| Composite Index System refers to an organic integrity composed of comprehensive evaluation of various characteristics of an evaluated object and its related indexes.It is an effective tool for people to understand an object scientifically and comprehensively and evaluate a certain object.Composite index is widely used in economics,demography,sociology,science,engineering,medicine and other fields,especially in the field of economics which in turn promotes the development of composite index construction theory.Based on the composite index construction theory and application researches and achievements at home and abroad,this paper summarizes the problems of lacking of theory and economics applications researches,as well as the situation that composite index construction model has been built increasingly mathematical and complicated,ignoring the scientificity and simplicity of evaluation method.This paper systematically sorts out the theoretical methods of the composite index construction,and put forwards a new model of'Composite index construction with expert opinion'combining subjective and objective weighting methods.This new model provides theoretical support for the relationship between the different methods and widely applications of composite index system,and introduces small sample and large sample real application in the field of'science and technology evaluation'.In addition,this paper attempts to extend from static composite index construction to dynamic composite index construction,and proposes a solving multicollinearity problem Repeat Sale Method to provide a new idea for composite index construction.This paper focuses on the theoretical model and empirical application of the composite index construction,and the contents of this study are as follows:Firstly,this part summarizes the current situation of application and theoretical research of composite index construction,as well as the theory of principal component analysis and its application in composite index.The above three parts of literatures are reviewed,and the shortcomings of the existing researches and the focuses of this part are pointed out.Secondly,composite index model with expert opinion is constructed,and the consistency and asymptotical normality of weighting estimators in large sample are proved under the framework of econometrics.This part defines the subjective information set of expert opinions,and adds the experts' subjective information set into the quadratic programming of principal component analysis estimation as a penalty term,so as to build a new composite index model.The geometrical significance,the path and property of the solution are discussed,in order to help to intuitively understand the model and the determination of penalty factor.Thirdly,Monte Carlo simulation experiments are carried out to verify the path and property of the weighting estimators under the large sample properties,and the property of penalty factor and the conclusion of cross validation.This part discusses the advantages of our new composite index method compared with the traditional principal component analysis and weighted experts' index model,and proposes that the optimal penalty factor can balance the information of objective data set and subjective experts'information set.If these two data samples are given,we can determine the optimal penalty factor and weighting estimators by cross validation.Fourthly,under the framework of scientific and technological evaluation,this part proposes a small sample empirical application that the composite index model with expert opinion is used to evaluate the comprehensive level of scientific and technological activity output of each province in China,to validate the applicability and effectiveness of the new method in the small sample situation.Fifthly,the composite index model with expert opinion is used to evaluate the innovation ability of industrial public companies in China.From the two aspects of innovation input and technological achievement transformation,a composite index of innovation performance of industrial public companies in China is constructed based on our new composite index with expert opinion,to validate the applicability and effectiveness of the new method.Sixthly,this part extends from 'the static comprehensive evaluation' to'dynamic comprehensive evaluation'.In the process of comprehensive evaluation of short time series,it is found that the composite index model with expert opinion is lack of operability.So this part produces a new method which is a composite index construction based on Repeat Sale Method.By discussing the consistency and asymptotic property of least squares estimation,we can solve the multicollinearity problem simply.Lastly,this part gives an empirical case of this new dynamic composite index method.The main conclusions of this paper are summarized as follows:Firstly,in the discussion of weighting method,there has always been a mistake in the research,that the objective weighting method is superior to the subjective weighting method,because that the objective weighting method is not affected by subjective arbitrariness.However,this paper argues that the best weighting method should not be based on whether the objective or subjective weighting method is adopted,but relies on whether the weights accurately or not reflects the true importance of the indicators.In order to solve this misunderstanding,this paper proposes a new'composite index model with expert opinion',in which the composite index is regarded as a common factor in the linear factor model.In addition,this paper defines the expert information set,which includes'importance scores','confidence score'and'expertise score'as three dimensions.The expert information set is added into the estimation of principal component analysis as a penalty term.Based on identifying the uncertainty of these two data sets,the optimal penalty factor Q is determined,so as to integrate the subjective and objective information through nonlinear quadratic programming.Monte Carlo simulation is used to verify that the paths of weighting estimators are continuous,and that the penalty factor Q changes with the change of the two data sets' information.Cross Validation is used to determine the optimal penalty factor Q.With the increase of sample size,sample Bias and Variance decrease gradually.Finally,it is concluded that the composite index model with expert opinion proposed in this paper can balance the objective data set and the subjective expert opinion compared with the traditional principal component analysis and weighted expert opinion model.What's more,compared with the weights obtained by PCA and weighted expert opinion model,the weighting estimators of our new model have better properties of smaller variance and are much closer to the real weights.It shows that our new composite index model has more certain advantages.Secondly,the composite index model with expert opinion can be applied to the comprehensive evaluation of the output of scientific and technological activities in all provinces.The output performance of scientific and technological activities in 31 provinces in China is empirically studied.Based on collecting subjective information sets of'importance scores','confidence score'and'expertise score'as three dimensions,we construct a composite index model.The comprehensive evaluated object of this problem is 31 provinces and 5 objective indicators.In the face of static comprehensive evaluation of small samples,this paper proposes to use lease-one-out Cross Validation to determine the optimal penalty factor Q.We use LOOCV to obtain cross-validation mean square error,which presents a "V" type,so the weighting estimators are jointly determined by objective data indicators and subjective expert opinion information.Therefore,our new model can determine the optimal penalty factor by identifying the noise of objective data indicators and subjective expert opinion information.As these two data sets could change,the optimal penalty factor Q would be different.Lastly,a relatively better composite index of the output of scientific and technological activities in 31 provinces of China is constructed.The empirical results show that the output of scientific and technological activities of 77.42%provinces are lower than the nationwide average,and the difference between the eastern and western region is relatively obvious.Shaanxi in the western region is above the nationwide average,and Sichuan,Chongqing,Gansu and Qinhai score high,high,partially due to the recent central government's strategic Western Development policy and the road-belt initiative have higher ranks.Thirdly,composite index model with expert opinion can be applied to the innovation performance evaluation of industrial public companies in China.In the face of static comprehensive evaluation of large samples,this paper proposes to use 5-folds Cross Validation to determine the optimal penalty factor Q,which is 0.1.And cross-validation mean square error presents a "V" type.It shows that the weighting estimators are jointly influenced by the data indicators of 1,882 industrial public companies and the subjective information of 25 experts'opinion,and are more affected by the objective data set than the subjective expert information.The new method proposed in this paper builds a composite index model on the basis of identifying the noise of these two data sets,and can solve the 'negative weighting'problem of other traditional weighting methods.Finally,innovation performance composite index of 1882 industrial public companies can be obtained according to the estimated weights.Fourthly,faced with the problem of short time series comprehensive,evaluation,composite index model with expert opinion and the traditional principal component analysis method are not applicable.So this paper proposes a solving multicollinearity problem Repeat Sale Method to provide a new idea for composite index construction by making full use of short time series data indicators.The empirical study shows that this method not only effectively solves the problem of missing variables and endogeneity of the model,but also overcomes the problem of too small sample size and sample selection deviation,so as to make the composite index estimation more accurate and comprehensive.In this paper,the dynamic composite index of repeat sale method is applied to the comprehensive evaluation of nationwide scientific and technological activities output.The feasible value of k,which is small enough,is determined by the proven asymptotic theory.So we can estimate the composite index with k.By comparing the traditional principal component analysis method and composite index with expert opinion,this repeat sale method can make full use of objective data information and has certain advantages when dealing with dynamic comprehensive evaluation. |
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