Theoretical Research And Applied Research Of A Class Of Summation Exponential Econometric Model

As to its simple form, convenient computation and easily-discussed theoretical nature, the linear model is extensively applied in both theoretical research and practice of the study of Econometrics. However, with the development of computer technology and the increase of information people can get, it is found that the linear method can not lead to a satisfying result in many circumstances, where the reason is that the intrinsic relationships among phenomena are usually some complicated non-linear relationships owing to the very complicated phenomena in the nature, human society and economic activities. In the research fields of technology, economy and society and other issues, lots of facts have showed that it is the non-linear relationship which the essence of complicated phenomena is. Therefore, it is the inexorable trend to move the study focus from the linear model deep to the nonlinear model.The complication of the relations between different economic variables determines the very existence of the interactions which, if ignored, will cause biased errors in model parameter estimation and blur the economic meaning. Based on this idea we propose a kind of power exponent summation econometrics model based on the definition of interaction, which includes the N-linear econometrics model making use of the common econometrics analysis and the Modified C-D production function applicable to the production function modeling. Based on the analysis of the advantages and disadvantages of N-linear econometrics model and combining the multivariate function interpolation, this article put forward a improved N-linear econometrics model.Based on some relevant studies, it was found that the N-linear econometrics models and their improved ones can reflect the interaction very well, which is very meaningful economically. In the linearization of models, we founded that replacing variables doesn't involve unknown model parameters, which means the model is quasi-linear and enables us to make use of the existing linear model theory to solve the unknown model parameters in order to overcome the fault of applying non-linear least square method to solve model parameters. This article put forward the selecting method of model reference points in the light of improved N-linear model, and proposed the estimators of parameters in N-linear model and its improved ones combining with the lease square method and maximum likelihood estimation. Combining with the basic conception in production function theory, this article proposed the mathematical expression of MCD production function and did further research on its natures under different assumptions. The study results have showed that the output elasticity, substitution elasticity and other important natures of MCD production function directly relate to the value of samples, which confirms to the economic activities very well. In this article, the author also put forward the necessary condition of eliminating the multicollinearity among sum term of model, and proved that, the MCD production function obeys the marginal benefit descending regularity in the field of mathematical economics, is quasi- concavity, and confirms to the Euler's theorem. So these studies have easily showed us the good economic natures of MCD production function. Concluded the cost function of MCD production function by means of the dual relationship between production function and cost function, found that the production factor output elasticity of MCD production function can be expressed by the multiple of the ratio of relevant factor-induced cost in the gross cost.The production function and cost function are closely related and mutually corresponding. This article deduced the corresponding cost function based on the MCD production function, analyzed the relationship between the yield and profit of enterprise under different scale returns, and studied the new meanings of the output elasticity and marginal substitution rate of MCD production function under the condition of cost function.This article applied the penalty function methods and Gauss-Newton iterative method to propose the optimal estimation method of MCD production function based on the assumption that the unknown parameters of MCD production function are non-negative, discussed the possible problems of optimal estimation method by analyzing the parameter estimation of typical production function model, put forward the series linear least square estimation method applicable to solve the production function model combining with the economic meanings of power exponents in the model and proposed the computing method of power exponent in the model which is highly applicable and will both linearize the non-linear problems and low down the difficulty of parameter estimation.At last, this article studied the kind of power exponent summation econometrics model from the view of application and compared the fitting degree of N-linear econometrics model with that of ordinary linear model through numerical examples. Besides, based on the optimal input idea and DEA method, this article made use of the corrected data to study the fitting result of MCD production model and output elasticity based on this model, the result of which showed that the MCD production function of China real estate industry is meaningful both economically and practically. Therefore, the research we have done is meaningful in theory and practice, which inrich the content of econometric theory and applied econometrics and provide a new idea about the reasch of the theoretical models and provide some theoretical and practical references to empirical analysis of management and economics.