RIETI International Seminar Handout Speaker: Prof. Elhanan HELPMAN

Research Institute of Economy, Trade and Industry (RIETI)

RIETI International Seminar

Handout

April 4, 2014

Speaker: Prof. Elhanan HELPMAN http://www.rieti.go.jp/jp/index.html

Matching and Sorting in the Global Economy

Gene Grossman Elhanan Helpman Philipp Kircher

Princeton University Harvard University University of Edinburgh

April 2014

April 2014 1 / 26 Grossman, Helpman and Kircher

()Matching and Sorting

Motivation

Observations about worker heterogeneity :

Grossman, Helpman and Kircher


April 2014 2 / 26

1

2

3

4

Much within-industry wage inequality: changes in income distribution re‡ect more than changes in relative rewards to broad factor classes (Helpman et al.

2013)

Distribution of factor “quality” (diversity) is a source of comparative advantage (Bombardini et al. 2013)

Positive assortative matching (PAM) between workers and …rms within industries

Exporter wage premium, but trade/openness a¤ects degree of PAM

Motivation


1 Much within-industry wage inequality: changes in income distribution re‡ect more than changes in relative rewards to broad factor classes (Helpman et al.

2013)



April 2014 2 / 26

2

3

4




Motivation


1

2


2013)




April 2014 2 / 26

3

4



Motivation


1

2

3


2013)





4 Exporter wage premium, but trade/openness a¤ects degree of PAM

Motivation


1

2

3

4


2013)






April 2014 2 / 26

Motivation

Observations about the distribution of earnings :



April 2014 3 / 26

We study the entire distribution of earnings ; the bottom and the top, which di¤er across countries

2000 2007

5/1 9/5 5/1 9/5

Canada

France #

# "

Germany

2.000

1.736

1.995

1.810

1.561

2.112

1.521

2.093

" # 1.649

1.820

1.783

1.816

Ireland

Japan "

" 1.814

1.892

1.941

1.976

1.592

1.730

1.618

1.774

Korea "

Norway

Sweden

UK # "

U.S.A.

"

1.973

1.881

2.205

2.131

" 1.440

1.495

1.577

1.548

" # 1.402

1.742

1.422

1.721

1.828

1.891

1.826

2.023

2.137

2.240

2.146

2.397

Decile ratios of men’s gross earnings.

Motivation





April 2014 3 / 26

2000 2007

5/1 9/5 5/1 9/5

Canada

France #

# "

Germany

2.000

1.736

1.995

1.810

1.561

2.112

1.521

2.093

" # 1.649

1.820

1.783

1.816

Ireland

Japan "

" 1.814

1.892

1.941

1.976

1.592

1.730

1.618

1.774

Korea "

Norway

Sweden

UK # "

U.S.A.

"

1.973

1.881

2.205

2.131

" 1.440

1.495

1.577

1.548

" # 1.402

1.742

1.422

1.721

1.828

1.891

1.826

2.023

2.137

2.240

2.146

2.397


Motivation



2000 2007

5/1 9/5 5/1 9/5

Canada

France #

# "

Germany

2.000

1.736

1.995

1.810

1.561

2.112

1.521

2.093

" # 1.649

1.820

1.783

1.816

1.814

1.892

1.941

1.976

Ireland

Japan "

"

Korea "

Norway "

1.592

1.730

1.618

1.774

1.973

1.881

2.205

2.131

1.440

1.495

1.577

1.548

Sweden

UK # "

U.S.A.

"

" # 1.402

1.742

1.422

1.721

1.828

1.891

1.826

2.023

2.137

2.240

2.146

2.397




April 2014 3 / 26

This Paper

Theoretical: Understand interactions between forces of matching and sorting in shaping trade and earnings



April 2014 4 / 26

Captures forces likely to be present in any reasonable model, even if not the only forces present

Uses a factor proportions framework with two heterogeneous inputs

(“workers” and “managers”)

Productivity of unit depends on factor types— with complementarity

Extends the framework to (directed) search and unemployment

Including Ricardo-Viner and Heckscher-Ohlin interactions

This Paper





April 2014 4 / 26






This Paper






April 2014 4 / 26





This Paper










This Paper










This Paper










April 2014 4 / 26

Questions We Address

Sorting of workers and managers to sectors



April 2014 5 / 26

Matching of workers and managers within sectors

Determinants of comparative advantage/pattern of trade (will not discuss today)

