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28 Mathematical Demography

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Handbook of Population

Part of the book series: Handbooks of Sociology and Social Research ((HSSR))

Abstract

Mathematical demography is the subfield of demography that is concerned with developing and refining measures and methods for studying population composition and change. Historically, demographers used population level data to compute measures of the key components of population change: fertility, mortality, and migration. However, the field has expanded considerably over the last half century to include predictors and consequences of demographic change. Sample data is now commonly used by demographers, and statistical methods are commonly used in conjunction with mathematical methods. In this chapter, we define key mathematical concepts that form the basis for historical and contemporary demographic analyses, including the population balancing equation and rates. We discuss the single decrement life table and its extensions to multiple decrements and multiple living states. Next, we discuss the stationary population theory that underlies life table computations and show its extension to stable and nonstable populations. Finally, we discuss several topics of contemporary concern, including population momentum, household projection methods, quantum and tempo adjustments, and methods for cohort analysis.

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References

  • Arias, E, Heron M, & Xu JQ. (2017). United States life tables, 2014. National vital statistics reports 66(4). Hyattsville, MD: National Center for Health Statistics.

    Google Scholar 

  • Bean, F.D. (1983). The Baby Boom and its explanations. The Sociological Quarterly 24(3), 353–365.

    Article  Google Scholar 

  • Bell, M. & Cooper, J. (1990). Household forecasting: Replacing the headship rate model. Paper presented at the Fifth National Conference, Australian Population Association, Melbourne, November.

    Google Scholar 

  • Bennett, N.G. & S. Horiuchi. (1981). Estimating the completeness of death registration in a closed population. Population Index 42, 207–21.

    Article  Google Scholar 

  • Berard-Chagnon, J. (2015). Using tax data to estimate the number of families and households in Canada. In N. N. Hoque & L. B. Potter (Eds.), Emerging techniques in applied demography (pp. 137–153). Springer: Dordrecht, The Netherlands.

    Google Scholar 

  • Blue, L. and Espenshade, T.J. (2011). Population momentum across the demographic transition. Population Development and Review 37(4), 721–747.

    Article  Google Scholar 

  • Bongaarts, J. & R.A. Bulatao. (1999). Completing the demographic transition. Population and Development Review 25, 515–29.

    Article  Google Scholar 

  • Bongaarts, J. & G. Feeney. (1998). On the quantum and tempo of fertility. Population and Development Review 24, 271–291.

    Article  Google Scholar 

  • Cai, L., Hayward, MD, Saito, Y., Lubitz, J., Hagedorn, A., & Crimmins, E. (2010). Estimation of multi-state life table functions and their variability from complex survey data using the SPACE program. Demographic Research 22(6), 129–158.

    Article  Google Scholar 

  • Chiang, C.-L. (1960). Stochastic study of the life table and its applications, II: Sample variance of the observed expectations of life and other biometric functions. Human Biology 32, 221–238.

    Google Scholar 

  • Chiang, C.-L. (1972). On constructing current life tables. Journal of the American Statistical Association 67, 538–541.

    Google Scholar 

  • Christiansen, S.G, & N. Keilman (2013). Probabilistic household forecasts based on register data – the case of Denmark and Finland. Demographic Research, 28, 1263–1302.

    Article  Google Scholar 

  • Coale, A.J. (1974). The history of human population. Scientific American 123(3), 41–51.

    Google Scholar 

  • Cox, D. R. (1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society B 34, 187–220.

    Google Scholar 

  • Crimmins, E. M., Y. Saito, & M. D. Hayward. (1993). Sullivan and multistate methods of estimating active life expectancy: Two methods, two answers. In J. M. Robine, C. D. Mathers, M. R. Bone, & I. Rommieu (eds) Calculation of Health Expectancies: Harmonization, Consensus Achieved and Future Perspectives (Pp. 155–160). Montrouge: John Libbey Eurotext.

    Google Scholar 

  • Dalton, M., B. O’Neill, A. Prskawetz, L. Jiang, & J. Pitkin. (2008). Population aging and future carbon emissions in the United States. Energy Economics 30, 642–675.

    Article  Google Scholar 

  • Ehrlich, P.R. (1968). The Population Bomb. New York: Ballantine.

