health insurance. hurley, chapters 9 and 10 -...

Demand for healthcare insurance.

Insurance.

Modeling behaviorunder risk.

Lemons.

Moral hazard.

Health insurance.Hurley, Chapters 9 and 10

Chris AuldEconomics 318

March 5, 2014


Insurance.


Lemons.

Moral hazard.

Information

I We grounded our discussion of physician behavior in thenotion of asymmetric information: some people havemore information than others.

I In this chapter, we consider how asymmetricinformation affects private markets for insurance.

I We will see that two problems arise: adverse selectionand moral hazard.


Insurance.


Lemons.

Moral hazard.

Risk pooling.

I The fundamental reason insurance exists is riskpooling.

I Risk pooling is when each member of a groupcontributes a small amount, and the pool of money isused to compensate those in the group who experiencesome loss.

I In effect, risk pooling allows you to transfer money fromgood states of the world (your house doesn’t burndown) to bad states (your house burns down).


Insurance.


Lemons.

Moral hazard.

Risk aversion.

I Why does it make sense to pool risk? That is, why arewe better off paying a small amount with certaintyrather than paying a large amount with some smallchance?

I People exhibit risk aversion: most people prefer acertain outcome over a risky outcome with the sameexpected payoff.

I e.g., would you prefer a gift of $10,000 with certainty,or a 50/50 chance of getting $0 or $20,000?


Insurance.


Lemons.

Moral hazard.

Modeling behavior under risk.

I Suppose one of two outcomes, outcome G or B, couldoccur.

I The probability of outcome B is p, and the probabilityof outcome G is then (1− p), where p is between 0 and1.

I You get W1 dollars if outcome B occurs and W2 >W1

if outcome G occurs.


Insurance.


Lemons.

Moral hazard.

Behavior under risk cont.

I The expected value (EV) of this lottery is then

EV = pW1 + (1− p)W2.

I e.g., you park at an expired meter, and you have a 20%chance of getting a ticket for $100, so

EV = 0.2(−100) + 0.8(0) = −20.

if you illegally parked over and over and over againmany times, on average you would pay $20.


Insurance.


Lemons.

Moral hazard.

St Petersburg Paradox

I One model for behavior under risk: you are willing topay the EV of any lottery.

I But: consider this lottery: You are offered the chance toplay a game. A coin will be tossed as many times in arow as it comes up heads. If it comes up heads n times,you get $ 2n as a payout.

I e.g., get heads zero times, payout is 20=$ 1.

I get heads three times, payout is 23 = $8.

I What would you pay to play?


Insurance.


Lemons.

Moral hazard.

Paradox cont.

I The expected value of this lottery is

EV = (1/2)1 + (1/4)2 + (1/8)4 + (1/16)8 + ....

= 1/2 + 1/2 + 1/2 + ... →∞.

I But most people are willing to pay about $ 7 to play.


Insurance.


Lemons.

Moral hazard.

Expected utility.

I A better way to model behavior under risk is to assumepeople act as if they maximize expected utility. Withtwo outcomes as before

EU = pU(W1) + (1− p)U(W2)

I Notice this nests EV, because we get EV if we setU(X ) = X .


Insurance.


Lemons.

Moral hazard.

Expected utility cont.

I e.g., a person has wealth $ 50,000, surgery costs $20,000, and the probability they will be ill and needsurgery is p = 0.6.

I The expected loss is 0.6(20, 000) = 12, 000, soexpected wealth is $50,000 - $12,000 = $38,000.


Insurance.


Lemons.

Moral hazard.

I Suppose for this person U(X ) =√X . Then

EU =p√

wealth if ill + (1− p)√

wealth if not ill

=0.6√

30, 000 + 0.4√

50, 000 ≈ 193.

I On the other hand, if they had to pay $ 12,000 withcertainty, then

EU =√

38, 000 ≈ 195.

I so we see that this person is indeed risk averse.


Insurance.


Lemons.

Moral hazard.

