market structure and firm investment

Market Structure and Firm Investment

Alberto Polo, Peifan Wu

February 26, 2020UBC Macro Lunch

Motivation

Market Structure: competition, concentration, ...

Question:– Why market structure? gap between macro and IO– Does that matter? cross-sectional implication; aggregate fluctuation

Facts:– literature: linking market concentration (rise of “superstar” firms) to

– firm / industry labor shares– profit margins / markups– pricing behavior– firm investment

– market concentration varies across time and industries

1 / 21

Facts on Market Concentration

1972 1977 1982 1987 1992 1997 2002 2007 2012 20172017201720172017201720170

10

20

30

40

50

60

70

80Perc

enta

ge p

oin

tsTop-4-firms market share

Median

p10-p90

Concentration ratios: manufacturing, SIC 4-digitSubstantial cross-sectional variation in concentration

2 / 21

Facts on Market Concentration

1977 1982 1987 1992 1997 2002 2007 2012 2017201720172017201740

30

20

10

0

10

20

30

40

Perc

enta

ge p

oin

tsp25-p75 % change from 5 years before

Top-4-firms market share



25th-75th percentile ranges of changes: substantial variability over time

3 / 21

Roadmap

Goal: a model to– market structure → firm’s production, markup, investment decisions– show the channel of strategic substitution

Results:– cross-sectional model implications match empirical evidence– firm investment under different market concentration

– changes in levels– sensitivity in business cycle

4 / 21

Full Model – Environment Illustrative Toy Model

Discrete time, infinite horizon, aggregate TFP shock

Representative household:– consume final good, provide labor– nested CES demand on firm products

Heterogeneous firms and industries:– a continuum of industries, two firms in each industry– hire labor, choose production quantities– hold capital, invest with cost

Timing:1. Aggregate shock realizes2. First Stage: Firms choose labor for quantity (Cournot) competition3. Second Stage: Investment cost shocks realize, firms choose investment

5 / 21

Full Model – First Stage

Demand function for firm i in industry s:

pi (s) =(

ci (s)c (s)

)− 1σ(

c (s)C

)P

where c (s) =(

c1 (s)σ−1

σ + c2 (s)σ−1

σ

) σσ−1

C =

(∫c (s)

η−1η ds

) ηη−1

η < σ: substitutability across sectors < within a sector

6 / 21

Full Model – First Stage

For firms i = 1, 2 within an industry:

Production:

yi = Zkαi l1−α

i

log Z′ = ρ log Z + σϵ′

Firm’s profit maximization:

πi = maxli

pi (yi, y−i) yi − wli

Firms i = 1, 2 choose li simultaneously → Cournot duopoly

7 / 21

Full Model – Second Stage

Capital accumulation:k′i = (1 − δ) ki + xi

Costs of investment:– Fixed cost: pay θi ∼ F (θ) if investment xi ̸= 0, private information– Variable cost: convex on investment xi

Φ (xi, ki) =ϕ

2

(xiki

)2

ki

Firms i = 1, 2 invest simultaneously → dynamic duopoly

8 / 21

Full Model – Value Function

Firm’s value function at the beginning of a period:

Vi (ki, k−i; Z) = πi (ki, k−i; Z) +∫

max{

VNAi , VA

i − θi

}dF (θi)

VNAi (ki, k−i; Z) = βEVi

((1 − δ) ki, k′−i (θ−i) ; Z′)

VAi (ki, k−i; Z) = max

xi(ki,k−i;Z)−xi − Φ (xi, ki) + βEVi

(k′i, k′−i (θ−i) ; Z′)

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Characterization

Key Mechanism: Strategic Substitutability

Dynamic duopoly by choosing quantities:– strategic substitutability– opposite as choosing prices (strategic complementarity)

... in other words– less production comparing to no opponent case

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First Stage

The static effect from the opponent:– shifts the demand curve– affect markups

Price elasticity of demand ϵ of firm i

∂ ln yi∂ ln pi

= − 11η ζ + 1

σ (1 − ζ)

ζ ≡y

σ−1σ

i

yσ−1

σi + y

σ−1σ

−i

∈ (0, 1)

y−i ↑⇒ ζ ↓⇒ |ϵ| ↓11 / 21

First Stage

The static effect from the opponent:– shifts the demand curve– affect markups

Markup µi: ratio between the price and the marginal cost of production

pi = µiw

MPLi

µi =

[(1 − 1

σ

)+

(1σ− 1

η

)(yi

y (s)

