Monotonic Constraints in Credit Models: Why a Model Should Never Punish Paying Down Debt
Monotonic Constraints in Credit Models: Why a Model Should Never Punish Paying Down Debt
Fit a credit model to 8,000 accounts without constraints and it will learn the sample's accidents along with its patterns. In a stylized test, 6 of 19 utilization steps ran backwards, and a borrower paying a card down from 32% to 27% was estimated as riskier. Forcing risk to rise with utilization removed every reversal and scored slightly better on 40,000 new accounts. Where the direction of risk is known, a constraint costs nothing and protects borrowers, reason codes and the lender.
What you'll learn
A model that punishes paying down debt
Credit card utilization is one of the most predictive variables in consumer credit, and its direction is not in dispute: holding everything else equal, a borrower using more of their available credit is riskier. Fit it from data, though, and the data will not always agree.
Take a stylized training sample of 8,000 accounts in which the true default rate rises smoothly with utilization. Split utilization into twenty five-point bands and estimate the default rate in each band directly from the sample.
| Utilization band | Accounts | Estimated default rate | True default rate |
|---|---|---|---|
| 25% to 30% | 641 | 7.55% | 6.18% |
| 30% to 35% | 637 | 6.50% | 7.18% |
Neither band is small. Each holds over 600 accounts, and the reversal is still produced by ordinary sampling variation. Per our small numbers analysis, a default rate estimated on a few hundred observations carries a confidence interval wide enough to swallow the difference between neighbouring bands. Across all twenty bands, 6 of the 19 steps run in the wrong direction.
A flexible model fitted to this data will learn those reversals. Gradient-boosted trees and similar methods are designed to find structure, and they will find it in noise unless told otherwise. The result is a model that, for some borrowers, rewards running up a balance and penalizes paying it down.
What a monotonic constraint does
A monotonic constraint tells the fitting procedure that the predicted risk must move in only one direction as a given variable increases. Isotonic regression, the classical version of the idea, pools adjacent bands that violate the ordering into a single estimate; modern tree-boosting libraries implement the same restriction directly in how trees are grown.
Apply it to the same sample and evaluate both versions on 40,000 fresh accounts.
| Model | Out-of-sample Gini | Reversals |
|---|---|---|
| Unconstrained band estimates | 0.3780 | 6 of 19 steps |
| Monotone-constrained estimates | 0.3792 | None |
The constrained model is slightly better on new data, not worse. The reversals were noise, so removing them removes error. That is the usual finding where the direction of an effect is genuinely known: the constraint costs nothing in discrimination and often gains a little, because it prevents the model from fitting the sample's accidents. Per our validation analysis, the improvement shows up only out of sample, which is exactly where it matters.
The gain is largest where data is thinnest. In this sample the biggest reversal sits at the top of the range, where the 90% to 95% band has 46 accounts and the 95% to 100% band only 16, and the unconstrained estimate actually falls from 30.9% to 26.5% as utilization approaches its limit. A borrower at the limit would be scored as safer than one slightly below it.
Why it matters beyond accuracy
- Adverse action reasons. Lenders must give applicants the principal reasons for a denial. Per our adverse action analysis and the CFPB's guidance on complex models, those reasons must be accurate. A non-monotone model can produce a reason such as "utilization too low" or imply that paying down a balance would hurt, which is both wrong and indefensible.
- Consumer behaviour. Per our utilization analysis, consumers are told to reduce utilization to improve their standing. A model that contradicts that advice for some ranges punishes people for following it.
- Gaming. Per our target analysis, any non-monotone region is a place where a borrower can improve a score by doing something riskier, and over time someone finds it.
- Fairness review. Per our proxy analysis, an erratic response curve is harder to examine for proxy effects, because its shape cannot be explained by the variable's meaning.
- Stability. Per our monitoring analysis, a model fitted to noise reacts to the next sample's noise, so its behaviour drifts between rebuilds for no real reason.
The first point is where the regulatory consequence lands. Per our explainability analysis, the explanation requirement is not satisfied by a mechanically correct attribution if the model's underlying behaviour is not sensible, and monotonic constraints are among the cheapest ways to make behaviour sensible by construction.
A credit model should never punish paying down a balance
Fitted without constraints, 6 of 19 utilization steps ran backwards in this sample, and the constrained model scored better on new data. HL Hunt AI Underwriting applies monotonic constraints wherever the direction of risk is known, so reason codes stay accurate and borrowers are never penalized for reducing debt.
