Can the Signaling Game Serve as a Model of Statistical Discrimination?
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Can the Signaling Game Serve as a Model of Statistical Discrimination?

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Presented at Advances in Rational Choice Social Research, Preconference of the Rationality and Society Section, 108th Annual Meeting of the American Sociological Association, Hilton New York Midtoun, ...

Presented at Advances in Rational Choice Social Research, Preconference of the Rationality and Society Section, 108th Annual Meeting of the American Sociological Association, Hilton New York Midtoun, New York, August 9, 2013.

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Can the Signaling Game Serve as a Model of Statistical Discrimination? Can the Signaling Game Serve as a Model of Statistical Discrimination? Presentation Transcript

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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 C1 WM(y) C2 1 yM 2 y 2 1
  • 11 C1 WF(y) C2 .5 yF 1 y 2 1
  • 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*
  • 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*
  • 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. 15
  • 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.
  • 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. 18
  • 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
  • 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
  • 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