Globalization and the Organization of Firms and Markets
Munich, 10-11 February 2007
CEPR
Supported by Volkswagen Stiftung
Firm Heterogeneity, Intra-Firm Trade, and the Role of
Central Locations in Structure of Multinational
Activity
Stephen R Yeaple
We are grateful to the following institutions for their financial and organizational support: The University of Munich and Volkswagen Stiftung.
The views expressed in this paper are those of the author(s) and not those of the funding organization(s) or of CEPR, which takes no
institutional policy positions.
Firm Heterogeneity, Intra-Firm Trade, and the Role of
Central Locations in Structure of Multinational Activity
By Stephen Ross Yeaple
February 2, 2007
University of Colorado,
Princeton University,
And NBER
1
Introduction
Multinational Enterprises, those …rms that produce in more than one country, play a
key role in the conduct of international commerce. According to UNCTAD (2004) the
volume of sales of the foreign a¢ liates of multinational enterprises are more than twice
the volume global exports. Further, multinational enterprises (MNE) account for much of
international trade: approximately half of U.S. exports are conducted intra-…rm between
the parents of U.S. MNE and their foreign a¢ liates (Hanson, Mataloni, and Slaughter
2003). Given the importance of MNE in the conduct of international commerce, it may
seem surprising that the literature in international trade has made little progress in understanding the foreign investment decisions of these …rms. Indeed, a recent review of the
literature on foreign direct investment (Blonigen, 2005) concludes that this literature is
“in its infancy.”
The limited progress in the literature is less surprising when one ponders the many
complex problems facing a …rm that has decided to invest abroad. In which of the world’s
countries will a …rm’s good be sold? What con…guration of production locations will
minimize the cost of serving these markets? Since a good that is sold to …nal customers
might require hundreds or even thousands of di¤erent types of intermediate inputs, the
logistics of acquiring components represents a daunting problem.
Even without considering arm’s length transactions, the extent of vertical specialization within multinational production networks is substantial. According to the results of
the 1999 benchmark survey of U.S. multinational enterprises conducted by the Bureau of
Economic Analysis (BEA), the value of the sales of the foreign a¢ liates of U.S. multinationals were $2,219 billion while the the total value of intra-…rm trade between units of
U.S. multinationals located in di¤erent countries amounted to $571 billion. Moreover, the
1
importance of vertical specialization within multinational production networks is growing.
Between 1989 and 1999 the foreign sales of multinational a¢ liates grew by 117 percent
while the value added of these a¢ liates grew by only 75 percent.1 The interpretation
of these facts as evidence of increasing vertical specialization of individual a¢ liates is
supported by the fact that intra-…rm trade, which is dominated by trade in intermediate
inputs, is the fastest growing component of multinational sales. The volume of import
of intermediates inputs by a¢ liates2 from their parents increased by 130 percent and the
volume of intra-…rm trade between the foreign a¢ liates of U.S. multinationals increased
by 128 percent.
Further complicating our ability to understand the structure of international production is the substantial degree of heterogeneity across …rms in terms of their international
organization. To get an idea of the extent of this heterogeneity, consider the data for
1994 from the Bureau of Economic Analysis that is shown in Figure 1. This …gure shows
the number of countries in which each of approximately 1,500 U.S. multinational enterprises (MNEs) in manufacturing industries owns a foreign a¢ liate. The height of each bar
corresponds to the number of …rms in the size categories (number of countries per …rm)
shown on the horizontal axis. Few multinationals own a¢ liates in more than a handful of
foreign locations: more than a third of all U.S. multinationals produce in only one foreign
country and the median number of foreign locations is two.
Given the tradition in the international trade literature of analyzing the motives for
and consequences of international commerce in a two-country framework in which all
…rms are identical, it is not surprising at all that existing work falls far short of explaining
the structure of multinational production. This paper presents a framework that makes
the analysis of many of the complex logistical problems facing multinational enterprises
1
2
These data are taken from Mataloni and Yorgason (2002).
Exports to a¢ liates of goods for further manufacture
2
tractable. The model has three key features. First, the world is composed of two regions,
one of which is composed of many countries arrayed in a “hub and spokes”con…guration.
Geography matters in this framework because there are both inter-regional and intraregional transport costs. Transport costs within the region are lowest between the hub,
which we refer to as the “central location,” and each of the spokes, which we refer to as
the “peripheral countries.”Second, the model features a production technology in which
…nal goods are assembled from a continuum of tradable intermediate inputs. There are
…xed costs to opening each assembly plant and to opening a plant to produce a speci…c
intermediate input. Third, …rms are heterogeneous.
Firms maximize their pro…ts by (i) choosing the set of countries in which they will
assemble their …nal product, and (ii) choosing from which countries they will source their
intermediate inputs. Hence, the model endogenizes not only a …rm’s choice of which
countries to own an a¢ liate but also the value-added at each location and the volume
and direction of intra-…rm trade. Since …rms are heterogeneous, they each organize their
international operations di¤erently. Thus, the aggregate structure of FDI across countries
features both an extensive margin (the number of active …rms) and an intensive margin
(the volume of activity at the average …rm).
We use the model to develop a rich set of predictions over the relationship between
a …rm’s characteristics and the structure of its international operations. We show that
small multinationals concentrate their foreign operations exclusively in central locations,
and source their intermediate inputs either from local plants or from their parent …rms,
while larger multinationals open assembly facilities in many foreign countries and source
intermediates from both plants located in central locations and from their U.S. parents.
For all but the largest multinationals, the central location plays a key role in the structure
of a …rm’s international operations by acting either as an “export platform”for shipping
3
…nal goods or as a primary location for producing intermediates that are in turn shipped
to assembly plants elsewhere. These predictions are consistent with several empirical
facts that we highlight below and are also consistent with recent empirical studies that
explore the relationship between a country’s “foreign market potential,”as measured by its
geographic location, and its ability to attract multinational enterprises (see for instance,
Blonigen et al 2005, and Lai and Zhu 2006).
We also derive the general result that multinational enterprises that concentrate their
production in one foreign location should engage in less intra-…rm trade with their parent
…rms, ceteris paribus. Firms that concentrate their foreign production in one location
will have a large volume of output at that location and so will gain relatively more by
lowering its marginal cost than a …rm that disperses its production over many locations.
Since the import of intermediates from the parent …rm incurs transport costs, marginal
cost is lowered by increasing the extent of local content.
