Adverse Selection , Signaling , Screening.ppt

1、Adverse Selection , Signaling , Screening,Introduction : One of the implicit assumption of the fundamental welfare theorems is that the characteristics of all commodities are observable to all market participants. Without this condition , distinct markets cannot exist for goods having different char

2、acteristics , and so the complete markets assumption cannot hold . In reality , however , this kind of information is often asymmetrically held by market participants 1- used car markets 2- firms hiring the worker and does not know the innate ability of the workers ,3- automobile insurance,13 MAS_CO

3、LLEL CH,1,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,1- How do we characterize market equilibrium in the presence of asymmetric information. 2- what are the properties of this equilibrium.3- Are there possibilities for welfare-improving market equilibrium. In the

4、 presence of asymmetric information , market equilibrium often fails to be pareto-optimal . Constrained pareto-optimal allocation are all allocations that cannot be pareto improved upon by a central authorities who, like market participants , cannot observe individuals privately held information . S

5、ignaling ; informed individuals may find ways to signal information about their unobservable knowledge through observable actions. Seller of a used car could offer to allow a prospective buyer to take the car to a mechanic . Screening ; the possibility that uninformed parties may develop mechanism t

6、o distinguish , or screen , informed individuals who have different information . An insurance company may offer two policies ; one with no deductible at a high premium and another with a high deductible at a much lower premium .,13 MAS_COLLEL CH,2,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selec

7、tion , Signaling , Screening,Informational Asymmetric and Adverse Selection ; Assumptions ; Many identical potential firms that can hire workers . Constant return to scale technology . Labor is the only input . Firms are risk neutral , Expected Profit maximize and price taker Price of the firms outp

8、ut equals to one .i is the expected level of productivity for each labor i. L , H R denotes the set of possible worker productivity levels ls where 0 L H F() = proportion of workers with productivity of or less .there are at least two types of workers . Total number of workers is Nworkers seek to ma

9、ximize the amount of income they earn . r() is the opportunity cost to a worker of type of accepting employment .,13 MAS_COLLEL CH,3,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,1-a- Competitive equilibrium when workers productivity level is observable.There is a d

10、istinct equilibrium wage w* () for each type of worker . II . Given the competitive and constant return to scale nature of the firm in the equilibrium we will have w* () = VMP = (1) () = As would be expected from the first fundamental welfare theorem , this competitive equilibrium is Pareto-Optimal

11、. Since the perfectly competitive equilibrium is prevailed and in this relation wage rate is equal to the value of marginal product . Workers are willing to be employed if the opportunity cost of getting employed for them is less than the wage they will be paid. So when productivity level is observe

12、d , each worker will be paid based her VMP and the result is pareto-optimal.,13 MAS_COLLEL CH,4,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,1-b- Competitive equilibrium when workers productivity level is not observable When workers type in terms of their productiv

13、ity is not observable , the wage rate should be independent of a workers type and we will have a single wage rate for all the workers. The set of worker types who are willing to accept employment at wage rate w are those ; (w) = :r() w If a firm believes that the average productivity of workers who

14、accept employment is , its demand for a labor is given by z(w) : z(w) = 0 , if w If worker type in the set are accepting employment offers in a competitive equilibrium . Then = E ; This implies that demand for labor will be equal to supply of labor if and only if = w = E ; ,13 MAS_COLLEL CH,5,ADVERS

15、E SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,definition 13.B.1: In the competitive labor market model with unobservable worker productivity levels , a competitive equilibrium is a wage rate w* and a set workers types who accept employment such that ;condition 13.B.6 The

16、above condition involves rational expectations on the part of the firms. That is , firms correctly anticipate the average productivity of those workers who accept employment in the equilibrium . Asymmetric Information and Pareto Inefficiency : typically a competitive equilibrium defined in the 1-a s

17、ection will fail to be pareto-optimal in Asymmetric Information case . Suppose that r()= r for all . And F(r) = (0,1). That is ; pareto optimal allocation of labor has workers with r accepting employment at a firm , and those with r not doing so .,13 MAS_COLLEL CH,6,ADVERSE SELECTION SIGNALING SCREE

