Stochastic population forecasts for the United Kingdom Emma Wright & Mita Saha Office for National Statistics

National population projections Dependent on assumptions about future levels of fertility, mortality and migration which are reviewed every two years Latest projections based on the population at mid-2006 Results on GAD website and National Statistics Online

Uncertainty in population projections Demographic behaviour is inherently uncertain Any set of projections will inevitably be proved wrong to a greater or lesser extent

Past UK population projections

Mean projection error by age group Past UK projections

Principal & variant projections Principal projections - based on assumptions thought to be the best at the time they are adopted Variant projections – plausible alternative scenarios, NOT upper or lower limits. Limitation - principal and variant projections are deterministic, no measure of probability

Total UK Population 2006-based principal and variant projections

ONS Stochastic forecasting project Aim To develop a model that will enable the degree of uncertainty in UK national population projections to be specified Approach –Express fertility, mortality and migration assumptions in terms of probability distributions –Generate random values from these probability distributions to produce predictive distributions for any projection result

Probability distributions How can we estimate future probability distributions? Three approaches: Analysis of accuracy of past projections Expert opinion Time series analysis No ‘right’ answer – subjective judgement

Model Drivers Fertility – Total Fertility Rate Mortality – Male and female period life expectancy at birth Migration – Total net migration

Deriving probability distributions for the ONS model Expert opinion - NPP expert advisory group questionnaire Past projection errors - GAD historic projections database

Expert Opinion National Population Projections Expert Advisory Group (set up via BSPS): David ColemanPhil Rees Mike MurphyRobert Wright John SaltJohn Hollis Expressed opinions on the most likely levels and 67% confidence intervals for TFR, period life expectancy at birth and net migration in 2010 and 2030.

Generating sample paths Random walk with drift model: Driver(T)= Driver(T-1) + ValueDriver(T) + DriftDriver(T)

UK TFR 250 sample paths with 67% confidence intervals

UK TFR Probability distribution v 2006-based assumptions

UK male period life expectancy at birth Probability distribution

UK net migration Probability distribution

Program Based on cohort component model UK only Random numbers generated Age distributions 5,000 simulations projection period

Provisional results UK age structure 2031

Provisional results UK age structure 2056

Provisional results: UK total dependency ratio Predictive intervals

Provisional results: Probability of the number of children in the UK exceeding the SPA population

Illustrative probabilities Based on current provisional assumptions, there is a…. 48% chance that TFR will exceed replacement level 9% chance that male period life expectancy at birth will exceed 90 yrs 20% chance that there will be negative annual net migration 2% chance that the population will fall below the 2006 base level … at some point between 2006 and 2056.

Limitations Do not know true probability distributions Validity of results wholly dependent on assumptions underlying model Inflated sense of precision Communicating results and limitations may be a challenge BUT….if aware of the limitations, then stochastic forecasting can be a useful approach

Estimates of the UK TFR in 2049/2050 Median and 80% confidence intervals

Quality Assurance Prof Phil Rees (University of Leeds) Prof Nico Keilman (University of Oslo) Prof Wolfgang Lutz (Vienna Institute of Demography) ONS Methodology Directorate

Future plans ONS plans to publish a set of 2006-based stochastic forecasts for the UK as ‘Experimental Statistics’ during 2009 If you would like to feed in any comments on this work, please