A Grey CES Production Function Model and Its Application in Calculating the Contribution Rate of Economic Growth Factors

In analyses of economic growth factors, people generally use the CES (Constant Elasticity of Substitution) production function model to calculate the contribution rates of the factors that influence economic growth. However, the traditional CES function model that is built directly from economic data often shows apparent errors in parameter estimation due to data fluctuations. Such a model also may cause a negative calculation of the contribution rates of economic growth factors, or it may create abnormal fluctuations for some periods, and thus it fails to meet economic growth laws. In this paper, we propose a grey CES production function that can eliminate the random fluctuations of data and make the estimated parameters more reasonable, and this model can reflect the relationship between inputs and outputs more accurately. With regard to model application, the paper puts forward a scientific calculation method to avoid the calculation deviations caused by the substitution of difference equation for a differential equation with Solow’s formula. With the grey two-level nested CES production function model and the calculation method proposed, the paper makes an empirical analysis of the contribution rates of factors that influence China’s economic growth.