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.5 [S( ks ,ks| θg, θd )+S( ks +1,ks+1| θg, θd) -S( ks ,ks+1| θg, θd )-S( ks+1,ks| θg, θd )]

is an adjustment for the fact that the data are discrete time.

Let Bw be defined as

Bw (kf, ks | θf ,θg,θd,) = Pf ( kf | θf ) Pw( ks | θg,θd ), for w=g, d, and sc,

Bw( kf, ks| θf g,θd ) = Pf ( kf | θf ), for w = fc,

where kf denotes the waiting duration to first college enrollment and ks denotes the duration of college
enrollment.

Summing over the N different triplets of location parameters ( θf ,θg, θd) , the unconditional
probabilities can be written as follows.

Bw(kf,ks) = ∕>nl!w(kf,ksθf,θg,θd),
n=1

where

N

pn = 1.
n=1

Let qfci be an indicator variable which equals one if individual i did not enroll in any college by the end of
survey year; qg
i is an indicator variable that equals one if this individual graduates, and qdi is an indicator
variable that equals one if individual i drops out from the higher education system, and qfc
i is an indicator
variable that equals one if individual i enrolled but the enrollment spell is incomplete or right-censored, i=
1, * ,∙m.

The log-likelihood function is then given by

M
logL=∑ ∑qiwlog(Bw(kif,kis))
i= 1 wW

and W={fc, d, g, sc}.

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