Bayesian Robust Inference of Sample Selection Using Selection-t Models

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection-t model to perform frequentist' robust analysis of sample selection. Instead of using their maximum likelihood estimates, our paper develops new Bayesian procedures for the selection-t models with either continuous or binary outcomes. By exploiting the Normal mixture representation of the t distribution, we can use data augmentation to impute the missing data, and use parameter expansion to sample the restricted covariance matrices. The Bayesian procedures only involve simple steps, without calculating analytical or numerical derivatives of the complicated log likelihood functions. Simulation studies show the vulnerability of the selection models with Normal errors, as well as the robustness of the selection models with t errors. Interestingly, we find evidence of heavy-tailedness in three real examples analyzed by previous studies, and the conclusions about the existence of selection effect are very sensitive to the distributional assumptions of the error terms.Comment: Journal of Multivariate Analysis (2014

Dynamic Bivariate Normal Copula

Normal copula with a correlation coefficient between $-1$ and $1$ is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H\"usler and Reiss (1989) showed that the tail can become asymptotically dependent. In this paper, we extend this result by deriving the limit of the normalized maximum of $n$ independent observations, where the $i$-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of $i/n$. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition in H\"usler and Reiss (1989). A simulation study and real data analysis are presented too.Comment: 22pages, 4 figure