E¤ects of trade on (entire) income distribution

E¤ects of trade on distribution of unemployment rates (will not discuss today)






April 2014 5 / 26










April 2014 5 / 26










April 2014 5 / 26










Economic Environment

Country characteristics:



April 2014 6 / 26

Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)

Densities continuous and strictly positive on bounded supports (intervals): S

L

S

H

,

Two industries

Overall CRS in quantities, competitive equilibrium

Primitive technology could give output as function of list of types

But Eeckhout and Kircher (2012) show: No reason for …rm to hire multiple types of workers in Lucas-type model of span of control

To save on notation, write the output in industry i of one manager of type q

H and ` workers of type q

L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF

> 0 for i = 1 , 2 ; F = H , L (refer to q as “ability” or “quality”)



Labor:

¯

,

φ

L

( q

L

)



April 2014 6 / 26

Managers:

¯

,

φ

H

( q

H

)


L

S

H

,

Two industries






L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF




Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)



April 2014 6 / 26


L

,

S

H

Two industries






L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF




Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,



April 2014 6 / 26

Two industries






L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF




Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries



April 2014 6 / 26





L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF





Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries




April 2014 6 / 26




L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF





Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries





April 2014 6 / 26



L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF





Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries





L as x i

=

ψ i

( q

H

, q

L

) ` γ i



April 2014 6 / 26

Assume

ψ iF





Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries





L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF




April 2014 6 / 26




Labor:

¯

,

φ

Managers:

L

H ,

( q

φ

L

H

)

( q

H

)


L

S

H

,

Two industries





L as x i

=

ψ i

( q

H

, q

L

) ` γ i

Assume

ψ iF





April 2014 6 / 26

Strictly Log Supermodular Productivity Functions

Assume:

ψ i

( q

H

, q

L

) is strictly increasing, twice continuously di¤erentiable, and strictly log supermodular for i = 1 , 2



April 2014 7 / 26

Implies PAM within sectors

Can have unconnected intervals of managers or workers that sort into a sector

From FOCs : In interior of set of factors allocated to sector i , m ( q

H

)

ψ iL

γ i

ψ i

[ q

H

, m ( q

H

[ q

H

, m ( q

H

)]

)]

=

ε w

[ m ( q

H

)] q

H ψ iH

[

( 1

γ i

)

ψ i q

H

[ q

, m

H

( q

H

)]

, m ( q

H

)]

=

ε r

( q

H

)

Factor market clearing:

Z q

H q

Ha

( 1

γ i r

γ i

( q )

) w [ m ( q )]

φ

H

( q ) dq =

¯

Z m ( q

H

) m ( q

Ha

)

φ

L

[ m ( q )] dq for all q

H


Assume:

ψ i

( q

H

, q

L





April 2014 7 / 26



H

)

ψ iL

γ i

ψ i

[ q

H

, m ( q

H

[ q

H

, m ( q

H

)]

)]

=

ε w

[ m ( q

H

)] q

H ψ iH

[

( 1

γ i

)

ψ i q

H

[ q

, m

H

( q

H

)]

, m ( q

H

)]

=

ε r

( q

H

)


Z q

H q

Ha

( 1

γ i r

γ i

( q )

) w [ m ( q )]

φ

H

( q ) dq =

¯

Z m ( q

H

) m ( q

Ha

)

φ

L


H


Assume:

ψ i

( q

H

, q

L






April 2014 7 / 26


H

)

ψ iL

γ i

ψ i

[ q

H

, m ( q

H

[ q

H

, m ( q

H

)]

)]

=

ε w

[ m ( q

H

)] q

H ψ iH

[

( 1

γ i

)

ψ i q

H

[ q

, m

H

( q

H

)]

, m ( q

H

)]

=

ε r

( q

H

)


Z q

H q

Ha

( 1

γ i r

γ i

( q )

) w [ m ( q )]

φ

H

( q ) dq =

¯

Z m ( q

H

) m ( q

Ha

)

φ

L


H


Assume:

