Education Signaling & Screening

1. Education Signaling & Screening Lent Term Lecture 5 Dr. Radha Iyengar

2. The course so far… Skill biased changes  increased returns to ed (lecture 2) Model of human acquisition (lecture 3) Variation in marginal costs (lecture 4) Estimating returns to schooling Big differences in Wage Structure across groups & time periods (lecture 1) Signaling/Screening Models (lecture 5) Credit Constraints Group/Cohort specific differences unexplained by general skills (lectures 6-10) Education Production Variation in marginal benefits Specific Capital Discrimination Illegal Labor Markets

3. Today • Sorting Models (signaling and screening) • Signalling models as a way of revealing underlying variation in the cost parameter (e.g. ability)—Basic Spence Model • Such models may lead to multiple equilibria which • Are not necessarily socially optimal (e.g. lead to over-investment in schooling because of divergence between private returns and total returns) • Have very different welfare implications

4. Human Capital & Information • So far, we’ve had individuals investing in education as productivity enhancing • Employers know the value of that enhancement and it’s the same for everyone at that level of investment • Don’t worry about underlying parameters that led employees to choose that level of education • The level of schooling perfectly describes the productivity of all workers with that level of education

5. Heterogeneity • There is some heterogeneity in the underlying ability of individuals • This underlying variation may be directly related to productivity (e.g. better at producing cogs) or indirectly related (e.g. less likely to take sick days, shirk, etc.) • The variation in ability also varies the cost of education (the “signal”)

6. Imperfect Information • Individuals know their own cost parameter • employers do not • we will consider later whether the econometrician studying the market can observe the parameter • Key Idea: some type of cost information which is negatively correlated with ability. • This is a prerequisite for the an observable, alterable characteristic to be a persistently informative signal in the market.

7. Screening (Stiglitz, 1975) • What if employer required a “screening” criteria (you have to take a test) • This “screen” is more costly for low ability types than high ability types • Employers want types to reveal themselves by having H types take the screen and L types not • Whether this actually happens on relative costs of screen (c) and fraction of H versus L types (λ)

8. Why? • The screen costs cHfor H types and cL for L types • if wH – c < λ wH + (1- λ) wL • High ability types have no incentive to screen because by they make more in the pooling equilibrium • Does this make sense as a sustainable equilibrium? (We’ll do this formally in a bit)

9. Some Big Points • Education when used as a screening mechanism (e.g. if education provides information as well as skills), it can actually lead to worse social conditions • Why? To begin note that: • Private and public returns to schooling differ • There is a region of tradeoff between firms and workers • Restrictions education as screening may just shift screening and actually lead to worse conditions

10. Private-Public Returns differ • Social returns to education differ from private returns. • while screening has productivity returns, it will decrease equality. • For some regions there is a tradeoff between efficiency and distributional concerns.

11. Over-consumption • There is also a region in which education expenditure may both increase inequality and decrease net national income. • Overspending happens because the median voter does not pay the median share of education and thus has an incentive to over consume—especially in publicly funded schools

12. For these things to be true • Highly stylized model and may not hold without these assumptions • The more able are better in every relevant sense, so there is an unambiguous ranking of abilities • Labor supply is inelastic • Individuals have perfect information • there is not method of on-the-job screening • the screening is accurate • The information acquired is “general”, i.e. not firm specific

13. The way the model works • There is an information feedback loop. • As new market information comes into an employer (through either observation, hiring, etc.) they form beliefs on productive capabilities • These are related to observable signals and adjust their beliefs accordingly • To start consider a case where employers get 1 signal, pre-hiring, and then do not learn/adjust wages

14. Model Set-up • Two types of workers • H: productivity level yH • L: productivity level yL • Fraction of H workers in the population is λ with the fraction of L workers then being (1 – λ) • Workers know their type, employers don’t

15. Education Investment • Individuals can engage in education investment or not so that the choose education level eЄ {0, 1} • If choose e=1, there is a cost • H: cH • L: cL • Education does not increase theproductivity of either type of worker • After choosing eworkers enter the labor market

16. Single Crossing Assumption • Crucial assumption is that: cL > cH • That is, education is more costly for low ability workers. • Makes sure that in the space of education and wages, the indifference curves of high and low types intersect only once.

17. All the Assumptions of the model • Assumptions: • Ability is private information • Absent information, all firms (which are risk neutral) treat individuals the same • Productivity of a single employee cannot bet determined • Single crossing of costs assumption • These together imply that: • Hiring competitive among alarge number of risk-neutral firms • workers will be paid theirexpected productivity

18. Defining an Equilibrium • An equilibrium is when a set of employer beliefs generate offered wage schedules, applicant signaling decisions, hiring and ultimately new market data over time that are consistent with the initial beliefs. • To find an equilibrium: we guess a set of self-confirming beliefs and then check that they are indeed confirmed by the feedback loop.