The comparative statics of the model highlight the importance of accounting for …rm
heterogeneity and regional geography. For instance, an increase in the distance between
regions induces a larger set of …rms to concentrate their foreign production in the single
central location. This result obtains because …rms that centralize production optimally
source a smaller percentage of their intermediates from their parent …rm and so are less
a¤ected by the larger shipping costs associated with greater inter-regional distance. This
mechanism provides a plausible explanation for why empirical studies typically …nd that
greater distance between countries predicts smaller volumes of both exports and FDI
between them.
Changes in regional characteristics, such as the level of intra-regional transport costs
or the number of countries within the region, are shown to a¤ect on the structure of the
international organization that operates through two channels. First, holding …xed the
4
location of a …rm’s foreign assembly plants, a change in regional characteristics a¤ects
the manner in which that …rm sources its intermediate inputs, thereby altering the local
content of foreign production and the volume of inter-…rm trade in intermediates. Second,
a change in regional characteristics induces some …rms to alter the structure of its network
of foreign assembly plants. Since the optimal sourcing of intermediate inputs depends on
this con…guration, the volume of intra-…rm trade volumes is further altered.
This paper is unique in endogenizing (i) the location of multinational a¢ liates, (ii) the
sourcing of intermediates from parent …rms, and (iii) the export of both …nal goods and
intermediate inputs by foreign a¢ liates within a framework of …rm heterogeneity. Nevertheless, it is related to several papers in the literature. Its closest relative is Helpman,
Melitz, and Yeaple (2004), which analyzes the trade-o¤ between exporting and foreign
direct investment in serving any given foreign market. This paper goes further than Helpman, Melitz, and Yeaple in incorporating key features of problems facing multinational
enterprises. In particular, the analysis in this paper considers a regional geography in
which there are “central locations”and allows for a rich pattern of intra-…rm trade.
Our analysis is also related to the work on export platform FDI by Ekholm, Forslid,
and Markusen (2003) and models of “complex”FDI as presented in Yeaple (2003) and in
Grossman, Helpman, and Szeidl (2003). Unlike these papers, however, the focus here is
on the importance of regional geography and not on factor prices as the motive for export
platform and complex FDI strategies. Moreover, the production structure considered in
our framework allows for the analysis of a much richer pattern of intermediate sourcing.
The remainder of the paper is organized into …ve sections. In the next section, we
introduce a simple analytical framework in which “central” locations play a key role. In
section 3, we characterize the optimal structure of a …rm’s international operation as a
function of its size. Comparative statics on the model’s key variables are conducted in
5
section 4. Several of the model’s key predictions are evaluated empirically in section 5.
In the …nal section, we discuss the results and suggest extensions.
2
The Model
The analytical framework introduced in this section has three key components. First, to
analyze the sourcing of intermediates we specify a technology in which a …nal good is
assembled from a continuum of inputs. Second, to analyze the role of regional geography,
we consider a multiple country setting in which countries di¤er in their relative foreign
market potential. Finally, to introduce an extensive margin of foreign direct investment
we allow for …rm heterogeneity so that …rms sort into mode of foreign market access.
A …nal good is produced according to a Leontief technology with a continuum of inputs
indexed by ! on the unit interval. Hence, if the marginal cost of producing intermediate
! is c(!), then the cost of producing one unit of the …nal good is
C=
Z
1
c(!)d!
(1)
0
The advantage of a Leontief technology is that marginal cost of supplying the …nal good
is linear in the marginal cost of each intermediate input. Any number of alternative
technologies (e.g. Cobb-Douglas, CES) would deliver similar results.
The production of intermediate inputs involves both …xed and variable costs. Once
an intermediate speci…c plant has been built, each intermediate input produced requires
b units of labor, which we normalize to zero. Intermediates vary in terms of the size of
the …xed cost required to open a plant. The …xed cost to build a plant that is speci…c to
intermediate ! is
6
f (!) = f !:
(2)
Once a plant has been built to assemble the …nal good from intermediates, assembly
requires no additional inputs. To build an assembly plant requires a …rm to incur a …xed
cost FA . To keep the analysis simple, we assume that a …rm produces all of intermediates
itself rather than outsource their production to outside contractors.
There are two regions. One region is composed of a country called home. The other
region is composed of M + 1 countries. M of these countries are identical and called
peripheral. The other country is called center. Factor prices are the same in all countries.
To ship a good (either intermediate or …nal) internationally incurs per unit (speci…c)
transport costs. The cost of shipping an assembled …nal good between home and any of
the countries in the other region is . Within region, …nal goods can be shipped between
the central country and any of the M countries in the periphery but incur speci…c transport
cost t. For simplicity assume that shipping costs between countries in the periphery are
su¢ ciently large that it does not occur.3 Goods are more costly to ship between regions
than within region so that
> t.
Intermediate inputs are also costly to ship between regions and countries within a
region. The cost of shipping a unit of an intermediate input between regions is
while
the cost of shipping an intermediate input between the cetnral country and a peripheral
country is t, where
2 [0; 1] measures di¤erences in the transportability of intermediates
relative to …nal goods. Note that these transport costs are independent of !.
Firms that originate from home vary in terms of the demand for their product in
any given country. In each of the M peripheral countries there are ' consumers each
willing to pay no more that p for each unit of a …rm of type-'’s output. For simplicity
3
This formulation is consistent with “hub and spokes” framework that occasionally appears in economic geography models.
7
there are no consumers in the central country. This formulation of …rm heterogeneity
di¤ers from other formulations found in the literature such as Melitz (2003) or Helpman,
Melitz, and Yeaple (2004), where …rms vary in terms of their productivity. What induces
sorting of …rms into modes of foreign market access in Helpman, Melitz and Yeaple (2004)
is not productivity di¤erences per se, however, but the fact that more productive …rms
sell a larger number of units in any given market. By assuming that …rms di¤er in the
number of customers rather than their productivity, we capture the key implications of
…rm heterogeneity in productivity in a simple and notationally-clean way. Many of the
results derived below would also obtain in a more complicated general equilibrium setting
with monopolistically competitive …rms and heterogeneity in terms of productivity.4
To serve the foreign market, a …rm can either export the good from the home country
or engage in FDI in the foreign region. Firms are assumed to be endowed with a plant to
produce each intermediate in the home country, so that there are no …xed costs associated
with exporting to a foreign market. Once they have chosen in which of the M + 1
foreign countries they wish to assemble the …nal good, they organize their international
production of intermediate inputs so as to minimize its total cost. Should intermediates
be produced in the country of assembly, should they be imported from home, or should
their production be concentrated in the “central”country and exported to a¢ liates within
the region?