ψ i

( q

H

, q

L





H

)

ψ iL

γ i

ψ i

[ q

H

, m ( q

H

[ q

H

, m ( q

H

)]

)]

=

ε w

[ m ( q

H

)] q

H ψ iH

[

( 1

γ i

)

ψ i q

H

[ q

, m

H

( q

H

)]

, m ( q

H

)]

=

ε r

( q

H

)




Z q

H q

Ha

( 1

γ i r

γ i

( q )

) w [ m ( q )]

φ

H

( q ) dq =

¯

Z m ( q

H

) m ( q

Ha

)

φ

L


H


Assume:

ψ i

( q

H

, q

L





H

)

ψ iL

γ i

ψ i

[ q

H

, m ( q

H

[ q

H

, m ( q

H

)]

)]

=

ε w

[ m ( q

H

)] q

H ψ iH

[

( 1

γ i

)

ψ i q

H

[ q

, m

H

( q

H

)]

, m ( q

H

)]

=

ε r

( q

H

)


Z q

H q

Ha

( 1

γ i r

γ i

( q )

) w [ m ( q )]

φ

H

( q ) dq =

¯

Z m ( q

H

)

φ

L


H m ( q

Ha

)



April 2014 7 / 26

Equilibrium Requirements

Three di¤erential equations for w ( q

L

) , r ( q

H

) , m ( q

H

)

Di¤erentiate factor market clearing condition wrt q

H

:

γ i r ( q

H

)

( 1

γ i

) w [ m ( q

H

)]

φ

H

( q

H

) =

¯

φ

L

[ m ( q

H

)] m

0

( q

H

)



April 2014 8 / 26

Sorting: w

0

[ m ( q

H

)] w [ m ( q

H

)]

= r

0

( q

H

) r ( q

H

)

=

ψ iL

[ q

H

, m ( q

H

)]

γ i ψ i

[ q

H

, m ( q

H

)] q

H ψ iH

[ q

( 1

γ i

)

ψ i

H

[ q

, m

H

,

( q m

H

( q

)]

H

)]

Boundary conditions : depend on sorting pattern

Continuity : w elsewhere)

( ) and r ( ) increasing and continuous at boundaries (and

Slope conditions : At any boundary, slope of w greater than slope to left. Same for slope of r

( q

L

( q

H

) to right of boundary

) .



L

) , r ( q

H

) , m ( q

H

)


H

:

γ i r ( q

H

)

( 1

γ i

) w [ m ( q

H

)]

φ

H

( q

H

) =

¯

φ

L

[ m ( q

H

)] m

0

( q

H

)

Sorting: w

0

[ m ( q

H

)] w [ m ( q

H

)]

= r

0

( q

H

) r ( q

H

)

=

ψ iL

[ q

H

, m ( q

H

)]

γ i ψ i

[ q

H

, m ( q

H

)] q

H ψ iH

[ q

( 1

γ i

)

ψ i

H

[ q

, m

H

,

( q m

H

( q

)]

H

)]



April 2014 8 / 26





( q

L

( q

H


) .



L

) , r ( q

H

) , m ( q

H

)


H

:

γ i r ( q

H

)

( 1

γ i

) w [ m ( q

H

)]

φ

H

( q

H

) =

¯

φ

L

[ m ( q

H

)] m

0

( q

H

)

Sorting: w

0

[ m ( q

H

)] w [ m ( q

H

)]

= r

0

( q

H

) r ( q

H

)

=

ψ iL

[ q

H

, m ( q

H

)]

γ i ψ i

[ q

H

, m ( q

H

)] q

H ψ iH

[ q

( 1

γ i

)

ψ i

H

[ q

, m

H

,

( q m

H

( q

)]

H

)]




April 2014 8 / 26




( q

L

( q

H


) .



L

) , r ( q

H

) , m ( q

H

)


H

:

γ i r ( q

H

)

( 1

γ i

) w [ m ( q

H

)]

φ

H

( q

H

) =

¯

φ

L

[ m ( q

H

)] m

0

( q

H

)

Sorting: w

0

[ m ( q

H

)] w [ m ( q

H

)]

= r

0

( q

H

) r ( q

H

)

=

ψ iL

[ q

H

, m ( q

H

)]

γ i ψ i

[ q

H

, m ( q

H

)] q

H ψ iH

[ q

( 1

γ i

)

ψ i

H

[ q

, m

H

,

( q m

H

( q

)]

H

)]






April 2014 8 / 26


( q

L

( q

H


) .



