Combining%20Deterministic%20and%20Stochastic%20Population%20Projections

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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

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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 experts opinion)
• Variants combinations of alternative sets of
  deterministic quantitative assumptions

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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

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Stochastic projections

• Four main methods
• Time series analysis
• Ex-post projections errors
• Experts judgements
• Micro-simulations

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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

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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

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An (ongoing) application to EUROPOP2008
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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

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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

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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

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Ex-post forecast intervals

• First method

• Second method

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Particular ex-post intervals

• If sd0

• If sdss

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Towards a mixed approach

• No overlapping/substitution between deterministic
  or stochastic approaches, but complementariness
• Deterministic assumptions drive the
  projections, whose uncertainty is stochastically
  assessed