Inequality and Matching(based on work with M. Kremer)

E. Maskin

Jerusalem Summer School in Economic Theory

June 2014

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• In last 30 years, significant increase in income inequality– in many rich countries (including U.S.)– in many poor countries (including India and

Mexico)

• referring here to inequality increases within countries– inequality has been falling across countries– many poor countries (especially India and China)

are catching up

• Increases are theoretically puzzling

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First, take inequality increase in U.S.• well accepted relationship

wage education/training (skill)• dispersion of skill has risen in U.S. (also the

median)• but not nearly so much as dispersion in income

– holding wage as a function of skill fixed, shift in skill distribution explains only 20% of increase in income dispersion between 1980 and 2000

– but wage schedule not fixed

• Why not?

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• One popular answer: skill-biased technological change– technology biased in favor of high skills– marginal product of high-skill workers enhanced

their wages rise relative to low-skill workers’ wages

• Objection:– difficult to measure such technological change– rather complicated theory

• Propose a different (simpler) theory based on matching– firm matches workers of different skills to produce output– as skill dispersion and median increase, pattern of matching

between workers of different skills within firm changes– can induce even bigger increase in income dispersion– leads to greater relative segregation of skill within firms

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• This last prediction is novel to our theory:variation of skills within firm falls relative to variation across firms

• Illustrative examples– General Motors: typical large firm of generation ago

mixed high-skill labor (engineers) with low-skill labor (assembly-line workers)

– typical firms of today:Microsoft (mainly high-skill) andMcDonald’s (mainly low-skill)

• segregation prediction borne out by evidence for U.S., U.K., and France

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Second, growth of inequality in Mexico• followed a period of liberalized trade

– Mexico joined GATT in 1985– in 2 years average tariffs fell by 50%– FDI quadrupled

• white-collar wages increased by 16%

• blue-collar wages fell by 14%

• globalization (increase in trade) aggravated inequality

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Contradicts Heckscher-Ohlin theory• Mexico has comparative advantage in low-skill labor• in autarky,

– high-skill labor in short supply, so commands especially high wage

– low-skill labor paid correspondingly poorly

• opposite true in U.S.:– high-skill labor gets comparatively low wage– low-skill labor paid comparatively well

• after trade opened, factor prices should equalize– high-skill wages in Mexico should fall– low-skill wages in Mexico rise

• trade should decrease inequality in Mexico

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• Will argue that same matching model explains Mexico’s higher inequality

• But first return to inequality in U.S. (also U.K. and France)

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• 1-good economy

• good produced by competitive firms

• labor only input

• labor comes in 3 skill levels q

L < M < H

• proportion of workers having skill q p q

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All firms have same production process• 2 tasks

– one “managerial” - - sensitive to skill level– one “subordinate” - - less sensitive to skill

output =

• formula incorporates 3 critical features(i) workers of different skills imperfect substitutes(ii) different tasks within firm complementary(iii) different tasks differentially sensitive to skill

2s mq q

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(i) workers of different skills imperfect substitutes

• if perfect substitutability, q-worker (worker of skill q) can be replaced by 2 -workers

• so, no prediction about skill levels in firm - - no segregation

• q-worker always paid twice as much as -worker– so inequality between q-worker and

-worker can’t increase 2

q

2

q

2

q

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(ii) different tasks complementary

• if instead

optimal choice of independent of that of

• so again no prediction about combination of skill levels in firm

output s mf q g q

sq mq

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(iii) different tasks differentially sensitive to skill• if instead

get complete segregation of skill:– fully assortative matching

• differential sensitivity

– still have some assortative matching– also have second force

• balance of two forces determines equilibrium matching

output ,s mq q

s mq q

implies m sq q

2output s mq q

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Competitive equilibrium• wage schedule• matching rule

2

, ,

, arg max , (output maximized)q q

q q q q

, equilibrium fraction of matches with

, s m

q q

q q q q

w q

20q q w q w q

equality if , 0 (no profit in equilibrium)q q

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suppose

•

• so

• if then

13, , ,L M L H M H

claim: if low dispersion ( 2 ), thenH L

13p L p M p H

, 0 ( -workers "self-matched")L L L

, 0 from (1)M M

3 2 23 3 34 2 2 , and soL L L

2 3 3(1) 2LM L M

1616

− +− hence,

− but• hence,

• +

, 0; similarly , , 0L L M M H H

2 3 3 similarly, , 0 because 2 H H LH L H

, 0M H 2 2 3 2 , contradictionLM LH L MH

2 ,LM w L w M

2 ,LH w L w H

2MH w M w H

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•

• Notice

Proposition 1: Starting from low skill dispersion, , increase in median skill reduces inequality in wages (and raises mean and median wage)

