The 7 Billion Mark, Uncertainty & New Methods for Total Fertility Projections

1. The 7 Billion Mark, Uncertainty& New Methods for Total Fertility Projections LeontineAlkema National University of Singapore Needs Assessment Conference on Census Analysis in Asia (NACCA) 23-25 November 2011, Bali Joint work with A.E.Raftery, P. Gerland, S. Clark, F. Pelletier, T. Buettner and G.Heilig University of Washington and United Nations Population Division

2. 7,000,000,000,000 • October 31, 2011 was 7-billion day • How (un)certain are we of the timing of this event? • UN Population Divison, Patrick Gerland: • At least one or two percent error in population estimate • 1% means 70 million people (e.g. population of Thailand) • 2% means 140 million (e.g. population of Russia) • WPP2010: net growth of about 78 million people in 2011 • 1% error in measuring the world population => roughly +/- 1 year uncertainty in timing • Likely to be even greater than that • IASSA: http://www.iiasa.ac.at/Admin/PUB/Documents/IR-11-002.pdf

3. Total Fertility (TF) Projections • New TF projection methods incorporated in World Population Prospects WPP 2010 • Key differences with projection methods from WPP 2008: • More country-specific • No floor of 1.85 • Uncertainty assessment included

4. TF projections: WPP 2008 (blue) and 2010 (red)

5. TF projections: WPP 2008 (blue) and 2010 (red)

6. TF projections: WPP 2008 (blue) and 2010 (red)

7. Introduction of new TF method • Motivation: • To understand UN projections • To use yourself on subnational level

8. TF projections are informed by the past

9. 3-phase model TFR time series since 1950 can be described with 3 phases: • Pre-transition high fertility • Fertility transition • Post-transition low fertility • Use this information to make projections: • 1. Find out which phase a country is in (Phase II or III) • 2. Use observed changes during that phase • to find the range of expected changes in TFR

10. Is your country in Phase III yet? • We defined the start of Phase III in observation period (before 2005-2010): midpoint of earliest two subsequent increases below 2 • Observed in 21 countries(Belgium, Bulgaria, Channel Islands, Czech Republic, Denmark, Estonia, Finland, France, Germany, Ireland, Italy, Latvia, Luxembourg, Netherlands, Norway, Russian Federation, Singapore, Spain, Sweden, United Kingdom, United States of America)

11. Phase II: Observed declines

12. TF projection for high fertility countries • Extension of 2008 UN method (5-year periods): • TF(t+1) = TF(t) - 5year decline • 5year declinegiven by “decline curve” • For each country, estimate decline curved(θc ,fc,t) • fc,t= TF for country c, 5-year period t • Parameter vector θcdeterminesitsshape

13. Estimating decline curves: How? • Exchange information between countries: • For a specific country, its parameter estimates are determined by its observed declines, as well as the world level experience • Example: maximum 5-year decline (height) for Mozambique More formally: use a Bayesian hierarchical model • Bayesian inference: unknown parameters have probability distributions, which are “updated” with new information • Unknown decline parameters are distributed around a “world average” • Use Markov Chain Monte Carlo (MCMC) algorithm to get many samples of the set of model parameters, e.g. θc’s

14. Country-specific TF decline curves

15. Country-specific TF decline curves

16. TF projection • Each decline curve gives a future TF trajectory: • Decline curve gives expected change in next period • Add random distortion/error • Repeat until start of Phase III: when increase has been observed below a threshold parameter • Result: • Each set of model parameters gives a future TFR trajectory • Many sets →Many TFR trajectories →Median projection and projection intervals

17. Example: Indonesia • How did we project the TF in Phase III, after the turn-around?

18. What happens post-fertility-transition? • Again, use observed changes in Phase III to inform expected changes • Assume TF will eventually fluctuate around 2.1, e.g. • we expect • Increase if TF <2.1 • No change if TF=2.1 • Decrease if TF >2.1 • Allow for uncertainty in future outcomes by adding distortion/errors/random fluctuations

