Outline of Lecture on Health Insurance

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Outline of Lecture on Health Insurance

• Overview of trends in coverage
• Built upon aversion to risk
• Core analysis for risk averter
• Modifications to core model
• Risk neutral/risk taker
• Stop-loss Analysis of all or nothing, income
  based public coverage
• Change in quality
• Moral Hazard
• Nearly certain demand
• Role of taxes
• Why insurance companies have loading fees
• Role of Deductible, co-pays and co-insurance
• Alternative View John Nyman
• Tax subsidy analysis
• Why employer based-common explanations
• A model explaining why firms offer coverage
• Various Applications
• Price sensitivity of Demand for insurance or to
  what extent has the recent increase in medical
  care expenditures and premiums led to a decrease
  in coverage--empirical studies
• Difficulty in measuring price of insurance

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Characteristics of those insured and not insured
by education
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Model of Demand for Health Insurance
BackgroundExpectation fair value

• Take money prizes, or a lotttery and form their
  expectation.
• Fair values are expected values.
• Think of the actuarial value as equal to the
  expected cost of a loss times the probability of
  that loss.

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Utility as a function of income
100
95
100
86
73
50
0
0
100
Y
22
2/3
4M
Expected value 3M
1M
1/3
100
95
100
86
73
80
80
Expected utility 80
50
0
0
0
1
2
3
4
5
2.538
Certainty equivalent wealth 2.538
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Expected utility an example u(w) ln(w)

• Expected utility .924
• Certainty equivalent solveln(CE).924
• Certainty equivalent 2.519M

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Expected utility an alternative preference
structureu(w) w.5

• Expected utility 1.666675/3
• Certainty equivalent solveu(CE)5/3 CE.5
  5/3
• Certainty equivalent 25/9 2.7777

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Key concept

• Value (utility) depends upon preferences.
• If marginal utility falls as wealth rises, the
  consumer is averse to risk.

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Arrow-Pratt measure An attribute of a utility
function. Risk Aversion Denote a utility
function by u(c). The Arrow-Pratt measure of
absolute risk aversion is defined
by RA-u''(y)/u'(y) This is a measure of the
curvature of the utility function. This measure
is invariant to affine (affine adjective,
describing a function with a constant slope.)
transformation of the utility function, which is
a useful attributed because such transformation
do not affect the preferences expressed by
u(). If RA() is decreasing in y, then u()
displays decreasing absolute risk aversion. If
RA() is increasing in y, then u() displays
increasing absolute risk aversion. If RA() is
constant with respect to changes in y, then u()
displays constant absolute risk aversion.
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E(U) 86 with insurance
100
95
UTIL
86
73
80
80
Expected utility 80 without insurance
50
E(L)
0
0
1 YL
2
3
4 Ya
Y/W
2.538
Risk premium Max .462
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Modifications to basic model of demand for
insurance

• Risk taker or risk neutral
• Stop-loss insurance (Medicaid as example)
• Role of taxes
• Increase in cost of medical care and quality
• Moral Hazard
• Nearly certain demand (dental care, eye exam,
  etc.)
• Move to board for these examples.

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EQUILIBRIUM IN COMPETITIVE INSURANCE MARKETS AN
ESSAY ON THE ECONOMICS OF IMPERFECT INFORMATION
MICHAEL ROTHSCHILD AND JOSEPH STIGLITZ
QUARTERLY JOURNAL OF ECONOMICS Best known
classic article in field of economics of
insurance coverage
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Consider an individual who will have an income of
size W if he is lucky enough to avoid accident.
In the event an accident occurs, his income
will be only W - d. The individual can insure
himself against this accident by paying to an
insurance company a premium a1, in return for
which he will be paid ?2 if an accident occurs.
Without insurance his income in the two states,
"accident," "no accident," was (W, W - d) with
insurance it is now (W - ai, W - d a2), where
a2 ?2 a1. The vector a (a1, a 2)
completely describes the insurance contract.
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On an insurance market, insurance contracts (the
a's) are traded. To describe how the market
works, it is necessary to describe the supply
and demand functions of the participants in the
market. There are only two kinds of
participants, individuals who buy insurance and
companies that sell it. Determining individual
demand for insurance contracts is
straightforward. An individual purchases an
insurance contract so as to alter his pattern of
income across states of nature. Let W1 denote
his income if there is no accident and W2 his
income if an accident occurs the expected
utility theorem states that under relatively
mild assumptions preferences for income in these
two states of nature are described by a function
of the form, (1) V(P, W1, W2) (1
p)U(W1) pU(W2). where U( represents the
utility of money income and p the probability
of an accident. Individual demands may be
derived from (1). A contract a is worth V (p, a
) V(p, W - ai, W - d a2). Individuals select
from all possible insurance contracts the one
that maximizes V (p, a ). An individual will
never purchase a contract that makes him worse
off than without any insurance contract.
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Supply of Insurance Contracts

