公司财务预警LOGIT模型最优分界点实证研究

An Empirical Study on the Optimal Critical Value of Logit Model for Company Financial Early Warning

在利用Logit模型对企业的财务困境或违约进行预测时,现有文献往往将0.5作为判别财务困境或违约与否的标准,没有考虑最优分界点与样本配比和误判成本之间的联系。最优分界点的选择应当满足使整体错误分类率达到最小,或者使整体错误分类成本达到最小。分界点的设置不仅取决于两类错误的成本,还取决于模型构建者在样本选择时所设置的样本配比比例。本文给出了在误判成本最小化基础上最优分界点的理论推导过程和计算步骤,并对1:1和1:3样本配比情况下的最优分界点进行比较研究,发现无论是1:1还是1:3样本配比,第一类错误相对于第二类错误的成本越大,最优分界点就应该选择较小的值;在设定的1/1、1/5、1/10这三种成本比值下,两种样本配比情况下的最优分界点都小于0.5;在1:3的样本配比下,适当的分界点不仅能保证分类的准确性,还能更好地控制第一类错误,减小分类错误成本,而样本配比比例进一步提高可能会出现分界点过小的情况。

When Logit model is applied to predict company financial early warning or default probability, most literatures use 0. 5 as critical value to forecast financial distress, however, this practice overlooks the relationship between the optimal critical value and sample pairing proportion or misclassification cost. The choice of the optimal critical value of Logit model shall meet the requirements to minimize the overall misclassification rate or integral misclassification cost, that is, the optimal critical value not only depends on the cost of two types of misclassification, but also depends on the sample pairing proportion that reflects the prior probability. Based on minimizing the integral misclassification cost, the theoretical analysis, formula deduction and practical calculation procedures of the optimal critical value are given and the comparative study in different setting of sample pairing proportion （ 1 ： 1 and 1 ： 3） are also presented in this paper. The results show that, either 1 ： 1 or 1 ： 3 sample pairing proportion, the larger the cost of the first type of error is, the smaller optimal critical value should be chosen; when cost ratio is set to 1/1, 1/5 and 1/10, the optimal critical value is less than 0. 5 on either 1 ： 1 or 1 ： 3 sample pairing proportion ; when sample pairing proportion is 1 ： 3, a proper optimal critical value not only can ensure the accuracy of the classification, but also can control the first type of error and reduce the misclassification cost; further increases on sample pairing proportion may cause a much smaller optimal critical value.