# Trends in the Quantiles of the Life Table Survivorship Function

## Abstract

We offer a new approach for modeling past trends in the quantiles of the life table survivorship function. Trends in the quantiles are estimated, and the extent to which the observed patterns fit the unit root hypothesis or, alternatively, an innovative outlier model, are conducted. Then a factor model is applied to the detrended data, and it is used to construct quantile cycles. We enrich the ongoing discussion about human longevity extension by calculating specific improvements in the distribution of the survivorship function, across its full range, and not only at the central-age ranges. To illustrate our proposal, we use data for the UK from 1922 to 2013. We find that there is no sign in the data of any reduction in the pace of longevity extension during the last decades.

## Keywords

Survivorship function quantiles Longevity extension Structural breaks Population aging Longevity risk## Notes

### Acknowledgements

The support received from the Spanish Ministry of Science/FEDER ECO2013-48326-C2-1-P, ECO2015-66314-R, and FEDER ECO2016 -76203-C2-2-P, is acknowledged. The second author thanks ICREA Academia.

### Compliance with Ethical Standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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