• How do insurance companies decide which
  contracts they should offer for sale and to which
  people?
• The return from an insurance contract is a
  random variable. Assume that companies are
  risk-neutral, that they are concerned only with
  expected profits, so that contract a when sold to
  an individual who has a probability of incurring
  an accident of p, is worth
• (2) ?(p, ) (1 - p) a1 - p a2 ai - p(a1
  a2).
• Even if firms are not expected profit maximizers,
  on a well-organized competitive market they are
  likely to behave as if they maximize (2).
• Insurance companies have financial resources such
  that they are willing and able to sell any
  number of contracts that they think will make an
  expected profit. The market is competitive in
  that there is free entry. Together these
  assumptions guarantee that any contract that is
  demanded and that is expected to be profitable
  will be supplied.

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Equilibrium in a competitive insurance market
is a set of contracts such that, when customers
choose contracts to maximize expected utility,
(i) no contract in the equilibrium set makes
negative expected profits and (ii) there is no
contract outside the equilibrium set that, if
offered, will make a nonnegative profit. This
notion of equilibrium is of the Cournot-Nash
type each firm assumes that the contracts its
competitors offer are independent of its own
actions. However, when customers have different
accident probabilities, insurance companies have
imperfect information. They wish to learn about
this prior to selling them insurance.
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• Linking the Contingent Claims and Expected
  Utility Approaches to Choice under Uncertainty
• Consider an individual who derives utility from
  consumption in two possible states of nature. In
  the bad state of nature there is an accident,
  which occurs with probability ?B. Let
• cB consumption in the bad state of nature
  (i.e., if the accident occurs)
• cG consumption in the good state of nature
  (i.e., if the accident does not occur)
• W the initial endowment of wealth
• A the amount of the accident
• K the amount of insurance coverage
• ? the price per dollar of insurance (i.e., the
  premium).
• The preferences for the consumer are represented
  with a Von Neuman-Morgenstern utility function
• u(cB , cG ?B ,1-?B ) ?B cB? (1-?B) cG?. The
  usual expected utility diagram is shown in the
  upper quadrant of figure one. Figure one is drawn
  for parameter values ?B 0.25, ? 0.35, ?
  0.4.

