## Develop a theory-driven mortality forecasting strategy

### Ambition 3

Developing pension and other social and health policies for the older population requires forecasts of the numbers and lifespans of older people. Various forecasting methods have been proposed and applied. Our aim is to develop and apply theory-based forecasting methods that go well beyond the state of the art to predict lifespan distributions (and inequalities)—and to quantify the uncertainties in these predictions.

1 **Forecasts should follow the mortality-pattern regularities observed in the past.** If not, some cogent explanation should be provided about why a forecast predicts a new kind of mortality regime. If, for instance, a forecast predicts a radical narrowing of lifespan inequalities, then the reasonableness of this has to be carefully considered. Fig. 5 shows such a narrowing for the Catch-Up forecast in 2070: this seems implausible because it implies a sharp increase in the rate at which death rates increase with age. The reasonableness of such rapid aging would have to be investigated. Instead of neglecting or not even considering such discrepancies or providing ad hoc explanations (or excuses) for why a forecast deviates from past patterns, it would be advantageous to use a forecasting strategy that is designed to predict future patterns consistent with or at least not qualitatively different from past patterns. We will try to develop such a strategy that produces forecasts consistent with the 8 observed regularities of mortality patterns after age 50 in long-lived populations.

2 **Forecasts of distributions of lifespans are so important for individuals, governments and financial institutions**—and for scientific study of possible challenges of the future—**that even a marginal improvement in the accuracy of forecasts of lifespan distributions would be of huge value**. The more than a billion people who live in the countries we plan to study will be substantially impacted by increases in retirement ages and in how much they have to contribute to cover the costs of retirement. These changes will hinge on forecasts of the length and variation of how long individuals will live.

3 **It is possible that the hypothesis is correct that senescence is being delayed to higher ages resulting in a advancing frontier of survival**. A good forecasting strategy should be able to handle this situation if it is true. Methods based on extrapolation of averages of historical rates of improvement in age-specific mortality, including Lee-Carter, are inadequate for this challenge.

**Forecasts of life expectancy have generally been too low.**^{ }Expert judgments about life expectancy increases have been very poor. It is hard to incorporate covariates because they have to be forecasted—perhaps the most feasible is smoking behavior—and their relation with mortality is not always well understood. In the proposed research we will use methods of extrapolation without covariates: a great deal is known about these methods and they have proven to be useful. Modern forecasting methods developed by Lee and Carter and others, extrapolate age-specific death rates, or other age-specific mortality statistics. These methods rely on one of the regularities of mortality statistics, namely that age-specific death rates tend to decline at the same age-specific rate over extended periods of time, but the methods do not systematically take into account any or at most only one or two of the 7 other regularities of mortality at older ages in long-lived populations—and the methods have generally produced life expectancy forecasts that have proven too low.

An alternative, much-less-developed approach extrapolates some measure of average lifespans, most often life expectancy at birth, and then uses the regularity of decline in age-specific death rates to estimate the trajectory of mortality consistent with the life expectancy prediction. The two approaches lead to very different forecasts, as illustrated by the forecasts by the Lee-Carter and Catch-Up methods shown in Fig. 9.

**The Lee-Carter approach generally works well and is now widely used. **Various extensions and variants related to it produce even more accurate forecasts. An advantage of these methods is that they can be used to model a wide variety of mortality data, from birth to high ages and in populations with low life expectancy as well as long-lived populations. If forecasts only have to be made above age 50 and only for long-lived populations, then some flexibility can be sacrificed.

My basic

James W. Vaupelidea is to develop a targeted forecasting method that is molded by the 8 regularities of mortality patterns above age 50 and in long-lived populations such that forecasts are consistent with the 8 regularities. Demographers know a great deal about mortality at older ages in long-lived populations: it seems to me to be worthwhile to try to design a forecasting strategy that takes advantage of this ancillary knowledge. Many statisticians often prefer to fit models to specific datasets, ignoring results from other datasets: Lee-Carter-like approaches basically follow this strategy although sometimes «coherent» models are used based on data for several populations.

We think it is time to embrace the ancillary knowledge demographers have and to try to develop a theory-based approach that uses this knowledge. Bayesian statisticians feel more comfortable about this than classical statisticians. We strive to develop a theory-based forecasting model that forecasts lifespan distributions based on forecasts of a single statistic.