A Probabilistic Version of the World Population Prospects (P-WPP): First Results

1. A Probabilistic Version of theWorld Population Prospects (P-WPP): First Results Gerhard K. Heilig, Thomas Buettner, Nan Li, Patrick Gerland Leontine Alkema, Jennifer Chunn, Adrian Raftery United Nations, Department of Economic and Social Affairs (DESA)Population Division - Population Estimates and Projections Sectionwww.unpopulation.orgRevision 1, 30 March 2010

2. WPP work cycle, data sources, data quality WPP approach to projecting fertility and mortality Bayesian Hierarchical Model (BMH) + Autoregressive time-series model [AR(1)] Comparison: WPP2008 and P-WPP First results and conclusions Overview 0 1 2 3 4

3. 0 United Nations, World Population ProspectsWork Cycle - Data Sources – Data Quality

4. WPP revision cycle: 230 countries / territories 0 Start of WPP Start of WUP Projection, Aggregation, Checking Output Production Data Collection, Estimation 1 2 3 Data Collection230 countries / territories Uploading to Database Calculation of Variants Early Release Data 3 CD-ROMs AdjustmentsEstimations Aggregation of Regions Online DatabaseWeb Site Checking of Results Epidem. Modelingfor AIDS Countries Fixing of Errors Statistical ReportsVol. 1, 2 65% of Workload 15% of Workload Wall Chart Methodological Report Vol. III Update and development of new Databases and software tools,database maintenance, backup 20% of Workload

5. Census data(from United Nations Demographic Yearbook database and National Statistical Offices) All available demographic and health surveys(DHS, DSS, MICS, WHS, etc.) for estimating fertility and child mortality Estimates from population and vital registers(from statistical reports of National Statistical Offices or their web sites) Scientific reports and data collections(Human Mortality Database, child mortality estimates, etc.) Data and estimates provided by other international agencies(CELADE, Regional Commissions, EUROSTAT, ESCAP, UNICEF, UNAIDS, WHO) WPP data sources 0

6. Availability of population by age and sex 0

7. Availability of population by age and sex 0 ≈ 2/3 of countries have insufficient population estimates by age and sex

8. Example Bhutan: Census data 0

9. Example Bhutan: Population reconstruction 0

10. Bangladesh: Empirical ASFR 0 Lines are weighted cubic spline and loess regression trends

11. Bangladesh: Empirical ASFR - Problems 0 Lines are weighted cubic spline and loess regression trends

12. Afghanistan: Mortality estimation - 5q0 0

13. Afghanistan: Mortality estimation - 5q0 0 ≈ 180 difference

14. WPP data quality assessment 0

15. DemoData: Empirical Database: Mortality (5q0) 0 Different Data Sources

16. 1 UN approach to projecting fertility and mortality Bi-logistic models of fertility and mortality decline

17. Fertility Projection: Decrements of fertility decline 1

18. Decrements modeled by bi-logistic function 0.14 0.12 0.10 0.08 Fertility decline 0.06 0.04 0.02 0.00 10 9 8 7 6 5 4 3 2 1 Children per woman Fast/Fast Fast/Slow Slow/Slow 1 Model: Bi-logistic function to estimate the rate of fertility decline

19. Fertility projections: Constraints 4 8 7 6 3 5 Children per woman Children per woman 4 2 3 2 1 1 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 Year Year Fast/Fast Fast/Slow Slow/Slow Floor Fast/Fast Fast/Slow Slow/Slow Floor 1 A. From high to low fertility B. From medium to 1.85

20. Low Fertility Countries (TFR < 2.1): Continue at current level for 5-15 years; increase linearly at a rate of 0.05 children per 5-year period; stay below TFR of 1.85 Medium Fertility Countries (TFR > 2.1, but declining):Follow path of fertility decline derived from past experience, but not below a TFR of 1.85 High Fertility Countries (no decline in TFR)Follow path of fertility decline derived from past experience, but not below a TFR of 1.85; extend transition period; select slow / slow model Some flexibility in extending or reducing the transition period Fertility projections: Assumptions 1

21. United Nations model of fertility projection 1 (1) k = Saturation level or asymptote of the diffusion process α = Growth rate of the s-curve β = Length of time the curve takes to reach the midpoint of the growth trajectory. For modelling purposes, function (1) is re-parameterized to (2) by substituting (2) . tm = Midpoint of the growth/diffusion process Δt = Duration for the growth process to proceed from 10 per cent to 90 per cent of the asymptote (k). (3)

