decision is essentially arbitrary, and however it is done, inconsistencies in the high-low ranges will result (see Lee, 1999).8

A second approach, called ex post analysis, analyzes the past record of success of forecasts prepared by an agency as a guide to the uncertainty of future forecasts. If the forecasting method has not changed too much over time, this method can be very useful. An unusually careful ex post analysis of the United Nations projections was provided by the National Research Council (2000).

A third approach might be called “random scenarios.” It assumes a certain probability distribution of the true outcome in relation to high and low bounds provided by experts. Given this distribution, a process like the one described above can be used to generate possible future paths for each vital rate (Lutz, Sanderson, and Scherbov, 2004; Tuljapurkar, Li, and Boe, 2000).

A fourth approach is based on time-series analysis, which combines demographic methods with well-established statistical methods to model, analyze, and forecast historical data on fertility, mortality or migration (Lee and Tuljapurkar, 1994). The models capture not only the trend but also the typical patterns and degree of persistence of fluctuations. One can draw random numbers that, combined with the models, generate one possible version of the future of a particular rate—say fertility—that is consistent with the typical past patterns (Lee, 1999; 2011). In the same way, possible futures can be generated for mortality and net immigration. Then this set of randomly generated fertility, mortality, and migration outcomes can be used to generate a possible future trajectory for the population and its age distribution, say up to 2050. By repeating this process with a new set of random numbers, another possible future is generated. After 1,000 such repetitions, it becomes clear which outcomes are most likely and which are less likely, and it is possible to derive a probability distribution. This method produces not only a probability distribution of outcomes for a given year, but also a distribution of trajectories. Such an approach is valuable because some outcomes of interest, such as the projected Trust Fund balance for Social Security in a given year, depend not only on the demography of that particular year but also on the whole demographic trajectory leading up to that point, with all its ups and downs. In fact, the Social Security Trustees have included in their annual reports a stochastic forecast of this sort for the system’s finances.

Figure 3-18 shows a probabilistic forecast of the OADR based on a stochastic version of the committee’s single-sex population projection, for

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8In effect, the scenario method assumes that projection errors in each component are perfectly correlated over time (always too high or always too low), and that errors in the different components are always perfectly positively or negatively correlated with one another (if fertility is high, then mortality or immigration is low, for example). Neither assumption is correct.



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