The Estimation Of The SUR Tobit Model With Skew Hormal Errors And Its Application

In health economics, medical expense data is censored data, which contains a part of zero, and the data which is not zero often appears to be continuous and biased. Then the errors of the Tobit model based on normal or t distribution may not be suitable to describe the data. Therefore we discuss the SUR Tobit model with skew-normal errors. People usually describe the correlation between the errors of the SUR Tobit model with bivariate distribution, especially with the bivariate normal distribution. But it has many limitations, one of which is that the linear relationship between the marginal distribution. In order to avoid these problems, we use Copula to describe the correlation between the errors of the SUR Tobit model. The parameter estimation methods of the model are also studied in this paper, including the maximum likelihood estimation method, the two stage KM (Kaplan-Meier) estimation method, and the MIFM method. The simulations show that the Tobit model and the estimation methods are effective.The purpose of this paper is to select a suitable model for the U. S. out-of-pocket and non-out-of-pocket medical expenses data, which contains 3206 cross-section ob-servations from the Health and Retirement Survey. Approximately 12% of these indi-viduals report zero out-of-pocket expenses, and approximately 20% report zero non-out-of-pocket expenses. The MIFM is used for parameter estimation. The analysis result using our selected model is proper and common-sensible, while further illus-trate the methodology and validity of our parameter estimation method.