ON MODELING HETEROSKEDASTICITY - THE STUDENTS T AND ELLIPTIC LINEAR-REGRESSION MODELS

This paper proposes a new approach to modeling heteroskedasticity whic h enables the modeler to utilize information conveyed by data plots in making informed decisions on the form and structure of heteroskedasti city. It extends the well-known normal/linear/homoskedastic models to a family of non-normal/linear/heteroskedastic models. The non-normalit y is kept within the bounds of the elliptically symmetric family of mu ltivariate distributions (and in particular the Student's t distributi on) that lead to several forms of heteroskedasticity, including quadra tic and exponential functions of the conditioning variables. The choic e of the latter family is motivated by the fact that it enables us to model some of the main sources of heteroskedasticity: ''thick-tails,'' individual heterogeneity, and nonlinear dependence. A common feature of the proposed class of regression models is that the weak exogeneity assumption is inappropriate. The estimation of these models, without the weak exogeneity assumption, is discussed, and the results are illu strated by using cross-section data on charitable contributions.