4
In the case of monopolistic competition with CES preferences, a …rm’s revenues are monotonically
decreasing in its marginal cost, which in turn is decreasing in a …rm’s productivity. What this speci…cation
rules out are certain types of “complementarities”that can arise when the reduction of a …rm’s marginal
cost raises the volume of its sales. See, for instance, Grossman, Helpman, and Szeidl (2006).
8
3
Analysis
Firms can choose from three broad strategies for serving the foreign region that are de…ned
by the location of assembly plants. First, they could assemble the …nal good exclusively
in the home country and then export it to each foreign market. Second, they could open
a single assembly plant in the central country and then serve the remaining M markets
in the region by exporting the …nal good from the central country. This option corresponds to “export platform” FDI, which has received an increasing amount of attention
in the literature. Since this mode involves complete centralization of foreign activity in
one country, we refer to this option as centralized FDI. Third, they could open an assembly plant in each of the foreign markets and avoid shipping the …nal good across any
borders. This type of …rm may still produce intermediates in the centralized country and
so engage in intra-…rm trade in intermediates within region. We refer to this strategy as
decentralized FDI.
In our analysis, we characterize the optimal intermediate input sourcing behavior of
…rms choosing each of these strategies and the pro…ts associated with these strategies in
turn. We then turn to sorting of …rms into strategies on the basis of their type.
3.1
Exporting
Consider …rst the pro…ts associated with exporting the …nal good from the home country
to each of the M markets of the foreign region. Clearly, a …rm that assembles the …nal
good in its home country will also produce all of its intermediates there as well. Hence,
such a …rm incurs no …xed costs or shipping costs associated with the intermediate inputs.
Since each …nal good shipped is subject to the inter-regional transport cost of , the pro…ts
9
associated with exporting for a …rm of type-' are
X (')
= M '(p
)
(3)
To make exporting a viable option, we assume that the p > .
3.2
Centralized FDI
Now consider the behavior and pro…ts of a …rm that engages in centralized FDI. A …rm
that has opened an assembly plant in the central country can then export the good to
the M peripheral countries and incur a transport cost t <
on …nal goods. The …rm
must then decide from where to obtain intermediates. A …rm following a centralized FDI
strategy will never produce the intermediates in a peripheral country because doing so
will incur the …xed cost of building an additional plant and the transport cost of shipping
the intermediate to center. This transport cost could be avoided by simply producing the
intermediate in center.
There are two viable options for sourcing intermediate inputs. First, the …rm may
produce the intermediates in home and then ship them to central. This option avoids
…xed costs, but incurs inter-regional transport costs. Second, a …rm may produce the
intermediate locally in center, thereby avoiding transport costs but incurring the …xed cost
of building local plants. Figure 2 provides a schematic of the location of production and
implied trade patterns for a …rm following a centralized FDI strategy. Since intermediates
share the same transport cost between home and center ( t) and since intermediates with
a lower index of ! involve a lower …xed cost, the pro…tability of moving the production
of an intermediate o¤shore is decreasing in !. It follows that there is a threshold ! such
that for ! < ! intermediates are produced in center while the remaining intermediates
10
are imported from home by the assembly a¢ liate in center.
Since the …nal good must be shipped from the center to the periphery incurring transport cost t while the measure (1
! ) of intermediates incur transport cost
, it follows
from (1) that the marginal cost of serving a peripheral country for a …rm that chooses
cuto¤ intermediate ! is
CCI (! ) = t + (1
! )
:
The total …xed cost for a …rm that opens a single foreign assembly plant and an intermediate input plant for all ! < ! is
FA + f
Z
!
!d! = FA +
0
f
(! )2 :
2
It follows that the pro…ts that a …rm of type-' with investment threshold ! are
CI (')
= M 'p
fM 't + FA g
M '(1
! )
+
f
(! )2 :
2
(4)
The pro…ts of a …rm following a centralized FDI strategy has three components. The …rst
component is the revenue of the …rm, which is given by the …rst term on the r.h.s. of (4).
The second term in (4) is the cost associated with assembly and moving the …nal good
to foreign locations, which we refer to as the “downstream costs.” The last term is the
cost associated with providing intermediates to assembly plants, which we refer to as the
“upstream costs.”
A …rm that has chosen a centralized FDI strategy minimizes its “upstream costs” by
choosing ! . The …rst-order condition is
M'
f ! = 0;
11
which implies the following solution for the optimal cuto¤ between building an intermediate in home and building it in the central location
! (') =
where
8
>
<
M
f
>
:
' if '
1
' =
'
(5)
otherwise
f
M
(6)
The sourcing of intermediate inputs by a centralized multinational across …rms with different market sizes is depicted in …gure 3. As a …rm’s market size becomes larger, the
goal of reducing total costs induces the …rm to source an increasing share of its intermediates from plants within the central country. As such, the share intra-…rm imports of
intermediate inputs from the home country in total value-added is decreasing in a …rm’s
foreign output.
Note that as a …rm’s becomes larger, its marginal costs of serving foreign market fall
endogenously as the …rm reorganizes production to avoid transport costs. The observation
is interesting because the predictions of standard models of …rm heterogeneity run from
lower marginal costs to higher market size and not the reverse.
Combining equations (4) and (5) yields the expression for the maximum pro…ts that
a …rm of type-' can earn by engaging in centralized FDI:
CI (')
=
8
>
< M 'p
>
:
(M 't + FA )
M 'p
(M 't + FA )
')2
(M
M'
2f
f
2
if '
'
(7)
otherwise
A few features of this pro…t function are notable. First, notice that while the function
is continuous in ' its …rst derivative is discontinuous at ' as a …rm with this market
12
share has moved the production of all its intermediate inputs o¤shore. Second, as a …rm’s
market share ' rises its upstream costs rise, but at a slower rate than if it could not adjust
the sourcing of its intermediate inputs. This makes the pro…t function strictly convex for
'.
