International Shocks and Domestic Prices:
How Large Are Strategic Complementarities?
Preliminary and Incomplete
Mary Amiti
Oleg Itskhoki
Jozef Konings
NY FRB
Princeton
Leuven and BNB
ERWIT
Sciences Po, Paris
June 2015
1 / 31
Motivation
• How strong are strategic complementarities across firms
in price setting?
— do firms mostly respond to own cost shocks or put a large
weight on the prices of their competitors?
— a fundamental mechanism in both micro- and macroeconomics
1 / 31
Motivation
• How strong are strategic complementarities across firms
in price setting?
— do firms mostly respond to own cost shocks or put a large
weight on the prices of their competitors?
— a fundamental mechanism in both micro- and macroeconomics
• A particular application:
— How do international shocks affect domestic marginal costs,
markups and prices?
1 / 31
Motivation
• How strong are strategic complementarities across firms
in price setting?
— do firms mostly respond to own cost shocks or put a large
weight on the prices of their competitors?
— a fundamental mechanism in both micro- and macroeconomics
• A particular application:
— How do international shocks affect domestic marginal costs,
markups and prices?
• Other applications: slope of the Phillips Curve in Monetary
Economics
1 / 31
Our Approach
1
Directly estimate extent of strategic complementarities
across a broad set of manufacturing industries
(a) Develop a general accounting framework
— decompose firm price changes into response to own
cost shocks and to changes in competitor prices
(b) Develop an identification strategy
— two major challenges: simultaneity of price setting and
measurement error in firm marginal costs
(c) Construct a new micro-level dataset for Belgium
manufacturing to carry out this estimation
— intensive data requirements on firm prices, marginal costs, and
firm’s competitor prices within sectors
2
Develop a quantitative framework to evaluate
counterfactual scenarios
— a flexible model tightly calibrated to the Belgian microdata
— explore response of firm markups and prices to various shocks
2 / 31
Main Findings
1
Strong evidence of strategic complementarities:
(i) response to own marginal cost
= 0.65–0.70
(or idiosyncratic cost pass-through elasticity)
(ii) response to competitor prices
= 0.35–0.40
(or strategic complementarities elasticity)
2
These are average (sales-weighted) responses.
Yet, a lot of heterogeneity in responses across firms:
— small firms: no strategic complementarities
(as in standard models)
— large firms: strong strategic complementarities
and variable markups
3
Implications for aggregate pass-through
— decomposition across firms
— variation across sectors
3 / 31
Related Literature
1
IO-style studies:
— Industry studies: Feenstra et al. (1996, cars), Nakamura and
Zerom (2010, coffee), Goldberg and Hellerstein (2013, beer)
— Alternative: De Loecker and Warzynski (2012), De Loecker
and Goldberg (2014)
2
Domestic prices and exchange rates:
— industry-level: Goldberg and Campa (2010)
— product level: Auer and Schoenle (2013), Cao, Dong and
Tomlin (2012), Pennings (2012)
3
International prices and exchange rates:
— Gopinath and Itskhoki (2011)
— Berman, Martin and Mayer (2012), Amiti, Itskhoki and
Konings (2014)
4
Domestic prices and trade shocks:
— De Loecker, Goldberg, Khandelwal and Pavcnik (2012)
— Edmond, Midrigan and Xu (2012)
4 / 31
THEORETICAL FRAMEWORK
5 / 31
Accounting Framework
• Log markup:
µit = pit − mcit
• Markup elasticities:
Γit = −∂µit /∂pit
and
Γ−i,t = ∂µit /∂p−i,t
• Change in markup:
∆µit = −Γit ∆pit + Γ−i,t ∆p−i,t + ε̃it
• Decomposition of price change:
∆pit =
Non-CRS case
PT and Heterogeneity
Γ−i,t
1
∆mcit +
∆p−i,t + εit
1 + Γit
1 + Γit
5 / 31
A Model of
Strategic Complementarities
• Modeling variable markups requires relaxing either CES or
monopolistic competition assumptions
• We follow Atkeson and Burstein (2008) by adopting a
CES-model with oligopolistic competition
— nested-CES demand
— finite number of firms within sector and Cournot competition
— flexible price setting
— focus on industry equilibrium
6 / 31
Demand
• Nested-CES demand:
Qit = ξit Pit−ρ Ptρ−η Dt ,
ρ > η ≥ 1,
where s industry (omitted) and i firm-product
• Sectoral price index:
Pt ≡
hP
1−ρ
N
i=1 ξit Pit
i
1
1−ρ
h
i 1
1−ρ 1−ρ
= ξit Pit1−ρ + (1 − ξit )P−i,t
where N is a finite number of firms in the industry
• Market share:
Pit Qit
Sit ≡ PN
j=1 Pjt Qjt
= ξit
Pit
Pt
1−ρ
∈ [0, 1]
7 / 31
Market Structure
• Cournot (quantity) competition across firms results in
optimal markup pricing rule:
Pit = Mit · MCit ,
Mit =
σit
σit − 1
Fixed Point
Why Cournot?
