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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