)1− 1σ

]−1

y−i ↑⇒ µi ↓

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First StageThe static effect from the opponent:

– shifts the demand curve– affects markups

Firm i’s markup in equilibrium

Other's capacity

1

2

3

4

5

6

Own

capa

city

1

2

3

4

5

6

1.05

1.10

1.15

1.20

1.025

1.050

1.075

1.100

1.125

1.150

1.175

1.200

1.225

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Second Stage

Threshold policy for active investment:

θ̄i (ki, k−i) = VA (ki, k−i)− VNAi (ki, k−i)

First-order condition for active investment:

1 +∂Φ

(x∗i , ki

)∂x∗i

= β∂Eθ−i,ZVi

(k′i, k′−i (θ−i) ; Z′)∂x∗i

The dynamic effect from the opponent:– Large opponent hinders my investment

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Second Stage

1 2 3 4 5 6

Own capacity

0

1

2

3

4

5

6Other's capacity

0.01

0.89

1.77

2.65

3.53

4.41

5.3

6.0

y10

Active investment policy functions0.0 2.5 5.0

0.0

2.5

5.0

0.0000

0.0004

0.0008

0.0012

0.0016

0.0020

0.0024

0.0028

Stationary distribution of industries15 / 21

Cross-sectional Implications

Market Concentration and Labor ShareFirm’s labor share as function of market share

ωi =wlipiyi

= MPLiliyi

[(1 − 1

σ

)+

(1σ− 1

η

)vi

]= (1 − α)

[(1 − 1

σ

)+

(1σ− 1

η

)vi

]

Industry’s labor share

wl1 + wl2p (s) y (s)

= (1 − α)

(1 − 1σ

)+

(1σ− 1

η

)(v2

1 + v22

)︸︷︷︸

HHI

HHI ↑ ⇒ Industry labor share ↓

16 / 21

Market Concentration and Labor Share Parameters

0 10 20 30 40 50 60 70 80 90 100Top-4-firms market share

25

20

15

10

5

0

5

% c

hange w

rt t

op-4

mark

et

share

∈[0,1

4) Semi-elasticity of labor share to market concentration

50 55 60 65 70 75 80 85 90 95 100Top-firm market share

5

4

3

2

1

0

1

% c

hange w

rt t

op m

ark

et

share

∈[5

0,52

)

Semi-elasticity of labor share to market concentration

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Market Concentration and Investment Parameters

Dependent Variable: Net investment rateIndustry Variable GP (2017) Simulated

Average Q (t-1) 0.101 0.145(4.78) (14.30)

Marginal Q (t-1) 0.108(14.48)

Revenue HHI (t-1) -0.028 -0.038 -0.018(-1.70) (-3.54) (-1.89)

log(assets) (t-1) included -0.154 -0.191(-14.24) (-19.68)

t-statistics in brackets.

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Market Structure and Investment Cyclicality

Model Prediction

0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4Strategic firm's capital

Small

Medium

Large

NON-strategic firm's capital

Δ strategic firm's

inv.

rate

(%

points)

Large opponent → investment sensitivity to TFP shock ↓19 / 21

Empirical Exercise

Iijt

Kijt−1= β1CONit ∗ yt + β2CONit + γ · Xjt + ϵijt

LHS: firm investment rate / firm research intensity Distribution

RHS:– CONit: market concentration measure– yt: HP-detrended GDP– Xjt: control variables – firm size, age, average Q, firm dummies– Robustness Check

20 / 21

Table: Firm-level OLS Results

(1) (2) (3) (4) (5) (6) (7)I/K ∆K/K I/K (95% cut) XRD/K

CON ∗ yt 1.916∗∗∗ 1.599∗∗∗ 1.740∗∗∗ 1.720∗∗∗ 1.182∗∗∗ 0.405∗∗

(2.969) (2.528) (2.717) (2.626) (3.445) (2.363)

