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This paper extends the analysis of bivariate seemingly unrelated regression(SUR) Tobit model by modeling its nonlinear dependence structure through theClayton copula. The ability in capturing/modeling the lower tail dependence ofthe SUR Tobit model where some data are censored (generally, at zero point) isan additionally useful feature of the Clayton copula. We propose a modifiedversion of the inference function for margins (IFM) method (Joe and Xu, 1996),which we refer to as MIFM method, to obtain the estimates of the marginalparameters and a better (satisfactory) estimate of the copula associationparameter. More specifically, we employ the data augmentation technique in thesecond stage of the IFM method to generate the censored observations (i.e. toobtain continuous marginal distributions, which ensures the uniqueness of thecopula) and then estimate the dependence parameter. Resampling procedures(bootstrap methods) are also proposed for obtaining confidence intervals forthe model parameters. A simulation study is performed in order to verify thebehavior of the MIFM estimates (we focus on the copula parameter estimation)and the coverage probability of different confidence intervals in datasets withdifferent percentages of censoring and degrees of dependence. The satisfactoryresults from the simulation (under certain conditions) and empirical studyindicate the good performance of our proposed model and methods where they areapplied to model the U.S. ready-to-eat breakfast cereals and fluid milkconsumption data.

A modified version of the inference function for margins and interval  estimation for the bivariate Clayton copula SUR Tobit model: An simulation  approach