How we predict closure
Every private college in the database carries odds like “1 in 40”: of the colleges that looked like it, about one in forty closed within four years. This page explains where that number comes from. Two statistical models score each college; their scores are combined into a single ranking; the ranking is turned into odds by checking it against thirteen years of real closures; and the odds are raised for colleges showing any of five red flags.
- 1Describe each college, each year Enrollment and admissions from fall of the year being scored; finances from two fiscal years earlier, the newest that are public.
- 2aHazard logit A weighted checklist of eight factors.→ probability pH2bLightGBM 250 small decision trees, added together.→ probability pG
- 3Rank, then average Each model’s probability becomes a percentile among that year’s colleges. The blend score is the average of the two.
- 4Turn the rank into odds Look up how often colleges at that rank actually closed within four years, 2008–2020.
- 5Red-flag correction Raise the odds for colleges with any of five warning signs the models under-read.
- =Odds of closing within four years Shown as “1 in N”, where N is about one divided by the probability.
What exactly is predicted
The unit is a college-year: one college, described as it stood in one year. For each, the question has a yes-or-no answer: did the college close in the next four years? Closing means it stopped operating. A college absorbed by another counts as a merger, which gets its own odds; a name change is not an event at all. These labels were built from the federal IPEDS directory and the Education Department’s closed-school file, then checked by hand against known cases: Mills College’s absorption by Northeastern is a merger, Birmingham-Southern is a closure, and Sweet Briar, which announced it would close and was rescued, is neither.
The models cover private nonprofit four-year colleges that enrolled at least 200 undergraduates at some point. That is 1,498 colleges since 1998, 1,191 of them open in fall 2024. Over those years 175 closed and 56 merged. Smaller institutions, mostly yeshivas, seminaries and bible colleges kept alive by a religious sponsor, survive by different rules and are left out, and so are public colleges, which almost never close.
Every forecast uses only what was public at the time. A score for year t reads enrollment and admissions from fall t, but finances from fiscal year t−2, because the federal finance data is published about two years late. The 2024 scores read fiscal 2022 balance sheets. Automated tests check that the finances are lagged this way and that no training row’s outcome reaches into the years being forecast.
For college \(i\) in year \(t\), the outcome is
\[ y_{it} = \begin{cases} 1 & \text{if it closes in year } t+1, \dots, t+4 \\ 0 & \text{otherwise} \end{cases} \]and every model estimates \(\Pr(y_{it}=1 \mid x_{it})\), where \(x_{it}\) holds the inputs known in year \(t\).
Model 1: the hazard logit
The first model is a logistic regression, which works like a weighted checklist. Each factor multiplies the odds of closing by a fixed amount, and the multipliers stack. It is called a discrete-time hazard model because each year is treated as one more chance to close: a college that survives comes back the next year as a new row, with updated numbers.
It uses eight factors. Before fitting, each is trimmed at its 1st and 99th percentiles (so a college going from 20 students to 400 doesn’t swamp everything), gaps are filled with the typical value, and each is rescaled into standard deviations so the weights can be compared. The six institutional factors behave exactly as you would expect:
Show the numbers
The model also carries two demographic terms: the projected change in the number of high-school graduates in the college’s state, and that change for colleges that admit nearly everyone. Their weight comes from timing, not from which colleges close: closures rose in the same years the projections turned down. Treat them as controls for the era, not as evidence of the demographic cliff (see the Cox check below).
\(\tilde{x}\) is the trimmed and filled input, and \(\mu_k, \sigma_k\) are its mean and standard deviation in the training years only. The \(\beta\)s are fit by maximum likelihood, and \(e^{\beta_k}\) is the odds multiplier plotted above.
Model 2: LightGBM
The second model is a gradient-boosted tree ensemble, built with the LightGBM library. A single decision tree asks a few yes-or-no questions (enrollment down more than 30%? endowment under half a year of spending?) and gives each path through the questions its own risk. Boosting grows 250 small trees in sequence, each one aimed at the mistakes of the trees before it, and adds up their answers.
Trees find what the logit’s straight-line weights can’t. One is thresholds: risk barely changes as a college’s admit rate climbs from 35% to 95%, then jumps near 100%. Another is combinations: a small college that is also losing students is in more trouble than either fact alone suggests. LightGBM reads 15 inputs: the logit’s factors plus the application trend, the admit rate, the change in operating margin, years on record, and flags for colleges that stopped reporting admissions or finances (going quiet is itself a warning sign). The enrollment trend carries 29% of its splitting gain, endowment cover 14% and size 13%.
