10 What the number is, and what it is not
An effect on the treated, and the limits that go with it
10.1 The answer
Running on a raised credit limit increases the chance of being 30+ days past due by +0.086 percentage points (SE 0.017, t = 5.0), against a base rate of 1.58%.
Small in absolute terms, and the opposite sign to where we started 1.58 pp away on chapter 2. ## What the number is, and what it is not
The estimate is an average effect on the treated. It describes what happened to the 13,819 accounts that actually received an increase.
That distinction has teeth here, because we know exactly how unlike the rest of the book those accounts are — chapter 2 put them at 0.022% delinquency against 1.669% for the others. So:
- It answers: for a customer like the ones we have been raising limits for, what does another increase cost? Good enough to price the decision you are already making.
- It does not answer: what would happen if we raised limits across the whole book? The accounts nobody raised are different in ways we cannot measure, which is the entire finding of chapters 1 and 2. Extrapolating onto them would repeat the mistake.
In units, yes. Both are linear probability models, so both are in percentage points of delinquency, and they belong on the same axis — which is why the chart on the overview puts all four together.
As quantities, no. The -1.585 pp from chapter 1 is not a bad estimate of the same thing; it estimates something else. It is a correct description of an association in this book: account-months on a raised limit really do show less delinquency than the rest. What it is not is the effect of raising a limit. Calling it “wrong” throughout is shorthand for “wrong answer to the question we asked”, not “badly computed”.
Keeping those apart matters when someone hands you a model. The question is rarely whether the number is calculated correctly. It is almost always which quantity it is a number for.
10.2 What this still does not settle
A fixed effect removes what is constant. It does nothing about what moves. If the lender raised limits in response to something that itself foreshadowed trouble — a jump in spending, a change in circumstances — that something is still in the residual, and this design cannot see it.
The flat pre-period above is reassuring but it is not proof. It says the treated accounts were not already drifting on the outcome we happen to measure. Something could still have moved in the months before the increase that this data does not record, and that the lender was reacting to.
Two more things are outside what was done here.
The timing chart is a diagnostic, not the estimator. Reading a profile like that properly — choosing the comparison group, handling the fact that different accounts get treated in different months, testing the pre-period as a formal assumption rather than eyeballing it — is its own method, with its own literature and its own failure modes. It gets a separate repository.
The effect is small and this is one dataset. +0.086 pp on a base of 1.58% is real and precisely estimated, and it is still one product, one lender, one stretch of time. Nothing here says the same number would appear elsewhere.
Everything above runs from 10-what-it-is.qmd. Shared setup R/_common.R. The panel itself is built by R/01-build.R.