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John Nyman Why do people purchase health
insurance? Many economists would answer that it
permits purchasers to avoid risk of financial
loss. This note suggests that health insurance
is also demanded because it represents a
mechanism for gaining access to health care that
would otherwise be unaffordable. For example,
although a US300,000 procedure is unaffordable
to a person with US50,000 in net worth, access
is possible through insurance because the annual
premium is only a fraction of the procedure's
cost. The value of insurance for coverage of
unaffordable care is derived from the value of
the medical care that insurance makes
accessible consumer surplus from the health care
services that would otherwise be inaccessible.
This value may be large, especially if the
procedure that insurance made possible were
life-saving. In this model, consumers derive
utility from disposable wealth w and health H. H
is a function of Medical care M and utility
derived from w and M may differ by your health
state. U ui (w, M) where I is healthy or
sick. Uw) and uww
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Nyman continuedConsider an illness where
the standard treatment protocol's cost, M,
exceeds endowed wealth, W. For example, a
consumer might have US50,000 in net worth from
all sources and be considering the purchase of
insurance coverage for a liver transplant that
costs US300,000 for the entire treatment
protocol. If diagnosed, there might be no time or
ability to save the extra amount out of income,
and lending institutions are unlikely to write a
US250,000 (the difference between the cost of
the procedure and what the patient is able to
raise by selling all his assets) uncollateralized
loan because of the riskiness of the procedure
and possibility that the loan will not be repaid.
For health care purchases like this, there might
be no private mechanism for gaining access to
this procedure if ill, save for already having
purchased health insurance coverage.An
individuals gain from insurance is access to M
expenditures of medical care is ill at a cost of
the premium p. Insurance allows individuals
access to care they could otherwise not afford.
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Current tax laws
Under current tax law, health insurance premiums
are largely tax exempt if the insurance is
provided through an employer but generally are
not deductible when a person purchases insurance
directly. The share of the premium paid by the
employer is not counted as income to workers and
retirees under the federal income and Social
Security payroll taxes. The employees share of
the premium also can be tax-exempt in firms with
flexible spending plans (such as Section 125
cafeteria plans). Out-of-pocket health spending
in excess of 7.5 percent of adjusted gross income
is tax-deductible for all individuals. Also, many
employees have access to a reimbursement account
under their employers flexible spending plan,
through which out-of-pocket health costs can be
paid in pretax dollars.
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Cost to Government of subsidies to health
insurance via the tax system tax expenditures
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Value to consumer of tax subsidy by family income
level
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Equity (lack thereof) of Tax Subsidy
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Modifications of tax subsidy

• For some forms of medical care, tax subsidy is
  really a direct subsidy that reduces the price of
  care
• Dental care
• Eye care
• Form of subsidy means that high income families
  receive the largest subsidies.
• Possible reform
• Only cover expenditures that are high risk and
  unlikelydisallow coverage of routine care

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Modifications of tax subsidy -2

• Regressive nature of subsidy
• Set maximum premium subject to subsidy
• Set uniform subsidy rate
• Set uniform subsidy rate and make it refundable
• Set uniform rate but with an income/asset test so
  it is reduced as income increases (income/asset
  test)
• Combine income/asset test with refundable credit
  and set maximum premium that is eligible for
  subsidy

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Why employer based-common explanations

• Economies of scale re administration
• Pool of risk large firms minimize risk for
  insurer or company if self insure.

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Introduction to model of why firms offer coverage

• If employees value health insurance, employers
  should be able to reduce cash compensation in
  return for providing insurance. Pauly (1997)
  refers to offering of health insurance to reduce
  the total cost of compensation as the economic
  theory of ESI.
• Definitions.
• Potential surplus the difference between
  employee valuation
• of ESI and the total cost to the employer of
  covering employees of that type.
• If potential surplus is positive, the best the
  employer could do would be to capture the entire
  potential surplus by holding cash wages at the
  point where the employee is indifferent between
  cash only compensation and compensation with
  health benefits.
• Extractable surplus the portion of potential
  surplus that the firm can actually obtain to
  reduce its cost of compensation.
• the size of the extractable surplus depends on
• the size of the potential surplus (and hence on
  factors such as the marginal tax rate of each
  worker, expected medical expenses and the
  difference in the cost of an individual private
  policy
• and a comparable employer-sponsored policy).

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Why do firms offer insurance?Traditional view
keep employees (stability of work force). Here
is an alternativedecrease cost of labor.
Starting point is equilibrium without insurance
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ROLE OF TAX SUBSIDY IN IMPROVING OPPORTUNITIES
FOR FIRM TO INCREASE PROFITS

• Under tax-exclusion, an employees own
  expenditure of x/(1t) purchases coverage
  equivalent to an employers expenditure of x, so
  that potential surplus increases by x/(1t)x
  (t/(1t))x (where t represents an appropriate
  aggregation of federal, state and payroll taxes).
• Ex. Of 30 MTR
• Premium for policy is 6000 per year. Load factor
  is 10 so total premium 6,600. If employee
  paid the 6,600 as wage, would have only 4,620
  to spend. (tax .36,600). To buy this plan,
  employee have to add 1980 in other income to
  this increase in pay or buy less expensive
  policy. Tax subsidy here is 1980. Under most
  circumstances this means the employee buys the
  policy below the actuarially fair value.
• The effective price of this insurance policy to
  the employee, taking the load as the price, is
  negative! (L - .3 TP) or (600- .36600)
  (600-1980 -1380).
• Add in Social Security and state and local taxes
  adds to the subsidy in the same manner.
• Implication one factor influences potential
  gain to firm is family income of workers. Bigger
  potential gain when have high wage employees.