18、NING,Adverse Selection , Signaling , Screening,If we consider a competitive equilibrium when r() = r for all . The equilibrium wage rate (w* ) should be equal to the expected productivity level which is E. So if E r , then all the workers accept employment at a firm , and if E r , then none will acc

19、ept . Which type of equilibrium arises depends on the relative fraction of good and bad workers. a- If there is high fraction of low-productivity workers , because firms cannot distinguish good from bad one , they will be unwilling to hire any workers at a wage rate ( at least r )that is sufficient

20、to have them accept employment . Too few workers are employed compared to pareto- optimal allocation. b- on the other hand if there are very few low productivity workers , then the average productivity of workers will be above r , and so the firms will be willing to hire workers at a wage rate that

21、they willing to accept . Too many workers are employed compared to pareto-optimal allocation. Cause of this failure of competitive allocation to be pareto-optimal is the inability of firms to distinguish among workers of different productivities which is the reason why market cannot allocate workers

22、 efficiently between firms and the best alternative situation .,13 MAS_COLLEL CH,7,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,Adverse selection and market unraveling r() rises with . Adverse selection is said to occur when an informed individual trading decision

23、depends on her unobservable characteristics in a manner that adversely affects the uninformed agent in the market When a less capable workers are willing to accept a firms employment offer at any given wage . Adverse selection can have a striking effect on market equilibrium . To see the power of ad

24、verse selection, suppose that r() for all , and pareto-optimal allocation is prevailing. And r(.) is a strictly increasing function . Which means that workers who are more productive at firm are also more productive at home .,13 MAS_COLLEL CH,8,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection

25、 , Signaling , Screening,It is this assumption that generates adverse selection . Because the payoff of home production is greater for more capable workers , only less capable workers accept employment at any given wage rate . The expected value of worker productivity depends on the wage rate . As w

26、age increase , more productive workers become willing to accept employment at a firm , and average productivity of those workers accepting employment will increase . F(.) has an associated density function f(.) with f() 0 for all . This assures that the average productivity of those workers willing

27、to accept employment , E ; r()w, varies continuously with wage rate . Equilibrium wage rate = w* which is equal to ;w* = E; r() w* ,8,9,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,We can see the equilibrium in the following figure :,13 MAS_COLLEL CH,10,ADVERSE SEL

28、ECTION SIGNALING SCREENING,W,45o,E; r() w = expected value of who would choose to work for a firm when the prevailing wage is w . Has a minimum value of when w= r(L ) and maximum when w r(H ) .,H,L,r (H),r (L ),w*,w*,H,L,E ,Competitive equilibrium at which w* = E; r() w* All of these workers have av

29、erage productivity equal to w* .,Adverse Selection , Signaling , Screening,We can see from the figure that the market equilibrium need not be efficient . To get the best workers to accept employment at a firm , we need the wage to be at least r(H ). But according to the figure , because of the inabi

30、lity of the firms to observe the productivity of the workers , they could have an expected output of E r(H ) from each worker . This makes the firm loose . The presence of the enough low productivity workers therefore forces the wage down below r(H ) and best workers are driven out of the market . T

31、herefore the average productivity of the workers will fall . Therefore firms are willing to pay further lower wages . This will follow with the next best workers driven out of the market . How far this process can go ? This process can continue until only type L (worst type) accept employment with w

32、* = L . But in this case the firm may not be willing to employ any labor .,13 MAS_COLLEL CH,11,ADVERSE SELECTION SIGNALING SCREENING,Adverse Selection , Signaling , Screening,The competitive equilibrium which is shown in the page 10 need not to be unique . The expected average productivity curve may

33、 intersect the 45 degree line in more than one point .,13 MAS_COLLEL CH,12,ADVERSE SELECTION SIGNALING SCREENING,W1*,W2*,W3*,r(L ),L,H,H,W,E; r() w ,Note that the equilibrium in this figure can be pareto ranked . Firms can earn zero profits in any equilibrium , and workers are better off if the wage

34、 rate is higher . Thus the equilibrium with the higher wage pareto dominates all the others . The low wage , pareto dominated equilibrium may arise because of a coordination failure. The wage is too low because firms expect that the productivity of workers accepting employment is poor and at the sam

35、e time , only the bad workers accept employment precisely because the wage is low .,Adverse Selection , Signaling , Screening,A game theoretical approach Consider the equilibrium wage rate w2* on page 12 . In this equilibrium the firm with a small increase in the wage rate to w w2* would raise its p

