The name is absent

Appendix

In this appendix we derive the likelihood function for the empirical model described by equations (1) and

(2) in the text. For simplicity of notation, we drop from the notation the dependence of functions on the
predictor variables z and x and, where appropriate, T^f. Let P^f(k^f∣θ^f) denote the probability ofenrolling in
college at time k^f conditional on θ^f and P^fc(k^f]θ^f) equal the probability ofthe spell lasting longer than k^f.

Then,

P^f( k^f | θ^f ) = S^f( k^f | θ^f ) - S^f(k^f+1 | θ^f ),                                                                                  (A1)

P^fc( k^f | θf ) = S^f( k^f | θ^f ).                                                                                                  (A2)

In a manner similar to McCall (1996, p. 679), let Pg (k^s | θg, θ^d), P^d(k^s | θ^g, θ^d) and P^sc(k^s ^^g, θ^d) be the
probability ofgraduation after k^s years ofenrollment; dropping out after k^s years ofenrollment; and right
censored after k^s years of enrollment, respectively. Thus,

P^g( k^s | θ^g, θ^d ) = S( k^s ,k^s| θ^g, θ^d )-S( k^s+1,k^s| θ^g, θ^d )-.5 [S( k^s ,k^s| θ^g, θ^d )+S( k^s +1,k^s+1| θ^g, θ^d)

-S( k^s ,k^s+1| θ^g, θ^d )-S( k^s+1,k^s| θ^g, θ^d )],                                                    (A3)

P^d( k^s | θ^g, θ^d ) = S( k^s ,k^s| θ^g, θ^d )-S( k^s ,k^s+1| θ^g, θ^d )-.5 [S( k^s ,k^s| θ^g, θ^d )+S( k^s +1,k^s+1| θ^g, θ^d)

-S( k^s ,k^s+1| θ^g, θ^d )-S( k^s+1,k^s| θ^g, θ^d )],                                                    (A4)

and

P^sc( k^s | θ^g, θ^d ) = S( k^s ,k^s| θ^g, θ^d )                                                                                        (A5)

where the term

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