Bimodal t-ratios: The Impact of Thick Tails onInference

This paper studies the distribution of the classical t-ratio with datagenerated from distributions with no finite moments and shows how classical testing isaspected by bimodality. A key condition in generating bimodality is independence of theobservations in the underlying data generating process (DGP). The paper highlightsthe strikingly different implications of lack of correlation versus statistical independencein DGPs with infinite moments and shows how standard inference can be invalidatedin such cases, thereby pointing to the need for adapting estimation and inference procedures to the special problems induced by thick-tailed (TT) distributions.The paper presents theoretical results for the Cauchy case and develops a new distribution termed the \double Pareto," which allows the thickness of the tails and theexistence of moments to be determined parametrically. It also investigates the relativeimportance of tail thickness in case of finite moments by using TT distributions truncated on a compact support, showing that bimodality can persist even in such cases.Simulation results highlight the dangers of relying on naive testing in the face of TTdistributions. Novel density estimation kernel methods are employed, given that ourtheoretical results yield cases that exhibit density discontinuities.[...]