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Open AccessArticle

Jackknife Bias Reduction in the Presence of a Near-Unit Root

1
Department of Economics, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, UK
2
Department of Economics, University of Southampton, Southampton SO17 1BJ, UK
*
Author to whom correspondence should be addressed.
Econometrics 2018, 6(1), 11; https://doi.org/10.3390/econometrics6010011
Received: 29 September 2017 / Revised: 9 February 2018 / Accepted: 22 February 2018 / Published: 5 March 2018
(This article belongs to the Special Issue Celebrated Econometricians: Peter Phillips)
This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error, as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter and a quantity that is related to the long-run variance of the disturbance process, which are typically unknown in practice, and so, this dependence is characterised fully and a discussion provided of the issues that arise in practice in the most general settings. View Full-Text
Keywords: Jackknife; bias reduction; near-unit root; moment generating function Jackknife; bias reduction; near-unit root; moment generating function
MDPI and ACS Style

Chambers, M.J.; Kyriacou, M. Jackknife Bias Reduction in the Presence of a Near-Unit Root. Econometrics 2018, 6, 11.

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