Plenary_Talk_1_Zweifel

The Division of Labor between Private
and Social Insurance
First Swiss Health Economics Workshop
Lucerne (Switzerland), 13 September 2013
Peter Zweifel, Prof. em. University of Zurich
peter.zweifel@econ.uzh.ch
Text: Zweifel, P. (2013), „The division of labor between private and social
insurance, in: G. Dionne (ed.), Handbook of Insurance, ch. 37.

16.09.2013 / 2Luzern / Zweifel Sept. 2013
Outline
1. Motivation and objectives
2. The efficiency view of social insurance
3. The optimal amount of Social Insurance
4. The crowding-out phenomenon
5. Could the division of labor between private and social insurance
be improved?
6. Conclusion and outlook

1 Motivation and objectives I
• At present, private and social insurance jointly claim roughly one-
third of a worker’s pay in industrial countries
• The United States is markedly below but other OECD countries
above this benchmark (see Table 1 and footnote).
• In social insurance (SI), benefits paid constitute the measure
• In private insurance, it is premiums paid for life and health and life
private insurance (PI)
• In spite of this lack of consistency, PI and SI together are a major
expenditure item in today’s household budgets

1 Motivation and objectives II
Table 1: Social (SI) and private (PI) insurance in some OECD
countries, in percent of GDP
Country 1980 1990 2000 2009a
Germany SI 22.1 21.7 26.6 25.2
PI n.a. 2.4 3.0 3.4
France SI n.a. 20.8 24.9 27.7
PI 3.4 6.7 8.4 7.4
United Kingdom SI 10.5 16.8 18.6 20.5
PI n.a. 6.8 12.8 10.4
Italy SI 18.0 20.0 23.3 24.9
PI n.a. 0.6 3.5 8.4
Note: SI includes benefits (e.g. for housing) that are part of public
welfare PI: is premiums paid for life and health insurance, estimated
from graphs published by Sigma 4/1992, 6/2001, and 2/2010.

1 Motivation and objectives III
Table 1: Social (SI) and private (PI) insurance in some OECD
countries, in percent of GDP (cont’d)
Country 1980 1990 2000 2009
Japan SI 10.4 11.3 16.5 18.7
PI n.a. 7.0 8.1 7.5
United States SI 13.2 13.5 14.5 10.2
PI n.a. 4.1 4.5 2.9
Switzerland SI 13.8 13.5 17.8 20.0
PI n.a. n.a. 7.6a 5.4
Note: a 2001
SI includes benefits (e.g. for housing) that are part of public welfare
PI is premiums paid for life and health insurance, estimated from
graphs published by Sigma 4/1992, 6/2001, 4/2004, and 2/2010.

1 Motivation and objectives IV
• Admittedly, personal lines of PI comprise more than just health and
life
• Yet it is evident from Table 1 that even in the United Kingdom, one
of the major markets for personal PI, the SI component is about
twice as important as the PI component
• In the United States, it is even about three times as important
• In Switzerland, the current ratio is almost 4:1
• Both the high GDP share of SI and PI combined and the
preponderance of SI are mainly the result of a remarkable
expansion of SI
• Detail not reported in Table 1 but provided by OECD shows that the
expansion of SI was led by health, with pensions second

1 Motivation and objectives V
• Much of the economics literature has justified the existence and
even the preponderance of SI by its efficiency-enhancing properties
• The argument is that SI can mend or at least mitigate market
failures of private insurance (PI)
• However, there have been concerns about SI crowding out
(efficient) PI, e.g. by Feldstein (1995, JPE)

1 Motivation and objectives VI
• This presentation seeks to shed light on this debate in four ways
• (1) it reviews the efficiency reasons supporting the view that there
is a need for SI, possibly complemented by PI. The theoretical
mainstay is provided by the famous Rothschild-Stiglitz (1976, QJE)
model
• (2) Some empirical evidence concerning the alleged ‘death spiral’
(Akerlof, 1970, QJE) and insurer behavior in the face of their lack of
information is examined
• (3) The alternative ‘public choice’ view emphasizing the interests
of voters and politicians is expounded
• (4) Normative issues are addressed by asking whether and in
which lines of insurance the future division of labor between PI and
SI could be improved

2 The efficiency view of social
insurance I
• Theoretical explanations of the existence of SI usually refer to
two main shortcomings of private insurance markets due to
asymmetric information, moral hazard and adverse selection.
• Moral hazard is the consequence of the fact that the insured
agent does not reap the full benefit of preventive effort anymore
• The insurer participates in any reduction of expected loss, while
the insured bears the full cost of this effort
• The observable consequence is a positive correlation
between the degree of insurance coverage and
- the probability of loss (ex-ante moral hazard)
- the amount of loss (ex-post moral hazard).