    Google Scholar 

  • Elandt-Johnson, R. C. and N. L. Johnson. (1980). Survival models and data analysis. New York: Wiley.

    Google Scholar 

  • Espenshade, T. Olgiati, A., & Levin, S. (2011). On nonstable and stable population momentum. Demography 48(4), 1581–1599.

    Article  Google Scholar 

  • Feng, Q., Z. Wang, D. Gu, & Y. Zeng. (2011). Household vehicle consumption forecasts in the United States, 2000 to 2025. International Journal of Market Research 53(5), 593–618.

    Article  Google Scholar 

  • Feng, Q., J. W. Yeung, Z. Wang, & Y. Zeng. (2018). Age of retirement and human capital in an aging China, 2015–2050. European Journal of Population doi:https://doi.org/10.1007/s10680-018-9467-3.

  • Gavrilov, L.A. & Gavrilova, N.S. (2011). Mortality measurement at advanced ages: A study of the Social Security Administration Death Master File. North American Actuarial Journal 15(3), 432–447.

    Article  Google Scholar 

  • Goldstein, J.R. (2002). Population momentum for gradual demographic transitions: An alternative approach. Demography 39, 65–73.

    Article  Google Scholar 

  • Goldstein, J.R. & G. Stecklov. (2002). Long-range population projections made simple. Population and Development Review 28, 121–41.

    Article  Google Scholar 

  • Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115, 513–585.

    Article  Google Scholar 

  • Greenberg, B.G., J. J. Wright, & C. G. Sheps. (1950). A technique for analyzing some factors affecting the incidence of syphilis. Journal of the American Statistical Association 45, 373–399.

    Article  Google Scholar 

  • Hammel, E.A., Mason, C., Wachter, K.W., Wang, F., & Yang, H. (1991). Rapid population change and kinship: The effects of unstable demographic changes on Chinese kinship networks, 1750–2250. Pp. 243 271 Consequences of Rapid Population Growth in Developing Countries: Proceedings of the United Nations. New York: Taylor & Francis.

    Google Scholar 

  • Hayward, M. D. & W. R. Grady. (1990). Work and retirement among a cohort of older men in the United States. Demography 27, 337–356.

    Article  Google Scholar 

  • Hayward, M. D., Rendall, M., & Crimmins, E. (1999). Evaluating group differences in healthy life expectancy: The estimation of confidence intervals for multistate life table expectancies. Paper presented at the annual meeting of the Gerontological Society of America, San Francisco, CA.

    Google Scholar 

  • Heigl, Andreas. (2001). Demographic fact book. http : //www. hypovereinsbank. de/media/pdf/resechandefaboWelt. pdf.

    Google Scholar 

  • Hobcraft, John, Jane Menken, & Samuel H. Preston. (1982). Age, period, and cohort effects in demography: A review. Population Index 48, 4–43.

    Article  Google Scholar 

  • Hoem, Jan M. & M. S. Fong. (1976). A Markov chain model of working life tables. Working Paper No. 2, Laboratory of Actuarial Mathematics, University of Copenhagen, Denmark.

    Google Scholar 

  • Hullen, Gert. (2000). Projections of living arrangement, household and family structures using ProFamy. Warschau, Deutsch-polnisch-ungarisches Demographentreffen, October, 2000.

    Google Scholar 

  • Hullen, Gert. (2001). New macrosimulations of living arrangements and households in Germany. Paper presented at Population Association of America, 2001 Annual Meeting, March, 2001.

    Google Scholar 

  • Hullen, Gert. (2003). Living arrangements and households: methods and results of demographic projection. A book (reader) published by the German Federal Institute for Population Research (BIB), with Forward writhen by Charlotte Hohn, Director of BIB. http : //www. gert − hullen. privat. t − online. de/manuskripte/materialienhu29072003. pdf.

    Google Scholar 

  • Imai, K. & Soneji, S. (2007). On the estimation of disability-free life expectancy. Journal of the American Statistical Association 102(480), 1199–1211.

    Article  Google Scholar 

  • Jiang, Leiwen & A. Kuijsten. (1999a). Effects of changing households on environment – case studies in two regions of China. Paper presented at workshop Population and Environment: Modeling and Simulating This Complex Interaction, organized by Max Planck Institute for Demographic Research at Rostock, Germany, August 12–13, 1999.