L

) , r ( q

H

) , m ( q

H

)


H

:

γ i r ( q

H

)

( 1

γ i

) w [ m ( q

H

)]

φ

H

( q

H

) =

¯

φ

L

[ m ( q

H

)] m

0

( q

H

)

Sorting: w

0

[ m ( q

H

)] w [ m ( q

H

)]

= r

0

( q

H

) r ( q

H

)

=

ψ iL

[ q

H

, m ( q

H

)]

γ i ψ i

[ q

H

, m ( q

H

)] q

H ψ iH

[ q

( 1

γ i

)

ψ i

H

[ q

, m

H

,

( q m

H

( q

)]

H

)]





( q

L

( q

H


) .



April 2014 8 / 26

Wage Inequality

From the di¤erential equation for wages: w q

00

L w q

0

L

= exp

"

Z q 0

L q 00

L

ψ iL m

ψ i

[ m 1

1

( z ) , z

( z ) , z ] dz

# for q

0

L

, q

00

L

2 Q int iL



April 2014 9 / 26

Log supermodularity implies that better matches for workers raise wage inequality

Similarly for salaries

Wage Inequality


00

L w q

0

L

= exp

"

Z q 0

L q 00

L

ψ iL m

ψ i

[ m 1

1

( z ) , z

( z ) , z ] dz

# for q

0

L

, q

00

L

2 Q int iL





Wage Inequality


00

L w q

0

L

= exp

"

Z q 0

L q 00

L

ψ iL m

ψ i

[ m 1

1

( z ) , z

( z ) , z ] dz

# for q

0

L

, q

00

L

2 Q int iL





Sorting I

If

ψ

1 L

( q

H min

, q

L

)

γ

1

ψ

1

( q

H min

, q

L

)

>

ψ

2 L

( q

H max

, q

L

)

γ

2

ψ

2

( q

H max

, q

L

) for all q

L

2 S

L then high-ability workers are employed in sector 1 and low-ability workers are employed in sector 2, for some q

L



April 2014 10 / 26

Under this su¢ cient condition, the incentives for high-ability workers to sort to sector 1 does not depend on the sorting of managers

Analogous condition for sorting of managers (better managers might go to sector 1 or sector 2)

If both conditions satis…ed, have “threshold” equilibrium: either HH / LL or

HL / LH

Sorting I

If

ψ

1 L

( q

H min

, q

L

)

γ

1

ψ

1

( q

H min

, q

L

)

>

ψ

2 L

( q

H max

, q

L

)

γ

2

ψ

2

( q

H max

, q

L

) for all q

L

2 S


L




April 2014 10 / 26



HL / LH

Sorting I

If

ψ

1 L

( q

H min

, q

L

)

γ

1

ψ

1

( q

H min

, q

L

)

>

ψ

2 L

( q

H max

, q

L

)

γ

2

ψ

2

( q

H max

, q

L

) for all q

L

2 S


L





April 2014 10 / 26


HL / LH

Sorting I

If

ψ

1 L

( q

H min

, q

L

)

γ

1

ψ

1

( q

H min

, q

L

)

>

ψ

2 L

( q

H max

, q

L

)

γ

2

ψ

2

( q

H max

, q

L

) for all q

L

2 S


L




HL / LH



April 2014 10 / 26

An Equilibrium with HL/LH Sorting q

H q

H max sector 2 q *

H q

H min q

L min

Grossman, Helpman and Kircher sector 1 q *

L


q

L max q

L

April 2014 11 / 26

Sorting II: Su¢ cient Condition for HH/LL

Suppose that:

ψ

1 L

( q

H

, q

L

)

γ 1 ψ

1

( q

H

, q

L

)

>

ψ

2 L

γ 2 ψ

2

( q

H

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

.



April 2014 12 / 26 and (!!!)

