Industry-level Econometric Estimates of Energy-capital-labour Substitution with a Nested CES Production Function
Bibliographic record
Abstract
Despite substantial interest in the role of energy in the economy, the degree of substitutability between energy and other production inputs, and the way energy should be included in the production function remain unresolved issues. Our study provides industry-level parameter estimates of two-level constant elasticity of substitution (CES) functions that include capital, labour and energy inputs and allow for technological change for Canada. In contrast to many existing studies, we do not impose prior restrictions on the order of input nesting, and we report the estimates for three possible specifications. We find that a nested production structure which first combines labour and energy into a composite good that is then combined with capital, fits the Canadian data best, in terms of respecting the restrictions imposed by cost minimization. We also find rather low elasticities of substitution between capital and labour, and limited evidence of exogenous technological change. / Malgré l'intérêt considérable par rapport au rôle de l'énergie dans l'économie, le degré de substituabilité entre l'énergie et autres facteurs de production, et la façon dont l'énergie devrait être introduite dans la fonction de production restent des questions non résolues. Notre étude fournit, pour le Canada, des estimations sectorielles des élasticités de substitution de fonctions de production de type CES emboîtées à deux niveaux, qui combinent le capital, le travail et l'énergie, et qui prennent en compte le changement technologique. Contrairement à de nombreuses études existantes, nous n'imposons pas de restrictions a priori sur l’ordre de l’emboîtement dans les fonctions CES, et nous présentons les estimations pour les trois spécifications possibles. Nous avons trouvé qu'une structure de production imbriquée qui allie le travail et l'énergie dans un facteur composite, qui est ensuite combiné avec le capital, correspond mieux aux données canadiennes, en ce qui a trait au respect des restrictions imposées par la minimisation des coûts. Nous avons également trouvé des élasticités de substitution relativement faibles entre le capital et le travail, et une très faible évidence pour un changement technologique exogène.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".