W PS 2579-
POLICY RESEARCH WORKING PAPER   2574
How  Adverse Selection                                               There may be a price to pay
(in terms of inefficient
Affects  the   H ealth                                               coverage) if competition
Insurance Market                                                     among health insurers is
encouraged as a way to give
patients greater choice and to
Paolo Belli                                                          achieve better control over
insurance providers
The World Bank
Development Research Group
Public Economics
March 2001



POLICY RESEARCH WORKING PAPER 2574
Summary findings
Adverse selection can be defined as strategic behavior by    analyzes the following policy options relating to the
the more informed partner in a contract against the          public provision of insurance:
interest of the less informed partner(s). In the health         * Full public insurance.
insurance field, this manifests itself through healthy          * Partial public insurance with or without the
people choosing managed care and less healthy people         possibility of acquiring supplementary insurance and
choosing more generous plans.                                with or without the possibility of opting out.
Drawing on theoretical literature on the problem of         In recent plans implemented in Germany and the
adverse selection in the health insurance market, Belli      Netherlands, where competition among several health
synthesizes concepts developed piecemeal over more           funds and insurance companies was promoted, a public
than 20 years, using two examples and revisiting the         fund was created to discourage risk screening practices
classical contributions of Rothschild and Stiglitz. He       by providing the necessary compensation across risk
highlights key insights, especially from the literature on   groups. But only "objective" risk adjusters (such as age,
"equilibrium refinements" and on the theory of "second       gender, and region) were used to decide which contracts
best."                                                       to subsidize. Those criteria alone cannot correct the
The government can correct spontaneous market              effects of adverse selection.
dynamics in the health insurance market by directly            Regulation can exacerbate the problem of adverse
subsidizing insurance or through regulation; the two         selection and lead to chronic market instability, so
forms of intervention provide different results. Providing   certain steps must be taken to prevent risk screening and
partial public insurance, even supplemented by the           preserve competition for the market.
possibility of opting out, can lead to second-best             Belli considers the following three policy options for
equilibria. The same result holds as long as the             regulating the private insurance market:
government can subsidize contracts with higher-than-            * A standard contract with full coverage.
average premium-benefit ratios and can tax contracts            * Imposition of a minimum insurance requirement.
with lower-than-average premium-benefit ratios. Belli           * Imposition of premium rate restrictions.
This paper-a product of Public Economics, Development Research Group-is part of a larger effort in the group to
improve social service delivery in developing countries. Copies of the paper are available free from the World Bank, 1818
H Street NW, Washington, DC 20433. Please contact Hedy Sladovich, room MC2-609, telephone 202-473-7698, fax 202-
522-1154, email address hsladovich@worldbank.org. Policy Research Working Papers are also posted on the Web at http:/
/econ.worldbank.org. The author may be contacted at pbelli@hsph.harvard.edu or pbellil@worldbank.org. March 2001.
(31 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Ceniter



How Adverse Selection Affects the Health
Insurance Market
Paolo Belli
Harvard School of Public Health
Dr. Paolo Belli, Department of Population and International Health, Harvard School of Public
Health, 677 Huntington Avenue, Boston MA 02115, Tel: 617-432-1185, Fax: 617-432-2181.
Email: pbelliRhsph.harvard.edu. For their support and comments, the author is grateful to Jeffrey
Hammer, Jean Dreze and Silvya Topolyn. The findings, interpretations; and conclusions
expressed in this paper are entirely those of the author. They do not necessarily represent the
views of the World Bank, its Executive Directors, or the countries they represent.






1. Introduction
Adverse selection can be defined as strategic behavior by the more informed partner in a
contract, against the interest of the less informed partner(s). In the health insurance
market it is relevant because each individual chooses among the set of contracts offered
by insurance companies according to his/her expected probability of using health
services. In brief, those who foresee an intense use of health services will tend to choose
more generous plans than those who expect a more limited use of them. In the extreme,
for each premium and degree of coverage, those who will decide to purchase that
particular health insurance contract are those who expect to have health expenditure
greater or equal to the premium paid. Then, whatever the premium, the insurance
company may end up with a loss on each customer.
Insurance companies anticipate this purchasing behavior and devise contract offers
in order to screen individuals. This "screening" strategy is even more critical to success
in the market whenever there is regulation in place that does not allow health premiums
to reflect individual risk (premium rate restrictions) or does not permit to acquire
information on potential customers' health conditions before making contract offers (such
as an open enrolment requirement). In any case, the screening practice by insurance
companies hinders the achievement of an efficient risk pooling across individuals.
There is a growing body of evidence that suggests that adverse selection is an
important phenomenon in health insurance markets. Cutler writes (1996, p.30): "Almost
all health insurance systems where individuals are allowed choice of insurance have
experienced adverse selection. Medicare enrollees who choose managed carel are
healthier than... [those] who do not. The Federal Employees Health Benefits
Program.. .has adverse selection between more and less generous policies. The spread in
premiums between more and less generous policies is 68 percent greater than benefits
alone would dictate.. .And almost every large firm that has encouraged employee choice
has found the cost of the most generous policies increases sufficiently rapidly than these
policies are no longer viable" (this last phenomenon is named in the literature "price
death spiral" and refers to the increase in the price of ffore generous insurance plans vis-
a-vis moderate plans). It is also expected that in the United States, as the insurance
market becomes more competitive and individuals are brought to face the true marginal
cost of health insurance, the phenomenon of adverse selection will become more severe.2
'Managed care plans imnpose stricter controls and restrictions over use of health services than
traditional indemnity plans.
2In the past, emnployers would pay a large share of the premniums. Increasingly, employees are offered
lump-sum transfers for health insurance and they face almost entirely the relative marginal costs of
alternative plans.
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Adverse selection is often advocated as the main justification for the provision of
compulsory universal public health insurance. The claim is that the state would ultimately
bear a significant share of the total health costs even if it chose to subsidize health care
only for those who are left out of the private insurance market, because adverse selection
would lead to insufficient insurance coverage for those who most in need and because
health expenditure is highly concentrated within a few segments of the population.3
Therefore, it would be preferable to force all individuals into the same insurance pool,
where cross-subsidies are more transparent.
The existing theoretical literature that we will survey in this work seems to suggest
that the main consequence to be expected from screening strategies by insurance
companies would be the incomplete coverage of low-risk rather than the exclusion of
high-risk groups. So, the above "price death spiral" for generous plans is not really
captured by the existing theory. This gap between theory and reality may reflect an
insufficiency in the existing analytical framework. Moreover, the theory does not
consider that high-risk individuals may be unable to pay a premium adequate to cover
their expected health expenditure even in a world of perfect information, nor extends the
analysis to a dynamic setting (if it is possible to write only incomplete and short-term
contracts, those who end up having a probability of the loss close to one, for example
patients who become chronically ill, ex post are not insurable, even if that is ex-ante
inefficient).
We will first illustrate the problem of adverse selection in the health insurance
market by way of two examples and then present a survey of the existing theoretical
literature. In the second part, the paper analyses different policy options to correct
spontaneous market dynamics, either by direct public provision of health insurance or by
regulation of private insurers. We shall try to provide a unitary representation of a set of
concepts that have developed piece-meal over a period of more than twenty years. Given
the aim of our survey and the broadness of the literature, our attention is focused on
giving an intuitive understanding of the main results, rather than in presenting them
rigorously. Whenever possible, we will make use of diagrammatical proofs.
2. Two Examples
The first example builds on a similar case presented by Cutler and Zeckhauser
(1997). Consider two health plans offered in a particular market, a generous and a
moderate plan, and two types of individuals, high-risk and low-risk, each group making
up 50 percent of the entire population.
3 International studies agree in showing that a small minority, consisting of about 5-7 per cent of the
population, is generally responsible for 60-65 per cent of total health expenditure.
2