insurance II
• SI is subject to the same moral hazard effects as PI
• Exception: Institutions of SI can observe preventive behavior
• In the case of health, accidents, disability, and old age, this is
clearly not true, to the contrary
• PI usually tailors the parameters of their contracts to individual
behavior reflecting (the control of) moral hazard
• One way is granting rebates for no claims
• SI is strongly bound to the solidarity principle
• The solidarity principle calls for equal ex-ante benefits for equal
(rates of) contributions
PI has an efficiency advantage over SI when it comes to
controlling moral hazard

insurance III
• But: In the case of health, SI might better than PI count on
physicians as agents for the verification of claims
• However, this does not seem to be true, as shown by Dionne
and St. Michel (1991, REcStat)
• They study an increase in generosity in the public workplace
accident scheme of Quebec
• According to their evidence, physicians helped workers to
benefit from this change
• The driver was lack of observability (‘fuzzy’ diagnoses)
The so-called loading for moral hazard is not necessarily lower
for SI than PI, at least in health insurance

insurance IV
• The one remaining component of the loading is acquisition
expense
• This expense is negligible in the case of SI because SI
constitutes a monopoly
This cost advantage of SI has to be weighed against the
imposed efficiency loss as soon as preferences with regard to
insurance differ within the population
• For instance, preferences w.r.t. health insurance seem to differ:
- Zweifel et al. (2006, JRE) and Leukert-Becker and Zweifel
(2008, Patt) in the case of Switzerland
- MacLean and Zweifel (2011, EuJHE), Leukert-Becker and
Zweifel (2013, subm. JPubE) in the case of D and NL

insurance V
• Adverse selection is seen as the crucial market failure of PI
• The theoretical mainstay is provided by the Rothschild-Stiglitz
(1976) model
• Combined with the dynamics of Akerlof’s (1970) ‘market for
lemons’, the ‘good’ insurers (offering a pooling contract) are
driven out by the ‘bad’ ones (who skim the favorable risks)
• Note: The model assumes that private insurers do not (and
never will) know the true probability of loss of consumers
A pooling contract reflecting the average probability in the
population is the best PI can come up with

insurance VI
• However, the trade-off between premium and coverage is valued
differently by high and low risks
A challenger can always offer a contract with less coverage but a
lower premium that appeals to the favorable but not the high
risks
• Note: Adverse selection induces a positive correlation
between the amount of insurance coverage and the probability of
loss
• The same prediction follows from ex-ante moral hazard
• But in the case of adverse selection, the incumbent insurer is
stuck with its unfavorable risks

insurance VII
• The incumbent insurer is forced to increase the pooling
premium to maintain financial equilibrium
The favorable risks have an even stronger incentive to leave the
pooling contract
• Note: The challenger writes a pooling contract, too!
It can in turn be challenged
The process may become a ‘death spiral’, where ‘good’ (the
insurer with the pooling contract) is driven out by the ‘bad’
• This is like Akerlof’s (1970, QJE) ’market for lemons’
• The market for PI may collapse

insurance VIII
• Especially health insurers are very much concerned by the
threat of adverse selection
• Policy makers see monopolistic SI as a remedy against adverse
selection
• But: Where is the evidence?

insurance IX
• Puelz and Snow (1994, JPE) presented evidence suggesting
that there was adverse selection in U.S. automobile insurance
• However, Dionne, Gouriéroux, and Vanasse (2001, JPE) using
data from Quebec, challenge this finding
• When they include non-linear terms of explanatory variables,
the positive correlation between coverage and probability of loss
disappears
• Chiappori and Salanié (2000, JPE) analyze French automobile
insurance data
• They do condition on a large set of potential confounding
variables
• They find evidence of adverse selection

insurance X
• Cawley and Philipson (1999, AER) analyze U.S. life insurance
• Given adverse selection, unit premiums are predicted to
increase with the amount of coverage
• In this way, the insurer can compensate for the positive
correlation between coverage and probability of loss
• However, premiums for term life insurance in fact decrease with
coverage
• Also low risks hold more coverage than high ones
There are no competing insurers siphoning off low risks with a
low-premium, low-coverage alternative

insurance XI
• Einav, Finkelstein, and Cullen (2010, QJE) seek to exclude
reverse causation due to moral hazard
• Under moral hazard, the insurer’s cost increases, causing
premiums to rise
Variation in cost should be exogenous!
• The authors do have exogenous cost variation
• In 2004, Alcoa let the presidents of some forty business units
set the contribution their employees had to pay for health
insurance
• They did not have access to information about their employees’
past healthcare expenditure

