Closure Lead-Time Analysis
Purpose. Measure how early the validated joint-weak G+A signal appears before a closure event in the validated lane. Specifically, score panel rows at T-1, T-2, T-3, T-4, and T-5 (years before the closure year T) for institutions that closed within the panel window, and compare these scores with the within-cohort distribution.
Method
- Restricted to FASB × Sector 2 institutions whose closure year was identified through HD
CLOSEDAT. - 108 closing institutions in the validated lane within the panel window.
- 269 pre-closure institution-year rows scoreable across T-1 through T-5 (subject to panel-window constraints; not every closing institution has a complete five-year pre-closure trail).
- Scores computed using the locked Phase-15 transforms (winsorisation bounds and robust-z parameters fit on the locked train years 2014–2016).
- The reference top-decile cutoff for joint-weak (≈ 0.974) is taken from the locked test cohort 2017–2018; pre-closure rows are flagged at this cutoff for descriptive purposes, not as a held-out validation step.
Score distribution by years-to-closure
| Years to closure | Pre-closure rows | Median joint-weak | Mean joint-weak |
|---|---|---|---|
| T-1 | 46 | 0.888 | 1.095 |
| T-2 | 54 | 0.846 | 1.036 |
| T-3 | 55 | 0.996 | 0.884 |
| T-4 | 52 | 1.097 | 0.874 |
| T-5 | 62 | 0.941 | 0.833 |
For context: the within-stratum median joint-weak score in the locked test cohort is approximately 0.06. Pre-closure medians of 0.85–1.10 are well elevated above the typical within-cohort score across the full T-1 through T-5 horizon.
Top-decile capture by years-to-closure
At the locked test-cohort top-decile cutoff for joint-weak (≈ 0.974), what fraction of pre-closure rows would have been flagged?
| Years to closure | Pre-closure rows | Flagged at top-decile cutoff | Capture rate |
|---|---|---|---|
| T-1 | 46 | 6 | 13.0 % |
| T-2 | 54 | 10 | 18.5 % |
| T-3 | 55 | 11 | 20.0 % |
| T-4 | 52 | 14 | 26.9 % |
| T-5 | 62 | 16 | 25.8 % |
Reading
- Lead time is at least five years. Joint-weak scores for closing institutions are elevated above the within-cohort median as early as T-5.
- The pattern is slow-burn, not late-stage acute. Median joint-weak score at T-1 (≈ 0.89) is similar to the median at T-5 (≈ 0.94). The geometry produces a multi-year early-warning signal rather than a coincident T-1 alarm.
- Top-decile capture across T-1 through T-5 is about 13 % to 27 %. Higher capture rates at T-4 and T-5 than at T-1 are most likely a panel-attrition artifact — some closing institutions stop filing IPEDS forms in the final year before closure, so T-1 has fewer scoreable rows.
What this does and does not establish
Useful precision–recall trade, not a perfect screen. About 74 % of T-5 pre-closure rows are not flagged by the top-decile cutoff. A subset of closing institutions in the validated lane is identifiable in the joint-weak top decile years before closure; many are not. This is consistent with a research-grade screen, not a per-institution prediction product.
- This analysis does not establish a per-institution closure-prediction claim, and it does not justify publishing per-institution scores or rankings.
- It does not extend the validated lane.
- It does not establish that joint-weak is uniquely structured to give early warning; G-only follows a similar pattern with slightly lower magnitudes.