C:\Users\auld\Desktop\Files\E317\Hurley_HealthEconomics_Figures_Tables.doc 3-114

Chapter 9 Figure 9.1: The Welfare Gain of Risk Pooling through Insurance

Figure 9.1: This figure depicts the welfare gains from insurance for a risk-averse individual. The curved line represents utility deferred over wealth. If this individual has $50,000 at the beginning of the year and faces a 60 percent chance of falling ill and incurring $20,000 in health care expenditures, their expected level of wealth is $38,000 and the expected level of utility is 193 utils (pt C). If they can buy full insurance at an actuarially fair premium of $12,000, they can attain utility level 195 (pt D) with certainty. The

$30,000 $37,249 $38,000 $50,000 Wealth

U(W0) = U($50,000) = 224

U(p(W0-L)+(1-p)W0) = U($38,000) = 195

pU(W0-L) + (1-p)U(W0) = 193

U(W0-L) = U($30,000) = 173

A

D

E

B

C

Actuarially Fair Premium

A

Risk Premium

Total Utility (U)

expected loss

U = U(W) = wealth


Insurance.


Lemons.

Moral hazard.

I Since the person is better off if they pay 12,000 withcertainty rather than facing risk, they’d be willing to paymore than 12,000 to completely insure against the risk.

I Let X be the amount they’d be willing to pay. Then

U(50, 000− X ) = 0.6√

30, 000 + 0.4√

50, 000√50, 000− X = 193

50, 000− X = 1932

X = 50000− 1932 = 12, 751.


Insurance.


Lemons.

Moral hazard.

I Recap: the person faces a 60% chance of a loss of20,000.

I The expected loss is 0.6(20,000) = 12,000.

I The EU of the lottery is 193.

I EU if there were instead a certain loss of 12,000 is 195.

I The person would be willing to pay 12,751 to fullyinsure against the expected loss of 12,000.

I Therefore, if an insurance company can turn a profit byinsurance against this loss for a price between 0 and $751, both parties benefit.


Insurance.


Lemons.

Moral hazard.

Actuarially fair insurance.

I Suppose insurance is actuarially fair, ie, the price ofthe contract is equal to the expected payout from thecontract.

I Then buying more insurance has no effect on expectedwealth.

I Then risk averse people will fully insure: they will buycontracts which pay out L if the loss is L.

I Actuarially fair insurance cannot exist because theinsurance firm would make negative profits.


Insurance.


Lemons.

Moral hazard.

Curvature.

I The person’s risk preference is represented by the shapeof the utility function:

I If the utility function u(w) is linear, the uncertainoutcome is worth the outcome’s expected value to theagent.

I If the utility function is strictly concave, the agent isrisk averse, she is willing to pay less than the expectedvalue.

I If the utility function is strictly convex, the agent is riskloving, she is willing to pay more than the expectedvalue.


Insurance.


Lemons.

Moral hazard.

Information problems.

I Now that we know why markets for insurance can formand make everyone better off even if the insurance isnot actuarially fair, we should consider two obstacles,both of which arise from information issues.

I If you are insured against some risk, you may changeyour behavior in a way which increases either theprobability of loss or the value of the loss. This is calledmoral hazard.

I You may know more about the probability and value ofthe loss than the insurer. Then people with more tolose, on average, may be more likely to buy insurancethan others. This is called adverse selection.


Insurance.


Lemons.

Moral hazard.

Adverse selection and lemons

I Why do cars plummet in value as soon as you drivethem off the lot?

I Basic idea: someone is trying to sell you a used car.You would be right to suspect that there’s some hiddenproblem with the car, a problem you cannot easily findbut which prompts the sale. You should take that intoaccount when making an offer, and it turns out thisinformation asymmetry may have large effects on themarket for used cars.


Insurance.


Lemons.

Moral hazard.


Insurance.


Lemons.

Moral hazard.

A model of the used car market.

I There are 9 used cars for sale. These cars have qualitiesQ ∈ {0, 14 ,

12 , ..., 1

34 , 2}

I Sellers value cars at $5,000Q, buyers at $7,500Q.

I That is, sellers value the 9 cars{0, 1250, 2500, 3750, ..., 8750, 10000}and buyers value the cars{0, 1875, 3750, 5625, ..., 13125, 15000}.


Insurance.


Lemons.

Moral hazard.

Assumptions

I Everyone is risk neutral (U(W ) is linear), so buyers arewilling to purchase a car if they think that on averagethe car they get is of sufficient quality.

I e.g., if a buyer thought it was equally likely a car waseither a Q=0, Q=0.25, or Q=0.5, they treat thesituation as if they are offered the Q=0.25 car.

I Everyone knows the distribution of Q.

