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

\* MERGEFORMAT (.)

Under the assumption that is a first order Markov process, the copula density in
equation (1.3) can be decomposed into the product of a sequence of bivariate copula
densities which describe the dependence structure between adjacent observations of
wa

Obj112

\* MERGEFORMAT (.)

Obj113

Since, under the first order Markov assumption, an observation will correspond to a
vector of length two, , the log likelihood function for the sample is

Obj114

\* MERGEFORMAT (.)

t*j115

To estimate the model, we use the two-step pseudo-maximum likelihood procedure of
Genest, Ghoudi and Rivest (1995). We first estimate the sequence of marginal
distribution functions using the re-scaled conditional empirical distributions, denoted
below. We then replace the true distribution with the empirical one in the likelihood
function and maximise the resulting function with respect to the copula parameters:

\* MERGEFORMAT (.)   6

This two-step semi-parametric approach has the advantage that inference about the
copula parameters and copula model selection is robust to misspecification of the
marginal distributions. However, it is not efficient, and a more efficient one-step
estimator is provided in Chen, Fan and Tsyrennikov (2006). However, we favour the
two-step approach mainly for reasons of computational efficiency.³³

33 Note also that the two-step approach allows one the flexibility of using two different data sets to
estimate marginal distributions and mobility. This feature is exploited in Dearden et al (2006), who use
large samples of good quality cross-sectional earnings data to estimate the marginals.

37

<<   34   35   36   37   38   >>

More intriguing information