2 2 2

2

LM LH MHw L

2 2 2

2

LM MH LHw M

2 2 2

2

LH MH LMw H

0 0

w L w H

M M

2 H L

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But opposite occurs if skill distribution dispersed– claim: this what happened in U.S., U.K., and France

Proposition 2: Starting from sufficiently dispersed skill distribution

and if either L-workers or M-workers not self-matched, at least one equality strict

increase in median inequality:M magnifies

0 and 0,

w L w H

M M

343 2 and ,M L H M

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Proof: Suppose(2)

•

•

•

•

•

•

•

, 0 because L H H L

315 5p L p H p M

3

(from self-matching)2

Mw M

243

32 0, since

2

w L MLM M L

M

2 15 5, , ,L M M H M M

3 3

2 2,2 2

M Mw L LM w H MH

22 3

2

30, since

2

w H MH H M

M

2 3 3 2 3 32 2LM L M MH M H

* * ( , ) = ( , ) = 0 from (2)L L H H

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Segregation

Index of relative segregation

B = skill variation between firms

W = skill variation within firms

2

2 - , mean skill in populationq q

q q

q q

,B

B W

2 *2 ,q q

q q

q q q

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Proposition 2: Suppose

If dispersion of skills big enough, i.e.,

then mean-preserving spread in distribution increases segregation index

1 5

2H L

mean skillp L p M M p H H M M

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Proof: Suppose

•

• So

• B =

• W =

• B increasing in

• W decreasing in

• So

• intuitively, W low if most weight is in either tail,

• as dispersion of skills gets high, W high

2 3 2 3Then 2 2MH L ML H

1 13 32, 3, 4 and 2L M H p L p H p M

2 2 2

1 1 16 2 3 2 3

2 2 2

L L M H H HL M H

2 2 2

1 1 16 2 3 2 3

2 2 2

L L M H H HM M M

increasing in B

B W

13, 2M H

, 3H H

1 16 2,L L

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Return to globalization and Mexico Puzzles:• Mexico has comparative advantage in low-skill labor

but trade increased gap between high- and low-skill workers– contradicts Heckscher-Ohlin theory

• H-O implies thatas 2 countries become more different (in factor endowments), should trade more– hence, U.S. and Malawi should trade more than U.S. and Mexico

(Malawi more different than Mexico from U.S.)– but Mexico trades much more than Malawi with U.S.

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Resolution:

• think of globalization as increase in international production– Delhi call centers (outsourcing)– computers

designed in U.S.

programmed in Europe

assembled in China

• due to lower communication/transport costs

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• 2 countries – one rich, one poor– rich country

– workers of skill levels A and B

– poor country– workers of skill levels C and D

• production• before globalization (i.e., in autarky), workers can

match only domestically• after globalization, international matching possible

A B C D (conclusions still hold if )C B

2output s mq q

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Proposition 3: If D-workers have sufficiently low skill, i.e.,

(*)

then globalization increases inequality in poor country

countrypoor

countryrich

DCBA

1 5,

2B D

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Proof: 2 cases

Case I

•

•

•

• Hence,

1 5(*)

2B D

rich poor

country country

A B C D

, 0 (because, from (*), -worker can't match with - or -worker)g D D D A B

3

2a g

Dw D w D

- - globalization causes rise in inequalityg g a aw C w D w C w D

p D p C

, 0,a D D

because of possible matching with or g aw C w C B A

autarky post-globalizationa g

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Case II

•

•

•

• Hence, again

- - at worst -workers can self-match g aw C w C C

3

2max ,2a a

Dw D DC w C

3 3 3

2 2max , max ,2 2 2g g a

D D Cw D DC w C w D DC

p D p C

3

, 02a a

CC C w C

rises with globalizationw C w D

rich poor

A B C D

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Model also explains Malawi:

• workers in Malawi have very low skills no international matching opportunities

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Policy?

• How can D-workers benefit from globalization?• Suppose can increase q by at cost

– may give D better matching opportunities• who will bear cost?

– not firm - -education raises worker’s productivity, but then have to pay higher wage

– not workerperhaps can’t afford to pay

– role for investment by third partiesdomestic governmentinternational agencies, NGOsforeign aidprivate foundations

q c q