I For convenience, assume an agent will make a deal ifshe’s indifferent, e.g, if a buyer is willing to pay $10,000and the price is exactly $10,000, they offer to buy.


Insurance.


Lemons.

Moral hazard.

Case I: perfect information.

I If everyone could observe the quality of the cars Q, allcars would be sold for somewhere between 5000Q and7500Q.

I Buyers and sellers are both better off given a marketforms and they trade with one another.

I e.g., if the Q = 1 car sells for $6,000, the buyer is betteroff because he was willing to pay $7,500 and the selleris better off because he was willing to accept $5,000.

I Upshot: all cars are sold, everyone in the market isbetter off after trades take place.


Insurance.


Lemons.

Moral hazard.

Case II: uncertainty but no asymmetricinformation.

I Suppose that there is uncertainty, but everyone has thesame information: no one knows which car is which.

I Both buyers and sellers know the average car amongthe 9 has quality Q = 1.

I First consider p = 10, 000. At this price all sellers offertheir cars for sale, because sellers value any car (giventhey cannot observe Q) at 5,000. But buyers value anycar at 7,500, so no one buys.

I At a price of p = 7500, all sellers are willing to sell, andall buyers are willing to buy.

I The market clears: all cars are sold.


Insurance.


Lemons.

Moral hazard.

Case III: Asymmetric information.

I Now suppose that only sellers know the quality of thecars for sale:

I Each seller knows Q for his car.

I Buyers do not know which car is which, but they doknow that Q is equally likely to be any of the 9 valueslisted above.

I There is uncertainty—buyers do not know Q—andthere is asymmetric information as sellers do know Q.


Insurance.


Lemons.

Moral hazard.

model cont.

I What happens to prices and quantities?

I Suppose first the price is p = 10, 000.

I At this price, every seller is willing to sell his car.

I Buyers see every car is for sale but cannot tell which iswhich.

I Since buyers are risk neutral, they are willing to pay forthe average car offered for sale.

I The average car for sale has quality Q = 1, so buyersare willing to pay $7,500. No trade takes place at thisprice.


Insurance.


Lemons.

Moral hazard.

model cont.

I So what if the price is $7,500?

I At this price the two sellers with the highest quality cars(which the sellers value at $8,750 and $10,000) refuseto sell.

I Among the remaining 7 cars which are offered for saleat this price, the average quality is Q = 3/4 and buyersare willing to offer (3/4)(7500) = $5, 625.

I No trade takes place at this price either.


Insurance.


Lemons.

Moral hazard.

model cont.

I As we keep trying lower prices, more and more sellersrefuse to sell, and the average quality of cars for salefalls.

I As the average quality of cars for sale falls, buyers arewilling to pay less and less.

I In this example there is no price which clears themarket!

I No market forms and no trade takes place, even thoughwe saw that everyone can be made better by trade.

I Upshot: Asymmetric information can really mess upmarkets!


Insurance.


Lemons.

Moral hazard.


Chapter 10 Table 10.1: Market Failure Cause by Adverse Selection

Expected

Costs Risk

Premium Wilingness

to Pay Period 1

Premium = $112 Period 2

Premium = $167 Period 3

Premium = $200 Person 1 $10 $1 $11 Don't buy Don't buy Don't buy Person 2 $50 $6 $56 Don't buy Don't buy Don't buy Person 3 $100 $15 $115 Buy Don't buy Don't buy Person 4 $150 $25 $175 Buy Buy Don't buy Person 5 $250 $50 $300 Buy Buy Buy Total $560 Mean $112 Insurer Revenue $336 $334 $200 Insurer Expenses $500 $400 $250 Profit ($164) ($66) ($50) Table 10.1: Assume that five risk-averse people with differing expected costs are in the insurance pool. For each person the table lists the expected costs, the risk premium the person is willing to pay and the total amount the person is willing to pay for insurance. The mean expected cost across all five individuals is $112. Let this be the premium the insurer charges. What will happen? In period 1, only 3, 4 and 5 will purchase insurance. This will provide the insurer with revenue of $336 but expenses of $500, leading to negative profits. In response, the insurer raises the premium to $167 in period 2. But this causes person 3 to drop insurance. This continues until the market disappears. Adverse selection caused market failure.


Insurance.


Lemons.

Moral hazard.

Adverse selection in insurance markets.

