Using Copulas to Model Time Dependence in Stochastic Frontier Models
Why this work is in the frame
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Bibliographic record
Abstract
We consider stochastic frontier models in a panel data setting where there is dependence over time. Current methods of modelling time dependence in this setting are either unduly restrictive or computationally infeasible. Some impose restrictive assumptions on the nature of dependence such as the "scaling" property. Others involve T-dimensional integration, where T is the number of cross-sections, which may be large. Moreover, no known multivariate distribution has the property of having commonly used, convenient marginals such as normal/half-normal. We show how to use copulas to resolve these issues. The range of dependence we allow for is unrestricted and the computational task involved is easy compared to the alternatives. Also, the resulting estimators are more efficient than those that assume independence over time. We propose two alternative specifications. One applies a copula function to the distribution of the composed error term. This permits the use of MLE and GMM. The other applies a copula to the distribution of the one-sided error term. This allows for a simulated MLE and improved estimation of inefficiencies. An application demonstrates the usefulness of our approach.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it