ψ

1 H

( q

H

( 1

γ

1

)

ψ

1

, q

L

)

( q

H

, q

L

)

>

ψ

2 H

( q

H

( 1

γ

2

)

ψ

2

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

,

Then high-ability managers and workers are employed in sector 1 and low-ability managers and workers are employed in sector 2, for some pair of cut-points, q

H and q

L

.


Suppose that:

ψ

1 L

( q

H

, q

L

)

γ 1 ψ

1

( q

H

, q

L

)

>

ψ

2 L

γ 2 ψ

2

( q

H

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

.

and (!!!)



April 2014 12 / 26

ψ

1 H

( q

H

( 1

γ

1

)

ψ

1

, q

L

)

( q

H

, q

L

)

>

ψ

2 H

( q

H

( 1

γ

2

)

ψ

2

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

,


H and q

L

.


Suppose that:

ψ

1 L

( q

H

, q

L

)

γ 1 ψ

1

( q

H

, q

L

)

>

ψ

2 L

γ 2 ψ

2

( q

H

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

.

and (!!!)

ψ

1 H

( q

H

( 1

γ

1

)

ψ

1

, q

L

)

( q

H

, q

L

)

>

ψ

2 H

( q

H

( 1

γ

2

)

ψ

2

, q

L

)

( q

H

, q

L

) for all q

H

2 S

H

, q

L

2 S

L

,


H and q

L

.



April 2014 12 / 26

An Equilibrium with HH/LL Sorting q

H max q

H q

H

* q

H min q

L min sector 2 q

L

* sector 1 q

L max q

L



April 2014 13 / 26

Sorting III: Sorting Reversals

1.1

1.09

1.08

1.07

1.06

1.05

1.04

1.03

1.02

1.01

1

1 1.1

1.2

1.3

1.4

1.5

q

L

1.6

1.7

1.8

Sector 1

Sector 2

1.9

2



April 2014 14 / 26

Sweden 2004

Figure: Variation across manufacturing industries of log mean salary of managers and log mean wage of workers in Sweden: 2004. Source: private communication, Anders

Akerman.



April 2014 15 / 26

Brazil 1994

Figure: Variation across manufacturing industries of log mean salary of managers and log mean wage of workers in Brazil: 1994. Source: own calculations.



April 2014 16 / 26

Limiting Case: C-D

Production functions:

ψ i

( q

H

, q

L

) = q

β i

H q α i

L for i = 1 , 2;

α i

,

β i

> 0 implies no unique matching within sectors



April 2014 17 / 26

Sorting is unique: according to

α i

/

γ i

Sectoral wage and salary functions: and

β i

/ ( 1

γ i

) w ( q

L

) = w i q

α i

/ γ i

L for q

L

2 Q int

Li r ( q

H

) = r i q

β

H i

/ ( 1

γ i

) for q

H

2 Q int

Hi where w i and r i are wage and salary anchors in sector i

Rise in price of good 2, say due to trade, does not a¤ect wage nor salary inequality within sectors; Ricardo-Viner plus Heckscher-Ohlin e¤ects only

Limiting Case: C-D


ψ i

( q

H

, q

L

) = q

β i

H q α i

L for i = 1 , 2;

α i

,

β i



α i

/

γ i and

β i

/ ( 1

γ i

)



April 2014 17 / 26

Sectoral wage and salary functions: w ( q

L

) = w i q

α i

/ γ i

L for q

L

2 Q int

Li r ( q

H

) = r i q

β

H i

/ ( 1

γ i

) for q

H

2 Q int



Limiting Case: C-D


ψ i

( q

H

, q

L

) = q

β i

H q α i

L for i = 1 , 2;

α i

,

β i



α i

/

γ i


β i

/ ( 1

γ i

) w ( q

L

) = w i q

α i

/ γ i

L for q

L

2 Q int

Li r ( q

H

) = r i q

β i

H

/ ( 1

γ i

) for q

H

2 Q int




April 2014 17 / 26


Limiting Case: C-D


ψ i

( q

H

, q

L

) = q

β i

H q α i

L for i = 1 , 2;