I The market for insurance is like the market for usedcars, with insurance buyers taking the place of carsellers, and insurance companies taking the place of carbuyers.

I Consumers know more about their own health statusthan insurance companies do.

I At a given price for insurance, “high quality” consumers(consumers with low expected health expenditures) willrefuse to buy insurance much like high quality cars arewithheld from the used car market: “high quality”consumers select out of the market, so the remainingconsumers are adversely selected.


Insurance.


Lemons.

Moral hazard.I We could use exactly the same model as before: let Qnow represent health status; a person with health Q iswilling to pay 7500Q for insurance and an insurancecompany is willing to accept 5000Q. We conclude thatno market forms.


Insurance.


Lemons.

Moral hazard.

A slightly different model for health insurance.

I Suppose there is a large population of people who varyin health expenditures. Expenditures are uniformlydistributed between 0 and M.

I People know the value of their expected healthexpenditures, insurers do not.

I A person chooses to buy insurance if the price is lessthan their expected expenditures.


Insurance.


Lemons.

Moral hazard.

I Suppose first p = 0. All buyers would like to buy, soaverage expenditures are (1/2)M. Firms lose moneysince revenues are zero but they payout.

I Suppose p = 12M. Now only the buyers with

expenditures greater than 12M choose to purchase. In

this group average expenditures are 34M, so again firms

lose money.

I Let the price be 0 ≤ p < M. Then average expendituresare (M + p)/2 > M. No price clears the market, excepttrivially p = M and only highest-expenditure personbuys.

I There is no price which clears this market. The marketfails to form.


Insurance.


Lemons.

Moral hazard.

Implications.

I If insurance firms could observe every person’s riskiness,markets would work as predicted by conventional theory.

I If insurance firms cannot observe people’s riskiness,then we should expect adverse selection to occur.

I Adverse selection implies that markets may not evenform.


Insurance.


Lemons.

Moral hazard.

Implications cont.

I If markets do form, they may be distorted: low-riskpeople will tend to underinsure (see Appendix toChapter 10).

I Intuition: if insurers offered contracts which are fair forthe average person, high-risk people would buy andlow-risk would not.

I So we wind up with contracts which are fair for highrisk people, so they fully insure, and contracts whichonly partially insure low risk people.


Insurance.


Lemons.

Moral hazard.

Policy implications.

I The simplest solution to adverse selection is to requireeveryone to insure!

I This observation helps explain nationalized healthinsurance in Canada and parallel policies elsewhere.

I Obama mandate, (to a lesser extent) group insurancepolicies.

I Policies which prevent insurers from acquiringinformation may backfire, e.g., genetic testing, HIV+status, etc.


Insurance.


Lemons.

Moral hazard.

Moral hazard

I Generally, moral hazard refers to a change in behaviorinduced by the presence of insurance.

I e.g., buy a crappy bike lock if you have good bike theftinsurance.

I In the context of health care, insurance often changesthe price paid out of pocket for care.

I When the price the consumer faces decreases, she maychoose to consume more care. This is a form of moralhazard.

I e.g. Blue Cross pays 50% of a dental procedure. Agiven person with Blue Cross will be more likely tochoose the procedure than if he does not have BlueCross.


Insurance.


Lemons.

Moral hazard.

Moral hazard and demand for care

I How much extra care people consume when insureddepends on the elasticity of demand.

I Insurance implies extra resource costs: the insurer mustcharge a premium that covers the risk and the extracare that an insured person will demand.

I Optimal insurance makes a good tradeoff between thebenefit of reduced risk and the cost of too much care.


Insurance.


Lemons.

Moral hazard.

Moral hazard may lead to overuse of health care

I Suppose we imagine we live in a world in which thedemand curve is the same as the social marginalbenefits world.

I In this world, the competitive equilibrium is efficient.

I Insurance induces consumers to purchase more carethan they would if they faced the full price.

I Under these assumptions, too much care is consumedand market prices are too high.


Insurance.


Lemons.

Moral hazard.


