Download The Margins of Global Sourcing: Theory and

The Margins of Global Sourcing:
Theory and Evidence from U.S. Firms∗
Pol Antràs
Harvard University
and NBER
Teresa C. Fort
Tuck School at Dartmouth
and NBER
Felix Tintelnot
University of Chicago
and NBER
April 14, 2017
Abstract
We develop a quantifiable multi-country sourcing model in which firms self-select into importing based on their productivity and country-specific variables. In contrast to canonical export
models where firm profits are additively separable across destination markets, global sourcing decisions naturally interact through the firm’s cost function. We show that, under an empirically
relevant condition, selection into importing exhibits complementarities across source markets. We
exploit these complementarities to solve the firm’s problem and estimate the model. Comparing
counterfactual predictions to reduced-form evidence highlights the importance of interdependencies in firms’ sourcing decisions across markets, which generate heterogeneous domestic sourcing
responses to trade shocks.
∗
Any opinions and conclusions expressed herein are those of the authors and do not necessarily represent the views
of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information is disclosed.
We are grateful to Treb Allen, Isaiah Andrews, Andy Bernard, Emily Blanchard, Ariel Burstein, Arnaud Costinot,
Pablo Fajgelbaum, Paul Grieco, Gene Grossman, Elhanan Helpman, Sam Kortum, Marc Melitz, Eduardo Morales, and
Michael Peters for useful conversations, to Andrés Rodrı́guez-Clare for his comments while discussing the paper at the
NBER, to the editor (Penny Goldberg) and two anonymous referees for their constructive comments, and to Xiang
Ding, BooKang Seol and Linh Vu for excellent research assistance. We have also benefited from very useful feedback
from seminar audiences at Aarhus, AEA Meetings in Boston, Barcelona GSE, Bank of Spain, Boston College, Boston
University, Brown, Cambridge University, Chicago Booth, Dartmouth, ECARES, the Econometric Society Meeting in
Minneapolis, ERWIT in Oslo, Harvard, IMF, John Hopkins SAIS, LSE, Michigan, MIT, UQ à Montreal, National
Bank of Belgium, NBER Summer Institute, Northwestern, Princeton, Sciences Po in Paris, SED in Toronto, Stanford,
Syracuse, Tsinghua, UBC, UC Berkeley, UC Davis, UC San Diego, Urbana-Champaign, Virginia, and Yale. We thank
Jim Davis at the Boston RDC for invaluable support with the disclosure process.
1
Introduction
During the last three decades, the world has become increasingly globalized. Dramatic advances
in communication, information, and transportation technologies have revolutionized how and where
firms produce their goods. Intermediate inputs account for approximately two thirds of international
trade (Johnson and Noguera, 2016), and vertical specialization across countries is an important and
growing feature of the world economy (Hummels et al., 2001; Hanson et al., 2005). As global value
chains rise in importance, a firm’s production is more likely than ever to span multiple countries.
There is also mounting evidence that firm-level decisions play a critical role in explaining trade
patterns (Bernard et al., 2009), and that they have important ramifications for aggregate productivity,
employment, and welfare (Goldberg et al., 2010; Hummels et al., 2014).
Despite the growing importance of global production sharing, the canonical model of firm-level
trade decisions (cf. Melitz, 2003) focuses on exporting rather than importing. Since every international trade transaction involves an exporter and an importer, a natural question is: can one use the
structure of the well-known exporting framework to analyze firms’ import decisions? Existing export
models cannot be applied directly to analyze foreign sourcing for a simple – yet powerful – reason.
While the canonical export model ensures that a firm’s decision to enter each market can be analyzed
separately by assuming constant marginal costs, a firm chooses to import precisely because it seeks
to lower its marginal costs. In a world in which firm heterogeneity interacts with fixed sourcing costs,
the firm’s decision to import from one market will also affect whether it is optimal to import from
another market. Foreign sourcing decisions are therefore interdependent across markets, making a
model about importing much more complicated to solve theoretically and to estimate empirically.
In this paper, we develop a new framework to analyze firm-level sourcing decisions in a multicountry world. An important focus of the model is on firms’ extensive margin decisions about which
products to offshore and the countries from which to purchase them. Bernard et al. (2009) find
that these margins account for about 65 percent of the cross-country variation in U.S. imports, and
Bernard et al. (2007) show that U.S. importers are on average more than twice as large and about 12
percent more productive than non-importers.1 In Figure 1, we extend this evidence to show not only
that importers are larger than non-importers, but also that their relative size advantage is increasing
in the number of countries from which they source. The figure indicates that firms that import from
one country are more than twice the size of non-importers, firms that source from 13 countries are
about four log points larger, and firms sourcing from 25 or more countries are over six log points
bigger than non-importers. These importer size advantages are suggestive of sizable country-level
fixed costs of sourcing, which limit the ability of small firms to select into importing from a large
number of countries.2
1
We obtain very similar findings when replicating these analyses for the sample of U.S. manufacturing firms used in
our empirical analysis (see the Online Appendix, section C.2).
2
To construct the figure, we regress the log of firm sales on cumulative dummies for the number of countries from
which a firm sources and industry controls. The omitted category is non-importers, so the premia are interpreted as the
difference in size between non-importers and firms that import from at least one country, at least two countries, etc.
The horizontal axis denotes the number of countries from which a firm sources, with 1 corresponding to firms that use
only domestic inputs. These premia are robust to controlling for the number of products a firm imports and the number
of products it exports, and thus do not merely capture the fact that larger firms import more products. Consistent with
1
0
1
2
Premium
3
4
5
6
Figure 1: Sales premia and minimum number of sourcing countries in 2007
1
3
5
7
9
11
13
15
17
19
21
23
Minimum number of countries from which firm sources
Premium
25
95% CI
Not only do country-level fixed costs of importing appear to be empirically relevant, but they also
seem to be heterogeneous across countries. To illustrate this variation, Table 1 shows the number of
U.S. firms that import from a country versus total sourcing from that country. The table lists the top
ten source countries for U.S. manufacturers in 2007, based on the number of importing firms. These
countries account for 93 percent of importers in our sample and 74 percent of imports. The first
two columns show that Canada ranks number one based on the number of U.S. importers and total
import value. For most other countries, however, country rank based on the number of importers
does not equal the rank based on import values. China is number two for firms but only number three
for value; and Mexico, the number two country in terms of value, ranks eighth in terms of number of
importers.
