1. No category

Firm-to-Firm Trade:
Imports, Exports, and the Labor
Market
Jonathan Eaton, Samuel Kortum, Francis Kramarz
April 2015
Panel B: Normalized Entry
5000000
JAP
entry normalized by French market share
USA
GER
UNK
AUL
SWI
CHN
GEE
BRA
ITA
TAI
AUT
SPA
BUL
FRA
NZE
SWE
NET
ARG
FIN
YUG
NOR
SOU
CZE
BEL
ROM
ISR DEN
KOR
MEX
HOK
GRE
VIE
VEN IND
IRE
HUN
MAY
SAU
SIN
CHICUB
POR TUR
COL
ALG
IRN
EGY
ECU
SUD
PER INO
COTSYR
PHI
ZIM
CAM
PAN
PAK
TRIURU
MOR
ALB
COS
THA
JOR KUW
TAN
DOMTUN
SRI
ETH
ELS
GUA
BUK
BOLPAR
SEN
IRQ
HON
ZAIOMA
PAP
BAN NIA
MAS
JAMANG
TOG
LIY
SOM
CHA
MAL
MAD
NIC KEN
UGA
BEN
NEP
RWA
NIG
MOZ
CEN BUR ZAM GHA
MAU AFG LIB
MAW
100000
10000
1000
USR
CAN
1000000
SIE
.1
1
10
100
market size ($ billions)
1000
10000
Introduction
Micro data, Bernard and Jensen ...
Treat exporting and exporting symmetrically
Holmes vision vs. Melitz model
Imports vs. labor within …rms
Lucas, Ober…eld, Garetto
A Peek at the Data
Thanks to: Kramarz, Martin, Mejean (2014)
32000
Figure 1: French Exporters and Market Size
BE
number of French exporters
2000
4000
8000
16000
ES
DE
IT
GB
NL
PT
LU
DK ATPL
GR
SE
IE CZ
FI
HU
LT
SK
CY
LV
EE
1000
MT
SI
1
10
100
market size ($ billions)
1000
10000
French exporters, adjusted for market share
10000
100000
1000000
Figure 2: French Exporters and Market Size
IT DE
GB
ES
NL
FI ATPL
PT
IE
DK
SE
GR
CZ
BE
SK
HU
LV
LT
CY LU
EE
SI
MT
1
10
100
market size ($ billions)
1000
10000
32
Figure 3: Buyers per French Exporter, by Destination
IT
ES
DE
BE
buyers per exporter
4
8
16
GB
PT
NL
GR AT
IE
LU
SE
DKFI
MT
CY
LVEE
SI
HU CZ
SK
2
LT
PL
1
10
100
market size ($ billions)
1000
10000
Table21:2Customers2per2French2Exporter
Destination2Market
Lithuania
Denmark
UK
Market2Size2($billions)
18
94
882
Customers2per2Exporter:
Mean
4.2
7.1
17.9
Percentiles:
25th
1
1
1
50th
2
2
3
75th
4
5
9
90th
9
12
25
95th
15
21
48
99th
40
77
224
Data2are2for22005.
Germany
1480
24.9
2
4
12
35
70
329
Table21:2Customers2per2French2Exporter
Destination2Market
Lithuania
Denmark
UK
Market2Size2($billions)
18
94
882
Customers2per2Exporter:
Mean
4.2
7.1
17.9
Percentiles:
25th
1
1
1
50th
2
2
3
75th
4
5
9
90th
9
12
25
95th
15
21
48
99th
40
77
224
Data2are2for22005.
Germany
1480
24.9
2
4
12
35
70
329
0
20
centile
40
60
80
100
Dist. of the Share of Production Labor
0
.2
.4
.6
share in total variable cost
.8
1
0
20
centile
40
60
80
100
Dist. of the Share of Non-Skilled Production Labor
0
.2
.4
.6
share in total variable cost
.8
1
Related Literature
Firm-level imports: Biscourp and Kramarz (2007); Hummels, Jorgenson,
Munch, and Xiang (2011); Blaum, Lelarge, and Peters (2014); Kramarz,
Martin, and Mejean (2014); Eaton, Eslava, Jinkins, Krizan, and Tybout
(2014); Antras, Tintelnot ...
