  This paper extends the analysis of bivariate seemingly unrelated regression
(SUR) Tobit model by modeling its nonlinear dependence structure through the
Clayton copula. The ability in capturing/modeling the lower tail dependence of
the SUR Tobit model where some data are censored (generally, at zero point) is
an additionally useful feature of the Clayton copula. We propose a modified
version 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 marginal
parameters and a better (satisfactory) estimate of the copula association
parameter. More specifically, we employ the data augmentation technique in the
second stage of the IFM method to generate the censored observations (i.e. to
obtain continuous marginal distributions, which ensures the uniqueness of the
copula) and then estimate the dependence parameter. Resampling procedures
(bootstrap methods) are also proposed for obtaining confidence intervals for
the model parameters. A simulation study is performed in order to verify the
behavior of the MIFM estimates (we focus on the copula parameter estimation)
and the coverage probability of different confidence intervals in datasets with
different percentages of censoring and degrees of dependence. The satisfactory
results from the simulation (under certain conditions) and empirical study
indicate the good performance of our proposed model and methods where they are
applied to model the U.S. ready-to-eat breakfast cereals and fluid milk
consumption data.
