运用重复交易模型编制综合指数中的多重共线性问题:基于参数改进的解决方法

The treatment of multicollinearity in repeated trading model to construct the composite index:A solution based on parameter improvement

编制综合指数是科学监测现代经济社会发展的重要途径和技术手段.我国的宏观指标以“小样本、短时间”为特征,重复交易模型在其编制综合指数中应用广泛.而在重复交易模型编制综合指数的过程中通常面临严重的多重共线性问题.处理多重共线性的方法有消除解释变量的相关性、扩大样本量避免选择误差、重新确定模型形式和参数改进方法等,前三种在重复交易模型编制综合指数中并不适用.文章以最小二乘估计为基础,从参数改进思路出发,探讨区别于岭回归的处理多重共线性的方法.通过重复交易模型的可估模型,寻找参数的可用估计,为处理其中的多重共线性问题提供新的思路和视角.最后,以2010年至2017年全国科技活动产出综合指数为例,通过足够小的k可行值编制综合指数,并将其与传统岭回归方法、主成分回归方法相比,讨论该方法在处理重复交易模型共线性问题的有效性和适用性,进一步体现本文处理重复交易模型多重共线性方法的应用价值.

Composite index construction is an important way and technical method to monitor the development of modern economy and society.Macro indicators of our country are characterized by ’small sample and short time’,and the repeated trading model is widely used in the construction of comprehensive index.There are some methods to deal with multicollinearity:Eliminating the correlation of explanatory variables,enlarging the sample size to avoid selection bias,redefining the model form and improving the parameters ’ estimation.The first three are not applicable in the repeated trading model.In this paper,based on the least square estimation,a new method for multicollinearity treatment,which is different from ridge regression,is discussed.By designing the estimable model,we can find the available estimators of parameters.It provides a new perspective for dealing with multicollinearity problems in the repeated trading model.Finally,the empirical analysis on constructing national science and technology activity output index from 2010 to 2017 is carried out,and we construct the estimable model,using a very small k as a feasible value to estimate the composite index.Compared with the traditional ridge regression method and principal component regression method,we discuss the effectiveness and applicability of this new method to further reflect the practical applications of the new method in this paper.