the global decline of the labor sharestatic.zybuluo.com/fanxy/wdlxdf4xa0guh56u0ef44et3/the...Ø...

THE GLOBAL DECLINE OF THE LABOR SHARE

Shi Zhengyang, Huang Yiguo, Ma Chengchao, Xie Yuchen

June 5, 2018

Author-Loukas KarabarbounisAcademic Position

Associate professor, Department of Economics, University of Minnesota

Research Area

Macroeconomics, Labor Economics

PublicationØ “Capital Allocation and Productivity in South Europe.” Quarterly Journal of Economics, 132(4), 1915-1967, November 2017.

(With Gita Gopinath, Sebnem Kalemli-Ozcan, and Carolina Villegas-Sanchez.)

Ø “The Global Rise of Corporate Saving.” Journal of Monetary Economics, 89, 1-19, August 2017. Lead Article. (With Peter Chen

and Brent Neiman.)

Ø “The Cyclicality of the Opportunity Cost of Employment.” Journal of Political Economy, 124(6), 1563-1618, December 2016.

(With Gabriel Chodorow-Reich.)

Ø “Home Production, Labor Wedges, and International Business Cycles.” Journal of Monetary Economics, 64, 68-84, May 2014.

Ø “The Labor Wedge: MRS vs. MPN.” Review of Economic Dynamics, 17(2), 206-223, April 2014.

Ø “The Global Decline of the Labor Share.” Quarterly Journal of Economics, 129(1), 61-103, February 2014. Winner of the

Emerald Citation of Excellence Award. (With Brent Neiman.)

Author-Brent NeimanAcademic Position

Professor, Booth School of Business, University of Chicago

Research Area

Macroeconomics, International Finance

PublicationØ “The Global Rise of Corporate Saving” (with Peter Chen and Loukas Karabarbounis) Journal of Monetary Economics, 2017, 89, p.1-

19. Lead Article.

Ø “Trade and the Global Recession” (with Jonathan Eaton, Sam Kortum, and John Romalis) American Economic Review, 2016, 106(11),

p. 3401-3438.

Ø “Currency Unions, Product Introductions, and the Real Exchange Rate” (with Alberto Cavalloand Roberto Rigobon) Quarterly Journal

of Economics, 2014, 129(2), p.529-595.

Ø “The Global Decline of the Labor Share” (with Loukas Karabarbounis) Quarterly Journal of Economics, 2014, 129(1), p.61-103.

Content:

Ø Introduction

Ø Model

Ø Estimation of Elasticity

Ø Conclusion and Implication

Introduction

𝑌 = 𝐴𝐾%𝐿'(%

𝐸*𝐸= 1− 𝛼

𝐸*: Expenditure on Labor, 𝐸: Total Expenditure

Motivation:

• A significant decline of global labor share since 1980s

• A significant decline in relative price of investment goods.

Trends in Labor Share

Data :

• Country-level statistics in the corporate sector

• Sources: BEA, UN, OECD, KLEMS

• Time Period:1975-2012

• Country: 59 countries that have at least 15 years of data


Labor share change:

• Changing size of industries with different level of labor share

• Changes in labor shares within industry

𝜔/ ,1 : 𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑘=𝑠𝑠ℎ𝑎𝑟𝑒𝑖𝑛𝑐𝑜𝑢𝑡𝑟𝑦𝑖=𝑠𝑣𝑎𝑙𝑢𝑒𝑎𝑑𝑑𝑒𝑑

𝑆*/ ,1: 𝑙𝑎𝑏𝑜𝑟𝑠ℎ𝑎𝑟𝑒𝑖𝑛𝑐𝑜𝑢𝑛𝑡𝑟𝑖=𝑠𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝑘

Trends in Relative Price of Investment Goods

Data :

• Country-level

• Sources: PWT, WDI, KLEMS

• Time Period:1950-2012

Trends in Relative Price of Investment Goods

A Model of The Labor Share

A. Final Consumption Good1

1 1

0( ( ) )

t t

t tt tC c z dz

ε εε ε−

−= ∫1

1 1 1

0( ( ) ) 1t tc

t tP p z dzε ε− −= =∫( )( ) ( ) tt

t tct

p zc z CP

ε−=

1

01 1

( ) ( )

1 ( ) ( ) 0( ) 1

t t

ct t t t

c t tt t t t

t t t

P C p z c z dz

d P C c z p zdc z

ε ε

π

ε επε ε

−

= −

−= − =

−

∫

Proof for cost minimization:

B. Final Investment Good

11 1

0

11 1 1

0

1 ( ( ) )

( ( ) )

( )( ) ( ) ( )

t t

t t

t t

t t

t tt

xt t t t

tt t t t t tc

t

X x z dz

P p z dz

p zx z X p z XP

ε εε ε

ε ε

ε ε

ξ

ξ ξ

ξ ξ

−

−

− −

− −

=

= =

= =

∫

∫

C. Producers of Intermediate Inputs

Given:

