Oldest-Old Mortality Rates and the Gompertz Law:
A Theoretical and Empirical Study Based on Four Countries
Jack C. Yue
Abstract
Testing the Gompertz law (i.e. the law of geometrical progression) for elderly mortality rates has long been discussed in the literature, but tests based on a set of yearly age-specific data have not been fully explored yet. In the first part of this paper, we propose a standard operating procedure for testing the Gompertz assumption using yearly age-specific mortality data. Methods used in the procedure include estimation of parameters in the Gompertz law and their standard errors via bootstrap simulation. In addition to the oldest-old (i.e. ages 80 and above) data from Japan, Sweden, France, and the U.S. (Data sources: Berkeley Mortality Database and Kannisto, 1994), a simulation study is used to demonstrate the validity of the proposed procedure. In practice the period of data collection is often prolonged to 5 or 10 years in order to accumulate sufficient sample sizes. However, a longer data collection period is likely to mix data with different attributes and cause problems in the parameter estimation. Thus, in the second part of this paper, we discuss the impacts of the data collection period and population sizes on the testing results.
Key Words: Gompertz’s law, mortality rates of the elderly, simulation, maximum likelihood, weighted least square
