Combining Deterministic and Stochastic Population Projections

1. Combining Deterministic and Stochastic Population Projections Salvatore BERTINO University “La Sapienza” of Rome Eugenio SONNINO University “La Sapienza” of Rome Giampaolo LANZIERI EUROSTAT

2. Dealing with uncertainty in deterministic projections • Scenarios: theoretical frameworks with base assumptions about future developments of demographic drivers • Models: quantification of the theoretical assumptions (including expert’s opinion) • Variants: combinations of alternative sets of deterministic quantitative assumptions Joint Eurostat/UNECE Work Session on Demographic Projections

3. How much uncertain? • Common output: Medium/Base, Low and High variants • Users seek for forecasts! • Pitfalls of deterministic approach about uncertainty: • no indication of preference between variants (sometimes also ambiguous labels) • no associated probability Joint Eurostat/UNECE Work Session on Demographic Projections

4. Stochastic projections • Four main methods: • Time series analysis • Ex-post projections errors • Experts’ judgements • Micro-simulations Joint Eurostat/UNECE Work Session on Demographic Projections

5. Adopting a fully stochastic approach? • Some arguments on the difficulties of their implementation in official projections exercises: • Technically demanding • Difficult to incorporate “demographic knowledge” • Persisting subjectivity in “technical” choices (e.g., sensitivity to base period) • Wide range of outcomes of little use for practical purposes Joint Eurostat/UNECE Work Session on Demographic Projections

6. Merging the two approaches • Bertino and Sonnino method (2007) based on point-event processes of fertility, mortality and migration • It requires instantaneous rates for Poisson processes for each age-sex category of the demographic components • Deterministic rates as input for the simulation procedure Joint Eurostat/UNECE Work Session on Demographic Projections

7. An (ongoing) application to EUROPOP2008 Joint Eurostat/UNECE Work Session on Demographic Projections

8. Deterministic uncertainty • Two simple ways for the calculation of the variability of a statistic of interest: • an estimate of the variability is available before computing the deterministic projections (e.g., expert opinion, output of a model) • the variability is calculated from the different variants after computation of the deterministic projections Joint Eurostat/UNECE Work Session on Demographic Projections

9. Linking deterministic and stochastic uncertainty - 1 • Ex-ante approach: alternative sets of deterministic rates are used as input for the micro-simulations • The number of simulations executed for each set of assumptions can be used as proxy of the confidence attributed to the given set • The formula for the prediction intervals does not change: Joint Eurostat/UNECE Work Session on Demographic Projections

10. Linking deterministic and stochastic uncertainty - 2 • Ex-post approach: the available estimate of deterministic uncertainty is used directly in the formula for projections intervals • first method: the two variances are considered independent and p is the weight attributed to the deterministic component • second method: Bayesian approach Joint Eurostat/UNECE Work Session on Demographic Projections

11. Ex-post forecast intervals • First method: • Second method: Joint Eurostat/UNECE Work Session on Demographic Projections

12. Particular ex-post intervals • If σd=0: • If σd=σs: Joint Eurostat/UNECE Work Session on Demographic Projections

13. Towards a mixed approach • No overlapping/substitution between deterministic or stochastic approaches, but complementariness • Deterministic assumptions “drive” the projections, whose uncertainty is stochastically assessed Joint Eurostat/UNECE Work Session on Demographic Projections