Market Structure and Firm Investment
Transcript of 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
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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
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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
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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
Top-8-firms market share
Top-20-firms market share
25th-75th percentile ranges of changes: substantial variability over time
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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
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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
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Model
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
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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
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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
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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
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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
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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
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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
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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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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 ↓
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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
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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
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An Illustrative Model back
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
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An Illustrative Model back
Three analytical results: larger q−i
– shrinks firm i’s demand– hinders firm i’s investment– making q′i less sensitive to c
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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)
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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
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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
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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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