samlet årgang - Økonomisk Institut - Københavns Universitet

86
NATIONALØKONOMISK TIDSSKRIFT 2005. NR. 1
incurred each year spent studying. As students are liquidity constrained, they need to
supplement their income with labour market earnings equal to wH, where w is the current
wage rate and H the hours supplied to the labour market while studying, and the
financial aid grant G, which may be a declining function of the number of years taken
to complete the education. Further, there could be Z, individual background factors, P
certain program-specific factors and U, which is individual unobserved ability affecting
the value.
The problem would be to choose both t, the years taken to complete the education,
and H, the hours of concurrent work, given the predetermined variables in the value
function. In the empirical formulation, we abstract away from the hours choice, treating
current earnings as a given, and focus only on the choice of t. A more complete
study could potentially consider the joint determination of both variables.
The maximized value of completion V(t * ) is attained after t * periods in the program,
where t * , based on the above model depends on earnings before and after completion,
probability of unemployment after completion, unemployment benefits, costs, financial
aid, individual background factors, spell-specific factors and individual unobserved
heterogeneity.
While the theoretical considerations above are supposed to show the tradeoffs between
for example, working and studying and other factors affecting students’ choices,
in the empirical specification, we estimate the distribution of completion times conditional
on characteristics, by constructing suitable regressors in an empirical model of
observed durations until completion. As direct costs of education and unemployment
benefits do not vary much across individuals in Denmark, these are suppressed in the
empirical work. Thus, the main arguments should influence completion time as follows:
t * (X) = t * (Y –
, +
,w +
H, G +
,U –
,..,) (3.2)
IV. Empirical Model
For the empirical analysis, we adopt a hazard-function approach to model duration
of education spells. Let T n be the duration in years for individual n. X n (t) is a vector of
observed covariates, some of which may be time-varying. Let U n denote unobserved
heterogeneity with distribution function G(u).
(A) Model Specification
We start with the specification of the hazard function h(t) for T n , that is, h(t) measures
the conditional probability density function, given the spell is at least t: h(t) =
f(t)/P(T > t). The following assumptions are made.