Closures are rare, about one college-year in sixty. To stop the trees ignoring them, each closure counts about 59 times as much as a survival. That makes the trees pay attention, but it inflates the raw probabilities: in 2024 the median college reads 3.7% and the highest 97%. That is why LightGBM’s probabilities are used only to rank colleges, never as odds.
Each \(f_m\) is a tree with at most 15 leaves and at least 30 college-years per leaf, fit to the gradient of the weighted log-loss left by the trees before it. The learning rate is \(\nu = 0.04\). Closures carry weight \(w = n_0/n_1 \approx 59\), the ratio of survivals to closures in training. Each tree sees a random 80% of rows and of inputs. A missing value is sent down whichever side of each split fits the data better.
Testing without peeking
A model scored on the same data it learned from always looks better than it is. So every score on this site comes from a rolling backtest. To score year T, both models are retrained from scratch using only college-years whose four-year outcome was already known by then, which means years up to T−5. Then they score year T. This is repeated for every year from 2008 to 2024. The 2016 scores never benefited from knowing who closed in 2017–2020, and the 2024 forecast was trained on 1998–2019: 27,195 college-years, 452 of them followed by a closure.
Both models are refit this way for every \(T\) from 2008 to 2024. A row from year \(t\) has its outcome settled by the end of \(t+4\), so \(t \le T-5\) is the latest training year that is fully settled before year \(T\) begins.
Combining the two models
The two models speak in different units. In 2024 the logit’s median college reads 1.0% and its highest 58%; LightGBM’s median reads 3.7% and its highest 97%. A plain average would let LightGBM’s inflated scale do all the talking. So each model’s probability is first turned into a percentile among that year’s colleges, and the blend score is the average of the two percentiles: an equal vote.
\(\operatorname{pct}_t\) is the share of year-\(t\) colleges with a lower probability, so \(s\) runs from 0 (safest) to 1 (riskiest).
The blend ranks better than either model alone (see how well it works).
From rank to odds
A rank says who is riskier, not how risky. To turn it into odds we look at history: among the 16,200 college-years from 2008 to 2020 whose outcome is known, how often did colleges at each blend score close within four years? An isotonic regression answers with a staircase that can only go up, so a riskier rank never gets lower odds, and otherwise follows the data as closely as it can.
Show the numbers
\(\mathcal{R}\) is the 16,200 resolved college-years of 2008–2020, 397 of them followed by a closure. The fit is the pool-adjacent-violators algorithm, interpolated linearly between its steps.
The red-flag correction
The staircase only sees the blend score. Two colleges with the same score get the same odds, even if one is failing the Education Department’s financial test and the other is not. Checked against history, colleges raising any of five red flags closed 1.4 to 1.9 times as often as their odds said. So each flag adds a fixed bump to the odds:
| Red flag | Raised when | Odds × |
|---|---|---|
| Failing ED score | The Education Department’s financial-responsibility composite score is below 1.0 (failing), fiscal year t−2. Scores for fiscal 2014–16 couldn’t be located, so the latest score up to three years older stands in. | 1.67 |
| Enrollment collapse | Lost a quarter of its undergraduates in three years. | 1.59 |
| Retention break | Under 60% of first-year students return, and enrollment is falling. | 1.40 |
| Small and shrinking | Under 400 undergraduates, and down more than 10% in three years. | 1.09 |
| Chronic deficit | Operating deficits three years running (fiscal t−4 to t−2), with under six months of spending in the endowment. | 1.05 |
Flags stack: a college with two flags gets both multipliers. A college with none keeps the staircase odds exactly. The last two flags add little once the others are counted. Most small, shrinking colleges have also lost a quarter of their students. And a chronic deficit on its own is already priced in, because the models read operating margin and endowment directly: chronic-deficit colleges with no other flag closed at 4.8%, against odds of 4.6%. The three enrollment and retention flags are the same ones that hold the demand grade at D or below. The two financial flags no longer affect the grade, but they still move the odds.
\(\ell(p) = \ln\frac{p}{1-p}\) is the log-odds, and \(\mathbf{1}_{f,it}\) is 1 if college \(i\) raises flag \(f\) in year \(t\).
The \(b_f\) are fit by maximum likelihood on the same 2008–2020 history, with \(\ell(p^{\text{base}})\) held fixed and no intercept. Leaving the intercept out is what keeps colleges without a flag exactly where the staircase put them. A bump that would come out negative is dropped, so a flag can only raise the odds. The multiplier in the table is \(e^{b_f}\).
