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Abstract
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.
Highlights
IntroductionThe study of the production function is very important. In 1928, Cobb and Douglas verified the relationship between the output and the input factors of labor and capital with a statistical approach in their study of American economic growth, and they first proposed the famous CobbDouglas production function (C-D production function), which has been applied widely [1,2,3]
In economics, the study of the production function is very important
We propose a grey Constant Elasticity of Substitution (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
Summary
The study of the production function is very important. In 1928, Cobb and Douglas verified the relationship between the output and the input factors of labor and capital with a statistical approach in their study of American economic growth, and they first proposed the famous CobbDouglas production function (C-D production function), which has been applied widely [1,2,3]. In the application of the CES production function model, an important aspect is calculating the contribution rates of influencing factors on economic growth. Building a production function using the grey model to substitute for data with random fluctuations eliminates abnormal fluctuations or negative calculations of the contribution rates of the economic growth factors. The paper uses a grey two-level nested CES production function model and calculates the contribution rates of influencing factors on Chinese economic growth. Besides calculating the contribution rates of economic growth factors, the grey two-level nested CES production function model can be applied in other fields, such as analyzing production factors’ output elasticity and substitution elasticity, calculating the potential growth of the economy, predicting economic growth, and so on
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