Firms’and Countries’Comparative
advantage
(Comparative Advantage and
Within-Industry Firms Performance.)
Matthieu Crozet and Federico Trionfettiy
y
Université Paris 1 and CEPII
Aix-Marseille Université
1
Motivation and main result.
1. Factor intensities di¤er across …rms within any industry. In our data, for instance, 67% of total variance in …rm-level capital/labor ratios is within the same
country-industry group. Yet, most models assume Hicks-neutral productivity
di¤erences across …rms (identical factor intensites).
2. We build a HO model where factors RMP di¤er across …rms. Hence,
heterogeneity in factor intensity.
3. The main result is that countries’comparative advantage gives rise to …rm’s
comparative advantage.
2
Contribution to the literature.
1. First …rm-level veri…cation of the Heckscher-Ohlin theory.
2. We break the within/between dichotomy: countries’comparative advantage
matters for within-industry relative performance …rms.
3. Provide evidence that factor intensity is an important source of heterogeneity
across …rms.
3
Related literature.
1. Concerning veri…cations of HO theory:
Leamer (1980), Tre‡er (1993, 1995), Davis and Weinstein (2001), Romalis
(2004).
2. Concerning Firms Heterogeneity and Comparative Advantage:
Bernard, Redding and Schott (2003), Acemoglu (2002, 2003); Burstein
and Vogel, (2010); Costinot and Vogel, (2010).
4
The Model
Two-by-two HO model with monopolistic competition and heterogenous …rms.
Countries, c = H; F ; Goods, i = Y; Z ; Factors, j = K; L.
Endowments cj > 0 of world’s endowments, K and L.
H .
To …x ideas, H
>
K
L
4.1
Heterogeneity
The marginal cost for a …rm in industry i of country c, mcci, is:
mcci =
Normalization
tion, ci, is:
c
i
=
2
14
( i)
= 1 and
(! c )
w
!
c 1
+ (1
i)
r
!
c 1
2 (0; 1). The relative K
( i) ( )
1
; where
!c
wc=r c
3
1
1
5
(1)
:
intensity in produc-
, i=
1
i
i
(2)
c
To …x ideas, let Y > Z . The average factor intensity, i , as
c
i
=
(! c )
wgere
ec =
i
"
1
1
G
i
c
h i
( i) e
Z 1
i
c
1g (
1
(3)
:
)d
#
1
1
;
Notes:
(1) No restriction on K-int and productivity (Normalization).
c
(2) Independence from existence and direction of factor bias ( e i =
6 1).
(4)
4.2
Demand
Dixit-Stiglitz preferences yielding
pH
id
PiH
sH
id ( ) =
!1 &
iI
H;
sH
ix ( ) =
pH
ix
PiF
!1 &
iI
F
(5)
Note that for any two …rms with draws 0 and 00we have
sci
0
sci
00
=
"
mcci
mcci
0
00
#1 &
;
= d; x:
(6)
4.3
Supply.
c
c , a …xed entry cost F c m
gcci
g
Firms pay a …xed production cost Ficm
c
i
i
ie
c
c
gci
and, if they export, a …x exporting cost Fixm
i .
The cut o¤ values of
conditions:
, by de…nition
gcci ( i c) ,
scid ( i c) = Fim
i
c
and
c
ix ,
i
c
satisfy the zero pro…t
gcci ( i c) :
scix ( ixc) = Fixm
(7)
4.4
Equilibrium
The model counts …fteen independent equilibrium conditions that, together
with one normalization, determine sixteen endogenous variables.
a) Four free-entry conditions,
b) Any three out of the four goods market equilibrium conditions
c) Four relationships between foreign and domestic sales
d) Four factors market equilibrium conditions.
c , Four zero
The endogenous are: Four zero-pro…t productivity cut-o¤
i
c
c ; r c g,
exporting pro…tsn productivity
cut-o¤
,
the
four
factors
prices
fw
o
ix
c
the four masses Mi . The equilibrium value of all other endogenous variables
can be computed from these.
5
Comparative advantage and relative sales
We de…ne
c
i,
c
i
c
i
mcci
mcci
c
i
c
i
,
De…nition: A …rm is K (L) intensive i¤
another …rm i¤ it has lower ci.
sci
sci
RSic
(8)
> (<) 1 and it has a CA over
Proposition 0: A …rm in industry i and country c has a comparative cost
advantage over another …rm with same but in a di¤erent country and industry
if it is intensive in the factor intensively used in i and of which c is relatively
well endowed. Formally:
for any
0
such that ci
0
=
c
i,
H
Y
Q
F
Z
as
R 1.