Suppose that the cost of treating individuals under the two plans, and their gains in
benefit from the generous plan vis-a-vis the moderate plan, are as follows:
Resource cost          Resource cost         Benefit difference
of coverage (moderate)    of coverage (generous)    (generous - moderate)
Low-risk              40                     60                     15
High-risk             70                    100                     40
Suppose that the insurance market is competitive (in equilibrium premiums are
equal to expected costs) and that insurers do not know individuals' risk type, but know
that there is an equal probability that each potential customer is either low or high-risk.
They can also compute the cost of coverage for both groups and the expected costs of the
contract that pools together both groups.
First note that the first best equilibrium, which in this case would see the high-risk
individuals enrolled in the generous plan for a price of 100 and the low-risk individuals in
the moderate plan for a price of 40, is not an equilibrium with incomplete information. At
these prices both groups would buy the moderate plan, which would start making losses
and whose price would have to be increased.
Suppose that initially a unique plan, the generous one, is offered in the market. If
the market is competitive in equilibrium such plan must break even and it would be
offered to everybody for a price of 80. Then, the moderate plan is devised and offered for
a price of 64, which is low enough to attract low-risk individuals. All low-risks switch to
the new plan (they can save 16 in exchange for a benefit loss of 15). In the new situation,
the generous plan becomes unprofitable and its price has to be increased. At the same
time, competition drives down the price for the moderate plan. As the price differential
between the two plans exceeds 40 (given the above assumptions, it will eventually do so,
because in equilibrium premiums must reflect relative costs), all high-risk individuals
switch to the moderate plan and the generous plan has to be terminated. Then, the
moderate plan also becomes unprofitable, as it has to shoulder all risk types, and its price
has to be increased. New opportunities arise to undercut low-risk by offering even less
generous and cheaper plans. The market is characterized by chronic instability.
Now, consider the equilibrium that the market would reach by changing the above
figures for net benefits as follows:
Resource cost           Resource cost          Benefit difference
of coverage (moderate)  of coverage (generous)   (generous - moderate)
Low-risk             40                      60                       25
High-risk            70                      100                      60
As before, suppose that insurers do not know individuals' risk type. It is evident
that the full-information equilibrium, that would in this case see both risk groups
3



purchasing the generous plan for a price of 60 (low-risk) and 100 (high-risk), can never
be an equilibrium with incomplete information for the same reasons as before. Moreover,
starting from the same initial situation considered in the first example (generous plan
offered for a price of 80), it is profitable for low-risks to switch to the moderate plan as
long as it is offered for a price lower than 55 (80-55 = 25 is now equal to the benefit
difference between the generous and the moderate plan for low-risk individuals). Then,
competition will drive the price of the moderate plan down to 40, while the price of the
generous plan, burdened just with high-risk, will rise up to 100. Unlike the previous
example, the price differential of 60 is not sufficient to induce high-risk to switch to the
moderate plan (in fact, they are just indifferent between switching and maintaining the
generous insurance plan). Thus, in this case the situation in which high-risk pay 100 for
full insurance and low-risk pay 40 for incomplete insurance is an equilibrium. In this
equilibrium low-risk are worse off than in the full information equilibrium, as they obtain
only partial insurance, but the market equilibrium is stable. The market "sorts" out low-
risk individuals from high-risks in a separating equilibrium, by offering plans with less
than optimal coverage.
3. Rothschild-Stiglitz and the Equilibrium in Competitive Insurance Markets:
An Essay on the Economics of Imperfect Information
The first article to analytically investigate the problem of adverse selection in the
insurance market is that by Rothschild and Stiglitz (1976). We will begin our survey of
the theoretical literature by presenting a detailed summary of their model because it
provides the basic conceptual framework that is going to be used for presenting also
subsequent contributions.
On the demand side of the market, individuals' income without insurance is:
WI = W, if 'accident' does not occur.
W2 = W - d, if 'accident' occurs.
Insurance companies offer indemnity a^2 if accident occurs in exchange for a
premium cc. Individuals' income with insurance becomes respectively:
W1 = W- a1 and
W2 = W - clI + a2- d = W + a2 - d, where c2 = aA2 - XI
If the probability of accident is p we can apply the expected utility theorem and
represent individuals' preferences for income in the two states in the following way:
V(p, aI,a2C) = (1-p)U(W-al) + pU(W + X2 - d)                     (1)
Given p, each individual maximizes V( ) with respect to {al ,a2 }.
4



Rothschild and Stiglitz (hereafter, R.-S.) assume that individuals are risk averse, i.e.
U"( ) < 0. So, V() being a linear combination of concave functions, is quasi-concave.
They also assume that there is no moral hazard. The amount of the loss, as well as the
probability p, are not influenced by the presence of insurance coverage.
On the supply side of the market insurance companies are considered risk-neutral
and only interested in expected profits. A contract offer C1 consists of a bundle {aI,a2}
containing specific 'amounts of insurance' that the individual can buy and a particular
price for that bundle (in the following diagrams we will frequently refer to points C1 as
"contracts C," rather than as "wealth in the two states generated by the net premium-
indemnity pair U1,OC2"). R-S assume that individuals can buy at most one insurance
contract, thus recognizing that insurance companies are able to ration the degree of
insurance coverage offered to individuals. On the other hand, the market is assumed
perfectly competitive, such as that in equilibrium premiums are equal to expected costs.
Expected profit for a contract offer to an individual who has probability p of
incurring in a loss is:
7C (P, aC,02) =0 -p) al -p (aC2 - al) = (1-p) al -P p  2             (2)
The equilibrium set of contracts is defined as:
* customers maximize expected utility;
* no contract in the equilibrium set entails negative expected profits;
* no contract outside the equilibrium set, if offered, would make a positive profit.
The equilibrium concept adopted is that of Nash-Cournot: each agent maximizes
his/her objective function, independently of other agents' reaction.
Finally, R-S make a strong assumption about information: when deciding to sign a
contract, agents know the probability of the loss, while insurance companies do not.
3.1 Equilibrium with Identical Customers
Let us first consider the equilibrium with identical customers. In Figure 1 we
represent on the horizontal axis income if no loss occurs and on the vertical axis income
if the loss occurs. Situations of full insurance correspond to points on the bisetrix, while
situations of incomplete insurance lie to the right of the bisetrix (where WI >W2).
Point E corresponds to the situation of no insurance. Each point to the northwest of
E represents a specific insurance contract uniquely identified by a certain premium
a l and a certain net indemnnity ax2 in case of accident. The segment EF represents the
zero profit, or actuarial ("fair") odds line. Trading income in the two states at a rate equal
S



