Abstract
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from “before” and “after” cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to “variable-r” methods. Unlike those methods, however, the new technique does not require specialized computer programming or iterative calculations, and event rates can be calculated directly from cross-sectional data in simple spreadsheets. The article includes a formal mathematical exposition of the method, simulation tests, and several examples.
Similar content being viewed by others
References
Arthur, W.B. and J.W. Vaupel. 1984. “Some General Relationships in Population Dynamics.” Population Index 50:214–26.
Becker, N.G. and I.C. Marschner. 1993. “A Method for Estimating the Age-Specific Relative Risk of HIV Infection From AIDS Incidence Data.” Biometrika 80:165–78.
Bennett, N.G. and S. Horiuchi. 1981. “Estimating the Completeness of Death Registration in a Closed Population.” Population Index 47:207–21.
—. 1984. “Mortality Estimation From Registered Deaths in Less Developed Countries.” Demography 21:217–33.
Borjas, G.J. 1994. “The Economics of Immigration.” Journal of Economic Literature 32:1667–717.
Brewster, K.L. and I. Padavic. 2000. “Changes in Gender Ideology, 1977–1996: The Contributions of Intracohort Change and Population Turnover.” Journal of Marriage and the Family 62:477–87.
Coale, A.J. 1984. “Life Table Construction on the Basis of Two Enumerations of a Closed Population.” Population Index 50:193–213.
— 1985. “An Extension and Simplification of a New Synthesis of Age Structure and Growth.” Asian and Pacific Census Forum 12(1):5–8.
Coale, A.J. and P. Demeny. 1966. Regional Model Life Tables and Stable Populations. Princeton, NJ: Princeton University Press.
Coale, A.J., A.M. John, and T. Richards. 1985. “Calculation of Age-Specific Fertility Schedules From Tabulations of Parity in Two Censuses.” Demography 22:611–23.
Davis, J.A. 1992. “Changeable Weather in a Cooling Climate Atop the Liberal Plateau: Conversion and Replacement in Forty-Two General Social Survey Items, 1972–1989.” Public Opinion Quarterly 56(3):261–306.
Heuser, R.L. 1976. Fertility Tables for Birth Cohorts by Color. U.S. Department of Health, Education, and Welfare. DHEW Publication No. (HRA)76-1152. Available on-line with additional data for 1974–1980 at http://opr.princeton.edu/archive/other/heuser.html.
Hoem, J.M., D. Madsen, J.L. Nielsen, E-M Ohlsen, H.O. Hansen, and B. Rennermalm. 1981. “Experiments in Modelling Recent Danish Fertility Curves.” Demography 18:231–44.
Hofferth, S.L., J.R. Kahn, and W. Baldwin. 1987. “Premarital Sexual Activity Among U.S. Teenage Women Over the Past Three Decades.” Family Planning Perspectives 19(2):46–53.
McNeil, D.R., T.J. Trussell, and J.C. Turner. 1977. “Spline Interpolation of Demographic Data.” Demography 14:245–52.
Nagelkerke, N., S. Heisterkamp, M. Borgdorff, J. Broekmans, and H. van Houwelingen. 1999. “Semi-Parametric Estimation of Age-Time Specific Infection Incidence From Serial Prevalence Data.” Statistics in Medicine 18:307–20.
Coale, A.J. Coale, A.J. National Center for Health Statistics. 2000. “Births: Final Data for 1998.” National Vital Statistics Reports, Vol. 48 No. 3. Available on-line at http://www.cdc.gov/nchs/data/nvsr/nvsr48/ nvs48_03.pdf [retrieved March 18, 2002].
Preston, S.H. 1983. “An Integrated System for Demographic Estimation From Two Age Distributions.” Demography 20:213–26.
Preston, S.H. and A.J. Coale. 1982. “Age Structure, Growth, Attrition, and Accession: A New Synthesis.” Population Index 48:217–59.
—. 1986. “Age Intervals and Time Intervals: Reply to Kim.” Demography 23:463–65.
Ross, J.A. 1992. “Sterilization: Past, Present, and Future.” Studies in Family Planning 23(3):187–98.
Ruggles, S., M. Sobek et al. 1997. Integrated Public Use Microdata Series: Version 2.0. Minneapolis: Historical Census Projects, University of Minnesota. Available on-line at http:// www.ipums.umn.edu.
Smith, J.P. and M.P. Ward, 1985. “Time-Series Growth in the Female Labor Force.” Journal of Labor Economics 3(1, pt. 2):59–90.
Stoto, M.A. 1988. “Estimating Age-Specific Transition Rates for Population Subgroups From Successive Surveys: Changes in Adult Rates of Cigarette Smoking.” Population Studies 42:227–39.
Stupp, P.W. 1988. “Estimating Intercensal Age Schedules by Intracohort Interpolation.” Population Index 54:209–24.
Zeng, Y., A.J. Coale, M.K. Choe, L. Zhiwu, and L. Li. 1994. “Leaving the Parental Home: Census-Based Estimates for China, Japan, South-Korea, United States, France, and Sweden.” Population Studies 48:65–80
Author information
Authors and Affiliations
Corresponding author
Additional information
Earlier versions of this article were presented at the 2000 Southern Demographic Association meetings in New Orleans and at the 2001 annual meetings of the Population Association of America in Washington, DC. I thank Monica Boyd, Tom Bryan, Joe Potter, Ken Wachter, and an anonymous reviewer for their helpful comments and critiques.
Rights and permissions
About this article
Cite this article
Schmertmann, C.P. A Simple method for estimating age-specific rates from sequential cross sections. Demography 39, 287–310 (2002). https://doi.org/10.1353/dem.2002.0018
Issue Date:
DOI: https://doi.org/10.1353/dem.2002.0018