Strategic Gains from Labor Market Discrimination Internal seminar, January 19, 2016 Johan N. M. Lagerl¨ of Dept. of Economics, U. of Copenhagen Email: johan.lagerlof@econ.ku.dk Website: www.johanlagerlof.com January 19, 2016 J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 1 / 19
Introduction (1/4) A business man or an entrepreneur who expresses preferences in his business activities that are not related to productive efficiency is at a disadvantage compared to other individuals who do not. Such an individual is in effect imposing higher costs on himself than are other individuals who do not have such preferences. Hence, in a free market they will tend to drive him out. (Milton Friedman, 1962, pp. 109-110) A classical economics argument (Becker 1957/71) : By discriminating, a firm handicaps itself. If lots of competition, discrimination can’t persist in the long run. More generally, more competition leads to less discrimination. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 2 / 19
Introduction (2/4) [. . . ] by“binding oneself”[thus also imposing a cost on oneself] a party can credibly commit to a pattern of competitive actions or reactions, and therefore affect the expectations and actions of other parties and the resulting competitive dynamics. (Metin Sengul et al., 2012, p. 378, crediting Thomas Schelling, 1956) A classical game theory argument: An economic agent may benefit from handicapping herself. Other applications: strategic delegation; location choices in Hotelling’s model; capacity choices in Kreps-Scheinkman’s model; Stackelberg oligopoly. What I will do and argue: Study discrimination in labor market with imperfect competition. Show that it can be beneficial to be a discriminating firm. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 3 / 19
Introduction (3/4): My results 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 Jan. 19, 2016 4 / 19
Introduction (4/4): Further ideas and results 1 Discrimination can be an endogenous response to competition: Desirable to find an exogenous measure of competition. 2 Relationship discrimination-competition can be non-monotone . In the analysis, this was the case when wage discr. was possible. 3 Crucial distinguish competition in product and labor market . In this analysis, only competition in labor market mattered. 4 For discrimination to occur for the reasons studied here, firms’ choice variables must be strategic complements . If strategic substitutes, we should not expect discrimination. 5 Sometimes upside down comparative statics: more competition leads to lower wage and to higher profit . J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 5 / 19
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 Jan. 19, 2016 6 / 19
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 Jan. 19, 2016 7 / 19
A model of discriminating firms (1/3) Firm 1 Firm 2 0 1 1 / 2 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 Two firms located at the edges of the unit line. CRTS technology. Labor only input. Output sold at 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. J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 8 / 19
A model of discriminating firms (2/3) Utility of a worker who is located at x ∈ [0 , 1]: w 1 − tx if working at firm 1 u ( x ) = w 2 − t (1 − x ) if working at firm 2 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 ) = (3+ γ B ) 2 +18 γ B (1 − γ B ) φ ( γ B ) γ B 00 1 2 J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 9 / 19
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 Jan. 19, 2016 10 / 19
Analysis (1/7) 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 where π A | C is a firm’s profit if it chose A and rival chose C . Etc. Four categories of stage 2 subgames: 1 Firms addressing different segments (two monopsonies). 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 Jan. 19, 2016 11 / 19
Analysis (2/7) Case 4 : One C , other A / B . For concreteness: ( y 1 , y 2 ) = ( A , C ). A market Firm 1 Firm 2 0 1 = w 1 − w 2 + t def x 2 t 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 Jan. 19, 2016 12 / 19
Analysis (3/7) wage profit w C | C π D | A w A | C w C | A π C | A π A | C High- Middle- Low- wage eq wage wage eq π C | C eq 00 00 1 2 t 1 2 t φ ( γ B ) 3(1 − γ B ) φ ( γ B ) 3(1 − γ B ) 2 3 p 2 3 p 2(3 − γ B ) 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 Jan. 19, 2016 13 / 19
Analysis (4/7) t p 2 2 3 3 Ω I 1 √ 1 − γ B 2 3 Ω II 2 7 9(1 − γ B ) 1 21 − 13 γ B 3 Ω III ϕ ( γ B ) γ B 00 3 1 7 2 In region Ω I , the set of eq. is { ( C , C ) , ( C , D ) , ( D , C ) , ( D , D ) }} . In region Ω II , the set of eq. is { ( A , C ) , ( C , A ) , ( D , D ) }} . In region Ω III , the set of eq. is { ( D , D ) }} . For the firms, ( A , C ) and ( C , A ) payoff-dominate ( D , D ). J. Lagerl¨ of (U of Copenhagen) Labor Market Discrimination Jan. 19, 2016 14 / 19
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