where
and
σit ≡
−1
1
1
Sit + (1 − Sit )
η
ρ
• Markup elasticity:
Γit = Γ−i,t =
(ρ − η)(ρ − 1)σit Sit (1 − Sit )
ρη(σit − 1)
increases in market share (over relevant range)
• Decomposition of price change in the model:
∆pit =
1
Γit
Γit
∆ξit
∆mcit +
∆p−i,t +
1 + Γit
1 + Γit
1 + Γit (ρ − 1)(1 − Sit )
8 / 31
Cost Structure
• Total Cost:
TCit = AVCit · Yit + Fit
• Average Total Cost:
MCit = AVCit =
TVCit
Yit
• Marginal cost:
MCit =
Wit1−φit (Vit∗ Et )φit
e it
Ω
• Marginal cost in log changes:
∆mcit = φit ∆vit + (1 − φit )∆wit + (vi,t−1 − wi,t−1 )∆φit − ∆e
ωit ,
∆mcit∗ = φit ∆vit
9 / 31
DATA
10 / 31
Dataset
1
Belgium firm-product level data 1995-2008 on values and
quantities
— PC 8-digit (1,700 products)
— All manufacturing firms with minimum of 10 employees
2
Import and export data on values and quantities at HS 8-digit
(over 10,000 products)
3
Firm-level data on firm characteristics
— includes material costs, wagebill and employment
10 / 31
Variables
• Domestic Prices:
∆pijt = ∆ log
Domestic Valueijt
Domestic Quantityijt
• Marginal Cost Variable:
∆mcit = ∆ log
TVCit
Yit
• Instrument:
∆mcit∗ = φit
P
m
ωimt ∆vimt
where ∆vimt is the log change in firm input prices
(m is at source-country–HS-8-digit level)
11 / 31
Variables
• Competition Variables:
D
F
∆p−i,t = (1 − θst )∆p−i,t
+ θst ∆pst
X
X
D
F
∆p−i,t
=
ωjt−i ∆pjt ,
∆pst
=
ωjtF ∆pjt
j∈Ds ,j6=i
j∈Fs
• Instruments:
ωjt−i ∆mcjt∗
P
2 Trade Weighted Industry Exchange Rate: ∆est =
ωmt ∆emt
1
∗
Competitor marginal cost: ∆mc−i,t
=
3
eu
Change in export prices to other EU countries: ∆pst
P
j6=i
12 / 31
EMPIRICAL FINDINGS
13 / 31
Strategic Comlementarities
• Our main empirical specification:
∆pijt =
Γ−i,t
1
∆mcit +
∆p−i,t + εit
1 + Γit
1 + Γit
OLS
Dep. var: ∆pit
(1)
IV
(2)
(3)
(4)
∆mcit
0.348∗∗∗
(0.040)
0.348∗∗∗
(0.041)
0.667∗∗∗
(0.117)
0.757∗∗∗
(0.150)
∆p−i,t
0.400∗∗∗
(0.079)
no
0.321∗∗∗
(0.095)
yes
0.467∗∗∗
(0.143)
no
0.315∗∗
(0.151)
yes
Industry FE
Warmup ERPT regressions
• IV regressions:
First Stage
1 pass weak instrument test
2 pass over-id test
3 cannot reject the equality to 1 of the sum of the coef.
