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"Estimating Aging Effects in Running Events,"
with Edward H. Kaplan, January 2018, forthcoming The Review of
Economics and Statistics.
This paper uses world running records by age to estimate a biological
frontier of decline rates. Two models are compared: a linear/quadratic
(LQ) model and a nonparameteric model. Two estimation methods are used:
1) minimizing the squared difference between the observed records
and the modeled biological frontier and 2) using extreme value theory to
estimate the biological frontier that maximizes the probability of
observing the existing world records by age.
The results support the LQ model and suggest there is linear percentage
decline up to the late 70's and quadradic decline after that. The
extreme value estimates suggest that the true biological frontier is on
average about 8 percent below the existing world records. The
estimated age factors
are also compared to the World Master Athletics (WMA) age factors.
The two sets of age factors are close except at
the old ages, where the WMA factors are
noticeably smaller. Also, the WMA age factors do not meet an important