Proposition 1: For any two …rms with same
the …rm in the industry and
country of its comparative advantage has larger relative sales.
For any
0
such that ci
0
=
c
H
i , RSY
F ( ) as
( ) R RSZ
R 1.
Intuition rests on two mechanisms:
1. Firm’s factor intensity ( ) and industry technology ( i): =) For any
c
c as
such that ci 0 = i , RSYc R RSZ
R 1, 8c.
0
2. Firm’s factor intensity ( ) and relative factors price ( c): =) For any 0
c
such that ci 0 = i , RSiH R RSiF as R 1, 8i and for any 2 (0; 1).
Proposition 2. When heterogeneity is Hicks-neutral relative sales are identical
in all industries and countries.
Formally, for any
RS = '
1;
c = H; F ;
0
i
= 'e
such that
0
i
i = Y; Z ;
8' > 0;
i
c
we have:
8 2 [0; 1] :
(9)
6
Relating theory to empirics.
c
Structural estimations [Tables 2 and 3] A …rm with draws 0 = ' e i and
c
0 such that c 0 =
i will have log of relative sales given by:
i
ln RSic ('; ) = (&
aci
c c 1
>
i (! )
1) ln ' +
1
1
&
ln
"
#
c
1 + ai
;
c
1 + ai
(10)
0. We estimate (10) and expect
F
aH
>
a
Y
Z
(11)
Equation (10) is log-linear in the …rst term but not in the second. We operate
a Taylor expansion to obtain:
ln RSic
= (&
1
1) ln ' +
1
1 1
2 1
&
&
aci
(
c
1 + ai
aci
1 + aci
!2
(
(12)
1)
1)2
1
+
1
& c
"i ;
where "ci, the remainder. We also estimate (12) and again expect
F
aH
Y > aZ
(13)
Table 2: Impact of relative TFP and K intensity on relative sales: structural estimations of Taylor Expansion (Eq. 25)
Dependant variable: ln …rms’relative sales (ln (sci =sci ))
Countries
All
K abundant
L abundant
Industries
All
K intensive
L intensive
(1)
(2)
(3)
a
a
(& 1)
1.123
1.201
1.129a
(0.031)
(0.039)
(0.048)
c
1 & ai
a
a
0.572
0.755
0.388a
1
1+aci
(0.032)
(0.048)
(0.034)
11 &
21
aci
1+aci
R2
Observations
&
aci
2
-0.132a
(0.026)
0.315
372829
2.123
1.909
0.862
-0.181a
(0.041)
0.329
1112015
2.201
1.763
0.921
-0.081a
(0.014)
0.343
58045
2.129
2.22
0.721
Notes: Equation (??). Linear regressions with country-industry …xed effects. Regressions are weighted by the total production within countryindustry groups. Firms with a K
intensity beyond their respective
country-industry 5th and 95th percentile are excluded from the sample.
Robust standard errors adjusted for country-industry clusters in parentheses. Signi…cance level: a p < 0:01.
34
Table 3: Impact of relative TFP and K intensity on relative sales: structural estimates of Eq. (24)
Dependant variable: ln …rms’relative sales (ln (sci =sci ))
Countries
All
K abundant
L abundant
Industries
All
K intensive
L intensive
= 1:91
(1)
(2)
(3)
a
a
&
2.046
1.982
2.146a
(0.029)
(0.0413)
(0.043)
c
a
a
ai
0.675
2.469
0.014a
(0.079)
(0.488)
(0.007)
a
a
Intercept
-1.029
-1.002
-0.997a
(0.034)
(0.051)
(0.025)
R2
0.286
0.302
0.339
Observations 412386
123965
64102
1.91
1.76
2.22
(4)
(5)
(6)
a
a
&
2.046
2.004
2.144a
(0.029)
(0.042)
(0.043)
c
a
a
ai
0.675
1.236
0.032a
(0.079)
(0.205)
(0.012)
Intercept
-1.029a
-1.084a
-0.997a
(0.034)
(0.053)
(0.025)
R2
0.286
0.291
0.339
Observations 412386
123965
64102
36 squared. Starting values: aci = 1
Notes: Equation (24). Non-linear least
and & = 3. Regressions are weighted by the total production within countryindustry groups. Robust standard errors adjusted for country-industry clusters in parentheses. Signi…cance level: a p < 0:01.
Non-structural estimations [Table 4] In two steps:
The …rst step consists in estimating the following non-structural form of equation (10) separately for KK and LL group:
ln
sci
sci
!
=z+
ln
c( 0)
i
c
i
!