    Google Scholar 

  • Jiang, Leiwen & A. Kuijsten. (1999b). Household projections for two regions of China. Paper presented at the European Population Conference, the Hague, The Netherlands, August 30 – September 3, 1999.

    Google Scholar 

  • Jiang, L, & B. C. O’Neill. (2007). Impacts of demographic trends on US household size and structure. Population and Development Review 33(3), 567–591.

    Article  Google Scholar 

  • Jordan, C. W., Jr. (1975). Life contingencies. 2nd ed. Chicago: The Society of Actuaries.

    Google Scholar 

  • Kalbfleisch, J. D. & R. L. Prentice. (2002). The statistical analysis of failure time data (2nd ed.) New York: Wiley.

    Google Scholar 

  • Katz, S., L. G. Branch, M. H. Branson, J. A. Papsidero, J. C. Beck, & D. S. Greer. (1983). Active life expectancy. New England Journal of Medicine 309, 1218–1224.

    Google Scholar 

  • Keilman, N. (1988). Dynamic household models. In N. Keilman, A. Kuijsten, & A. Vossen (Eds.), Modelling household formation and dissolution (Pp. 123–138). Oxford: Clarendon Press.

    Google Scholar 

  • Keilman, N. (1994). Translation formulae for non-repeatable events. Population Studies 48, 341–357.

    Article  Google Scholar 

  • Keilman, N. & E. V. Imhoff. (1995). Cohort quantum as a function of time-dependent period quantum for non-repeatable events Population Studies 49, 347–352.

    Google Scholar 

  • Keyfitz, N. (1968). A life table that agrees with the data: II. Journal of the American Statistical Association 63, 1253–1268.

    Article  Google Scholar 

  • Keyfitz, N. (1970). Finding probabilities from observed rates, or how to make a life table. The American Statistician 24, 28–33.

    Google Scholar 

  • Keyfitz, N. (1971). On the momentum of population growth. Demography 8, 71–80.

    Article  Google Scholar 

  • Keyfitz, N. (1977). Introduction to the mathematics of population with revisions. Reading, Mass: Addsion-Wesley.

    Google Scholar 

  • Keyfitz, N. (1985). Applied mathematical demography. 2nd ed. New York: Wiley.

    Book  Google Scholar 

  • Kim, Y.J. & R. Schoen. (1993). Crossovers that link populations with the same vital rates. Mathematical Population Studies 4, 1–19.

    Article  Google Scholar 

  • Kim, Y.J. (1997). Population momentum expresses population aging. Demography 34, 421–8.

    Article  Google Scholar 

  • Kim, Y.J., R. Schoen, & P.S. Sarma. (1991). Momentum and the growth-free segment of a population. Demography 28, 159–76.

    Article  Google Scholar 

  • Kohler, H. P. & M. Philipov. (1999). Variance effects in the Bongaarts-Feeney formula. Demography 38 (1), 1–16.

    Article  Google Scholar 

  • Kreager, P. (1993). Histories of demography: A review article.’ Population Studies 47, 519–539.

    Google Scholar 

  • Kupper, Lawrence L., Joseph M. Janis, Azza Karmous, & Bernard G. Greenberg. (1985). Statistical age-period-cohort analysis: A review and critique. Journal of Chronic Disease 38, 811–30.

    Google Scholar 

  • Kye, B. (2014). A method of estimating number of households using the ProFamy model. Statistics Korea (Requested Research Report). (in Korean)

    Google Scholar 

  • Laditka, S.B. & Wolf, D.A. (1998). New methods for analyzing active life expectancy. Journal of Aging and Health 10, 214–241.

    Article  Google Scholar 

  • Land, K.C. & G. C. Hough, Jr. (1989). New methods for tables of school life, with applications to U.S. data from recent school years. Journal of the American Statistical Association 84 (March), 63–75.

    Google Scholar 

  • Land, K.C., J. M. Guralnik, & D. G. Blazer. (1994). Estimating increment-decrement life tables with multiple covariates from panel data: The case of active life expectancy. Demography 31 (May), 297–319.