insurance XII
• Einav, Finkelstein, and Cullen (2010, AER) find that the
insurer’s marginal and average cost increases significantly with
the premium
• This points to adverse selection
• But: The loss of consumer surplus is a mere 3 percent of
aggregate willingness to pay
• For all the theoretical emphasis on adverse selection as a
source of inefficiency of PI, this is a remarkably small figure

insurance XIII
• Still, could a competitive market for PI survive under the threat
of a ‘death spiral’?
• Cutler and Reber (1998, QJE) perform a case study
• In 1995, Harvard University employees had to come up with a
much higher personal contribution to health insurance
• Those with a favorable cost record migrated from the contract
with comprehensive coverage to a more restrictive but cheaper
alternative
• Those with an unfavorable record kept their comprehensive
policies
Within two years, the more generous contracts had to be
withdrawn

insurance XIV
• However, it is not clear that the insurers writing them
approached insolvency
• Quite possibly, they withdrew loss-making contracts to find a
new equilibrium
• This was theoretically described by Wilson (1977, JET) and
Miyazaki (1977, BellJ)
• These papers show that a challenge à la Rothschild/Stiglitz
(1976) amounts to a ‘Kamikaze action’ if the PI market is
concentrated
• The unfavorable risks end up with the challenger!

insurance XV
• Still, the challenger might consider such a ‘Kamikaze action’ if
its planning horizon is short enough
• Note: Current risk adjustment schemes in health insurers
impose a (partial) 1-year planning horizon on insurers
Risk adjustment may well encourage ‘Kamikaze actions’
• At the very least, its annual procedure makes for a shortened
planning horizon of insurers

insurance XVI
• Private insurers can deal with adverse selection, but at a price
• They can design separating contracts
• The L-contract has a low premium but offers limited coverage so
attracts the favorable risks
• The H-contract has a high premium but offers full coverage so
attracts the unfavorable risks
• But: At the (low) going premium, the favorable risks would like
to buy more coverage
• They cannot have this because the contract would begin to
attract unfavorable risks, too
The favorable risks are rationed!

insurance XVII
• This is the downside of separating contracts
• Dahlby (1981, PubCh) shows that SI can be Pareto-increasing
in this situation
• SI benefits the unfavorable risks for sure because they are
cross-subsidized
• Partial SI coverage may benefit the favorable risks, too
• Since the unfavorable risks start from a higher expected utility
level, they are less likely to infiltrate the L-contract
The rationing constraint imposed on the favorable risks can be
relaxed!
Both risk types may benefit from (partial) mandatory SI

insurance XVIII
While this analysis on the whole motivates the existence of SI, it
has three shortcomings:
(1) It fails to explain why the political debate invariably focuses on
the inability of high risks to obtain PI coverage rather than the
rationing of coverage imposed on the low ones
(2) It does not determine the optimal amount of partial SI
(3) It does not explain the expansion of SI over time (from a few
percent of GDP prior to World War II to some 25 percent at
present (see Table 1)

insurance IXX
• Shortcoming (1) can be easily remedied
• Transaction costs for PI may be particularly high for unfavorable
risks due to high loss variance
• This may make the loading excessive for unfavorable risks,
who prefer to go without coverage
• Loss variance and hence loading is reduced by SI [see Zweifel
and Eisen (2012), Ch. 9.2.1.4]
Partial SI enables unfavorable risks to obtain supplementary PI
coverage
• Shortcomings (2) and (3) will be addressed below

3 The optimal amount of SI I
• There are two main approaches:
- A benevolent government optimizes the amount of SI
- The amount of SI is determined by self-interested voters
• An interesting example of the first approach is Petretto (1999,
JHE), typical for health insurance
• His model comprises three stages:
1. The government introduces SI with a degree of coverage α
2. Consumers select their preferred amount of supplementary
PI
3. Consumers decide their healthcare expenditure (HCE) and
labor supply
The amount of loss falling on PI is not exogenous; there is
moral hazard

3 The optimal amount of SI II
• As usual, the model is solved backwards
• For the optimal degree of PI coverage, Petretto (1999) obtains
(1)
with > 0 an elasticity (in absolute value) relating the loss
borne by PI to the net cost borne by the insured (a moral
hazard effect)
• Note: The higher the ratio , the higher the degree of
PI coverage
[ ] ( )
( )
11 1
1
*
ii i
*
i i i
u Loss uk
k u e
λ
λ
′ ′− +−
= ⋅
+
* *
(1 )/i ik k−