to the slope of EF (da2/dal = (1-p)/p = -dW2/dWI) leaves the insurance company with
exactly zero profit. Starting from point E, any point to the south-west of EF entails
positive profits and cannot be an equilibrium contract (as it can always be undercut by a
new contract that attracts all customers and still earns positive profits), while any point to
the north-east of EF entails negative profits and it is therefore not feasible. So, given free-
entry and perfect competition in long-term equilibrium individuals find their preferred
contract along the set of contracts belonging to the "zero profit" line, where s(p, al a2)
= (1-p) a1 - pa2= 0. The zero-profit line identifies the "best" budget constraint available
to the individual for trading income in the two states.
We can represent individuals' preferences with a map of indifference curves. Given
risk-aversion, the indifference curves are convex.4 Given any indifference curve, all the
points to the northeast entail higher utility and all the points to the southwest entail lower
utility.
Equilibrium lies in correspondence to the highest indifference curve compatible
with the expected budget constraint (point C5). In C5 the slope of the indifference curve is
equal to the slope of EF.
Figure 1: Equilibrium with Identical Customers
12      1
II
W2  -                     F
d{} .                             I I ;F . 
l~~~~~~~~~~ >
WWd      .
6aA
450                 I
I 
W-al                                     WI~~I 



From the equation of the indifference curve:
(l-p)[dU( )/dWl]dWl + p[dU( )/dW2]dW2 = 0, if we denote:
dU( )/dWl=U'(Wl) and dU( )/dW2 =U(W2),
the slope of the indifference curve is equal to:
dW2/dWl = [U'(Wl)/U(W2)][(1-p)/p]                                  (3)
The tangency condition entails:
[U' (W1)/U'(W2)][(l-p)/p] = (l-p)/p '> U' (W1) = U' (W2) *  W1= W2, given
that
U" (.)<0                                                           (4)
Thus, given that individuals are risk averse and insurance companies are risk
neutral, the first best is characterized by full insurance. Whenever the premium is set at a
higher level than the actuarially fair premium, the degree of insurance coverage chosen
by individuals is lower, but under R-S hypothesis of free entry it will then be undercut by
competition until the zero-profit equilibrium is reached.
3.2 Equilibrium with Two Classes of Customers
Let us now consider a market consisting of two groups of customers. They are
characterized by the same utility function for income in the two states, U(.), but by
different accident probabilities.
h
*  high-risk individuals, with probability of accident = p
*  low-risk individuals, with probability of accident = p ,with p h> p
Let the percentage of high-risk individuals be equal to x RS. The average probability
EXP=_RS h              1_RSP
of accident is then equal to: p    = X  p ±(1 X  ) p
In this case, it is possible to distinguish between two types of equilibrium:
* pooling equilibria, in which both groups buy the same contract.
4A mathematical property states that the level curves of a quasi-concave function are convex.
7



In any pooling equilibrium, the zero profit condition must hold across all the
individual types:
EXP    EXP
(I-p    )aC - p    a2 =.
* separating equilibria, in which different risk-groups choose different contracts.
In any separating equilibrium, both contracts must yield zero expected profits:
h       h                I      1
(i-p ) al - p a2 = 0 and (l-p ) a, - p a2 = ()
In Figure 2 we denote with the letter L and H the indifference curves and zero
profit lines relative to respectively low-risk and high-risk individuals. Note that the slope
of the zero profit line for low-risk individuals (L, with a slope equal to (1-pl)/pl) is steeper
than that relative to high-risk individuals (H, with a slope equal to (l-ph)Iph ). From
Figure 2 and equation (3) note also that the slope of the low-risk indifference curve
passing through each point {W1; W2}is higher than that of the high-risk indifference
curve through the same point. In other words, each high and low-risk indifference curve
can intersect only once ("single-crossing property").
When there are two different groups of individuals first best equilibria are no
longer sustainable, as they violate the high-risk group incentive-compatibility constraint.
These constraints entail that, whenever two different contracts are offered to the two risk
groups, they must be devised so that each group prefers the contract specific to its own
risk group to the contract set for the other risk group. No one can be cheated or forced to
buy a contract different from the most preferred one available in the market.
Formally, if we denote by ah the set of contracts meant for the high-risk group and
with a' the set of contracts meant for the low-risk group:
V(ph, ah ) 2 V(ph, al ) and V(pI, al ) 2 V(pI, ah )      (I.C. constraints)
First-best equilibria violate the first of these constraints. As Figure 2 shows, if
contracts Cl and C2 are offered, all individuals would choose Cl. Then C, would make
losses. As we have shown for the case of identical customers, only contracts on the line
EF, such as C3 and C4, can be sustained as pooling equilibria.
8



Figure 2: Equilibrium with Two Classes of Customers
W2  A              L   L4
H3H4              L
F
E
0>45
WI
The second, important result that R-S graphically prove is that there cannot be a
pooling equilibrium.
Figure 3: Impossibility of a Pooling Equilibrium
:~~
L
3
F (l EXP
-(1-p')/ pi
WI
As Figure 3 shows, contract C3 can always be upset by a contract offer in the full
area, such as contract C6. All low-risk individuals are induced to purchase the new
contract when it is offered alongside C3. Contract C3 thus becomes unprofitable and
cannot be sustained as an equilibrium. The impossibility of pooling contracts derives
from the "single-crossing" property.
9



The only possible equilibrium with different risk-types is a sel)arating equilibrium:
we can graphically represent the separating equilibrium in the WI W2 space and in the
al,7aA2 space respectively.
Figure 4: Separating Equilibrium with Two Risk Types
a)
W2 L
Ar-C
W
b)
-   Ho   P  a) (p = Oh)  HI
2                          71(pEXPa)=O
itr(p',aI)=
E
d                    aA 2=cal+a2
10



