# Using posterior variable in credit risk model

I am rebuilding a credit risk model using logistic regression (either ridge penalty or elasticnet) to predict first payment default. Historically, the company approves an applicant for a loan to purchase products. The approval amount is based upon the historical model's predictive probability of default. The approval amount is very correlated with the overall risk of the applicant.

The applicant then can use up to the approval amount to purchase products. The actual loan dollar amount is the amount the customer used for purchases. So if a person gets approved for \$10k he could only use$3k to purchase products.

My question is this. Should I input the approval amount as an additional predictor in the model? i.e. if a person was approved for \$10k or$5k. A person's approval amount affects how much he could borrow and consequently affects his ability to repay.

The problem is that when the model is used in production we use the output of the model to determine the max approval amount for an applicant.

My current thought is to use the approval amount as a predictor. When the model is in production input a median value for the prediction amount. I.E. if the median person is approved for \$8K then everyone will get$8k as the value for the approval amount independent variable.

I should also mention that I am less interested in prediction accuracy but more in discriminative power (i.e. AUC or KS stat).

• Based on your explanations I don't think "approval amount " would be a meaningful predictor for 3 reasons (1) it seems that amount actually borrowed is smaller than approval amount , (2) actual amount and approval amount are likely to be highly correlated, and (3) approval amount seems to be an endogenous variable (at least to some extent) – Umka Feb 27 '19 at 10:14
• It's true that 'approval amount' is an endogenous variable. The problem with excluding it is that it would make 1. Sampling bias even worse (there is already bias because we only have performance data on people who are approved & take the loan) 2. bias the model (since giving smaller approval amounts to riskier applicants would cause their probability of default to drop) Do you have any ideas to correct for these issues? – Shall Way Feb 27 '19 at 16:47
• Difficult to answer your question. I would use instrumental variables (see stats.stackexchange.com/questions/172508/…) but don't know whether in your case this is possible at all. – Umka Feb 27 '19 at 19:11