Multiperiod contracting with non-portable imformation : the case of sticky insurance prices

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FACULTY WORKING
PAPER NO. 1257

Multiperiod Contracting with Non-Portable
Information: The Case of Sticky Insurance Prices

Stephen P. D'Arcy
Neil A. Doherty

College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois, Urbana-Champaign

BEBR

FACULTY WORKING PAPER NO. 1257
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
May 1986

Multiperiod Contracting with Non-Portable Information:
The Case of Sticky Insurance Prices

Stephen P. D'Arcy, Assistant Professor
Department of Finance

Neil A. Doherty, Professor
Department of Finance

Many helpful comments were received during presentations of earlier
drafts at the University of Illinois Finance Workshop and at the Risk
Theory Seminar.

Multiperiod Contracting with Non-Portable Information
The Case of Sticky Insurance Prices

ABSTRACT

In a multiperiod contract, the generation of information over the
life of the contract may be used to redress problems of information
asymmetry existing at inception. In much of the earlier literature,
sequential information becomes impounded in prices thereby relieving
problems such as adverse selection and moral hazard as the contract
matures. We model and illustrate a different response observed in
insurance markets. If sequentially generated information is non-
portable, prices may become sticky over the contract life. However, new
information will permit the insurer to practice reverse selection against
its clients as their contracts come up for renewal. In competing for
the right to extract quasi rents from selected future renewals, insurers
write new business at a loss. This form of "low balling" describes an
alternative market response to adverse selection when sequentially
generated information is non-portable.

I. Introduction

In contracts of any sort between two parties, characteristics of
one party that are observable by the other party may affect the price
and other terms of the contract. Characteristics of the creditworthi-
ness of the borrower impact interest rates, collateral requirements
and covenants in debt contracts. Reputation and past reliability
affect the price consumers are willing to pay for brand name consumer
goods. A manager's ability and performance record play a role in
determining the salary and perquisites a firm is willing to offer as
compensation. So, too, are observable characteristics of an insured,
such as age, sex, driving record, type of vehicle and garage location,
priced into automobile insurance contracts. However, at the time the
contract is written, not all information that is relevant to contract
performance may be observable. The resulting information asymmetry
may give rise to problems of agency, adverse selection and moral
hazard. If contracts are set up for a single period, these problems
may act as a deterrent to the negotiation of contracts with ensuing
welfare loss. Multiperiod contracting permits performance monitoring
with indirect observation of material characteristics. The opportunity
for performance related pricing suggests that multiperiod contracts
often dominate single period contracts (see Radner (1981) and (1985),
Townsend (1982), Rubinstein and Yaari (1983), Dionne and Lasserre
(1985), Chan, Greenbaum and Thakor (1985)).

The analyses of Rubinstein and Yaari and of Dionne and Lasserre
address a particular form of multiperiod pricing of insurance
contracts. Information relevant to the estimation of an individual's

-2-

loss distribution (past losses) is revealed to the insurance firm
progressively over time. This information is translated into premium
incentives which partially offset the effects of moral hazard and
adverse selection. With this reasoning in mind, consider what might
happen if an insurer wrote a cohort of policies at time t, and left
these policies on the books for a number of years. Presumably, as the
insurer received informational updates it would revise its estimates
of the loss distribution of the individuals concerned and correspon-
dingly change the premium to restore appropriate contracted incen-
tives. If, in addition, the market for insurance products is assumed
to be competitive, the price changes should roughly match the changes
in loss expectancy. However, in examining cohorts of policies,
pricing behavior appears to be very different. The ratio of losses
incurred to premiums earned (termed the loss ratio) shows a clear and
dramatic tendency to decline as policies age on the books of the
insurer. Typically, new policies are written at a loss but the
insurer is able to extract quasi rents from policyholders who have
been with the firm for a number of years. If this pattern is driven
by the generation of progressive information, it is apparent that this
information is not fully impounded in prices. The declining loss
ratio is accompanied by declines in both the frequency and severity of
losses causing the numerator of the loss ratio to decline. When con-
sidered together, these various trends suggest that insurance premiums
tend to be inflexible in a downward direction. These patterns appear
to be well known in the insurance industry and sometimes referred to
as the "aging phenomenon. "

-3-

The aging pattern appears to be a form of "low balling" and has
analogies elsewhere. Low balling (setting opening prices below aver-
age cost in order to extract quasi rent on future renewal business)
has been noted, inter alia, in bidding for franchises (Goldberg 1976)
bidding for cable television contracts (Williamson 1975), the provi-
sion of auditing services (DeAngelo 1981) and in employment contracts
(Lazear 1979). Our model most closely relates to that of DeAngelo in
that we will show that competition for new contracts, which over time
will generate future client specific quasi rents, will drive the price
for new business below average cost. In our model, these client speci-
fic quasi rents are generated by the progressive production of non-
portable information which is not shared by the existing firm with
rival producers. This information permits the insurer to practice
reverse adverse selection against its clients thereby progressively
reducing claim costs on each cohort of policies.