α i

,

β i



α i

/

γ i


β i

/ ( 1

γ i

) w ( q

L

) = w i q

α i

/ γ i

L for q

L

2 Q int

Li r ( q

H

) = r i q

β i

H

/ ( 1

γ i

) for q

H

2 Q int





April 2014 17 / 26

Distribution of Earnings: HL/LH Equilibrium

Proposition Suppose that the sorting conditions are satis…ed for an HL/LH equilibrium in which the best workers sort into sector 1. Then an increase in the price of good 2:



April 2014 18 / 26

1

2

3

4

5 raises the labor cuto¤ q

L and reduces the manager cuto¤ workers and more mangers are employed in sector 2; q

H so that more worsens the matching of all workers except those who switch from sector 1 to sector 2; improves the matching of all managers except those who switch from sector 1 to sector 2; reduces inequality of wages everywhere; and increases inequality of salaries everywhere.

An increase in the price of good 1 has opposite e¤ects





H so that more



April 2014 18 / 26

2

3

4

5 worsens the matching of all workers except those who switch from sector 1 to sector 2; improves the matching of all managers except those who switch from sector 1 to sector 2; reduces inequality of wages everywhere; and increases inequality of salaries everywhere.




1



H so that more worsens the matching of all workers except those who switch from sector 1 to sector 2;



April 2014 18 / 26

3

4

5 improves the matching of all managers except those who switch from sector 1 to sector 2; reduces inequality of wages everywhere; and increases inequality of salaries everywhere.




1

2



H so that more worsens the matching of all workers except those who switch from sector 1 to sector 2; improves the matching of all managers except those who switch from sector 1 to sector 2;



4

5 reduces inequality of wages everywhere; and increases inequality of salaries everywhere.




1

2

3



H so that more worsens the matching of all workers except those who switch from sector 1 to sector 2; improves the matching of all managers except those who switch from sector 1 to sector 2; reduces inequality of wages everywhere; and



5 increases inequality of salaries everywhere.




1

2

3

4






April 2014 18 / 26




1

2

3

4







April 2014 18 / 26

Sorting and Matching Response in HL/LH Equilibrium

Increase p

2

) raises cut-o¤ q

L and reduces cut-o¤ and managers employed in sector q

H

, so that more workers q

H q

H max d d' sector 2 q * q

H

*

H q

H min c c' q

L min sector 1 a q

L

* a' q

*

L b b' q

L max q

L



April 2014 19 / 26

Worsens matching for all workers and improves matching for all managers except those that switch sectors.


Increase p

2

) raises cut-o¤ q


H


H q


H

*

H q

H min c c' q


L

* a' q

*

L b b' q

L max q

L



April 2014 19 / 26



Increase p

2

) raises cut-o¤ q


H


H q


H

*

H q

H min c c' q


L

* a' q

*

L b b' q

L max q

L




April 2014 19 / 26

Compensation Response in HL/LH Equilibrium

5% rise in p_2



April 2014 20 / 26

Evidence: Brazil 1986-1994



April 2014 21 / 26

Sorting and Matching Response in HH/LL Equilibrium q

L and q

H rise q

H max q

H c q

*

H q

H min a q

L min sector 2

Grossman, Helpman and Kircher b

1 b

3 b

2 b q *

L sector 1 q

L max q

L


April 2014 22 / 26

Worker matching can improve and deteriorate in sector 2 ( b

3

)

( b

1

) , deteriorate ( b

2

) , or improve in sector 1

Sorting and Matching Response in HH/LL Equilibrium q

L and q

H rise

Worker matching can improve and deteriorate in sector 2 ( b

3

)

( b

1

) , deteriorate ( b

2

) , or improve in sector 1 q

H max q

H c q

*

H q

H min a q

L min sector 2

Grossman, Helpman and Kircher b

1 b

3 b

2 b q *

L sector 1 q

L max q

L


April 2014 22 / 26

Sorting and Matching Response in HH/LL Equilibrium

Proposition Suppose that the sorting conditions are satis…ed for an HH/LL equilibrium in which the best workers and managers sort into sector 1. Then an increase in the price of good 2:



April 2014 23 / 26

1


L and the manager cuto¤ more mangers are employed in sector 2; q

H has one of the following e¤ects on matching: so that more workers and

1

2

3

4 improves matching for all workers and deteriorates for all managers; deteriorates matching for all workers and improves for all managers; improves matching for low ability inputs of the factor in which sector 2 is intensive and deteriorates for higher ability inputs of this factor, and the opposite for the other input; only (a) or (b) are possible when factor intensities are the same in both sectors, i.e., when

γ

1

=

γ

2

.





