The Palestinian Economy. Theoretical and Practical Challenges

Proceedings “The Palestinian Economy: Theoretical and Practical Challenges” 365
two specifications: if there is collinearity, the TPM is more reliable, given that it performs
better than the SSM in terms of mean-squared error. Indeed, our data is characterised by a
quite high correlation between the inverse Mill’s ratio and the explanatory variables of
the second-step equation (the correlation coefficient ranges between 0.86 and 0.89). On
the other hand, although the HM and TPM are often regarded in the count data literature
as being synonymous, Pohlmeier and Ulrich (1995) show that a limitation of the HM is
that it treats the measure of frequent visits as being related to a single-spell of
illness/treatment. This attests to be problematic, providing that health care use data are
usually specific to a period of calendar time during which the first visit is not necessarily
the initial one in a course of treatment.
An alternative modelling to count data was proposed by Deb and Trivedi (2002),
who argue that counts data are sampled from a mixture of populations that differ with
respect to their underlying latent health (severely-ill vs. perfectly-healthy), and thus, in
their demands for health care (high-frequency-users vs. non-users). To suitably capture
this feature of data, the authors propose using the so-called “latent class models”; e.g., the
FMM. Jimenez-Martin et al. (2002) compare FMM with TPM using three waves of data
for 12 European countries. Their empirical results show that the FMM may perform
better than the TPM, but this was only true when parameter homogeneity is imposed
(across countries) and for GP visits. For homogeneous parameter specification and SP
visits, the TPM was preferred to the FMM. The authors explain the difference in the
preferred specification for GP and SP by the fact that over a period of one year multiplespells
of illness/treatment are more likely to be observed for GP, whereas SP visits are
more likely to represent a single-spell. Thus, the TPM, with its rationalisation through
principal-agent story, should be more suited to representing (annual) SP visit data.
Furthermore, a problem with the FMM, apart from the fact that its specification is not
derived from an economic theory of health care demand, is that it involves estimating a
large number of parameters; something that can lead to non-convergence of likelihood
and to over-parameterisation problems.
Given the above suggesting that the TPM may perform better when compared with
others, we have chosen to adopt for the purpose of this analysis a TPM, distinguishing
between the probability of positive usage and the conditional amount of usage given
positive use in the reference period. Various specifications of the TPM have been
proposed in the literature (Jones and O’Donnell 2002). The choice depends mainly on
statistical considerations regarding health care use (cf. e.g., Pohlmeier and Ulrich 1995).
The TPM specifications we have used are based on a logit for the first-part equation (i.e.,