As Figure 4a) shows, contract C2, characterized by full insurance, is offered to
high-risk individuals. To break even it must lie on the high-risk zero profit line. Then,
contract C7 is offered to low-risk. C7 lies on the zero profit line for low-risks and it is the
most preferred contract by the low-risks among all contracts that respect the high-risk
group's incentive-compatibility constraint. Given C2, any contract along the low-risk
group zero profit line above C7 would be purchased by both groups and would therefore
yield negative profits (when both groups purchase the same contract, such contract must
lie on segment EF). When the vector of contracts C2-C7 is offered, the high-risk incentive
compatibility constraint is binding and the two groups of individuals sort themselves out
by purchasing two separate insurance plans:
HI= V(ph, C7 )  V(ph, C2)
As Figures 4 shows, in any separating equilibrium the low-risk group gets
incomplete insurance (C7 lays to the right of the bisetrix). Point C7 is not at the tangency
point between any indifference curve for low-risks and their budget constraint.
The same couple of separating equilibrium contracts can be represented in the
al,a A2 space. Given C2, the best low-risk types can obtain along segment L is C7, which
is characterized by incomplete insurance (acA2<d).
Thus, in the R-S model, patients are characterized by private information over their
health status and this information influences their decision to buy insurance. Insurance
companies, in tum, know that patients' purchasing decision is influenced by their
(perceived) health status and offer less than optimal coverage contracts in order to screen
low-risk from high-risk individuals.
In specific circumstances, a separating equilibrium may fail to exist; in this case the
competitive insurance market has no equilibrium. This occurs when:
*  the cost of pooling for low-risk is not substantial while cost of separating, thus
accepting incomplete insurance, is high (high degree of risk aversion for low-risk);
*  there are few high-risk;
*  the probability of the loss occurring to low-risks is not very dissimilar from that of
high-risk.
Let us show a situation in which an equilibrium may fail to exist:
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Figure 5: Impossibility of a Separating Equilibrium
L
F
H3 \3. 
3
L
H1 
C2
WI
Contracts C2-C7 are upset by contract C8 that attracts both risk groups. Contract C8
lies on segment EF, so it is sustainable when both groups purchase it. The separating
equilibrium is unstable whenever at least a segment of EF, the pooling contracts zero
profit line, lies above LI, that represents the low-risk indifference curve in
correspondence to the separating equilibrium. In turn, as we showed before, any contract
that pools both risk groups together, such as contract C8, cannot be a stable equilibrium.
3.3 Final Remarks on the R-S Model and Introduction to Subsequent Developments in the
Literature
R-S show that in a situation of information asymmetry insurance companies can
limit the amount of insurance guaranteed in order to improve available information on
customers' risk. R-S result is robust to changes in hypotheses as long as individuals with
different risk properties differ in some characteristics that can be linked to their purchase
of insurance and, somehow, insurance companies can discover that link.
When R-S published their seminal work economic theory still lacked a solid
foundation for welfare analysis under conditions of imperfect information. However, R-S
had the intuition that the separating equilibrium reached by the insurance market entailed
a welfare loss. In the separating equilibrium low-risk obtain less than optimal coverage
12



while high-risk individuals do not improve their situation with respect to the first best. In
other words, high-risk impose a negative externality on low-risk. In fact, R-S show that
when each insurance company can offer more than one contract, the separating
equilibrium is Pareto inferior to a set of contracts characterized by some positive
redistribution from low-risk to high-risk (Rothschild and Stiglitz, 1976, pp.644-645),
unless there are enough high-risk people.
Building on R-S contribution, one stream of microeconomic literature, that labeled
of "equilibrium refinements", changed the hypotheses underlying firms' or individuals'
behavior in order to overcome R-S puzzling result that in certain circumstances no
equilibrium may exist in the insurance market. A second stream of literature set the
foundation for welfare analysis under conditions of imperfect information by looking at
the properties of "second best" equilibria. Such equilibria emerge when the individuals'
maximization problem is not only constrained by resource availability but also by agents'
incentive-compatibility constraints.
We will provide a brief account of both streams of analysis and then focus our
attention on the main policy implications that can be drawn from the comparison of
market outcomes and second best equilibria.
4. Equilibrium Refinements
R-S assume myopic (Nash) behavior by insurers and insured: neither firms nor
individuals anticipate others' possible reaction when deciding their strategy. Wilson
(1976) is the first to remove this hypothesis and to assume that insurance companies
behave strategically, in accordance with the analysis of firms' behavior in oligopolistic
markets. Wilson gives the following characterization of the equilibrium set of contracts:
* customers maximize expected utility;
* no contract in the equilibrium set entails negative expected profits;
* there does not exist any new contract still profitable even when all loss-making
contracts are withdrawn from the market as a result of this entry.
So, unlike R-S, any deviation from the equilibrium must continue to be profitable
even after all non-profitable contracts are discontinued.
A second contribution to the literature of "equilibrium refinements" is that by
Grossman (1979), who makes the hypothesis of "dissembling" behavior by high-risk
individuals. According to Grossman, all potential health insurance customers know that
in equilibrium any loss-making contract will be withdrawn from the market. Therefore,
when high-risk individuals submit their application for insurance they self-restrain their
choice between the set of contracts chosen by low-risk and those which would not entail
losses even if chosen only by high-risk individuals. By anticipating insurers' strategy,
13



high-risk individuals realize that any other strategy would ultimately lead them to be
completely excluded from the market.
Under Grossman's as well as Wilson's hypotheses the same set of equilibria is
selected. The R-S separating equilibrium continues to hold when the proportion of high-
risk X is greater than a certain threshold XRS, where X's is the percentage of high-risk
individuals that guarantees the existence of the separating equilibriumn in the R-S model.
However, when X < XRs the pooling equilibrium preferred by low-risk becomes a stable
equilibrium. When the percentage of high-risk individuals is small enough, low-risk
prefer to cross-subsidize contracts for high-risk in the pooling equilibrium rather than
accept a lower level of coverage in the separating equilibrium. Thus, the pooling
equilibrium preferred by low-risk becomes stable. Let us see why.
Figure 6: Under Wilson's and Grossman's Hypothesis, Pooling Equilibrium
Preferred by the Low-Risk Group Becomes Stable when There Are Few High-Risk
Groups in the Market
W2                                    L
F
L4
iH4
H
v C7
C 2
E
WI
Under the new assumptions about insurance companies' (Wilson) or individuals'
(Grossman) behavior, pooling equilibrium Cl0 is stable. Recall that in the R-S model any
new contract offer in the full area was able to upset Cl0 by attracting only low-risk
individuals. However, the new contract offer would lead to terminate contract CIO,
burdened by all high-risk and above the high-risk group zero profit line. Once CI0 is
14