Which variables should be constrained
| Variable | Direction | Constrain? |
|---|---|---|
| Utilization | Higher is riskier | Yes |
| Number of recent delinquencies | More is riskier | Yes |
| Months since most recent delinquency | Longer is safer | Yes |
| Debt-to-income ratio | Higher is riskier | Yes. Per our income estimation analysis, also handle estimation noise near thresholds |
| Age of oldest account | Older is generally safer | Usually yes |
| Number of open accounts | Non-monotone in reality: none and very many are both risky | No. Constrain only a transformed version, or leave it free |
| Recent inquiries | More is generally riskier | Usually yes, with care for rate-shopping windows |
The sixth row is the warning. A constraint imposed on a relationship that is genuinely non-monotone forces the model to be wrong. A thin-file borrower with no open accounts and a borrower with dozens are both riskier than one with a handful, and forcing a single direction loses that. The discipline is to constrain only where domain knowledge is clear, and to document the reason for each constraint.
The case against constraining by default
Some practitioners resist monotonic constraints on the grounds that the data should speak and that domain beliefs encode the past. A relationship that was monotone in one economic period may not be in the next, and a constraint can hide a genuine change. The argument has merit for variables whose meaning is ambiguous. It is weak for variables like utilization and delinquency, where the direction follows from what the variable measures, not from historical correlation. The defensible position is to constrain those, leave ambiguous variables free, and monitor the partial dependence of free variables for reversals that would warrant a constraint later. Per our stability analysis, a population shift is a reason to re-check constraints, not to abandon them.
Building it in
- List every variable with a known direction and record the reason in the model documentation.
- Apply constraints in the fitting procedure, not by post-hoc adjustment of scores.
- Compare constrained and unconstrained models out of sample. Per our point-in-time analysis, use an out-of-time holdout, since that is where noise-fitting shows.
- Inspect partial dependence for every unconstrained variable and investigate any reversal.
- Test reason codes on borrowers who improve a constrained variable. The reason for their remaining risk should never be the improvement.
- Re-check constraints at each rebuild and when the population shifts.
Item five is the test that catches problems constraints miss. Interactions between variables can still produce behaviour that looks non-monotone along one dimension even when each variable is individually constrained. Per our model deployment analysis, a simple counterfactual test, lowering one borrower's utilization and checking that the score improves, belongs in every release.
Constraints, documented, and tested on every release
Monotonic constraints cost nothing in accuracy where the direction is known, and they keep reason codes defensible. HL Hunt AI Underwriting documents every constraint, compares constrained and unconstrained models out of time, and tests that improving a borrower's profile always improves the score.
Frequently asked questions
A rule forcing predicted risk to move in one direction as a variable rises, such as higher utilization never lowering risk.
Because unconstrained models fit sampling noise. Here a borrower paying down from 32% to 27% utilization was estimated riskier.
Not where the direction is known; here the constrained model was slightly more accurate on new data, 0.3792 against 0.3780.
They keep reasons sensible, so a model never cites an improvement such as lower utilization as a reason for risk.
Key takeaways
- Flexible credit models fit sampling noise unless told the direction of known effects.
- In a stylized sample, 6 of 19 utilization steps ran backwards, even in bands of over 600 accounts.
- The unconstrained model estimated a borrower paying down from 32% to 27% utilization as riskier.
- The monotone-constrained model removed every reversal and scored 0.3792 against 0.3780 on new data.
- Reversals concentrate where data is thin, such as the extremes of a variable's range.
- Direction matters for accurate adverse action reasons, consumer incentives, gaming, fairness review and stability.
- Constrain only where direction is clear; number of open accounts, for example, is risky at both extremes.
- Test every release by improving one borrower's profile and checking the score improves.
References
- Barlow, R. E., Bartholomew, D. J., Bremner, J. M., & Brunk, H. D. (1972). Statistical Inference Under Order Restrictions: The Theory and Application of Isotonic Regression. Wiley.
- Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794.
- Equal Credit Opportunity Act, 15 U.S.C. § 1691 et seq.; Regulation B, 12 C.F.R. § 1002.9 (notifications of action taken).
- Consumer Financial Protection Bureau. Circular 2022-03, Adverse action notification requirements in connection with credit decisions based on complex algorithms (May 2022).
This guide is educational and does not constitute legal, compliance, or model risk advice. All figures are stylized illustrations from a simulated sample with an assumed default curve, utilization distribution, sample sizes and band widths, and do not describe any particular model, lender or portfolio. Results from real data will differ. Adverse action, fair lending and model risk management requirements are governed by federal and state law and supervisory guidance; consult qualified advisers before relying on any approach described here.