Projecting Fatalities in Crashes Involving Older Drivers, 2000-2025

C.3. DECREASING GROWTH RATES OF DRIVER PROJECTIONS
We constructed these decreasing growth rates by comparing the growth rates (the
coefficient of the year trend variable) estimated on 1977-95 and 1977-90 samples; these
results are reported in Table C.2. With declining growth rates, we expected the estimated
coefficients on the time trend to be larger in absolute magnitude in the shorter sample period
(1977-90) than in the longer one (1977-95), and in all but a very few cases this expectation
proved correct. We used the ratio of the coefficient values from the 1977-95 sample to those
from the 1977-90 sample to represent the pattern of declining growth rate to use in the future.
This procedure yielded ratios of later growth rates to earlier growth rates, which were smaller
than one. In the few cases in which the longer sample period yielded larger time trend
coefficients, we interpolated the ratio of growth rates from adjoining age/gender groups. In
projecting the driver rates, we multiplied each subsequent year’s time trend coefficient by this
ratio. For example, in projecting the 2000 driver percentages, we multiplied the estimated
age-and-gender-specific time trend coefficients by the corresponding growth rate factors to
obtain a lower time effect; then in projecting the 2000 driver percentages, we multiplied the
growth factor used for the 1995-2000 projection by the same growth-rate factor, further
depressing the pure time effect.
This method of creating a decreasing autonomous effect of time improved the
projections— using the estimated time coefficients generally yielded values of one for every
age and gender group by 2010 to 2015— but still yielded age and gender patterns of driver
rates that were not “smooth” in the sense of having older groups systematically having lower
driver ratios at each projection time. The set of modified time-trend coefficients performed
satisfactorily in projections for 65-69 males, which we considered the base group against
which the behavior of the other groups reasonably could be compared. We had clear
anticipations (Bayesian priors) on how the other older age groups should behave over time
(and by 2025) relative to this group: lower driver ratios for each older age group, and
generally lower rates for women, which would otherwise parallel the trend for men of
corresponding age unless influenced otherwise by other variables. While the ratio-adjusted
GM Project G.6 C - 2
October 2000