CON -0.060∗∗∗ -0.060∗∗∗ 0.004 0.004 0.004 -0.004 -0.002(4.172) (4.140) (0.300) (0.297) (0.252) (0.453) (0.589)

yt 0.917∗∗∗ 0.871∗∗∗ 0.628∗∗∗ 1.751∗∗∗ 1.929∗∗∗ 0.856∗∗∗ -0.192**(6.294) (5.943) (4.350) (4.494) (4.830) (4.070) (1.999)

log (ATt−1) -0.041∗∗∗ -0.041∗∗∗ -0.027∗∗∗ -0.015∗∗∗ -0.034∗∗∗

log (ATt−1) ∗ yt -0.021 -0.008 0.042 0.020

qt−1 0.016∗∗∗ 0.018∗∗∗ 0.019∗∗∗ 0.011∗∗∗ 0.005∗∗∗

qt−1 ∗ yt -0.257∗∗∗ -0.172∗∗∗ -0.147∗∗∗ 0.038∗∗∗

Age -0.001∗∗∗ -0.001∗∗∗ -0.003∗∗∗ -0.002∗∗∗ 0.003∗∗

Age∗yt -0.029∗∗ -0.042∗∗ -0.019∗∗ 0.001

Constant 0.091 0.084 0.205 0.202 0.053 0.143 0.050N 19547 19311 18543 15148R2 0.28 0.28 0.31 0.31 0.18 0.31 0.76

t-statistics in brackets∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

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Thank you!

An Illustrative Model back

A simple two-firm static Cournot competition

– Firms i = 1, 2 hold initial production quantity qi

– Firms choose q′i facing– Demand function p′i = a − 1

b

(q′i + γq′−i

)– Quadratic investment adjustment cost − ϕ

2

(q′iqi

)2qi

– Marginal cost of production c

22 / 21


Best response function of firm i

q′i =(a − c)− γ

b q′−i2b +

ϕqi

Pure strategy NE solution

q′i =bqi (a − c) (bϕ + q−i (2 − γ))

(bϕ + 2qi) (bϕ + 2q−i)− qiq−iγ2

23 / 21


Three analytical results: larger q−i

– shrinks firm i’s demand– hinders firm i’s investment– making q′i less sensitive to c

24 / 21

Parameters back

Table: Parameters

Parameter Description Value Remark

α Capital share 13

σ Elasticity within industry ∞ Perfect substitutesη Elasticity between industries 5.0β Discount rate 0.98δ Capital depreciation rate 0.1 Annual rateϕ Quadratic capital adj. cost 1.0

F (θ) Fixed capital adj. cost θ ∼ Exp (1.0)

25 / 21

Investment Rate Distributions

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Gross Investment Rate

0.0

0.5

1.0

1.5

2.0

2.5

3.0Prob

abilit

y

26 / 21

Investment Rate Distributions back

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0Changes in Capital

0.0

0.5

1.0

1.5

2.0

2.5

3.0Pr

obab

ility

27 / 21

Table: Additional Robustness Checks

(1) (2) (3) (4) (5)top 8 top 20 top 50 HHI q = MV

PPENTCON ∗ yt 2.350∗∗∗ 3.583∗∗∗ 3.900∗∗ 1.091∗∗∗ 2.172∗∗∗

(2.752) (2.717) (1.940) (2.599) (3.391)

CON 0.018 0.034 0.056 -0.005 0.013(0.909) (1.159) (1.317) (0.614) (0.919)

yt 1.734∗∗∗ 1.726∗∗∗ 1.705∗∗∗ 1.564∗∗∗ 1.437∗∗∗

(4.460) (4.439) (4.376) (3.643) (3.962)

log (ATt−1) -0.041∗∗∗ -0.041∗∗∗ -0.041∗∗∗ -0.042∗∗∗ -0.048∗∗∗

log (ATt−1) ∗ yt -0.019 -0.017 -0.014 0.034 -0.023

qt−1 0.018∗∗∗ 0.018∗∗∗ 0.018∗∗∗ 0.018∗∗∗ 0.001∗∗∗

qt−1 ∗ yt -0.254∗∗∗ -0.253∗∗∗ -0.251∗∗∗ -0.251∗∗∗ -0.001∗∗∗

Age -0.002∗∗∗ -0.002∗∗∗ -0.002∗∗∗ -0.002∗∗∗ -0.001∗∗∗

Age∗yt -0.029∗∗ -0.028∗∗ -0.027∗ -0.034∗∗ -0.028∗∗

Constant 0.203 0.203 0.206 0.228 0.252N 19572 19561 19538 17881 19547R2 0.31 0.31 0.31 0.32 0.31

t-statistics in brackets∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

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market structure and firm investment

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