labor shares and income inequality - working papermkredler/readgr/lionadamsetal14.pdf · cv yl...

Labor Shares and Income InequalityWorking Paper

Adams, Karabarbounis and Neiman

Presented by Meng Li

15 March, 2017

Adams, Karabarbounis and Neiman Income Inequality 15/3/2017 1 / 21

Introduction

Introduction

Motivating Facts

Declining labor shares in income; Declining labor shares

Rise in income inequality.


Introduction

Introduction

The relationship between factor shares and inequality is NOT simple in arich model.

CV (y) = αL · ρ(y l)· CV

(y l)

+ (1− αL) · ρ(yk)· CV

(yk)


Introduction

Introduction

Question: develop a framework where all above terms are jointlydetermined to evaluate quantitatively the relationship between the changesin labor share and total income inequality.


Model

Households

Heterogeneous in

labor income shocks z ;

skill levels h;

ages j ;

assets a.

Distribution of households: λ(a, z , h, j).


Model

Households

Endowed with zΦ(h, j)(1− h) units of unskilled labor and zΦ(h, j)hunits of skilled labor;

Skill levels h: drawn from the distribution πh(h | j) when householdsare born and constant over time;

Labor income shocks z follow a Markov chain with a distributionπz(z ′ | z , h).


Model

Households

n: endogenous part of household’s labor supply;

Wu and Ws : wage per unit of unskilled and skilled labor supply;

Pre-tax labor income zΦ(h, j)(Wu(1− h) + Wsh)n.


Model

Households

Accumulate assets a;

r : interest rate;

Exogenous borrowing limit ψ.


Model

Households

Ages j ∈ J = 1, 2, ...,Nj , where Nj denotes the maximum number ofperiods that a household lives.

Deaths are realized at the end of each period.

µhj : probability that a household with skill h and age j survives toperiod j + 1, with µhNj = 0.

Death rate in the aggregate economy is∑

hj (1− µhj)λhj .


Model

The Household’s Problem

v(a, z , h, j) = maxc,n,a′

{u(c, n) + βµhj

∑z ′∈Z

πz(z ′ | z , h

)v(a′, z ′, h, j + 1)+

+ (1− µhj) v̄(a′, j)}

subject to

c+a′−a = (1− τn) zΦ(h, j)(Wu(1−h)+Wsh)n+ra+T (a, z , h, j)+B(a, z , h, j)

a′ ∈ A = [ψ,∞).

v̄ (a′, j): value that a dying household of age j derives from leaving abequest equal to a′.

T (a, z , h, j): lump-sum transfers to a household.

B(a, z , h, j): inherited bequests.


Model

Production

3 goods: consumption good C , IT capital good Xs and non-IT capitalgood Xu;

Perfectly competitive representative firm using unskilled labor U,skilled labor S , non-IT capital Ku, and IT capital Ks .

F = A (Ku)φu

φsφkK

εk − 1

εks + (1− φk) S

εk − 1

εk

εk

εk − 1

εs − 1

εs

+

(1− φs)U

εs − 1

εs

εs

εs − 1(1−φu)

.


Model

Production

Labor hired at prices Wu and Ws .

Capital rented from intermediaries at prices R̃u and R̃s .

Corporate tax τc on sales net of labor expense.


Model

Profit Maximization Problem

maxUg ,Sg ,Kg

u ,Kgs

Πg = (1− τc) (pgG −WuUg −WsS

g )− R̃uKgu − R̃sK

gs ,

subject to

G ≤ FG =1

ξgF (Ug , Sg ,K g

u ,Kgs ) .

Normalize1

ξc= 1


Model

Intermediaries of Capital

Intermediaries purchase investment goods Xu and Xs from the finalgood producer at prices ξu and ξs ;

Augment capital stock:

K ′u = (1− δu)Ku + Xu,

K ′s = (1− δs)Ks + Xs ;

Rent two types of capital to the final good producer at before-taxrates of R̃u and R̃s .


Model

Intermediaries of Capital

Maximize the cum-dividend value of firm W

W (Ku,Ks) = maxK ′u ,K

′s

D +1

1 + rW(K ′u,K

′s

),

where D = R̃uKu + R̃sKs − ξuXu − ξsXs .

Owned by mutual fund invested by households.


Model

Measure Shares

Aggregate across sectors,

Y = C + ξuXu + ξsXs = WuU + WsS + RuKu + RsKs ,

where Ru =R̃u

1− τcand Rs =

R̃s

1− τc: user cost of capital.

Define factor income shares:

αLu =WuU

Y, αLs =

WsS

Y, αKu =

RuKu

Y, and αKs =

RsKs

Y;

Labor share:αL = αLu + αLs ;

Capital share:αK = αKu + αKs


Results

Calibration

Calibrate the share parameters to match the factor income sharesobserved in the US around 1980;

Choose the ratio of the supply of unskilled to skilled labor U/S tomatch the skill premium observed in the US data in 1980;

Estimate the depreciation rates for IT and non-IT capital fromKLEMS data;

Calibrate borrowing limit to target the share of households withnegative asset holdings observed in the data.


Results

Experiments

Introduce a shock which results in a new stationary state.


Results

Changes in the Relative Price of IT Capital Goods

Decrease the price of IT capital goods: reduce ξs/ξu by 86%.


Results

Changes in the Relative Price of IT Capital Goods

Table: Key Steady-State Moments inSimulated Experiments

Moment Baseline Value Lower Price of Capital Goods

Ks/Y 0.035 0.726αKs 0.024 0.070Ws/Wu 1.522 1.682αLs 0.185 0.185αKu 0.308 0.308αLu 0.483 0.437αL 0.668 0.622

CV(y l)

0.696 0.718

CV(yk

)1.128 1.086

ρ(y l)

0.938 0.931

ρ(yk

)0.626 0.650

CV (y) 0.664 0.678

Results: labor share declines; income inequality rises.


Conclusions

Conclusions

1 Develop a framework to evaluate quantitatively the relationshipbetween the changes in labor share and total income inequality;

2 A decline in relative price of IT capital can partially explain thedecrease in labor share and the rise in income inequality.


Declining Labor Shares

main


labor shares and income inequality - working papermkredler/readgr/lionadamsetal14.pdf · cv yl...

Documents