'
3.3
Decentralized FDI
A …rm that follows a decentralized FDI strategy opens an assembly plant in each foreign
country incurs the …xed cost M FA and pays no shipping costs on the …nal good. The
…rm must then decide where to produce each intermediate input. There are three options
for sourcing a given intermediate. If an intermediate ! is imported from home then no
additional …xed costs are incurred and the marginal cost of serving a foreign plant is
c(!) =
. If the production of intermediate ! is concentrated in the central country
then the additional …xed cost in (2) is incurred and the marginal cost of serving a foreign
assembly plant is c(!) = t. Finally, if a plant to product intermediate ! is opened in
each of the M foreign markets then the …xed cost associated with this intermediate is
M f ! and the marginal cost is c(!) = 0. Figure 4 provides a schematic for the structure
of production and implied trade patterns of a …rm following a decentralized FDI strategy.
Since the …xed cost is increasing in ! it follows that if any intermediates are produced
exclusively in home then it is those with the largest !, and the intermediates that are
produced in each of the M countries will be those intermediates with the smallest !.
Therefore, there exists two thresholds ! 2 and ! 1 such that intermediates !
! 2 are
produced in home and imported by assembly plants, intermediates ! 2 (! 1 ; ! 2 ) are produced in central and imported by assembly plants within the region, and intermediates
!
! 1 are produced in each foreign country. Using (1), the marginal cost equation can
13
be written
CDI (! 1 ; ! 2 ) = (! 2
! 1 ) t + (1
!2)
The …rst term on the right-hand side is the cost of delivering intermediates produced in
center, and the second is the cost of importing intermediates from home. The total …xed
cost is
M FA + M f
Z
!1
!d! + f
Z
!2
!d! = M FA +
!1
0
f
(M
2
1)! 21 + ! 22 :
It follows immediately that the pro…ts that a …rm of type-' with investment thresholds
! 2 and ! 1 are
DI (! 1 ; ! 2 ; ')
= M 'p
M FA
M' [
(
t)! 2
! 1 t] +
f
(M
2
1)! 21 + ! 22
(8)
The three terms in (8) correspond to revenue, “downstream”costs, and “upstream”costs
respectively.
Assuming an interior solution, the …rst-order condition for pro…t maximization with
respect to ! 2 is
M' (
t)! 2
f = 0;
which implies the following solution for the optimal cuto¤ ! 2 between building an intermediate in home and building it in the central location:
! 2 (') =
8
>
<
>
:
M (
f
1
14
t)
' if '
'0
otherwise
(9)
where
f
M (
'0 =
(10)
t)
Assuming an interior solution, the …rst-order condition for pro…t maximization with respect to ! 1 is
M 't
(M
1)f ! 1 = 0;
which implies the following solution for the optimal cuto¤ ! 1 between building an intermediate in the each country and building it exclusively in central:
! 1 (') =
where
8
>
<
M t
'
f (M 1)
>
:
'00 =
1
if '
'00
f (M 1)
:
M t
Note that for the case in which we are interested ! 2 > ! 1 to arise, we require
M t=(M
(11)
otherwise
(12)
>
1). This condition will be satis…ed if inter-regional transport costs are large
relative to intra-regional transport costs and the number of markets in the region is large.
This condition also ensures that '00 > '0 .
This simple framework predicts a rich pattern of intra-…rm trade across …rms following
decentralized FDI strategies as shown in …gure 5. As a …rm’s market size ' increases, the
share of intermediates that it sources from home is decreasing (the dotted and dashed
line), the share of intermediates that it produces locally is increasing (the small dotted
line), and the share of intermediates that it sources from the central country is …rst increasing as centrally produced intermediates substitute for imports from the home country
and then decreasing as locally produced intermediates substitute for centrally produced
15
intermediates.
Combining equations (8)-(12) yields the expression for the maximum pro…ts that a
…rm of type-' can earn by engaging in decentralized foreign investment:
DI (')
8
>
>
M 'p
>
>
<
>
>
>
>
:
M FA
M 'p
n
M'
M FA
M2
2(
2f
n
M' t +
M ('p
t)2
FA
f
2
f
)
2
'
2
(M t)2
'2
2f (M 1)
(M t)2
'2
2f (M 1)
o
o
if '
'0
if ' 2 ('0 ; '00 )
otherwise
(13)
As was the case with centralized FDI, the pro…ts of decentralized are convex in a …rm’s
market size as a …rm adjusts its upstream costs. While upstream costs are strictly increasing in ' they are bounded above by M f =2 the cost of opening plants to produce
each intermediate input in each country.
3.4
The Structure of International Commerce
The analysis of the selection of …rms into modes of serving foreign markets involves comparing the pro…t functions (3), (7), and (13). Since …rms’ revenues are independent of
their mode choice, the decision between modes depends solely on which mode o¤ers the
lowest cost of supplying the market. Further, modes di¤er in the relative magnitudes of
their “upstream”and “down stream costs.”Our analysis of mode choice presented in this
section will thus depend substantially on the relative importance of these two types of
costs which is governed at least in part by the cost of transporting intermediates relative
to the cost of transporting …nal goods ( ).
We begin our analysis with the case in which
= 0 so that intermediates can be
costlessly shipped and upstream costs are zero for all modes. When intermediates can
be costlessly shipped, …rms face a simple tradeo¤ between lowering their marginal costs
16
associated with shipping the …nal good versus the …xed costs of building assembly plants.
Since, the …xed costs are greatest for decentralized FDI, lowest for exports, and
@
DI (')
@'
>
@
CI (')
@'
>
@
X (')
@'
(14)
;
it follows that the …rms with the largest market sizes will opt for decentralized FDI, …rms
with moderate market sizes will opt for centralized FDI, and the least productive …rms
will export. This sorting is akin to the type found in Helpman, Melitz, and Yeaple (2004).
The main di¤erence is that the structure of FDI here features a geography that gives rise
to “centralized FDI.”
Complications arise for the case in which
> 0. To see why note that the “upstream”
cost associated with obtaining components varies across modes in a systematic way. They
are highest for …rms following a decentralized FDI strategy and are zero for …rms choosing
to export the …nal good from the home country to the foreign region. Moreover, since
these upstream costs di¤er across modes in terms of their responsiveness to a …rm’s market
size, it is not generally possible to establish an ordering akin to (14) that holds for all
values of '.
