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1  Introduction

Many policy models require projections of future population size and structure. Macroeconomic models that include variables for the labour force or the size of the tax base, for instance, require data on the size and age-distribution of the working-age population. Forecasts of future needs for hospitals, schools, or prisons all require data on potential occupants.

Sometimes modellers use only one projection variant, typically the ‘central’, ‘median’, or ‘medium’ series prepared by the relevant statistical agency. Often, however, modellers require some indication of how uncertainty concerning the demographic variables affects the robustness of the model results. The standard tool for doing so is projection variants.

Projection variants are generated by varying assumptions about future paths for fertility, mortality, and migration. The status and interpretation of the projection variants is often ambiguous. Demographers are generally unwilling to attach explicit probabilities to the variants, and commentaries on the projections often warn the reader that the variants are hypothetical scenarios rather than predictions. However, the commentaries often refer to some variants as more plausible than others, or state that certain events, such as the population reaching a given level, are ‘likely’.

Most modellers appear to take a pragmatic stance towards these conceptual ambiguities. They enter the variants into their policy models, and compare the outcomes. If the outcomes are similar for all variants, modellers state that their forecasts are insensitive to demographic uncertainty. If the outcomes differ, modellers warn their readers accordingly and call for further research. Few modellers give any indication that they are dissatisfied with this situation.

This paper argues that the conventional approach is seriously flawed. It presents examples in which population variants provide a misleading indication of uncertainty about demographic variables. The paper explores the underlying reason for these problems, and argues that they prevent effective sensitivity testing.

The paper considers only national projections. Projections for groups of countries or for regions within countries involve addition difficulties, discussed in Lee (1998: 164-5), Bongaarts and Bulatao (2000: 198), and Siegel (2002: 460-82).

Section 2 of the paper sets out a framework for assessing the value of demographic sensitivity tests with policy models. The four subsequent sections describe specific problems. Section 3 describes how the omission of random shocks from trajectories for fertility, mortality, and migration leads to actual population sizes exceeding all projected population sizes soon after the projections are published. Section 4 describes how the absence of low-fertility, low-mortality variants and high-fertility, high-mortality variants reduces the range covered by projected dependency ratios. Section 5 looks at how variants that bracket a substantial range for one population variable may bracket only a narrow range for another population variable. Section 6 examines how the practice of restricting fertility changes to the beginning of the projection interval can lead to confusing results for trends in age structure. The paper concludes with a discussion of stochastic population projections, which are a promising alternative to the variants approach.

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