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

[email protected]

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 majorexpenditure 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 welfarePI 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 correlationbetween the degree of insurance coverage and

- the probability of loss (ex-ante moral hazard)

- the amount of loss (ex-post moral hazard).


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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 correlationbetween 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


2 The efficiency view of social 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


2 The efficiency view of social 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?


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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


2 The efficiency view of social 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!


2 The efficiency view of social 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


2 The efficiency view of social 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!


2 The efficiency view of social 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


2 The efficiency view of social 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)


2 The efficiency view of social 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

′ ′− +−= ⋅

+

( )i

e

( )i

e


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 iii

ni

i i

i

Cov u Loss ,NetLoss n u Loss Cov u / u',NetLoss / NetLoss NetLoss

Netlossu 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 iii

ni

i i

i



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 iii

ni

i i

i



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 iii

ni

i i

i



α∗

′ ′ ′+ ⋅ − ⋅

∂ ′= − − + ∂

∑

∑

( )1i

k∗−

( ) ( )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 11

1

k k k kk k k k k

kW , W ,

Cov u ',W u Ws 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 11

1

k k k kk k k k k

kW , W ,


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 11

1

k k k kk k k k k

kW , W ,


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 11

1

k k k k

k k k k k

kW , W ,


e u W e u Wτ τ

τ

τ∗

− −

′ ⋅= − + ⋅ − − ⋅

′ ′− ⋅ ⋅∑

kr

kr

(1 )k

t−(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 11

1

k k k k

k k k k k

kW , W ,


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 11

1

k k k k

k k k k k

kW , W ,


e u W e u Wτ τ

τ

τ∗

− −

′ ⋅= − + ⋅ − − ⋅

′ ′− ⋅ ⋅∑

ks

/k

u u′ ′ /k

W W

1k W ,e / e

τ− ( )k kt t∗ −

( )1k

r−


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


4 The crowding-out phenomenon 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)


4 The crowding-out phenomenon 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!


4 The crowding-out phenomenon 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 mitigateor even neutralize these correlations


5 Could the division of labor between private and social 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

aX

aX x+

x =

aY =

y =


5 Could the division of labor between private and social 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 aVar X x Y y Var X Var x Var Y Var y

+ ++ +

+ + + = + + +

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )0 0 0 0

2 2 2 2 2 2a a a a a a

?

Cov X ,x Cov X ,Y Cov X ,y Cov Y ,y Cov Y ,x Cov x,y .+

+ + + + + +

( , ) 0, ( , ) 0a a

Cov X x Cov Y y⇒ = =

( , ) 0, ( , ) 0a a

Cov X y Cov Y x⇒ = =

( )Cov x, y


5 Could the division of labor between private and social 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


5 Could the division of labor between private and social 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


5 Could the division of labor between private and social 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


5 Could the division of labor between private and social 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


5 Could the division of labor between private and social insurance be improved? VIII

• Swiss consumers are exposed to excessive total assetvariance

• 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


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P.A. Chiappori and B. Salanié, “Testing for asymmetric information in insurance markets”, in: Journal of Political Economy 108 (1) (2000), 56-78.

.


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D.M. Cutler and J. Gruber, “The effect of Medicaid expansion on public insurance, private insurance and redistribution”, in: American

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References III

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References V

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Plenary_Talk_1_Zweifel

Economy & Finance

social si

social insurance si

private pi insurance

switzerland si

life private insurance

si component

preponderance of si

japan si