Notes onLabor Share, Concentration, Markup

Investment, Intangibles

Vu T. Chau

Harvard University

May 7, 2019

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Outline

Declining Labor Share

• Karabarbounis and Neiman (2014), Autor et al. (2018)

Markup and Concentration

• de Loecker and Eeckhout (2018), Gutierrez and Philippon

(2018)

Intangible Capital

• Crouzet and Eberly (2019)

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Labor Share

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Labor Share

Cost-minimization:

C (r ,w ,Y ) ≡ minK ,L

{wL+ rK } s.t. F (K , L) ≥ Y

First-order condition:

r = λFK , w = λFL

Note: The Lagrange multiplier is marginal cost:

λ = ∂C∂Y = MC (Envelope Theorem).

Labor share:

sL ≡wL

pY=λFLL

pY=

λ

p︸︷︷︸=1/µ

FLL

Y=

1

µ

FLL

Y

For Cobb-Douglas: FLL/Y = (1 − α), so sL = (1 − α)/µ

(constant).

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Elasticity of substitution

If the production function is CES:

Y = F (K , L) =[(AKK )1−

1σ + (ALL)

1− 1σ

] σσ−1

Optimal factors demand:

lnrK

wL= (1 − σ) ln

r

w

where r ≡ r/AK , w ≡ w/AL.

Elasticity:d ln (rK/(wL))

d ln(r/w)= 1 − σ

Suppose capital got relatively cheaper (r/w ↓). The laborshare would decline (rK/(wL) ↑) if and only if σ > 1.

• Note: rKwL = rK/(pY )

wL/(pY ) = sKsL

. We have sK + sL + sΠ = 1. To

make the argument that sK/sL ↑ implies sL ↓, implicitly

assumed constant sΠ. (True under monopolistic competition.)

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Is σ > 1?

Antras (2004): σ ∈ [0.5, 0.9], even when controlling for biased

technological change.

Oberfield and Raval (2018, WP): σ ≈ 0.7 for manufacturing.

• Estimate plant-level elasticity:

lnrKni

wLni= (σn − 1) lnwMSA

ni + controls + εni

• Assume r roughly constant across MSA (capital is perfectly

mobile).• Potential endogeneity: AL/AK correlates with w at MSA level→ solve by Bartik instruments.

• Aggregating plant-level elasticities:

σAGG = (1 − χ)σ+ χε, χ ≡∑ (αi − α)

2

α(1 − α)θi

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Karabarbounis and Neiman (2014)

Identify σ from variation of relative price of investment goods

(ξ) in the cross-section of countries:

sL,j1 − sL,j

sL,j = γ+ (σ− 1)ξj + ui

ξ influences the rental rate of capital R: ξ = R.

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Autor et al. (2017)

Document:1 The rise of “superstar firms” and rising concentration.2 Sectors with highest rise in concentration see largest decline in

labor share.3 Aggregate decline in labor share mostly due to re-allocation

between firms, not a general decline within.

Organizing framework: model with fixed overhead labor

sL =1

µ

FLL

Y+

wF

piYi=

1 − α

µ+

wF

piYi

A superstar firm can have lower sL because it has:

• higher markup µ.• high productivity Ai → high piYi → lower F/(piYi ).

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Detour: Measuring Concentration

Measure 1: Herfindahl - Hirschman Index (HHI)

HHI ≡∑i

s2i

where si ≡ salei∑j salej

is the sale share of firm i .

• Value between 0 to 1 (or 0 to 10000, if share = 1 for 1%)• HHI = 1 corresponds to monopoly. HHI ≈ 0 corresponds to

perfect competition.

Measure 2: sale shares of top 4 / 8 / 20 firms (CR4, CR8,CR20).

• Often correlates with HHI, but not always.• Statistics readily available on Census’ website.

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Detour: Concentration and Data Availability

Using Census data vs. Compustat:

Census has universe of firms. Compustat only publicly listed

firms.

Census only provides HHI for manufacturing (last time I

check), problematic if you do not have firm-level data.

Census only available for census years (1997, 2002, 2007 etc.)

• So it depends on at which frequency you want to run your

analysis.

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Autor et al. (2017): Rising Concentration

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Autor et al. (2017): Aggregate decline causedby reallocation

S =∑i

ωiSi = S +∑

(ωi −ω)(Si − S)

∆S = ∆S︸︷︷︸within

+∆[∑

(ωi −ω)(Si − S)]

︸ ︷︷ ︸between

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Markup

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De Loecker, Eeckhout, Unger (2018)

Recall FOC from cost-minimization for any variable input:

PVit = λit

∂Yit

∂Vit⇒ PV

it Vit

PitYit︸ ︷︷ ︸sVit

=λit

Pit︸︷︷︸=1/µit

∂Yit

∂Vit

Vit

Yit︸ ︷︷ ︸≡θVit

Thus, markup is given by:

µit =θit

sVit

Estimate θit a la Olley - Pakes (1996)

Calculate sVit using Compustat’s Cost of Goods Sold (COGS).

• Controversial

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De Loecker, Eeckhout, Unger (2018)

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Gutierrez and Philippon (2018)

Investment has been weak despite high Q.

Potential explanations:

• Financial frictions: external finance, bank dependence• Measurement errors: intangibles, globalization• Lack of competition: regulation, concentration due to other

factors• Tighter governance: ownership and shareholder activism.

Find evidence in support of declining competition hypothesis.

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Gutierrez and Philippon (2018): Q

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Gutierrez and Philippon (2018): BusinessDynamism

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Gutierrez and Philippon (2018): RegressionResults

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Eberly and Crouzet (2018)

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