macroeconomic risk and the labor share of income (slides)

Macroeconomic Risk and the Labor Share of Income

Gregor Schubert

June 27, 2014

Gregor Schubert Macroeconomic Risk and the Labor Share of Income June 27, 2014 1 / 23

Motivation

In the mid-20th century, economists considered it an empirical‘stylized fact’ that labor shares of income were constant (e.g. Kaldor(1961))

I “For a long time, the idea accepted by most economists anduncritically repeated in textbooks was that the relative shares of laborand capital in national income were quite stable over the long run.”– Thomas Piketty (2014), “Capital in the Twenty-First Century”

In theory, Cobb-Douglas production function with competitive factormarkets implies constant factor shares of income

BUT: Recent data show large variations in the labor share bothwithin and between countries (e.g. Karabarbounis & Neiman (2014))


Motivation

-6-4

-20

2

1975 1980 1985 1990 1995 2000 2005 2010

Corporate LS Total LS

Change in the Labor Share since 1975 (in ppt)

Source: Author’s calculation based on data from Karabarbounis & Neiman (2014)


Motivation

Several different explanations have been advanced to explain thesechanges in the labor share:

I Capital account openness (e.g. Jayadev(2007)) and trade shares(Harrison (2005))

I Relative price of investment goods (Karabarbounis & Neiman (2014))I Decline in Unionization and rise of offshoring (Elsby et al. (2013))

This paper provides a new explanation based on changes inmacroeconomic risk over time


This Paper

1 Develops a tractable theoretical model of the determination of thelabor share of income, incorporating risk premia for macroeconomicfluctuations into factor supply functions

2 Identifies two macro-risk factors that should affect the labor share:I Inflation varianceI Covariance of inflation and productivity shocks

3 Tests the predicted effect of these macro-risk factors empirically incross-country panel of OECD countries (1975-2010)

I Compares alternative explanations for variations in the labor shareagainst macro-risk story

I Explores impact of macro-risk factors on labor force participation rate


Theoretical Model - Key Assumptions

Both workers and capital investors are risk-averse

Workers’ household income comes from wages, while capital investors’income depends on firm profitability and aggregate productivityshocks

CES production technology with low elasticity of substitution (σ < 1):

Yt = θt

[(1 − α)L

σ−1σ

t + αKσ−1σ

t

] σσ−1

Nominal wages are determined in advance before inflation shocks areobserved

Workers are heterogeneous with regard to risk aversion and firms canwage-discriminate between workers based on reservation wage


Theoretical Results1 Higher inflation risk leads to a lower labor share of income

I Workers demand higher risk premium proportional to their risk aversionI Difference between marginal wage and average wage increases, which

decreases the non-capital share of income going to labor

LD

LS(σ2π,3)

LS2(σ2π,2)

LS1(σ2π,3)

L∗2

w∗2

Ut

LI2

Labor Force

Wage


Theoretical Results2 Higher covariance between inflation and productivity growth leads to

a lower labor share of incomeI Capital investors demand higher risk premium because single firm

profits become more correlated with the overall portfolio performanceI Capital share of income increases with rental rate due to low elasticity

of substitution

LD2 (r2)

LD1 (r1)

LS

L∗2

w∗2

Ut

LI2

Labor Force

Wage


Theoretical Results

3 Higher out-of-work benefits lead to a higher labor share of income.I Higher wage demanded at every level of risk aversion raises non-capital

share of income due to low elasticity of substitution


Empirical Strategy

Data:I Unbalanced panel of 18 OECD countries for 1975-2010I Focus on corporate labor share (CLS) to avoid measurement issues for

unincorp. businesses

Estimation: IV regression in first differences, instrumenting forlagged diff. of CLS using 2nd and 3rd lags of CLS and unemp. rate

Specification

sL,t = δ0 + δ1sL,t−1 + δ2σθ,π,t + δ3σπ,t + δ4Ut + β′Xt + ui + εt

I sL,t : Labor share of income (in %)I σθ,π,t : Covariance of RGDP growth and CPI inflation (5 years trailing)I σπ,t : Standard deviation of CPI inflation (5 years trailing)I Ut : Social expenditures (% of GDP)I Xt : Control variables (e.g. GDP(PPP) per cap., Population, Risk-free

interest rate)I ui : Country-fixed effect


Empirical Results

Estimated effects of the macro-risk factors on the labor share areconsistently negative and statistically and economically significant

