Forecasting University Funding: A Non-Linear Approach
Bibliographic record
Abstract
Are enrollment-based funding formulas really dependent on enrollment? The recent changes in funding for universities in the province of Quebec, Canada, suggests a disconnect between subsidies and enrollment despite the funding being enrollment based. This disconnection is observed when using a linear model to forecast the funding of the different universities in Quebec. The results show that simply considering linear mechanisms in the models consistently underestimates the funding. This paper explores the importance of taking into consideration these non-linear mechanisms in the funding formula. We estimate the funding models with non-linear vector autoregressive and the margins of error with bootstrap methods. This allows us to directly estimate the funding formula, and thus the non-linear components. We find that the non-linearities are important to explain the funding trends. In particular, the smoothing mechanism, the increase in funding per student and other exceptions leads subsidies to increase despite a stagnation or a decline in enrollment. Moreover, the model developed in this article also provides a ready-made recipe for forecasts in other jurisdictions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".