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Firms with low wage workers have less opportunity
to profit from offering insurance the minimum
wage presents a floor below which firmscannot
trade implicit wage reductions for insurance
premiums.
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Allowing worker valuations of coverage to differ
Offer two different packages a and b to maximize
potential profit
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Adverse selection a leftward shift in the firms
break-eveniso-cost line E0, where the amount of
the shift equals the PV of future premium
increases incurred by insuring high cost
employees.
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Modifications to basic model of why firms offer
coverage

• Value to employees
• Taxes
• Possibility of spousal based coverage
• Multiple types of employees

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Other factors influence profitability of offering
coverage

• Health of workers expenditures on medical care
• Cost of coverage
• Tax subsidy
• Composition of work force wage level,
  willingness to pay, if have another worker in
  facmily

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How are premiums determined?

• Fully insured plans determine their premiums
  based upon the sum of expected medical costs or
  claims, margin or reserve for higher than
  anticipated costs, expected expenses (i.e.,
  administration), and profit/contribution to
  surplus funds. Expected claims are determined
  using the past experience of the insurers group
  insurance business(particularly for employers of
  a similar type), the past experience of the group
  itself, and data from inter-company studies.22
  This means that employers with above average
  claims experience in the past (those with sicker
  enrollees) and those employers of a type (e.g.,
  industry, size) that tend to have above average
  costs will face higher premiums. Because of
  uncertainty about claims costs, insurers also
  include a protective
• financial margin in the premium rate. This margin
  will vary with the size of the
• employer, since average claims for large groups
  are considerably more consistent over
• time than are the average claims of small groups.
  The expense/administration charge is
• generally calculated as a share of premiums, and
  decreases as a percentage as the size of
• the group increases, reflecting real economies of
  scale.

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Why do premiums increase?

• More medical care use
• Increase in price of care
• Improvement in quality (technology change)
• Poor performance of insurance companys
  investments
• Increase in administrative costs
• Adverse selection

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Why the recent decrease in private coverage?

• Possibilities firms less likely to offer fewer
  workers eligible firms pass more of cost on to
  employee (line shifts to left) firms try to
  discourage take-up.
• Cost of health coverage up
• Cutler Take-up ratei ß0 ß1 Employee Costi
  ß2 Premiumi Xi ß ei

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Cutlers findings
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Does racial composition play a role?
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Has composition of employment by firm size
changed?
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What those eligible report re not taking up
coverage
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Competing for spouses firm to provide coverage

• Dranove et al 2002 JHE argue that these patterns
  of health insurance contributions may be driven,
  at least in part, by the presence of two-career
  couples and employer competition to be the
  employer not chosen for insurance. They present
  a model in which
• competitive forces lead employers to raise
  contributions to encourage their workers to
  switch plans and obtain insurance from their
  spouses employers instead.
• They attempt to model a choice by firms that the
  equilibrium required employee contribution is
  sensitive to several critical
• Factors
• the cost of insurance,
• the percentage of two-career couples,
• The income tax rate,
• the heterogeneity of plans and employee
  preferences
• In their model, firms are symmetrical and all
  workers are married.
• If there is only one worker, and the MTR is
  substantial, firms will prefer to directly pay
  for the full cost of the premium (Vanness-Wolfe
  model explains why this is preferred.)
• The higher the MTR, the higher the proportion the
  firm pays
• The higher the proportion of workers with a
  working spouse, the higher the required premium
  contribution.
• Predictions consistent with generally observed
  facts employees asked to pay higher share there
  are more spouses working and the MTR are lower.