22. Projections: Mortality models and empirical data 1

23. UN Models for projecting life expectancy at birth 1

24. UN Models for projecting life expectancy at births 1 Illustration of the double-logistic function (based on a curve from Japan). The left plot illustrates the double-logistic function of 5-year gains in life expectancy. The right plot is a time-series of life expectancy, e(0), with gains modeled according to the double-logistic function

25. UN Models for projecting life expectancy at births 1

26. Bayesian Hierarchical Model (BHM) 2 for fertility and mortality decline

27. BHM: a fertility transition model 2 Phase I: All countries above TF of 5.5. Ends when the most recent period is lower than 0.5 children of the global maximum of the TFR within that country. Not modeled. Phase II: Fertility transition, modeled by BHM Phase III: Sub-replacement recovery starts the first time two 5-year increases below a TFR of 2 are observed (20 countries), modeled with a first order autoregressive time series model [AR(1)], with its mean fixed at the approximate replacement-level fertility of 2.1 as proposed by Lee and Tuljapurkar (1994)

28. WPP: Model of fertility decline 2 Model: Bi-logistic function to estimate the rate of fertility decline In probabilistic fertility projection: Parameters values are replaced bydistributions. Some 100,000 trajectories of fertility decline are calculated by sampling from these parameter distributions.

29. BHM: Distribution of bi-logistic functions 2

30. BHM: Bi-logistic functions + TF projections 2

31. BHM: Bi-logistic functions + TF projections 2

32. BHM: Bi-logistic functions + TF projections 2

33. Total Fertility: 2008 2

34. Total Fertility: 2048 2

35. Total Fertility: 2098 2

36. Probabilistic mortality projection 2 • Data: • Male life expectancy at birth from 1950 through 2005; • Estimates from UN World Population Prospects (WPP2006)

37. WPP2008 / P-WPP: e0 male 2

38. Comparison: WPP2008 and P-WPP 3 (1)Comparison of the median P-WPP with WPP2008 medium variant.(2)Analysis of 95% confidence interval in P-WPP, as compared to high and low variant of WPP2008

39. WPP2008 / P-WPP: Total Population 1990-2050 3 Deterministic WPP2008 - Probabilistic WPP: - stochastic median almost identical to medium variant - 95% Confidence interval very close to high/low variant

40. WPP2008 / P-WPP: Total Population 1990-2050 3 Deterministic WPP2008 - Probabilistic WPP: - stochastic median very different to medium variant, and/or - 95% Confidence interval very different to high/low variant

41. WPP2008 / P-WPP: Total Population 1990-2050 3

42. WPP2008 / P-WPP: Total Population 1990-2050 3

43. P-WPP Median vs. WPP2008 Medium Variant 3

44. P-WPP Median vs. WPP2008 Medium Variant 3

45. P-WPPConfidence Interval – WPP2008 High/Low Range 3

46. Probabilistic population projections were carried out for 196 countries of the world (based on probabilistic projections of fertility and mortality) including 151 developing countries In more than 80% of the countries, probabilistic medians in projected total population (P-WPP) differ less than 10% from the medium variant of WPP2008. In about 60% of the countries, the deterministic WPP2008 high-low scenarioslie within the 95% confidence interval of the probabilistic population projections. The range of uncertainty as measured by a 95% projection interval in P-WPP for 2050 was much larger for some countries (mainly Least Developed Countries) than the high-low variant range in the deterministic WPP2008. Summary of results 4

47. Probabilistic projections for all countries of the world – not just developed countries or major regions Uncertainty is derived from estimates, which are based on empirical data (not expert opinion of uncertainty). BHM is using the well established and robust concept of a bi-logistic curve for modeling rates of change The approach will be fully reproducible with open source code (in “R”) for the fertility and mortality projections What is new? 4

48. Correlation problems are still unsolved (concerning aggregation, male-female life expectancy, and relation between fertility and mortality) – affect uncertainty. Input data of BHM model are the relatively smooth estimates – not the original empirical data. This might lead to underestimation of uncertainty. Projections of fertility and mortality are mainly data-driven.There is no room for analysts’ background knowledge of economic, political, environmental or social conditions in a particular country that might affect future trends. The methodology of probabilistic projections is very difficult (if not impossible) to explain to laypersons or politicians. What are the problems / disadvantages 4

49. More than 50% of the world population will soon have sub-replacement fertility. There is no theory or model for future trends in fertility of sub-replacement countries. Biggest problem 4

50. Thank You ! www.unpopulation.org