When bias contributes to variance: true limit theory in functional coefficient cointegrating regression
When bias contributes to variance: true limit theory in functional coefficient cointegrating regression
Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics. The errors in the literature arise because random variability in the bias term has been neglected in earlier research. In stationary regression this random variability is of smaller order and can be ignored in asymptotic analysis but not without consequences for finite sample performance. Implications of the findings for rate efficient estimation are discussed. Simulations in the Online Supplement provide further evidence supporting the new limit theory in nonstationary functional coefficient regressions.
Bandwidth selection, Bias variability, Functional coefficient cointegration, Kernel regression, Nonstationarity
469-489
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Ying
d3edca3d-0b0a-44f7-8301-e105b438ee3c
1 February 2023
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Ying
d3edca3d-0b0a-44f7-8301-e105b438ee3c
Phillips, Peter Charles Bonest and Wang, Ying
(2023)
When bias contributes to variance: true limit theory in functional coefficient cointegrating regression.
Journal of Econometrics, 232 (2), .
(doi:10.1016/j.jeconom.2021.09.007).
Abstract
Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics. The errors in the literature arise because random variability in the bias term has been neglected in earlier research. In stationary regression this random variability is of smaller order and can be ignored in asymptotic analysis but not without consequences for finite sample performance. Implications of the findings for rate efficient estimation are discussed. Simulations in the Online Supplement provide further evidence supporting the new limit theory in nonstationary functional coefficient regressions.
Text
Correct_FC_limit_2021-20_September_pcb
- Accepted Manuscript
More information
Accepted/In Press date: 20 September 2021
e-pub ahead of print date: 20 October 2021
Published date: 1 February 2023
Additional Information:
Funding Information:
Our thanks go to Serena Ng and the Associate Editor for helpful guidance on the revision and two referees for useful comments on directions for further research. The authors acknowledge Marsden Grant 16-UOA-239 support at the University of Auckland. Phillips acknowledges research support from the NSF under Grant No. SES 18-50860 at Yale University and a Kelly Fellowship at the University of Auckland . Wang acknowledges support from the National Natural Science Foundation of China (Grant 72103197 ) and Beijing municipal fund for building world-class universities(disciplines) of Renmin University of China.
Publisher Copyright:
© 2021 Elsevier B.V.
Keywords:
Bandwidth selection, Bias variability, Functional coefficient cointegration, Kernel regression, Nonstationarity
Identifiers
Local EPrints ID: 451713
URI: http://eprints.soton.ac.uk/id/eprint/451713
ISSN: 0304-4076
PURE UUID: fe239ea3-0d0a-487b-9ddb-1a27a46c5943
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Date deposited: 21 Oct 2021 16:31
Last modified: 17 Mar 2024 06:50
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Author:
Ying Wang
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