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Reconsidering the Moral HazardRisk Aversion Tradeoff
Joseph P. Newhouse, © 2006
Many thanks to David Cutler, Richard Frank, Jon Gruber,
Tom McGuire, and Richard Zeckhauser for comments.
Some Prefatory Remarks
 I thought about several topics for this talk
 How and when does a subfield of economics
get established? When is it recognized by the
AEA classification system? When is there a
field journal? A professional society?
 Clear that health economics is established; JHE
and HE now 1 and 2 in citation counts among
all economics and policy journals taken jointly!
 The questions at the top were too hard
JHE and HE citation counts: Kodrzycki and Pingkang 2005, http://www.bos.frb.org/economic/wp/wp2005/wp0512.pdf.
The Future
 Another natural topic: the future of the field
 This is something of a fool’s errand, but
several factors suggest continued vitality:
Technological change and cost pressures
 Use of administered pricing
 Off-frontier production, e.g. variations
 A second-best world; few unambiguous
predictions; need for empirical verification

Cost Sharing in Health Insurance
 Instead of these topics I went back to what I
worked on at the beginning of my career;
the structure of cost sharing in health
insurance
For example, the size of a deductible
 Although I assume a health insurance context,
the issues are also relevant in a health service
context

Outline of Talk
 Received theory and empirics
 The context for reconsidering
 An elaboration of received theory
 Incorporating time-inconsistent preferences
Received Theory
 Cost sharing in health insurance is
traditionally framed as finding the optimal
tradeoff between moral hazard and risk
From Arrow (1963, 1968), Pauly (1968),
Zeckhauser (1970)
 This is how our textbooks present it; e.g.,
Phelps, ch. 10, Feldstein, ch. 6, Zweifel and
Breyer, ch. 6

Arrow, AER, 1963, 53(5): 941-978; 1968, 58(3):537-539; Pauly, AER, 1968, 58(3):531-537; Zeckhauser, JET, 2(1):10-26.
Optimal Cost Sharing? - 1
 Using the framework of trading off moral
hazard and risk, the RAND Health
Insurance Experiment calculated the
optimal cost sharing in 1983 dollars to be a
$200 individual deductible, followed by
25% coinsurance, to a $1,500 stop loss
Newhouse and the Insurance Experiment Group, Free for All?, chapter 4.
Optimal Cost Sharing? - 2
 These values were slightly above those in
early 1980s indemnity policies, but….
 The RAND calculations didn’t consider the
tax subsidy to employer paid premiums nor
liquidity constraints, which would have
lowered the optimal cost sharing

On the other hand, the calculations assumed
actuarily fair insurance
What Happened?
 Instead of cost sharing escalating with
medical spending, we entered the era of
managed care with lower cost sharing
 Lower cost sharing was consistent with the
idea that greater supply-side cost sharing
had altered the moral hazard-risk tradeoff,
which it probably did, but…
Two Problems Remained
 Supply-side cost sharing was not well
placed to affect the decision to initiate
treatment for an episode, which the RAND
data suggested was the principal margin that
demand-side cost sharing affected, and…
Did Supply-Side Cost Sharing
Reduce Deadweight Loss?
 With minimal demand-side cost sharing and
reliance on supply-side cost sharing there
was no mechanism to reveal willingness-topay, so that services a consumer would have
been willing to pay for might have been
denied
 Did this play a role in the managed care
backlash?
Pauly and Ramsey, JHE, 1999, 18(4) 443-458; Rosenthal and Newhouse, Jnl Hlth Care Fin, 2002,28(4):1-10.
And Now…
 Whether because of the backlash or because
supply-side cost sharing was about one-off
effects, or both, demand-side cost sharing is
now coming back on the table
 The 2003 legislation authorizing Health
Savings Accounts prescribed a minimum
$1,050 deductible (individual), maximum
$5,250 stop-loss (2006 values)
HSAs and Optimal Cost Sharing
 Despite product change, the HSA figures
are not so far from the RAND calculations
Health spending from 1983-2006 grew by ~5X
 Ignoring the product change and using 5X to
inflate, the HSA deductible is in line
 The stop loss is larger by 3.5X, but medical
care is a larger share of income, so a less than
proportional increase would be optimal