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Empirical Studies

• Families with single worker
• Feldman et al (1989) 3,000 employees in 17 firms
  in Minneopolis nested logit model.
• Price elasticities of -.53 to -.15
• Royalty and Solomon(1999) university employees
• own price elasticities of -.96 to 1.75
• Buchmueller and Feldstien (1996) university
  employees.
• If monthly premium increases by 10, 26 of
  health plan enrollees switch to lower prices
  plan.
• Bottom line employees on average are price
  sensitive with respect to choice of plans.
• Families with two workers and choice of plan
• Blumberg et al (2002) 1996 MEPS data.
• Individual worker less likely to take up coverage
  if spouse also offered coverage at work.
• Small price elasticity -.09 to -.01
• Dranove, et al (2000)1993 RWJF employer health
  insurance survey.
• Model predicts that firms will try to encourage
  employees to take up coverage with spouses
  employer. Firms with more employees with two
  sources of coverage will be less generous.
• Findings employee required contributions higher
  when more employees have working spouses. Also
  firms with higher costs of coverage have much
  higher required contributions.

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• Institutional Options for ESI 1
• An employer interested in sponsoring a health
  insurance plan for its workers and their
  dependents has a number of options.
• The first is fully insured products for single
  employers (as distinguished from contracts
  written for groups of employers). This option
  represents the purchase of an employment-based
  group health insurance policy from a licensed,
  risk-bearing carrier.
• Blue Cross Blue Shield , commercial, and health
  maintenance organizations (HMO).
• Within these types, various products are made
  available, including indemnity plans, HMOs,
  preferred provider organizations (PPO), and
  point-of-service (POS) options for HMO products.
• Fully insured plans are subject to state
  regulation in addition to some federal regulation
  (notably, the Health Insurance Portability and
  Accountability Act (HIPAA) of 1996).

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Institutional Options for ESI 2

• The second type of insurance option facing
  employers is to insure themselves or
• what is sometimes called "singly" self-insure.
• Firms can establish reserves and manage their own
  cash flow in such a way as to insure or
• indemnify their own workers against most
  health-related expenses.
• Federal law, the Employee Retirement Insurance
  Security Act (ERISA 1974), exempts employers from
  state insurance regulations as long as they are
  providing self-funded health insurance
  arrangements for their own workers. Self-insured
  employers are not exempt from the
• federal HIPAA law.
• ..

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Institutional Options for ESI 3

• The third broad category of insurance options are
  those which allow multiple employers to enter
  into insurance arrangements together.
• These options include Multiple Employer Welfare
  Arrangements (MEWAs), multi-employer plans
  (Taft-Hartley plans), business coalitions, and
  health insurance purchasing cooperatives.
• A MEWA is an insurance arrangement that offers
  benefits to the workers of more than one
  employer.
• A MEWA represents an agreement among employers
  alone it is not collectively bargained by
  workers representatives and multiple employers

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• PREMIUM SUBSIDIES HAVE SMALL EFFECT ON
  COVERAGEFederal employees gained the ability to
  pay health insurance premiums with pre-tax
  dollars, with the subsidy extended to postal
  employees in 1994 and then to remaining employees
  in 2001. A study by Jonathan Gruber and Ebonya
  Washington, takes advantage of this natural
  experiment to estimate the effects of premium
  subsidies on coverage rates among federal
  employees.
• FINDINGSSmall Effects of Premium Subsidies on
  CoverageWorker responses to the subsidy suggest
  an elasticity of take up with respect to premiums
  of roughly 0.02, similar in scale but lower than
  the response found in other studies.
• For family coverage, the regression coefficient
  implies that each 10 percent of premium the
  employee bears makes the employee 0.68 percent
  less likely to take up insurance. Employees pay
  roughly 20 percent of premium mean family take
  up was 61.5 percent. The arc elasticity of price
  with respect to premium over the range 0 to 20
  percent is thus -.022.
• Large Effects of Premium Subsidies on
  CostsSimulations of the effect of the policy
  change on the number insured show the number of
  newly insured persons ranging from 8,261 to
  17,954. The range reflects assumptions about what
  share of newly insured were previously uninsured
  (50 percent at the low end 100 percent at the
  high end.) Total costs are 693 million, of which
  647 million represents the revenue loss
  associated with allowing employees to pay
  premiums with pre-tax dollars, resulting in
  yearly costs per newly-insured person that range
  from 31,000 to 83,000.
• Small Effects of Premium Subsidies on Choice of
  Health Plan In contrast to previous work,
  federal employees appear less likely to switch
  health plans in response to a change in the
  employee share of premium. Such choices lead
  employees to offset only about 2.5 of the
  additional premiums.
• POLICY IMPLICATIONS This paper suggests that tax
  credits will not be very effective at increasing
  coverage rates among the uninsured who work for
  firms that offer coverage, and may be very costly
  to the federal government.