13 / 31
Strategic Complementarities
Robustness
Two-period
Dep. var.: differences
∆pit
(1)
Alternative
input definition
(2)
Major
product
(3)
5-digit
industry
(4)
∆mcit
0.642∗∗∗
(0.245)
0.684∗∗∗
(0.148)
0.658∗∗∗
(0.173)
0.750∗∗∗
(0.167)
∆p−i,t
0.434∗
(0.234)
0.388∗
(0.200)
0.374∗
(0.200)
0.410∗∗∗
(0.147)
# obs.
50,600
64,320
27,027
63,511
14 / 31
Strategic Complementarities
Firm Heterogeneity
Dep. var: ∆pijt
∆mcit
Employment ≥ 100
(1)
(2)
(3)
0.929∗∗∗
(0.152)
∆mcit × Largeit
∆P−i,t
49,462
0.947∗∗∗
(0.226)
0.599∗∗ −0.315
(0.237)
(0.351)
−0.270
(0.356)
0.142
(0.225)
0.063
(0.180)
0.469∗∗
(0.202)
0.279
(0.319)
0.355
(0.325)
15,353
64,815
64,815
0.078
(0.189)
∆P−i,t ×Largeit
# observations
0.949∗∗∗
(0.201)
Top 20%
(4)
15 / 31
QUANTITATIVE MODEL
16 / 31
Quantitative Model
• Atkeson-Burstein demand and market structure:
— Nested CES demand with elasticities ρ > η ≥ 1
— Oligopolistic quantity (Cournot) competition
• Firms differ in size (productivity) and import intensity,
with the joint distribution approximating the data
• Industry equilibrium model: firm costs follow exogenous
processes. We use the model to calculate the evolution of
Price setting
markups and prices
• We simulate multiple industries calibrated to approximate
typical Belgian 4-digit sectors
16 / 31
Cost Structure
• Marginal cost:
Wt1−ϕi Vt Et
MCit =
Ωit
ϕi
• Trade-weighted exchange rate (in logs: et ≡ log Et ):
et = et−1 + σe ut ,
ut ∼ iidN (0, 1)
• Idiosyncratic productivity (in logs: ωit ≡ log Ωit )
ωit = µ + ωi,t−1 + σω vit ,
vit ∼ iidN (0, 1),
with a reflecting barrier at ω to ensure an ergodic Pareto
distribution of productivities in the cross-section
17 / 31
Three Types of Firms
1
2
3
Belgian (domestic) firms
European (non-Belgian) firms
Non-European firms
• The groups of firms differ in two respects:
(i) Exchange rate exposure, ϕi
(ii) Mass of entrants
• Conditional on entry, the firms in each group have the same
market share distribution (Eaton, Kortum and Sotelo 2013)
• Exchange rate exposure of domestic firms:
X
E
X
B
ϕi = φEi ψ E + φX
i ψ + (1 − φi − φi )ψ
18 / 31
Calibration
Parameter
Expected number firms:
— Belgian
— European union
— Non-EU
Elasticity of substitution:
— across sectors
— within sectors
Productivity distribution:
— Pareto shape parameter
— St.dev. of innovation
— Drift
— Reflecting barrier
St.dev. of ∆et
Exchange rate exposure:
— European firms
— Non-EU firms
— Belgian firms
— Pass-through
— Import intensity
Value
Moment in the data
N̄B = 48
N̄E = 21
N̄X = 9
Number of Belgian firms
Sales share
Sales share
η=1
ρ=8
Pass-through heterogeneity
k = 6.6
σω = 0.034
2 /2
µ = −kσω
ω=0
σe = 0.06
Size distribution of firms
std(∆sit ) = 0.0042
Distribution stationarity
Normalization
Trade-weighted ER
ϕE = 0.8
ϕX = 1
φB ψB + φE ψE + φX ψX
ψB = 0.15, ψE = 0.6,
ψX = 1
φE , φX ∼ Beta
Aggregate pass-through
Aggregate pass-through
Pass-through into input prices
Import intensity
19 / 31
Moments
Moment
Data
Number of firms:
— Belgian
