A Theory of Prepayment,
Managed Care, Deductibles and
Copayments
Allen C. Goodman, Wayne State U.
Maia Platt, U. of Detroit – Mercy
Seminar
University of South Florida
March 30, 2012
Managed Care
• Managed Care has largely taken over the
non-Medicare market for health care
provision, and is making in-roads into
Medicare.
• Fee-for-service is essentially moribund in
the US. See following chart.
Managed Care Plans
Theory of MCOs?
• There’s been no theory.
• What characterizes MCOs?
• Is the Veterans’ Administration an MCO?
(Probably is).
Theory of MC?
• Kaiser Permanente
– Vertically integrated
– Very little choice
– “Managed Care heavy”
• PPOs, POS, etc.
– Less heavy handed
– More choice
– “Managed Care light”
Theory of MC?
• Utilization Review
– Prospective
– Concurrent
– Retrospective
– Everyone does it now
Selective Contracting
• Morrisey argues that the ability to exclude
some (higher cost, noncompliant)
providers allows MCOs to reduce costs.
• Providers give up potentially higher
payments per activity for the promise of
more clients.
• Contracts are extraordinarily complicated.
I can give personal examples.
A “Health Services” Perspective
• We had this diagram in FGS-2  FGS-4.
Shortell et al
How good are the
information systems?
How well do they
communicate with
each other
Some point to the VA
as a prime example of
one that works!.
Stylized Facts
• Economists love stylized facts!
– Most Americans get their health care risk
pooling through the workplace (btw, PPACA
won’t change that).
– Health insurance (HI) is largely (entirely?)
paid for by the worker in the form of reduced
wages.
– In many ways at least some portion of HI can
be considered as “prepayment” for services.
More Stylized Facts
– Although coinsurance rates are negatively
correlated with use,
– Deductibles are as often positively correlated
as negatively correlated.
– Consumers most often have access to a few,
discrete opportunities. How do they choose
among them?
Who Pays – Mkt Analysis
Who Pays – Firm Level
High loading costs may force
firms to hire fewer workers, or (with
minimum wage) not offer insurance
Some Notation
• Household chooses among options in its
health insurance package. The health
insurance will essentially pre-pay for wellcare, and some expected illness.
• The household also may need additional
insurable care with probability w. How do
they choose among MCO plans?
• At WSU we have 2 HMOs, 2 PPOs, and 1
FFS plan.
Some Notation
Suppose there are three plans n, where n = i, j, k,
with
w = probability of needing insurable care
Ei , Ej, Ek = expenditures necessary if care is
needed.
bi ,bj, bk = coinsurance rate faced by household
Ri ,Rj, Rk = deductible faced by household
Si, Sj, Sk = out of plan expenditures
Annual Fees Fi ,Fj ,Fk for levels of care
v i ,v j ,v k respectively.
Without loss of generality Qi = Qk , Qj > Qi ,Qk .
Proposition 1
• Proposition 1: Criterion for choosing among
MCOs – “less than or equal.”
• Unless a MCO matches household’s
preferences (point A) for prepaid care exactly,
with number of visits vA, the household will pick
one that provides less care.
– A household can purchase additional health care outof-plan, but cannot sell surplus care.
– With the current individual’s preferences, then, plans i
and k dominate plan j. The insured may or may not
choose to purchase additional care out of pocket. For
purposes of this exposition, we will assume that Sn =
0, so that the insured uses care level v i = v k
MCOi, MCOk
MCOj
Plan
Annual
Cost
Other
Goods
Out of Plan, or
Deductible (coinsurance rate = 1)
A
Pure Risk Premium
vi = vk
vA
vj
Visits
Proposition 2
• Consumers sort themselves into MCOs based
on expected need for insurable care, and on the
characteristics of the MCOs as defined by
coinsurance rate and deductible.
• For empirical work, across large numbers of
MCOs, higher deductibles may very well be
related to higher levels of utilization or
expenditures rather than lower levels.
• In contrast, higher coinsurance rates, holding
deductibles constant, will always, in this model,
lead to more utilization and expenditures.
