the limit itself. Why would the various values of follow separate, linear paths until the point of convergence but then merge and remain constant (around 85 years) thereafter? Equally consistent with the empirical evidence—and more plausible theoretically—is a prediction that the values of may move closer over time along curvilinear paths but never become equal. From this perspective, these curves might or might not be thought to possess an upper limit.

Most evidence from demographic trends seems inconsistent with the notion of a finite mortality limit, but there are some important questions of interpretation. If there exists a non-zero lower bound for age-specific death rates, how would we know if it were approaching? Most authors seem to assume that the approach to a limit would be characterized by a slowdown in the rate of mortality decline over time. The absence of deceleration in the rate of mortality decline, then, is taken as evidence that we are not currently approaching a lower limit in mortality rates.

For example, the reduction in age-specific death rates for most developed countries has been a stable, long-term process. This conclusion is illustrated for the United States in Figure 3-7, which shows age-adjusted death rates for women and men during 1900-1992 based on Social Security data (Bell et al., 1992). This figure is drawn using a semilogarithmic scale to conform with standard practice. Thus, it is the relative, not absolute, rate of mortality decline that has been stable.

If Figure 3-7 showed trends in death rates for separate age groups, the general conclusion (of stable decline) would not change. It would be evident, however, that the rate of decrease has varied enormously by age: although the pattern has changed in recent years, death rates have typically fallen much more rapidly at younger than at older ages. When making mortality projections, it is typical to assume that the differences by age in the pace of mortality decline will continue into the future (Pollard, 1987; Lee and Carter, 1992).

Thus, the trend in Figure 3-7 is influenced by the enormous decline in infant and child mortality, and also by smaller reductions in death rates at older ages. Over the time period shown here, the relative importance to the overall mortality decline of changes in younger and older age groups has reversed itself. As discussed below, the most rapid decreases in mortality are now occurring at older ages, whereas the opposite was true in earlier eras of mortality decline. Thus, it is all the more remarkable that the trend in Figure 3-7, which is a composite of trends across the age range, moves downward with such regularity.

The pace of overall mortality decline has not, however, been constant. From Figure 3-7, it is evident not only that there have been periods of acceleration and deceleration but also death rates have moved steadily downward over the long run. Perhaps the most curious feature of Figure 3-7 is the plateau that appears from around 1954 to 1968, especially for men. A detailed discussion of this phenomenon is given by Crimmins (1981), who analyzes these trends in terms of underlying causes of death. The period around the 1940s was characterized by very rapid mortality decline, owing at least in part to the increased use of drug



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