Networks: Chaney (2014); Eaton, Eslava, Jinkins, Krizan, and Tybout
(2014), Bernard, Moxnes, and Saito (2014)
Theoretical elements: BEJK (2003); Melitz (2003); EKK (2011); EKS
(2013); Garretto (2013); Ober…eld (2014)
A Model of Firm-to-Firm Trade
Setting
Many countries
Iceberg trade costs, dni
Continuum of …rms
Firms supply intermediates to each other
Each buyer encounters only a handful of suppliers
Buyers have all the bargaining power
Tasks
Firm must carry out k = 1; :::; K tasks, using labor or an intermediate
bought from another …rm:
– Labor paid wk;i, random e¢ ciency Q
– Intermediate available at random price P
n
o
– Cost of carrying out task: C = min P; wk;i=Q
Production
Task outputs combine in constant-returns Cobb-Douglas production function
Firm j ’s unit cost function:
K
Y
1
ck (j )
c(j ) =
z (j ) k=1
bk
k
!
Firms di¤er in e¢ ciency z (j ) and task-speci…c realized costs ck (j )
Endowments
Factors: country i endowed with Lli units of type l labor (skill types)
– Type l labor is capable of performing tasks k 2
l
– Equilibrium wage wil so that wk;i = wil for k 2
l
Technology: country i endowed with measure
ciency > z
z (z )
i
of …rms with e¢ -
Distributions
Measure of …rms in i with e¢ ciency > z ( > 0):
z (z )
i
= Tiz
Probability workers perform a task at e¢ ciency below q (0 <
F (q ) = e q
):
Matching
Buyer encounters individual supplier with intensity (0 <
1):
ek;n(c) = k;n n(c)
Here n(c) is the measure of …rms that supply n at a cost below c
Number of suppliers a buyer encounters at cost below c is distributed
Poisson with parameter:
k;n(c) =
Z c
0
ek;n(x)d n(x) =
k;n
1
1
n (c)
Conjecture
Assume:
= (1
)
Then:
n (c)
=
nc
Implications for Intermediates Prices
Price distribution of low-cost intermediate:
Pr [P
pk ] = 1
k;n (pk )
e
Expected price:
pk;n = (1 + 1= )
k;n
=
n
1=
1=
= ' k;n
n
1=
Implications for Task-Speci…c Costs
Distribution of the cost of performing task k:
h
n
o
Gk;n(ck ) = Pr min P; wk;i=Q
where:
k;n
=
i
ck = 1
' pk;n + wk;n
e
k;n ck ;
Implications for Labor’s Share
Probability that task k is performed by workers:
k;n
=
wk;n
k;n
Share of type l labor:
l
n
=
X
k k;n
K
X
k k;n
k2 l
Aggregate labor share:
L
n
=
k=1
Completing the Circle I
Unit cost of …rm j from i delivering to n (given cost of performing tasks):
K
dni Y
c(j ) =
ck k =bk
zi(j ) k=1
Measure of such …rms that can supply n at a cost below c:
ni (c)
=
Z 1
0
:::
Z 1
0
1
K
Y
z @ dni
ck k =bk A dG1;i(c1):::dGK;i(cK )
i
c k=1
0
Completing the Circle II
Note that:
ni (c)
= Tidni c
K
Y
bk
k=1
Z 1
0
ck
k dG
k;i(ck )
Simpli…es (by prudent choice of bk ’s):
ni (c) =
Q
k
k;i
k
!
Tidni c
Completing the Circle III
Summing across sources veri…es our conjecture:
n (c)
=
N
X
ni (c)
=
nc
i=1
With
n
satisfying:
n
=
X
i
Tidni
K
Y
k=1
=
k;i
i
+ wk;i
!
k
;
a contraction mapping if at least 1 task can’t be outsourced ( k;i = 0 for
some k)
Partial Equilibrium
Aggregate Representation
Consider a representative …rms taking wages wk;i and intermediate prices
pk;i as given
Its production function is CES nested within Cobb-Douglas:
Yi =
K
Y
'
~ Lk;i
=( +1)
+ (1
'
~ ) Mk;i
=( +1)
k=1
with elasticity of substitution 1 +
'
~=
and share parameter
1 + ' =(1+ )
1
k(
+1)=
Aggregate Representation II
Firm will choose:
wk;iLk;i
pk;iIk;i
= '
wk;i
pk;i
!
