CHAPTER 29 Job market signaling Market for lemons 1-1

Transcription

1 . CHAPTER 29 Job market signaling Market for lemons 1-1

2 Two applications of PBE A PBE insist on rationality of beliefs as well as of strategies: Definition: Consider a pair (s,b) consisting of a profile of strategies and beliefs ate every information set. We say (s,b) is a Perfect Bayesian Equilibrium (PBE) it specifies that (1) each player s strategy is optimal, given his beliefs and the other players strategies (2) beliefs are updated by Bayes rule whenever applicable This concept yields two insights today: -education as a signal of ability in job market -inefficient markets if participants asymmetrically informed 1-2

3 Why is college education valuable? A college education has various benefits that are intuitive: -learning is fun - building a future network of colleagues - practicing time-management, presentation, preparation, - increasing one s productivity Michael Spence shared the 2001 Economics Nobel for his model of a subtler benefit: Education signals one s ability to prospective employers We argue by assumingthat a college education has none of the above benefitsyet showingthat some invest in it, just to be deemed as highly able by prospective employers 1-3

4 Educational signaling Nature endows Person with ability that is Highor Low Ability known to person, not to employer-firm incomplete info Person, knowing her ability, chooses b/w Education or None Firm observes education, makes person Manager or Clerk Education costs Person 4, 7 according as High or Low ability Education does not affect firm s profit (only manager s ability) 1-4

5 Separating equilibrium implies education signals ability Higher ability is defined by lower utility cost of education In a separating PBE, persons with different abilities acquire different educations. By Bayes rule, firm s belief about ability must be correct So in a separating PBE, education effectively signals ability We will verify that the following separating (s,b) is a PBE: -s Person : If High ability, get Education; if Low ability, Not -s Firm : If Educated, hire as Manager; if Not, hire as Clerk -b : b(e) = 1, b(n) = 0 ( q, p in the efg) Recall, b: {E,N} [0,1] is firm s assessment of probability person s ability is High. Here, it is for sure High if educated, for sure Low if uneducated Note, it is this belief that makes education an effective signal of ability 1-5

6 Is this separating (s, b) a bona fide PBE? It is clear that this is separating It is clear that this belief is consistent with Bayes rule: Given person s strategy, all educated applicants are of high ability, all uneducated ones are of low ability Bayes requires firm to get it believe educated = High, uneducated = Low The question of whether this is a PBE is then just the question of whether the person s educational choices are optimal, anticipating firm s elitist belief in particular, is it really optimal for a Low ability person not to get educated and become a Clerk, rather than get educated and become a Manager? 1-6

7 Verification -s Person : If High ability, get Education; if Low ability, Not -s Firm : If Educated, hire as Manager; if Not, hire as Clerk -b : b(e) = 1, b(n) = 0 High type: E leads via M to +6, N leads via C to +4: E optimal Low type: E leads via M to +0, N leads via C to +3: N optimal Firm observing E: M leads to +10 and C to +4: M is optimal Firm observing N: If N, M leads to +0 and C to +4: C is optimal 1-7

8 Discussion -theory This PBE is inefficient, because a more efficient one would have High not acquire costly, useless education The PBE completes the Firm s incomplete information about the job applicant s ability by separating signals Though the Firm benefits (by correctly employing applicant) from deducing ability (by educational signal), it pays none of the cost of the signal the high ability type pays all. For a low ability type, the pay raise from becoming educated (pretending to be high ability) is not worth the pain. So education has a value as a signal, above and beyondany value as a productivity enhancer, fun generator, etc 1-8

9 Discussion -data Empirically, is there evidence that education is a signal of ability/productivity? If so, how large is this educational signal s value? One studyestimates GED s signaling value to boost earnings by 10-19%. Another studyestimates it to be small, if employers upon hiring can observe performance that is correlated with ability/productivity, even if such learning is slow. Further, it finds that the longer the job experirnce, the smaller the educational signal s value (intuitively, job performance becomes the more informative and relevant signal) 1-9

