Quantile Regression Of Instrumental Variable Aided Variable Coefficient Measurement Error Models And Its Applications

In today's society,even with the rapid development of science and technology,the measurement data contains measurement errors due to inadequate equipment and improper use in many research fields.Direct use of data containing measurement errors will adversely affect the estimation of the model.How to eliminate the deviation of estimation caused by measurement error is worth discussing deeply.At present,there are many methods to correct the measurement error data,but for quantile regression model,it is difficult to directly correct the deviation caused by the measurement error.Therefore,aiming at the varying-cofficient measurement error model,this paper chooses to introduce the instrumental variables to correct the deviation caused by the measurement error.Firstly,the instrumental variables are introduced to correct the covariates containing measurement errors.Secondly,the function coefficients are estimated by constructing quantile regression objective function,so as to obtain the estimation of coefficient functions at different loci.The asymptotic normal-ity of the proposed estimator is proved under some regularity c onditions.Naive estimators,the proposed quantile regression estimators using instrume ntal variables,and the least squares estimators using instrumental variables are compar ed in simulation study,the simulation results show that the proposed method is superio r to the existing methods.In application,the method proposed in this paper is used to analyze the influencing factors of the balance of financial assets of rural residents in China.The final results show that the household debt balance coefficient presents a U-shaped change,and the household income coefficient presents an inverted U-shaped change.Young people for consumption and the pursuit of more and more people's quality of life can lead to the back of personal debt,the elderly showed a trend of excessive debt that may be caused by such as rent and property prices corresponding pension is low,at the same time the two age groups of household income decreases,household incomes have negative effects on financial assets.Middle-aged people have a stronger sense of saving and use most of their money for savings,so their debt is relatively low and their income increases.