596 Panel Data Methods
In this kind of application it is quite likely that the unobserved individual effect
will be correlated with the observed regressors, such as household income. To
allow for this possibility Contoyanniset al.(2004b) parameterize the individual
effect (Chamberlain, 1984; Mundlak, 1978; Wooldridge, 2005). This allows for
correlation between the individual effects and the means of the regressors. In addi-
tion, because they are estimating dynamic models, they need to take account
of the problem of initial conditions. It is well known that in dynamic specifica-
tions the individual effect will be correlated with the lagged dependent variable,
which gives rise to what is known as theinitial conditions problem, that an individ-
ual’s health at the start of the panel is not randomly distributed and will reflect
the individual’s previous experience and be influenced by the unobservable indi-
vidual heterogeneity. To deal with the initial conditions an attractively simple
approach suggested by Wooldridge (2005) is used. This involves parameterizing
the distribution of the individual effects as a linear function of initial health at the
first wave of the panel and of the within-individual means of the regressors, and
assuming that it has a conditional normal distribution. As long as the correlation
between the individual effect and initial health and the regressors is captured by
this equation it will control for the problem of correlated effects. Its ease of imple-
mentation stems from the fact that the equation foruican be substituted back
into the main equation and the model can then be estimated as a pooled ordered
probit or a random effects ordered probit using standard software to retrieve the
parameters of interest. Contoyanniset al.(2004b) find that SAH is characterized
by substantial positive state dependence and unobserved permanent heterogene-
ity. Including state dependence dramatically reduces the impact of individual
heterogeneity. Conditioning on the initial period health outcomes and within-
individual averages of the exogenous variables reduces the impact of heterogeneity
and state dependence. Unobservable heterogeneity accounts for around 30% of the
unexplained variation in health.
Similar dynamic panel probit models are used by Gannon (2005). In her case
the outcome of interest is a binary measure of labor force participation, which is
assumed to be a function of past labor force participation and health limitations.
This gives dynamic panel probit models that are estimated in pooled and random
effects versions using the Wooldridge (2005) approach to deal with the initial con-
ditions problem. The models are estimated with the Living in Ireland Survey (LIS),
which is the Irish component of the ECHP. Nolan (2007) also uses the LIS, but uses
a dynamic random effects Poisson specification to model GP visits. She adopts the
Wooldridge approach to model the initial conditions. In contrast, Arulampalam
and Bhalotra (2006) use Heckman’s approach to specify the initial conditions in a
Markov model of infant deaths among Indian families.
12.5.2.2 GMM estimators
In Jones and Labeaga (2003) a panel of Spanish households is used to test the empir-
ical formulation of the rational addiction model (Beckeret al.,1994). This dataset
raises problems of measurement errors, censoring, and unobservable heterogeneity.
Jones and Labeaga (2003) use sample separation information to exclude those