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.
-  C. Yan and L. Gong, “R&D Ratio, R&D Structure and Economic Growth,” Nankai Economic Studies, No.170, pp. 3-19, 2013 (in Chinese).
-  W. Zou, R. Seifert, and L. Fang, “What Factors of Production Determine Economic Growth?,” Shanghai J. of Economics, No.4, pp. 3-14, 2015 (in Chinese).
-  S. Zhang and B. Xu, “Analysis of China’s Unbalanced Economic Growth,” The J. of Quantitative & Technical Economics, Vol.32, No.3, pp. 94-110, 2015 (in Chinese).
-  S. Zhang and B. Xu, “Production Functions with Time-Varying Elasticities and Under the Catch-up Consensus: Total Factor Productivity,” China Economic Quarterly, Vol.8, No.2, pp. 551-568, 2009 (in Chinese).
-  J. Chen and J. Ding, “A Review of Technologies on Quantile Regression,” Statistics & Information Forum, Vol.23, No.3, pp. 89-96, 2008 (in Chinese).
-  M.-O. Kim, “Quantile regression with varying coefficients,” The Annals of Statistics, Vol.35, No.1, pp. 92-108, 2007.
-  H. Zeng and P. Xiong, “Research on the two step estimation method of the semi-parametric dynamic varying-coefficient quantile regression model,” Nei Jiang Ke Ji, Vol.36, No.9, pp. 115+99, 2015 (in Chinese).
-  T. Hastie and R. Tibshirani, “Varying-Coefficient Models,” J. of the Royal Statistical Society: Series B (Methodological), Vol.55, No.4, pp. 757-796, 1993.
-  Z. Cai, J. Fan, and Q. Yao, “Functional-Coefficient Regression Models for Nonlinear Time Series,” J. of the American Statistical Association, Vol.95, No.451, pp. 941-956, 2000.
-  J. Fan and W. Zhang, “Statistical estimation in varying-coefficient models,” The Annals of Statistics, Vol.27, No.5, pp. 1491-1518, 1999.
-  J. Fan and J. T. Zhang, “Two-Step Estimation of Functional Linear Models with Applications to Longitudinal Data,” J. of the Royal Statistical Society, Vol.62, No.2, pp. 303-322, 2000.
-  C. Mei, W. Zhang, and Y. Leung, “Statistical inferences for varying-coefficint models based on locally weighted regression technique,” Acta Mathematicae Applicatae Sinica, Vol.17, Issue 3, pp. 407-417.
-  R. Zhang and Y. Lu, “Varying-Coefficient Model,” Science Press, 2004 (in Chinese).
-  Z. Cai and X. Xu, “Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models,” J. of the American Statistical Association, Vol.104, Issue 485, pp. 1595-1608, 2008.
-  Y. Weng, “Semiparametric Functional Coefficient Quantile Regression and Its Two-Step Estimation Provedure,” Master Thesis, Xiamen University, 2008 (in Chinese).
-  National Bureau of Statistics of China, “China Statistical Yearbook 2014,” China Statistics Press, 2014.
-  J. Zhang, G. Wu, and J. Zhang, “The estimation of China’s Provincial capital stock: 1952–2000,” Jingji Yanjin (Economic Research J.), Vol.39, No.10, pp. 35-44, 2004 (in Chinese).
-  J. Cao, “The Aggregate Production Function and Contribution Rate of Technical Change to Economic Growth in China,” The J. of Quantitative & Technical Economics, Vol.24, No.11, pp. 37-46, 2007 (in Chinese).