Two-Stage Estimation Of Ordered Probit Model With Measurement Error

The subject of measurement error is a hot issue of international studies.Measurement errors are errors in independent variables which are unavailable or cannot be observed accurately.Due to measurement error,estimation results obtained by the traditional methods of model estimation are no longer unbiased and consistent and the traditional methods are not applicable any more.Ordered probit model has wide-range application in many fields such as economics,biostatistics and sociology,but few people have studied the ordered probit model with measurement error so far.As a result,based on ordered probit model,the paper introduces measurement error and focuses on statistical inference of ordered probit model with measurement error.The main research work and achievements of the paper are as follows: firstly,this paper proposes two-stage estimation method in theory.In other words,consistent and unbiased estimation of parameters are obtained by two stages.In the first stage,the instrumental variable method is adopted to change the model with measurement error into a new model without measurement error and then the maximum likelihood method is utilized to obtain the consistent and unbiased estimation of the new model.In the second stage,the minimum distance method is employed to obtain the consistent and unbiased estimation of the model.Besides,the asymptotic normality of estimators is proved in the paper.Secondly,the R statistical software is applied to give out the simulation results,and the stability of the two-stage method is validated by changing the sample size and the distribution of the variable and setting some of the independent variables with measurement error in this paper and then the results show that the two-stage method has very good sample properties and good robustness.At the same time,the simulation results of two-stage method are compared with the simulation results of instrumental variable method and the moment method which study the same model and comparison results show that the two-stage method is simple and easy to handle.Lastly,the two-stage method is applied to the real data from the fifth national health service survey and the relationship between the Tianjin public health score and the related influence is studied and analyzed.