Matching as Signal

1. Matching as Signal Kyushu University Nobuaki Hori 産業組織研究会

2. Introduction • Motivation • Why is ranking of universities (vertically and/or horizontally) stable, (in some cases,) irrelevantly to the quality of research or instruction ? • ⇒Matching + Signaling • Matching between workers and schools • Names of universities work as “signals”

3. Introduction • Signaling with a continuum of differential types • Mailath (1987): direct choice of vertical signal (education) • This model : matching　→　Pooling is robust • Matching between the workers and univ. • Epple, Romano and Sieg (2006), Akabayashi and Naoi (2008) ↑Univ. are intrinsically differentiated. • This model: potentially identical

4. Introduction • Matching tournament • Cole, Mailath and Postlewaite (1992, 95, 98, 2001), Hopkins(2006) : matching is goal. • This model: matching is instrument.

5. Main results • Various types of ranking are realized as a self-enforcing belief • While potentially identical, highly ranked universities can enjoy the status by charging higher tuition fees. • When matching is assortative, a rent absorption of tuition fee implements efficient level of educational performance.

6. Model • Workers (=students) • heterogeneous in innate abilities, a • Educational performance, e • workplace productivity • cost of performance • Assumptions

7. Model • Utility function • But e and a are not observable ⇒ Incentives for Signaling • Matches between workers and universities work as a signaling device.

8. Timing • Universities simultaneously set tuition fees p(j) ↓ • Students and universities make one-to-one matches, bargaining over educational performances e ↓ • Workers are paid w(s) in the labor market.

9. Model • Universities • Continuous, indexed by • ⇒ Positive measure of students can not go to universities • Lexicographic Preference (1)p (2)e • Interpretation of educational performance • educational service offered by universities • score of achievement test prior to entrance

10. Model • Assumptions for the labor market • A worker’s info. • Perfect competition

11. Equilibrium Concepts • Perfect Bayesian Nash eq. • Stable matching

12. Image of self-enforcing rank • Universities are ranked by • ⇒ Matching is “assortative”

13. A social belief • J (set of university) could have some pooling sub-ranges,

14. A social belief • : The probability that the innate ability of the graduate is higher than that of . • When the both belong to a same sub-range • Otherwise

15. The social belief (Image M=2)

16. Matching stage • is given. • stable matching

17. Matching stage Lemma 1 If an equilibrium contains a pooling range for any pair universities which belong to it, • : equilibrium performance of a • : equilibrium payment of a Lemma 2 In equilibrium,

18. Matching stage • rational expectations • In equilibrium,

19. Image of stable match (separating)

20. Boundary conditions • Initial boundary condition • Boundary condition for two ranges

21. Image of stable match (separating)

22. Fee setting stage Definition Lemma 3

23. Graphical image

24. Equilibrium performances

25. Equilibrium performances

26. Tuition fees

28. Equilibrium performances