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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

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

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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.”

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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.”

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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.

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1. Signaling Game as a Model of Statistical Discrimination?

Can the signaling game (with an “index”) really serve as a model of statistical discrimination?

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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!

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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.

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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

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10

C1

WM(y)

C2

1 yM 2 y

2

1

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C1

WF(y)

C2

.5 yF 1 y

2

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2. Spence’s Model Revisited

One type of signaling equilibria: where 1 < yM* < 2 and 0.5 < yF* < 1

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Male Female

Productivity Wage Return Wage Return

1 1 1 1 1

2 2 1 − yM*/2 2 1 − yF*

2. Spence’s Model Revisited

One type of signaling equilibria: where 1 < yM* < 2 and 0.5 < yF* < 1

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Male Female

Productivity Wage Return Wage Return

1 1 1 1 1

2 2 1 − yM*/2 2 1 − yF*

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

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.

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4. Data from Japan

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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)

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(1000 yen)

Figure 1. Mean Starting Salary by Education and Gender: Japan, 1989-2010.

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

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.

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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.

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Appendix. Another Type of Equilibria

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Male Female

Productivity Wage Return Wage Return

1 1 1 2−q 2−q

2 2 1 − yM*/2 2−q

2−q

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