To make progress, we consider the case in which
is small so that “upstream” costs
are small relative to“downstream”costs. In particular, it can be shown that if
<
min
(
t
;
+
M
t
M 1
)
;
then the ordering given by (14) is preserved. To see the implication of costly to ship
intermediates on the mapping from a …rm’s market size to its mode choice consider …gure
6.5 The solid lines in this …gure correspond to the case in which
5
= 0 while the broken
Note that parameter values have been chosen so that the cuto¤ market sizes between the three modes
17
lines correspond to the case in which
>
> 0. In both cases, the pro…t associated with
decentralized FDI is highest for …rms with the largest market shares, the pro…t associated
with exports is highest for the smallest …rms, while the pro…t for centralized FDI is highest
for …rms in between these extremes. Because exporters have the lowest “upstream”costs
(they are zero) and because decentralized FDI has the highest upstream costs, an increase
in
expands the range of market sizes for which export is the favored mode and shrinks
the range of market sizes for which …rms opt for decentralized FDI.
Let the cuto¤ market size between exporting and centralized FDI be given by '1 and
let the cuto¤ market size between centralized FDI and decentralized FDI be given by '2 :
Choosing parameter values6 such that these cuto¤s fall below ' (that is at these cuto¤s
…rms import some intermediates from their parent …rms), the threshold '1 is implicitly
de…ned by the function
('1 ) = M '1 (
t)
FA
M
'1
(M
'1 )2
=0
2f
(15)
and the threshold is implicitly de…ned by the function
('2 ) = M '2 t
(M
2
2 (M '2 )
1)FA
2f
t 2
Mt
= 0:
M 1
(16)
The last term in the equations (15) and (16) correspond to the di¤erences in the “upstream
costs” of the di¤erent modes. Note that
can be derived from these expressions and
the de…nition of an interior equilibrium. In summary, …rms with size ' < '1 engage
exclusively in export and own no foreign a¢ liates, …rms with size ' 2 ('1 ; '2 ) invest
exclusively in the central country, and …rms with market size ' > '2 invest in all M
occur for values of ' such that at these thresholds, …rms engaged in FDI import at least sum intermediates
from their parent …rms.
6
To obtain such an interior solution, one only need assume that FA is su¢ ciently small.
18
markets in the foreign region.
Now consider the pattern of intra-…rm trade between parent and a¢ liate as a function
of a …rm’s type. The share of intermediates that are imported from the parent is given
by (1
!
b ). For …rms pursuing a centralized FDI strategy !
b is given by (5) while for
…rms pursuing a decentralized FDI strategy !
b is given by (9). Notice that the threshold
intermediate cuto¤ given by (5) exceeds the threshold intermediate cuto¤ given by (9).
For a given ' the a¢ liates of …rms pursuing a centralized FDI strategy import a smaller
share of their intermediate inputs from the parent …rm than the a¢ liates of …rms that
pursue a decentralized FDI strategy.
Firms that concentrate their assembly in one location can lower their cost of delivering
a unit of intermediate input to the assembly plant by
. Firms that concentrate the
marginal intermediate’s production in center must still export that intermediate plant
to a¢ liates located in the periphery and so moving the production of an intermediate
to center reduces the cost by only
(
t). Since on the margin, …rms face the same
…xed cost of moving the production of an intermediate o¤shore, it follows that …rms that
concentrate assembly in center have a stronger incentive to reduce their imports from
their parent …rm. Hence, local content tends to be higher for centralized …rms. This has
the implication that the relationship between the share of intermediates imported from
the parent and a …rm’s size is non-monotonic and discontinuous at '2 the cuto¤ threshold
…rm size between those …rms that pursue a centralized FDI strategy and those that pursue
a decentralized FDI strategy as shown in …gure 7.
Figure 7 has important implications for empirical work. Suppose that a researcher
is interested in understanding the relationship between a …rm’s characteristics and the
extent of intra-…rm trade. A regression of the share of trade between parent …rm and
a¢ liate on …rm size could yield a positive, negative or zero coe¢ cient depending on
19
the distribution of …rm sizes in the sample. Holding …xed a mode choice, however, the
relationship between …rm size and propensity to import intermediates is clearly negative.
4
Comparative Statics
We now consider the e¤ect of changes in key exogenous variables on two components of
the structure of FDI. First, a change in an exogenous variable will alter the mode choice of
…rms. These e¤ects can be obtained by di¤erentiating the threshold conditions (15) and
(16). Second, holding …xed a …rm’s mode choice a change in an exogenous variable will
alter the structure of FDI within modes by inducing …rms to change their intermediate
input sourcing policies. These e¤ects can be obtained by di¤erentiating equations (5),
(11) and (9). Since the sourcing of intermediate inputs depends in part on mode choice,
the total change in the location of intermediate input production depends upon both
e¤ects.
First consider an increase in the inter-regional transport cost. An increase in
induces
a decrease in '1 and an increase in '2 . Higher inter-regional transport costs are therefore
associated with a smaller share of …rms engaged in exporting and a smaller share of
…rms engaged in decentralized FDI. The decrease in '1 is a straightforward result of the
proximity concentration tradeo¤ built into the model.
The increase in '2 requires more explanation. This result obtains because the “upstream” costs of …rms engaged in centralized FDI are more sensitive to inter-regional
trade costs than the“upstream” costs of …rms engaged in decentralized FDI (see …gure
7). The result has the interesting implication that for any peripheral country, higher
inter-regional transport costs are associated with a smaller number of foreign investors
entering the country. This might help explain why many studies …nd that FDI is actually
20
decreasing on average in distance between the host and the source country. Moreover,
it has the interesting implication that the e¤ect of distance on the volume of FDI to a
country interacts with that country’s “centrality:” distance between a source and host
country increases the volume of FDI in “central locations” and reduces it in “peripheral
locations.”
Now consider the e¤ect of an increase in inter-regional trade costs on the sourcing
of intermediates. Di¤erentiating equations (5), (11) and (9) establishes that an increase
in inter-regional trade costs induces a decrease in the share of intermediates sourced
from the home country. This result is consistent with the …nding in Hanson, Mataloni,
and Slaughter (2005) who show that imports of intermediate inputs by the a¢ liates of
U.S. multinational enterprises is decreasing in trade costs between the U.S. and the host
country. Inter-a¢ liate trade in the aggregate also falls because of the decrease in '2 : …rms
engaged in centralized FDI demand fewer inputs from Home.
Next consider the e¤ect of an increase in intra-regional trade costs. Total di¤erentiation of (15) establishes that an increase in t results in an increase in the threshold '1 .