MCOi, MCOk
MCOj
Plan
Annual
Cost
MCOi, MCOk provide same basic
care.
MCOi – higher deductible and lower
coinsurance rate
MCOk – lower deductible, lower
coinsurance rate.
Out of Plan, or
Deductible (coinsurance rate = 1)
Other
Goods
Rk
A
B
biwEi(bi)Ri
bkwEk(bk)Rk
vi = vk
vA
vj
v k
Visits
v i
Proposition 3
• There may be heterogeneous preferences within
individual MCOs.
• Suppose that there are only 2 MCOs available,
MCOi and MCOj, and there are two households
as noted in Figure 3. In these circumstances,
both households will prefer MCOi to MCOj. As
drawn, however:
– a low deductible and a high coinsurance rate will be
preferred by Household 1,
– while a higher deductible and a lower coinsurance
rate will be preferred by Household 2.
Proposition 3 – cont.
• At the lower deductible Rk and higher
coinsurance rate bk, Household 1, if faced
with an insurable event will purchase v i1+
2+
v
visits, while Household 2 would purchase i
visits.
• By inspection, we can see that with a
higher deductible Ri and a lower
coinsurance rate bi Household 1 will be
worse off, whereas Household 2 will
2++
v
purchase i visits and be better off.
U1
U1
A1 and A2 represent
ideal amounts of prepaid care
MCOi, MCOk
U2 U2 U2
Other
Goods
Plan
Annual
Cost
A1
A2
vi = vk
v i1
v i2
vi2
Visits
Observations
• There’s a lot of public finance in this
model.
• It suggests yet another reason why MCOs
may “under-provide” services – i.e.
consumers don’t want to pay for
something they might not use.
• Suggests ways to model the willingness to
pay for insurance, and the structures of
copayments and deductibles.
Other Issues
• Given the taste and income distributions
what is the optimal number of MCOs?
• Merging of MCOs?
• Disintegration of one MCO into 2 or more?
Other issues
• Does not model the production from
MCOs. In other work, Goodman and
Stano (2000) argue that there will be a
bias toward MCOs that :
– are too small;
– offer too little service;
– offer service that is too “low tech.”
Questions or Comments?
Figure 1: Choosing Among MCOs
MCOj
MCOi, MCOk
Plan
Annual
Cost
{
MCOi and MCOk provide same basic
package. MCOi has higher deductible
and lower coinsurance rate. It is preferable
for larger amounts of expected incremental care.
MCOk is preferable for smaller amounts
of expected incremental care.
Rk
Other Goods
Ri
A
B
biwEi(bi)
bk wEk(bk )
vi  vk
vA
v j vk
vi
Visits
Figure 1: Choosing Among MCOs
MCOj
MCOi, MCOk
Plan
Annual
Cost
{
MCOi and MCOk provide same basic
package. MCOi has higher deductible
and lower coinsurance rate. It is preferable
for larger amounts of expected incremental care.
MCOk is preferable for smaller amounts
of expected incremental care.
Rk
Other Goods
Ri
A
B
biwEi(bi)
bk wEk(bk )
This assumes NO “pure” insurance
against risk. If we want to show
pure insurance, we have a parallel
downward shift and everything else
follows as before.
vi  vk
vA
v j vk
vi
Visits
Figure 1: Choosing Among MCOs
MCOj
MCOi, MCOk
Plan
Annual
Cost
{
MCOi and MCOk provide same basic
package. MCOi has higher deductible
and lower coinsurance rate. It is preferable
for larger amounts of expected incremental care.
MCOk is preferable for smaller amounts
of expected incremental care.
Rk
Other Goods
Ri
A
B
biwEi(bi)
bk wEk(bk )
vi  vk
vA
v j vk
vi
Visits
Figure 2: Heterogeneity within a MCO
U1
MCOi U' U''
2
2
MCOj
U2
Plan
Annual
Cost
{
Rk
Other Goods
Ri
A1
A2
A1 and A2 represent
ideal amounts of
prepaid care.
v i1  v i2
vi1
biwEi(bi)
bk wEk (bk )
vj
vi2
vi2
Visits