    Article  Google Scholar 

  • Land, K.C. & A. Rogers (eds.). (1982). Multidimensional mathematical demography. New York: Academic Press.

    Google Scholar 

  • Lee, M.A. & Rendall, M.S. (2001). Self-employment disadvantage in the working lives of blacks and females. Population Research and Policy Review 20, 291–320.

    Article  Google Scholar 

  • Leslie, P. H. (1945). On the use of matrices in certain population mathematics. Biometrika 33(3), 183–212.

    Article  Google Scholar 

  • Leslie, P.H. (1948). Some further notes on the use of matrices in population mathematics. Biometrika 35(3–4), 213–245.

    Article  Google Scholar 

  • Li, N. & S. Tuljapurkar. (1999). Population momentum for gradual demographic transitions. Population Studies 53, 255–62.

    Article  Google Scholar 

  • Li, N. (2000). The solution of time-dependent population models. Mathematical Population Studies 7, 311–29.

    Article  Google Scholar 

  • Lièvre, A, Brouard, N. & Heathcote, C. (2003). The estimation of health expectancies from cross-longitudinal surveys. Mathematical Population Studies 10(4), 211–248.

    Article  Google Scholar 

  • Lynch, S.M. (2003). Cohort and life-course patterns in the relationship between education and health: a hierarchical approach. em Demography 40(2), 309–331.

    Article  Google Scholar 

  • Lynch, S.M. (2006). Explaining life course and cohort variation in the relationship between education and health: the role of income. Journal of Health and Social Behavior 47(4), 324–338.

    Article  Google Scholar 

  • Lynch, S.M, & Brown J.S. (2005). A new approach to estimating life tables with covariates and constructing interval estimates of life table quantities. Sociological Methodology 35, 177–225.

    Google Scholar 

  • Lynch, S.M. & Brown J.S. (2010). Obtaining multistate life table distributions for highly refined subpopulations from cross-sectional data: A Bayesian extension of Sullivan’s method. Demography 47(4),1053–1077.

    Article  Google Scholar 

  • Malthus, T.R. (1798). Essay on the Principle of Population. London: J. Johnson, in St. Paul’s Church-yard (retrieved from the web, 9/15/2018).

    Google Scholar 

  • Mason, A. & Racelis, R. (1992). A comparison of four methods for projecting households. International Journal of Forecasting 8, 509–527.

    Article  Google Scholar 

  • Mason, Karen Oppenheim, William M. Mason, H. H. Winsborough, & W. Kenneth Poole. (1973). Some methodological issues in cohort analysis of archival data. American Sociological Review 38, 242–258.

    Article  Google Scholar 

  • Mason, William M. & N. H. Wolfinger. (2002). Cohort analysis. In International Encyclopedia of the Social and Behavioral Sciences (pp. 151–228). New York: Elsevier.

    Google Scholar 

  • Masters, R.K.., R.A. Hummer, & D.A. Powers. (2012). Educational differences in U.S. adult mortality risk: a cohort perspective. American Sociological Review 77(4), 548–572.

    Article  Google Scholar 

  • Merli, G. (1998). Mortality in Vietnam, 1979–1989. Demography 35, 345–60.

    Article  Google Scholar 

  • Miyazaki, Yasuo & Stephen W. Raudenbush. (2000). Tests for linkage of multiple cohorts in an accelerated longitudinal design. Psychological Methods 5, 44–63.

    Article  Google Scholar 

  • Molla, MT, Wagener, DK, & Madans, JH. (2001). Summary measures of population health: methods for calculating healthy life expectancy. Healthy People Statistical Notes No. 21. National Center for Health Statistics, Hyattsville, MD.

    Google Scholar 

  • Morgan, S. P. & S. M. Lynch. (2001). Success and future of demography: The role of data and methods. Special Issue on Population Health and Aging: Strengthening the Dialogue between Epidemiology and Demography. Annals of the New York Academy of Sciences 954, 35–51.

    Google Scholar 

  • Murphy, M.. (1991). Modelling households: A synthesis. In M.J. Murphy & J. Hobcraft (Eds.), Population Research in Britain, A Supplement to Population Studies, Vol. 45 (pp. 157–176). London: Population Investigation Committee, London School of Economics.