In developing this "low balling" model of insurance we extend and
qualify the literature on multiperiod insurance pricing (notably
Rubinstein and Yaari (1983), Dionne and Lasserre (1985), Boyer and Dionne
(198b), Landsberger (1984)). That literature had focussed on the
unfolding of loss experience and using each "Bayesian update" to revise
insurance premiums. This process is seen as an antidote to the moral
hazard and adverse selection problems present in new business. However
the portability of new information, and therefore its disposition, has
not been examined. We show that, when unfolding information is
non-portable, this information will be used by the existing insurer for
selective renewal. As a consequence, renewal prices will not impound

-4-

new information and prices will tend to be sticky over time. The
structure of our model resembles Sweezy's (1939) kinked demand curve
used for analyzing oligopolistic structures. Our model well explains
the observed "aging phenomenon."

II. The Aging Effect In A Cohort of Insurance Policies

In this section examples of insurance pricing are presented that
appear to be consistent with "low balling." The examples were pro-
vided by two major insurers with large automobile lines. The firms
asked not to be identified. In our discussions with actuaries from many
other firms, we have received verbal confirmation that the aging pattern
is widespread. The examples relate to automobile insurance and, to
provide a focus, we will continue to discuss this line of business. The
examples are presented in Table 1. The loss ratios (the ratio of
incurred losses to earned premiums) decline clearly and dramatically
with the age of the policy. For firm A the severity and frequencies of
losses classified by policy age are also shown. Both loss frequency and

loss severity show a definite tendency to decline with age. Thus,

2
although the effects of changes in the denominator (premiums) cannot

be dismissed, the declining loss ratio may be sufficiently explained by

progressive reduction in the numerator (losses) as the policies' age.

Given expenses and investment income, it is evident that firm A is

losing value on its new business but is recouping the loss on older

business. At this juncture, it is unclear whether the value of the

book of business as a whole, capitalized at the time when contracts

are first written, will include monopoly rents. For this reason we

-5-

will refer to the apparent rents which the firm extracts from its
older policies as quasi rents since these may simply offset subsidies
offered when the policies were new.

In the following sections we offer an explanation of the aging
pattern. We address the generation of information over the lifetime
of insurance contracts. If this information is non-portable, then it
may be used by the contracting insurance firm to exercise selective
renewal. This is, in effect, reverse adverse selection by the insurer
against its clients. This would explain the declining loss experience.
But the non-portability of information also leads to the prediction
that prices would be sticky as the insurance policies age. Together
the declining losses and sticky prices provide an explanation of aging.
This is developed in Section IV. But first we must examine the dispo-
sition of information generated in insurance contracts.

Insert Table 1 about here

III. The Disposition of Information in Multiperiod Insurance Contracts

For convenience, the notation used in this paper is summarized below:

I = set of behavioral characteristics of insured that affect
loss density function. Insured observes full set I.

i = characteristics of insured observed by all insurers at
inception, i c I.

Ai = characteristics observed by contracting insurer, but not
by rival firms, at renewal i + Ai C I.

f ( L 1 1 ) = insured's estimate of his(her) loss density function
conditional on observation of I.

g.(L|i) = insurers estimate of the insured's density function at

time j conditional on observation of information subset i.

-6-

F. = demand function at time j for a cohort of insureds
exhibiting observable characteristics i to insurer.

p = premium per policy.

q = number of policies issued.

L = expected value of losses per policies, capitalized to the
beginning of the year in which the policy is written or
renewed.

g = initial estimate of the probability that an insured is a
"good" risk (i.e. , expected losses are below average for
the rating class).

it = number of policies on which adverse information is revealed
in the first year it C q.

k = proportion of it which is renewed in second year.

j = proportion of the residual group (q— it) (i.e., for which no
adverse information is received) that is renewed in second
year.

A = subscript to denote policies in sub group tt (adverse
information) .

N = subscript to denote policies in sub group q-Tr (no adverse
information) .

