Bimodal t-ratios: The Surprising Impact of Thick Tails on Statistical Inference --- EXTENDED ONLINE VERSION
by
Carlo Fiorio, Vassilis Hajivassiliou, and Peter Phillips
April 2008
Abstract
This paper analyses the distribution of the classical t-ratio with data generated from distributions with no finite moments and shows how classical testing is affected. Some surprising results are obtained in terms of bimodality vs. the usual unimodality of the standard studentized t-distribution that prevails under classical conditions. The paper develops a new distribution termed the ``double Pareto,'' which allows the thickness of the tails and the existence of moments to be determined parametrically. We also consider a Cauchy distribution truncated on a compact support to investigate the relative importance of tail thickness in case of finite moments. We find that the bimodality persists even in such cases. Simulation results are used to highlight the dangers of relying on naive testing in the face of thick-tailed (TT) distributions. Special cases analyzed include one- and two-sample statistical inference problems, as well as linear regressions with TT errors. The paper highlights the strikingly different implications of lack of correlation versus statistical independence with DGPs with infinite moments and illustrates how standard inference is invalidated with such DGPs. The paper raises powerful alarms for the need of adapting suitably estimation and inference procedures to the special problems induced by TT distributions.
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