principal-agent modeling

1、1,Principal-agent Modeling 責(zé)任代理模式,Dr. Chak-Tong Chau 仇澤棠博士U.S. Fulbright Professor中美交流富布萊特教授,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,2,我請(qǐng)您們考慮一些問題,A small medical insurance scenario 一個(gè)醫(yī)療保健的問題When you ha

2、ve a small illness, do you normally see your doctor? 當(dāng)你有小病的時(shí)候，你會(huì)不會(huì)自費(fèi)看醫(yī)生？What about, if your firm pay for your expense?但是，如果是單位付錢呢，那又怎樣？,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,3,我請(qǐng)您們考慮一些問題,A car mainte

3、nance scenario 一個(gè)汽車維修的問題Your car is being rented for 2 months. Supposedly, it needs oiling every month. How likely you will remember to do so?你的汽車是租來用兩個(gè)月的，它需要每月潤(rùn)滑上油一次。你會(huì)不會(huì)依時(shí)地去上油？How about if this is your own car?

4、如果這是你自己的汽車，你又會(huì)不會(huì)去做？,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,4,我請(qǐng)您們考慮一些問題,A medical insurance problem 自費(fèi)醫(yī)療保險(xiǎn)的問題When we purchase medical insurance, the insurance company usually requires that you disclose yo

5、ur medical history. Pre-conditions are usually excluded from the coverage.購(gòu)買保險(xiǎn)的時(shí)候，它們通常要求你列出你的病歷。但是如果你有大病的話，很可能保險(xiǎn)公司不愿意受保。,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,5,我請(qǐng)您們考慮一些問題,If you do in fact have some maj

6、or medical problems that require expensive treatments, would you disclose these problems?如果你真的有大病, 你會(huì)不會(huì)真實(shí)地上報(bào)？What do all these tell us about certain human behavior?這些問題表明了一些什么的人性行為？,Dr. Chak-Tong Chau,Fulbright Gu

7、est Lecture Materials,6,Agency Problems and Behavior代理人的行為與問題,A moral hazard problem (道德危機(jī)問題)when an individual has an incentive to deviate from the contract and take self-interested actions because the other party ha

8、s insufficient information to know if the contract was honored.醫(yī)療保健 雖然我知道我與雇主的契約明確列出我不要浪費(fèi)公司的資源。但是用公司的好過用我的嘛！而且公司又不會(huì)知道我未能遵守契約。,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,7,Agency Problems and Behavior代理人的行為與問

9、題,A horizon problem 水平界線問題If one party’s risk or compensation is not the same as the other party’s, the one with a shorter horizon will tend to secretly maximize the short-term benefits, at the expense of the other lon

10、ger-term party.汽車維修 我明白汽車不維修壽命不會(huì)長(zhǎng)。但是，兩個(gè)月以后這車子變成怎么樣與我無關(guān)了吧。,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,8,Agency Problems and Behavior代理人的行為與問題,An adverse selection problem 逆向選擇問題The tendency of individuals w

11、ith private information about something that affects a potential trading partner’s benefits to make offers that are detrimental to the trading partner.自費(fèi)醫(yī)療保險(xiǎn):雖然我知道保險(xiǎn)公司需要知道我的病歷從而決定保險(xiǎn)費(fèi)。但是誠(chéng)實(shí)的代價(jià)是較高的費(fèi)用。此外，我不說，誰知道。,Dr. Chak-

12、Tong Chau,Fulbright Guest Lecture Materials,9,誰是代理人？什么是代理成本？,An agent is someone who has certain special expertise that is desired by the principal to use for his/her benefits. The agent is usually risk adverse, has deci

13、sion rights to manage, but does not own, the organization’s assets. 代理人(agent) 是任何人在公司有決策權(quán)力，但是并非產(chǎn)權(quán)的最終所有者。代理人通常有較佳的專長(zhǎng)，更好的資訊，和對(duì)風(fēng)險(xiǎn)抱保守的態(tài)度(risk adverse)。,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,10,誰是代理人？什么是代理成

14、本？,There are three (3) types of agency costs. 代理成本有三類：設(shè)計(jì)限制性契約的成本 (bonding costs)建立監(jiān)督制度的成本 (monitoring costs)剩餘的損耗 (residual loss)Note that some costs are bornt by the principal but some are bornt by the agent.注意的是，

15、有時(shí)這些成本是由委托人(principal)負(fù)擔(dān)。不過有時(shí)這些成本是由代理人自己負(fù)擔(dān)的。,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,11,Agency Costs,Bonding costs – costs incurred, before entering the contract, to convince the principal that such agency r