3 The optimal amount of SI III
The optimal degree of PI coverage is the higher,
• the higher , which reflects the degree of risk
aversion of individual i;
• the lower the proportional loading λ and hence the ‘true’
price of insurance;
• the smaller the ex-post moral hazard effect
[ ] iu Loss / u′
[ ] ( )
( )
11 1
1
*
ii i
*
i i i
u Loss uk
k u e
λ
λ
′ ′− +−
= ⋅
+
( )ie
( )ie

3 The optimal amount of SI IV
The optimal value of α is implicitly given by the condition,
(2)
• The marginal benefit associated with an increase of α is
shown on the left-hand side
• The summed term is a social risk-sharing gain
It is high if over the n individuals considered, there is a marked
covariance between their marginal utility of wealth in the loss
state and the amount of net loss (recall that
PI coverage is only partial)
[ ]( ) [ ] ( )
[ ] ( )( )
1
1 1
n
ii i ii
i
n
i
i i
i
Cov u Loss ,NetLoss n u Loss Cov u / u',NetLoss / NetLoss NetLoss
Netloss
u Loss * k *α α
α
∗
 ′ ′ ′+ ⋅ − ⋅
 
∂
 ′= − − +  ∂
∑
∑
Cov
iNetLoss[ ]i i
u Loss′

3 The optimal amount of SI V
• The second term on the left-hand side is the social
redistribution gain
• Its main term is the covariance between the individual’s
relative average marginal utility and his or her relative net
loss
The individuals considered have a strong interest in
redistribution through SI if this covariance is high
[ ]( ) [ ] ( )
[ ] ( )( )
1
1 1
n
ii i ii
i
n
i
i i
i
Netloss
u Loss * k *α α
α
∗
 ′ ′ ′+ ⋅ − ⋅
 
∂
 ′= − − +  ∂
∑
∑
iu / u'′
( )iNetLoss / NetLoss

3 The optimal amount of SI VI
• The marginal cost associated with an increase of α is shown
on the right-hand side
• It consists of three multiplicative components
• The last factor is the basic trigger: It shows how
strongly the expected net loss of individual i reacts to an
expansion of SI
• This is the ex-post moral hazard effect induced by SI
[ ]( ) [ ] ( )
[ ] ( )( )
1
1 1
n
ii i ii
i
n
i
i i
i
Netloss
u Loss * k *α α
α
∗
 ′ ′ ′+ ⋅ − ⋅
 
∂
 ′= − − +  ∂
∑
∑
/iNetloss α∂ ∂

3 The optimal amount of SI VII
• The second multiplicative component of marginal cost
shows how both SI and PI coverage act as
amplifiers
• The main impulse comes from α* itself
• However, PI covers the remainder (1 – α*) to the tune of
• The first term transforms these effects into a utility value
• It reflects the marginal utility in the loss state because ex-post
moral hazard occurs in the loss state by definition
[ ]( ) [ ] ( )
[ ] ( )( )
1
1 1
n
ii i ii
i
n
i
i i
i
Netloss
u Loss * k *α α
α
∗
 ′ ′ ′+ ⋅ − ⋅
 
∂
 ′= − − +  ∂
∑
∑
( )1 ik∗
−
( )( )1 1 i* k *α α∗
 − − + 

3 The optimal amount of SI VIII
• Criticism: An expansion of SI does not does not increase
total insurance coverage in step
• SI typically displaces (‘crowds out’) PI to some degree
• Feldstein (1974, JPE) was the first to call attention to this
‘crowding out’ effect
• Donder and Hindricks (2003, JPubE) adopt a public choice
approach to theoretically predict complete crowding out of PI
by SI
• However, they have to use Yaari‘s (1987, Ectra ) dual
formulation (not shown here) to derive this result

3 The optimal amount of SI IX
• Chetty and Saez (2009, AEJ) take ‘crowding out’ into account
in their modeling of unemployment insurance
• The explicit contribution rate is levied by the government
• The implicit contribution rate is levied by the employer
• Again, there is a benevolent government who seeks to
maximize citizens’ expected utilities
• Through setting , it also determines the benefit rate α of
the preceding section
τ
kt
τ

3 The optimal amount of SI X
• Chetty and Saez (2009, AEJ) show that the optimum explicit
contribution rate is given by
(3)
• Note that the left-hand side of eq. (3) is increasing in
• Moral hazard is reflected by two parameters
• The first is the elasticity
• It indicates how strongly (labor) income averaged over the
loss and the no-loss state reacts to , the amount that the
worker retains per Dollar earned
The stronger this response, the more the benefits of SI have
to be adjusted downwards
( ) ( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
W
1 τ−
τ
1W ,
e τ−