E = capitalized earnings on a cohort of policies.

D = discount factor.

x = annual expenses per policy.

m = additional expenses incurred at beginning of year 1 per
policy (primarily marketing and underwriting expenses).

e = demand elasticity.

The asymmetry of information under an insurance contract gives

rise to the familiar issues of adverse selection and moral hazard.

The nature of the asymmetry usually analyzed (e.g. , Rothschild and

Stiglitz (1976), Wilson (1977), Shavel (1979), Rubinstein and Yaari

(1983), and Riley (1985)) is as follows. The insured possesses certain

characteristics that are associated with the propensity for loss. The

insurer attempts to induce the insured into signalling his or her true

-7-

loss propensity by selecting a particular policy or amount of coverage
or to redress an undercharge in earlier periods by increasing rates for
insureds with losses. In these situations, all insurers have access to
the same information set about the insured. In this analysis, the
existing insurer is assumed to develop information about its insureds
that is not portable and thus not necessarily impounded in prices.
The full set of information relevant to estimation of the loss
distribution is denoted I. Some of these characteristics (e.g., age,
sex, type of vehicle driven, geographical location, number of prior
accidents etc.) are observable to the insurer at the time the contract
is written. This subset of information is denoted i.

i C I

The information asymmetry usually recognized reflects on the dif-
ference between I and i. The insured is well aware of his (her) own
behavior and characteristics. Thus, the insured's conditional esti-
mate of his (her) loss distribution is

f(L|l)

But the insurer's conditional estimate of the loss distribution at the
inception of the policy is:

gjCLli) where gjCLJI) = f(L |l).

When the insurance policy is due for renewal (perhaps after one
year), the information set may have changed. One possibility is that
the observable characteristics of the insured may have changed (e.g. ,

-8-

the insured is one year older, the vehicle has been changed, the drivers
may have been involved in accidents, or there is a change in the
location of the risk). Such changes would redefine the information set
I but the asymmetry may persist because the "hidden" characteristics of
the insured may still be unobservable to the insurer. The observable
changes could change the basic insurance premium charged. Moreover, if
the policyholder were to take his business to another firm, the new
insurer presumably would record the changed observable features and
charge an appropriate premium. Such changes in observable characteris-
tics are not pursued here; instead this analysis focuses on information
updates which redress the information asymmetry. Thus the information
set 1 is held constant over time.

Although the insurer observes only some portion i of the infor-
mation set I when the policy is first contracted, it may well be that
as the contract unfolds, the insurer is offered an opportunity to
monitor the insured and to observe directly or indirectly some of
those characteristics that were hidden at inception. For example, the
insurer can observe the conduct of the insured in bargaining and
testifying, in following the contract conditions, or in making timely
premium payments. Moreover, the insurer gets a full report on the
number and circumstances of any claims made on the policy. Thus, after
the contract has been in force for some time, the insurer can be
expected to know its insured better. At renewal of a two period
contract (i.e., at the start of the second period), the information
available to the insurer is (i+Ai) CI. Correspondingly, the insurer's
estimate of the loss distribution at renewal is

-9-

g2(L|(i+Ai)) where g2(L|l) = f(L|l)

It is convenient to refer to the information set i as PATENTLY
OBSERVABLE, and to the set Ai as LATENTLY OBSERVABLE. The latently
observable information is, by definition, not observable to the
insurer at the inception of the policy and is only generated through
the proximity of the contractual relationship. Although this infor-
mation may be available to the existing insurer at renewal, it will
not be observable to rival firms who might compete for the renewal
business, unless the existing firm chooses to share this information.
Thus, if the policy were not renewed with the same firm but a new
policy were contracted with another insurance firm, the new firm would
record only patently observable information i. The salient character-
istic of the latently observable information is its non-portability.

Following through the dynamics of these thoughts, a new insurance
contract with one firm faces information asymmetry between the insured
and the insurer. Over time the asymmetry may diminish as the
existing insurer can monitor its own insureds. But such monitoring is
not undertaken by rival firms. Thus the diminishing asymmetry between
the insured and the contracting insurer may be replaced by a widening
asymmetry between the contracting insurer and its rivals. Of course,
the issue is not confined to insurance contracts. The current
employer of a manager will have a comparative advantage in assessing
managerial skills vis a vis rival firms who have not had the
opportunity to monitor his (her) performance. Likewise, the existing
insurer has a comparative advantage in estimating the loss distributions

-10-

of its own existing book of business vis a vis rival insurance firms who

might compete for that business.

