Bayesian Hierarchical Estimation and Impact Analysis of Generalized Production Functions

Bayesian model is constructed to estimate the missing data of capital stock, and the impact of three industrial structures on the tertiary industry is discussed. The results show that: the maximum MC error with missing data on capital stock estimated by Bayesian is 0.4963, the maximum MC error of production function estimated by Bayesian stratation is 0.3276, the standard deviation is 0.0890 and the accuracy is high; from 1993 to 2018, the sum of capital output elasticity and labor output elasticity in the tertiary industry in Yunnan Province was greater than 1, and the scale compensation was increasing; the level of technological progress, the growth rate of all factors, the elasticity of capital output and the elasticity of labor output were all close to stable, and the ranges of changes were 0.2714-0.3252, -0.0680-0.0390, 0.5615-0.5858 and 0.4522-0.4784, respectively; the elasticity of capital output was greater than that of labor force output, and the tertiary industry in Yunnan Province was more dependent on the elasticity of capital output.