Using Copulas to Model Time Dependence in Stochastic Frontier Models
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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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 | 0.008 | 0.025 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".