Imposing Theoretical Regularity on Flexible Functional Forms
Bibliographic record
Abstract
In this paper we build on work by Gallant and Golub (1984 Gallant , A. R. , Golub , G. ( 1984 ). Imposing curvature restrictions on flexible functional forms . Journal of Econometrics 26 : 295 – 321 .[Crossref], [Web of Science ®] , [Google Scholar]), Diewert and Wales (1987 Diewert , W. E. , Wales , T. J. ( 1987 ). Flexible functional forms and global curvature conditions . Econometrica 55 : 43 – 68 .[Crossref], [Web of Science ®] , [Google Scholar]), and Barnett (2002 Barnett , W. A. ( 2002 ). Tastes and technology: Curvature is not sufficient for regularity . Journal of Econometrics 108 : 199 – 202 .[Crossref], [Web of Science ®] , [Google Scholar]) and provide a comparison among three different methods of imposing theoretical regularity on flexible functional forms—reparameterization using Cholesky factorization, constrained optimization, and Bayesian methodology. We apply the methodology to a translog cost and share equation system and make a distinction between local, regional, pointwise, and global regularity. We find that the imposition of curvature at a single point does not always assure regularity. We also find that the imposition of global concavity (at all possible, positive input prices), irrespective of the method used, exaggerates the elasticity estimates and rules out the possibility of a complementarity relationship among the inputs. Finally, we find that constrained optimization and the Bayesian methodology with regional (over a neighborhood of data points in the sample) or pointwise (at every data point in the sample) concavity imposed can guarantee inference consistent with neoclassical microeconomic theory, without compromising much of the flexibility of the functional form.
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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 | 0.016 | 0.095 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".