10 One other equilibrium There is one other PBE. Case-by-case: Separating PBE with NE (N if High, E is Low)?If so, then belief would be b(e)=0, b(n)=1 so Low type should choose N instead (more pay, less pain) and is not optimizing. No such PBE. Pooling with EE?If so, b(e) = prior = 1/3, and firm s optimal choice is C. But then Low type gets a negative payoff, should choose N instead, and is not optimizing. No such PBE. Pooling with NN?If so, b(e) = unrestricted, b(n) = prior = 1/3. Firm s optimal choice is CC if b(e) < 2/5 (pessimistic). Both types optimally choose Not educating, anticipating CC : s Person : NN s Firm : CC b: b(e) < 2/5, b(n) = 1/3 Interestingly, it is the firm s pessimistic attitude in an event that never occurs that underlies this (inefficient) PBE. 1-10

11 Market for lemons Lemon, peach is slang for used car of poor, good quality. Key feature of the private market for lemons is that seller of used car knows more about its quality than does the buyer. Traders said to have asymmetric information George Akerlof of UC-Berkeley shared the 2001 Economics Nobel for his insight that asymmetric information can cause trading to cease even when trade is efficient. Again, incomplete information can make equilibria inefficient. 1-11

12 Asymmetrically informed traders Car s quality (Peach, Lemon) random to buyer, known to seller Jerry (buyer) and Freddie (seller) meet to possibly trade Trade is efficient, for car is worth more to buyer than to seller: If Peach, worth 3000 > 2000; if Lemon, worth 1000 > 0. If no trade, buyer gets 0, seller gets 2000 or 0 (keeps car) If trade at p, buyer gets 3000-p or 1000-p, seller gets p (sells) Trade occurs if and only if both prefer trade T to no trade N 1-12

13 No pooling equilibrium if used cars typically lemons This p-efg is of incomplete information: seller of two types A pooling strategy has seller behave the same for any type and Bayes rule implies belief b(t) = prior = nature s q For which prices p is the following (s,b) a PBE? s buyer : T (choose to buy) s seller : T P T L (choose to sell) b= q,q - Buyer: Given belief and seller s strategy, payoff of buying is (q (1-q)1000) p = q2000 p and at least that of not (0) iff price is low enough, p q Seller: Selling pays off (p) at least as well as not, for any type, iff p Trade occurs(optimal for both) iff 2000 p q2000 Such a p exists iff q ½ (nature is peachy). Conclusion: There is no pooling PBE if used cars tend to be lemons 1-13

14 A separating equilibrium: buyers skeptical, only lemons sold A separating strategy has seller behave according to type N P T L (sell only lemons) or T P N L (sell only peaches) Consider former. Bayes rule implies belief b(t) = 0, i.e. conditional on knowing that only lemons are sold, if seller wishes to sell, zero probability car is peach. Optimality: Buyer: Given this belief, buyer chooses trade iff p 1000 Seller: Given p 1000, seller chooses trade iff lemon (peach is worth 2000 to him, lemon is worth 0) So for any p 1000 this is a PBE: s buyer : T (choose to buy) s seller : N P T L (sell lemons) b= 0, any This PBE is inefficient, as peach not traded 1-14

15 No separating equilibrium with only peaches sold A separating strategy has seller behave according to type N P T L (sell only lemons) or T P N L (sell only peaches) Consider latter. Bayes rule implies belief b(t) = 1, i.e. conditional on knowing that only peaches are sold, if seller wishes to sell, unit probability car is peach. Optimality: Buyer: Given this belief, buyer chooses trade iff p 3000 Seller: p 2000 needed for seller to choose to sell a peach, but then it also chooses to sell lemon (worth less to him) that is, T P N L is not optimal Conclusion: No separating PBE with only peaches sold 1-15

16 Discussion When seller is informed better than buyer of object s quality, trade of high quality good is impaired: -there is no pooling PBE, if quality is typically poor - only separating PBE has only low quality object traded -so if quality is typically poor, high quality is never traded What solutions are there? Signaling high quality is one solution: -Sale with warranty: seller offers to pay for repairs - Sale with inspection: seller lets buyer hire mechanic 1-16