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Can Population Projections be Used for Sensitivity Tests on Policy Models? - WP 03/07

7  A solution: Stochastic population projections

In the typology set out in Table 1, Cases 3, 4, 5 can all be obtained using a variants-based approach to sensitivity testing, and all produce useful results. However, designing a sensitivity test so that these cases occur, and are known to occur, can be difficult. The previous four sections illustrate these difficulties.

There is, however, a promising alternative to variants-based testing. Over recent years, demographers have made considerable progress in developing stochastic population projections (Lee 1998; Lutz, Sanderson, and Scherbov 2001). Stochastic population projections all use some method for randomly generating large sets of realistic paths for fertility, mortality, and migration. Some methods apply time series methods to obtain means and variances (Lee and Tuljapurkar 1994), while others rely more on expert judgement (Lutz et al 2001). Results depend crucially on the covariance between different variables. The standard assumption is that age-specific rates for same variable, such as fertility, are perfectly correlated, while adjacent years are partly correlated, and distinct variables, such as fertility and mortality, are uncorrelated (Lee 1998).

The fertility, mortality, and migration trajectories are entered into standard population projection models, to produce large sets of population projections. Demographers summarize these sets by calculating means, variances, and confidence intervals for key variables such as population size and the dependency rate. Carrying out sensitivity tests on a policy model is simplest when the model requires only the key variables. In this case, users can simply enter values that, on the basis of the variance and confidence intervals, appear suitably extreme. Testing is more difficult with models that require highly detailed demographic inputs, such as models of health expenditure. Users may, in this case, need to enter the full set of population projections, rather than summary statistics.

Stochastic population projections can, accordingly, be unwieldy. They are also technically demanding, and, in the case of time series methods, require long series of historical data. Furthermore, existing methods for randomly generating fertility, mortality, and migration paths are still not entirely satisfactory. Even with time series methods, for instance, users still need to specify a long-term trend level for fertility (Lee and Tuljapurkar 1994). Some demographers argue, in addition, that the assumption of perfect correlations between age-specific rates can and should be relaxed (Booth, Maindonald, and Smith 2002).

Stochastic population projections do, however, allow the user to obtain Cases 1 and 2 of the typology in Table 1. These are the cases in which the plausible ranges for fertility, mortality, and migration, and hence the ranges for the population variables, are adequately covered. Adequate coverage of these ranges means that the results from sensitivity tests can be interpreted easily and safely. Stochastic population projections can put sensitivity testing on a surer footing.

Applications of stochastic population projections to important policy questions have begun to appear. The United States Congressional Budget Office (2001), for instance, has used stochastic population projections to forecast social security expenditures. The New Zealand Treasury has carried out similar work for social expenditures by the New Zealand government (Creedy and Scobie 2002). Variant-based population projections are still, however, more commonly used than stochastic projections.

Demographers sometimes try to promote greater use of stochastic projections by pointing out that stochastic projections have clearer conceptual status than variant-based projections, or by noting how stochastic projections can be incorporated into an elegant Bayesian decision-making framework (Tuljapurkar 1992). It seems unlikely, however, that practical minded users of policy models will be persuaded that these benefits outweigh stochastic projections’ additional costs. Users of policy models may be more interested in the capacity of variant-based and stochastic projections to support meaningful sensitivity tests. On this measure, stochastic projections clearly outperform variant-based projections. This suggests that stochastic projections will become increasingly popular.

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