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The jacknife statistic: an application in econometrics

David Owen, Anthony (1977) The jacknife statistic: an application in econometrics. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.94565) (KAR id:94565)

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https://doi.org/10.22024/UniKent/01.02.94565

Abstract

Quenouille has developed a procedure, later termed the jackknife by Tukey, for reducing the bias of a consistent estimator of an unknown parameter. A measure of the variance of the resulting estimator can be obtained and used to provide approximate confidence intervals and tests of significance. Thus the jackknife technique may be especially interesting when the estimator under consideration is biased but consistent and mathematically intractable distribution theory prevents the construction of exact confidence intervals.

Considerable research has been devoted to studying the jackknife technique, predominantly in the fields of biometrics, statistics and numerical analysis. So far the use of the jackknife method in econometrics has been negligible, although one very important class of econometric estimators, the simultaneous equation estimators, is biased in finite samples and, in general, has a mathematically intractable distribution.

In this thesis we investigate the application of the jackknife technique to the Two-Stage Least Squares (2SLS) structural parameter estimator in a simultaneous equation system. The bias reducing property was found to be present in the majority of cases considered in an investigation of the effects of jackknifing on the exact bias of the 2SLS estimator in a two equation model. Conditions are given for which it is unlikely that jackknifing will reduce the bias of the 2SLS estimator.

Since the exact variance of the jackknifed 2SLS estimator is unknown, an examination of the effect on the variance of 2SLS of applying the jackknife had to be made by a simulation experiment.

Whilst the 2SLS estimator always had a smaller mean square error than the jackknifed 2SLS estimator, a comparison of absolute errors rarely produced a significant difference between them.

Finally, it was observed that t statistics formed using the 2SLS estimator may not be distributed according to the Student t distribution. The actual distribution may be highly skewed and serious errors could result if the postulated theoretical distribution was used for statistical inference. In general, this feature was less noticeable for the J2SLS estimator which appeared to have a reasonably symmetric distribution, and consequently there is less likelihood of serious errors being made if the postulated theoretical distribution is used for the purpose of statistical inference.

Item Type: Thesis (Doctor of Philosophy (PhD))
DOI/Identification number: 10.22024/UniKent/01.02.94565
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 25 April 2022 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives (https://creativecommons.org/licenses/by-nc-nd/4.0/) licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies (https://www.kent.ac.uk/is/strategy/docs/Kent%20Open%20Access%20policy.pdf). If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at ResearchSupport@kent.ac.uk and we will seriously consider your claim under the terms of our Take-Down Policy (https://www.kent.ac.uk/is/regulations/library/kar-take-down-policy.html).
Uncontrolled keywords: Econometrics
Subjects: H Social Sciences > HB Economic Theory
Divisions: Divisions > Division of Human and Social Sciences > School of Economics
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 21 Nov 2022 12:16 UTC
Last Modified: 21 Nov 2023 14:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/94565 (The current URI for this page, for reference purposes)
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