The considerable divergence between the intensive and extensive margins presented in Table 1
suggests that countries differ not only in terms of their potential as a marginal cost-reducing source
of inputs, but also in terms of the fixed costs firms must incur to import from them. In section 2, we
develop a quantifiable multi-country sourcing model that allows for this possibility. Heterogeneous
firms self-select into importing based on their productivity and country-specific characteristics (wages,
trade costs, and technology). The model delivers a simple closed-form solution for firm profits, in
which marginal costs are decreasing in a firm’s sourcing capability, which is itself a function of the
set of countries from which a firm imports, as well as those countries’ characteristics. Firms can, in
principle, buy intermediate inputs from any country in the world, but acquiring the ability to import
from a country entails a market-specific fixed cost. As a result, relatively unproductive firms may
opt out of importing from high fixed cost countries, even if they are particularly attractive sources of
inputs.
In this environment, the optimality of importing from one country generically depends on the
selection into importing, the same qualitative pattern is also evident among firms that did not import in 2002, and when
using employment or productivity rather than sales. See section C.3 of the Online Appendix for additional details.
2
Table 1: Top 10 source countries for U.S. firms, by number of firms
Rank by:
Canada
China
Germany
United Kingdom
Taiwan
Italy
Japan
Mexico
France
South Korea
Number of Importers
Value of Imports
Firms
Value
Firms
% of Total
Imports
% of Total
1
2
3
4
5
6
7
8
9
10
1
3
5
6
11
13
4
2
9
10
37,800
21,500
13,000
11,500
10,500
8,500
8,000
7,800
6,100
5,600
58
33
20
18
16
13
12
12
9
9
145,740
121,990
62,930
30,750
16,630
13,230
112,250
125,980
22,980
20,390
16
14
7
3
2
1
13
14
3
2
Notes: Sample is U.S. firms with some manufacturing activity in 2007. Number of firms rounded to
nearest 100 for disclosure avoidance. Imports in millions of $s, rounded to nearest 10 million for disclosure
avoidance.
other countries from which a firm sources its inputs. This stands in sharp contrast to standard
export models, where the assumption of constant marginal costs ensures that the decision to sell
in one market is independent of export decisions in other markets. This constant marginal cost
assumption is clearly not tenable for sourcing decisions, since the firm chooses to import precisely in
order to lower its marginal costs. The resulting interdependence in a firm’s extensive margin import
decisions complicates the firm’s problem considerably, as it now involves a combinatorial problem
with 2J possible choices, where J denotes the number of possible source countries.
Despite these complications, we provide the first characterization of the firm’s extensive margin
sourcing decisions. First, we show that source countries can be complements or substitutes, depending
only on a parametric restriction that relates the elasticity of demand faced by the final-good producer
to the dispersion of input productivities across locations. When demand is inelastic or input efficiency
differences are small, the addition of a country to a firm’s global sourcing strategy reduces the marginal
gain from adding other locations. In such a “substitutes case,” the firm’s optimal choice of countries
to include in its sourcing strategy is extremely hard to characterize, both analytically as well as
quantitatively. High productivity firms may opt into countries with high fixed costs but with the
potential for high marginal cost savings, thus rendering further marginal cost reductions less beneficial.
Although low productivity firms would also like to source from these locations, the high fixed costs
may preclude them from doing so. In this scenario, high productivity firms will always source from
(weakly) better countries, but they may source from fewer countries than low productivity firms.
Global sourcing therefore magnifies any pre-existing differences in underlying firm productivity and
increases the skewness in the size distribution of firms, but does not necessarily lead to the hierarchical
entry predictions that are well-known for exporting.
Conversely, selection into importing features complementarity across markets when demand is
3
relatively elastic (so profits are particularly responsive to variable cost reductions) and input efficiency
levels are relatively heterogeneous across markets (so that the reduction in expected costs from adding
an extra country in the set of active locations is relatively high). This case is much more tractable,
and delivers sharp results rationalizing the monotonicity in the sales premia observed in Figure 1.
In particular, we use standard tools from the monotone comparative statics literature to show that,
in such a case, the sourcing strategies of firms follow a strict hierarchical structure in which the
number of countries in a firm’s sourcing strategy increases (weakly) with the firm’s core productivity
level.3 Crucially, despite this hierarchical sourcing structure, the model also generates the type of
discrepancies between the intensive and extensive margins of importing evident in Table 1. We
explicitly show that this is not possible in a model that abstracts from country-specific fixed costs.
Our quantitative analysis enables separate identification of the sourcing potential of a country
– a function of technology, trade costs, and wages capturing the potential of a country as source
of marginal cost savings – and the fixed cost of sourcing from that country. We use 2007 Census
data on U.S. manufacturers’ mark-ups and import shares to recover the sourcing potential of 66
foreign countries, as well as the average elasticity of demand and dispersion of input productivities
faced by U.S. firms. Consistent with the pattern documented in Figure 1, we find robust evidence
suggesting that the extensive margin sourcing decisions of U.S. firms are complements. This finding
paves the way for an additional methodological contribution of our paper –namely, to solve the firm’s
problem and estimate the model structurally. To do so, we apply an iterative algorithm developed
by Jia (2008), which exploits the complementarities in the ‘entry’ decisions of firms, and uses lattice
theory to reduce the dimensionality of the firm’s optimal sourcing strategy problem. We can therefore
estimate the fixed costs of sourcing, which range from a median of 10,000 to 56,000 USD, are around
13 percent lower for countries with a common language, and increase in distance with an elasticity
of 0.19. In line with the premise that countries differ along two dimensions, the relative rankings of
these fixed costs are also quite different from the rankings of countries’ potential to reduce marginal
costs.4
The structural estimation of the model is informative not only because it shows the importance
of marginal cost savings versus fixed cost heterogeneity across countries, but also because it allows
for counterfactual exercises.5 We exploit this capability by studying the implications of an increase
in China’s sourcing potential calibrated to match the observed growth in the share of U.S. firms
importing from China between 1997 and 2007. These years are governed both by data availability,
and the fact that they span China’s accession to the World Trade Organization (WTO). Consistent
with other quantitative models of trade, the China shock increases the competitive environment by
decreasing the equilibrium industry-level U.S. price index and driving some U.S. final good producers
out of the market. Although the net result of these forces is a marked decrease in domestic sourcing
3
The seminal applications of the mathematics of complementarity in the economics literature are Vives (1990) and
Milgrom and Roberts (1990). Grossman and Maggi (2000) and Costinot (2009) are particularly influential applications
of these techniques in international trade environments.