Capitalà𝑅HLaborà𝑊H

Aggregate Demand：

( ) ( ( ), ( ))t t ty z F k z n z=

t t t tY C Xξ= +

max ( ) ( ) ( ) ( ) ( )

. . ( ) ( ) ( ) ( ) ( ) ( )t t

t t t t t t t

t t t t t t t t t

z p z y z R k z W n z

s t y z c z x z p z C X p z Yε εξ− −

Π = − −

= + = + =

C. Producers of Intermediate Inputs

1 1 11

1

,

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( ) 1(1 )( ) ( ) 0( ) ( )

t t t

t

tt t t t t t t t t t t t

t

t tk t t

t t t

Yz y z R k z W n z Y y z R k z W n zy z

z Y F z Rk z y z

ε ε ε

ε

ε

−

Π = − − = − −

∂Π= − − =

∂

,

,

( ) ( )( ) ( )

1

t n t t t

t k t t t

tt

t

p z F z Wp z F z R

µ

µ

εµ

ε

=

=

=−

Proof:

The first order condition with respect to capital:

D. Household0

0

11

1 0

max ( , ; )

. .(1 )

(1 ) ( ( ) ( ) ( ))

t tt t t

t t

t t t

t t t t t t t t t t t

V C N

s tK K X

C X B r B W n z R k z z dz

β χ

δ

ξ

∞−

=

+

+

= − +

+ + − + = + +Π

∑

∫

1

01

0

( )

( )

t t

t t

N n z dz

K k z dz

=

=

∫

∫

The first order condition with respect to capital:

1 1 1

11 1

(1 ) (1 )( , )1( , )

t t t t

c t tt

c t t

R rV C NrV C N

ξ ξ δ

β

+ + +

++ +

= + − −

+ =

0

0

1

1 10

( , ; )

1( 1) ( ( ) (1 )

t tt t t

t t

t t t t t t t t t t t tt

L V C N

K K z dz W N R K r B B C

β χ

λ δξ

∞−

=

+ +

= +

⎡ ⎤+ − − Π + + + + − −⎢ ⎥

⎣ ⎦

∑

∫

0 ( , ) / 0t tC t t t t

t

L V C NC

β λ ξ−∂= + =

∂

1 ( 1 / ) 0t t t tt

L RK

λ λ δ ξ−

∂= + − − =

∂

Lagrange

0

1

10

( , ; )

1 ( ( ) (1 )

t tt t t

t t t t t t t t t t tt

H V C N

K z dz W N R K r B B C

β χ

λ δξ

−

+

= +

⎡ ⎤− + Π + + + + − −⎢ ⎥⎣ ⎦

∫

0 ( , ) / 0t tC t t t t

t

H V C NC

β λ ξ−∂= − =

∂

1( / )t t t t tt

H RK

λ δ ξ λ λ−

∂= − + = −

∂

Hamilton

1 1 1 1 1( ,{ ( )}, , , ) max ( , , ) ( , , )t t t t t t t t t t tU C n z X K B V C N V C Nχ β χ+ + + + += +

1 1 1 1

1 1 1 1

1 1 1 1

( , , ) ( , , )

( , ) ( , )[ ( 1)] 0

t t t t t t t t

t t t t t

C t t t C t t t t

V C N C V C N CUK C K C KV C N V C N R

χ χβ

ξ β ξ δ

+ + + +

+ + + +

+ + + +

∂ ∂ ∂ ∂∂= +

∂ ∂ ∂ ∂ ∂

= − + − − =

Bellman

E. Equilibrium

( ) 1, ( ) , ( ) , ( ) ,( ) , ( ) , ( , )

ct t t t t t t t

t t t t t t t t t t

p z P k z K n z N c z Cx z X y z C X Y F K Nξ ξ

= = = = =

= = + =

,

,

,

1

1

11

t t t tL t

t t t t t t

t t t tK t

t t t t t t

tt

t t

W N W NsY W N R KR K R KsY W N R K

sY

µ

µ

µΠ

= =+

= =+

Π= = −

Where , , , 1L t K t ts s sΠ+ + =

F. The Production Function

1 11

, ,( , ) ( ( ) (1 )( ) )t t t k K t t k N t tY F K N A K A Nσ σ σσ σ σα α− −

−= = + −

1 1

, ,

1 1

, ,

( )

(1 ) ( )

tK t k K t t t

t

tN t k N t t t

t

YF A RK

YF A WN

σσ σ

σσ σ

α µ

α µ

−

−

= =

= − =

G. The Labor Share

, 1,

, ' 1, ' '

' '

'

1

1 ( )

1 ( )

1

11 (1 (1 ) (1 )) ( )1 (1 )(1 )

K tL t t k

t t

K tL t t k

t t

t

t

KLL

L

As

RA

sR

ZZZ

As ss R

σ σ

σ σ

σ

µ αµ

µ αµ

µ µµ µ

−

−

−

− =

− =

= −

+− + + =

− + +!