3 The optimal amount of SI XI
(3)
• corresponds to the elasticity in Petretto (1999, JHE)
• The second is the elasticity , which indicates the response
of to the overall retention per Dollar earned, given by
The stronger this group-specific effect of PI (relative to SI), the
more the scaling down of SI occasioned by has to be
corrected in favor of SI again
( )
( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
1W ,
e τ− ie
ke
W
(1 )(1 )ktτ− −
1W ,
e τ−

3 The optimal amount of SI XII
(3)
• Adverse selection: This is represented by
• This is the difference between the PI contribution rate levied
by the employer in the absence of the self-selection constraint
and in its presence
This difference is positive due to the rationing effect of
adverse selection in PI, indicating a benefit favoring SI
( )
( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
( )k kt t∗
−
kt∗
kt

3 The optimal amount of SI XIII
(3)
• Crowding out: This is reflected by the group-specific
parameter > 0
• is the elasticity of the PI retention rate with respect
to the SI retention rate
• This elasticity indirectly indicates how much of employer-
provided coverage is crowded out by SI
The greater , the smaller should be the optimal extent of
SI, ceteris paribus
( )
( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
kr
kr
(1 )kt−
(1 )τ−
kr

3 The optimal amount of SI XIV
(3)
• The term / represents the consumption
smoothing benefit of SI and PI combined
• For each group k of the population, their marginal utility of
income (averaged over the loss and the no-loss state) is
compared with of the population as a whole
• This ratio is high (due to the concavity of the risk utility
function) when relative income of group k is low
In this case, there is negative covariance; together with the
negative sign, this amounts to a benefit
( )
( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
( )k kCov u ',W
ku '
u′
u W′ ⋅

3 The optimal amount of SI XV
(3)
• The summation in the second term is over the population
shares
• The summation involves and
• It amounts to a covariance between (relative) marginal utility
and income levels again
• Qualifying elements: The moral hazard effect of PI relative to
SI , the rationing due to adverse selection ,
and the crowding-out effect
( )
( ) ( )
1 1
1 1
1
1
k k k k
k k k k k
kW , W ,
Cov u ',W u W
s r e t t
e u W e u Wτ τ
τ
τ
∗
− −
′ ⋅
= − + ⋅ − − ⋅
′ ′− ⋅ ⋅
∑
ks
/ku u′ ′ /kW W
1k W ,
e / e τ− ( )k kt t∗
−
( )1 kr−

4 The crowding-out phenomenon I
• There is ample evidence of crowding out of PI by SI in the
United States
• The most convincing evidence comes from Hubbard, Skinner,
and Zeldes (1995, JPE)
• When it comes to private savings, banks hardly need to
impose separating contracts
• There are no ‘unfavorable’ savers who could infiltrate
contracts designed for ‘favorable’ savers
• The authors find the hump shape predicted by the life-cycle
consumption model to occur only among households with a
college degree
• For low-income households, the age profile is rather flat

4 The crowding-out phenomenon
II
• Hubbard, Skinner, and Zeldes (1995, JPE) consider three
explanations for this difference:
(1) high-income families may have a bequest motive
(2) low-income households have a higher share of
consumption covered by SI after retirement
(3) low-income households have a higher rate of time
preference
• The authors show that these explanations fail to provide a
convincing explanation of observed patterns
(4) Asset means-tested SI is the likely reason for the flat age
profile of consumption an saving among the poor

III
• Gruber and Yelowitz (1999, JPE) provide confirming evidence
• The analyze the U.S. Medicaid (for the poor) program
• Between 1984 and 1993, expenses of Medicaid increased by
500 percent
• Some U.S. member states adopted changes quickly, others
slowly
Source of exogenous variation
• Medicaid eligible Dollars (MED) = Medicaid benefit * lieklihood
of being eligible
• Net wealth is found to decrease by an estimated 2.9 percent
for every $ 1,000 of MED
Substantial crowding-out effect amounting to a cumulative
reduction of 8.2 percent over 10 years (1984 to 1993)

IV
• Criticism: Gruber and Yelowitz (1999, JPE) do not provide
evidence regarding the crowding out of PI by SI
• Cutler and Gruber (1996, AER) again study the impact of U.S.
Medicaid expansion, this time on private health insurance
(PHI)
• They find eligibility of children to reduce the take-up of PHI in
their favor by 31 percent per percentage point of Medicaid
expansion
4 percent expansion (recall the 500 percent) is sufficient to
wipe out PHI for poor children!

