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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.00032 |
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| _version_ | 1866908387670753280 |
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| author | Smirnov, Roman G. |
| author_facet | Smirnov, Roman G. |
| contents | In their seminal 1928 work, Charles Cobb and Paul Douglas empirically validated the Cobb-Douglas production function through statistical analysis of U.S. economic data from 1899 to 1923. While this established the function's theoretical foundation for growth models like Solow-Swan and its extensions, it simultaneously revealed a fundamental limitation: their methodology could not determine whether alternative production functions might equally explain the observed data.
This paper presents a novel dynamical systems approach to production function estimation. By modeling economic growth trajectories as dynamical systems, we derive production functions as time-independent invariants -- a method that systematically generates all possible functional forms compatible with observed data.
Applying this framework to Cobb and Douglas's original dataset yields two key results: First, we demonstrate that the Cobb-Douglas form emerges naturally from exponential growth dynamics in labor, capital, and production. Second, we show how combining fundamental invariants of this exponential system generates the CES production function as a special case. Our methodology bridges statistical analysis with mathematical systems theory, providing both a verification mechanism for classical results and a tool for discovering new functional relationships. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deriving Production Functions in Economics Through Data-Driven Dynamical Systems Smirnov, Roman G. Applications 91B55, 37N40 In their seminal 1928 work, Charles Cobb and Paul Douglas empirically validated the Cobb-Douglas production function through statistical analysis of U.S. economic data from 1899 to 1923. While this established the function's theoretical foundation for growth models like Solow-Swan and its extensions, it simultaneously revealed a fundamental limitation: their methodology could not determine whether alternative production functions might equally explain the observed data. This paper presents a novel dynamical systems approach to production function estimation. By modeling economic growth trajectories as dynamical systems, we derive production functions as time-independent invariants -- a method that systematically generates all possible functional forms compatible with observed data. Applying this framework to Cobb and Douglas's original dataset yields two key results: First, we demonstrate that the Cobb-Douglas form emerges naturally from exponential growth dynamics in labor, capital, and production. Second, we show how combining fundamental invariants of this exponential system generates the CES production function as a special case. Our methodology bridges statistical analysis with mathematical systems theory, providing both a verification mechanism for classical results and a tool for discovering new functional relationships. |
| title | Deriving Production Functions in Economics Through Data-Driven Dynamical Systems |
| topic | Applications 91B55, 37N40 |
| url | https://arxiv.org/abs/2506.00032 |