Estimation and Dynamic Evolution of Provincial Factor-Output Elasticity in China

China is currently in a new phase of transition from high-speed growth to high-quality growth, and accurate estimation of element outputs is essential for the smooth progress of the transition. Using the back-fitting method, this study constructed a model of a spatiotemporal-varying elasticity production function to estimate the factor-output elasticity from 1993 to 2017 in 31 Chinese provinces. Nonparametric kernel density method was applied to describe the spatiotemporal evolution characteristics of factor-output elasticity. The results show that the factor-output elasticity of different provinces shows a nonlinear change trend over time and between regions. Overall, the elasticity of labor output shows a decreasing trend, the elasticity of capital output shows an increasing tendency, the eastern region has the lowest level of labor-output elasticity, but the highest level of capital-output elasticity. The western region has the highest level of labor-output elasticity but the lowest level of capital-output elasticity. On the whole, regions with higher resilience in labor output gradually shift towards the West, while capital shifts towards the East.