Now consider the demand function for insurance assuming that the

firm has categorized its new policyholders according to observed

characteristics. Thus, there is a set of rating groups,

each group containing observably homogeneous policyholders. The demand

for one such group is examined. The distribution of the aggregate loss

payout (as estimated by the policyholders who have full information on

their loss characteristics) is assumed to be described completely by its

first "n" moments, M, . The demand for new policies from this group is

f n

Fl = Fl(Mfn' P; V V

where p is the price charged by the firm in question, p is the vector

c

of prices of rivals and 9 is the set of nonprice variables (e.g., per-
ceived service, financial solidity, etc.) that may affect demand. At
renewal, the demand is

F2 = F2(Mfn; p; p^ B,).

Since the information set I has not changed for each insured, the
demand function will shift in price quantity space only if the prices
charged by rival firms change or if there are changes in the nonprice
variable (e.g., the client becomes dissatisfied with the firm's
service). Unless the existing firm shares information from the set Ai,
there is no reason for the prices charged by rival firms to change. At
the beginning of period 1 rivals could observe only i and at the
beginning of period 2 they will still observe only i. Consequently, the

-11-

demand function will shift only in response to changes in nonprice
factors defined by the vector 9.

IV. A Model of Insurance Selection and Pricing with
Non-Portable Information

A two-period wealth maximizing strategy for the insurer is now

determined. The assumptions used to generate this model are:

1) All insureds in a cohort display identical observable
characteristics i.

2) All insurers observe these characteristics at inception. At
this time all insurers share the same information.

3) However, insureds may differ with respect to non-observed
characteristics. The group is divided between "good" and "bad"
risks but the relevant characterstics which distinguish any
individual are known only to that individual. Thus, the
insured observes the full information set I that determines
this loss density function. The underlying characteristics

of each insured, as defined by the set I, are constant over
time.

4) Each firm is a price taker on new business.

5) Firms write new policies at the beginning of the first period.
Further information (Ai) is revealed to the contracting insurer
on its own policyholders at the end of the first period. This
information is not revealed to rival firms. The existing firm
will invite or decline renewal of its own policies at the
beginning of the second period. If renewal is invited, an
appropriate premium is charged.

6) The insurer is a wealth maximizer. Wealth is defined as the
sum of all profits capitalized at the beginning of the first
period.

7) Initial expenses, m, per policy decline with the number of
policies issued. Other costs (i.e., renewal costs, x, and the
expected loss per policy, L) are invariant with respect to
quantity. These restrictions are not fundamental to the
insights of the model but permit considerable simplication.

These assumptions are intended to describe a market that is competitive

with respect to patently observable information. However, information

-12-

asymmetries do exist. The insured has a comparative information advan-
tage with respect to all insurers. However as policies mature, this
comparative advantage is reduced. In its place, the contracting insurer
develops a comparative advantage over rival firms with respect to its
own policyholders.

Little generality is lost by concentrating on a cohort of new
policies that are observably similar and are charged the same premium at
inception. However within this group there are "good" and "bad" risks
distinguished by hidden or latent characteristics. "Good" risks have a
lower than average expected loss, signified by L_, for the group and
"bad" risks have a higher than average loss expectance for the group,
signified by L. Each insurer knows that its new policyholders may
include a disproportionate number of "lemons." These are risks for
which previous insurers have accrued adverse information and have
declined to renew. But this information is not revealed by the previous
insurer and the new insurer is unable to distinguish lemons from other
new policyholders. Thus, the new firm estimates that with probability g,
a new policyholder will be a "good" risk and with probability (1-g), a
bad risk. This probability may be based on previous experience. Since
all insurers have the same (i.e. , observable only) information on new
policyholders, they all hold the same estimate "g." Thus, a single
price, p, exists in the market for new policies.

Now consider the effects of the generation of latent information on
some subset of policies it c q. The information revealed to the contracting
insurer on these policies is unfavorable in the sense that it causes the

-13-

insurer to reduce its probability that each of these policyholders will
be a good risk. For each individual n in the subset tt ,

Prob n C it being a good risk is g_ where g_ < g.

Policies renewed from the subset tt will be denoted by subscript A.
The insurer receives no information on policyholders in the residual
subset (q— it). However, the average expected losses in this group will
have changed since it now excludes the subgroup tt who are likely to be
worse than average. The probability that an individual n in this subset
is a good risk is,

_ _ qg - TTg
Prob n C (q-rr ) being good risk is g =

Since g_ < g, then g > g. Under this scheme, "No news is good news!"
Policies renewed from the residual subset (q— ir) will be denoted by
subscript N.