    Google Scholar 

  • National Research Council. (2000). Beyond six billion: Forecasting the world’s population. Edited by J. a. R. A. B. Bongaarts. Washington, D.C.: National Academy Press.

    Google Scholar 

  • Oh, J. (2015). Review of recent trend in diverse methods of estimating future households. Statistics Korea (Policy Report): 1–18. (in Korean)

    Google Scholar 

  • O’Neill, B. C. & B. S. Chen. (2002). Demographic determinants of household energy use in the United States. Population and Development Review 28(S), 53–88.

    Google Scholar 

  • O’Neill, B. C. & L. Jiang. (2007). Projecting U.S. Household Changes with a New Household Model. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-07-017.

    Google Scholar 

  • Preston, S. H. (1986). The Relation between actual and intrinsic growth rates. Population Studies 40, 343–51.

    Article  Google Scholar 

  • Preston, S. H. & N. Bennett. (1983). A census-based method for estimating adult mortality. Population Studies 37, 91–104.

    Article  Google Scholar 

  • Preston, S. H. & A. J. Coale. (1982). Age structure, growth, attrition and accession: A new synthesis. Population Index 48, 17–59.

    Article  Google Scholar 

  • Preston, S.H., I.T. Elo, I. Rosenwaike, & M. Hill. (1996). African-American mortality at older ages: Results of a matching study. Demography 35,1–21.

    Article  Google Scholar 

  • Preston, S.H. & M. Guillot. (1997). Population dynamics in an age of declining fertility. Genus 53, 15–31.

    Google Scholar 

  • Preston, S. H., P. Heuveline, & M. Guillot. (2000). Demography: Measuring and modeling population processes. Malden, MA: Blackwell.

    Google Scholar 

  • Preston, S. H., N. Keyfitz, & R. Schoen. (1972). Causes of death: Life tables for national populations. New York: Seminar Press.

    Google Scholar 

  • Prskawetz, A., L. Jiang, & B. O’Neill. (2004). Demographic composition and projections of car use in Austria. Vienna Yearbook of Population Research 2, 274–326.

    Google Scholar 

  • Reither, E. N., S. J. Olshansky, & Y. Yang. (2011). New forecasting methodology indicates more disease and earlier mortality ahead for today’s younger Americans. Health Affairs 30, 1562–1568.

    Article  Google Scholar 

  • Rogers, A. (1975). Introduction to multiregional mathematical demography. New York: ?

    Google Scholar 

  • Ruggles, S. (1987). Prolonged connections: The rise of the extended family in nineteenth century England and America. Madison: University of Wisconsin Press.

    Google Scholar 

  • Ruggles, S. (1993). Confessions of a microsimulator: Problems in modeling the demography of kinship. Historical Methods 26(4), 161–169.

    Article  Google Scholar 

  • Ryder, N. B. (1956). Problems of trend determination during a translation in fertility. Milbank Memorial Fund Quarterly 34(1), 5–21.

    Article  Google Scholar 

  • Ryder, N. B. (1959). An appraisal of fertility trends in the United States. Pp. 38–49 in Thirty Years of Research in Human Fertility: Retrospect and Prospect, 1959, New York: Milbank Memorial Fund.

    Google Scholar 

  • Ryder, N. B. (1964). The process of demographic translation. Demography 1, 74–82.

    Article  Google Scholar 

  • Ryder, N. B. (1980). Components of temporal variations in American fertility. In R. W. Hiorns (Ed.), Demographic Patterns in Developed Societies (pp. 15–54). London: Taylor Francis.

    Google Scholar 

  • Ryder, N. B. (1983). Cohort and period measures of changing fertility. In Rodolfo A. Bulatao & Ronald D. Lee with Paula E. Hollerbach & John Bongaarts (Eds.), Determinants of fertility in developing countries (pp. 737–756). New York: Academic Press.

    Google Scholar 

  • Schoen, R. (1975). Constructing increment-decrement life tables. Demography 13, 313–324.

    Article  Google Scholar 

  • Schoen, R. (1978). Calculating life tables by estimating Chianga. Demography 15, 625–635.