Implies share of type l same as that generated by …rm-to-…rm trade:
l
i
=
X
k2 l
wk;i
k
k;i
Households and the Cost of Living
Utility function is like the production function but with
k
in place of k
Households choose …nal goods like …rms choosing intermediates
Exact price index for households:
PnC
=
Q
k=
k
k;n
Bilateral Trade Shares
Probability that a …rm (that can supply an intermediate good to n at a
cost below c) is from i:
ni (c)
=
=
ni
n (c)
Tidni
Q
=
k
k;i
i
+ wk;i
n
Since household choices mimic those of …rms, this probability becomes the
bilateral trade share:
Xni
= ni
Xn
General Equilibrium
General Equilibrium I
Total production in country i:
Yi =
N
X
n=1
ni
h
(1
L )X C
n
n
L )Y
n n
+ (1
i
where the aggregate labor share in production is
L
n
=
K
X
k=1
and for households
L
n
wk;n
k
k;n
is de…ned in parallel, with
k
in place of k
General Equilibrium II
Trade balance and income:
XiC
=
YiL
=
X
wil Lli
l
=
X
wk;iLk;i
k
Labor market equilibrium:
wil Lli = liYiL + liYi
where li (and likewise
l,
i
with
l
i
=
k
in place of k ) are given by:
X
k2 l
wk;i
k
k;i
Numerical Exploration of Aggregates
Table 2: Baseline Parameter Settings for Simulation
Parameter
Pareto parameters:
efficiency distribution
price distribution
Technology level per person
World labor force
Labor by type (fractions of labor force):
nonproduction (service)
production
Iceberg trade cost
Tasks, by type:
service tasks:
number of tasks
total share
production tasks:
number of tasks
total share
Task shares in consumption (same as for production)
Outsourcing parameters:
service
production
symbol
value
theta
phi
T_i/L_i
L
L^l
d
K
beta
5
2
3.6
1
0.6
0.4
1.2
4
0.4
K
beta
alpha
lambda
12
0.6
0
0.2
Table 3: Aggregate Results of Simulation
L=0.001
L=0.009
Country Size
L=0.09
L=0.2
Production value added:
Share of GDP
0.126
0.126
0.128
Share of gross production
0.31
0.31
0.30
Fraction of production tasks outsourced:
0.48
0.48
0.50
Import share of production
1.00
0.97
0.79
Wage:
service
0.87
0.87
0.91
production
1.02
1.02
1.03
Skill premium (service/production)
0.85
0.86
0.88
Real wage:
service
1.45
1.46
1.50
production
1.71
1.71
1.70
Welfare (real per capita consumption)
1.55
1.56
1.58
1. Production value added does not include service tasks (i.e. purchased services)
2. Wage is normalized so that labor income of the World is 1
L=0.3
L=0.4
0.130
0.29
0.51
0.61
0.131
0.28
0.53
0.49
0.132
0.28
0.54
0.39
0.94
1.03
0.91
0.98
1.04
0.94
1.00
1.05
0.96
1.55
1.69
1.61
1.58
1.69
1.63
1.62
1.69
1.64
Table 4: Aggregate Results with Different Trade Costs
Trade Cost (small country, L=.009)
10.00 1.80 1.20 1.05 1.00
Production value added:
Share of GDP
0.06 0.09 0.13 0.13 0.13
Share of gross production
0.49 0.43 0.31 0.27 0.26
Fraction of prod. tasks outsourced:
0.19 0.29 0.48 0.55 0.57
Import share of production
0.00 0.76 0.97 0.99 0.99
Wage:
service
0.73 0.62 0.87 0.98 1.02
production
1.34 1.00 1.02 0.99 0.97
Skill premium (service/production)
0.55 0.62 0.86 0.99 1.04
Real wage:
service
0.98 1.10 1.46 1.66 1.74
production
1.78 1.76 1.71 1.68 1.67
Welfare (real per capita cons.)
