Nonparametric Estimates of Career Duration To help understand career duration in MLB, we calculate yearly hazard functions
Table 1 shows that when the exponential distribution is used for the hazard function
, the RMSE is 87.
We first specify the shape parameters of the hazard function
An actuarial hazard function
is simply a series of actuarial hazard rates strung together in chronological order.
The hazard function
of this distribution is defined as
0](t) denotes a baseline hazard function
, x denotes a set of characteristics, and [C.
For the Weibull model, the hazard function
is specified as follows:
After determining that none of the covariates violated the proportional hazards assumptions required by the Cox Model, the model was refitted to determine the effects of the predictors on the hazard function
1) Our model permitted the hazard function
to vary over the duration with changes differing across individuals, in contrast to standard reduced form models which restricted to uniformity for all individuals, ceteris paribus.
The hazard rate or hazard function
is the conditional probability that a person leaves employment in a very short time period, given that the person remains employed until that time period.
Carroll (1984b: 85) has summarized the tenor of most findings, referring to the Makeham function as the most common representation of the continuous-decline hypothesis: "Makeham's Law, a stochastic model of the hazard function
with age-dependent properties, is becoming accepted as the baseline model for the study of organizational mortality.
Assume the corresponding hazard function
for this set of firms is the one arbitrarily depicted as the dotted line in Figure 1A.