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Testing For A Unit Root In Lee–Carter Mortality Model

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  • Leng, Xuan
  • Peng, Liang

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.

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  • Leng, Xuan & Peng, Liang, 2017. "Testing For A Unit Root In Lee–Carter Mortality Model," ASTIN Bulletin, Cambridge University Press, vol. 47(3), pages 715-735, September.
    • Handle: RePEc:cup:astinb:v:47:y:2017:i:03:p:715-735_00
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    Cited by:

    1. Deyuan Li & Chen Ling & Qing Liu & Liang Peng, 2022. "Inference for the Lee-Carter Model With An AR(2) Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 991-1019, June.

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