withdrawn, also the new contract in the full area would become unprofitable. Thus, under
Wilson's hypothesis, the new contract is not a profitable deviation from CIO. Under
Grossman's hypothesis of strategic behavior on the part of individuals, high-risk would
immediately "follow" low-risk in any deviation from CIO in the full area, thus making any
such deviation unprofitable. If they didn't, they would immediately be "recognized" as
high-risk and offered a contract on the high-risk zero profit line, which would entail a
lower utility level. High-risk "dissemble" as low-risk by choosing the low-risk
individuals' preferred contract as long as this entails a level of utility higher than what
they can gain in C2. Note that under Grossman's hypothesis, unlike R-S's, both risk
groups are subject to a negative externality because of the asymmetry of information.
A third contribution to the literature of "equilibrium refinements" is that by
Miyazaki and Wilson (1977): they adopt Wilson's concept of equilibrium, but also
make the hypothesis that each insurance company is able to offer a plurality of contracts
and to cross-subsidize unprofitable contracts with profitable ones. Under their hypothesis
the equilibrium is always characterized by a positive cross-subsidy, unless the percentage
of high-risk x is greater than a certain threshold XMW, in which case the R-S separating
equilibrium prevails. Riley (1979) shows that if we extend the R-S model to a continuum
of types under the same behavioral hypotheses, the insurance market may fail to have a
stable equilibrium under any distribution of risk types. Riley also modifies R-S
hypothesis of Nash behavior on the part of the insurers and develops the concept of
reactive equilibria: insurers do not offer contracts that they know will become
unprofitable after induced entry adjustments are completed. Stiglitz (1978) extends the
analysis of the equilibria in the insurance market to the case of monopoly, showing that
when there are only two risk groups the only possible equilibrium is a separating
equilibrium in which high-risk achieve full insurance and low-risk individuals may be
only partially insured. In any case, low-risk are always subject to terms that make them
indifferent between buying insurance or be uninsured and, if the percentage of high-risk
is large enough, they end up buying no insurance. Thus, in case of monopoly, although
the distribution of surplus is more favorable to the insurer than in competition, some of
the qualitative results that characterize the analysis of competitive markets are reinforced.
Introducing partial market imperfections, however, may lead to better results.
Newhouse (1996) shows that if there are positive transaction costs, the pooling
equilibrium can become stable even under R-S behavioral hypotheses because the net
gain from upsetting it can be more than compensated by the additional transaction costs
necessary to devise a new contract. Ercinosa and Sappington (1997) show that market
power and scale economies can facilitate the coincidence between socially preferred and
market outcomes. In the spirit of the literature on "contestable markets", they show that
if there are positive sunk-costs (costs of entry that cannot be recovered once sustained)
there exist market equilibria where the incumbent insurance company cross-subsidizes
loss making contracts (those on high-risk) with profitable ones (those on low-risk). The
15



intuition is that in presence of scale economies a firm that serves onlly low-risk patients
faces higher average costs of production than a firm that serves both risk groups does. So,
the potential advantage of screening risks may wither away.
In summary, the contributions to the literature known as "equilibrium refinements"
highlight that the final characterization of the equilibrium in the health insurance market
will depend on the type of market structure (which determine firms' behavior and
constraints). It is clear for example that M-W equilibria, characterized by a positive
subsidy across risks, will tend to become unstable as competition in the market becomes
harsher and so the incentive to terminate unprofitable contracts increases.
5. Second Best Equilibria
Second best analysis represented an important breakthrough in the economics of
imperfect information as it provided a benchmark against which market equilibria under
conditions of asymmetric information could be evaluated. The core concept, first
developed by Harris and Townsend (1981) and then explicitly applied to the insurance
market by Crocker and Snow (1985) is that of constrained Pareto-efficiency. A market
allocation is constrained-Pareto efficient, or second best, if it is Pareto efficient among all
possible allocations satisfying:
- resource constraints;
- incentive compatibility, or self-selection constraints.
In other words, Pareto-constrained equilibria are "the best" (in terms of agents'
utility) that can be achieved whenever a self-selection or incentive compatibility
constraint (according to which agents must be induced to reveal their private information)
is present alongside a resource constraint.
As before, let us define ah the set of contracts meant for the high-risk group and a'
the set of contracts meant for the low-risk group. The formal structure of the problem to
characterize second-best equilibria is the following:
Max al ah JV(ph, ah ) + (I- _)V(pl, al)                                (5)
S.T.
1.  7C(ph, a h) + (1-X) 7t(p, aC )   X[(l_ph) ahl -phah2l + (1-X) [(]-p') all - pa2] 2 0
(resource constraint).
2. V(ph, Ca ) 2 V(ph, al)
3. V(p', a') 2 V(p', ao) (self-selection or incentive-compatibility constraints).
p is an arbitrary weight given to high-risk in the welfare function: p Ee [0,1].
Second best contracts are Pareto-efficient contracts among those satisfying constraints 1-
2-3.
16



If we exclude equilibria characterized by over-insurance5 (where individuals would
end up having higher wealth in case the loss occurs), the characterization of second best
equilibria is the following (necessary conditions):
a) ah provides full insurance to high-risk.
b) high-risk are indifferent between ah and a'
c) eventual losses (gains) on high-risk contracts ah are exactly compensated by gains
(losses) on low-risk contracts a'.
Graphically:
Figure 7: Second Best Equilibria
W2
L
C12~~C
E
0                                                            W
In Figure 7, J1F represents the set of contracts for low-risk that, in combination
with full insurance contracts for high-risk along C2F, satisfy conditions a), b) and c)
above. In C2-C7, the separating market equilibrium, there is no cross-subsidy between
risk groups. As we move along J1F starting from C7 and towards F from C2, the cross-
subsidy from low to high-risk increases: low-risk are paying progressively more than a
"fair" premium (shown on the segment EL) for receiving more coverage and this extra-
money is transferred to high-risk, who are paying progressively less than in C2 to obtain
full insurance. In Figure 2.7 low-risk initially increase their utility level (up to C1l)
5Forrnally, we are imnposing that X 2 t, i.e., the proportion of high-risks is higher than their weight in
the social welfare function.
17



moving from C7 along J1F. In parallel, high-risks' utility increases moving from C2 to C12.
We are therefore moving from Pareto-dominated to Pareto-superior contracts. In the
example considered, from C7 (the separating equilibrium contract) low-risk are willing to
pay more than a fair extra premium in order to receive more coverage. By cross
subsidizing high-risk, they are able to relax the high-risks' incentive compatibility
constraint and receive more coverage while still separating from high-risk.
C11-C12 is the low-risks' preferred equilibrium among second best equilibria. If we
further increase the degree of redistribution across risks, moving from C11-C12 towards F,
high-risks' utility further increases while low-risks' utility decreases. So, the
combinations of contracts along FJ' from Cl1 to F for low-risk individuals, which
corresponds to contracts on segment C12 to F for high-risk, are not Pareto comparable and
represent the set of (constrained) Pareto-optimal contracts. In general second best some
positive level of redistribution characterizes equilibria across risks. This is a very
important result for the health insurance market.
In health it is possible to justify redistribution across risks on the basis of different
principles:
1. First, on equity grounds, by pointing out that in a democratic society it ought to be
public responsibility to care for the health needs of those, like the old and the
chronically ill, who would otherwise be unable to afford to pay directly for services
or to buy insurance at a premium that reflects their health risk.
2. Or one can motivate redistribution by appealing to a life-cycle argument: the young
and healthy (low-risk) accept to pay more than they consume because they know that
in the future, when they will become old and sick, they will in turn be able to benefit
from subsidized health insurance coverage.
3. The above analysis, though, provides a third argument in favor of redistribution or
cross-subsidization by showing that even in a static context a positive level of
cross-subsidization across risks may be welfare improving. In other words, even
without considering the future, it may be in the low-risk group's interest to provide
some form of subsidy in favor of the high-risk individuals as a means to achieve a
degree of coverage closer to their preferred full coverage contract and still be
separated from the high risks.
6. Optimality of Market Equilibria
It is possible to use the conceptual framework sketched above as a benchmark to
analyze the optimality of private insurance market equilibria, according to different
behavioral hypotheses.
18



