score, ROC curve and bad rate, we conclude that the proposed bound and collapse Bayesian imputation procedure will efficiently improve classification power of the small business credit scoring evolution model, which indicates that BC method is of great efficiency in the small business credit scoring to relieve the sample selection problem due to missing data not at random...