612 Panel Data Methods
correlated with the outcome and with the allocation of treatment. In this sense, the
DD estimator combines selection on unobservables with selection on observables,
so long as the unobservables are time invariant. The time effects (ν) take account
of any time trend in the data that is common to both the treatment and control
groups. This implies a “parallel trend” assumption. When the DD estimator is
applied to repeated cross-section data a further assumption is required: that the
composition of the treatment and control groups remains stable over time.
The DD estimator in equation (12.40) is defined above by using the interaction
between the post-treatment period (P) and belonging to the treatment group (T).
In some applications exposure to treatment may be defined by the interaction
between more than two factors. For example, in Schmidt’s (2007) evaluation of
the impact of infertility insurance mandates on birth rates in the US, an indicator
of whether states have mandates is interacted with whether or not women are
over 35, as those over 35 are most likely to suffer infertility. Multiple interactions
can be used to define exactly who is exposed to treatment and also to allow for
heterogeneity in the size of the treatment effect. This approach is often labeled
difference-in-difference-in-differences (DDD).
Chalkley and Tilley (2006) show how economic incentives can influence dental
practice. This study exploits the comparison between self-employed and salaried
dentists working for the NHS in Scotland to show that the financial incentives of
FFS increase the intensity of treatment by around 21%. Using a DD approach, the
paper finds that self-employed dentists treat exempt patients, who are assumed
to be more likely to be influenced by supplier inducement, more intensively than
non-exempt patients, relative to salaried dentists who do not face the financial
incentive of FFS. These findings are based on an administrative database, the Man-
agement Information and Dental Accounting System (MIDAS), that records claims
for self-employed and salaried dentists. The database provides a panel of dentists
and patients and can be used to control for the practice style of individual dentists
as well as measures of patient need.
In January 1994 the health authorities in Belgium increased co-payment rates
for home and office visits to GPs and for visits to specialists. The increases were
substantial: 35% for GP home visits, 45% for GP office visits and 60% for specialist
visits. Cockx and Brasseur (2003) use this change in prices as a natural experiment.
To create a control group they use those who were exempt from charges due to
low income among widows, orphans, the disabled and retired. This means that
identification relies on the treatment and control groups being comparable and
the authors note that identification can only be achieved for low-income groups. A
DD estimator is applied to the logarithm of utilization and the model is extended
to a Rotterdam demand system to accommodate substitution effects induced by
the change in relative prices. Interaction terms are used to allow for heterogeneity
in the treatment effects. A similar set of reforms in Germany is used as a natural
experiment by Winkelmann (2004b). In this case co-payments for prescription
drugs increased by 6 DM on July 1, 1997, leading to relative price increases of up
to 200% depending on the pack size. The policy is evaluated using data from the
GSOEP for the years around the reform, 1995–96 and 1998–99. The control group