As we showed above, the R-S separating equilibrium may not be second best
optimal (in Figure 7, C2-C7, the R-S separating equilibrium, is Pareto-dominated by Cl,
C12). That is because the separating equilibrium is characterized by an excessive degree
of market segmentation: different risk groups are screened through the provision of
different contracts and in equilibrium each contract must break even. The market cannot
provide both separation of risks and cross-subsidization. Therefore, whenever second best
equilibria are characterized by positive cross-subsidization, the market separating
equilibrium is sub-optimal. This is not necessarily true. R-S separating equilibrium can be
second best optimal when the percentage of high-risk individuals is sufficiently large, as
in Figure 8:
Figure 8: R-S Separating Equilibrium May Be Optimal
If The Percentage of High-Risk Is High Enough
/LI     LL
Hi
.     ..............
E
J'       w  I
The intuition is that as the percentage of high-risk increases it becomes more and
more expensive for low-risk to cross-subsidize them. So, above a certain threshold X the
extra benefit low-risk gain from increasing their insurance coverage relative to the R-S
equilibrium level is not sufficient to justify the extra costs they must sustain to cross-
subsidize high-risk. They prefer the separating equilibrium contract, with no cross-
subsidy. The same result holds if low-risk are not very risk-averse, or if their probability
of incurring the loss is low. It turns out that the threshold X, which we will denote XMW,
is greater than XRs, the percentage of high-risk above which the R-S separating
equilibrium exists and holds under Wilson's as well as Grossman's hypotheses. There is
19



an interval Xas < X< XMW where the R-S separating equilibrium exists and it is sub-
optimal.
When X < XRs we have seen that under Wilson's as well as Grossman's hypotheses
the pooling equilibrium preferred by low-risk becomes stable. Such pooling equilibrium
is never second best optimal because it violates condition a) for second best equilibria,
i.e., it does not provide full insurance to high-risk. The pooling equilibrium, however,
may not be Pareto comparable with the second best pair of equilibrium contracts
preferred by low-risk (contracts Cl I and C12 in the previous Figure may be characterized
by a level of utility for high-risk lower than in the pooling equilibrium) and with the
second best equilibrium preferred by high-risk (point F corresponding to full insurance on
the pooling line, entails a level of utility for low-risk lower than in the pooling
equilibrium). This situation is represented using a Utility Possibility Frontier graph in
Figure 9 below. In general, though, from a pooling equilibrium it is possible to reach
Pareto-superior points by allowing a restructuring of cross-subsidies that separates the
different risk  groups.   Finally, the Miyazaki-Wilson  pooling  equilibrium  exactly
coincides with the second best equilibrium preferred by low-risk whenever X<XMW.
Otherwise, under the M-W hypothesis, the R-S separating equilibriun is selected. Thus,
M-W equilibria coincide with second best equilibria.
Figure 9: Second Best and Pooling Equilibria
F=Full insurance pooling
. i   e ulibrium
Set of 2nd best Pareto optimal
Ut High Risks                   equilibria
Market
pooling
equilibrium      \     --CIIC12=Second best
equilibrium preferred by
low risks
'I.
Ut Low Risks
20



7. Policy Analysis
The previous section showed that private market equilibria do not always lead to
Pareto-optimal outcomes, not even in a constrained sense. However, theoretical analysis
also suggests that if there are transaction costs or entry costs, the market can achieve a
second best equilibrium characterized by positive cross-subsidies. In other words,
phenomena which are normally considered frictions, obstacles to the full display of the
"beneficial effects" of competition, in the insurance market may play a positive role by
making contracts that imply a cross-subsidization across risk groups sustainable. At the
same time, as Newhouse (1984) noted, transaction costs may also exacerbate the effects
of the adverse selection problem. If switching individuals across insurance plans is
difficult, insurers will be extra-careful before making an offer to a potential high-risk
consumer. If it is impossible or too costly for an insurer to risk-rate a new applicant, the
insurer may either reject the applicant or ask an extremely high premium.
It is possible to use the conceptual framework developed so far to analyze the
effects of different policy options that correct spontaneous health insurance market
dynamics. We will build upon the contribution of Neudeck and Podczeck, 1996 (hereafter
N-P). N-P adopt Grossman's hypothesis about high-risk individuals' dissembling
behavior, according to which insurers eventually turn down non-profitable contracts. So,
no cross subsidization of contracts takes place in the separating equilibrium. The set of
policy options they consider is the following:
1) Public provision of insurance/subsidies. Four cases are discussed:
a) Full public insurance.
b) Partial compulsory public insurance, without or with possibility of acquiring
supplementary insurance from the private sector (topping up).
c) Full public insurance with possibility of opting out.
d) Risk-adjusted premium subsidies.
2) Regulation of the private insurance market. Three cases are discussed:
a) Standard contract with full-coverage.
b) Minimum insurance.
c) Premium rate restrictions.
Let us analyze first the full coverage public insurance and the partial compulsory
insurance options, with or without the possibility of acquiring supplementary insurance
from the private sector. We will utilize the analytical framework developed in the
preceding sections.
Full public insurance leads to the second best equilibrium preferred by high risk
individuals, that is the pooling, full insurance equilibrium F. Point F is characterized by
21



maximum redistribution across risk types and may be not Pareto-comparable with the
market separating equilibrium C2-C7 (low risk may be better off in C7 than in F).
Partial public insurance brings both risk groups along the pooling line, EF, say to
point D. Figure 10 shows that, starting from point D, it is possible to reach Pareto-
superior points by allowing individuals to purchase supplementary insurance from the
private sector. By these means, from point D separating contracts ClI C12 can be reached,
which are those preferred by low risk among second best contracts. By varying the
degree of public insurance (which is equivalent to moving the initial endowment point
along segment EF) and by allowing supplementary private insurance all second best
contracts can be obtained as separating market equilibria. The higher is the degree of
public insurance coverage, the higher is the degree of redistribution from low to high-risk
individuals and the higher is the utility of high risk.
Figure 10: Full Public Insurance and Partial Public Insurance
w2
L
jh        c1  /             i
,,- s~~~~~~~~~~-
Wi
The third type of public intervention N-P consider consists of full public insurance
with possibility of opting out. Those who believe in competition as a means to stimulate
greater efficiency in the health insurance market often advocate this possibility. The
possibility of opting-out would allow private insurers to enter into the market and offer
health coverage in competition with the public scheme. Those who oppose such
liberalization, however, claim that the public sector would then lose the low risk
individuals' contribution and would still be burdened by all the high-risk, which are
cream-skimmed by the private sector. In fact, N-P show that this option is able to lead to
a second-best outcome, as long as low risks accept to continue subsidizing the provision
22



of public insurance even when they are not benefiting from it any more. So, in the context
of adverse selection models it is not necessarily true that allowing low risk to opt out of
the public insurance scheme will inevitably lead to an unbalanced financial situation and
to worse high-risk individuals' condition. However, the issue left aside by these models is
how to maintain a political consensus for the cross-subsidy provided by the public
scheme, once the latter does not serve any more those who are supposed to be its net-
contributors.6
Figure 11 can be used to illustrate N-P's result:
Figure 11: Full Public Insurance with Possibility of Opting Out
W?.
L
jh ~      C 12   L'
W6-d                           ------ 9. 
Suppose that the government offers contract C12, characterized by full insurance
and preferred to the competitive equilibrium contract C2 by high risk. Such contract is
subsidized and it is above the actuarial or "fair" odds line for high risk. The total per
capita loss for the government would be equal to W*-W6+t+p d (contract C12 gives with
certainty wealth W* from an expected after-tax endowment equal to W6-t-phd).
6 If those who opt-out of the public scheme are also directed towards a different network of providers,
another parallel issue not considered by N-P concerns the problem of maintaining quality standards within
the provider network still utilised by high risk individuals, once those who would be most able to exert
23