These information effects produce a somewhat familiar form to the
function for renewal business for the contracting firm. By assump-
tion, all firms observe the information subset i and each firm is a
price taker on new business. Thus, after one year, if the contracting
insurer increases the price for renewal of its policies above the new
price, it will lose the renewal business to rivals. Policyholders can
take their business elsewhere and be offered the market determined new
price. But the infinite demand elasticity does not extend to price
reductions since we are not discussing new business to the contracting
firm but its renewal business. Although a price reduction may affect
the proportion of policyholders that renew their policies, this

-14-

proportion is naturally bounded at unity. Consequently, the demand
curve for policy renewals will be kinked at the new business price.

The firm maximizes its profits with respect to the quantity of new
policies q, the proportion k of renewals from subset it and the propor-
tion j of renewals from subset (q-rr).

(1) MAX E

MAX

q.k.j

MAX [q(p -x-gL-(l-g)L-m)]

q

,-i

+ MAX { [D \k(p -x-gL-(l-g)L)]

k,j

2A

.-1-

[DH-L(q-Tr)j(p2N-x-gL-(l-g)L)]}

Solving recursively, we first look at the derivatives for k and j,
These are respectively

(2) DN1(q-rr)[P2N(l - |) - (x+j |*- + gL+(l-g)L)]

(3) D^tt [P2A(1 " |) " (x+k ^| + gL+(l-g)L)]

A

Unless there is a sizable reduction in marginal expenses, condition
(3) will be negative at the new price. The new price can be no greater
than the marginal cost of new business, given wealth maximization and
competition for new business. The marginal cost of the subset tt will be
higher than that for new business. Attempts to increase the price for
this business will encounter the high (infinite) elasticity of the
demand curve. This situation is depicted in Figure 1 which shows the
kink in the demand curve at the new price p and infinite elasticity

-15-

with respect to price increases. Given the restrictions imposed, the
marginal cost curve is constant and, for the "bad" risk group, lies
above p . The firm renews no policies in this case since MC > MR at
all quantities.

The lower portion of the demand curve has different features.
Recalling the discussion between latent and patent information, it was
assumed that information revealed to the insurer at renewal repre-
sented a redress of an opening information asymmetry between the
insured and insurer. Thus, while the insurer may revise its loss
probabilities on acquiring this information, the insured still has the
same information, I. Unless there are other disturbances (death of
policyholders, dissatisfaction with nonprice features of the insurance
contract, changes in tastes, etc.) there would be no change in the
demand function. In this circumstance, all those buying new policies
at the new price would continue to renew at the same price. In con-
sequence, the demand curve would have zero elasticity of the value j=l
(i.e. , all policyholders in the set q— it would renew and the demand
curve would be vertical at j=l). With disturbances of the form
described, some policyholders may indeed fail to renew at the current
price but may be persuaded to renew if the price were to fall. In
this case the demand curve would exhibit some positive elasticity at
quantities below j=l. But since renewals are constrained at j=l, the
demand curve would revert to zero elasticity at this volume. With
these thoughts in mind, we show an inelastic lower segment to the
demand schedule and now address underwriting renewal strategy for the
subset (q-rr). In proceeding, the reader may bear in mind the strong

-16-

anologies with kinked demand curve developed by Sweezy (1939) to
analyze oligopoly and its predictions of price stability.

If the insurer is to sell policies to the subgroup (q-ir), it is
apparent that the (constant) marginal cost must be no greater than margi-
nal revenue at new current price p . In fact, since costs have fallen
due to the weeding out of the set ir , condition (3) will be positive at
the new price p . But the discontinuity in the marginal revenue curve
implies that a small price reduction would cause a discrete change in
the sign of condition (3) from positive to negative. Consequently it
is optimal for the insurer to renew j* policies at the prevailing
price p .

Putting these thoughts together, it is observed that policies

would be renewed at the new price or renewal would be declined by the

insurer. A possible exception to this observed price stickiness may

arise if both (a) the improvement in loss expectancy for the set

(q-ir) is dramatic and (b) demand below p is of elasticity in excess

of unity. Condition (b) is required to ensure equality of marginal

cost and marginal revenue in the positive quadrant. This possibility

is illustrated in Figure 2; the new price and proportion renewed are

p and j*. Having discussed this prospect, we think it unlikely. For
R

reasons stated earlier, the information released to the insurer repre-
sents a correction of a prior asymmetry vis a vis the insured. There-
fore, insureds have no cause to revise their loss expectations and, in
the absence of major exogenous changes, demand should be inelastic
(possibly of zero elasticity) in this region.

