Solving the Time-Varying Cobb-Douglas Production Function Using a Varying-Coefficient Quantile Regression Model
Shangfeng Zhang*,, Jiani Zhu*, Qi Fang*, Yaoxin Liu*, Siwa Xu*, and Ming-Hsueh Tsai**
*Research Institute of Quantitative Economics, Zhejiang Gongshang University
18 Xuezheng Street, Xiasha Education Park, Hangzhou, Zhejiang 310018, China
**National Academy for Educational Research
No.2 Sanshu Road, Sanxia District, New Taipei City 23703, Taiwan
The output elasticity estimated by the traditional Cobb-Douglas production function is a fixed constant that describes developed countries with relative stable factor shares well. While the fixed constant fails to describe developing countries with changing factor shares during economic transitional periods, such as China. In this paper, we construct a time-varying elasticity production function model and extend the Cobb-Douglas production function to a time-varying elasticity Cobb-Douglas production function. The semi-parametric varying-coefficient quantile model, together with the local polynomial and the two-phase methods, is used for the estimation of the time-varying elasticity of the capital coefficient and the labor force. Empirical research on Chinese economic growth shows that the time-varying elasticity of capital is declining and the time-varying elasticity of the labor force is increasing gradually.
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