Let us consider the following policy: the government levies the tax t, on all
individuals and then opens the possibility of opting out. In figure 11, the tax switches the
low risk individuals' initial endowment from E to E' and their fair odds line from
segment EL to EV'. As the figure shows, from C12 low risk (unlike high-risk individuals)
prefer to deviate and choose contract Cl1 if this contract is offered. Contract C1l is the
best low risk can achieve along their after tax fair odds line (E'L') among the set of
contracts not preferred to C12 by high risk (so it is the best contract compatible with
separation of risk groups). It is possible to show that C11-C12, is an equilibrium and it is
actually the only equilibrium, given the full insurance contract offer C12 and the tax on
initial endowments. In equilibrium the fraction of beneficiaries to taxpayers would be
determined by the fraction of high-risk individuals in the population,, X. Then, the lump
sum (capitation) tax on initial endowments necessary to sustain contract C12, if this
contract is chosen by high risk only, would be equal to:
Xt, + (1-X)tl = k( W* - W6 + ti + phd)
ti = k/(l-k)(W* - W6 + phd)
Note that any attempt at undercutting C,, in order to attract low risk (such as
contTact Z) would lie to the right of EL' and would be unfeasible given the low risk
individuals' after-tax endowment. Moreover, there is no contract offer along the zero
profit pooling line able to attract low risk (so there cannot be any pooling equilibrium).
Also note that there is no other separating contract that would be able to attract high risk
(all the points on segment EH lie below C12).
C11-C12 is the second best equilibrium preferred by low risk individuals. With a
different full insurance contract offer on segment C12-F along the bisetrix and a different
tax on initial endowments any second best equilibrium can be reached. Similar results
could also be obtained through an opting-out fee. It is only critical that the government
be able to maintain a positive cross-subsidy across risk groups.
We can use Figure 11 to illustrate also the effects of a risk-related premium
subsidy for the high-risk persons, funded through a mandatory contribution to a
solidarity fund from the low risk. The contribution would increase the accessibility and
affordability of health insurance for the high-risk, allowing them to purchase contract C12
and it would at the same time shift the low-risks' actuarial odds line from EL to El'L..
Insurers' interest in selectively attracting low risk through contract offers such as Z
would be limited and the low-risk would be able to achieve higher coverage in a
separating equilibrium. The cross-subsidy would be earmarked for purchasing health
insurance with a specified health insurance coverage (in Figure 3.2, full coverage) and it
"voice", in Hirshman's (1970) terminology, can instead choose to "exit."
24



would be exclusively based on individuals' relevant risk characteristics (the lower the
risk, the higher the contribution, or the lower the subsidy). Unlike a premium tax
7
deduction, it would be unrelated to the premium amount that individuals actually pay.
Van de Ven et al. (2000) and Van de Ven and Ellis (2000) provide a detailed analysis of
the different ways through which risk-adjusted cross subsidies may be implemented and
of the different possible risk-sharing mechanisms among insurees, insurers and the
solidarity fund. In the implementation of the risk-adjusted subsidies two main issues
arise. The first concerns the criteria according to which the different risk categories are
determined. In the above example with just two risk groups and with a residual
subsidized public insurance contract, the low risk were self-selecting themselves by
opting out of the public scheme. With more than two categories, van de Ven suggests the
adoption of a nationwide standard rating model as a basis for determining the subsidy
value per risk category, as well as a sharing of information between insurance companies
regarding the risk factors of those who decide to switch to another insurer. The second,
related issue, is how to determine the subsidy/contribution for the different risk
categories. Newhouse (1989) proposes that a combination of prospective risk-adjustment
methods and of cost-utilization based payments be used. Purely prospective risk-adjusters
are able to capture but a fraction of the variability in individuals' future health
expenditure. On the other hand, cost-based payments hinder insurers' incentive in
improving efficiency and searching for the more cost-effective care available in the
market.
In alternative to direct public provision/subsidization of insurance, the government
could try to regulate the private insurance market. This is the alternative advocated by
those who consider private insurers much more efficient than public agencies at
managing insurance funds and at stimulating greater consumer responsiveness from
providers. If the same results obtained through public insurance could be reached through
appropriate regulation of the private insurance market, there would be no need for direct
public provision of insurance. N-P show that the above argument is actually wrong. The
first form of regulation they consider consists in an obligation imposed on all private
insurance companies to offer a standard contract with full coverage open to any
individual. In this case private companies are free to offer any other contract they wish,
alongside the standard contract. N-P show that with this form of regulation no
equilibrium may exist. Let us consider Figure 12 below. The standard full insurance
contract imposed by regulation must lie on segment C2-F along the bisetrix (contract
offers to the south-west of C2 are ineffective, as nobody would choose them, while
7When the amount of the deduction increases with the total premium individuals, their "fair odds
line" (which is their budget constraint, showing the best rate at which they are able to exchange income
between the two staes) changes inclination. Then we would observe a subsitution as well as an income
effect, and most likely a larger equilibrium level of insurance (unless a large negative income effect
compensated the substitution effect).
25



contract offers to the north-east of F are unfeasible). Let us consider a compulsory full
insurance contract offer in C12. As explained before, such contract entails a positive
subsidy in favor of high risks from low risk individuals in any separating equilibrium. It
was also proved that no pooling equilibrium exists, as it can always be upset by contract
offers (such as contract C14 in the shaded area comprised within the pooling zero profit
line, the high risk indifference curve through C12 and the low-risk after tax zero profit
line) able to attract low risk and to induce high risk to accept standard contract C12, which
is the best they can achieve in any separating equilibrium.  From  C14 Bertrand
competition for low risk will eventually bring contract offers for low risk to C1l, along
segment E'L'. C1 I-C12 is a separating equilibrium and the only possible equilibrium when
E'L' is low risk zero profit line. In this case E'L' is the new budget line for low risk when
they subsidize standard contract C12 and all insurance companies gel: the same share of
high and low risk individuals.
Figure 12: Standard Contract with Full Coverage
w2
H                       ~~~~~z
W * .........
W 'o  - d...........
Wo
WI
However, the cross-subsidy necessary to sustain C1I-CI2, which was previously
achieved through taxation, cannot be imposed on private insurers: now contract Cl can
further be undercut by contract offers such as Z. This contract is prolitable (being to the
left of EL), as long as the deviating insurer is able to attract all low risk and gets an equal
share of high risk individuals. Thus, the standard contract policy leads to market
instability unless all insurance companies are required to have the same proportion of
26