4
Building on Jia (2008), in a recent interesting paper Arkolakis and Eckert (2017) develop an algorithm that can
solve large combinatorial discrete choice problems in the case in which the firm’s discrete choices are substitutes.
5
This is in contrast to moment inequality methods, which were first adopted in an international trade context by
Morales et al. (2014).
4
(and U.S. employment) in that sector, the net decline masks significant heterogeneity in how the shock
affects the sourcing decisions of firms at different points in the size distribution. More specifically, the
shock induces a range of U.S. firms to select into sourcing from China, and on average, these firms
increase their input purchases not only from China, but also from the U.S. and other countries. The
existence of gross changes in sourcing that operate in different directions is a distinctive feature of our
framework that does not arise in the absence of fixed costs of offshoring or whenever entry decisions
are independent across markets.
To assess the empirical relevance of these channels, we compare the model’s counterfactual predictions to the observed changes in U.S. manufacturers’ sourcing from the U.S. and third markets
between 1997 and 2007. We first show that the same qualitative patterns predicted by the model are
evident in the raw data. Firms that begin importing from China over this period grow their domestic
and third market sourcing the most, continuing importers have smaller but still positive sourcing
changes, and firms that never import from China shrink their domestic sourcing and increase thirdmarket sourcing by a substantially smaller amount than both new and continuing China importers.
To ensure that the patterns observed in the raw data are not driven solely by firm-specific demand or
productivity shocks, we construct a plausibly exogenous firm-level shock to Chinese sourcing potential in the spirit of Autor et al. (2013) and Hummels et al. (2014). The results show that exogenous
increases in firm-level imports from China do not decrease domestic and third market sourcing –
as might be expected in a world with no interdependencies in sourcing decisions– but instead are
associated with increased firm-level sourcing from other markets. We thus provide both structural
and reduced-form evidence of the empirical relevance of interdependencies in firms’ extensive margin
import decisions.
Our paper contributes to three distinct literatures. First, we add to a large body of theoretical
work on foreign sourcing. We follow existing theory that adapts the Melitz (2003) model to characterize heterogeneous firms’ foreign sourcing decisions (e.g., Antràs and Helpman, 2004, 2008), but
our framework also shares features with a parallel literature that uses the Eaton and Kortum (2002)
model to study offshoring (Rodrı́guez-Clare, 2010; Garetto, 2013). More specifically, we build on the
approach in Tintelnot (forthcoming) of embedding the Eaton and Kortum (2002) stochastic representation of technology into the problem of a firm, though in our context firms choose optimal sourcing
rather than final-good production locations. This approach allows us to move beyond the two-country
frameworks that have pervaded the literature and develop a tractable multi-country model. A key
theoretical insight from our model is that a positive shock to sourcing from one location could lead a
firm either to decrease its sourcing from other locations as it substitutes away from them, or instead
to grow sufficiently so that it increases its net sourcing from other locations. This prediction is reminiscent of Grossman and Rossi-Hansberg (2008), who show that an offshoring industry may expand
domestic employment if a “productivity effect” dominates a “substitution effect.” An important
difference is that in our framework, these effects take place within a firm rather than an industry.
Our paper also relates to an extensive empirical literature on offshoring. A number of papers
provide reduced form evidence on the determinants of offshoring (Fort, forthcoming), as well as its
impact on firm performance and aggregate productivity (Amiti and Konings, 2007; Goldberg et al.,
5
2010; De Loecker et al., 2016). A related set of papers uses a more structural approach to quantify
the effect of importing on firm productivity and prices (Halpern et al., 2015; Gopinath and Neiman,
2014; Blaum et al., 2017). The first part of our estimation provides a similar quantification, implying
that a firm sourcing from all foreign countries faces nine percent lower variable costs and achieves 32
percent higher sales than when sourcing exclusively from domestic suppliers.6 The most important
distinction between those papers and ours is that we provide evidence not just on the intensive margin
implications of importing, but also on the firm’s extensive margin sourcing decisions in a multi-country
setting with heterogeneous fixed costs across countries. While Blaum et al. (2013) discuss the existence
of interdependencies across sourcing decisions in a model with an arbitrary number of countries and
inputs, ours is the first paper to characterize the extensive margin of importing in this setting and to
solve the firm’s problem quantitatively.
Finally, we contribute to a growing body of work that analyzes interdependencies in firm-level
decisions. Yeaple (2003) and Grossman et al. (2006) first described the inherent difficulties in solving
for the extensive margin of imports in a multi-country model with multiple intermediate inputs and
heterogeneous fixed costs of sourcing. Those authors obtained partial characterizations of the problem
in models with at most three countries and two inputs. We provide the first characterization of the
firm’s extensive margin sourcing decision in this setting with multiple inputs and countries, and
show how these decisions can be aggregated to describe trade flows across countries. These trade
flow equations collapse to the well-known Eaton and Kortum (2002) gravity equation whenever fixed
costs are zero (so that there is universal importing), or to the Chaney (2008) gravity equation in the
knife-edge case that shuts down interdependencies across markets. In a general setting, our model
delivers an extended gravity equation reminiscent of Morales et al. (2014), who estimate a model with
interdependencies in firms’ export decisions. That paper uses moment inequalities to partially identify
the cost parameters and does not conduct any counterfactual analysis. Tintelnot (forthcoming) solves
the optimal plant location problem of multinational firms in a general equilibrium model, however,
in a setting with much fewer countries. We overcome the challenges in prior work by combining
the theoretical insights on complementarity with Jia’s (2008) algorithm for solving Walmart’s and
Kmart’s decisions about whether and where to open new retail establishments. Our paper is the first
to adopt this algorithm in an international setting or in a setting with more than two firms.
