Workshop BY ERIC STALLARD
New Perspectives on the
Compression of Morbidity and Mortality
THE DYNAMICS OF MORBIDITY AND MORTALITY are central
concerns in actuarial practice, having major implications for life, health,
pension, and long-term care (LTC) insurers; for Medicare, Medicaid, and
Social Security programs; for public policy planners; and for career and
retirement planning among the general public.
In his classic paper “Aging, Natural
Death, and the Compression of Morbidity,” published in 1980 in the New England
Journal of Medicine, James Fries identified two aspects of those dynamics—the
compression of morbidity and the compression of mortality—as critically
important to a proper understanding of
the past, which, in turn, was essential in
developing valid forecasts of the future.
Despite the central importance of the
two types of compression to Fries’ thesis, his presentation of those concepts
wasn’t sufficiently rigorous to avoid a
fundamental error that has continued
uncorrected to the present time. His use
of the word rectangularization where
others have used compression of mortality underscores the lack of consistent
To continue, the reader needs to
intuitively understand two statistical
concepts: the mean length of
life, or lifetime, also
called the life expectancy (LE);
and the standard deviation of lifetime.
■ ■ For any group of individuals, the
mean lifetime is defined as the arithmetic average value of the individual
■ ■ For the same group of individuals, the
standard deviation of lifetime measures the dispersion of the individual
lifetimes around the mean lifetime.
For technical reasons, the standard
deviation is defined as the square root
of the average sums of squares of deviations of the individual lifetimes
from the mean lifetime.
The important intuitive concept is
that the dispersion of the individual
lifetimes is proportional to the standard
deviation of lifetime. When the standard
deviation declines, the dispersion declines, and vice versa. Both are typically
measured in years.
Compression of Mortality
We begin by visualizing the rectangu-
larization process, using Social Security
Administration (SSA) life tables for the
period 1900–2000, shown in Figure 1 for
males and females, respectively.
The survival curves for males and
females in the top panels both display
the well-known property of rectangu-
larization—the survival function values
at each age initially appear to move up-
ward while the ages at which the largest
declines in the function occur appear to
move progressively to the right.
The remaining LE at each age in each
calendar year is computed as the area
under the corresponding survival curve.
By convention, this calculation assumes
the existence of a hypothetical group
exposed to the mortality conditions in
effect during the selected calendar year.
For males in 1900, the LE at birth (age 0)
was 46 years, which increased to 74 years
in 2000; for females, the corresponding
values were 49 years and 79 years.
Ryan Edwards and Shripad Tuljapurkar noted in 2005 that the
rectangularization effects starting at age
0 were greatly reduced when recomputed starting at age 10, which they argued
was a better anchor point for studying
divergences in mortality in developed
countries. Starting at age 10 could also
be justified using the ontogenesis model proposed by Daniel Levitis in 2011,
in which declines in mortality between
conception and maturity were tied to genetic and developmental malfunctions.
Starting at age 10 is actually necessary to
implement Fries’ preferred method for
quantifying the degree of rectangularization, as indicated below.
However justified, the pattern of rectangularization was altered substantially,
as shown in the middle panels of Figure
1. For males in 1900, the LE at age 10 was
50 years, which increased to 65 years in