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TESTING FOR A UNIT ROOT IN LEE–CARTER MORTALITY MODEL

Published online by Cambridge University Press:  29 August 2017

Xuan Leng  and
Liang Peng
Xuan Leng
Affiliation:
Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, E-Mail: leng@ese.eur.nl
Liang Peng*
Affiliation:
Department of Risk Management and Insurance, Robinson College of Business, Georgia State University, Atlanta, GA 30303, USA
*
E-Mail: lpeng@gsu.edu
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Abstract

Motivated by a recent discovery that the two-step inference for the Lee–Carter mortality model may be inconsistent when the mortality index does not follow from a nearly integrated AR(1) process, we propose a test for a unit root in a Lee–Carter model with an AR(p) process for the mortality index. Although testing for a unit root has been studied extensively in econometrics, the method and asymptotic results developed in this paper are unconventional. Unlike a blind application of existing R packages for implementing the two-step inference procedure in Lee and Carter (1992) to the U.S. mortality rate data, the proposed test rejects the null hypothesis that the mortality index follows from a unit root AR(1) process, which calls for serious attention on using the future mortality projections based on the Lee–Carter model in policy making, pricing annuities and hedging longevity risk. A simulation study is conducted to examine the finite sample behavior of the proposed test too.

Keywords

AR processLee–Carter modelunit root
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 715 - 735
Copyright
Copyright © Astin Bulletin 2017 

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