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. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections2 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

3. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections3 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

4. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections4 Stochastic projections  Four main methods: Time series analysis Ex-post projections errors Experts’ judgements Micro-simulations

5. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections5 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

6. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections6 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

7. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections7 An (ongoing) application to EUROPOP2008

8. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections8 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

9. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections9 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:

10. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections10 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

11. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections11  First method:  Second method: Ex-post forecast intervals

12. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections12  If σ d =0:  If σ d =σ s : Particular ex-post intervals

13. Lisbon, 28-30 April 2010 Joint Eurostat/UNECE Work Session on Demographic Projections13 Towards a mixed approach  No overlapping/substitution between deterministic or stochastic approaches, but complementariness  Deterministic assumptions “drive” the projections, whose uncertainty is stochastically assessed