Law Says Preventive Services
Can Be Exempt
 The Treasury defines preventive services as:
periodic health examinations; routine
prenatal and well-child care; tobacco
cessation programs; immunizations; weight
loss programs; various screening programs
 Importantly for my story, the Treasury
excludes services that treat existing
conditions; they are subject to cost sharing
Should More Services be
Exempt?
 In particular, should cost sharing be reduced
for chronic maintenance drugs and routine
maintenance visits for chronic conditions?
Considerable evidence that compliance
increases with less cost sharing
 In some cases this may lower total lifetime cost;
in others it may not, but it may improve health

Evidence on Capped Drug
Benefits - 1
 The following slides compare results from
two matched groups at Kaiser Northern
California
 One group had a drug benefit capped at
$1,000 of member spending (no benefits
after that), and the other group had no cap

All were Medicare eligibles over 65 years of
age
Evidence on Capped Drug
Benefits - 2
 The comparisons are for those who had
diabetes, hyperlipidemia, or hypertension,
and who filled a prescription for an antidiabetic drug, a lipid-lowering drug, or an
anti-hypertensive in the prior year
 The tables show drug consumption, nonadherence, and physiologic outcomes

Adherence is having ≥ 80% of days covered
Diabetics
Benefit Not
Benefit
Odds Ratio
Capped (%) Capped (%) (95% C.I.)
Drug
Quantity ($)
--
--
Drug NonAdherence
21.2
26.2
Glycated
Hg > 8%
17.0
19.7
0.79
(0.73-0.86)
1.33
(1.18-1.48)
1.23
(1.03-1.46)
Odds ratio = capped/non-capped; Source: Hsu, et al., NEJM, June 1, 2006
Odds Ratio results control for age, sex, race, comorbidities, office, ED copays. Physiologic odds ratio controls for initial value.
High Cholesterol
Benefit Not
Benefit
Odds Ratio
Capped (%) Capped (%) (95% C.I.)
Drug
Quantity ($)
--
--
Drug NonAdherence
26.5
31.4
LDL>130
mg/dl
19.6
21.3
0.73
(0.70-0.77)
1.27
(1.19-1.34)
1.13
(1.03-1.25)
Odds ratio = capped/non-capped; Source: Hsu, et al., NEJM, June 1, 2006
Odds Ratio results control for age, sex, race, comorbidities, office, ED copays. Physiologic odds ratio controls for initial value.
Hypertensives
Benefit Not
Benefit
Odds Ratio
Capped (%) Capped (%) (95% C.I.)
Drug
Quantity ($)
--
--
Drug NonAdherence
14.6
18.1
SBP>140
mm Hg
38.5
39.5
0.85
(0.82-0.89)
1.30
(1.23-1.38)
1.05
(1.00-1.09)
Odds ratio = capped/non-capped; Source: Hsu, et al., NEJM, June 1, 2006
Odds Ratio results control for age, sex, race, comorbidities, office, ED copays. Physiologic odds ratio controls for initial value.
Use and Costs, Rate/100
Benefit Not
Capped
Benefit
Capped
Odds Ratio
(95% C.I.)
ED Visits
45.2
49.2
Nonelective
Admissions
Total Cost
16.6
18.7
1.09
(1.04-1.14)
1.13
(1.05-1.21)
--
--
0.99
(0.94-1.04)
Odds Ratio results control for age, sex, race, years of Kaiser membership, comorbidities, office, ED copays.
Conclusion from Kaiser Study
 A drug benefit capped at $1,000 versus no
cap led to less compliance with chronic
disease regimens, poorer physiologic health,
and cost increases in other medical services
that about equaled the savings in drug costs