1.30 1.36 1.56 1.67 1.71
1. Production value added does not include service tasks (i.e. purchased services)
2. Wage is normalized so that labor income of the World is 1
Trade Cost (large country, L=0.3)
10.00 1.80 1.20 1.05 1.00
0.12
0.32
0.47
0.00
0.13
0.31
0.48
0.11
0.13
0.28
0.53
0.49
0.13
0.26
0.56
0.65
0.13
0.26
0.57
0.70
0.93
1.11
0.83
0.94
1.11
0.85
0.98
1.04
0.94
1.00
0.99
1.01
1.02
0.97
1.04
1.42
1.71
1.54
1.45
1.71
1.55
1.58
1.69
1.63
1.69
1.68
1.69
1.74
1.67
1.71
Firm-Level Implications
Buyers
Poisson number of customers in n for a …rm delivering there at cost c:
n (c)
= (Ln + Mn)
X
h
ek;n(c) 1
k
i
Gk;n(c)
Poisson number of customers anywhere for a …rm from i with cost c (at
home):
W (c)
i
=
X
n
n (cdni )
Probability of …rm in i with cost c exporting to n:
1
e
n (cdni )
Firm Entry
Measure of …rm producing in i:
Mi =
Z 1
0
1
e
W (c)
i
d ii(c)
Measure of …rms from i selling in n:
Nni =
Z 1
0
1
e
n (c)
d ni(c)
From these expressions we can compute entry and how it relates to market
size (even though no …xed cost)
Table 5: Firm-­‐Level Results of Simulation
Measures of firms:
producing selling
Measures normalized by Labor:
producing
selling
Fraction of firms selling domestically:
Mean # customers per firm:
Size distribution (percentiles):
25th
50th
75th
90th
95th
99th
Country Size
L=0.09
L=0.2
L=0.001
L=0.009
L=0.3
L=0.4
0.02
0.08
0.14
0.61
1.60
3.93
3.95
7.38
6.32
10.15
8.80
12.67
15.7
84.9
0.02
1.13
15.9
67.6
0.11
1.44
17.8
43.7
0.53
2.56
19.8
36.9
0.74
3.47
21.1
33.8
0.83
4.12
22.0
31.7
0.88
4.68
1
1
1
1
2
3
1
1
1
2
3
8
1
1
2
4
7
22
1
1
2
5
10
34
1
1
3
6
12
43
1
1
3
7
14
51
Table 6: Firm-­‐Level Results with Different Trade Costs
Measures of firms:
producing selling
Measures normalized by Labor:
producing
selling
Fraction of firms selling domestically:
Mean # customers per firm:
Size distribution (percentiles):
25th
50th
75th
90th
95th
99th
Trade Cost (small country, L=.009)
10.00 1.80 1.20 1.05 1.00
0.29
0.29
0.09
0.21
0.14
0.61
0.22
1.07
11.4
11.4
9.6
10.8
6.3
10.1
6.8
11.7
7.3
12.7
31.9
31.9
1.00
2.33
9.5
23.7
0.60
1.52
15.9 21.6 24.4
67.6 101.6 118.5
0.11 0.06 0.04
1.44 1.47 1.48
37.9
37.9
1.00
5.73
32.0
36.1
1.00
5.23
21.1
33.8
0.83
4.12
22.6
38.9
0.61
4.08
24.4
42.4
0.52
4.14
1
1
2
4
6
19
1
1
1
2
3
9
1
1
3
9
17
66
1
1
3
8
16
59
1
1
3
6
12
43
1
1
3
6
12
43
1
1
3
6
12
44
1
1
1
2
3
8
0.19
0.91
Trade Cost (large country, L=0.3)
10.00 1.80 1.20 1.05 1.00
1
1
1
2
3
8
1
1
1
2
3
8
Figure 5: Suppliers and Market Size
country A suppliers, adjusted for market share
.1
1
10
f
d
c
b
a
.001
.01
.0001
e
.01
market size
.1
1
8
Figure 6: Buyers per Supplier, by Destination
f
buyers per supplier
2
4
e
d
c
b
1
a
.0001
.001
.01
market size
.1
1