high-risk individuals. Let us illustrate the point by an example. Suppose each high-risk
individual receives $20 over his/her "fair odds" premium in the standard contract C12.
There are 10 high-risk individuals and so the total cross-subsidy to high risk is equal to
$200. Suppose there are two competing insurers in the market, each of which has to
shoulder half of the high-risk individuals. If there are 20 low risk individuals and if low
risks are evenly distributed across the competing insurers, each low risk individual would
have to pay $10 = $20 (1/3)/(2/3) above her fair-odds premium, regardless the insurer she
was insured by. In terms of figure 12, we can imagine that such cross-subsidy shifts the
low risk zero profit line to E'L'. However, suppose that one of the two insurance
companies offers a contract such as Z and attracts all low risk individuals, at the same
time maintaining an equal share of high-risk individuals with the mandatory standard
contract. As before the total cross-subsidy that each insurance company needs to collect
from low risk individuals to sustain the standard contract is equal to 100, half the total
subsidy. However, in the new situation the 20 low risk individuals that choose contract Z
can pay such cross-subsidy $5 each [$5 = $20(1/5)/(4/5)].
Thus, the imposition of a standard contract may cause chronic instability in the
market, as competitors try to undercut each other in order to spread the burden of the
standard contract across a relatively larger pool of low risk.
The second form of regulation that N-P consider is that consisting of a minimum
insurance requirement. In our graphs, a minimum insurance requirement is equivalent to
imposing a lower bound on the wealth level in case the accident occurs, measured on the
vertical axis. In figure 13, if the starting point is the separating equilibrium, we can
distinguish three cases:
*  A minimum insurance requirement comprised between Ml and M2. In this case the
minimum insurance constraint is binding only for low risk and the high risk
individuals' indifference curve through C2 (Hi in Figure 13) lies above the highest
indifference curve for low risk along the pooling line EF (L4 in Figure 13). In that
case the utility that low risk can gain by still separating from high risk (choosing a
point along HI between C7 and C15) is higher than the maximum utility they can
achieve in any pooling equilibrium. Then, the minimum insurance constraint will be
binding for low risk and the latter will choose a separating contract along HI, such as
C15, while high risk will choose the separating equilibrium contract C2.
*  A minimum insurance requirement between M2 and M3. In this case the minimum
insurance requirement is not binding, as low risk prefer to switch to the pooling
equilibrium C10. Given Grossman's hypothesis of dissembling behavior by high risk,
this equilibrium will be stable as any deviation able to attract low risk will also attract
high risk (who would otherwise be offered the separating contract C2) and will then
become unprofitable.
* A minimum insurance requirement above M3. In this case the equilibrium will be
27



found on the pooling line in correspondence to the intersection with the minimum
insurance requirement. So, the constraint is binding for low risk arnd, above C2, is also
binding for high risk. In the extreme, the regulator can impose the full insurance
pooling equilibrium in F.
In general, the equilibrium with a minimum insurance requirement is not second
best and cannot be compared with the market equilibrium. However, by a minimum
insurance requirement the regulator can pose a limit to the practice of underwriting
existing contracts in order to attract low risk and can stimulate a positive cross-
subsidization across risk types.
Figure 13: Imposition of a Minimum Insurance Requirement
W2
M3                                  15
M2  >-A-C
WI
The last form of regulation we consider is premium rate restrictions. Rate restrictions are
assumed to apply to a specified health insurance coverage.8 In terms of the above graphs,
such form of regulation entails a restriction on the allowable gap between the rates
charged to high-risk vis-a-vis those set for low-risk individuals. That is equivalent to
force a cross-subsidy between the two groups, aimed at making health coverage more
accessible for the high risk. Similarly to the case of the standard contract regulation,
imposing rate-restrictions may actually exacerbate the effects of adverse selection, as
8 To prevent the insurers from rejecting new applicants or from cream-skimming high risk individuals,
the regulator may complement premium rate restrictions with a periodic open enrolment requirement.
28



insurance companies struggle to dilute the share of loss-making contracts in their pool, by
discouraging subscription of high-risk individuals and by competing for low risk
individuals.
8. Conclusion
The paper discussed the consequences of adverse selection on the functioning of
insurance markets. To isolate the effects of adverse selection from other confounding
factors, the paper considers a benchmark situation with no moral hazard and perfectly
competitive market. In those circumstances, the full information equilibrium is
characterized by complete insurance coverage. With incomplete information, however,
insurance companies underbid each other's contract offers in order to attract low risk.
The equilibrium is characterized by less than optimal insurance coverage and, under the
hypothesis of myopic behavior by insurers and insurees, no equilibrium may exist. We
have also shown that for a relevant range of parameters second best equilibria are
characterized by a positive cross-subsidy across risk types and that in these circumstances
the market separating equilibrium is in general sub-optimal.
The government can intervene in the health insurance market in two ways: by
directly providing subsidizing insurance or by regulation. Following Neudeck and
Podczeck (1996), the paper shows that the two forms of intervention do not lead to
identical results. Provision of partial public insurance, even supplemented by the
possibility of opting out, can lead to second best equilibria. This same result holds as
long as the government is able to subsidize contracts with higher than average
premium/benefit ratios and to tax contracts with lower than average premium/benefit
ratios. This theoretical conclusion seems to be of practical relevance. In recent reform
plans implemented in Germany and Holland where competition among several health
funds and insurance companies was promoted, to discourage risk screening practices a
Public Fund was also created in order to provide the necessary compensation across risk
groups. Unfortunately, only "objective" risk adjusters such as age, gender and region,
have been used for deciding which contracts were to be subsidized. These criteria alone
are not able to completely correct the consequences of adverse selection (Van de Ven and
Van Vliet, 1992).
Regulation of the private insurance market by imposition of a standard contract or
by restricting premium rates, on the other hand, can exacerbate the problem of adverse
selection and lead to chronic market instability. If the government is willing to safeguard
competition in the insurance market to tame the consequences of risk screening it is
necessary either to: a) impose limits to the possibility of undercutting existing contracts
(through a minimum insurance requirement; b) impose limits for insurance companies on
the possibility of selecting their insurees' pool. That explains why in Diamonds' original
proposal (1992) for regulating the American health insurance market insurance
29



companies were obliged to serve all members of a Health Alliance. Competition for the
market would have been preserved, but competition within each market (the market being
identified by the population of each Health Alliance) had to be limited to avoid risk
screening. In general, the above analysis has shown that there may be a price to pay in
terms of inefficient coverage by enhancing competition among health insurers as a means
to achieve greater patients' choice and better control over providers.
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