Finally, there is the question of how many policies the firm
should initially underwrite at the prevailing market price p1 . Bearing

-17-

in mind that no policies will be renewed for the subset it (i.e., k*=0)
and that p = p, the first order condition of (1) with respect to q is

{[Pl] - [x+gL+(l-g)L+m+q ||]}

(4)

" {CDNlj(1 ~^1] ~ [DNlj(1 -^)(^gL+(l-g)L)]} = 0

We assume that this condition may be satisfied given the "U" shape
initial costs m. The expression shows the marginal costs and marginal
revenues on year 1 business (first braces) and on year 2 business
(second braces). The analysis of condition (2) reveals that the term
in the second braces will be positive (p > (x+gL+(l-g)L) which
implies that marginal cost will exceed price on first year business.
(The term is the first braces will be negative.) The intuition of
this result is straightforward. Tbe firm will apparently oversell
(marginal policies are written at a loss) new policies in order to
increase the number of profitable renewals remaining in the residual
set (q-n). It is also apparent from condition (4) that the firm will
make normal capitalized profits on the cohort as a whole in light of
the perfectly competitive nature of the new business market. The
price p will be set below that necessary to cover average cost of the
representative firm on year 1 business. Any different opening price
would be corrected by the entry and exit of new firms.

V. Some Signaling Issues

The prediction of price stickiness rests upon the privacy of new
information to the contracting insurer. The asymmetry between the

-18-

contracting insurer and its rivals may be closed if a clear signal can
be transmitted that cannot be mimicked (see Spence (1974), Rothschild
and Stiglitz (1976), Riley (1975)). At renewal, the existing insurer
has no incentive to send such a signal but those insureds, for whom
adverse information has not been revealed, would benefit from such a
signal. However, it appears that the contracting insurer may be
forced to disclose the information it has acquired on its own clients,
Ai, by its invitation to renew. Simply by requiring new clients to
bring evidence of invited renewal from their previous insurer, a rival
can exactly replicate the dichotomous renewal strategy of the con-
tracting insurer. In these circumstances, the prediction of price
stickiness will fail. At the beginning of the second period, all
insurers would now separate policies along the lines of the contract-
ing insurer. We would observe separate contracts being offered to the
two groups for which different information was revealed.

In practice, the prevalence of declining loss ratios implies either
that firms fail to pick up the renewal signal or the information signal
is more cloudy and is unable to fully transmit the information subset
Ai. In the example developed above, the information gap between the
contracting insurer and its rivals was closed only because one signal
(the invitation to renew) was required to convey a single piece of
information (whether adverse information had arisen). In fact, the

information set Ai is likely to be more complex, represented by an "n"
element vector, and may be used to classify into more than two groups.
Clearly one signal is inadequate.

-19-

A second consideration is that the contracting insurer has an
incentive to "scramble" the renewal signal and thereby make it more
costly for rival firms to observe. In a different context, many
employees are "fired" not by undertaking a formal dismissal procedure
but by use of devices which make it attractive for the employee to seek
other employment (e.g., no raise, no promotion, assignment of "dirty"
jobs, etc.). Similarly the insurer can often "persuade" insureds not
to renew by use of devices such as lowering policy limits or increasing
deductibles, taking a less than generous position in settling a claim or
imposition of an unacceptable premium increase. Under such circumstances,
the invitation to renew has little meaning.

It is possible that rivals could monitor the whole range of behavior
of the contracting insurer with respect to individual clients and
indirectly infer the information Ai. But observing this myriad of
signals is costly to rivals, thereby maintaining the comparative
advantage of the contracting firm.

VI. Discussion

The underwriting and pricing strategy developed here may be
characterized on the following lines. By writing new policies, the
contracting insurer purchases an option to renew those contracts in
subsequent periods. The selective option to renew at a constant price
yields quasi rents on renewals. The fixed striking (renewal) price
arises from the nonportability of sequential information. The loss
taken on new contracts may be thought of as the price of the renewal
option. In a competitive market this option price would eaual the

-20-

capitalized value of future quasi rents, thus the cohort as a whole

would not generate monopoly rents.