    Article  Google Scholar 

  • Schoen, R. (1988). Modeling multigroup populations. New York: Plenum.

    Book  Google Scholar 

  • Schoen, R. & S.H. Jonsson. (2003). Modeling momentum in gradual demographic transitions. Demography 40, 621–35.

    Article  Google Scholar 

  • Schoen, R. (1998). Momentum under a gradual approach to zero growth. Population Studies 52, 295–99.

    Article  Google Scholar 

  • Schoen, R. & K. C. Land. (1979). A general algorithm for estimating a Markov-generated increment-decrement life table with applications to marital status patterns. Journal of the American Statistical Association 74, 761–776.

    Article  Google Scholar 

  • Schulhofer-Wohl, Sam & Yang Claire Yang. (2016). Modeling the evolution of age and cohort effects. Pp. 313 “ 336 In R. Schoen (Ed.), Dynamic Demographic Analysis (pp. 313–336). Springer.

    Google Scholar 

  • Smith, S. K., S. Rayer, & E. A. Smith. (2008). Aging and disability: Implications for the housing industry and housing policy in the United States. Journal of the American Planning Association 74(3), 289–306.

    Article  Google Scholar 

  • Smith, S. K., S. Rayer, E. A. Smith, Z. Wang, & Y. Zeng. (2012). Population aging, disability and housing accessibility: Implications for sub-national areas in the United States. Housing Studies 27(2), 252–266.

    Article  Google Scholar 

  • Spicer, K., Diamond, I. & Ni Bhrolchain, M. (1992). Into the twenty-first century with British households. International Journal of Forecasting 8, 529–539.

    Article  Google Scholar 

  • Sullivan, D. F. (1971). A single index of mortality and morbidity. HSMHA Health Report 86, 347–354.

    Article  Google Scholar 

  • Thatcher, A.R., V. Kannisto, & J.W. Vaupel. (1998). The force of mortality at ages 80 to 120. Odense: Odense University Press. Online at http://www.demogr.mpg.de/Papers/Books/Monograph5/ForMort.htm.

    Google Scholar 

  • Trussell, J. & Hammerslough, C. (1983). A hazards-model analysis of the covariates of infant and child mortality in Sri Lanka. Demography 20(1), 1–26.

    Article  Google Scholar 

  • United Nations. (1983). Manual X: Indirect techniques for demographic estimation. New York: United Nations.

    Google Scholar 

  • Van Imhoff, E. & Keilman, N. (1992). LIPRO 2.0: An application of a dynamic demographic projection model to household structure in the Netherlands. Amsterdam, Netherlands: Swets & Zeithinger.

    Google Scholar 

  • Van Imhoff, E. & Post, W. (1998). Microsimulation methods for population projection. New Methodological Approaches in the Social Sciences, Population: An English Selection 10(1), 97–138.

    Google Scholar 

  • Van Imhoff, E. & N. Keilman. (2000). On the quantum and tempo of fertility: Comment. Population and Development Review 26, 549–53.

    Article  Google Scholar 

  • Van Imhoff, E. (2005). LIPRO 4.0. Tutorial. The Hague: NIDI. http://www.nidi. knaw.nl/shared/content/output/lipro/LIPRO%204.0%20Tutorial.pdf.

    Google Scholar 

  • Wachter, K.W. (1987). Microsimulation of household cycles. In E. Bongaarts, T.K. Burch, & K.W. Wachter (Eds.), Family Demography: Methods and Applications (pp. 215–227). Oxford: Clarendon Press.

    Google Scholar 

  • Willekens, F.J., I. Shah, J.M. Shah & P. Ramachandran. (1982). Multistate analysis of marital status life tables: theory and application. Population Studies Vol. 36, No. 1, pp. 129–144.

    Article  Google Scholar 

  • Wilson, T. (2013). The sequential propensity household projection model. Demographic Research, 28, 681–712.

    Article  Google Scholar 

  • Wolf, D.A. (1988). Kinship and family support in aging societies. In Economic and social implications of population aging, (pp. 305–330). Population Division, United Nations.

    Google Scholar 

  • Yang, C. & Y. Zeng. (2000). Household projections for Taiwan. Taiwanese Journal of Sociology 24, 239–79.

