Demography

, Volume 48, Issue 3, pp 815–839

Probabilistic Projections of the Total Fertility Rate for All Countries

  • Leontine Alkema
  • Adrian E. Raftery
  • Patrick Gerland
  • Samuel J. Clark
  • François Pelletier
  • Thomas Buettner
  • Gerhard K. Heilig
Article

Abstract

We describe a Bayesian projection model to produce country-specific projections of the total fertility rate (TFR) for all countries. The model decomposes the evolution of TFR into three phases: pre-transition high fertility, the fertility transition, and post-transition low fertility. The model for the fertility decline builds on the United Nations Population Division’s current deterministic projection methodology, which assumes that fertility will eventually fall below replacement level. It models the decline in TFR as the sum of two logistic functions that depend on the current TFR level, and a random term. A Bayesian hierarchical model is used to project future TFR based on both the country’s TFR history and the pattern of all countries. It is estimated from United Nations estimates of past TFR in all countries using a Markov chain Monte Carlo algorithm. The post-transition low fertility phase is modeled using an autoregressive model, in which long-term TFR projections converge toward and oscillate around replacement level. The method is evaluated using out-of-sample projections for the period since 1980 and the period since 1995, and is found to be well calibrated.

Keywords

Autoregressive model Bayesian hierarchical model Fertility projection methodology Markov chain Monte Carlo United Nations World Population Prospects 

Supplementary material

13524_2011_40_MOESM1_ESM.pdf (1 mb)
(PDF 1.04 MB)

