Strategic Gains from Labor Market Discrimination Seminar at Universidade do Minho, December 10, 2014 Johan N. M. Lagerl¨ of Dept. of Economics, U. of Copenhagen Email: johan.lagerlof@econ.ku.dk Website: www.johanlagerlof.org December 7, 2014 J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 1 / 17
Introduction (1/2) A classical argument: (Becker 1957/71) If lots of competition, discrimination can’t persist in the long run. More generally, more competition leads to less discrimination. The reason: A firm handicaps itself if it is not willing to serve some potential customers or hire some potential employees. Hence it can’t compete against a firm that is not discriminating. But we also know from game theory that... An economic agent may benefit from handicapping herself. Cort´ ez ordered his men to burn the ships they had arrived with. What I will argue: In a labor market with imperfect competition, it can be beneficial to be a discriminating firm. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 2 / 17
Introduction (2/2) I will make a distinction between: Wage discrimination, and discrimination in hiring. Two main results in the paper: 1 Discrimination in hiring can be part of an equilibrium. 2 A ban of wage discrimination may lead to discrim’n in hiring. Why profitable to discriminate in hiring? Broadly: discrimination helps to segment the market. But the logic is a bit subtle. It relies on some key assumptions: 1 Imperfect competition. 2 The firms’ choice variables are strategic complements. 3 The firms cannot do, or have deselected, wage discrimination. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 3 / 17
Literature Review (1/2) Becker (1957/71): Taste-based discrimination: (i) Employers, (ii) employees, or (iii) customers are prejudiced. Utility cost of interacting with members of a certain group. Arrow (1972): “[Becker’s employer discrimination model] predicts the absence of the phenomenon it was designed to explain.” Prejudiced employers sacrifice profits by discriminating. Hence competition should, in the long run, eliminate them. As a response to this problem, there were two developments: 1 Search literature (Black, 1995, and others): pointed to frictions that may hinder the logic from working. 2 Statistical discrimination (Arrow, 1973, and Phelps, 1972): an alternative logic that doesn’t rely on a taste for discrimination. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 4 / 17
Literature review (2/2) The two closest contributions: 1 Bhaskar, Manning, To (JEconPersp, 2002). Using similar logic, they show the possibility of racial pay gaps. But their result is about wage discr., not discr. in hiring. Brief analysis in the form of a figure, with one paragraph of text. 2 Targeted advertising: Galeotti and Moraga-Gonz´ alez (2008). Firms compete in product market and choose which consumer group to target in advertising. Model perfect (Bertrand) compeition. Therefore only mixed eq. So (i) other application & (ii) fixed (full) degree of competition. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 5 / 17
A model of discriminating firms (1/3) Firm 1 Firm 2 0 1 1 / 2 Two firms on the unit line, located at � x 1 = 0 and � x 2 = 1. CRTS production technology, with labor as only input. Output sold at some exogenous price p . Firm i ’s profit: π i = ( p − w i ) l i ( w 1 , w 2 ) , where l i ( w 1 , w 2 ) is the mass of people working for firm i and w i is firm i ’s posted wage. Two groups of workers, uniformly distributed on the unit line: Majority group A (mass γ A ), and minority group B (mass γ B ). � � 0 , 1 Assume γ A + γ B = 1 and γ B ∈ . 2 T J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 6 / 17
A model of discriminating firms (2/3) Utility of a worker who is located at x ∈ [0 , 1]: � w i − t | x − � x i | if working at firm i u ( x ) = 0 if working at neither firm, t > 0 measures the worker’s mismatch cost. Firms observe group membership ( A or B ), but not location x . To obtain pure strategy equilibria, I assume: ϕ ( γ B ) ≤ t p ≤ 2 3 . t 2 p 3 def 18 γ B (1 − γ B ) where ϕ ( γ B ) = φ ( γ B ) (4 − γ B ) 2 +18 γ B (1 − γ B ) γ B 00 1 2 J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 7 / 17
