Are Cohort Mortality Rates Autocorrelated?

Abstract

In this paper the author examines the proposition that heterogeneity in individual frailty leads to autocorrelation in cohort mortality rates. A simple model is used to construct analytic expressions for the covariance of cohort mortality rates at different ages under a number of alternative assumptions about the stochastic process generating shocks in mortality. The model then is used to construct a procedure that uses correlations in cohort mortality rates to estimate the extent of heterogeneity in a population without relying on strong assumptions about the distribution of frailty or the shape of the underlying hazard. The procedure then is used to show that cohort mortality data from France are consistent with a generalized random-effects model in which frailty is gamma-distributed. nt]mis|Initial stages of this work were carried out at the University of California, Berkeley and were supported by a Population Council Graduate Fellowship. Additional support was provided by a grant from the University of Pennsylvania Research Foundation. I am indebted to Kenneth Wachter for suggesting that a formal analysis of this question might prove interesting and to John Wilmoth for making the French data available. I am grateful to Kenneth Wachter, Ronald Lee, John Wilmoth, George Alter, and Samuel Preston for their comments and suggestions. Any remaining errors are of course my own responsibility. © 1991 Population Association of America.