Estimation And Analysis Of My Country's Educational Return Rate Under The Condition Of Missing Data

The relationship between personal income and the level of education can be measured by the rate of return to education,which is a measure of the future net economic payoff to an individual or to society of increasing the amount of education taken,and it is very useful for evaluating education productivity.When we take a survey of personal income,however,some people might not answer the inquiry and then income data occur to be missing.Missingness brings difficulty to estimate the returns to education in a more precision.When the data is missing,it is possible to have a great impact on the statistical result by ignoring the missingness directly,such as the deviation of the estimators.In order to establish statistical model for missing data,Rubin(1976)introduced the concept of the missing mechanism,and divided the missing mechanisms into three categories,namely missing completely at random,missing at random and not missing at random.The missing completely at random and missing at random are also called ignorable missing mechanism,and the not missing at random is called nonignorable missing mechanism.Generally,the common missing mechanism models include Logistic model,Probit model,C-loglog model and so on.In this paper,the annul income of the urban workers in China in 2002 and 2013 has carried on statistical inference based on the Mincerian function under the nonignorable missing data mechanism.The selected variable includes year of education,age of the educatees and annual income.Because annual income involve personal privacy,there will be no response in the survey.Among the data collected in this paper,the missing rate of annual income in 2002 and 2013 are approximately 6.0% and 22.4% respectively.We use the Logistic model to fit missingness mechanism,construct joint likelihood function and then estimate all parameters.Under the assumption that the joint likelihood function satisfies parameter identification.We show that the estimators are consistent and asymptotically normal.Real data analysis shows that the returns to education in our country under nonignorable missing data mechanism has decreased form 9.62% in 2002 to 8.56% in 2013.