IV. The Elasticity of Substitution

A. Relative Price of Investment

B. Markups

C. Capital-Augmenting Technological Progress

D. Skilled versus Unskilled Labor

A.RelativePriceofInvestment

�̂�L,j=ln sL,j , 𝜉L𝑗=ln 𝜉j

Set𝜇 = 1, 𝜇O = 0, 𝐴L𝐾=0

First-order approximation:

1( 1 )j j jj

R ξ δβ

= − +

,,

,

ˆˆ ( 1)1

L jL j j j

L j

ss u

sγ σ ξ= + − +

−

111 (1 (1 ) (1 )) ( )1 (1 )(1 )

KLL

L

As ss R

σµ µµ µ

−+− + + =

− + +!

A. Results

A. Visualization

B. Markups

( )

, , ,

,

, , , ,

,,

,

1 11

1( 1 )

1/ 1

1ˆˆ ˆ( )

ˆˆ ˆ ˆ((1 )(1 ) 1) ( 1)1

jj L j K j

j j jj

jj

j

j j j j j jK j

j j j

jj L j L j K j K j

L j jL j j j j j

L j j

s s s

R

XK

R K Xs

Y Y

s s s ss

s us

π

µ

ξ δβ

δ

ξ β δ

δ

µµ

µµ γ σ ξ µ

µ

= =− +

= − +

=

⎛ ⎞⎛ ⎞− += = ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

=+

+ + − = + − + +−

B. Results


Set 𝜇 = 1, �̂� = 0

First-order approximation:

,, ,

,

ˆ ˆˆ ( 1) (1 )1

L jL j j K j j

L j

ss A u

sγ σ ξ σ= + − + − +

−

111 (1 (1 ) (1 )) ( )1 (1 )(1 )

KLL

L

As ss R

σµ µµ µ

−+− + + =

− + +!


( ) ( )( ),

ˆˆ ˆ(1 ) ,

ˆK

K j j

sd Acorr A

sdσ σ σ ξ

ξ− = −!

1.251.20

σ

σ

=

=

!

D. Skilled versus Unskilled Labor

How to nest the three inputs: skilled labor, unskilled labor and the capital stock?

(1)

(2)

(3)

1 11 1 11

1 2 2 1

^

,,

,

(1 ) (1 )

ˆˆ ( 1)1

t t t t

L j jL j j j

L j j

Y K U S

s Us u

s K

σρ σ σ

ρ ρ σρ σρ ρ σφ φ φ φ

γ σ ξ κ

− −⋅− − −−⎛ ⎞

⎛ ⎞⎜ ⎟= + − + −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎜ ⎟

⎝ ⎠

⎛ ⎞= + − + +⎜ ⎟⎜ ⎟− ⎝ ⎠

1 11 1 11

1 2 2 1

^

,,

,

(1 ) (1 )

ˆˆ ( 1)1

t t t t

L j jL j j j

L j j

Y K S U

s Ss u

s K

σρ σ σ

ρ ρ σρ σρ ρ σφ φ φ φ

γ σ ξ κ

− −⋅− − −−⎛ ⎞

⎛ ⎞⎜ ⎟= + − + −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎜ ⎟

⎝ ⎠

⎛ ⎞= + − + +⎜ ⎟⎜ ⎟− ⎝ ⎠

( ),t t t tN N S U=

D. Results

V. The Decline in the Labor Share

Ⅵ . Conclusion

• Offer an explanation for the decline of global labor share

• Estimate the shape of the production function

• Explore the macroeconomic and welfare implications

( ) ( )( )( )

( )( )( )( )

( )( )( )( )

1

1

1

2

ˆ1 1ˆ ˆ1 1 1ˆ1 ˆ1 1

11ˆ 1ˆ1

1

ˆ11 1 ˆˆ1 1ˆ 1

ˆ1

ˆ11 1ˆˆ1 1ˆ

ˆ ˆ1

LL

L

L

L

L

AS SS R

S

ASR

SS

ASRdS

d S

σ

σ

σ

µ µµ µ

σ

µσ

µµ

µ µ

σ µµ

µ µ µ

−

−

−

⎡ ⎤⎛ ⎞ +⎡ ⎤ ⎢ ⎥− + + =⎜ ⎟ ⎣ ⎦− ⎢ ⎥+ +⎝ ⎠ ⎣ ⎦=

= −+

>

⎡ ⎤+⎢ ⎥− −⎢ ⎥+ +⎣ ⎦= −

+

⎡ ⎤+⎢ ⎥− −⎢ ⎥+ +⎣ ⎦=

+( )

ˆ ˆ1 1ˆ0 1ˆˆ 11 L

dS Ad SR

µµ σ µ

⎡ ⎤+= ⇒ = −⎢ ⎥

−+ ⎣ ⎦

How does S change with μ, A, R Implication

Thank you

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