41 (48)
[22,87]
— EU
—
Model
std(∆sit )
0.0042
48
[40,57]
21
[16,27]
— Non-EU
—
9
[5,13]
Top Belgian
10% (12%) 11%
market share [5%,21%] [6%,23%]
0.0042
corr(sit , si,t+12 ) 0.90 (0.85)
[0.69, 0.98]
0.88
Moment
Sales share:
— Belgian
Data
corr(sit , φB
i )
0.26 (0.24)
[0,0.44]
0.05 (0.08)
[-0.03, 0.37]
Model
0.64 (0.62)
0.62
[0.39,0.86] [0.46,0.77]
— EU
0.26 (0.27)
0.26
[0.12,0.42] [0.14,0.41]
— Non-EU
0.08 (0.11)
0.09
[0.01,0.25] [0.04, 0.22]
Inverse HHI
16.4 (20.8)
13.7
for Belgian firms [7.1,38.4] [6.5,24.3]
B
corr sit , φX
i /φi
0.28
0.16
20 / 31
Market Share Distribution
Log r ank of fir m, logR a n k ( k )
3
Model Median
Data Median
Data 10%
Data 90%
2.5
2
1.5
1
0.5
0
−3
−2.5
−2
−1.5
−1
−0.5
0
Log r e lat ive mar ke t s har e , log[s ( k ) /s ( 1) ]
21 / 31
Import Intensity
Belgian Firms
(b) Kernel Density (model)
(a) Averages by firm rank
15
3
Outside Euro Zone
Outside Belgium
Model
Data
Log rank of firm, log Rank(k)
2.5
10
2
Outside
Belgium
1.5
1
5
Outside
Euro Zone
0.5
0
0
0.05
0.1
0.15
0.2
0.25
Average import intensity
0.3
0.35
0.4
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Import intensity
22 / 31
SIMULATION RESULTS
23 / 31
Aggregate ERPT
• Sector-level and pooled firm-level regressions reproduce the
aggregate pass-through patterns in the data
See data
Sector-level
All firms
MC
Price
0.494 0.488
Domestic firms
MC
Price
0.286 0.321
Foreign firms
MC
Price
0.866 0.792
Firm-level pooled:
— unweighted
— sales-weighted
0.460
0.473
0.233
0.268
0.828
0.836
0.460
0.464
0.247
0.308
0.804
0.751
23 / 31
Strategic complementarities
Dep. var.: ∆ log Pit
∆ log MCit
∆ log MCit ×Largeit
∆ log P−i,t
∆ log P−i,t ×Largeit
OLS
W/out size
W/size
interaction interaction
0.778
0.952
—
−0.258
0.183
0.041
—
0.223
IV
W/out size
interaction
0.779
—
0.221
—
W/size
interaction
0.952
−0.258
0.047
0.262
• The model slightly underpredicts the extent of strategic
complementarities among the large firms
• IV for competitor prices is important for large firms
24 / 31
Strategic Complementarities
Across firm-size deciles
1.2
Strategic Complementarities
Marginal Cost
Pass-through elasticity
1
0.8
0.6
0.4
0.2
0
0
0.5
1
2
3
5
7.5
10
15
25
40
Market share bins (%)
Γ
1
−i
• Estimates of 1+Γ
and 1+Γ
by firm size deciles
i
i
Without IV
25 / 31
ERPT heterogeneity
Across firm-size deciles
0.45
Markup
Marginal Cost
Exchange rate pass-through
0.4
0.35
0.3
0.25
0.2
0.15
0
0.5
1
2
3
5
7.5
10
15
25
40
Market share bins (%)
• ERPT into MC (red) and prices (red+blue) by firm-size deciles
26 / 31
COUNTERFACTUALS
27 / 31
ERPT Decomposition
• Aggregate ER pass-through of 0.35 is split as follows:
Marginal Cost
Markup
Small
Firms
39.3%
2.2%
41.5%
Large
Firms
51.1%
7.4%
58.5%
90.4%
9.6%
• 10% of the largest firms account for 50% of sales
and almost 60% of pass-through
• Small firms’ markups are stable, while for large firms they
account for about 15% of price adjustment
27 / 31
Response to a 10% Depreciation
Prices
0.5
Price ERPT