V
• Brown and Finkelstein (2008, AER) study the impact of
Medicaid on private long-term care (LTC) insurance
• Note: PI benefits must be used up used up until wealth falls to
the (low) Medicaid threshold
• The authors derive willingness-to-pay (WTP) values for LTC
coverage in the presence of Medicaid
• They find values of $ -20,700 for women and $ -18,200 for
men at the 30th percentile of the U.S. wealth distribution
• The WTP values turn positive at the 60th percentile
• The implicit tax on PI is close to 100 percent for wealth levels
below the 30th percentile
Medicaid is found to crowd out private LTC insurance

5 Could the division of labor
between private and social
insurance be improved? I
• Criticism: All the research cited considers only one risk at the
time
• However, many impulses affect individual assets
• They are wealth, health, and skills (‘wisdom’) [Zweifel and
Eisen (2012), Ch. 1.6].
• For instance, an illness episode lowers
- the level of health
- indirectly wealth (through reduced labor income)
- skills (through depreciation of human capital)
Losses are often positively correlated
Efficient insurance (SI and PI in combination) should mitigate
or even neutralize these correlations

insurance be improved? II
• Denote by the final value of health capital, with
= asset value after expected payment by insurance and
deviation between expected and actual payment by
insurance
• These deviations are the consequence of small print in
contracts
• Note: SI also has small print, often designed to limit moral
hazard
• Likewise, denote by Y the final value of skills, with
asset value after expected payment by insurance and
deviation between expected and actual payment by
insurance
a
X
a
X x+
x =
a
Y =
y =

insurance be improved? III
• Then, total asset variance is given by
• Standard assumptions:
- Expected and unexpected components of insurance benefits
are uncorrelated
- Expected benefits under title X are not related to unexpected
benefits under title Y
The crucial element determining residual asset variance is
( ) ( )
( )
( )
( )
( )
( )
( )
( )
a a a a
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insurance be improved? IV
• Schoder, Zweifel, and Eugster (2013, JInsIss) find that rates of
return of PI and SI have been similar in several countries
For measuring performance, it is sufficient to focus on
the covariance of deviations from expected insurance
benefits
• The authors fit time series of insurance benefits to quadratic
time trends to (roughly) account for both their expansion and
inflation
Residuals reflect unexpected deviations of benefits from their
expected value
• These residuals are then used to determine correlation
coefficients between two lines of insurance( , )x yρ

insurance be improved? V
Table 2: Correlations of trend deviations in Swiss private and
social insurance, 1980-2004
PLID PGI PLAI PHI
SDCB -0.274 (0.22) -0.337 (0.13) -0.111 (0.62) -0.324 (0.14)
SOIB 0.416 (0.18) 0.221 (0.49) 0.462 (0.13) 0.474 (0.12)
SOACB -0.008 (0.97) 0.305 (0.17) 0.612 (0.00) -0.170 (0.45)
SPSB -0.248 (0.44 ) 0.303 (0.34 ) 0.289 (0.36) -0.085 (0.79)
Note: Standard errors in parentheses; bold=significant at 5
percent or better -- PLID= life insurers' death payments,
PGI=general liability payments PLAI=life insurer's annuity
payments, PHI=health insurance payments;
SDCB=disability cash benefits, SOIB=accident (disability and
survivors); SOACB=old age cash benefits, SPSB=paid sick leave
benefits

insurance be improved? VI
Table 2: Correlations of trend deviations in Swiss private and
social insurance, 1980-2004 (cont’d)
PLID PGI PLAI PHI
SSB -0.028 (0.90) 0.323 (0.14) 0.526 (0.01) -0.541 (0.01)
SFCB -0.309 (0.16) -0.103 (0.65) 0.293 (0.19) 0.474 (0.12)
SHTB -0.053 (0.82) 0.357 (0.10) 0.580 (0.00) -0.259 (0.25 )
SUB -0.250 (0.26 ) -0.013 (0.95) -0.425 (0.05) -0.417 (0.05)
SHB 0.123 (0.59) 0.540 (0.01) 0.749 (0.00) 0.194 (0.39)
Note: Standard errors in parentheses; bold=significant at 5 percent
or better
PLID= life insurers' death, PGI= general liability, PLAI=life
insurers’ annuity, PHI=health insurance; SSB = survivors’ total;
SFCB=family cash; SHTB=housing total, SUB= unemployment,
SHB=health benefits

insurance be improved? VII
• There are only two (out 0f 36) negative correlation coefficients
• But 5 out of 36 correlation coefficients are positive
(1) Shortfalls in PGI (general liability payments) tend to be
exacerbated by SHB (housing benefits)
Shortfalls in PLAI (life annuity) tend to be exacerbated by
(2) SOACB (old age cash)
(3) SHTB (total housing benefits)
(4) SUB (unemployment benefits)
(5) SHB (health benefits) ( !)
Swiss PI and SI fail to complement each other

insurance be improved? VIII
• Swiss consumers are exposed to excessive total asset
variance
• Zweifel (2000, HlthCFin) found this to be true of Germany as
well (1975-1993 data)
• The United States perform better, both based on 1972-1992
and1980-2004 data
• However, this assessment derives from aggregate rather than
individual data