References

  1. Alders, M., Keilman, N., & Cruijsen, H. (2007). Assumptions for long-term stochastic population forecasts in 18 European countries. European Journal of Population, 23, 33–69.CrossRefGoogle Scholar
  2. Alho, J. M., Alders, M., Cruijsen, H., Keilman, N., Nikander, T., & Pham, D. Q. (2006). New forecast: Population decline postponed in Europe. Statistical Journal of the United Nations Economic Commission for Europe, 23, 1–10.Google Scholar
  3. Alho, J. M., Jensen, S. E. H., & Lassila, J. (2008). Uncertain demographics and fiscal sustainability. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  4. Alkema, L. (2008). Uncertainty assessments of demographic estimates and projections (Doctoral dissertation). University of Washington, Seattle.Google Scholar
  5. Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., & Pelletier, F. (2008a, April). Assessing uncertainty in fertility estimates and projections. Paper presented at the annual meeting of the Population Association of America, New Orleans, LA.Google Scholar
  6. Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., & Pelletier, F. (2008b). Estimating the total fertility rate from multiple imperfect data sources and assessing its uncertainty (Working Paper 89). Seattle: Center for Statistics and the Social Sciences, University of Washington. Retrieved from http://www.csss.washington.edu/Papers/wp89.pdf
  7. Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., & Pelletier, F. (2009, September). Probabilistic projections of the total fertility rate. Presented at the annual meeting of the International Union for the Scientific Study of Population, Marrakech, Morocco.Google Scholar
  8. Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., Pelletier, F., & Buettner, T. (2010). Probabilistic projections of the total fertility rate for all countries (Working Paper 97). Seattle: Center for Statistics and the Social Sciences, University of Washington. Retrieved from http://www.csss.washington.edu/Papers/wp97.pdf
  9. Billari, F. C., & Kohler, H.-P. (2004). Patterns of low and lowest-low fertility in Europe. Population Studies, 58, 161–176.CrossRefGoogle Scholar
  10. Bongaarts, J. (2002). The end of the fertility transition in the developing world. In Completing the fertility transition (UN document ESA/P/WP.172/Rev.1). New York: United Nations, Department of Economic and Social Affairs, Population Division. Retrieved from http://www.un.org/esa/population/publications/completingfertility/RevisedBONGAARTSpaper.PDF
  11. Bongaarts, J., & Bulatao, R. (2000). Beyond six billion: Forecasting the world’s population. Washington, DC: National Academy Press.Google Scholar
  12. Bongaarts, J., & Feeney, G. (1998). On the quantum and tempo of fertility. Population and Development Review, 24, 271–292.CrossRefGoogle Scholar
  13. Booth, H., Pennec, S., & Hyndman, R. (2009, September). Stochastic population forecasting using functional data methods: The case of France. Presented at the annual meeting of the International Union for the Scientific Study of Population, Marrakech, Morocco.Google Scholar
  14. Bos, E., Vu, M. T., Massiah, E., & Bulatao, R. (1994). World population projections 1994–95: Estimates and projections with related demographic statistics. Baltimore, MD: Johns Hopkins University Press for the World Bank.Google Scholar
  15. Cai, Y. (2008). Assessing fertility levels in China using variable-r method. Demography, 45, 371–381.Google Scholar
  16. Caltabiano, M., Castiglioni, M., & Rossina, A. (2009). Lowest-low fertility: Signs of a recovery in Italy? Demographic Research, 21, 681–718. doi:10.4054/DemRes.2009.21.23 CrossRefGoogle Scholar
  17. Casterline, J. B. (2001). The pace of fertility transition: National patterns in the second half of the twentieth century. Population and Development Review, 27(Suppl.), 17–52.Google Scholar
  18. Cleveland, W. S., & Devlin, S. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83, 596–610.CrossRefGoogle Scholar
  19. DellaPergola, S. (2007). Population trends and scenarios in Israel and Palestine. In A. M. Kacowicz & P. Lutomski (Eds.), Population resettlement in international conflicts: A comparative study (pp. 183–207). Lanham, MD: Rowman and Littlefield.Google Scholar
  20. DellaPergola, S. (2009). Actual, intended, and appropriate family size among Jews in Israel. Contemporary Jewry, 29, 127–152.CrossRefGoogle Scholar
  21. Frejka, T., & Sobotka, T. (2008). Fertility in Europe: Diverse, delayed and below replacement. Demographic Research, 19, 15–45. doi:10.4054/DemRes.2008.19.3 CrossRefGoogle Scholar
  22. Gelfand, A., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.CrossRefGoogle Scholar
  23. Gelman, A., Bois, F., & Jiang, J. (1996). Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association, 91, 1400–1412.CrossRefGoogle Scholar
  24. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data a nalysis (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
  25. Gu, B., & Cai, Y. (2009). Fertility prospects in China. In United Nations Expert Group Meeting on Recent and Future Trends in Fertility (UN document UN/POP/EGM-FERT/2009/6). New York: United Nations, Department of Economic and Social Affairs, Population Division. Retrieved from http://www.un.org/esa/population/meetings/EGM-Fertility2009/egm-fertility2009.html
  26. Guengant, J.-P., & May, J. F. (2002). Impact of the proximate determinants on the future course of fertility in sub-Saharan Africa. Population Bulletin of the United Nations, 46/47, 71–96.Google Scholar
  27. Hirschman, C. (1994). Why fertility changes. Annual Review of Sociology, 20, 203–233.CrossRefGoogle Scholar
  28. Hyndman, R. J., & Booth, H. (2008). Stochastic population forecasts using functional data models for mortality, fertility and migration. International Journal of Forecasting, 24, 323–342.CrossRefGoogle Scholar
  29. Keyfitz, N. (1981). The limits of population forecasting. Population and Development Review, 7, 579–593.CrossRefGoogle Scholar
