Estimation of capital stock and the elasticity of capital-labor substitution in provincial industries in China

Capital stock is an important indicator of the level and potential of economic development of a country or region. The capital-labor elasticity of substitution is an important influence on economic growth, income distribution and social welfare. This study utilizes the depreciation backward calculation method to estimate the capital stock of 19 industries across 31 provinces in China, and analyzes its industry characteristics and regional distribution. On this basis, this study constructs a spatial econometric model based on the Constant Elasticity of Substitution (CES) production function to estimate the capital-labor elasticity of substitution for the 19 industries. The findings indicate that the capital stock sizes of China's manufacturing and real estate industry are significantly larger than those of other industries. The average annual growth rate of the capital stock in the scientific research and technical services industry is the highest, reaching 20.89%. Furthermore, there is a phenomenon of capital aggregation in provinces radiated by the Bohai Economic Rim and the Guangdong-Hong Kong-Macao Greater Bay Area. In addition, the elasticity of capital-labor substitution for all industries are less than 1. Significant spatial correlation is observed in factor substitution for the mining, the transportation, warehousing and postal industry, the finance industry, the residential services, repair and other services industries as well as the education industry. Meanwhile, the substitution elasticity is positively correlated with industry capital intensity, technological intensity, skill intensity, and openness level. The results can provide basic data and decision-making references for the optimal allocation of resources and the improvement of economic efficiency in various provinces and industries, and can also provide benchmark parameters for many related studies. • Phased changes in depreciation rates are taken into account in the estimation process. • Spatial correlations are incorporated into the estimation of substitution elasticity. • Enrich the methodology for estimating capital stock in provincial industries.