19. The Equilibria • In this type of game, we use the equilibrium concept: Perfect Bayesian Equilibrium • The striking features are: • there are an infinite number of equilibrium for a given level of education that generates a maximum productivity that perfectly inform the employer • The equilibria are not equivalent in terms of welfare • There are also equilibria that do not perfectly inform the employer. • The assumption of negative correlation between signal cost and productivity is necessary but not sufficient for signaling. We need a significant number of signals

20. Two Classes of Equilibria • In this case: two types of equilibria • Separating: High ability group chooses e = 1 and low ability choose e = 0. Two different contracts are offered wHand wL • Pooling: everyone chooses the same level of education e and everyone gets an average wage wavg

21. Separating Equilibria- 1 • The basic idea: gain in earnings for high ability people enough to justify costs of education, gain in earnings for low ability workers not enough given high costs of education • Condition for equilibria: yH – cH > yL > yH – cL Possible since cH < cL • All high ability workers obtain education, and all low ability workers choose no education

22. Separating Equilibria-2 • Wages (conditional on education) are: • w(e = 1) = yH • w (e = 0) = yL • Notice that these wages are conditioned on education, and not directly on ability, since ability is not observed by employers

23. Separating Equilibria - Firms • Firms: • Given the strategies of workers, a worker with education has productivity yH while a worker with no education has productivity yL • Firms are competitive, so they must offer at most the marginal productivity of labor • Firms cannot offer less than this because rival firms will offer at least MPL • Thus firms cannot profitably deviate from this strategy

24. Separating Equilibria - Workers • High ability worker deviates: choose no education • Will get w (e = 0) = yL • w(e = 1) – cH = yH – cH > yL • Low ability worker deviates: obtaining education e = 1 • the market will treat as a high ability worker, and pay the higher wage w (e = 1) = yH • But yH – cL < yL

25. Separating Equilibria Summary • Education not productivity enhancing but a signal of underlying inherent worker productivity • Education is thus valuable only as a signal • Firms can condition wages on this signal (not the underlying parameter) and if we have single crossing—we can distinguish types

26. Pooling Equilibria • What if the reward to high workers or the cost of low ability workers was too low. Then both low and high ability workers do not obtain education • Suppose the wage structure is • w (e = 1) = (1 – λ)yL + λyH • w (e = 0) = (1 – λ)yL + λyH • This can happen in the situation where: • yH – cH > (1 – λ)yL + λyH • yL > yH – cL • No incentive to deviate by either workers or firms

27. Does Pooling Make Sense? • This equilibrium is being supported by the belief that the worker who gets education is no better than a worker who doesn’t • But education is more costly for low ability workers, so they should be less likely to deviate to obtaining education

28. Intuitive Criterion-1 • The underlying idea: if there exists a type who will never benefit from taking a particular deviation, then the uninformed parties (e.g. firms) should deduce that this deviation is very unlikely to come from this type • The overall conclusion is that if education is a valuable signal, then is that separating equilibria may be more likely than pooling equilibria

29. Intuitive Criteria-2 • This falls within the category of “forward induction” • Rather than solving the game simply backwards, we think about what type of inferences will others derive from a deviation. • Think of a relatively intuitive speech by the deviator along the following lines: • you have to deduce that I must be the high type deviating to choose e = 1 • low types would never ever consider such a deviation because it is not profitable even if they convince you they are the high type • I would find it profitable if I could convince you that I am indeed the high type even if I must bear the cost of the signal

30. Pooling Equilibria Refinement • For low ability individuals: it really doesn’t make sense to deviate because yL> yH – cL but they get (1 – λ)yL+ λyH >yL • Thus any deviation to e = 1 will be by high ability workers ability workers • Firms know this so can offer a wage to those who deviate breaking the pooling equilibrium

31. Continuous Education • Suppose education is continuous e Є[0,∞) • Cost functions for the high and low types are cH(e) and cL(e) • ci(.) is strictly increasing and convex for i = H, L • cH (0) = cL (0) = 0

32. New Single Crossing Property • The single crossing property is now: cH’(e) < cL’(e) for all e Є[0,∞) • This implies that the marginal cost of an additional unit of education is always higher for low types than H types • This is constrains our cost functions to cross only once, at e = 0

33. Single crossing property Illustrated Cost cL(e) cH(e) Education

34. Output for workers • Suppose that the output of the two types as a function of their educations • yH (e) and yL (e) • yH (e) > yL (e) for all e • Education may make you more productive in this model • yH (e) > yH (e’) for e’ > e • But return to education is the combination of that productivity effect and the signaling effect

