Strategic Gains from Labor Market Discrimination Seminar at - - PowerPoint PPT Presentation

Strategic Gains from Labor Market Discrimination

Seminar at Universidade do Minho, December 10, 2014 Johan N. M. Lagerl¨

• f
• Dept. of Economics, U. of Copenhagen

Email: johan.lagerlof@econ.ku.dk Website: www.johanlagerlof.org December 7, 2014

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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A model of discriminating firms (1/3)

Firm 1 Firm 2 1/2 1 Two firms on the unit line, located at x1 = 0 and x2 = 1.

CRTS production technology, with labor as only input. Output sold at some exogenous price p. Firm i’s profit: πi = (p − wi) li (w1, w2) , where li (w1, w2) is the mass of people working for firm i and wi is firm i’s posted wage.

Two groups of workers, uniformly distributed on the unit line:

Majority group A (mass γA), and minority group B (mass γB). Assume γA + γB = 1 and γB ∈

• 0, 1

2

• .

T

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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A model of discriminating firms (2/3)

Utility of a worker who is located at x ∈ [0, 1]: u (x) = wi − t |x − xi| if working at firm i 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(γB) ≤ t p ≤ 2 3 .

t p

γB

1 2 2 3

00 φ(γB) where ϕ(γB)

def

=

18γB(1−γB) (4−γB)2+18γB(1−γB)

• J. Lagerl¨
• f (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 yi ∈ {A, B, C, D}.

yi = A: Firm i can hire workers only from group A. yi = B: Firm i can hire workers only from group B. yi = C: Firm i free to hire from both groups, but no wage discr. yi = D: Firm i free to hire from both groups and to wage discr.

2 y1 and y2 observed by firms and they simultaneously post wages.

If yi ∈ {A, B, C}, then firm i posts a single wage: wi. If yi = D, then firm i posts two wages: wA

i

and wB

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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Analysis (1/10)

πA|C is a firm’s profit if it chose A and rival chose C. Etcetera. The reduced-form game at stage 1:

Firm 1 Firm 2

y2 = A y2 = B y2 = C y2 = D y1 = A πA|A, πA|A πA|B, πB|A πA|C, πC|A πA|D, πD|A y1 = B πB|A, πA|B πB|B, πB|B πB|C, πC|B πB|D, πD|B y1 = C πC|A, πA|C πC|B, πB|C πC|C, πC|C πC|D, πD|C y1 = D πD|A, πA|D πD|B, πB|D πD|C, πC|D πD|D, πD|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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Analysis (2/10)

Case 1: Firms addressing different segments (two monopolies). πj|k =

• γj(p − t)

if t

p < 1 2 γjp2 4t

if t

p ≥ 1 2

for (j, k) ∈ {(A, B), (B, A)} . Case 2: Firms addressing the same segment (standard case). Firm 1 Firm 2 x

def

= w1−w2+t

2t

1 p − t p − t w2 w1 πA|A = γAt 2 , πB|B = γBt 2 , πC|C = πD|D = πC|D = πD|C = t 2.

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Analysis (3/10)

Case 3: One D, the other A or B (combination of 1 and 2). πA|D = γAt 2 , πB|D = γBt 2 , πD|j =

• γk(p − t) + γjt

2

if t

p < 1 2 γkp2 4t + γjt 2

if t

p ≥ 1 2

for (j, k) ∈ {(A, B), (B, A)} . Case 4: One C, other A/B. For concreteness (y1, y2) = (A, C).

Firm 2’s profit function (B market covered or not?): π2 = (p − w2)

• γA (1 − x) + γB w2

t

• if w2 < t

(p − w2) [γA (1 − x) + γB] if w2 ≥ t. Firm 2’s best reply is upward-sloping, but with flat range.

Low-wage eq: Left of the flat range (where w2 < t). Middle-wage eq: Within the flat range (where w2 = t). High-wage eq: Right of the flat range (where w2 > t).

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Analysis (4/10)

2 3

φ(γB)

1 2 3(1−γB) 2(3−γB)

wage t 00 wC|C wA|C wC|A

Low- wage eq Middle- wage eq High- wage eq

If (y1, y2) = (A, C), firm 2 is a monopsonist in the B market. This lowers the labor supply elasticity firm 2 faces. So w2 down. The reaction functions are upward-sloping, so w1 also drops. This is the indirect benefit firm 1 gets from discriminating. Also a direct cost. Can the indirect strategic benefit dominate?

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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2 3

φ(γB)

1 2 3(1−γB) 2(3−γB)

profit t 00 πC|C πA|C πC|A πD|A 3

1 2 2 3 1 2 3 7 2 3 1 3 3 7 t p

γB 00

9(1−γB) 21−13γB √1−γB 2

φ(γB)

No discrimination Discrimination No discrimination

(y∗

1, y∗ 2) ∈ {(C, C), (C, D), (D, C), (D, D)}

(y∗

1, y∗ 2) ∈ {(D, D)}

(y∗

1, y∗ 2) ∈ {(A, C), (C, A)}

Figure 5: Eq. outcomes when S = {A, B, C, D}

Analysis (6/10)

Discussion of figure on previous slide In the gray area: (y1, y2) = (A, C) is an equilibrium.

For πA|C > πC|C and πC|A > πD|A. The other possible deviations also not profitable.

In the same gray area, (y1, y2) = (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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Analysis (9/10)

What if wage discrimination is not feasible? Coate and Loury (1993): “Discriminatory wages for the same work is a flagrant violation of equal-employment laws, and relatively easy to detect. Discrimination in job assignment [...] is a more subtle phenomenon.” What if the firms could not do wage discrimination (D), but still could discriminate in hiring (A and B)?

• Proposition. Assume S = {A, B, C}. Then:

1 In region ΩI, the set of eq. is (y∗ 1 , y∗ 2 ) ∈ {(C, C)}. 2 In region ΩII ∪ ΩIII, the set of eq. is (y∗ 1 , y∗ 2 ) ∈ {(A, C), (C, A)}.

See figure next slide!

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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1 2 2 3 1 2 2 3 t p

γB 00

√1−γB 2

φ(γB)

No discrimination Discrimination

(y∗

1, y∗ 2) ∈ {(A, C), (C, A)}

(y∗

1, y∗ 2) ∈ {(C, C)}

Figure 6: Eq. outcomes when S = {A, B, C}

Summing up (1/1)

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¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

15 / 17

Discussion (1/2)

Why is group X discriminated against? The story says nothing about why there is discrimination against, say, blacks: any identifiable group of the right size works.

But a traditionally targeted group may be focal.

Choosing to discriminate? Do firms really choose whether to discriminate? If they do, how can they make an irreversible commitment? My interpretation: These model features are analytical shortcuts. Firms/entrepreneurs have possibly prejudiced preferences.

Entry/exit game. Cultural transmission.

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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Discussion (2/2)

Relationship competition–discrimination Analysis suggested the possibility of a non-monotone rel’ship. For empirical work: measure of competition important, and it may be endogenous (here t was exogenous, but not w). Extensions I’m thinking of

1 Entry/exit.

Prejudiced and non-prejudiced employers can enter a market. Which ones have the greatest incentive to enter?

2 Targeted advertising.

Existing literature with similar logic study only case with t ≈ 0. New technology makes targeting easier. Effect on competition?

• J. Lagerl¨
• f (U of Copenhagen)

Labor Market Discrimination

• Dec. 10, 2014

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