6 Conclusions and outlook I
• The starting point of this presentation is the well-known
potential failures of private insurance (PI) markets
• Moral hazard and adverse selection might justify government
intervention, possibly in the guise of social insurance (SI)
• However, moral hazard effects are found to beset SI at least
as much as PI
• Adverse selection would constitute the crucial market failure
of PI
• Mandatory partial SI even has the potential to improve the
welfare of both high and low risks
• The benefit for the low risks is that PI can provide them with
more complementary coverage (relaxation of the rationing
constraint)

6 Conclusions and outlook II
• However, the optimal amount of SI and hence the optimal
division of labor between PI and SI is left undetermined
• Also, there is an overall moral hazard effect which must be
balanced against the benefit of risk pooling afforded by
additional SI coverage
• Still, this emphasis on efficiency fails to explain the historical
expansion of SI to the detriment of PI
• If one is willing to depart from the standard expected-utility
framework adopting (Yaari’s dual approach), it becomes
possible to predict that an expansion of SI will always find a
majority

6 Conclusions and outlook III
• This change in the division of labor has become known as the
crowding-out phenomenon
• The empirical evidence almost exclusively comes from the
United States
• It focuses on the rapid expansion of Medicaid (for the poor)
• This expansion is found to depress private saving and to
undermine interest in both private health and long-term care
(LTC) insurance
• These findings point to scope for an improved division of
labor between PI and SI
• However, it is appropriate to analyze jointly all the risks
impinging on individuals

6 Conclusions and outlook IV
• One way is to view the benefits of SI and PI as assets with
stochastic returns in the portfolio of an individual
• Fir efficient insurance, deviations from expected value should
be negatively correlated between PI and SI (and within the
lines of PI and SI)
• Aggregate data for Switzerland point to positive correlations
and hence a potential for an improved hedging of risks
confronting citizens
• Still, it is difficult to answer the two crucial questions for the
future,
(1) How will the division of labor between PI and SI evolve?
(2) How should this division be changed if at all?

6 Conclusions and outlook V
• As to the first (positive) question, the expansion of SI seems to
have come to a halt in several industrial countries (see Table 1
again)
• This may be the consequence of several exogenous
developments that may challenge SI more than PI:
• (1) The opening of economies not only to the international
flows of goods but of labor and capital as well (‘globalization’)
PI (but not SI) can pursue an investment policy that benefits
from the hedging provided by international capital markets
PI (but not SI) often grants full portability of benefits
Emigration and immigration threaten to undermine the financial
equilibrium of SI but not PI

6 Conclusions and outlook VI
• (2) The demographic change affects SI with its pay-as-you-go
finance much more directly than PI, which frequently is capital-
based
• Note: Demographic change is the consequence of individual
decisions
• Zweifel and Eugster (2008, GermJRI) find (spotty) evidence
suggesting that length of education, marriage, number of
children, age at retirement, and even longevity are influenced
by SI
• These influences exacerbate the financing problems of SI
The two challenges might explain the reversal in the trend
towards SI expansion

6 Conclusions and outlook VII
• The second question is normative: How should the division of
labor change (if at all)?
• Assumption: Governments implement and adjust SI in a way
reflecting reasonably informed self interest of the voting public
• This would presumably call for a great deal of stability in the
division of labor between PI and SI
• However, governments may pursue their own goals
• van Dalen and Swank (1996, PubCh) analyze budget
allocations of the Dutch government around (re)election times
• They find the government systematically boosting SI payments
– apparently in an attempt to gain votes

6 Conclusions and outlook VIII
• Knowing whether (and in which lines of insurance) the division
of labor between PI and SI ought to be changed is not enough
• The proposed adjustment need not be efficiency-enhancing
• Market failures that may beset PI have to be balanced against
and political failures that may beset SI
• This balance is far from evident -- and it may well change over
time

References I
G. A. Akerlof, “The Market for 'Lemons': Quality Uncertainty and the
Market Mechanism”, in: Quarterly Journal of Economics 84 (3) (1970),
488-500.
J.R. Brown and A. Finkelstein, “The interaction of public and private
insurance: Medicaid and the long-term care insurance market”, in:
American Economic Review 98 (3) (2008), 1083-1102.
J. Cawley and T. Philipson, “An empirical examination of information
barriers to trade in insurance”, in: American Economic Review 89 (4)
(1999), 827-846.
R. Chetty and E. Saez, “Optimal taxation and social insurance with
endogenous private insurance”, in: American Economic Journal:
Economic Policy 1 (2) (2009), 31-52.
P.A. Chiappori and B. Salanié, “Testing for asymmetric information in
insurance markets”, in: Journal of Political Economy 108 (1) (2000),
56-78.
.

