How does noise protection affect the accuracy of life expectancy and other demographic indicators?

TL;DR

This paper examines how adding noise to demographic data for confidentiality impacts the accuracy of key indicators like life expectancy, providing analytical tools to quantify the resulting uncertainties.

Contribution

It introduces a method to analytically assess the impact of noise protection on demographic indicator accuracy and derives a formula for life expectancy variance under noise.

Findings

Noise addition increases uncertainty in fertility and mortality rates.

Derived a closed-form expression for life expectancy variance considering noise.

Validated the analytical variance formula through numerical simulations.

Abstract

New and efficient methods based on noise addition to protect the confidentiality in population statistics have been developed, tested and applied in census production by various members of the European Statistical System over the past years. Basic demographic statistics - such as population stocks, live births and deaths by age, sex and region - may be protected in a similar way, but also form the raw input to calculate various demographic indicators. This paper analyses the impact on the accuracy of some selected indicators, namely fertility and mortality rates and life expectancies, under the assumption that the raw input counts are protected with a generic noise method with fixed variance parameter, by comparing the size of noise uncertainties with intrinsic statistical uncertainties using a Poisson model. As a by-product, we derive and validate numerically a closed analytical expression for the variance of life expectancies in a certain class of calculation models as a function of the variance of input mortality data. This expression also allows to calculate analytically the statistical uncertainty of life expectancies using the mentioned Poisson model for the input death counts.