The rest of the paper is structured as follows. We present the assumptions of our model in section
2 and solve for the equilibrium in section 3. In section 4, we introduce the data and provide descriptive
evidence supporting the assumptions underlying our theoretical framework. We estimate the model
structurally in section 5, and in section 6, we perform our counterfactual analysis and compare the
predictions of the model to reduced-form evidence. Section 7 concludes.
6
Quantitatively, this is lower than the findings of Halpern et al. (2015) for Hungarian firms. Using a two-country
model and a method similar to Olley and Pakes (1996), they find that importing all foreign varieties would increase
productivity of a Hungarian firm by 22 percent. Blaum et al. (2017) obtain even larger cost reduction estimates for
some French firms, perhaps due to an alternative interpretation of idiosyncratic differences in sourcing shares (e.g., as
measurement error in our context and as structural error in their paper).
6
2
Theoretical Framework
In this section, we develop our quantifiable multi-country model of global sourcing.
2.1
Preferences and Endowments
Consider a world consisting of J countries in which individuals value the consumption of differentiated
varieties of manufactured goods according to a standard symmetric CES aggregator
σ/(σ−1)

Z
UM i = 
qi (ω)(σ−1)/σ dω 
,
σ > 1,
(1)
ω∈Ωi
where Ωi is the set of manufacturing varieties available to consumers in country i ∈ J (with some
abuse of notation we denote by J both the number as well as the set of countries; we use subscripts
i and j to denote countries). These preferences are assumed to be common worldwide and give rise
to the following demand for variety ω in country i:
qi (ω) = Ei Piσ−1 pi (ω)−σ ,
(2)
where pi (ω) is the price of variety ω, Pi is the standard ideal price index associated with (1), and
Ei is aggregate spending on manufacturing goods in country i. For what follows it will be useful to
define a (manufacturing) market demand term for market i as:
1
Bi =
σ
σ
σ−1
1−σ
Ei Piσ−1 .
(3)
There is a unique factor of production, labor, which commands a wage wi in country i. When
we close the model in general equilibrium, we later introduce a freely tradable, non-manufacturing
sector into the economy. This non-manufacturing sector captures a constant share of the economy’s
spending, also employs labor, and is large enough to pin down wages in terms of that ‘outside’ sector’s
output.
2.2
Technology and Market Structure
There exists a measure Ni of final-good producers in each country i ∈ J, and each of these producers owns a blueprint to produce a single differentiated variety. The market structure of final good
production is characterized by monopolistic competition, and there is free entry into the industry.
Production of final-good varieties requires the assembly of a bundle of intermediates. We index
final-good firms by their ‘core productivity’, which we denote by ϕ, and which governs the mapping
between the bundle of inputs and final-good production. Following Melitz (2003), we assume that
firms only learn their productivity ϕ after incurring an entry cost equal to fei units of labor in country
i. This core productivity is drawn from a country-specific distribution gi (ϕ), with support in [ϕi , ∞),
and with an associated continuous cumulative distribution Gi (ϕ). For simplicity, we assume that
7
final-good varieties are prohibitively costly to trade across borders.
Intermediates can instead be traded internationally, and a key feature of the equilibrium will
be determining the location of production of different intermediates. The bundle of intermediates
contains a continuum of measure one of firm-specific inputs, assumed to be imperfectly substitutable
with each other, with a constant and symmetric elasticity of substitution equal to ρ. Very little
will depend on the particular value of ρ. All intermediates are produced with labor under constantreturns-to-scale technologies. We denote by aj (v, ϕ) the unit labor requirement associated with the
production of firm ϕ’s intermediate v ∈ [0, 1] in country j ∈ J.
Although intermediates are produced worldwide, a final-good producer based in country i only
acquires the capability to offshore in j after incurring a fixed cost equal to fij units of labor in country
i. We denote by Ji (ϕ) ⊆ J the set of countries for which a firm based in i with productivity ϕ has
paid the associated fixed cost of offshoring wi fij . For brevity, we will often refer to Ji (ϕ) as the
global sourcing strategy of that firm.
Intermediates are produced by a competitive fringe of suppliers who sell their products at marginal
cost.7 Shipping intermediates from country j to country i entails iceberg trade costs τij . As a result,
the cost at which firms from i can procure input v from country j is given by τij aj (v, ϕ) wj , and the
price that firm ϕ based in country i pays for input v can be denoted by
zi (v, ϕ; Ji (ϕ)) = min {τij aj (v, ϕ) wj } .
(4)
j∈Ji (ϕ)
We can then express the marginal cost for firm ϕ based in country i of producing a unit of a
final-good variety as
1
ci (ϕ) =
ϕ
Z
1
1−ρ
zi (v, ϕ; Ji (ϕ))
1/(1−ρ)
dv
.
(5)
0
Building on Eaton and Kortum (2002), we treat the (infinite-dimensional) vectors of firm-specific
intermediate input efficiencies 1/aj (v, ϕ) as the realization of an extreme value distribution. More
specifically, suppliers in j draw the value of 1/aj (v, ϕ) from the Fréchet distribution
θ
Pr(aj (v, ϕ) ≥ a) = e−Tj a ,
with Tj > 0.
(6)
These draws are assumed to be independent across locations and inputs. As in Eaton and Kortum
(2002), Tj governs the state of technology in country j, while θ determines the variability of productivity draws across inputs, with a lower θ fostering the emergence of comparative advantage within
the range of intermediates across countries.
