| Abstract: | In a recent issue of Population Index, Coale (1984) described a method of deriving a life table for an intercensal period separated by T years from 2 census single-year age distributions of a closed population. This note examines the formula used by Coale and points out that although it works well for all practical purposes, the formula with his new growth rate is an approximation, not an identity as is assumed by Coale. The Coale formula involves more steps than the usual method of estmating mortality and yields less accurate results. Coale's formula is explained. In general, in the case under consideration, if a larger cohort is followed by a smaller cohort, the survival probability calculated by the formula exceeds unity, whereas if a smaller cohort is followed by a larger cohort, the calculated survival probability becomes less than unity. The size of the relative cohorts determines the degree of error in the calculated probability. The formula does not give the survival probability of unity as it should if it were an identity. The formula in the continuous time is an identity. Feeney's alternative method presented in Coale's Computational Appendix 3 produces an exact life table without using any formula. Feeney's method is, however, less accurate than the usual method, given the same data, because it omits some information. The Coale procedure losses its usefulness in that it requires extra data manipulation, only to yield less accurate results. |
