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144 Maximum Billing Supplement KCE reports 80S
Simple descriptive statistics can be misleading, as they do not take differences in the
compared populations into account. We can therefore improve the comparison and get
a more precise estimate of the effect of the MAB by using the methodology of
Contoyannis et al. (2005) 13 (also applied by Li et al. 2007) 17 . They use a first difference
equation to capture the before-after comparison with an instrumental variable approach
to take the endogeneity of price into account.
The method boils down to estimating β in the underneath equation:
PX = I + γ + α Z + βC+
u
(1) it i t t i it it
where
L
l
it it
l=
1
PX = ∑ PX are total expenditures (price P times consumption X) in
period t (including supplements), I i is a household unobserved effect (that corrects for
time-invariant unobservables, for example time-invariant health status, hospital
insurance status, etc.), γ t is a time effect, Z i are time-invariant characteristics that are
allowed to have an effect upon total expenditures that change over time, uit is an error
l
CX
l it
term, and Cit
= l
PX
l it
∑ is the consumer price (co-payments + supplements) rate
∑
which measures the marginal price of care, assuming that individuals are myopic, i.e.
individuals do not anticipate they might surpass the cap, but once they have surpassed
the cap, they adapt their behaviour immediately. nn
By ‘first-differencing’ equation (1), i.e. taking the difference between periods in 2002 and
periodsin 2003 we can get rid of the individual specific unobservables:
Δ PX =Δ γ +Δ α Z + βΔ
C +Δ u
(2) i t t i i i
However, this does not solve the endogeneity of C it caused by the non-linear pricing
schedule. Therefore, Contoyannis et al. (2005) 13 suggest to use the ‘price to be paid had
consumption remained at the pre-period level’ as an instrument for the change inC it . In
other words, the correlation with current expenditures is removed and equation (3) is
estimated:
Δ C = C − C = a C − C + bZ + ε
(3)
it , −1 it , −1 { it , −1 , −1
it , −1}
i it PX i t PX it PX i t PX i i
C −
where a and b are coefficients. The term it PX should be calculated as the co-
it , 1
payments + supplements that would have been paid in 2003 with the 2002
consumption. oo Next, do an IV regression of equation (2) using the RHS variables of
nn Note also that this price takes account of lower co-payment rates for those receiving preferential
treatment. Unfortunately, differences in consumption behaviour (e.g. the composition of the categories)
might drive differences in the co-payment rates and little can be done about it (our IV procedure takes
this partially into account, see further). There is however a very good argument for analysing total
expenditures and not expenditures for one category, i.e. total expenditures will implicitly capture
substitution effects between different types of care, while an analysis for one health care type does not.
oo We proceed as follows:
Calculation of Ci, t-1
PX is straightforward; since drugs type C are not in the MAB in 2002 we simply
i, t-1
take co-payments and reference price supplements of 2002 and divide by the sum of reimbursements, copayments
and reference price supplements of 2002.
Calculation C is more complicated. We first calculate per CNK code (this is the specific drug
i, t
PXi,
t-1
and package) the reimbursement price for 2003 and divide by the reimbursement price in 2002. 2002
reimbursements are inflated with this rate. We do the same for the co-payments + supplements. Next,