2.3
Discussion of Assumptions
This completes the description of the key assumptions of the model. A number of dimensions of
our setup are worth discussing. First, although we have assumed that inputs are firm-specific, our
model is in fact isomorphic to one in which the unit measure of inputs, as well as their associated
7
Implicitly, we assume that contracts between final-good producers and suppliers are perfectly enforceable, so that
the firm-specificity of inputs is irrelevant for the prices at which inputs are transacted.
8
unit labor requirements aj (v, ϕ), are identical for all firms and denoted by aj (v). We emphasize the
firm-specificity of inputs to justify why intermediaries (e.g., wholesalers) would not trivially eliminate
the need for all firms to incur fixed costs of foreign sourcing. Second, to highlight the importance of
importing, we have assumed that final-good varieties cannot be traded across borders. In the Online
Appendix (section B.3), we relax this assumption and study the joint determination of the extensive
margins of both exports and imports, an approach that has been further pursued by Bernard et al.
(2016). Third, our model assumes that all final-good producers combine a measure one of inputs in
production. As we demonstrate in the Online Appendix (section B.3), it is simple to generalize our
framework to the case in which final-good producers also hire local labor to assemble the bundle of
inputs, and in which firms optimally choose the complexity of production, as captured by the measure
of inputs used in production (see Acemoglu et al., 2007). The qualitative results of these extensions
are analogous to those of our benchmark model, but incorporating these features would significantly
complicate the structural estimation. Fourth, tractability concerns also dictate our assumption that
wages are pinned down in a non-manufacturing sector, as we discuss at greater length in section
6. Finally, we have introduced an asymmetric market structure in the final- and intermediate-input
sectors because this allows our model to nest two key workhorse trade models developed in recent
years. It would be feasible to turn the intermediate-input sector into a monopolistically competitive
sector with a fixed mass of firms, and the relevant expressions would all be very similar.
3
Equilibrium
We solve for the equilibrium of the model in three steps. First, we describe optimal firm behavior
conditional on a given sourcing strategy Ji (ϕ). Second, we characterize the choice of this sourcing
strategy and relate our results to some of the stylized facts discussed in the Introduction. Third, we
aggregate the firm-level decisions and solve for the general equilibrium of the model. We conclude
this section by outlining the implications of our framework for bilateral trade flows across countries.
3.1
Firm Behavior Conditional on a Sourcing Strategy
Consider a firm based in country i with productivity ϕ that has incurred all fixed costs associated
with a given sourcing strategy Ji (ϕ). In light of the cost function in (5), it is clear that after learning
the vector of unit labor requirements for each country j ∈ Ji (ϕ), the firm will choose the location
of production for each input v that solves minj∈Ji (ϕ) {τij aj (v, ϕ) wj }. Using the properties of the
Fréchet distribution in (6), one can show that the firm will source a positive measure of intermediates
from each country in its sourcing strategy set Ji (ϕ). Furthermore, the share of intermediate input
purchases sourced from any country j (including the home country i) is simply given by
χij (ϕ) =
Tj (τij wj )−θ
Θi (ϕ)
9
if j ∈ Ji (ϕ)
(7)
and χij (ϕ) = 0 otherwise, where
X
Θi (ϕ) ≡
Tk (τik wk )−θ .
(8)
k∈Ji (ϕ)
The term Θi (ϕ) summarizes the sourcing capability of firm ϕ from i. Note that, in equation (7),
each country j’s market share in the firm’s purchases of intermediates corresponds to this country’s
contribution to its sourcing capability Θi (ϕ). Countries in the set Ji (ϕ) with lower wages wj , more
advanced technologies Tj , or lower trade costs when selling to country i will have higher market
shares in the intermediate input purchases of firms based in country i. We shall refer to the term
Tj (τij wj )−θ as the sourcing potential of country j from the point of view of firms in i.8
After choosing the least cost source of supply for each input v, the overall marginal cost faced by
firm ϕ from i can be expressed, after some cumbersome derivations, as
ci (ϕ) =
1
(γΘi (ϕ))−1/θ ,
ϕ
(9)
h iθ/(1−ρ)
and Γ is the gamma function.9 Note that in light of equation (8), the
where γ = Γ θ+1−ρ
θ
addition of a new location to the set Ji (ϕ) increases the sourcing capability of the firm and necessarily
lowers its effective marginal cost. Intuitively, an extra location grants the firm an additional cost draw
for all varieties v ∈ [0, 1], and it is thus natural that this greater competition among suppliers will
reduce the expected minimum sourcing cost per intermediate. In fact, the addition of a country to
Ji (ϕ) lowers the expected price paid for all varieties v, and not just for those that are ultimately
sourced from the country being added to Ji (ϕ).
Using the demand equation (2) and the derived marginal cost function in (9), we can express the
firm’s profits conditional on a sourcing strategy Ji (ϕ) as
πi (ϕ) = ϕσ−1 (γΘi (ϕ))(σ−1)/θ Bi − wi
X
fij ,
(10)
j∈Ji (ϕ)
where Bi is given in (3). As is clear from equation (10), when deciding whether to add a new country
j to the set Ji (ϕ), the firm trades off the reduction in costs associated with the inclusion of that
country in the set Ji (ϕ) – which increases the sourcing capability Θi (ϕ) – against the payment of
the additional fixed cost wi fij .
It is worth highlighting the connection between our modeling of the gains from importing intermediate inputs and the Armington-style approach that is standard in the literature on importing.10
More specifically, suppose that all suppliers in a given country produce the same intermediate input
8
It may seem surprising that the dependence of country j’s market share χij (ϕ) on wages and trade costs is shaped
by the Fréchet parameter θ and not by the substitutability across inputs, as governed by the parameter ρ in equation
(5). The reason for this, as in Eaton and Kortum (2002), is that variation in market shares is explained exclusively by
a product-level extensive margin.
9
These derivations are analogous to those performed by Eaton and Kortum (2002) to solve for the aggregate price
index in their model. To ensure a well-defined marginal cost index, we assume θ > ρ − 1. Apart from satisfying this
restriction, the value of ρ does not matter for any outcomes of interest and will be absorbed into a constant.
10
See, among others, Halpern et al. (2015), Goldberg et al. (2010), and Gopinath and Neiman (2014).
