Publication Type
Journal Article
Version
acceptedVersion
Publication Date
7-2010
Abstract
This paper studies the distribution of the classical t-ratio with data generated from distributions with no finite moments and shows how classical testing is affected by bimodality. A key condition in generating bimodality is independence of the observations in the underlying data-generating process (DGP). The paper highlights the strikingly different implications of lack of correlation versus statistical independence in DGPs with infinite moments and shows how standard inference can be invalidated in 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 the existence of moments to be determined parametrically. It also investigates the relative importance 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 TT distributions. Novel density estimation kernel methods are employed, given that our theoretical results yield cases that exhibit density discontinuities.
Keywords
Bimodality, Cauchy, Double-pareto, Thick tails, T- ratio
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometrics Journal
Volume
13
Issue
2
First Page
271
Last Page
289
ISSN
1368-4221
Identifier
10.1111/j.1368-423X.2010.00315.x
Publisher
Wiley
Citation
FIORO, Carlo V.; HAJIVASSILIOU, Vassilis A.; and Peter C. B. PHILLIPS.
Bimodal t-ratios: The impact of thick tails on inference. (2010). Econometrics Journal. 13, (2), 271-289.
Available at: https://ink.library.smu.edu.sg/soe_research/1817
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1111/j.1368-423X.2010.00315.x