《健康经济学》课件Chapter9.ppt

1、IntroPreviously,we studied:Demand for insuranceRisk aversion but no information asymmetryAkerlofs market for lemonsinformation asymmetry but no risk aversionThe Rothschild-Stiglitz Model(1976)puts these two together.Ch 9|Adverse Selection:The Rothschild-Stiglitz modelThe IH-IS spaceIH-IS spaceRecall

2、 the income-utility spaceTake HE and SE points and bundle them to one point E(endowment point)in IH-IS spacePoint E shows the income of an individual in both the healthy and the sick stateIH-IS spacePoint C represents a partial insurance contractHorizontal shift=premium(r)Vertical shift=payout if si

3、ck(q-r)IH-IS spaceGiven C1,C2,C3,C4,and endowment point E we can make some assumptions:Individual prefers C2 to C1Prefers C1 to C3Cannot compare preference between C1 to C4Cannot compare preferences to ECh 9|Adverse Selection:The Rothschild-Stiglitz modelINDIFFERENCE CURVES IN IH-IS SpaceIndifferenc

4、e curves in IH-IS space1)Downward slopingWilling to give up income in one state if compensated for more income in the other state2)ConvexMore downward-sloping at low levels of IH but flatter at high levelsIS and IH are imperfect substitutesResult of risk aversionCh 9|Adverse Selection:The Rothschild

5、-Stiglitz modelTHE FULL-INSURANCE LINEThe full-insurance lineThe 45%line is the full-insurance lineWhy?What does this have to do with state independence?Any point on this line represents a full insurance contract.Ch 9|Adverse Selection:The Rothschild-Stiglitz modelTHE ZERO-PROFIT LINEThe zero-profit

6、 lineRepresents the set of contracts such that the premium is exactly the same as the expected payout(no profits for insurance company)Zero-profit line runs through endowment point EAlso can be thought of as the actuarially-fair lineThe zero-profit line divides IH-IS space into profitable and unprof

7、itable zonesC1 lies below the zero-profit line and results in profits for insurance companiesC3 lies above the zero-profit line and results in a loss of money for companiesNo company will offer points above zero-profit lineWill customers be willing to take something below the zero-profit line?Ch 9|A

8、dverse Selection:The Rothschild-Stiglitz ModelTHE FEASIBLE CONTRACT WEDGEThe feasible contract wedgeR1=overfull insuranceGet more income if you are sick(implausible contract)R2=under indifference curve going through EIndividual prefers E to any contract offered in this regionR3=northeast of zero-pro

9、fit lineCompanies will lose money on these contractsF=feasible contract wedgeOnly area where both customers and insurance companies want to meetCh 9|Adverse Selection:The Rothschild-Stiglitz ModelFINDING AN EQUILIBRIUMEquilibriumA set of contracts is in equilibrium if:1)All individuals select the co

10、ntract that offers the most utility.2)No contract in the set earns negative profits for the firm offering it.3)There exists no contract or set of contracts outside the set that,if offered,would attract customers and earn at least zero profit.Case#1:symmetric information,homogeneous customersIs the s

11、et E,an equilibrium?lies on a higher indifference curve(satisfies equilibrium condition 1)is below the zero-profit line(satisfies condition 2)But can attract customers away from and still make positive profits(condition 3 violated)Case#1:symmetric information,homogeneous customersThe only valid equi

12、librium:Ch 9|Adverse Selection:The Rothschild-Stiglitz ModelHETEROGENEOUS RISK TYPESHeterogeneous risk typesRobust types have a low probability,p,of getting sickFrail types have a higher probability of getting sickSlope of zero-profit line depends on probability of sicknessWho has a steeper zero-pro

13、fit line?Why?The population zero-profit line will fall between the frail zero-profit line and the robust zero-profit line.Ch 9|Adverse Selection:The Rothschild-Stiglitz ModelINDIFFERENCE CURVES FOR THE ROBUST AND FRAILHeterogeneous risk typesHow do the indifference curves vary for robust and frail i

