| The paper is mainly about the composite model on the form ofto nonparametric matching estimation. Where g is linearly homogeneous, h is monotonic in g, and the concrete expression of the composite model is unknown.The composite model can be widely used in the practical problems of economics and management science, such as utility and production function applications. The estimation of h and g in the model can provide effective guidance to enterprise’s decision, the adjustment of industrial’s structure and allocation of factor of production etc.The purpose of the paper is to conduct initial estimation of h and g with nonparametric matching estimation method, and then use the method which is analogous to least squares estimation of parametric models to conduct the simultaneous estimators of h and g. The method can provide consistent, asymptotically normal estimators for the function g and h, and the convergence speed of the estimation can achieve optimal.We provide numerical simulation of the composite model with the nonparametric matching estimation method. Found that the simultaneous estimator and initial estimate did obey the asymptotic normal distribution, and the simultaneous estimator is better than the initial estimate.Finally, the composite model is applied to the production model of Chinese petroleum chemical industry, getting the nonparametric estimation of h and g, further getting the returns to scale and elasticity of substitution used in enterprises’ production. Where, returns to scale is defined as. The elasticity of substitution between captital K and labor L is defined as. According to the empirical results, we can draw the following two conclusions:First, the small and medium sized sub industry of Chinese petrochemical industry are undercapitalized, so their size need to be increased to achieve the optimal economies of scale and improve production efficiency. At present, the sub industry model of Chinese petrochemical industry could properly adjust their industrial structure and increase the amount of capital, thus obtain the optimal economics of scale.Second, the sub industry of Chinese petroleum chemical industry is relatively developed, and the industrial structure is generally reasonable, so its capital to labor ratio is appropriate, and the corresponding elasticity of substitution is large. However, for the sub sectors which are relatively less developed in Chinese petroleum chemical industry, may be due to its industrial structure is not reasonable, the capital to labor ratio is too low or too high, so that the elasticity of substitution is small. Therefore, according to the relationship of capital to labor ratio and elasticity of substitution in sub sectors of Chinese petroleum and chemical industry, we can conduct reasonable distribution between industrial structures of the sub sectors to achieve optimal allocation. |
