α-returns to scale with quasi-fixed inputs: an application to Québec hospitals
Bibliographic record
Abstract
This paper focuses on the determination and estimation of the optimal size of hospitals. To determine the optimal size of a production unit, we use the measurement of returns to scale (RTS) at the decision-making unit level. When the RTS are constant, the unit is deemed of optimal size as the average total cost is at its minimum. As we deal with public service in a non-market environment, we have to take into account the fact that hospitals may not operate efficiently. To estimate the required production frontier we adapt the α-returns to scale method (a DEA type algorithm compatible with non-convexity of the production set) to include quasi-fixed factors. This methodology is applied to Québec hospitals at different points in time in order to capture the effect of the restructuring of the public health system over the last three decades. We conclude that by relying more on larger institution the scale efficiency of the public system has increased. However, in spite of the large reduction in the number of small hospitals and their replacement by very large structures, the movement may have gone too far, as most of the large institutions tend to exhibits decreasing returns to scale.
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".