On the Parametric Estimation for Multivariate Copula-based Seemingly Unrelated Tobit Models

Paulo Henrique Ferreira

Here we perform the analysis of the multivariate Seemingly Unrelated Regression (SUR) Tobit model for left-censored or right-censored dependent variables by modeling its nonlinear dependence structure through copulas. In particular, we adopt different multivariate copulas (case of left-censored dependent variables), as well as its survival copula (case of right-censored dependent variables). Regarding model estimation, the use of copula methods enables the use of the (classical) Inference Function for Margins (IFM) method, which is more computationally attractive (feasible) than the full maximum likelihood approach. However, the IFM method provides a biased estimate of the copula association parameter in the presence of censored observations in the margins. In order to obtain an unbiased estimate of the copula parameter, we can use a modified version of the IFM method, the so called Inference Function for Augmented Margins (IFAM) method. We also consider resampling procedures (bootstrap methods) to obtain confidence intervals for the model parameters. We perform simulation and empirical studies in order to investigate the bias and mean square errors of the IFAM estimates as well as to check the coverage probabilities of bootstrap confidence intervals for the parameters of the multivariate copula-based SUR Tobit models. The results indicate the adequate performance of our proposed model and methods. We illustrate our proposed procedures on a customer churn data from a Brazilian commercial bank.