Evolution of production functions from Cobb–Douglas to machine learning methods

D.A. Kanametova

---

Abstract: The paper presents a comparative analysis of the classical Cobb-Douglas production function, its transcendental-logarithmic specification, and modern machine learning techniques used to model production processes.
Aim. The paper aims to show how increasing the complexity of the real-world production function leads to the superiority of machine learning methods for forecasting quality compared to the traditional Cobb–Douglas function, while still allowing for economic interpretation through the use of explainable artificial intelligence techniques.
Research materials and methods. A computational experiment was conducted with data including technological heterogeneity and nonlinear interactions between factors, ensuring an objective assessment of the accuracy of various approaches.
Results. It has been shown that the strict form of the Cobb–Douglas production function leads to systematic errors when applied to complex production structures, while the Translog model partially compensates for these limitations by incorporating interactions between quadratic terms. Machine learning methods, such as gradient boosting and multilayer neural networks, demonstrate the best forecast quality due to their ability to approximate complex, nonlinear relationships and account for hidden factors. The paper also discusses the potential of using SHAP techniques to interpret machine learning models, which helps to recover economically significant relationships and increase confidence in the results.
Conclusion: The outputs confirm the possibility of integrating machine learning algorithms into modern economic models of production functions

Keywords: Cobb–Douglas production function, transcendental logarithmic function, gradient boosting, machine learning, neural networks

For citation. Kanametova D.A. Evolution of production functions from Cobb–Douglas to machine learning methods. News of the Kabardino-Balkarian Scientific Center of RAS. 2025. Vol. 27. No. 6. Pp. 117–124. DOI: 10.35330/1991-6639-2025-27-6-117-124

References

1. Cobb C., Douglas P. Theory of production. American Economic Review. 1928. V. 18. No. 1. Pp. 139–165.
2. Arrow K.J., Chenery H.B., Minhas B.S., Solow R.M. Capital-Labor substitution and economic efficiency. Review of Economics and Statistics. 1961. Vol. 43. No. 3. Pp. 225–250.
3. Christensen L., Jorgenson D., Lau L. Transcendental logarithmic production frontiers. Review of Economics and Statistics. 1973. Vol. 55. No. 1. Pp. 28–45.
4. Вoldini D., Grisoni F., Kuhn D. et al. Practical guidelines for the use of gradient boosting for molecular property prediction. J Cheminform. 2023. Vol. 15. P. 73. DOI: 10.1186/s13321-023-00743-7
5. Rizkallah L.W. Enhancing the performance of gradient boosting trees on regression problems. J Big Data. 2025. Vol. 12. No. 35. P. 35.
6. Aggarwal Ch.C. Neural Networks and Deep Learning: textbook. Springer Cham, 2025. 529 p.
7. Chen T., Guestrin C. XGBoost: A scalable tree boosting system. KDD 16: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Pp. 785–794. DOI: 10.1145/2939672.2939785
8. Ke G., Meng Q., Finley T. et al. LightGBM: Highly efficient gradient boosting decision tree. Advances in Neural Information Processing Systems. 2017.
9. Tolstikhin I., Houlsby M., Kolesnikov A. et al. MLP-Mixer: An all-MLP architecture for vision. Neural Information Processing Systems. 2021. arXiv:2105.01601v4
10. Lundberg S., Lee S.I. A unified approach to interpreting model predictions. Conference: NIPS. 2017. DOI: 10.48550/arXiv.1705.07874
11. Tulio M., Singh S., Guastrin C. “Why should I trust you?”: Explaining the predictions of any classifier. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016. DOI: 10.1145/2939672.2939778

Information about the authors

Dana A. Kanametova, Candidate of Economic Sciences, Researcher, Institute of Applied Mathematics and Automation – branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
89 A, Shortanov street, Nalchik, 360000, Russia;
danocha_999@mail.ru, ORCID: https://orcid.org/0009-0000-6294-1015, SPIN-code: 6070-1196