10
using local labor under a constant-returns-to-scale technology featuring a unit labor requirement equal
to (γTj )−1/θ in each country j ∈ J. Assume, in addition, that inputs are differentiated by country of
origin with an elasticity of substitution across inputs from any two locations equal to 1 + θ. Finally,
as in our framework, assume that in order to import country j’s unique input, final-good producers
in i need to incur a fixed costs equal to wi fij and iceberg trade costs τij . Under these assumptions, it
is then straightforward to verify that the resulting firm profits will be identical to those in equation
(10) above.
This isomorphism between our model and the love-for-variety approach carries three significant
implications. First, it should be clear that the interdependencies in the firm’s extensive margin sourcing decisions are also a feature of the Armington-style models that have pervaded the literature on
importing. Second, it follows that the results below on the optimal determination of the sourcing
strategy Ji (ϕ), as well as the techniques we develop in section 5 to structurally estimate the model,
are also applicable in these types of models. Third, it implies that our model provides an intuitive microfoundation for why being able to import from (several) foreign countries is productivity-enhancing,
without resorting to the elusive notion of input differentiation by country of origin. With this in mind,
we next turn to an analysis of the optimal sourcing strategy of firms.
3.2
Optimal Sourcing Strategy
Each firm’s optimal sourcing strategy is a combinatorial optimization problem in which a set Ji (ϕ) ⊆
J of locations is chosen to maximize the firm’s profits πi (ϕ) in (10). We can alternatively express
this problem as

max
Iij ∈{0,1}J
j=1
πi (ϕ, Ii1 , Ii2 , ..., IiJ ) = ϕσ−1 γ
J
X
(σ−1)/θ
Iij Tj (τij wj )−θ 
j=1
B i − wi
J
X
Iij fij ,
(11)
j=1
where the indicator variable Iij takes a value of 1 when j ∈ Ji (ϕ), and 0 otherwise. The problem
in (11) is not straightforward to solve because the decision to include a country j in the set Ji (ϕ)
depends on the number and characteristics of the other countries in this set. In theory, one could
simply calculate firm profits for different combinations of locations and pick the unique strategy
yielding the highest level of profits. In practice, however, this would amount to computing profits
for 2J possible strategies, which is clearly infeasible unless one chooses a small enough number J of
candidate countries.
Inspection of (11) reveals, however, that the profit function πi is supermodular in ϕ and Θi (ϕ),
and features increasing differences in (Iij , Iik ) for j, k ∈ {1, ..., J} and j 6= k, whenever (σ − 1) /θ >
1. These properties of the problem in (11) allow us to establish the following result (the proof is
straightforward and is relegated to the Online Appendix):
Proposition 1. The solution Iij (ϕ) ∈ {0, 1}Jj=1 to the optimal sourcing problem (11) is such that:
J
P
Iij (ϕ) Tj (τij wj )−θ is nondecreasing in ϕ;
(a) a firm’s sourcing capability Θi (ϕ) =
j=1
(b) if (σ − 1) /θ ≥ 1, then Ji (ϕL ) ⊆ Ji (ϕH ) for ϕH ≥ ϕL , where Ji (ϕ) = {j : Iij (ϕ) = 1}.
11
Part (a) of Proposition 1 simply states that more productive firms choose a larger sourcing capability –either because they select into more countries or because they select into better countries–
thereby magnifying their cost advantage relative to less productive firms. This in turn implies that
the equilibrium size distribution of firms will feature more positive skewness than what would be
observed without foreign sourcing.
It is important to emphasize that this first result does not imply that the extensive margin of
sourcing at the firm level (i.e., the number of elements of Ji (ϕ)) is necessarily increasing in firm
productivity as well. For example, a highly productive firm from i might pay a large fixed cost to
offshore to a country j ∗ with a particularly high sourcing potential (i.e., a high value of Tj ∗ (τij ∗ wj ∗ )−θ )
– thus greatly increasing Θi – after which the firm might not have an incentive to add further locations
to its sourcing strategy. Instead, a low productivity firm from i might not be able to profitably offshore
to j ∗ , but may well find it optimal to source from two foreign countries with associated lower fixed
costs.
Part (b) of Proposition 1 states, however, that this possibility can only arise when (σ − 1) /θ < 1.
When instead (σ − 1) /θ ≥ 1, the cardinality of the set Ji (ϕ) is necessarily weakly increasing in ϕ.
Because firm size is increasing in core productivity ϕ, this prediction is consistent with the upward
sloping sales premium documented in Figure 1 in the Introduction. The intuition behind this second
result in Proposition 1 rests on the fact that, when (σ − 1) /θ > 1, the profit function πi (ϕ) features
increasing differences in (Iij , Iik ) for j, k ∈ {1, ..., J} and j 6= k, and thus the marginal gain from adding
a new location to the set Ji (ϕ) cannot possibly be reduced by the addition of other countries to the
set. This case is more likely to apply whenever demand is elastic and thus profits are particularly
responsive to variable cost reductions (high σ), and whenever input efficiency levels are relatively
heterogeneous across markets (low θ), so that one achieves a relatively high reduction of costs by
adding an extra country into the set of active locations.11
Part (b) of Proposition 1 also has the strong implication that there should be a strict hierarchical
order in the extensive margin of offshoring – a ‘pecking order’ which is reminiscent of the one typically
obtained in models of exporting with heterogeneous firms, such as Eaton et al. (2011). This prediction
is very strong and often violated in the data: it is not uncommon to observe less productive firms
sourcing from countries from which more productive firms do not source. Still, in section 4.2 we show
that 36 percent of U.S. firms follow the predicted pecking order from the top ten source countries,
whereas we would expect only 20 percent to do so if the probabilities to source from individual
countries were independent and equal to the share of importers that source from them.
A possible explanation for the violation of a strict hierarchy of import sources is the fact that fixed
costs of sourcing might be heterogeneous across firms. With that in mind, our structural estimation
in section 5 will incorporate such heterogeneity in fixed costs. In that section, a variant of part (b) of
Proposition 1 will be instrumental for reducing the dimensionality of the optimal sourcing problem.