3
The analogy with options is useful if not pushed too far. In

investment options, the value of the option is directly related to the
variance of the terminal value of the underlying asset. In our example,
the variance is determined, in part, by the unobserved variability in
new contracts. This unobserved variability is the feature that gives
rise to the "lemons" problem, i.e., to adverse selection against the
insurer. In this model the greater the hidden diversity, the more
valuable the option to renew at a fixed price. The insurer is quite
willing to write new policies at a loss knowing well of adverse selec-
tion. The greater the diversity, the greater the potential information
that can be revealed to the contracting insurer at renewal. By using
this information to practice selective renewal at a fixed price, the
insurer has at its disposal a (partial) antidote to the adverse selec-
tion problem. This mechanism is quite different to that offered by
other writers (Boyer and Dionne (1986), Dionne and Lasserre (1985),
Landsberger (1984)). These writers start with the proposition that
adverse selection stems from the inability to price correctly each
individual policy. But in their analysis the generation of sequential
information will affect price (e.g., through experience rating) and the
impounding of information in prices offers a solution (at least in
part) to adverse selection. Our model offers a different mechanism
based upon the privacy of sequential information to the contracting
insurer. Adverse selection is redressed not by using the generated
information to change prices, but by putting it to work, to practice

-21-

reverse selection by the insurer against its clients. The difference
between our model and prior models rests on the portability of infor-
mation. While not denying that some information is portable and may
feed into prices, the observed aging phenomenon implies that other
information is non-portable. This lends support to our nonprice/reverse
selection model as a complimentary antidote to adverse selection.

These thoughts also carry implications for long term contracting.
Typically, an insurance policy runs for a period of six months or one
year. Consider the case for a longer term contract that guarantees
renewal at a fixed price. Such a contract would be costly to the
insurer since it foregoes the right to select renewals. If the
composition of demand were fixed, and markets competitive with respect
to observable information, the loss taken on new business would provide
a measure of the value of potential long term contracts. However, the
demand for such contracts is likely to be concentrated amongst those
policyholders for whom short term contracts offer a high probability of
nonrenewal. Consequently, the loss taken on new business would provide
only a lower bound on the value of a potential guaranteed renewal
option since the renewal option itself would expose the insurer to
further adverse selection. This issue carries some regulatory implica-
tions since some states limit the right of insurers to decline renewal

(e.g., New York permits auto insurers to decline only up to 2% of their

4
current policies). This analysis implies that the introduction of

such a law, ceteris paribus , would lead insurers to increase prices for

new policies to cover the loss of the nonrenewal option and that

insurers would not exhibit such a dramatic "aging" pattern.

-22-

Finally the model developed here yields a set of specific predic-
tions which explain aging. The model predicts that insurers (a) will
write new business at a loss (they will oversell new policies) in
order to secure the option on client specific quasi rents on future
renewals, (b) will not disclose latently observable information con-
cerning their existing clients to rivals, (c) will selectively renew
policies on the basis of latent information, (d) will tend to maintain
the new price even though surviving policies are, on average, better
risks, and (e) will exhibit declining loss ratios as successive cohorts
of policies age. These features define a market response to adverse
selection when sequentially generated information is non-portable.

-23-

Footnotes

This price inflexibility is similar to the two examples cited by
Stiglitz (1984) in a description of imperfect information and price
stickiness. The use of price as an indicator of quality and the effect
of search costs were used by Stiglitz to explain sticky prices.

2
Had the severity and frequency data been available on the same

basis (e.g., both referring to all coverages or both referring to

physical damage) , we could isolate the effects of the numerator and

denominator on the loss ratio. Unfortunately, comparable frequency and

severity data were not available.

3
The reader will note that the insured also has an option to renew.

In effect we are dealing with a portfolio of different options.

4
The statutes regulating nonrenewal of automobile insurance policies

tend to give insurers free rein in electing not to renew a policy.
Thirty-three states and the District of Columbia do not restrict non-
renewals, five states restrict nonrenewals to the same grounds as
cancellations, and twelve states, including New York, legislate specific
grounds and other limitations on nonrenewals. For a complete analysis
of cancellation and nonrenewal provisions, see the American Insurance
Association (1986).

-24-

Ref erences

American Insurance Association. Summary of Selected State Laws and
Regulations Relating to Automobile Insurance. New York, NY:
American Insurance Association, 1986.

Boyer, Marcel and Dionne, Georges. "Moral Hazard and Experience Rating:
An Empirical Analysis." Presented to the Risk Theory Seminar,
Columbia, SC (April 1986).

