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Combining Deterministic and Stochastic Population Projections. Salvatore BERTINO University “La Sapienza” of Rome Eugenio SONNINO University “La Sapienza” of Rome Giampaolo LANZIERI EUROSTAT. Dealing with uncertainty in deterministic projections.
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Combining Deterministic and Stochastic Population Projections Salvatore BERTINO University “La Sapienza” of Rome Eugenio SONNINO University “La Sapienza” of Rome Giampaolo LANZIERI EUROSTAT
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
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
Stochastic projections • Four main methods: • Time series analysis • Ex-post projections errors • Experts’ judgements • Micro-simulations Joint Eurostat/UNECE Work Session on Demographic Projections
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
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
An (ongoing) application to EUROPOP2008 Joint Eurostat/UNECE Work Session on Demographic Projections
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
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
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
Ex-post forecast intervals • First method: • Second method: Joint Eurostat/UNECE Work Session on Demographic Projections
Particular ex-post intervals • If σd=0: • If σd=σs: Joint Eurostat/UNECE Work Session on Demographic Projections
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