Statistical inference in the presence of heavy tails

Income distributions are usually characterized by a heavy right-hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distributions admitted by econometric models. It is therefore important to determine the limits of conventional inference in the presence of heavy tails, and, in particular, of bootstrap inference. In this paper, recent progress in the field is reviewed, and examples given of how inference may fail, and of the sorts of conditions that can be imposed to ensure valid inference.