On the sources of instability of the Mitra model for years of life at old-age

Abstract

We explore sources of this instability of the Mitra [“Estimating the Expectation of Life at Older Ages.” Population Studies 38 (2):313–9] model for estimating the remaining life expectancy at old age by revisiting Mitra’s own derivation and keeping the terms of higher order necessary for our inquiry. Dropping the higher-order terms and errors in estimates of the mean population age appear to lead to only small errors of up to three percent of the true remaining life expectancy. The growth parameter’s inadequate estimates, however, lead to large estimation errors and are the source of the outliers of the model. Our results confirm that Mitra model’s biases are typically on the side of overestimating the life expectancy. This provides formal support for an earlier method [Ediev, Dalkhat M. 2018. “Expectation of Life at Old Age: Revisiting Horiuchi-Coale and Reconciling with Mitra.” Genus 74 (1)] based on combining the Mitra and the classical life table models. Based on the performed analysis, we also propose several alternative models of estimating the life expectancy at old age in stable and non-stable population contexts. Our iterative method of estimating the expectation of life at old age does not rely on approximate relations assumed in Mitra and other traditional models and performs as good as the Mitra model overall, yet, being free from outliers and skewedness of estimation errors characterizing the Mitra model.

Keywords:

• life expectancy
• age exaggeration
• Mitra model
• open age interval
• life table
• old-age mortality

Additional information

Funding

The work was supported by the Russian Foundation for Basic Research (grant no. 18-01-00289 “Mathematical models and methods of correcting the distortions of the age structure and mortality rates of elderly population”).