信用卡違約因素之研究 -Logit與Probit Model 之應用

Abstract

摘 要 近年來台灣地區卡債引發金融風暴，本文探討卡債問題的成因，其中因持卡人與金融機構資訊不對稱，產生的逆選擇問題，並出現道德風險，以致違約率提高。因此，為避免或減低銀行因信用卡呆帳金額之增加，導致提高其授信逾放比，而對發卡銀行之經營績效產生負面影響，在事先的預防重於事後的補救前提下，發卡銀行在發卡前之審核及對申請者的信用評比都須加以重視。 本文應用2007年國內A銀行六萬筆(五萬筆隨機抽樣正常戶及一萬筆隨機抽樣違約戶)的樣本資料進行違約因子相關性分析，並採用下列十個解釋變數: 性別、年齡、職業等級、教育程度、婚姻狀況、卡別、年消費金額、年循環金額、信用額度、居住地區等進行實證分析。 應用 Probit model 的實證分析結果得到以下的結論: 性別、年齡、職業等級年消費金額、卡別、年循環金額、信用額度、居住地區在統計顯著水準α=0.01 及0.05 時呈現和違約正相關:至於教育程度、婚姻狀況、年消費金額在α=0.05下都違約呈負相關。此外，也應用 Logit model分析得到幾乎相同的結論，但是其中有一個例外，即年循環金額在 Logit all sample model中不具解釋能力。 另外，為了檢視我們估計出的模型之優劣，進一步應用 CAP 曲線和 ROC 曲線對模型的預測能力進行比較分析，結果發現在樣本內資料， Probit model 和 Logit model 預測能力幾乎相同，預測能力都相當高。但在樣本外的部分，CAP 曲線和 ROC 曲線呈現相同的結果。都十分具有預測能力，其中 ROC 曲線的預測能力又比CAP曲線表現的更佳，幾乎在5%以後就不會發生預測錯誤的機率，因此從 CAP 曲線和 ROC 曲線可以發現兩個模型的預測能力都相當高。 本文提供了一個計量模型，使決策者能在給定特定條件下，估計出一個違約的機率的估計值，並供決策者進行參考。

Abstract This paper investigates the determinants of credit card default in Taiwan. Informational asymmetry between credit cardholders and financial institutions cause the problems of adverse selection, moral hazard and the violation of contract. Our sample includes 60,000 cardholders (both 50,000 from general data and 10,000 randomly selected data) from the Bank A in year 2006 to conduct empirical studies. We select 10 explanatory variables: sex, age, career, education, marriage status, credit card type, yearly expenditure, yearly recursion usage, credit amount, residence area etc. The empirical evidence with the Probit model and the Logit model shows that sex, age, career, credit card type, yearly expenditure, yearly recursion usage, credit amount and residence area are statistically significant to explain the default of credit card. However, there is one exception that the variable of yearly recursion usage cannot explain the default in the Logit model of all sample data. In addition, we use the CAP curve and the ROC curve to analyze the predictable ability and have found that the Logit model perform is the same as the Probit model. While both models have predictable ability with out of the sample, we also can say that two models perform perfect. The empirical evidence could provide a “standard” operational procedure to directly predict the violation probability of an credit card applicant.