Hence, a reduction in intra-regional trade costs, such as might occur with a preferential
trade agreement, reduces the volume of …nal good imports from Home and an increase in
the number of …rms conducting FDI in the foreign region. An increase in t also leads to a
decrease in the threshold '2 so that a reduction in intra-regional trade costs is associated
with a tendency for …rms to centralize their foreign production. These results are consistent with recent empirical work presented in Chen (2006). She …nds that the introduction
of a preferential trade agreement within a region tends to increase U.S. FDI to that region
but that FDI becomes more concentrated in particularly attractive countries within the
region.
With respect to the e¤ect of an increase in intra-regional transport costs on the sourc-
21
ing of intermediates, intermediate imports from Home increase for two reasons. First, as
…rms switch from a centralized to a decentralized FDI strategy, they increase their intermediates imports from Home because local content is higher among centralized multinationals. Second, holding …xed a …rm’s mode choice an increase in intra-regional trade
costs induce …rms to substitute the production of inputs away from Center toward Home.
Finally, an increase in the size of the foreign region as measured by the number of
markets in which there is demand M has very similar implications to a reduction in intraregional transport costs. First, there is an increase in '1 and a decrease in '2 : the number
of …rms engaged in centralized FDI expands at the expense of both exporters and of …rms
engaged in decentralized FDI. Second, local content increases as centralized FDI expands
at the expense of decentralized FDI and as a larger regional market induces …rms to incur
the additional …xed costs associated with moving production o¤shore.
5
Firm Heterogeneity and “Central Locations”: Empirics
In this section, we conduct several simple analyses of the data on U.S. multinational
enterprises (MNE) to two ends. First, we ask whether the assumptions of the model
are consistent with the behavior of U.S. MNE. Do you multinationals that enter centrally
located countries tend to export …nal goods and intermediates more than other countries?
Is the composition of multinationals that enter centrally located countries skewed toward
those …rms that produce in relatively few locations? Second, we test the implication of
the model that a country’s centrality is a more important characteristic the further it is
from the United States.
Our analysis relies on …rm-level data from the 1999 Benchmark Survey of the Bureau
22
of Economic Analysis (BEA). In benchmark years the BEA requires all U.S. …rms to list
all of the countries in which they own foreign a¢ liates. This requirement is independent
of the a¢ liate’s size so that the scope of this data is comprehensive. As an a¢ liate
becomes larger, the BEA requires the U.S. parent to provide an increasingly larger set
of information concerning the a¢ liate’s operations, including the volume of its a¢ liate’s
exports to both related and unrelated customers in other foreign countries. From this
database we consider all U.S. MNE whose main line of business is in manufacturing and
their manufacturing a¢ liates.
We begin the analysis by asking whether there is in fact a tendency for a¢ liates located
in centrally located to export heavily to third countries. We consider regressions of the
form:
yik =
i
+
F M Pk +
Zk + eik ;
(17)
where yik is a measure of the logarithm of a¢ liate i’s exports from country k: There are
two measures of exports. The …rst is the a¢ liate’s exports to related a¢ liates located
in other countries other than the United States. The second is the a¢ liate’s exports
to unrelated parties located in other countries other than the United States. The other
variables are F M Pk , which is a proxy for the centrality of country k, Zk is a vector of
controls for other characteristics of country k, and
i
is a …rm …xed e¤ect. The key
variable of interest is F M P , which stands for Foreign Market Potential. This variable is
a proxy for the “centrality”of a country’s location. It is calculated as
X GDPj
F M Pk = log
DISTkj
j6=k
!
;
where j indexes other countries, DISTkj is the distance between country j and country k,
23
is the proxy for the elasticity of transport costs with respect to distance (in the results
that follow we use
=0.8) and GDPj is the gross domestic product for country j.
The variables in Zk are standard controls from gravity equations. The gravity variables
include GDP , the logarithm of the host country’s GDP, EN GLISH which is the share of
the population that speaks English; DIST which is the logarithm of the distance between
the United States and the country in question, ADJ which is a dummy for Mexico and
Canada, and GDP P C which is the logarithm of a country’s GDP per capita. Industry
dummy variables where industry is de…ned at the 3-digit NAICS based BEA industry
classi…cation are included to control for heterogeneity across industries in the propensity
of …rms to invest abroad. Descriptive statistics for these variables are shown in Table 1.
The results of these regressions are shown in Table 2. The coe¢ cient estimates corresponding to intra-…rm trade is in column one and the results corresponding to unrelated
party exports are shown in column. Of particular interest is the result shown in the …rst
row. A¢ liates located in central locations export substantially more to both related and
unrelated parties than a¢ liates located elsewhere. Interestingly, the volume of both types
of exports is decreasing in a country’s GDP. The coe¢ cient on GDP P C is positive for
both types of exports but is statistically insigni…cant for related party exports while larger
and statistically signi…cant for unrelated party exports. Pure export platform FDI is more
common among developed countries while there is greater heterogeneity with respect to
related party trade.
Turning from …rm level dependent variables to country-industry level data, we now
consider the tendency for multinationals to sort into countries based on their degree of
centrality. We consider two measures of U.S. MNE activity to assess whether “central
locations”attract a large number of U.S. multinationals with small international production networks. The …rst measure V OLjk gauges the volume of activity of U.S. MNE in
24
country k and industry j. The second measure COM Pjk gauges the composition of U.S.
MNE entrants into country k and industry j. This variable is the number of countries
in which the median U.S. multinational entrant into country k owns a¢ liates. As this
variable becomes smaller, the composition of investors is becoming skewed toward …rms
with smaller multinational networks. The speci…cations we consider are akin to (17) with
three-digit NAICs industry …xed e¤ects replacing …rm …xed e¤ects. To cope with the
substantial number of observations for which there is no reported U.S. MNE activity, we
estimate each speci…cation via the two-step Heckman procedure.
The results of estimating these speci…cations via are shown in Table 3. Column one corresponds to coe¢ cient estimates from the …rst stage probit for both yik 2 fV OLik ; COM Pik g,
column two reports the second stage results for V OLik , and column three reports the second stage coe¢ cient estimates for COM Pik . Note …rst that the coe¢ cient estimates
in columns one and two are very similar in terms of their sign and magnitude. U.S.
multinationals are attracted to developed countries (GDP P C) with large foreign market
potential (F M P ), and large domestic markets (GDP ). They are also overrepresented in
countries with where English is the predominant language (EN GF RAC) and in Canada
and Mexico (ADJ). These …ndings are consistent with existing results in the literature.