14、ndividuals?Who values IS more relative to IH?Case#2:symmetric information,heterogeneous customersIdeal contract point lies on an individuals respective zero-profit lineIndifference curves lie tangent to zero-profit lineThese contracts are offered when firms can tell frail and robust individuals apar

15、t and can legally exclude certain risk types from certain contractsThis ideal contract is called the“symmetric information equilibrium”Ch 9|Adverse Selection:The Rothschild-Stiglitz ModelINFORMATION ASYMMETRY AND THE POOLING EQUILIBRIUMPooling equilibriumDefinition a contract that attracts both robu

16、st and frail individuals while also satisfying equilibrium conditions Why is this desirable?Case#3:asymmetric information,heterogeneous customersAny possible pooling equilibrium must be on the population zero-profit lineIf to the right of zero-profit,firm loses moneyIf to the left of zero-profit,the

17、n other firms can enter the marketCase#3:asymmetric information,heterogeneous customersContract:Both frail and robust individuals choose over EFirm makes zero profits because is on the zero-profit lineCase#3:asymmetric information,heterogeneous customersContract:Both frail and robust individuals cho

18、ose over EFirm makes zero profits because is on the zero-profit lineHowever,because robust and frail indifference curves are different slopes,other insurance firms can enter the market at and appeal to the robust individualsno pooling equilibrium can exist!creates adverse selection Only attracts the

19、 robust individualsGood for firm offering because expected payout is low and firms can expect positive profitsBad for firm offering because left with frail individuals and can expect to lose money due to increased payoutsYou can find a to spoil any pooling equilibrium anywhere on the zero-profit lin

20、eCh 9|Adverse Selection:The Rothschild-Stiglitz ModelFINDING A SEPARATING EQUILIBRIUM(SOMETIMES)Separating equilibriumDefinition:a set of contracts where one attracts frail individuals and the other attracts robust individuals,while satisfying equilibrium conditionsSeparating equilibriumRecall:1 and

21、 2 cannot co-exist because frail individuals will move to 2 from 1Need a contract 3 that will not tempt frail individuals to leave 1Separating equilibrium3 lies on the same indifference curve as 1 for frail individuals but most likely choose 1 Separating equilibrium3 lies on the same indifference cu

22、rve as 1 for frail individuals but most likely choose 1 Robust individuals prefer 3 to 1 Thus both robust and frail individuals are maximizing their utilitySeparating equilibriumR1 attracts the frail individuals but not the robust and therefore is unprofitable for a firmR2 both robust and frail are

23、attracted to this region but it is above the population zero-profit line and is therefore unprofitableR3 attracts robust,but is unprofitable for firms3 and 1 are a separating equilibriumSeparating equilibriums can breakExample:too many robust customersCreates new region,R4Who is harmed?When firms ca

24、nnot tell frail or robust individuals apart,frail customers still receive full insurance at an actuarially fair priceThe robust receive inferior insurance contracts that are not as full as they like the robust are quantity constrainedDoes this suggest the robust and the frail could make a pareto-imp

25、roving trade?Ch 9|Adverse Selection:The Rothschild-Stiglitz ModelCAN MARKETS SOLVE ADVERSE SELECTION?Solving adverse selectionGovernment forces everyone to buy the contract at the intersection of the full-insurance line and the population zero-profit lineBut there could be free market solutions,unde

26、r one crucial assumption:Health differences between robust and frail only appear over time as customers age.Solving adverse selectionLifetime insurance contractTwo customers pool together at age 18 and make a lifelong,contractually-binding commitmentBy age 50,one is robust and one is frailThis“solve

27、s”adverse selection but creates antagonistic relationships and may be legally unenforceable.Solving adverse selectionGuaranteed renewable contractPremiums are frontloaded so that robust and frail both want to remain in the contract voluntarilyBut still a problem:customers cant switch insurers so the

28、re is no competitive pressureCochrane lifetime contractInsurers also provide premium insuranceExample:If someone is diagnosed with cancer,they get a windfall payment to afford future health insurance premiums that will be very highConclusionThe Rothschild-Stiglitz model makes two major predictionsPooling equilibria cannot existIf a separating equilibrium exists,robust individuals will be quantity constrainedDoes the empirical evidence support this?