References II
D.M. Cutler and J. Gruber, “The effect of Medicaid expansion on public
insurance, private insurance and redistribution”, in: American
Economic Review 86 (2) (1996), 378-383
D.M. Cutler and S.J. Reber, “Paying for health insurance: The trade-off
between competition and adverse selection”, in: Quarterly Journal of
Economics 113 (2), 433-466.
B. Dahlby, “Adverse selection and Pareto improvements through
compulsory insurance”, in: Public Choice 37, 547-558.
Ph. de Donder and J. Hindricks, “The politics of redistributive social
insurance”, in: Journal of Public Economics 87 (12) (2003), 2639-
2660.
G. Dionne, C. Gouriéroux, and C. Vanasse, “Testing for evidence of
asymmetric information in insurance markets: Comment”, in: Journal
of Political Economy 109 (2) (2001), 444-453.

References III
G. Dionne and P. St-Michel, “Workers’ compensation and moral hazard”,
in: Review of Economics and Statistics 83 (2) (1991), 236-244.
L. Einav, A. Finkelstein, and M.R. Cullen, “Estimating welfare in insurance
markets using variation in prices”, in: Quarterly Journal of Economics,
125 (3) (2010), 877-921.
R. Eisen, H. Schlesinger, and P. Zweifel, “Korrelationen bei
versicherbaren Schäden und ihre langfristigen Folgen”, in: M. v.d.
Schulenberg, M. Balleer, and S. Hanekopf (eds.), Allokation der
Ressourcen by Sicherheit und Unsicherheit. Festschrift für Leonhard
Männer, Baden-Baden: Nomos, 29-50.
P. Eugster, P. Zweifel, and J. Schoder (2012), “Insurers, consumers, and
correlated risks”, forthcoming in: Journal of Insurance Issues.
M. Feldstein (1974), “Social security, induced retirement, and aggregate
capital accumulation”, in: Journal of Political Economy 82(5), 906-926.
J. Gruber and A.S. Yelowitz, “Public health insurance and private
savings”, in: Journal of Political Economy 107(2) (1999) , 1249-1274.

References IV
R.G. Hubbard, J. Skinner, and S.P. Zeldes, “Precautionary saving and
social insurance “, in: Journal of Political Economy 103 (2) (1995),
360-399.
K. Leukert-Becker and P. Zweifel, “Age and choice in health insurance:
Evidence from a discrete choice experiment”, in: The Patient 1 (1)
(2007), 27-40.
H. Miyazaki, “The rat race and internal labor markets”, in: Bell Journal of
Economics 8 (1977), 394-418.
A. Petretto, “Optimal social health insurance with supplementary private
insurance”, in: Journal of Health Economics 18 (1999), 727-745.
R. Puelz and A. Snow, “Evidence on adverse selection: Equilibrium
signalling and cross-subsidization in the insurance market”, in: Journal
of Political Economy 102 (2) (1994), 236-257.
M. Rothschild and J.E. Stiglitz, “Equilibrium in competitive insurance
markets: An essay on the economics of imperfect information”, in:
Quarterly Journal of Economics 90 (1976), 629-649.

References V
H.P. van Dalen and O.A. Swank, “Government spending cycles:
ideological or opportunistic?”, in: Public Choice 89 (1996), 183-200.
C.A. Wilson, “A model of insurance markets with incomplete information”,
in: Journal of Economic Theory 16 (1977), 167-207.
M.E. Yaari, “The dual theory of choice under risk”, in: Econometrica 55 (1)
(1987), 95-115.
P. Zweifel, “Criteria for the future division of labor between private and
social health insurance”, in: Journal of Health Care Finance 26 (3)
(2000), 38-55.
P. Zweifel and P. Eugster, “Life-cycle effects of social security in an open
economy: A theoretical and empirical survey”, in: German Journal of
Risk and Insurance 97 (1) (2008), 61-77.
P. Zweifel and R. Eisen, Insurance Economics (2012), Boston MA:
Springer.

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