A model of discriminating firms (3/3) Sequence of events 1 The firms (simultaneously) commit to y i ∈ { A , B , C , D } . y i = A : Firm i can hire workers only from group A . y i = B : Firm i can hire workers only from group B . y i = C : Firm i free to hire from both groups, but no wage discr. y i = D : Firm i free to hire from both groups and to wage discr. 2 y 1 and y 2 observed by firms and they simultaneously post wages. If y i ∈ { A , B , C } , then firm i posts a single wage: w i . If y i = D , then firm i posts two wages: w A and w B i . i 3 Workers decide which firm to work for (or not to work at all). A worker’s options may be limited, due to the stage 1 decisions. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 8 / 17
Analysis (1/10) π A | C is a firm’s profit if it chose A and rival chose C . Etcetera. The reduced-form game at stage 1: Firm 2 y 2 = A y 2 = B y 2 = C y 2 = D y 1 = A π A | A , π A | A π A | B , π B | A π A | C , π C | A π A | D , π D | A y 1 = B π B | A , π A | B π B | B , π B | B π B | C , π C | B π B | D , π D | B Firm 1 y 1 = C π C | A , π A | C π C | B , π B | C π C | C , π C | C π C | D , π D | C y 1 = D π D | A , π A | D π D | B , π B | D π D | C , π C | D π D | D , π D | D Four categories of stage 2 subgames: 1 Firms addressing different segments (two monopolies). 2 Firms addressing the same segment (competit’n, standard case). 3 One D , the other A or B (combination of 1 and 2). 4 One C , the other A or B (interrelated markets, novel case). J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 9 / 17
Analysis (2/10) Case 1 : Firms addressing different segments (two monopolies). � if t p < 1 γ j ( p − t ) 2 π j | k = for ( j , k ) ∈ { ( A , B ) , ( B , A ) } . γ j p 2 if t p ≥ 1 4 t 2 Case 2 : Firms addressing the same segment (standard case). w 1 p − t Firm 1 Firm 2 w 2 0 1 = w 1 − w 2 + t def x p − t 0 2 t π A | A = γ A t π B | B = γ B t π C | C = π D | D = π C | D = π D | C = t 2 , 2 , 2 . J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 10 / 17
Analysis (3/10) Case 3 : One D , the other A or B (combination of 1 and 2). � γ k ( p − t ) + γ j t if t p < 1 π A | D = γ A t 2 , π B | D = γ B t 2 2 2 , π D | j = γ k p 2 4 t + γ j t if t p ≥ 1 2 2 for ( j , k ) ∈ { ( A , B ) , ( B , A ) } . Case 4 : One C , other A / B . For concreteness ( y 1 , y 2 ) = ( A , C ). Firm 2’s profit function ( B market covered or not?): � ( p − w 2 ) � � γ A (1 − x ) + γ B w 2 if w 2 < t t π 2 = ( p − w 2 ) [ γ A (1 − x ) + γ B ] if w 2 ≥ t . Firm 2’s best reply is upward-sloping, but with flat range. Low-wage eq : Left of the flat range (where w 2 < t ). Middle-wage eq : Within the flat range (where w 2 = t ). High-wage eq : Right of the flat range (where w 2 > t ). J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 11 / 17
Analysis (4/10) wage w C | C w A | C w C | A High- Middle- Low- wage eq wage wage eq eq 00 t φ ( γ B ) 3(1 − γ B ) 1 2 2 3 2(3 − γ B ) If ( y 1 , y 2 ) = ( A , C ), firm 2 is a monopsonist in the B market. This lowers the labor supply elasticity firm 2 faces. So w 2 down. The reaction functions are upward-sloping, so w 1 also drops. This is the indirect benefit firm 1 gets from discriminating. Also a direct cost. Can the indirect strategic benefit dominate? J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 12 / 17
profit π D | A π C | A π A | C π C | C 00 t 1 2 φ ( γ B ) 3(1 − γ B ) 2 3 2(3 − γ B ) 3
t p 2 2 3 3 ( y ∗ 1 , y ∗ 2 ) ∈ { ( C, C ) , ( C, D ) , ( D, C ) , ( D, D ) } No discrimination 1 2 ( y ∗ 1 , y ∗ √ 1 − γ B 2 ) ∈ { ( A, C ) , ( C, A ) } 3 Discrimination 2 7 9(1 − γ B ) 1 21 − 13 γ B 3 ( y ∗ 1 , y ∗ 2 ) ∈ { ( D, D ) } No discrimination φ ( γ B ) γ B 00 3 1 7 2 Figure 5: Eq. outcomes when S = { A, B, C, D }
Analysis (6/10) Discussion of figure on previous slide In the gray area: ( y 1 , y 2 ) = ( A , C ) is an equilibrium. For π A | C > π C | C and π C | A > π D | A . The other possible deviations also not profitable. In the same gray area, ( y 1 , y 2 ) = ( D , D ) is also an equilibrium. If the rival chooses D , the two markets will be unrelated. Thus a firm cannot gain by choosing A . However, the equilibrium ( A , C ) payoff-dominates ( D , D ). So with that eq. selection criterion, discrimination in gray area. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Dec. 10, 2014 13 / 17
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