• Regional population projections can be produced either by distributing the projected national population between regions in ratio to (the trend in) their share of the population or by separate cohort-component projections.
• An integrated multi-regional cohort-component projection that explicitly models the flow of migrants from each region of a country to each other region is an example of a multistate projections model.
• Multistate projections models can be used to project any population divided into an exhaustive set of mutually-exclusive sub-groups such as different marital statuses or levels of educational attainment. They can be defined concisely and implemented most easily using matrix algebra.
• Labour-force participation, school enrolments, house headship (and thereby households), and similar characteristics can be forecast either using multistate models or by extrapolating age-sex-specific participation rates and applying them to the projected population as a whole to calculate the number of people with the characteristic of interest.

• All forecasting of vital rates is based on the assumption of some form of continuity between past and future and involves the extrapolation of past trends.
• When a past series of estimates exists to which one can fit a statistical model, the quantification and extrapolation of past trends is often undertaken using some form of regression analysis. Such models may incorporate explanatory factors or model trends purely as a function of time.
• Incorporating explanatory factors into the forecasting process is most effective when their effect on vital rates is lagged, so that their future impact can be gauged from their current values.
• It is important that the methods used for forecasting constrain future schedules of vital rates to plausible patterns and prevent any of the rates from going out of bounds. Using demographic models with a limited number of parameters for forecasting can help to achieve this. Relational models that use baseline data for the population concerned as standards are particularly well suited to this application.
• Projections also need to be designed to ensure consistency between the forecast numbers of vital events experienced by different sub-populations, such as men and women or the regions of a country.
• The session concludes by illustrating the approaches that different organizations use to forecast vital rates by means of two examples. They are the 2012-based forecasts developed for the official projections of the population of the United Kingdom and for the United Nations Population Division’s country-specific projections of World Population Prospects.

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