0.4
0.3
0.2
0.1
0
0.1
0.08
0.5
0.45
0.06
0.4
0.35
0.04
0.3
0.25
0.02
Market share
0
0.2
ER exposure
28 / 31
Response to a 10% Depreciation
Marginal costs
0.5
Marginal Cost ERPT
0.4
0.3
0.2
0.1
0
0.1
0.08
0.5
0.45
0.06
0.4
0.35
0.04
0.3
0.25
0.02
Market share
0
0.2
ER exposure
28 / 31
Response to a 10% Depreciation
Markups
Markup ERPT
0.15
0.1
0.05
0
0.1
0.08
0.5
0.45
0.06
0.4
0.35
0.04
0.3
0.25
0.02
Market share
0
0.2
ER exposure
28 / 31
Model distributions
Firm
percentiles
25
50
75
90
95
97.5
99
99.5
99.75
Sales
percentile
5.3
14.2
29.6
49.3
62.7
74.0
85.1
90.7
94.4
Market
share (%)
0.36
0.57
1.13
2.62
4.60
7.51
12.45
16.62
21.67
Exchange
rate exposure
0.199
0.244
0.289
0.333
0.363
0.392
0.425
0.450
0.472
Markup
1.147
1.149
1.156
1.174
1.198
1.236
1.305
1.371
1.460
29 / 31
EXPLORING INDUSTRY
HETEROGENEITY
30 / 31
Heterogeneity across sectors
I. By domestic sales share
0.4
Markup
Marginal cost
0.35
0.3
0.25
39.1
54.4
56.9
58.7
60.2
61.6
63
64.5
66.2
68.6
82.5
Domestic share bins (by number of firms, %)
• ERPT into MC (red) and prices (red+blue) across sectors
30 / 31
Heterogeneity across sectors
II. By sector import intensity
0.4
Markup
Marginal cost
0.35
0.3
0.25
21.9
26.1
26.8
27.4
27.9
28.4
28.9
29.5
30.2
31.4
44.6
Sector import intensity
• ERPT into MC (red) and prices (red+blue) across sectors
30 / 31
Heterogeneity across sectors
III. By market share of the largest domestic firm
0.4
Markup
Marginal cost
0.35
0.3
0.25
0.8
5.6
7
8.3
9.6
11
12.7
14.9
17.8
22.7
80
Market share bins (%)
• ERPT into MC (red) and prices (red+blue) across sectors
30 / 31
Heterogeneity across sectors
IV. By correlation b/w size and import intensity
0.4
Markup
Marginal cost
0.35
0.3
0.25
-24.1 18.9
25.1
29.5
33.4
36.9
40.5
44.3
48.6
54.2
82.1
Correlation (Sit , ϕi ) bins
• ERPT into MC (red) and prices (red+blue) across sectors
30 / 31
Conclusions
• We provide direct evidence on the strength of strategic
complementarities in firm price setting
— on average, responsiveness to own cost is 65–70% and
to competitor prices is 35–40%
• Uncover substantial heterogeneity in the extent of strategic
complementarities across firms:
— small firms do not respond to competitor prices and have
complete pass-through of own cost shocks
— large firms exhibit substantial strategic complementarities and
variable markups
• The interplay of these forces with heterogeneous exposure to
foreign inputs is crucial for understanding aggregate ERPT
31 / 31
APPENDIX
32 / 31
Generalization to non-CRS case
• Assume marginal cost equals:
MCit = Cit Yitα
where α is the DRS parameter (α = 0 under CRS)
• The decomposition in this case is:
∆pit =
Γ−i,t + ασ̃−i,t
1
∆cit +
∆p−i,t + εit
1 + Γit + ασ̃it
1 + Γit + ασ̃it
• Under Atkeson-Burstein demand, Γ−i,t = Γit and
σ̃it = σ̃−i,t + η, so that the sum of the coefficient equals:
ψit + γit = 1 − αηψit < 1
Back to slides
33 / 31
Heterogeneity Matters
• ERPT of firm i:
Back to slides
Ψit =
Γ−i,t
ϕit
+
Ψ−i,t
1 + Γit