If non-compliance were to continue and
physiologic health to deteriorate further, the
future increase in other medical spending may
exceed the decrease in drug spending
Additional Evidence - 1
 Soumerai, et al. studies on caps in two
Medicaid populations: 3 drug/month limit
saved 35% on drugs, but more than doubled
nursing home admissions

Among schizophrenics: Cap on mental health
drugs raised other spending by 17 times the
savings on drugs
Soumerai, et al., NEJM, 1991, 325:1072-1077, 1994, 331:650-655.
Are You Saying: So What?
 Did you already know that initial benefits
with caps were poor economics and policy?
 Then ask yourself whether an actuarily
equivalent deductible with full coverage
over the deductible would have yielded
better or worse compliance results?
 How many think better results?
Additional Evidence - 2
 In any event, if you don’t like caps, there
are analogous findings about drug copays
 Huskamp, et al. and Goldman, et al. find
that increased copays decreased the use of
ACE inhibitors, anti-hypertensives, antidiabetics, and statins, though they have no
data on other medical costs
Huskamp et al, NEJM, 2003, 349:2224-2232; Goldman, et al., JAMA, 2004, 291:2344-2350.
Additional Evidence – 3
 Tamblyn, et al. find imposing cost sharing
for drugs among the poor and the elderly in
Quebec reduced drug use by 15-22%, but
led to an approximate doubling of serious
adverse events, meaning death,
hospitalization, or nursing home admission

No cost data, but it seems likely that total costs
increased
Tamblyn, et al., JAMA, 2001, 285(4):421-429.
Additional Evidence - 4
 Rosen, et al. (2005) simulate that full
coverage of ACE inhibitors for Medicare
beneficiaries who are diabetic would
increase QALYs and save money relative to
the default cost sharing in Part D
Rosen, et al., Annals of Internal Med, 2005, 143(2):89-99.
An Extreme Example
 With Directly Observed Therapy,
tuberculosis patients are paid to be observed
swallowing their medications

Negative cost sharing!
3 Cases to Stretch the Usual
Risk-Moral Hazard Tradeoff
 An easy one to warm up
 A second one that is a straightforward
elaboration of received theory
 A third one that ventures further afield,
time-inconsistent preferences
An Easy Case
 The marginal social cost of another pill is
frequently negligible, so any induced
consumption has negligible deadweight loss
 Assuming no increase in costs elsewhere,
no moral hazard-risk aversion tradeoff
 I assume for the remainder of the talk that
marginal social cost is non-negligible

Of course, private costs of the pill are positive
Before Coming to Case 2: How Is
Cost Sharing Determined?
 For many cost sharing is determined by
employer or government choice

Even with choice among plans, employer may
have standardized cost sharing
 As a result:
In many cases cost sharing is exogenous
 And even with choice of plan, a person’s health
costs are shared with an insurance pool

The Employer’s Choice
 How does an employer choose cost sharing?
 Goldstein-Pauly (1976): Employers minimize
labor cost, look at benefit to marginal worker;
unions look at benefit to median worker
–

Labor cost = health care cost + productivity effects
Miller (2005): Employer who minimizes cost
and offers plan choice sells more generous plan
as an upgrade; a lump sum subsidy to all plans
is probably not optimal
Goldstein-Pauly, in Role of Health Insurance in the Health Services Sector, 1976; Miller, JHE,24(5):931-939.
Public Insurance
 Straightforward extension of Goldstein-
Pauly median employee model to median
voter?
An Implication
 Tenure in the employment group is relevant
for a cost-minimizing employer; ceteris
paribus, firms with longer job tenure will
provide insurance with less cost sharing if
those services reduce future costs