  30. Kohler, H.-P., Billari, F. C., & Ortega, J. A. (2002). The emergence of lowest-low fertility in Europe during the 1990s. Population and Development Review, 28, 641–680.CrossRefGoogle Scholar
  31. Lee, R. D. (1993). Modeling and forecasting the time series of US fertility: Age distribution, range, and ultimate level. International Journal of Forecasting, 9, 187–202.CrossRefGoogle Scholar
  32. Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659–671.CrossRefGoogle Scholar
  33. Lee, R. D., & Tuljapurkar, S. (1994). Stochastic population forecasts for the United States: Beyond high, medium and low. Journal of the American Statistical Association, 89, 1175–1189.CrossRefGoogle Scholar
  34. Lindley, D. V., & Smith, A. F. M. (1972). Bayes estimates for the linear model. Journal of the Royal Statistical Society, Series B, 34, 1–41.Google Scholar
  35. Lutz, W. (1994). Population-Development-Environment: Understanding Their Interactions in Mauritius. New York: Springer-Verlag.Google Scholar
  36. Lutz, W., Sanderson, W. C., & Scherbov, S. (2001). The end of world population growth. Nature, 412, 543–545.CrossRefGoogle Scholar
  37. Mason, K. O. (1997). Explaining fertility transitions. Demography, 34, 443–454.CrossRefGoogle Scholar
  38. Morgan, P. S., Guo, Z., & Hayford, S. R. (2009). China’s below-replacement fertility: Recent trends and future prospects. Population and Development Review, 35, 605–629.CrossRefGoogle Scholar
  39. Morgan, S. P., & Taylor, M. G. (2006). Low fertility at the turn of the twenty-first century. Annual Review of Sociology, 32, 375–399.CrossRefGoogle Scholar
  40. Moultrie, T. A., & Timaeus, I. M. (2009, September). Stopping, spacing and postponing—Evidence of a uniquely African pattern of fertility decline. Presented at the XXVI International Population Conference of the International Union for the Scientific Study of Population, Marrakesh, Morocco. Retrieved from http://iussp2009.princeton.edu/download.aspx?submissionId=90376
  41. Myrskyla, M., Kohler, H.-P., & Billari, F. C. (2009). Advances in development reverse fertility declines. Nature, 460, 741–743.CrossRefGoogle Scholar
  42. Nahmias, P., & Stecklov, G. (2007). The dynamics of fertility amongst Palestinians in Israel from 1980 to 2000. European Journal of Population, 23, 71–99.CrossRefGoogle Scholar
  43. Neal, R. M. (2003). Slice sampling. The Annals of Statistics, 31, 705–767.CrossRefGoogle Scholar
  44. Preston, S. H., & Hartnett, C. S. (2008). The future of American fertility (NBER Working Paper 14498). Cambridge, MA: National Bureau of Economic Research. Retrieved from http://www.nber.org/papers/w14498
  45. Raftery, A. E., Alkema, L., Gerland, P., Clark, S. J., Pelletier, F., Buettner, T., ...Ševčíková, H. (2009). White paper: Probabilistic projections of the total fertility rate for all countries for the 2010 World Population Prospects. In United Nations Expert Group Meeting on Recent and Future Trends in Fertility (UN document UN/POP/EGM-FERT/2009/16). New York: United Nations, Department of Economic and Social Affairs, Population Division. Retrieved from http://www.un.org/esa/population/meetings/EGM-Fertility2009/egm-fertility2009.html
  46. Raftery, A. E., Lewis, S. M., & Aghajanian, A. (1995). Demand or ideation? Evidence from the Iranian marital fertility decline. Demography, 32, 159–182.CrossRefGoogle Scholar
  47. Retherford, R., Choe, M. K., Chen, J., Li, X., & Cui, H. (2005). Fertility in China: How much has it really declined? Population and Development Review, 19, 57–84.CrossRefGoogle Scholar
  48. Sanderson, W. C. (1998). Knowledge can improve forecasts: A review of selected socioeconomic population projection models. Population and Development Review, 24(Suppl.), 88–117.CrossRefGoogle Scholar
  49. Stoto, M. (1983). The accuracy of population forecasts. Journal of the American Statistical Association, 78, 13–20.CrossRefGoogle Scholar
  50. Timaeus, I. M., & Moultrie, T. A. (2008). On postponement and birth intervals. Population and Development Review, 34, 483–510.CrossRefGoogle Scholar
  51. United Nations, Department of Economic and Social Affairs, Population Division. (2006). Methodology of the United Nations population estimates and projections. World P opulation Prospects: T he 2004 Revision (Vol. III, Chapter VI). Retrieved from http://www.un.org/esa/population/publications/WPP2004/WPP2004_Volume3.htm
  52. United Nations, Department of Economic and Social Affairs, Population Division. (2009). World Population Prospects: The 2008 Revision (CD-ROM Edition—Extended Dataset in Excel and ASCII formats). United Nations publication. Retrieved from http://www.un.org/esa/population/publications/wpp2008
  53. U.S. Census Bureau. (2009). International data base: Population estimates and projections methodology. Retrieved from http://www.census.gov/ipc/www/idb/estandproj.pdf
  54. Zhang, G., & Zhao, Z. (2006). Reexamining China’s fertility puzzle: Data collection and data use in the last two decades. Population and Development Review, 32, 293–321.CrossRefGoogle Scholar

Copyright information

© Population Association of America 2011

Authors and Affiliations

  • Leontine Alkema
    • 1
  • Adrian E. Raftery
    • 2
    • 3
  • Patrick Gerland
    • 4
  • Samuel J. Clark
    • 3
    • 5
    • 6
  • François Pelletier
    • 4
  • Thomas Buettner
    • 4
  • Gerhard K. Heilig
    • 4
  1. 1.Department of Statistics and Applied ProbabilityNational University of SingaporeSingaporeSingapore
  2. 2.Department of StatisticsUniversity of WashingtonSeattleUSA
  3. 3.Department of SociologyUniversity of WashingtonSeattleUSA
  4. 4.United Nations Population DivisionNew YorkUSA
  5. 5.MRC/Wits University Rural Public Health and Health Transitions Research Unit (Agincourt), School of Public HealthUniversity of WitwatersrandJohannesburgSouth Africa
  6. 6.INDEPTH NetworkDurbanSouth Africa

Personalised recommendations