1 + Γit
34 / 31
Heterogeneity Matters
• ERPT of firm i:
Back to slides
Ψit =
Γ−i,t
ϕit
+
Ψ−i,t
1 + Γit
1 + Γit
• Aggregate PT into marginal costs, prices and markups:
X
ΨMC
=Φ≡
Sit ϕit ,
t
X
1
Sit ϕit
ΨPt =
P Sit Γ−i,t
1+Γit ,
1−
1+Γit
XS Γ i
Xh
1
Γit
jt −j,t
ΨM
Sit ϕit
P Sit Γ−i,t
t =−
1+Γit −
1+Γjt
1−
1+Γit
• Cross-sectional heterogeneity:
ϕit , Sit , Γit , Γ−i,t
• Aggregate pass-through into domestic prices:
ΨD
t =
1
1−
P
D
SitD (1−StF )Γ−i,t
1+Γit
X
SitD
h
ϕit
1+Γit
+
StF Γ−i,t F
1+Γit Ψt
i
D
34 / 31
Price Setting
Fixed Point
• In each industry, given a vector of firm marginal costs {MCit },
we find the equilibrium vector of prices {Pit }
• This is a fixed point problem:
Pit = Mit · MCit ,
Mit = σit /(σit − 1),
−1
σit = η −1 Sit + ρ−1 (1 − Sit )
,
1−ρ
Sit = ξit Pit /Pt
,
PN
1−ρ 1/(1−ρ)
Pt =
i=1 ξit Pit
All prices are determined simultaneously
• The solution to this problem can be found numerically by
iteration
Market Structure
QModel
35 / 31
Sensitivity
Demand and Market Structure
(a) Markup, Mit =
σit
σit −1
(b) Pass-through, Ψit =
1
1+Γit
1
1.6
0.9
ρ =5
Be r t r and
Pas s -t hr ough, Ψ i t
Mar k up, M i t
1.5
1.4
1.3
0.8
η=2
0.7
0.6
ρ =5
0.5
η=2
1.2
0.4
Be r t r and
1.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0
0.05
Mar ke t s har e , s i t
0.1
0.15
0.2
0.25
Mar ke t s har e , s i t
Figure : Markups and pass-through in a calibrated model
Note: σit =
h
1
S
η it
+ ρ1 (1 − Sit )
i−1
under Cournot
and σit = [ηSit + ρ(1 − Sit )] under Bertrand.
Market Structure
Calibration
36 / 31
Exchange Rate Pass-Through
Firm-level regressions
Table : Aggregate ERPT
Dep. var.:
∆pst
0.489∗∗∗
(0.061)
∆est
D
∆pst
F
∆pst
0.311∗∗∗
(0.085)
0.642∗∗∗
(0.059)
Table : Firm-level ERPT
Dep. var.:
∆est
∆pijt
0.279
(0.187)
∆mcit
∆mcit∗
0.395∗∗
0.246∗∗∗
(0.187)
(0.040)
∆vit
0.651∗∗∗
(0.122)
Recall that ∆mcit = ∆mcit∗ + o.t. and ∆mcit∗ = φit ∆vit
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Warmup II
Non-importers
• Preliminary evidence on strategic complementarities:
Dep. var.:
∆est
∆est × Largeis
∆mcit
∆pijt
0.056
(0.129)
0.350∗∗
(0.153)
∆pijt
0.029
(0.138)
0.643∗∗
(0.325)
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Strategic Complementarities
First Stage Regressions
Column (3)
∆mcit
∆p−i,t
Column (4)
∆mcit
∆p−i,t
∆mcit∗
0.614∗∗∗
(0.111)
0.173∗∗∗
(0.039)
0.597∗∗∗
(0.014)
0.174∗∗∗
(0.033)
∆est
-0.222
(0.230)
0.270∗∗
(0.120)
-0.169
(0.258)
0.343∗∗
(0.144)
∗
∆mc−i,t
0.392∗∗∗
(0.098)
0.468∗∗
(0.148)
0.379∗∗∗
(0.124)
0.580∗∗∗
(0.106)
EU
∆pst
0.194∗∗∗
(0.054)
0.304∗∗∗
(0.053)
0.215∗∗∗
(0.049)
0.274∗∗∗
(0.053)
Dep. var.:
Ind. FE
no
no
yes
yes
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Strategic Complementarities
Across firm-size deciles—Without IV
1.2
Strategic Complementarities
Marginal Cost
Pass-through elasticity
1
0.8
0.6
0.4
0.2
0
0
0.5
1
2
3
5
7.5
10
15
25
40
Market share bins (%)
Γ
1
−i
• Estimates of 1+Γ
and 1+Γ
by firm size deciles
i
i
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