Bayesian Probabilistic Population Projections for All Countries

Transcription

1 Bayesian Probabilistic Population Projections for All Countries Adrian E. Raftery University of Washington Joint work with Leontine Alkema, Patrick Gerland, Sam Clark, Nan Li, Hana Ševčíková and Gerhard Heilig Supported by NICHD Workshop on Uncertainty in Forecasting March 18, 2013 Copyright c by Adrian E. Raftery and University of Washington All rights reserved

2 Outline UN population projections Probabilistic population projections Probabilistic TFR projections Probabilistic population projections: Results Basten critique and new model

3 UN Population Projections UN Population Division publishes projections of age- and sex-specific population counts and vital rates for all countries in 5-year periods to 2100, every two years in World Population Prospects (WPP) used throughout UN system (e.g. WHO, UNICEF, UNHCR, UNAIDS, IPCC), international organizations, governments, private sector, researchers. standard input for development planning, monitoring (e.g. MDGs) and global modeling (e.g. climate change) last Revision: WPP 2010, published in May 2011 projections to 2100 Uses cohort-component model: starts from current population estimates requires age- and sex-specific fertility, mortality and international net migration rates for each future 5-year period

4 Uncertainty in Population Projections UN projections are now deterministic: High, Medium and Low variants published High, Low variants: Medium fertility (TFR) plus or minus half a child per woman; mortality, migration same Scenarios, not uncertainty statements Aim: Probabilistic population projections to yield statistically valid uncertainty statements Probabilistic population projection = calibrated predictive probability distribution for all future population quantites calibrated: e.g., an 80% prediction interval contains the truth 80% of the time Why needed? assessment of accuracy assessing changes and differences between outcomes and expectations making decisions In WPP 2010, for the first time: Medium TFR variant based on a Bayesian hierarchical model (Alkema et al 2011) but projection remained deterministic

5 Previous (WPP 2008) UN Population Projection Methodology (Rough summary) Project TFR forwards deterministically using a double logistic function One of 3 possible parameter sets selected by analyst Project mortality summary forward ( 5 q 0, or 5 q 0 and 45 q 15, or e 0 ) using similar methodology Translate future TFR and mortality summaries to age-specific rates using national rates or model schedules Project net international migration forward Convert these rates to future age-specific populations and vital rates using a cohort-component projection model Scenarios: TFR ± 1 2 children (High, Low variants)

6 Towards Probabilistic Population Projections Build on current UN (deterministic) methodology Probabilistic projections of TFR sample from the predictive distribution of future TFR Mortality: Probabilistic projections of female e0 sample from the predictive distribution Probabilistic projection of the female-male gap in e0 using a regression model Convert each sample at each future year to age-specific mortality rates using a modified Lee-Carter method Kannisto method used for high ages Result: Sample from the joint predictive distribution of female and male age-specific mortality rates in each future time period Apply cohort-component projection model to each sample Yields a sample from the predictive distribution of any indicator Eventually also incorporate uncertainty about: migration age-specific schedules

7 Probabilistic TFR Projections (Source: Alkema et al, 2011, Demography) 3 phases: Phase I: high fertility pre-transition Phase II: fertility transition/decline to below replacement level Phase III: low fertility post-transition turnaround and fluctuations Fertility transition has started in all countries = Phase I not modeled

8 Phase II model: Fertility Transition Fertility transition: starts slowly accelerates decelerates stops below replacement level 5-year declines in TFR modeled by a double logistic function for each country Made probabilistic by adding a random error term = random walk with drift

9 Estimation: Bayesian Hierarchical Model Separate estimation for each country not feasible because of few data and only part of the evolution observed Solution: For each country, draw on information from other countries Hierarchical model: Model parameters distributed about world average Estimate for a specific country = weighted average of its estimate and world average Bayesian estimation using Markov chain Monte Carlo (MCMC) Gives a sample of many possible future trajectories of TFR

10 Phase III: Post-transition Turnaround and Fluctuations Start of Phase III defined by two consecutive 5-year increases below 2 Observed in 20 countries: 18 European countries, Singapore, USA 54 five-year periods

11 Phase III: AR(1) Model TFR t µ = ρ(tfr t 1 µ) + ε t Ultimately TFR will fluctuate around µ. µ = 2.1 Asymptotic prediction interval: [1.7, 2.5] Results to 2100 not very sensitive to µ (mean projection for 2100 is 1.85) Fits well: R 2 = 0.83

12 Probabilistic Population Projections: Brazil Key Indicators Total Fertility Rate median 80% PI 95% PI UN variants typical trajectory observed TFR Total population (in thousands) median 80% PI 95% PI UN projection UN variants typical trajectory observed Potential Support Ratio median 80% PI 95% PI UN projection UN variants typical trajectory observed Year

13 Probabilistic Life Expectancy Projections Female Life Expectancy median 80% PI 95% PI UN projection typical trajectory observed LifeExp Male Life Expectancy median 80% PI 95% PI UN projection typical trajectory observed LifeExp Male life expectancy UN projection Female life expectancy

14 Age-Specific Probabilistic Projections

15 Probabilistic Population Pyramids Male : Absolute Numbers Female Male : Proportions Female median % PI % PI median % PI % PI

16 Performance Out of sample validation for 159 countries, MARE SAPE Coverage (%) 80% PI 95% PI Total Fertility Rate Female life expectancy Male life expectancy Total population MARE = Mean Absolute Relative Error SAPE = median Standardized Absolute Prediction Error (theoretical value = 1). Method reasonably accurate and well calibrated for key indicators

17 Substantive Implications TFR projections assessed favorably by three-day UN Expert Group Meeting, December 2009 Projected slower decline in fertility in Africa than had previously been expected Projected (slow) increase in fertility in Europe Bayesian predictive TFR median used for UN medium projection in WPP 2010 (but UN projection still deterministic) Projected world population in 2050 increased from 9.1 to 9.3 billion Projected world population in 2100: 10.1 billion Basten critique of assumption that ultimately TFR will fluctuate around replacement level (PAA 2012): critique applies only to 5 advanced East Asian economies (Korea, Japan, Hong Kong, Singapore and Taiwan) TFRs there are well below 2.1 current expert opinion and evidence about fertility intentions do not predict increase to 2.1

18 Response: New Model with Country-Specific Asymptotes Instead of requiring every country in Phase III to follow the same model with µ = 2.1, allow both µ and ρ to vary between countries following a Bayesian hierarchical model (paper page 15). Netherlands Singapore TF TF For 19 of 20 countries in Phase III, not much change BUT for Singapore, projection for 2100 is 1.5 instead of 2.1! New model accomodates Basten critique.

19 Conclusions Method reasonably well calibrated in out-of-sample validation experiment BHM predictive median TFR used in WPP 2010 projections Experimental probabilistic population projections on UN website: esa.un.org/unpd/ppp References: Software: R packages: bayestfr bayeslife bayespop bayesdem (GUI)