In particular, because of increasing differences in the profit function when σ − 1 > θ, we can state
(see the Online Appendix for a formal proof):
11
Readers familiar with the work of Eaton and Kortum (2002) might expect that θ > σ − 1 is in fact implied by the
need for the firm’s marginal cost function to be well-defined. Note, however, that our parameter ρ plays the role of σ
in the Eaton-Kortum setup, and thus this technical condition is instead θ > ρ − 1 in our setup (see footnote 9).
12
Proposition 2. For all j ∈ {1, ..., J}, define the mapping Vi,j (ϕ, J ) to take a value of one whenever
including country j in the sourcing strategy J raises firm-level profits πi (ϕ, J ) , and to take a value
of zero otherwise. Then, whenever (σ − 1) /θ ≥ 1, Vi,j (ϕ, J 0 ) ≥ Vi,j (ϕ, J ) for J ⊆ J 0 .
The usefulness of this result is best demonstrated with an example. Suppose that one is trying
to assess whether a given country j belongs in the firm’s optimal sourcing strategy Ji (ϕ). Without
guidance from the theory, one would need to compute all 2J candidate sourcing strategies to answer
that question. Proposition 2 implies, however, that if for country j, Vi,j (ϕ, J ) = 1 when J is the
null set, then j is necessarily in Ji (ϕ), while if Vi,j (ϕ, J ) = 0 when J includes all countries except
for j, then j cannot possibly be in Ji (ϕ). In section 5 we will discuss Jia’s (2008) algorithm, which
leverages this logic to devise an iterative algorithm to solve the problem defined in (11) efficiently.
In our above discussion, we have focused on the ‘complements case’ (σ − 1 > θ), which allows one
to characterize some key properties of the optimal sourcing problem in (11) without any restriction on
the relationship between the various countries’ sourcing potentials and fixed costs of sourcing. In the
‘substitutes case’ (σ − 1 < θ), this is no longer feasible and one needs to make additional assumptions
to obtain a sharp characterization of the firm’s sourcing strategy. For instance, consider a situation
in which the fixed costs of offshoring are common for all foreign countries (as in Blaum et al., 2017),
so fij = fij 0 for all j, j 0 6= i. In such a case, and regardless of the value of (σ − 1) /θ, one could
then rank foreign locations j 6= i according to their sourcing potential Tj (τij wj )−θ and denote by
ir = {i1 , i2, ..., iJ−1 } the country with the r-th highest value of Tj (τij wj )−θ . Having constructed ir ,
it then follows that for any firm with productivity ϕ from i that offshores to at least one country, we
have i1 ∈ Ji (ϕ); for any firm that offshores to at least two countries, we have i2 ∈ Ji (ϕ); and so on.
In other words, the extensive margin of firms grows in a manner uniquely determined by the ranking
of the Tj (τij wj )−θ sourcing potential terms. It is important to emphasize, however, that this result
relies on the assumption of identical offshoring fixed costs across sourcing countries, an assumption
that appears particularly unlikely in light of the evidence documented in Table 1.
Even in the presence of cross-country differences in the fixed costs of offshoring, a similar sharp
result emerges in the knife-edge case in which (σ − 1) /θ = 1. In that case, the addition of an
element to the set Ji (ϕ) has no effect on the decision to add any other element to the set, and the
same pecking order pattern described in the previous paragraph applies, but when one ranks foreign
locations according to the ratio Tj (τij wj )−θ /fij rather than Tj (τij wj )−θ . This result is analogous to
the one obtained in standard models of selection into exporting featuring constant marginal costs, in
which the decision to service a given market is independent of that same decision in other markets.
We close this section by using the properties of the profit function to discuss comparative statics
that apply when holding constant the market demand level Bi . First, and quite naturally, a reduction
in any iceberg trade cost τij or fixed cost of sourcing fij (weakly) increases the firm’s sourcing
capability Θi (ϕ) and thus firm-level profits. Second, in the complements case, a reduction of any τij
or fij also (weakly) increases the extensive margin of global sourcing, in the sense that the set Ji (ϕ)
is nondecreasing in τij and fij for any j. Third, and perhaps more surprisingly, in the complements
case a reduction of any τij or fij (weakly) increases firm-level bilateral input purchases from all
countries. To see this, note that firm-level intermediate input purchases from any country j ∈ Ji (ϕ)
13
are a fraction (σ − 1) χij (ϕ) of firm profits, and using (7) and (10), they can thus be expressed as

 (σ − 1) B γ (σ−1)/θ ϕσ−1 (Θ (ϕ))(σ−1−θ)/θ T (τ w )−θ
i
i
j ij j
Mij (ϕ) =
 0
if j ∈ Ji (ϕ)
(12)
otherwise.
When (σ − 1) /θ ≥ 1, Mij (ϕ) is thus increasing in all the terms in Θi (ϕ). Intuitively, when
demand is sufficiently elastic (i.e., σ is high enough) or the strength of comparative advantage in the
intermediate-good sector across countries is sufficiently high (i.e., θ is low enough), the scale effect
through the demand response to lower costs dominates the direct substitution effect related to market
shares shifting towards the locations whose costs of sourcing have been reduced. It is useful to restate
this third result in the following way (see the Online Appendix for a formal proof):
Proposition 3. Holding constant the market demand level Bi , whenever (σ − 1) /θ ≥ 1, an increase
in the sourcing potential Tj (τij wj )−θ or a reduction in the fixed cost fj of any country j, (weakly)
increases the input purchases by firms in i not only from j, but also from all other countries.
It should be emphasized that the sharp results above only apply when holding market demand –
of which the price index is a key component – fixed. In general equilibrium, these same parameters
also affect the level of market demand. As we shall see in our counterfactual exercise in section 6,
the endogenous response of market demand is quantitatively important in our estimation, and thus
the implications we derive from changes in trade costs are much more nuanced than those discussed
above (see Bache and Laugesen, 2013). Despite these nuances, Proposition 3 will still prove to be very
useful in interpreting our counterfactual results and in relating them to the observed transformation
in the global sourcing practices of U.S. firms over the period 1997-2007.
