Estimation and Inference for Threshold Effects in Panel Data Stochastic Frontier Models
Bibliographic record
Abstract
One of the most enduring problems in cross-section or panel data models is heterogeneity among individual observations. Different approaches have been proposed to deal with this issue, but threshold regression models offer intuitively appealing econometric methods to account for heterogeneity. We propose three different estimators that can accommodate multiple thresholds. The first two, allowing respectively for fixed and random effects, assume that the firms' specific inefficiency scores are time-invariant while the third one allows for time-varying inefficiency scores. We rely on a likelihood ratio test with m − 1 regimes under the null against m regimes. Testing for threshold effects is problematic because of the presence of a nuisance parameter which is not identified under the null hypothesis. This is known as Davies problem. We apply procedures pioneered by Hansen (1999) to test for the presence of threshold effects and to obtain a confidence set for the threshold parameter. These procedures specifically account for Davies problem and are based on non-standard asymptotic theory. Finally, we perform an empirical application of the fixed effects model on a panel of Quebec dairy farms. The specifications involving a trend and the Cobb- Douglas and Translog functional forms support three thresholds or four regimes based on farm size. The efficiency scores vary between 0.95 and 1 in models with and without thresholds. Therefore, productivity differences across farm sizes are most likely due to technological heterogeneity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.020 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.004 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".