Now consider the coe¢ cient estimates in column three. The …rst key observation is
that the country characteristics that predict greater volume of U.S. multinational entry
also predict a di¤erent composition of entrants into that country. Of key interest to our
study is the negative and statistically signi…cant coe¢ cient estimate on F M P : countries
with greater foreign market potential tend to attract U.S. multinationals that are active
in fewer locations than countries with lower foreign market potential. This result is
consistent with the premise of the model: …rms that concentrate their production abroad
tend to locate their foreign production in “central locations”relative to those U.S. MNE
25
with a greater scope of foreign operations.
We now turn our attention to an implication of the model. According to the comparative statics, the attractiveness of central locations is increasing in the distance of a
region from the source country. To assess this prediction, we split the sample into two
sets of countries on the basis of their distance from the United States so that each set has
roughly the same number of observations. We de…ne a country as “near” if it is within
7,400 miles of the United States and “far” if it is further away. This choice of distance
creates two groups of countries of nearly identical number of observations (840 and 860
respectively). We then reestimate the speci…cation for the volume of activity (dependent
variable is V OLik ) for each group and compare the coe¢ cient estimates obtained from
each group.
The results are shown in Table 4. The …rst two columns report the …rst and second stage coe¢ cient estimates of the two-stage Heckman estimation respectively for the
“near”countries and the second two columns report the …rst and second stage coe¢ cient
estimates respectively for the “far”countries. For the key variable of interest F M P note
that the coe¢ cient estimates are positive in both samples but the probit coe¢ cient is
only statistically signi…cant for the “far”sample and the OLS coe¢ cient is twice as large
for the “far” sample as it is for the “near” sample. These results are consistent with the
prediction of the model that multinationals tend to concentrate their regional production
in “central locations”the further is that region from the source country. Note that there is
some evidence of an asymmetric e¤ect of distance on the importance of own country size.
The coe¢ cient on GDP is somewhat larger in the sample of “near” countries compared
to“far”countries.
26
6
Conclusion
This paper makes the case that it is important to account for …rm heterogeneity and
the geography of regions to understand the structure of multinational enterprises. We
analyzed a model that allows for both vertical and horizontally integrated multinationals
in a multi-country setting. The model captures in the simplest possible way the complex
logistical problems facing multinationals. Firms can choose between three broad strategies
for assembling their …nal goods for foreign markets: home assembly followed by interregional trade, assembly in a central foreign region followed by intra-regional trade, and
assembly in each foreign location thereby avoiding all trade. Once a …rm has chosen
where to assemble its product, it must then decide where to produce intermediate inputs.
Intermediates are costly to ship and since they vary in their transport costs so the optimal
production location may vary over intermediates.
The analysis shows that …rms with more popular products, and hence bigger market
shares in any given foreign country, will organize their production within foreign regions
in a very di¤erent fashion than …rms with smaller market shares. Smaller multinationals
centralize their production in “central”locations while larger …rms open assembly a¢ liates
in many countries, while centralizing the production of many components in “central”
locations. These results are consistent with our empirical …nding that countries with
large market potential attract a disproportionate number of multinational …rms and that
these …rms are on average less well represented in less centralized locations.
The model also has a number of interesting comparative statics. For instance, because
centralized …rms optimally concentrate a larger fraction of their intermediate inputs production within a foreign region, an increase in inter-regional transport costs reduces the
FDI in peripheral countries as …rm substitute a centralized FDI strategy for a decentral-
27
ized FDI strategy. This result may help us to understand why, as transport costs have
fallen, the value of foreign sales of the a¢ liates of U.S. multinationals has been increasing
faster than their value-added but more slowly than their volumes of trade to both a¢ liated and una¢ liated customers. Moreover, our empirical analysis shows that a country’s
“centrality” becomes more important as a predictor of U.S. FDI the further the country
is from the United States.
The key role played by central locations also suggests that regions that are not integrated attract fewer multinationals. This result may suggest why certain regions, such as
Latin America, continue to attract relatively little FDI. The model has other empirical
implications that would be worthwhile to test. For instance, as a¢ liates become larger,
their local content should be increasing, while their participation in inter-a¢ liate trade
relative to value-added should exhibit an inverted U-shape in a¢ liate size.
Finally, the framework has deliberately been kept as simple as possible for the purpose of exposition but could easily be extended. First, it is conceptually straightforward
to introduce product market competition and heterogeneity in productivity to generate
heterogeneity in market shares. Doing so, would introduce the types of complementarities
that have been identi…ed in the recent work of Yeaple (2003) and Grossman, Helpman,
and Szeidl (2006). Second, alternative speci…cations of technology could be considered
that would capture the sequential nature of production that is actually observed. Third,
factor price and market size di¤erences could be addressed. Finally, while we assumed
away the possibility of outsourcing for simplicity, the framework would be applied to situations in which some intermediates are produced by the …rm and others obtained arm’s
length on markets.
28
References
[1] Blonigen, Bruce. 2005. “A Review of the Empirical Literature on FDI Determinants.”
Atlantic Economic Journal 33: 383-403.
[2] Blonigen, Bruce, Ronald Davies, Glen Waddell, and Helen Naughton. 2005. “FDI in
Space: Spatial Autoregressive Relationships in Foreign Direct Investment.” Mimeo
University of Oregon.
[3] Chen, Maggie. 2006. “Regional Economic Integration and Geographic Concentration
of U.S. Multinational Firms.”Mimeo George Washington University.
[4] Ekholm, Karolina, Rikard Forslid, and James Markusen. 2003. “Export Platform
Foreign Direct Investment.”NBER working paper 9517.
[5] Grossman, Gene, Elhanan Helpman, and Adam Szeidl. 2006. “Optimal Integration
Strategies for the Multinational Firm.”Journal of International Economics 70: 216238.
[6] Hanson, Gordon, Raymond Mataloni, and Matthew Slaughter. 2001. “Expansion
Strategies of U.S. Multinational Firms,” in Dani Rodrik and Susan Collins, eds.
Brookings Trade Forum.
[7] Hanson, Gordon, Raymond Mataloni, and Matthew Slaughter. 2005. “Vertical Production Networks in Multinational Firms.” Review of Economics and Statistics 87:
664-678.
[8] Head, Keith, and Theirry Mayer. 2004. “Market Potential and the Location of
Japanese Investment in Europe.” Review of Economics and Statistics 86(4): 959972.
