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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Keywords AR process, Lee-Carter model, unit root
Persistent URL dx.doi.org/10.1017/asb.2017.24, hdl.handle.net/1765/101985
Journal ASTIN Bulletin
Citation
Leng, X. (Xuan), & Peng, L. (Liang). (2017). Testing for a unit root in Lee-Carter Mortality model. ASTIN Bulletin, 47(3), 715–735. doi:10.1017/asb.2017.24