36、rofit because it would attract workers with average productivity E ; r()ww ( average productivity is above 45 degree line ) . This could be repeated for any equilibrium point like w1* . Hence it seems unlikely that a model in which firms could change their offered wages would ever lead to this equil

37、ibrium (w1* or w2* ) outline . To be more formal about this idea , we could consider the more formal game theoretical model ; in stage 1 two firma simultaneously announce their wage offers. Then in stage 2 workers decide whether to work for a firm , and , if so , which one .,13 MAS_COLLEL CH,ADVERSE

38、 SELECTION SIGNALING SCREENING,13,Adverse Selection , Signaling , Screening,Constrained pareto-optimal and market intervention presence of asymmetric information often results in market equilibrium that fails to be pareto optimal . Central authority who knows all the agent private information and ca

39、n engage in lump-sum transfers among agents in the economy , can achieve a pareto improvement over these outcomes . In practice , however , a central authority may be no more able to observe agents private information than market participant . So the authorities will face additional constraints in a

40、chieving the pareto optimality. For pareto improving market intervention to be possible in this case , a more sophisticated test must therefore be passed . An allocation that can not be pareto improved by an authority who is unable to observe agents private information is known as a constrained ( or

41、 second-best ) pareto optimum . We might as well simply think of intervention schemes in which authorities run the firm herself and tries to achieve the pareto improvement for the workers . Since they can not distinguish among different types of workers , any differences in lump-sum transfer to or f

42、rom a worker can depend upon whether the worker is employed .,13 MAS_COLLEL CH,AVERSE SELECTION SIGNALING SCREENING,14,Adverse Selection , Signaling , Screening,The authorities offering a wage of we to those accepting employment , and unemployment benefit of wu to those who do not accept the employm

43、ent . Can the competitive equilibria of our adverse selection model be pareto-improved upon in this way . Consider first the competitive equilibria that are pareto dominated by some other competitive equilibria . The equilibrium with wage rate w1* shown in the figure in page 12 . A central authority

44、 who is unable to observe workers types can always implement the best competitive equilibrium . The authorities need to set we = w* , the highest competitive wage , and wu =0 . All workers whose their opportunity cost is less than w* will be employed in the firm and the autorities could balance the

45、budget . Thus , the outcome in such an equilibrium is not a constrained one , since the planner is essentially able to step in and solve the coordination failure that is keeping the market at the low wage equilibrium .,13 MAS_COLLEL CH,ADVERSE SELECTION SIGNALING SCREENING,15,Adverse Selection , Sig

46、naling , Screening,what about the highest-wage competitive equilibrium; as it could be proved any such equilibrium is a constrained pareto optimum in this model . If all workers are employed in the highest wage competitive equilibrium then the outcome is fully pareto-optimumal. So , suppose some are

47、 not employed . Note that for any wage we and unemployment benefit wu offered by the central authorities the set of worker types accepting employment has the form L , H for some it is ; wu + r() we Suppose , then, that the authorities attempts to implement an outcome in which worker types accept emp

48、loyment . To do so, she must choose ;wu + r( ) = we To balance the budget we should have ;we F( ) + wu (1- F( ) =,13 MAS_COLLEL CH,ADVERSE SELECTION SIGNALING SCREENING,16,Adverse Selection , Signaling , Screening,from these two functions we could find :Or equivalently :(1)(2),13 MAS_COLLEL CH,ADVER

49、SE SELECTION SIGNALING SCREENING,17,Adverse Selection , Signaling , Screening,If * denotes the highest worker type who accept employment in the highest wage competitive equilibrium . We know that ; r(* ) = E; * ) . Substituting this into (1) and (2) we will find that ;wu (*) =0 , and we (*) = r(* )

50、. Thus when the authorities set we will get exactly the same result as in the highest-wage competitive equilibrium . It could be examined and see that a pareto improvement is not possible by setting . Indeed in the adverse selection model the authority in unable to create a Pareto Improvement as long as the highest wage competitive equilibrium is the market outcome . More generally , whether pareto-improvement market intervention is possible in situation of asymmetric information depends on the specific of the market under study and on which equilibrium result .,