+ ln
where z is an intercept and ci is an error term.
KK
LL
We expect b
> b .
0
ec
i
!
+ ci;
(14)
c
The second step consists in testing whether these estimated coe¢ cients, b i ,
now speci…c to each country c and industry i, vary with the industry-level K
intensity and the country-level K abundance. According to Proposition 1
c
we expect b i to be signi…cantly larger in the KK-group than in the LL-group.
According to Proposition 2 we expect b to be the same across countries and
industries.
Table 4: Impact of relative TFP and K-intensity on relative sales: nonstructural log-linear model
(1)
(2)
(3)
(4)
(5)
lrelSale lrelSale lrelSale
lrelSale
lrelSale
Countries
All
All
All
K abundant L abundant
Industries
All
All
All
K intensive L intensive
(1)
(2)
(3)
(4)
(5)
Ln Rel. TFP
1.1189a 1.120a
1.184a
1.145a
(0.028) (0.028)
(0.031)
(0.049)
a
a
a
Ln Rel. K-intensity
0.297
0.315
0.426
0.151a
(0.017) (0.017)
(0.020)
(0.022)
a
Ln Rel. K-intensity 1
0.147
(0.020)
Ln Rel. K-intensity 2
0.252a
(0.011)
Ln Rel. K-intensity 3
0.226a
(0.014)
Ln Rel. K-intensity 4
0.309a
(0.024)
Ln Rel. K-intensity 5
0.491a
(0.025)
a
a
Constant
-1.250
-0.878
-0.874a
-0.944a
-0.845a
(0.016) (0.022) (0.017)
(0.024)
(0.018)
Observations
412386 412386 412386
123965
64102
2
R
0.062
0.342
0.349
0.368
0.359
Notes: Country-Industry …xed e¤ects for38all columns. Regressions are
weighted by the total production within country-industry groups. Robust standard errors adjusted for country-industry clusters in parentheses.
Within R2 are reported. Signi…cance levels: a p < 0:01
Testing the two mechanisms separately. [Table 5]. We regress b on
industry K-intensity and, separately, on country K-abundance. We expect a
positive coe¢ cient.
Table 5: Veri…cation of Mechanism 1 and 2 of Proposition 1.
c
Dependant Variable: b i
Test of mechanism 1
(1)
(2)
(3)
(4)
a
a
a
Industry K-intensity
0.276
0.239
0.246
0.256a
(0.024) (0.023) (0.015)
(0.016)
Observations
1471
1043
1471
1471
R2
0.172
0.199
0.389
0.378
Fixed e¤ects
Country
Test of mechanism 2
(5)
(6)
(7)
(8)
Country K-abundance 0.678a 0.616a 0.697a
0.740a
(0.092) (0.084) (0.064)
(0.066)
Observations
1471
1043
1471
1471
R2
0.056
0.058
0.361
0.359
Fixed e¤ects
Industry
Notes: Robust standard errors in parentheses. Signi…cance levels: b p <
0:05, a p < 0:01. Within R2 are reported. Regressions in columns (2) and
c
(6) only retain signi…cantly positive values of b i . Regressions in columns
c
(3) and (7) are performed with weight = 1/s.e.( b i ). Regressions in columns
(4) and (8) are performed with weight = degree of freedom in the …rst step
regression.
44
7
Data
Firm level balance sheet data on K and L and sales from Bureau Van Dijk’s
Amadeus database (2006 and 2007).
We proxy capital intensity ( ) by the ratio of tangible …xed assets on total
employment
We measure sales as the turnover of the …rm.
In Amadeus each company is assigned to a single 3-digit NACE-Rev2 code. We
restrict our empirical analysis to manufacturing sectors (including agrofood).
Capital abundance for each country, (K c=Lc), is built from ILO and UN.
Industry-level capital intensity is computed directly with our data.
For each country and industry, we compute the weighted average …rm-level
capital-labor ratio. Then, K
intensity for industry i, (Ki=Li), is the
industry-level average of these values across all countries, weighted by countries’
output of good i.
The …nal database is a panel of 445,853 …rms in 87 industries and 26 European
countries.z.
z Bosnia
and Herzegovina, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Italy, Latvia, Lithuania, Poland, Romania, Russian Federation,
Serbia, Slovakia, Slovenia, Spain, Sweden, Ukraine, United Kingdom.
8
Conclusion
1. Theory:
Countries comparative advantage =) …rms comparative advantage.
2. Empirics
K-intensive (L-intensive) …rms in KK (LL) sectors have larger RS.
Thanks for you attention.
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