Inferring a worker’s productivity

1. Issues in personnel economics Inferring a worker’s productivity In theory, a firm should hire a worker only if the value of his marginal product exceeds the pay he receives. (Marginal benefit vs. marginal cost) Ideally, the marginal product of each worker is known. For example, if you believe that hiring Mr. Doe as a manager will increase your profit by $50,000 a year, then $50,000 is the maximum amount you should be paying him. In most real-world cases, however, the future MP of a worker is unknown.

2. Worker’s marginal product depends on his inherent characteristics (talent, skills, physical strength, etc.) and the effort he decides to put in the job. All those variables are known to the worker but not to the firm – an example of asymmetric information. Keeping a worker who is not fit for the job is costly even when it is done for a limited time. If the firm wants to increase its chances of hiring the right person, it can use remedies common to any market with asymmetric information.

3. Screening– the uninformed party (the firm) does somethingthat gives it a better idea about the future productivity of a worker. • This effort is usually costly. (Keep in mind that future productivity cannot be determined with certainty. We can only measure some characteristic that we believe is correlated with abilities.)

5. Screening applicants is more justified when • The degree of correlation between the measured variable and the abilities is high. • The cost of screening is low. • A large portion of applicants will be refused employment as a result. • The spread in applicants’ abilities is large.

6. 2. Signaling– the informed party does something to signal their “type” to the uninformed party. In the labor market, high-ability workers signal their ability to the firm, thus distinguishing themselves from low-ability individuals. Examples: • Credentials (extra lines on the resume) • Education (CPA, Ph.D., bar exam, MBA,…)

7. As always, a signal has to be credible. Therefore, it has to be hard for the other type(s) to mimic it. The signal is more credible when: Obtaining the credential is easier for high-ability workers but more difficult for low-ability workers. • Also note that low-ability workers will try the harder to mimic the signal of high ability the more worthwhile it is to do so. Hence the signal is more credible when the difference in pay between high- and low-ability workers is small .

8. Education as a signal Model developed by Spence (a 2001 Nobel laureate). What do we learn in college? How relevant is the knowledge gained in college for our future career? If it is, then why do many firms, upon hiring college graduates, send them to some sort of job-specific training? What if a college degree (or our GPA) is nothing more than a signal of our abilities or our commitment to hard work?

9. Let us take this hypothesis to an extreme and assume (for the purpose of this model) that college, or any other form of education does not affect our innate abilities. Instead, it is sort of a tryout. Let’s say there are two different types of individuals in the economy, those of high ability and those of low ability. Once hired, they are capable of producing different marginal product, the high-ability types being more productive. Each worker is paid the value of his marginal product. Each worker knows his own type, but the firms don’t (hence we are dealing with asymmetric information).

10. IF firms HAD perfect information, they would pay each type what that type deserves, wHandwL, respectively. wH > wL Since firms cannot distinguish between high and low type workers, they pay everyone the same wage, equal to the expected value of the marginal product. Let us assume that the shares of the two types in the population are equal, αH= αL= 0.5. Then the average wage, equal to the expected value of the marginal product, is wAV= αH · wH + αL · wL = (wH + wL)/2. Because of incomplete information, high type workers are underpaid while low type are overpaid.

11. Now, suppose anyone can signal his ability by getting a college degree (or another form of education). Education is obtained at a cost. (This cost is not necessarily monetary – it can be expressed in the time spent and the amount of misery a person has to go through to get a degree.) This cost is different for the two types, cH < cL.

12. The selection of an equilibrium depends on model parameters.

13. Example 1. wH = 400 wL = 200(wH > wL) cH = 60 cL = 120(cH < cL)

14. Example 1. wH = 400 wL = 200(wH > wL) cH = 60 cL = 120(cH < cL) Under these parameters, everything works as it should – High ability individuals get education and get recognized as high ability; Low-ability don’t

15. Example 2. wH = 400 wL = 200(wH > wL) cH = 40 cL = 60(cH < cL) (getting education gets easier)

16. Example 2. wH = 400 wL = 200(wH > wL) cH = 40 cL = 60(cH < cL) (getting education gets easier) Both types choose to get education. Education is no longer a signal of abilities.

17. Formal definitions of the two types of equilibria: Separating equilibrium – a situation when it is possible to differentiate between the two types of people (or products, as in the lemons model). – see Example 1. Pooling equilibrium – different types behave alike and are therefore treated alike, as in Example 2.

18. It is possible to show that, • If wH - wL > 2 cL, then both types get education. A pooling equilibrium occurs. – Ex.2 • If 2 cL > wH - wL > 2 cH, then all high-ability individuals choose to get a degree, thus separating themselves from low-ability types. – Ex.1 A separating equilibrium occurs. • If 2 cH > wH - wL > cH, then either of the two equilibria may occur. • If wH - wL < cH, then none of the types chooses to get a degree. Another pooling equilibrium.

19. cH 2cH 2cL wH - wL • wH – wL: Which type gets degree: none none or H only both H only Type of equilibrium: Pooling Pooling or SeparatingPooling separating

20. Separating equilibrium leads to higher efficiency (think of an analogy with the lemons model). In order for education to serve as a signal, the cost of getting it has to be neither too high nor too low. This model raises several interesting issues. • What happens as getting a degree gets easier? (See example 2 above.) • Top schools and “regular” schools: In which case a degree is a more credible signal? Why?