16、elationship will not result in the above-mentioned agency problems. Examples are: reputation building, 3rd party guarantor, etc.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,12,Agency Costs,Monitoring costs – cos

17、ts incurred, after entering the contract, to ensure that such agency problems will not arise. Examples include auditing and inspection costs.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,13,Agency Costs,Residual

18、loss – loss unavoidably arise, despite the bonding and monitoring costs, the contract still cannot yield the utmost benefits, because:the agency problems do arise, ordue to the suspicion of the agency problems, the pri

19、ncipal refuses to pay the agent compensations that fully reflect his/her efforts.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,14,Examples of the Principal-agent Model,Dr. Chak-Tong Chau,Fulbright Guest Lecture M

20、aterials,15,Examples of the Principal-agent Model,,,Agent’s Utility Function: Xa½ - e2 ? 100 where: Xa = agent’s compensationse = the effort level used by the agent,Question 1: If you were the principal in ent

21、ering the contract, which level of effort (e1, e2, or e3) would you demand?,Question 2: If you, the principal, can closely monitor and observe the agent at all time, what are the amount andcondition of payment? And, w

22、hat is the expected payoff for the principal?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,16,Now, let’s assume that you cannot monitor and observethe agent directly. What would you, as the agent, do?,Now, can

23、you see the agency problems here?,Is it likely to have the “adverse selection” problem?,How about the “moral hazard” problem?,And, the horizon problem? Residual loss?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,

24、17,What can we say, up to this point?,Under condition of unobservability (incomplete information), fixed payments to agents (i.e. workers, employees) most likely do not work.What are then the alternatives?We can give t

25、he principal a fixed payment instead.Or, we can come up with an “incentive compatible” conditional contract.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,18,Fixed Payment to the Principal,Consider this new contr

26、act under which the principal gets$32,750 no matter what happens and the agent keeps therest. Will this work?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,19,Fixed Payment to the Principal,Thus, numerically thi

27、s will work to ensure that the agent gives the highest effort.However, there is nonetheless a loss to the principal (33,504-32,750)=754 which is in a sense a monitoring cost (maximum cost to pay for an information syste

28、m to reveal the agent’s effort level).But the most fundamental problem is that this type of contracts violates the “risk adverse” nature of the agent. Now the agent becomes the principal!,Dr. Chak-Tong Chau,Fulbright Gu

29、est Lecture Materials,20,Incentive Compatible Contract – Problem Setup,Maximize (55,000 – R55)Φ55(e1) + (40,000-R40)Φ40 (e1),Subject to:,R55½Φ55(e1) + R40½Φ40(e1) - e12 = 100,R55½Φ55(e1) + R40½Φ40(e1)

30、 - e12 ? R55½Φ55(e2) + R40½Φ40(e2) – e22,R55½Φ55(e1) + R40½Φ40(e1) - e12 ? R55½Φ55(e3) + R40½Φ40(e3) – e32,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,21,Incentive Compatible Contra

31、ct – Specific Solutions,Maximize (55,000 – R55)0.8 + (40,000-R40)0.2,Subject to:,R55½(0.8) + R40½(0.2) - 36 = 100,R55½(0.8) + R40½(0.2) - 36 ? R55½(0.6) + R40½Φ40(0.4) – 25,R55½(0.8) +

32、R40½(0.2) - 36 ? R55½(0.3) + R40½(0.7) – 16,Solutions:R55 = 21,609 R40 = 8,464Expected payoffs:Principal = 33,020Agent = 18,980,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,22,Summary

33、of Different Contracts,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,23,What do we know from these?,The best case scenario for the principal is when he can observe the agent’s effort level directly.The worst case

34、 scenario to the principal appears to be simply charging a fixed rent.The difference between the two ($754) represents the maximum amount to pay for an information system to reveal the agent’s effort.The middle, 2nd be

35、st solution (incentive compatible contract) may not always be the next best thing though!,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,24,Let’s say that we set the two variables, R55 and R40, to be18,769 and 11,

36、449 respectively.,Now, the principal is telling the agent NOT to work hard!,The $33,159 is actually better than the $33,020 under “incentive compatible” contract!,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,25,A

37、 Few Cautionary Remarks,This model presented here is a single-period model. Multiple-period (repeated games) can give very different answers.There can be multiple principals as well as multiple agents in the model. Such

38、 models, however, become extremely complex.Information systems are not considered here.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,26,Concluding Remarks,The Principal-agent model is theoretical elegant but mat

39、hematically tedious to use.Empirical (real-life) evidence seems to support the model well.The challenges, in my opinion, include: to come up with useful, testable hypotheses;to extend the model to more complex, but r