Combining forward and backward mortality estimation

Abstract

Demographers often form estimates by combining information from two data sources—a challenging problem when one or both data sources are incomplete. A classic example entails the construction of death probabilities, which requires death counts for the subpopulations under study and corresponding base population estimates. Approaches typically entail ‘back projection', as in Wrigley and Schofield's seminal analysis of historical English data, or ‘inverse’ or ‘forward projection’ as used by Lee in his important reanalysis of that work, both published in the 1980s. Our paper shows how forward and backward approaches can be optimally combined, using a generalized method of moments (GMM) framework. We apply the method to the estimation of death probabilities for relatively small subpopulations within the United States (men born 1930–39 by state of birth by birth cohort by race), combining data from vital statistics records and census samples.

Keywords:

• Mortality
• forward estimation
• backward estimation

Notes

1 Professor Lowell J. Taylor, Heinz College, Carnegie Mellon University, Pittsburgh, PA 15213, USA. E-mail: [email protected]

2 We gratefully acknowledge support from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (RO1 HD062747). The content is solely the responsibility of the authors and does not necessarily represent the official views of the Eunice Kennedy Shriver National Institute of Child Health and Human Development or the National Institutes of Health. We also wish to thank the Population Center at the University of Chicago for support. We appreciate comments from seminar participants at the University of Chicago, the Population Association of America, Princeton University, and the University of California at Berkeley. We particularly thank Donald Bogue, Ronald Lee, and Shiro Horiuchi for insightful comments on an earlier draft.