19. Post-transition projections continued • In math, use an AR(1) model: = with = autoregressive parameter with = standard deviation of the random errors • Example: Czech Republic • Lonngggg term 95% projection interval given by [1.6,2.4]

20. Summary TF Projection Model • Probabilistic projection model for 5-year changes during and after the fertility transition • During the fertility transition: • the 5-year decreases are modeled as a function of TF level and decline parameters, with random distortions added to it • the decline parameters are estimated with a Bayesian hierarchical model • After the fertility transition the TFR will converge to/fluctuate around 2.1, using an AR(1) model • Results: Set of country-specific projections • Model was validated using out-of-sample validation (projecting from 1980 and 1995 onwards, to compare projections with observations)

21. Population projections • WPP2010 population projections are based on median TF projections, and show +/- 0.5 child scenarios • Results from fully probabilistic projections as well! • Based on probabilistic projections of life expectancy Nathan Keyfitz (1981): "Demographers can no more be held responsible for inaccuracy in forecasting population 20 years ahead than geologists, meteorologists, or economists when they fail to announce earthquakes, cold winters, or depressions 20 years ahead. What we can be held responsible for is warning one another and our public what the error of our estimates is likely to be."

22. Probabilistic population projections

23. Probabilistic population projections

24. Subnational TF projections • TF projection model can be applied to any subpopulation, e.g. provinces/states • Method implemented in software R: free statistical software (http://cran.r-project.org/) • Approach: • Collect subnational TF (census) time series data and construct 5-year estimates • Import data into R • Install packages bayesTFR and bayesDem • Run software directly in R, or use GUI

25. Example: TF projections for states in Brazil • By Patrick Gerland, UN Population Division • Resulting subnational projections • based on experience of the fertility transition through the world in the past 60 years • combined with the experience of subnational units

26. Additional information • References (next slide) • More information: • UN Population Division: http://esa.un.org/unpd/wpp/ • Bayespop: • LeontineAlkema: alkema@nus.edu.sg • TF project funded by NICHD grant number 1 R01 HD054511 01 A1

27. References • Alkema L, Raftery AE, Gerland P, Clark SJ, Pelletier F, Buettner T , Heilig GK: Probabilistic Projections of the Total Fertility Rate for All Countries. in: Demography (2011), 48:815-839 • White Paper: Probabilistic Projections of the Total Fertility Rate for All Countries for the 2010 World Population ProspectsAdrian E. Raftery, LeontineAlkema, Patrick Gerland, Samuel J. Clark, Francois Pelletier, Thomas Buettner, Gerhard Heilig, Nan Li, Hana Sevckova. (United Nations population Division, Expert Group Meeting on Recent and Future Trends in Fertility, New York, 2-4 December 2009) • SevcikovaH, Alkema L, Raftery AE, (2011): bayesTFR: An R Package for Probabilistic Projections of the Total Fertility Rate. Journal of Statistical Software, 43(1), 1-29. • Sevcikova H., Alkema L, Raftery AE (2011). “bayesTFR: Bayesian Fertility Projection”. R Package and documentation: http://cran.r-project.org/web/packages/bayesTFR/index.html • Sevcikova H. (2011). “bayesDem: Graphical User Interface for bayesTFR and bayesLife”. R Package and documentation: http://cran.r-project.org/web/packages/bayesDem/index.html • Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2010 Revision- http://esa.un.org/unpd/wpp/

28. WPP 2010 findings (compared to 2008) • Variability among countries increases in 2045-2050 • For high-fertility countries in 2005-2010, the fertility decline is slower • For countries with 2 < TF < 3, decline is faster • For countries with TF < 2.1, slower rise to 2.1 • More countries fall below 1.85 child by 2045-2050 and return toward 1.85 by 2095-2100 • Slower convergence toward 1.85 child (reached in 2095-2100 instead of 2045-2050) • TF 95% intervals are generally wider than one child, especially for countries with TF > 2.1

29. Overview SE Asia

30. Overview Southern Asia

31. Overview Eastern Asia