602 Panel Data Methods
and with the observed covariates. A conditional logit is used to estimate the selec-
tion equation. Then the hours equation is estimated in first differences by weighted
least squares, with kernel weights applied to the difference in the linear index from
the selection equation between different periods. The aim is to difference observa-
tions across periods for which the probability of selection is (approximately) the
same. Rettenmaier and Wang (2006) use a semiparametric estimator for the Tobit
model to model persistence in Medicare reimbursements. The model allows for
fixed effects and a lagged dependent variable, but assumes that initial conditions
are fixed.
It is widely believed that income has a direct effect on health, but it is often argued
that indirect income effects due to relative deprivation may be equally important.
Wildman and Jones (2007) investigate these relationships using parametric and
semiparametric panel data models. By allowing for a flexible functional form for
income, they seek to ensure that coefficients on relative deprivation variables are
not an artifact of a highly non-linear relationship between health and income.
Parametric estimation may lead to biased coefficients if the parameterization of
the explanatory variables is incorrect. Semiparametric partially linear estimation
overcomes this problem by allowing an unspecified relationship between health
and income (Robinson, 1998). The results provide strong evidence for the impact
of income on self-reported measures of health for men and women. These results
are robust across a range of techniques and are resilient to the inclusion of measures
of relative deprivation. The parametric results for relative deprivation largely reject
its influence on health, although there is some evidence of an effect in the
semiparametric models.
12.6 Multiple equation models
12.6.1 Applications using MSL
Balia and Jones (2008) use the first wave of the British HALS from 1984 to 1985
along with the longitudinal follow-up from May 2003 to model the determinants
of premature mortality and to assess the relative contribution of lifestyle factors
to the gradient in mortality in Britain. A behavioral model, that relates mor-
tality to observable and unobservable factors, is used to motivate the empirical
specification. Death, SAH and a range of health-related behaviors are measured
as binary outcomes and, to capture the effect of lifestyles on mortality and mor-
bidity in the presence of common unobservable factors, the model is estimated
as a recursive multivariate probit. The full system is estimated by MSL and health
inequality is explored using a decomposition analysis of the Gini coefficient. The
results contradict the view that lifestyles only play a minor part in health
inequalities.
Deb and Trivedi (2006) and Debet al.(2006a) use a latent factor specification
to model selection into treatment in nonlinear models and adopt a MSL estima-
tor. The aim is to estimate causal effects using a structural model, motivated by
a selection on unobservables approach, in which the parametric distribution of