This document discusses using signaling games as models of statistical discrimination. The author argues that signaling games with indexes like gender cannot truly model statistical discrimination because they produce "curious consequences" from plausible equilibria. For example, one equilibrium suggests employers would offer equal wages to men and women with different education levels, contrary to real data showing gender wage gaps. The author proposes examining other statistical discrimination models and factors like employers' stereotypes to better understand these issues.

1. 1
Can the Signaling Game
Serve as a Model of
Statistical Discrimination?
Kunihiro Kimura
(Tohoku University, JAPAN)
Rationality and Society Pre-Conference
American Sociological Association
August 9, 2013, New York, USA

2. Outline of this presentation
1. Signaling Game as a Model of
Statistical Discrimination?
2. Spence’s Model Revisited
3. “Curious" Consequence Derived from
Seemingly Plausible Equilibria
4. Data from Japan
5. For the Future Research
2

3. 1. Signaling Game as a Model
of Statistical Discrimination?
 Aigner and Cain (1977)
 “In Spence’s model of market signaling,
[statistical] discrimination may result …”
 But “final judgments [on Spence’s model]
should be withheld.”
3

4. 1. Signaling Game as a Model
of Statistical Discrimination?
 Arai (1995)
 “… statistical discrimination arises when
employers have imperfect information …”
 “… employers determine hiring, job
allocations, wages, promotions, etc., … on
the basis of statistical attributes … of the
individual’s group.”
4

5. 1. Signaling Game as a Model
of Statistical Discrimination?
 Arai (1995) [continued]
 “Groups are classified … according to
characteristics such as race, sex, and
origin, …”
 “These characteristics are close to Spence’s
indexes.”
 Signal: education (years of schooling)
 Index: ethnicity, gender, class origin, etc.
5

6. 1. Signaling Game as a Model
of Statistical Discrimination?
 Can the signaling game (with an
“index”) really serve as a model of
statistical discrimination?
6

7. 1. Signaling Game as a Model
of Statistical Discrimination?
 Can the signaling game (with an
“index”) really serve as a model of
statistical discrimination?
 NO!
7

8. 1. Signaling Game as a Model
of Statistical Discrimination?
 Can the signaling game (with an
“index”) really serve as a model of
statistical discrimination?
 NO!
 “Curious” consequence derived from
seemingly plausible equilibria for
Spence’s model.
8

9. 2. Spence’s Model Revisited
Gender Productivity Proportion of
own Group
Education
Costs
Male 1 q y
Male 2 1 − q y/2
Female 1 q 2y
Female 2 1 − q y
9

10. 10
C1
WM(y)
C2
1 yM 2 y
2
1

11. 11
C1
WF(y)
C2
.5 yF 1 y
2
1

12. 2. Spence’s Model Revisited
 One type of signaling equilibria:
 where 1 < yM* < 2 and 0.5 < yF* < 1
12
Male Female
Productivity Wage Return Wage Return
1 1 1 1 1
2 2 1 − yM*/2 2 1 − yF*

13. 2. Spence’s Model Revisited
 One type of signaling equilibria:
 where 1 < yM* < 2 and 0.5 < yF* < 1
13
Male Female
Productivity Wage Return Wage Return
1 1 1 1 1
2 2 1 − yM*/2 2 1 − yF*

14. 3. “Curious" Consequence
 Employers’ beliefs:
 Educational costs (including the
psychological one) for women are greater
than those for men.
 Women with shorter years of education
have the same productivity as men with
longer years of education.
 Therefore, employers would offer the
same wage for the men and the
women. 14

15. 3. “Curious" Consequence
 In Japan, however, there exists the
gender gap in wage even for men and
women of the same educational level.
 The average wage for women with
shorter years of education are less than
that for men with longer years.
15

16. 4. Data from Japan
0
50
100
150
200
250
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
University (Male) Junior College (Male) High School (Male)
University (Female) Junior College (Female) High School (Female)
16
(1000 yen)
Figure 1. Mean Starting Salary by Education and Gender: Japan, 1989-2010.

17. 5. For the Future Research
 “Curious” consequence in other types of
equilibria for Spence’s model
 Examination of other models of
statistical discrimination
 Coate & Loury (1993); Yamaguchi (2010)
 Employers’ negative stereotypes
 Self-fulfilling prophecy
 “Cognitive rationality” (?)
17

18. Appendix.
Another Type of Equilibria
 Employers’ beliefs:
 If Male and y < yM*,
productivity = 1 with probability 1;
 If Male and y ≥ yM*,
productivity = 2 with probability 1;
 If Female and y < yF*,
productivity = 1 with probability q while
productivity = 2 with probability 1−q ;
 If Female and y ≥ yF*,
productivity = 2 with probability 1.
18

19. Appendix.
Another Type of Equilibria
 Equilibria (where 1 < yM* < 2, and yF* > q):
 Male with productivity = 1
will not go to university;
 Male with productivity = 2
will go to university;
 Female will not go to university regardless
of productivity.
19

20. Appendix.
Another Type of Equilibria
20
Male Female
Productivity Wage Return Wage Return
1 1 1 2−q 2−q
2 2 1 − yM*/2 2−q 2−q

21. 5. For the Future Research
 “Curious” consequence in other types of
equilibria for Spence’s model
 Examination of other models of
statistical discrimination
 Coate & Loury (1993); Yamaguchi (2010)
 Employers’ negative stereotypes
 Self-fulfilling prophecy
 “Cognitive rationality” (?)
21