594 Panel Data Methods
private and hospital or clinic); environmental characteristics, such as the dentist-
population ratio and annual household income; and whether the dentist practices
in a deprived area. The overall effect of global budgets is to constrain costs, but
there is evidence of a change in the mix of services. Male and younger dentists have
higher policy effects than female and older dentists. Global budgets favor dentists
in deprived areas and there is some evidence of increases in the expenditure per
visit and the volume of composite resin fillings.
Applications of linear models are not confined to longitudinal datasets. Moscone
et al.(2007) take a spatial panel approach to data on mental health expenditure
by local authorities in England. They compare specifications that allow for a spa-
tial autoregressive process in the error term; a random effects model with spatially
lagged dependent variables; and a random effects model with spatial autocorrela-
tion. The random effects model with lagged dependent variables proves to be the
preferred specification.
12.5.1.2 Dynamic panel data models: GMM estimators
Brownet al.(2005) apply dynamic panel data models to assess the impact of HMOs
on the supply of doctors at the local level. They construct a panel of Californian
counties for the years 1988–98 using data from the American Medical Association
and specify reduced-form models for the supply of doctors per 100,000 inhabitants
for both specialists and primary care. First differencing is used to deal with omit-
ted variables and dynamics are included to allow for inertia in supply responses.
The models are estimated by the systems version of the Arellano–Bond estimator
(Arellano and Bond, 1991; Arellano and Bover, 1995; Blundell and Bond, 1998),
with both one-step and two-step estimates of the standard errors. The internal
instruments, drawn from lagged variables, are augmented by some external instru-
ments. The tests for autocorrelation are consistent with the assumptions of the
Arellano–Bond model: there is evidence of first order autocorrelation in the resid-
uals, but not of higher order autocorrelation. The results show that the supply of
specialists is responsive to changes in the relative market penetration of HMOs,
but the supply of primary care doctors is not.
The Arellano–Bond approach is also adopted by Tammet al.(2007) to estimate
price effects on insurers’ market shares. They use an unbalanced panel of insurers,
who were active in the German social health insurance system between January
2001 and April 2004. This issue is important as price sensitivity among consumers is
a precursor for the success of reforms based on the notion of managed competition.
They adopt a dynamic panel data model for the logarithm of each insurer’s mar-
ket share. This aggregate model is motivated by an individual-level multinomial
logit model for the choice of insurer and dynamics are introduced to capture the
fact that only a fraction of consumers will switch companies during a given year.
The model is estimated using the Arellano–Bond estimator and the systems-GMM
estimator. The standard Arellano–Bond GMM estimator, which relies on lagged
levels to instrument lagged differences, may perform poorly. This suggests using
the systems approach, but this approach requires stronger restrictions on the ini-
tial conditions: the first-period error term and the first differences of the regressors