The name is absent

for the possibility of endogeneity. It is assumed that G has a point-mass structure. In
particular, we assume that there are N triplets of “location” parameters (θ^f, θ^g, θ^d) in the
population where each triplet (θ^f, θ^g, θ^d)_n occurs with proportion p_n:

N
∑ pn = 1
n=1

Controlling for unobserved heterogeneity is important in models of educational
attainment to mitigate potential selection bias (Willis and Rosen, 1979; Cameron and
Heckman,1998). The likelihood function associated with this duration - competing risks
(DCR) model is derived in the appendix.

High school graduates attending college may enroll in either two-year or four-year
institutions. Some individuals who complete a two-year degree may then continue on to
get a four-year degree. In equation (2) above, one predictor variable that included in the
specifications will indicate whether the individual first entered a two-year versus a four-
year institution. Moreover, we allow for the coefficient associated with this predictor
variable to be time-varying in both the college completion and dropout risks.

Alternatively, we model the duration until college enrollment as ending because
of two reasons: entry into a two-year institution or entry into a four-year institution.
Thus, we take a competing risks approach where T^f = min(T^2y, T^4y) and T^2yand T^4y

11

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