29
[9] Helpman, Elhanan, Marc Melitz, and Stephen Yeaple. 2004. “Exports versus FDI
with Heterogeneous Firms.”American Economic Review 94(1): 300-316.
[10] Lai, Huiwen and Susan Zhu. 2006. “U.S. Exports and Multinational Production.”
Review of Economics and Statistics 88(3): 531-548.
[11] Mataloni, Raymond, and Daniel Yorgason. 2002. “Operations of U.S. Multinational
Companies: Preliminary Results From the 1999 Benchmark Survey.”Survey of Current Business March.
[12] Melitz, Marc. 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.”Econometrica 71: 1695-1725.
[13] Redding, Stephen and Anthony Venables. 2004. “Economic Geography and International Inequality.”Journal of International Economics 62(1): 53-82.
[14] UNCTAD. 2004. World Investment Report.
[15] Yeaple, Stephen. 2003. “The Complex Integration Strategies of Multinationals and
Cross Country Dependencies in the Structure of Foreign Direct Investment.”Journal
of International Economics 60(2): 293-314.
[16] Yeaple, Stephen. 2005. “How do U.S. Multinationals Sort?” mimeo University of
Pennsylvania.
30
Figure 1: Number of Countries in which Manufacturing Firms have Affiliates
Number of Firms
700
600
500
400
300
200
100
0
1
2-5
6-10
11-20
21-30
31-40
41-50
Number of Countries per Firm
Periphery 1
Figure 2: Decentralized FDI
Strategy
Final Good
Home:
Intermediates
Center:
Assembly,
Intermediates
Intermediates
Final Good
Periphery 2
31
51+
Figure 3: The Sourcing of Intermediate Inputs by Centralized Multinationals
ω
ω * (ϕ )
1
1 − ω * (ϕ )
ϕ
ϕ*
Periphery 1:
Assembly,
Intermediates
Figure 4: Decentralized FDI
Strategy
Intermediates
Intermediates
Home:
Intermediates
Center:
Intermediates
Intermediates
Intermediates
Periphery 2:
Assembly,
Intermediates
32
Figure 5: The Sourcing of Intermediate Inputs by Decentralized Multinationals
ω
ω 2 (ϕ )
1
ω1 (ϕ )
ω 2 (ϕ ) − ω1 (ϕ )
1 − ω 2 (ϕ )
ϕ′
ϕ ′′
33
ϕ
Figure 6:
Profits as a Function of Market Size and Mode Choice
140
Decentralized FDI Profit,
alpha=0
120
100
80
Centralized FDI Profit,
alpha>0
60
Centralized FDI Profit,
alpha=0
40
Export Profit
20
0
Market Size
Decentralized FDI Profit,
alpha>0
-20
-40
-60
Figure 7: Imports from Parent Firms and Firm Size
1-ω
ϕ1
ϕ′
ϕ2
34
ϕ
Table 1: Descriptive Statistics
Mean
Std Dev.
Number
1.21
1.15
Median Locations
2.57
0.85
FMP
21.94
1.62
GDP
25.76
1.77
GDPPC
9.26
0.79
DIST
8.87
0.61
ENGFRAC
0.16
0.34
ADJ
0.05
0.22
All variables except ENGFRAC and ADJ are in logarithms.
Table 2: Exports and Central Locations
Logarithm of
Logarithm of
Intra-firm
Other Exports
Exports
FMP
0.820
0.827
(0.096)
(0.108)
GDP
-0.373
-0.529
(0.089)
(0.099)
GDPPC
0.149
0.524
(0.148)
(0.141)
DIST
-0.301
-0.077
(0.234)
(0.185)
ENGLISH
0.211
0.151
(0.190)
(0.141)
ADJ
-1.594
-1.142
(0.602)
(0.542)
N
1,536
1,354
R-square
0.174
0.222
Both Specifications include fixed effects by firm. Standard errors shown in parentheses are
adjusted for heteroskedascity and clustering by country.
35
Table 3: Volume and Composition as a function of country characteristics
(1)
Prob > 0
(2)
(3)
Number of
Median
Entrants
Locations
FMP
0.301
0.300
-0.163
(0.056)
(0.051)
(0.035)
GDP
0.251
0.271
-0.089
(0.045)
(0.041)
(0.028)
GDPPC
0.273
0.425
-0.141
(0.067)
(0.067)
(0.046)
DIST
0.004
0.022
0.047
(0.089)
(0.079)
(0.054)
ENGFRAC
1.233
0.851
-0.798
(0.177)
(0.131)
(0.089)
ADJ
1.134
0.916
-0.671
(0.408)
(0.234)
(0.159)
Lambda
1.075
-0.731
(0.143)
(0.097)
N
1,700
1,700
Uncensored
713
713
Chi-sq.
967
1,359
Column 1 corresponds to the probit equation. Column 2 corresponds to the logarithm of the
number of U.S. manufacturing multinationals that own an affiliate in a given country-industry
pair. Column 3 corresponds to the logarithm of the median number of foreign locations that an
U.S. multinational entrant operates an affiliates. All variables except ENGFRAC and ADJ are in
logarithms. Coefficients on three-digit industry dummies are suppressed. Standard errors are
shown in parentheses below the coefficient estimates.
36
Table 4: Volume as a function of country characteristics, Sample Split by Distance from
the United States
Near Countries
Far Countries
(1)
(2)
(3)
(4)
Prob > 0
Number
Prob > 0
Number
of
of
Entrants
Entrants
FMP
0.199
0.172
0.282
0.330
(0.114)
(0.077)
(0.069)
(0.083)
GDP
0.420
0.347
0.249
0.286
(0.110)
(0.067)
(0.052)
(0.061)
GDPPC
0.358
0.422
0.333
0.423
(0.126)
(0.088)
(0.090)
(0.106)
DIST
-0.427
-0.072
0.937
0.915
(0.245)
(0.130)
(0.266)
(0.300)
ENGFRAC
1.073
0.654
1.266
0.975
(0.246)
(0.132)
(0.356)
(0.248)
ADJ
0.529
0.575
(0.476)
(0.237)
Lambda
0.765
1.282
(0.128)
(0.283)
N
840
860
Uncensored
442
315
Chi-sq.
771
379
Near countries are defined as the set of countries that are within 7,400 miles of the United States,
while far are those further away. All variables except ENGFRAC and ADJ are in logarithms.
Coefficients on three-digit industry dummies are suppressed. Standard errors are shown in
parentheses below the coefficient estimates.
37