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Inference for the Lee-Carter Model With An AR(2) Process

Abstract

Researchers in studying longevity risk often employ the Lee-Carter model with a unit root AR(1) process for unobserved mortality indexes. When one models the mortality index by a stationary AR(1) process, the widely used two-step inference in Lee and Carter (1992) is inconsistent. Some mortality datasets reject the unit root hypothesis. This paper develops consistent statistical inferences for a modified Lee-Carter model using an AR(2) process to model unobserved mortality indexes. It also provides a simulation study to examine their finite sample performance before applying them to the US mortality rates.

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Notes

  1. 1.

    http://www.mortality.org/cgi-bin/hmd-country.php?cntr=USA&level=1

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Acknowledgements

We thank two reviewers for their helpful comments, which improve the presentation. Li's research was partially supported by the National Nature Science Foundations of China grant 11971115. Liu's research was partly supported by NSF of Jiangxi Province (No. 20192BAB201005), NSF project of Jiangxi Provincial Education Department (No. GJJ190261), and China Post doctoral Science Foundation (No. 2020M671961). Peng's research was partly supported by the Simons Foundation and the NSF grant, DMS-2012448.

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Correspondence to Liang Peng.

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Li, D., Ling, C., Liu, Q. et al. Inference for the Lee-Carter Model With An AR(2) Process. Methodol Comput Appl Probab (2021). https://doi.org/10.1007/s11009-021-09898-y

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Keywords

  • AR(2) model
  • Lee-Carter model
  • Mortality rates
  • Unit root