A Rejoinder to Mitra

Abstract

Professor Mitra's note is a convenient introduction to two interesting articles of his' that have received little attention: except for two self-citations, no article referencing either of these articles is listed in the Social Sciences Citation Index for 1978 through 1985. The twelfth of the 16 formulae in Mitra's Demography article is equivalent to the fifth of the fifteen formulae in my article ;2 the overlap in the content of the two articles is rather less. Had I known of Mitra's work, I would have added a reference to it in the discussion of the formula. The basic idea underlying the formula, which has been independently derived on at least one other occasion,3 is that the years of life expectancy lost as a result of death can be calculated by summing up the number of deaths at each age multiplied by the remaining life expectancy at each age. As Pollard remarks,4 this idea is 'well known'; Keyfitz5 discusses it, and numerous demographers, actuaries, epidemiologists and others have applied it, including myself.6 The contribution of my article was to apply some readily derived and unsurprising formulae to gain some insights about a question of interest to demographers, namely, how change in age-specific mortality affects life expectancy. Formulae (3), (9) and (10) in my article are exact. Perhaps Professor Mitra's comment refers to the approximations that have to be made to apply these formulae to discrete data, but every demographer understands this. Only in two short and incidental paragraphs in my article is a Gompertz curve used, as 'a simple model' to gain two insights. The first insight is that if mortality rates at younger ages are low and if mortality rates at older ages increase exponentially, then the age at which there is the greatest potential for saving years of life (as measured by q in my article) is 'roughly equal to life expectancy at birth'. The second insight is that steady progress against mortality may reduce H and hence the relative increase in life expectancy each year, but the absolute increase in life expectancy each year may be constant. If mortality rates follow a Gompertz trajectory with the coefficient 0.1 in the exponent, then steady progress in reducing mortality rates at all ages at the rate of one per cent per year will result in an increase in life expectancy of a decade every century.