I Results are robust to controlling for alternative drivers of CLSvariations: Trade Share, Cap. Acc. Openness, Union Density, RelativePrice of Inv. Goods

A one standard deviation (SD) increase in inflation risk decreases thelabor share by 1.3-2.0 ppt (0.4-0.6 SD)

A one SD increase in the covariance risk decreases the labor share by1.6-1.9 ppt (0.5-0.6 SD)

Higher social expenditures increase the labor share


Conclusions

1 Macroeconomic risk affects the labor share of incomeI Macroeconomic policy may matter for distribution questions

2 Changes in the labor share may reflect changing risk premiaI Variations in the labor share can be neutral for worker welfare


Thank you for your attention!


Appendix


Labor Supply

Workers decide between working and receiving uncertain real incomethat varies with inflation, or certain benefits of not-working.

Standard intertemporal optimization with CRRA utility implies thatworkers with consumption process ∆ct+1

ct= δ0 − δ1νt+1 - where νt+1 is

an inflation shock - demand a risk premium such that the real wage is

E [wRt+1] ≈ Ut+1 + wN

t+1γRβδ1σ2π,t+1

where Ut is the value of not-working, γ is the degree of risk aversion,R is the risk-free IR, β is the discount factor, and σ2

π,t is the varianceof inflation shocks

Assuming that workers are uniformly distributed over risk aversion,such that kL = γ, the labor supply will be given by

LSt =wNt − Ut

wNt kRβδ1σ2

π,t


Labor Demand and Capital Risk Premium

Capital investors receive returns that are a function of profits, andtherefore of inflation shocks (e.g. dividends):

Rt+1 = Et [Rt+1] + ρ1νt+1

Standard intertemporal optimization with CRRA utility and investor

consumption process∆ckt+1

ckt= τ0 + τ1εt+1 - where εt+1 is an

aggregate productivity shock - imply a rental rate of capital of

Et [rt+1] = Et [Rt+1] − 1 = R − 1 + γβRρ1τ1σπ,θ,t+1

where ρ1,τ1 are positive constants, and σ2π,θ,t is the covariance of

inflation and productivity shocks

Taking first-order conditions of standard profit maximization problemfor the firm, we can then find the labor demand function to be

LDt =Yt

θt

[(1 − α) + α

(α

1 − α

)σ−1(w∗trt

)σ−1] σ

1−σ


Labor Share of Income

We can write the labor share of income in the following way:

sL,t =LItYt

=LIt

w∗t L∗t

w∗t L∗t

Yt=

LItw∗t L

∗t

(1 − sK ,t)

Then, we use the FOC of the firm to replace sK ,t and integrate overwage demand curve to find LIt

After simplifying, the labor share is given by

sL,t = (1 − r1−σt (αθt)

σ)Ut ln

(w∗tUt

)(w∗t − Ut)

−1


Extension: Labor Force Participation Rate

Theoretical Predictions:1 Higher inflation risk leads to a lower labor force participation rate

(LFPR)2 Higher covariance risk leads to a higher LFPR3 Higher out-of-work benefits lead to a lower LFPR

Empirical Results:I Estimated inflation risk coefficient is robustly negativeI Results for covariance risk and benefits have the right sign but are not

significantI All three effect sizes are small empirically


Empirical Results: Risk and the Labor Share Table


Empirical Results: Robustness Checks Table


Empirical Results: Labor Force Participation Table


Labor Share for Biggest OECD Economies

5560

6570

Labo

r Sha

re

1975 1980 1985 1990 1995 2000 2005 2010Year

United States

5055

60La

bor S

hare

1975 1980 1985 1990 1995 2000 2005 2010Year

Japan

5560

6570

Labo

r Sha

re

1975 1980 1985 1990 1995 2000 2005 2010Year

Germany

5560

6570

Labo

r Sha

re

1975 1980 1985 1990 1995 2000 2005 2010Year

United Kingdom

5560

6570

75La

bor S

hare

1975 1980 1985 1990 1995 2000 2005 2010Year

France

5055

6065

Labo

r Sha

re

1975 1980 1985 1990 1995 2000 2005 2010Year

Italy

Labor Share of Income in Large OECD Economies

Source: Author’s calculation based on data from Karabarbounis & Neiman (2014)


Summary Statistics


macroeconomic risk and the labor share of income (slides)

Economy & Finance