    Google Scholar 

  • Yang, Yang, Wenjiang J. Fu, & Kenneth C. Land. (2004). A methodological comparison of age-period-cohort models: Intrinsic estimator and conventional generalized linear models. Sociological Methodology 34, 75–110.

    Article  Google Scholar 

  • Yang, Yang. (2006). Bayesian inference for hierarchical age-period-cohort models of repeated cross-section survey data. Sociological Methodology 36, 39–74.

    Article  Google Scholar 

  • Yang, Yang. (2007). Is old age depressing? Growth trajectories and cohort variations in late life depression. Journal of Health and Social Behavior 48, 16–32.

    Article  Google Scholar 

  • Yang, Yang & Kenneth C. Land. (2006). A mixed models approach to age-period-cohort analysis of repeated cross-section surveys: Trends in verbal test scores. Sociological Methodology 36, 75–97.

    Article  Google Scholar 

  • Yang, Y., & L. C. Lee. (2009). Sex and race disparities in health: Cohort variations in life course patterns. Social Forces 87, 2093–2124.

    Article  Google Scholar 

  • Yang, Y. & K. C. Land. (2013). Age-period-cohort analysis: New models, methods, and empirical applications. New York: Chapmen & Hall/CRC Press.

    Google Scholar 

  • Zang, E. & Lynch, SM. (2018). Bayesian multistate life table methods for complex, high-dimensional state spaces. Paper presented at the annual meeting of the Population Association of America, Chicago, IL.

    Google Scholar 

  • Zeng, Y. & K.C. Land. (2001). A sensitivity analysis of the Bongaarts-Feeney new method for adjusting bias in observed period total fertility rates. Demography, 38, 17–28.

    Article  Google Scholar 

  • Zeng, Y. (2002). Adjusting period tempo changes “ with an extension of Ryder basic translation equation. Demography, 39, 269–285.

    Google Scholar 

  • Zeng, Yi, D. Gu, & K. C. Land. (2004). A new method for correcting underestimation of disabled life expectancy and application to Chinese Oldest-Old. Demography 41 (2).

    Google Scholar 

  • Zeng, Yi., K. C. Land, Z. Wang, & D. Gu. (2006). U.S. family household momentum and dynamics: An extension and application of the ProFamy method. Population Research and Policy Review 25(1), 1–41.

    Article  Google Scholar 

  • Zeng, Y. (2007). Option for fertility policy transition in China. Population and Development Review 33(2), 215–246.

    Article  Google Scholar 

  • Zeng, Y., Z. Wang, L. Jiang, & D. Gu. (2008). Future trend of family households and elderly living arrangement in China. Genus 64(1/2), 9–36.

    Google Scholar 

  • Zeng, Y. (2011). Effects of demographic and retirement-age policies on future pension deficits, with an application to China. Population and Development Review 37(3), 553–569.

    Article  Google Scholar 

  • Zeng, Y., L. Li, Z. Wang, H. Huang, & J. Norris. (2013). Effects of changes in household structure on future housing demand in Hebei Province, China. Genus 69(2), 85–111.

    Google Scholar 

  • Zeng, Y., K. C. Land, D. Gu, & Z. Wang. (2014). Household and living arrangement projections: The extended cohort-component method and applications to the U.S. and China. New York: Springer Publisher.

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Sociology, Duke University, Durham, NC, USA

    Scott M. Lynch, Kenneth C. Land & Zeng Yi

  2. University of North Carolina, Chapel Hill, NC, USA

    Yang Claire Yang

Authors
  1. Scott M. Lynch
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  2. Kenneth C. Land
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  3. Yang Claire Yang
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  4. Zeng Yi
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Correspondence to Scott M. Lynch .

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Editors and Affiliations

  1. Department Sociology, Texas A&M University, College Station, TX, USA

    Dudley L. Poston Jr.

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Lynch, S.M., Land, K.C., Yang, Y.C., Yi, Z. (2019). 28 Mathematical Demography. In: Poston, D.L. (eds) Handbook of Population. Handbooks of Sociology and Social Research. Springer, Cham. https://doi.org/10.1007/978-3-030-10910-3_29

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  • DOI: https://doi.org/10.1007/978-3-030-10910-3_29

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