H so that more workers and



April 2014 23 / 26

2 has one of the following e¤ects on matching:

1

2

3


γ

1

=

γ

2

.



1






April 2014 23 / 26

1

2

3


γ

1

=

γ

2

.



1




1 improves matching for all workers and deteriorates for all managers;



April 2014 23 / 26

2

3

4 deteriorates matching for all workers and improves for all managers; improves matching for low ability inputs of the factor in which sector 2 is intensive and deteriorates for higher ability inputs of this factor, and the opposite for the other input; only (a) or (b) are possible when factor intensities are the same in both sectors, i.e., when

γ

1

=

γ

2

.



1




1

2 improves matching for all workers and deteriorates for all managers; deteriorates matching for all workers and improves for all managers;



April 2014 23 / 26

3

4 improves matching for low ability inputs of the factor in which sector 2 is intensive and deteriorates for higher ability inputs of this factor, and the opposite for the other input; only (a) or (b) are possible when factor intensities are the same in both sectors, i.e., when

γ

1

=

γ

2

.



1




1

2

3 improves matching for all workers and deteriorates for all managers; deteriorates matching for all workers and improves for all managers; improves matching for low ability inputs of the factor in which sector 2 is intensive and deteriorates for higher ability inputs of this factor, and the opposite for the other input;



April 2014 23 / 26

4 only (a) or (b) are possible when factor intensities are the same in both sectors, i.e., when

γ

1

=

γ

2

.



1




1

2

3


γ

1

=

γ

2

.



April 2014 23 / 26

Earnings Response in HH/LL Equilibrium

Proposition Suppose that the sorting conditions are satis…ed for an HH/LL equilibrium in which the best workers and managers sort into sector 1. Then an increase in the price of good 2 has one of the following e¤ects on inequality:



April 2014 24 / 26

1

2 if matching improves for all abilities of factor F

I abilities of factor F

D then inequality rises for F

I and deteriorates for all in every industry and declines between industries with the opposite for F

D if for factor F

I , 2

, F

I

, F

D

2 f H , L g ; matching improves in sector 2 and deteriorate in sector 1 then inequality rises among its low ability inputs and declines among its high ability inputs, while for factor F

D , 2

, whose matching deteriorates in sector 2, the opposite holds for F

I , 2

, F

D , 2

2 f H , L g .






I between industries with the opposite for F

D

, F

I and deteriorates for all in every industry and declines

, F

D

2 f H , L g ;



April 2014 24 / 26

2 if for factor F

I , 2 matching improves in sector 2 and deteriorate in sector 1 then inequality rises among its low ability inputs and declines among its high ability inputs, while for factor F

D , 2


I , 2

, F

D , 2

2 f H , L g .



1




I and deteriorates for all in every industry and declines between industries with the opposite for F

D if for factor F

I , 2

, F

I

, F

D

2 f H , L g ; matching improves in sector 2 and deteriorate in sector 1 then inequality rises among its low ability inputs and declines among its high ability inputs, while for factor F

D , 2


I , 2

, F

D , 2

2 f H , L g .



April 2014 24 / 26

Compensation Response in HH/LL Equilibrium

20% rise in p_2

Figure: Cuto¤ shifts to b

1 in previous …gure: Matching improves for all workers and worsens for all managers



April 2014 25 / 26

Conclusions

Can incorporate factor heterogeneity into familiar trade models

Factor comparative advantage generates speci…cities

Distributions of factors a¤ect pattern of trade



April 2014 26 / 26

If productivity of a unit is strictly log supermodular

Positive assortative matching within sectors

Sorting and matching are interdependent

Trade a¤ects within-industry income distribution and across

Future research: Growth and inequality, e¢ ciency and “mismatch”

Conclusions










April 2014 26 / 26


Conclusions











April 2014 26 / 26

RIETI International Seminar Handout Speaker: Prof. Elhanan HELPMAN

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