Exact Distribution of the F-statistic under Heteroskedasticity of Unknown Form for Improved Inference

Jianghao Chu (), Tae Hwy Lee, Aman Ullah and Haifeng Xu ()
Additional contact information
Jianghao Chu: Ford Motor Co
Haifeng Xu: Xiamen University

No 202027, Working Papers from University of California at Riverside, Department of Economics

Abstract: The exact finite sample distribution of the $F$ statistic using the heteroskedasticity-consistent (HC) covariance matrix estimators of the regression parameter estimators is unknown. In this paper, we derive the exact finite sample distribution of the $F$ ($=t^2$) statistic for a single linear restriction on the regression parameters. We show that the $F$ statistic can be expressed as a ratio of quadratic forms, and therefore its exact cumulative distribution under the null hypothesis can be derived from the result of Imhof (1961). A numerical calculation is carried out for the exact distribution of the $F$ statistic using various HC covariance matrix estimators, and the rejection probability under the null hypothesis (size) based on the exact distribution is examined. The results show the exact finite sample distribution is remarkably reliable, while, in comparison, the use of the $F$-table leads to a serious over-rejection when the sample is not large or leveraged/unbalanced. An empirical application highlights that the use of the exact distribution of the $F$ statistic will increase the accuracy of inference in empirical research.

Keywords: Heteroskedastisity; Finite sample theory; Imhof distribution (search for similar items in EconPapers)
JEL-codes: C1 C2 (search for similar items in EconPapers)
Pages: 28 Pages
Date: 2020-12
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations:

Forthcoming in Journal of Statistical Computation and Simulation

Downloads: (external link)
https://economics.ucr.edu/repec/ucr/wpaper/202027.pdf First version, 2020 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:202027

Access Statistics for this paper

More papers in Working Papers from University of California at Riverside, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kelvin Mac ().