Figure 10.1: The Standard Analysis of Moral Hazard

Figure 10.1: In the standard analysis of moral hazard based on Pauly (1968), health care is assumed to be exchanged in perfectly competitive markets. With no insurance, equilibrium price and quantity are Ppc and PC

NIHC respectively. Full insurance that lowers the price of care to PFI causes consumption to

increase to HCFI. This moral-hazard-induced increase in consumption creates a welfare loss equal to the shaded triangle abHCFI. Hence, the full welfare effects of insurance must consider both the welfare gains from risk reduction and the welfare losses from moral hazard in the health care market. The policy response to combat moral hazard is to impose patient cost-sharing, in this case, raising the price to PCS, reducing utilization to HCCS, and reducing the welfare loss from moral hazard from the triangle abHCFI to the triangle acHCCS.

$

Supply = MPC = MSC

Demand = MPB = MSB

a

HCFI HCCS

PPC

PCS

PFI PCNIHC

Welfare loss from increased utilization

b c


Insurance.


Lemons.

Moral hazard.

Example.

I Suppose demand is given by:

QD = 20− P

where P is the price faced by consumers. Supposesupply is

QS = P


Insurance.


Lemons.

Moral hazard.

Example cont.

I Then in the absence of insurance, the market clearswhen

20− P = P → P = 10,Q = 10.

I Now suppose a only a fraction (θ) of consumerexpenditures are covered by consumers, so θ = 1 meansno insurance and θ = 0 means complete coverage.

I Then the price faced by consumers is P = θPM , wherePM is the market price.


Insurance.


Lemons.

Moral hazard.

Example cont.

I Demand is now

QD = 20− P = 20− θPM

so the market clears when

20− θPM = PM

PM =20

1 + θ= Q


Insurance.


Lemons.

Moral hazard.

I We might then predict:

1. we should be more likely to see insurance marketsagainst risks with little possibility of moral hazard (e.g.,you can buy life insurance but not employmentinsurance).

2. more complete insurance against risks with littlepossibility of moral hazard.

3. insurance contracts which attempt to reduce moralhazard, e.g., no payout if it can be determined yourbicycle wasn’t stolen.


Insurance.


Lemons.

Moral hazard.

Moral hazard cont.

I Insurance then involves a tradeoff: decreasing theamount consumers pay out of pocket:

1. increases welfare because it reduces uncertainty2. decreases welfare because people do not face the correct

incentives to economize on care

I Theory suggests an optimal fraction of the price to bepaid out of pocket.

I In Canada, for “necessary” care the actual fraction iszero!


Insurance.


Lemons.

Moral hazard.

Complications.

I When markets are imperfect, argument may beweakened (or strengthened).

I e.g.: health care provided by a monopolist. Moralhazard increases output, which may correct thedistortion caused by the monopoly.

I Same for positive externalities: market outcomeinvolves too few treatments, so increase due totreatments may be good or bad.


Insurance.


Lemons.

Moral hazard.


Figure 10.2: Moral Hazard and Welfare Loss with Imperfect Competition

Figure 10.3. In an imperfectly competitive market price is higher than in a competitive market (PNPC vs. PPC) resulting in a lower level of output ( NPC

NIHC vs. PCNIHC ) that is below the socially optimal level.

The introduction of insurance therefore increases utilization from NPCNIHC to HCFI. But because the no-

insurance output level is below the socially optimal level, a portion of this increased utilization (that from NPC

NIHC to PCNIHC ) is welfare improving. The total welfare loss is therefore triangle abHCFI less the

triangle cad. The welfare loss is less than that indicated by the standard analysis that ignores the imperfect competition in the market for health care services.

$

Supply = MPC = MSC

Demand = MPB = MSB

a

HCFI

PPC

PNPC

PFI PCNIHC

b

c

NPCNIHC

d


Insurance.


Lemons.

Moral hazard.

Complications: behavioral

I Behavioral issues: analysis above assumes people arerational and informed, but there is evidence that manypeople do not evaluate some treatments rationally.

I e.g., eliminating a $20 copayment on heart medicationssuch as statins and beta blockers greatly increasedadherence in the U.S., but these drugs have large healtheffects.

I If people are rational and informed, people who wouldtake the drug at $0 but not at $20 must receive lessthan $20 worth of benefits, but evidence from RCTsuggests the improvement in health valued at $3, 000.

I Implication: possible that increase in treatments due toinsurance may not be overuse.


Insurance.


Lemons.

Moral hazard.

Policy.

I Gatekeeper model: people are prevented from frivoloususe of specialist care.

I Managed care (U.S.)

I Capacity control (public systems): reduce utilization bysimply not providing, e.g., many MRI machines.

I Supply-side incentives: attempt to pay physicians.

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