The correction was tested before it was adopted. Fitted only on 2008–2016 and scored on 2017–2020, it moved every flagged group’s results toward the target and left everyone else alone:
Show the numbers
Worked example
Northland College, a small liberal-arts college in Wisconsin, against Syracuse University, both scored on fall 2024 data. In fall 2024 Northland had 286 undergraduates, down 46% in three years; in fiscal 2022 it ran a −28% operating margin with 0.29 years of spending in its endowment.
| Step | Northland College | Syracuse University |
|---|---|---|
| 2a. Hazard logit | 15.1%97.4th percentile | 0.09%6.0th percentile |
| 2b. LightGBM | 96.9%99.9th percentile | 0.26%17.0th percentile |
| 3. Blend score | 98.7 | 11.5 |
| 4. Staircase odds | 20.7%about 1 in 5 | 0.05%the floor |
| 5. Red flags | ×4.1 on the oddsfailing ED score, enrollment collapse, retention break, small and shrinking | noneunchanged |
| Odds of closing by 2028 | 51.5%about 1 in 2 | 0.05%fewer than 1 in 1,000 |
Step 5 for Northland: odds of 20.7% are 0.207 ÷ 0.793 = 0.26 to 1. Its four flags multiply that by 1.67 × 1.59 × 1.40 × 1.09 ≈ 4.1, to 1.06 to 1, which is a probability of 1.06 ÷ 2.06 = 51.5%. Northland closed in 2025. Fontbonne University, which also closed in 2025, was scored at 16% (1 in 6).
How well it works
On the forecast years 2017–2020, scored by models and a calibration that never saw them, 4,993 college-years were followed by 186 closures, a base rate of 3.7%. Two measures of how well the odds rank colleges: ROC is the chance that a college which closed was ranked above one that didn’t (0.5 is a coin flip, 1.0 is perfect), and the top-50 hit rate is the share of each year’s 50 highest-ranked colleges that closed within four years.
| Ranking by | ROC | Top-50 hit rate |
|---|---|---|
| Hazard logit alone | 0.837 | 21.5% |
| LightGBM alone | 0.819 | 21.5% |
| Blend of the two | 0.842 | 22.5% |
| Published odds (blend + red flags) | 0.851 | 28.0% |
Of the 50 colleges the published odds ranked highest each year, 28% closed within four years: 7.5 times the base rate. The ranking is the strong part. The level of the odds is the weak part, and it is worth being plain about why.
Show the numbers
Closures have become more common. From 2005 to 2015 about four colleges in this group closed each year; since 2016 it has been about thirteen. A staircase learned from earlier years can only repeat the rate it saw. Fitted on 2008–2016, it under-called 2017–2020 by about 1.4 times overall, even after the red-flag correction. The published odds are fitted on 2008–2020, which includes the faster pace. But if closures keep accelerating as the high-school class shrinks, read the odds as a floor rather than a ceiling.
Two models that check, but don’t vote
A Cox proportional-hazards model audits the logit. It leaves the overall closure rate in each calendar year free, so every factor has to explain which colleges close, not when. It agrees with the logit on every institutional factor. The demographic terms are the one place it disagrees: they drop to insignificance, which is how we know their weight in the logit comes from timing. Because it confirms rather than adds, it isn’t blended into the odds.
\(h_0(t)\) is an unrestricted baseline hazard by calendar year, so anything common to a year is absorbed there rather than credited to a factor.
A two-variable benchmark, a logit with only the enrollment trend and tuition dependence, keeps the bigger models honest. It is the best of all at the very top of the list: over 2013–2020, 27.5% of its top 25 each year closed, against 19.5% for the blend. But it ranks the rest poorly (ROC 0.72). The lesson: for the most doomed colleges, collapsing enrollment at a tuition-dependent school is close to the whole story. The full models earn their place across the rest of the list.
Merger odds
The database’s merger odds come from the same pipeline, steps 1 to 4, with “merged into another institution within four years” as the outcome. The red-flag correction is not applied to them.
What it can’t do
- The numbers are small. 175 closures in 27 years. Every estimate on this page rests on them, which is why the logit has eight factors and not thirty.
- Finances arrive two years late. A college can deteriorate quickly between the balance sheet the model reads and the year it scores.
- Closure versus merger is sometimes a judgment call. Federal records list Pine Manor College, absorbed by Boston College, as a closure. We follow the official records and log the conflicts rather than overrule them.
- Public colleges get no odds. They almost never close; states merge or rescue them. Their profiles show what the private model would say “if it were private”, as a gauge of financial strain, not a forecast.
- The demographic cliff is not yet visible in closures. The graduating class peaked in 2025. Its real test comes with the classes of 2026 and later, and with it the rising base rate described above.