Higher education funding reforms in England: the distributional effects and the shifting balance of costs

observations for the same individual.¹⁰ In practice, the way in which this is done is
that within cells defined on the basis of age, gender and whether or not the individual
is a graduate¹¹, each individuals’ two observed wage levels are converted to ranks or
relative positions, and the parameters of the copula function that best capture the
dynamics of these ranks between the two periods are estimated using Maximum
Likelihood methods. This leads to a sequence of bivariate distributions across ages
spanning the working lifecycle for each gender/education group.¹² These are then
pieced together to form the group-specific overall lifetime earnings distributions.
Finally, we simulate a series of ranks from these joint probability distributions and
map on the observed wage levels corresponding to these ranks to form earnings paths.

One appealing feature of this approach is that the copula function allows us to model
the dependence in wages between ages, thus characterising the observed dynamics in
earnings (up to the first-order Markov assumption).¹³ But another important feature of
the earnings paths is that in simulating them, we allow for a stochastic component to
employment and assign earnings accordingly. In particular, if an individual is
unemployed in a particular period, (s)he is assigned zero earnings; if (s)he becomes
employed, his/her earnings are allowed to depend on the length of time unemployed,
and his/her wage when last employed. Not only does this generate realistic mobility
patterns in earnings and employments, but the cross-sectional distributions of
simulated earnings at each age, match those in the data.

Earnings simulations are based on data from the UK Labour Force Survey (LFS)
covering the period spanning 1993 through 2003.¹⁴ The LFS is a representative

10 A relaxation of first-order Markov to second-order Markov would come at a considerable technical
cost and would not enable us to use the LFS data which only has a maximum of two earnings
observations per individual.

11 A graduate is defined as an individual holding a Higher Education qualification. This includes
qualifications that constitute Levels 4 and 5 under the Qualifications and Curriculum Authority’s
original National Qualifications Framework: doctorates, masters degrees, postgraduate certificates and
diplomas, bachelors degrees, graduate certificates and diplomas, diplomas of higher education and
further education, foundation degrees, higher national diplomas.

12 We model the evolution of wages from ages 22(19) through 60 for graduates (non-graduates).

13 Note that the benefits from allowing for earnings mobility in this way accrue from examining the
entire distribution of lifetime earnings paths. If we were to focus on the effects of the policy on an
example “average” graduate then it would not be necessary to model the extent of intertemporal
dependence in earnings.

14 In Dearden et al (2006), we have used the British Household Panel Survey (BHPS) to estimate the
earnings models. This is because the analysis carried out in that paper relies on a panel of longer than
two years, so the relatively large sample sizes afforded by the LFS were traded off against this

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