I have not tested this
 In Medicare life cycle costs relevant
A Note on Measuring the RiskMoral Hazard Tradeoff
 Much empirical analysis, the RAND HIE
included, uses an annual time frame, but
lifetime risk is relevant with chronic disease
 Positive intertemporal correlation of health
spending from chronic disease raises risk
for a given level of positive cost sharing
Second Case: An Elaboration of
Received Theory
 Because costs are shared within a common
insurance pool, less cost sharing for those
services and/or individuals that lowers
overall spending for the pool is the usual
case of a subsidy to recognize an externality
Here too no moral hazard-risk aversion tradeoff
 Held-Pauly (1990) take up an analogous case,
but don’t frame the issue as optimal cost
sharing for all services

Held and Pauly, JHE, 1990, 9(4): 447-461.
A Third Case: Take Your
Medicine!
 We surely all heard that from our mothers
 So why as adults do some persons not take
drugs that will improve their future health
but may not save them money?
One Answer
 They are insured for other medical services
and place a low value on the uninsured
health costs such as pain, suffering
 The second part doesn’t seem very plausible
for the above cases of chronic disease
 Models of time-inconsistent behavior seem
relevant in this context
Models of Time-Consistent and
Time-Inconsistence Preferences
 Assume a standard health economics utility function:
Ut  U ( xt , Ht (m, x))
 With time-consistent preferences (standard discounting), or:
T t
i

 Ut  i
0<<1
i 0
 Time-inconsistent preferences, quasi-hyperbolic discounting:
T t
Ut     Ut  i
i
i 1
0 < β,  < 1
Maximize lifetime utility s.t. lifetime budget constraint
Strotz, 1956; Akerlof, 1991; Laibson, 1997; O'Donoghue and Rabin, 1999; Frederick, Loewenstein, and O'Donoghue, 2002.
Already a Health Application
 Gruber-Koszegi (2001, 2004) use a model
with time-inconsistent preferences to justify
much higher cigarette taxes to induce
“compliance” with not smoking

With this model cigarette taxes are less
regressive than usually assumed and may be
progressive because “internalities”
disproportionately accrue to the low income
Gruber-Koszegi, QJE, 2001, 116(4), 1261-1305; J Pub Econ, 2004,88(9-10): 1959-1987.
Time-Inconsistent Preferences
and Optimal Cost Sharing - 1
 Solutions in these models depend on
whether the individual is aware of the timeinconsistent preferences or not

Solutions are easier if unaware (naïve case)
 Also can depend on whether example is
immediate reward or immediate cost

Chronic disease application is immediate cost;
small difference between  and β can generate
large welfare losses if individual is naïve
Laibson, QJE, 1997, 112(2):443-477; O'Donoghue and Rabin, AER, 1999,89(1):103-124. .
Time-Inconsistent Preferences
and Optimal Cost Sharing - 2
 In other words, with time-inconsistent
preferences, induced compliance can be
welfare increasing, potentially by a large
amount, independent of risk
Specific Subsidies
 Very specific cost sharing structures such as
free ACE inhibitors for elderly diabetics are
not found in the market (selection), but
disease management and case management
use non-price methods toward similar ends

Medicare could adopt such a structure and there
could be mandates in private insurance
Conclusions: Social Perspective
 Current cost sharing structure may not be
optimal from society’s perspective
 Without considering risk, welfare may be
improved by selectively lowering cost
sharing for certain persons and/or certain
services
 Case 1: Negligible marginal social cost

From social perspective, negligible cost sharing
Social Perspective, cont.
 Case 2: Induced greater compliance that
adds cost for the specific good or service
but saves overall lifetime costs

Additional subsidy; externality
 Case 3:Induced greater compliance that
increases value of health by more than cost
Models of time-inconsistent behavior relevant?
 Marginal Benefit of health = MC compliance

Conclusions: Private Perspective
 From a private perspective:
Case 1 of negligible cost probably doesn’t exist
 Cases 2, 3: Optimal subsidy will generally be
less than from social perspective

Conclusions: Policy and
Research
 HSA legislation seems too restrictive
 More generally, current cost sharing
structure seems sub-optimal, even from a
private perspective
 Optimal cost sharing seems like a fruitful
field for future research