35. Finding an Equilibrium - 1 • Once again there will be multiple Perfect Bayesian Equilibria • some fully separating (know each type) • some pooling • some semi-separating (get a little of wrong type but mostly separate) • To narrow this down let’s first find the first-best education level for the low type in the perfect information case (called the “Riley Criterion”) yL’(eL* ) = cL’(el* )

36. Finding Equilibrium - 2 • Then we can write the incentive compatibility constraint for the low type • Low type obtains education eL • the low type does not try to mimic the high type. yL(eL*) – cL(eL*) ≥ w(e) – cL(e) for all e • Let eH be the level of education for high type • Remember we don’t want the low type to imitate the high type • That means this constraint holds as an equality yL(eL ) – cL(eL ) = yH (eH) – cL(eH) • That is: it is not profitable for type L to choose eH and pretend to be an H type

37. Defining the Equilibrium • The equilibrium is then a set of contracts such that: • yL(eL*) = w(eL) • yH(eH) = w(eH) • The characteristics are that: • L types do first best • H types over-invest in education

38. Why does this happen? • It comes from the single-crossing property (SC) and the incentive compatibility constraint (IC): yH(eH) – cH(eH) = yH(eH) – cL(eH) – (cH(eH) – cL(eH)) > yH(eH) – cL(eH) – (cH(eL*) – cL(eL*)) = yL(eL* ) – cL(eL*) – (cH(eL*) – cL(eL*)) = yL (eL*) – cH (eL*) • High ability workers investing in schooling more than they would have done in the perfect information case • Define yH’(eH* ) = cH’(eH* ) as the first best • Our equilibrium has eH > eH*

39. Diagram of Equilibrium Ed. Levels Ui = w(e) – ci(e) UH* UL* yH(e) UH yL(e) e eH* eL* eH

40. When is there no separating equilibrium? • The separating equilibrium may not exist in the following cases: • If there are self-employment opportunities that can realize the same returns that would have been realized by accurate screening without the screening • If individuals are perfectly certain of their abilities and can demonstrate them on the job • If individuals are very risk averse and not perfectly certain of their abilities

41. The Social benefits from Sorting • If signal/screen costs are low and labor supply is elastic then everyone can be made better off from screening by using an appropriate redistributive tax to compensate the worse off. • If there are returns to group homogeneity, then matching with screening may produce better allocation of labor

42. General Conclusions from Theory • there may be multiple equilibria • The equilibria can be pareto ranked • In both equilibria the presence of the lower type decreases the distorts the investment/wages of the higher type while the presence of the high type gives the low type at least their marginal product and maybe more • Social returns to screening mechanisms (e.g. education) differ from private returns. Which causes a divergence between pareto optimality and equality.

43. Empirical Evidence of Sorting Models • Different types of evidence: • Returns to GED? (Tyler, Munane, Willett) • Do compulsory schooling laws affect schooling levels for higher grades? (Lang and Kropp) • Do degrees matter? (Bedard—class paper) • Some of these are more informative in distinguishing the signaling model from human capital • Strong distinct predictions from models in both cases • Note that education can be both a signal and productivity enhancing • If both models are operating, may be hard to identify which is dominant all the time.

44. Returns to GED (Tyler, Murnane and Willett) • Why is this approach useful? • Passing grades in the Graduate Equivalent Degree (GED) differ by state  individual with the same grade in the GED exam will get a GED in one state, but not in another. • If the score in the exam is an unbiased measure of human capital, and there is no signaling, these two individuals should get the same wages • If the GED is a signal, and employers do not know where the individual took the GED exam, these two individuals should get different wages.

45. State Variation in Standards • TMW use 3 (of the possible seven different passing standards) that existed across the US in 1990. • a minimum score of at least 40 or a mean score of at least 45 • a minimum score of at least 35 and a mean score of at least 45 • a minimum score of at least 40 and a mean score of at least 45

46. Control and treatment groups Pass in some states—fail in others

47. Designing the Experiments • “Experiment 4” variation in GED status by state is in group 4 • the treatment states are those states that award a GED in score groups 4 and higher • the comparison states are those that award a GED in score groups 5 and higher • “Experiment 3” variation in GED status by state is in group 3 • the treatment states are those states that award a GED in score groups 3 and higher • the comparison states are those that award a GED in score groups 5 and higher • “Experiment 3*” variation in GED status by state is in group 3 • the treatment states are those states that award a GED in score groups 3 and higher • the comparison states are those that award a GED in score groups 4 and higher.

48. Difference-in-Difference Estimates

50. Why might results for minorities differ? -1 • Many minority men take GED while incarcerated • the stigma of incarceration may depress the post-prison earnings of dropouts, and eliminate any positive signaling value of the GED credential. • Many dropouts who obtained a GED while incarcerated may have zero earnings five years later because they are still in prison.