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Issues with empirical work in this area

• One of the key variables in determining coverage
  is the price of insurance.However defining and
  measuring that price is not straightforward.Conce
  ptual Issues How to deal with the large set of
  options heterogeneity in insurance products.
  In a full structural demand system, employers
  and employees would face a myriad of prices for a
  large number of potential products. Included
  would be publicly subsidized products. Employers
  may perceive (and act on) a set of prices that
  differs from the set relevant to employees.
  Identifying the right choice set for individuals
  is complicated. Another issues is the extent
  to which health insurance benefits influence
  worker selection into firms If so, the set of
  health plans in an individuals choice set may
  reflect all plans in the market (assuming the
  individual can select the firm with his preferred
  plan) or only those plans offered by his employer
  if no job sorting is assumed. The choice set
  should also reflect options for coverage through
  ones spouse.Should one use the full premium?
  or employee (or employer) share or some
  combination of the two as the relevant price
  measure? Depends on what one assumes about the
  extent to which health care premiums are shifted
  to groups of workers or to individual workers.

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Another alternative the premium

• One possible measure of price is the premium
  itself. Unlike the load, whichexplicitly
  incorporates benefit design into the definition
  of price (because benefitsdetermine the expected
  payout), use of the premium as the price measure
  requires controlling for benefit packages.
  Essentially this is equivalent to a hedonic
  pricing approach. Much of the work on competition
  in insurance markets has used this
  approach.However, if premium variation is due
  to variation in prices or costs of medicalcare
  we would expect elasticities to differ if the
  medical care price variation is driven by
  variation in the quality of medical care, the
  elasticity may well differ from what would be
  observed if the variation in medical care were
  due to variation in market power of medical care
  providers.Finally, over time health care
  premiums have risen, largely due to new
  medicaltechnology. Very little is known about
  how rising premiums will affect coverage rates
  over time. Elasticities based cross sectional
  variation in premiums, willgenerally not provide
  appropriate measures of the elasticities of
  coverage over time.

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Should We Measure Price at the market/ firm/ or
individual level?

• 1. Market Level View insurance as a composite
  good and assume prices vary at the market level.
  Uses variation in the menu of prices without
  worrying about the details of the endogenous
  choice of plans or benefit packages made by firms
  or workers. Avoids issues related to the joint
  insurance decisions within families. Because the
  market price approach does not use data on the
  relative prices of different benefits packages
  and plan designs within the market, it cannot
  address questions related to which plan a firm or
  worker would purchase it may be a reasonable
  method to address the decision to purchase
  coverage vs. to not purchase coverage.

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Should We Measure Price at the market/ firm/ or
individual level?

• Firm level The key question of interest at the
  firm level is the sensitivity of small firms to
  premiums. The problem is the lack of observed
  premiums for firms that do not offer coverage.

• Individual level LOAD, OUT-OF-POCKET OR PREMIUM?

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Conceptually measuring price

• The dominant paradigm today, reflected in widely
  used health economics textbooks, defines the
  price of insurance as the difference between the
  premium and the expected payout, commonly
  referred to as the load (Feldstein, 1999 Phelps,
  1997) The motivation for this approach reflects a
  definition of the insurance products as primarily
  afinancial instrument. Individuals pay a premium
  in exchange for an expected payout. As Phelps
  states in his textbook, If the loading fee 0,
  the premium just matches the expected benefits
  and the insurance itself would be free. In such
  a setting the relevant price for each health plan
  in an individuals choice set would be the
  loading fee.
• This does not end the problem of empirical
  estimation as we do not directly observe the
  loading fee.