Chan, Y. , Greenbaum, S. and Thakor , A. "Information Reusability and
Bank Arrest Quality." Banking Research Center Working Paper #126 ,
Northwestern University (1985).

DeAngelo, Linda E. "Auditor Independence, 'Low Balling' and Disclosure
Regulation." Journal of Accounting and Economics. 3 (August 1981):
113-27.

Dionne, Georges and Lasserre, Pierre. "Adverse Selection, Repeated

Insurance Contracts and Announcement Strategy. " Review of Economic
Studies. 70 (1985): 719-23.

Goldberg, V. "Regulation and Administered Contracts." Bell Journal of
Economics. 7 (1976): 426-48.

Grossman, Herschel I. "Adverse Selection, Dissembling and Competitive
Equilibrium." Bell Journal of Economics. 10 (1979): 336-43.

Landsberger, M. "The Optimality of Sequential Insurance Contracts Under
Asymmetric Information. " Presented to the Geneva Association, Rome
(September 1984).

Lazeas, Edward P. "Why is There Mandatory Retirement?" Journal of
Political Economy. 87 (December 1979): 1261-84.

Leland, Hayne E. , and Pyle , David H. "Informational Asymmetries,

Financial Structure and Financial Intermediation." The Journal of
Finance. 32 (May 1977): 371-87.

Mossin, J. "Aspects of Rational Insurance Purchasing." Journal of
Political Economy. 76 (1968): 553-68.

Radner, R. "Monitoring Cooperative Agreements in a Repeated

Principal-Agent Relationship." Econometrica. 49 (1981): 1127-48.

Radner, R. "Repeated Principal-Agent Games with Discounting."
Econometrica. 53 (1985): 1173-99.

Riley, John G. "Competition with Hidden Knowledge." Journal of
Political Economy. 93 (1985): 958-76.

-25-

Riley, John G. "Competitive Signalling." Journal of Economic Theory.
10 (April 1975): 174-86.

Rothschild, Michael and Stiglitz, Joseph E. "Equilibrium in Competitive
Insurance Markets: An Essay on the Economics of Imperfect
Information." Quarterly Journal of Economics. 90 (1976): 629-49.

Rubinstein, A. and Yaari , M. E. "Repeated Insurance Contracts and Moral
Hazard." Journal of Economic Theory. 30 (1983): 74-97.

Shavell, Steven. "On Moral Hazard and Insurance." Quarterly Journal of
Economics. 93 (1979): 541-62.

Smith, V. "Optimal Insurance Coverage." Journal of Political Economy.
68 (1968): 68-77.

Spence, Michael. Market Signaling: Informational Transfer in Hiring
and Related Screening Processes. Cambridge, MA, Harvard University
Press, 1976.

Stiglitz, Joseph E. "Price Rigidities and Market Structure." American
Economic Review. 74 (May 1984): 350-55.

Sweezy, P. M. "Demand Under Conditions of Oligopoly." Journal of
Political Economy. 47 (1939): 568-73.

Townsend, R. M. "Optimal Multiperiod Contracts and the Gain from
Enduring Relationships under Private Information." Journal of
Political Economy. 90 (1982): 1166-87.

Williamson, 0. Markets and Hierarchies: Analysis and Antitrust
Implications. " New York: Free Press, 1975.

Wilson, Charles. "A Model of Insurance Markets with Incomplete

Information." Journal of Economic Theory. 16 (1977): 167-207.

D/400

Price

Figure 1

New Price p I

Marginal Cost
(Subset it)

Marginal Cost
(Subset q,-ir)

Demand

Marginal
Revenue

Proportion of
Renewals in the
Respective Subset

Price

New Price p
Renewal P„

Price

Marginal Costs
Subset q.-TT

M

Demand

Margina

Proportion of
Renewals

1 Reveni

Table 1

Aging Phenomenon in
Private Passenger Automobile Insurance

Company A

.

Age of Policies

in Ye

ars

Loss Ratio
97.9

Frequency*
26.0

Severity**

1

664

2

87.7

23.8

604

3

74.7

21.0

569

4

76.2

19.7

592

5

67.6

18.9

564

6

63.2

17.9

568

7

58.2

17.5

504

8

63.1

17.8

538

9

60.0

17.7

482

10

55.8

17.4

NA

11

56.3

16.6

NA

12

53.1

Company

17.3
B

NA

1-4

53.7

5 and

over

39.1

*Total claims on all coverages combined per 100 policies,
**Physical damage claims only.

'ECKMAN

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JUN95

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