STOCHASTIC POPULATION PROJECTIONS

Stochastic forecasts of fertility and mortality rates by age and sex, together with initial population counts and a deterministic migration schedule, allow for the generation of stochastic population trajectories through time that reflect uncertainty or variation around a long-term trend. The stochastic population counts (denoted Ns,x,ti, where the indices are sex (s), age (x), and time (t) and where i indicates a specific trajectory) in turn yield stochastic support ratios, SRit.

The level of uncertainty is a function of the amount of natural variation in the historical vital rates and in the forecast uncertainties of mortality and fertility components. The methodology is that described in Lee and Tuljapurkar (1994), where the Lee-Carter model is used for both the mortality and fertility components.

Mortality

Stochastic mortality trajectories were generated following the coherent forecast technique of Li and Lee (2005), which is a Lee-Carter model. This coherent method lowers forecast uncertainty by grouping forecasts for 15 low-mortality countries. Inputs to the model are mortality rates for 1950–2007 from the Human Mortality Database (University of California, Berkeley, and Max Planck Institute for Demographic Research, 2011); output consists of 1,000 stochastic sex-age-time trajectories Ms,x,ti from the online LCfit program (available at http://simsoc.demog.berkeley.edu/). Each projection i is independent from projection j ≠, i, and any life table functional such as e0 may be computed from the set of underlying death rates by fixing the trajectory number, time, and sex. The median in 2050 of the 1,000 trajectories for combined-sex e0 is close to 84.5, the target value from the baseline deterministic mortality projections in Table A-1.

The trajectories Ms,x,ti are “calibrated” so that the median of e0 for each sex matches up with the baseline values in Table A-1. Specifically, multipliers zs,t near unity are calculated so that

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This affects the cloud of trajectories by changing the center while preserving the density of the cloud about the center.

Fertility

The fertility forecasts consist of simulations from a Lee-Carter model of age-specific fertility rates (ASFR), using data from the 2011 Trustees Re-



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