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college attendance duration can end either because the individual drops out of college or
because they graduate from college. Thus, for the second duration we take a competing
risks approach (see Katz, 1986, Hausman and Han, 1990; Anderson, 1992; Sueyoshi,
1992; and McCall, 1996, for example).

Let Tf be the waiting time between high school graduation and college enrollment.
Let Tg be the duration of college attendance until graduation (graduation duration) and let
Td be the duration of college attendance until dropout (dropout duration). Further, let Ts
= min(Tg, Td).

To incorporate the waiting duration into the statistical model, the survival
function conditional on the unobserved variable
θf and the vector of observed predictor
variables
z is assumed to have the following form

Sf (kfz,θf ) = P(Tf kfz,θf )

k f                               (1)


= exp[-θfexp(γrf + (βrf )z)]

r=1

where the parameters γfr are the baseline hazard parameters and the vector βfr measures the

(possibly time-varying) effects of the regressors on waiting time until college enrollment,



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