3.3
Industry and General Equilibrium
Consider now the general equilibrium of the model. As mentioned before, we simplify matters by
assuming that consumers spend a constant share (which we denote by η) of their income on manufacturing. The remaining share 1 − η of income is spent on a perfectly competitive non-manufacturing
sector that competes for labor with manufacturing firms. Technology in that sector is linear in labor,
and we assume that 1−η is large enough to guarantee that the wage rate wi in each country i is pinned
down by labor productivity in that sector. For simplicity, we also assume that this ‘outside’ sector’s
output is homogeneous, freely tradable across countries, and serves as a numeraire in the model. We
thus can treat wages as exogenous in solving for the equilibrium in each country’s manufacturing
sector.
We next turn to describing the equilibrium in the manufacturing sector. Given our assumption
that final-good producers only observe their productivity after paying the fixed cost of entry, we can
use equation (10) to express the free-entry condition in manufacturing as
Z
∞


ϕσ−1 (γΘi (ϕ))(σ−1)/θ Bi − wi
ϕ̃i
X
j∈Ji (ϕ)
14
fij  dGi (ϕ) = wi fei .
(13)
In the lower bound of the integral, ϕ̃i denotes the productivity of the least productive active firm
in country i. Firms with productivity ϕ < ϕ̃i cannot profitably source from any country and thus
exit upon observing their productivity level. Note that Bi affects expected operating profits both
directly via the explicit term on the left-hand side of (13), but also indirectly through its impact
on the determination of ϕ̃i , Ji (ϕ) and Θi (ϕ). Despite these rich effects (and the fact that the set
Ji (ϕ) is not easily determined), in the Online Appendix we show that one can appeal to monotone
comparative statics arguments to prove that:
Proposition 4. Equation (13) delivers a unique market demand level Bi for each country i ∈ J.
This result applies both in the complements case as well as in the substitutes case and ensures
the existence of a unique industry equilibrium. In particular, the firm-level combinatorial problem
in (11) delivers a unique solution given a market demand Bi and exogenous parameters (including
wages). Furthermore, the equilibrium measure Ni of entrants in the industry is easily solved from
equations (3) and (13), by appealing to the marginal cost in (9), to constant-mark-up pricing, and to
the fact that spending Ej in manufacturing is a share η of (labor) income. This delivers:
ηLi
Ni =
σ
R∞
ϕ̃i
P
!.
(14)
fij dGi (ϕ) + fei
j∈Ji (ϕ)
With this expression in hand, the equilibrium number of active firms is simply given by Ni [1 − Gi (ϕ̃i )].12
3.4
Gravity
In this section we explore the implications of our model for the aggregate volume of bilateral trade
in manufacturing goods across countries. Because we have assumed that final goods are nontradable,
we can focus on characterizing aggregate intermediate input trade flows between any two countries
i and j. Using equation (12) and aggregating across firms, we obtain the following expression for
aggregate manufacturing imports from country j by firms based in i:
Z
∞
Mij = Ni
Mij (ϕ)dGi (ϕ) = (σ − 1) γ (σ−1)/θ Ni Bi Tj (τij wj )−θ Λij ,
(15)
ϕ̃ij
where
Z
∞
Λij =
Iij (ϕ) (Θi (ϕ))(σ−1−θ)/θ ϕσ−1 dGi (ϕ) .
(16)
ϕ̃ij
In the second expression, ϕ̃ij denotes the productivity of the least productive firm from i offshoring
to j, while Iij (ϕ) = 1 for j ∈ Ji (ϕ) and Iij (ϕ) = 0 otherwise. We next re-express equation (15)
12
In the Online Appendix (section B.2), we show that in the complements case, and when ϕ is distributed Pareto
with shape parameter κ, we can further reduce equation (14) to Ni = (σ − 1) ηLi / (σκfei ). In such a case, the measure
of entrants is independent of trade costs. This result is analogous to that derived in canonical models of selection into
exporting (see, for instance, Arkolakis et al. (2012)), but note that it here applies in a setup with interdependent entry
decisions. It is important to stress, however, that this result relies on the existence of fixed costs of domestic sourcing
which generate a positive measure of inactive firms that do not source any inputs. Because in our empirical work all
firms are active and source inputs, we will set fii = 0, and the equilibrium measure of entrants will react to changes in
trade costs, wages, and technological parameters.
15
so that it is comparable to gravity equations used in empirical analyses. In particular, plugging the
equilibrium values for Bi and Ni in (13) and (14), and rearranging, we obtain
Mij =
Ei
1−σ
Pi /Ni
Qj
Ek
−θ
k P 1−σ /Nk τkj Λkj
k
×P
× τij−θ × Λij ,
(17)
where Ei equals country i’s total spending in manufacturing goods (which is a multiple σ/ (σ − 1) of
P
country i’s worldwide absorption of intermediate inputs), Qj = k Mkj denotes the total production
of intermediate inputs in country j, and Pi is the ideal manufacturing price index in country i.13
Equation (17) resembles a standard gravity equation relating bilateral trade flows to an importer
‘fixed effect’ (i.e., a term that is common for all exporters holding the importer country constant),
an analogous exporter fixed effect, and bilateral iceberg trade barriers τij . Notice, however, that
equation (17) incorporates an additional term Λij that typically varies both across importers and
exporters. In fact, the only case in which Λij does not vary across exporters is when the fixed costs
of offshoring are low enough to ensure that all firms acquire the capability to source inputs from all
countries. In such a case, we have
Λij =
X
−θ
!(σ−1−θ)/θ Z
∞
Tk (τik wk )
ϕσ−1 dGi (ϕ) = Λi ,
ϕ̃i
k∈J
and thus Λij gets ‘absorbed’ into the importer fixed effect. In this universal importing case, the elasticity of trade flows with respect to changes in these bilateral trade frictions is shaped by the Fréchet
parameter θ, just as in the Eaton and Kortum (2002) framework. This should not be surprising,
since, in the absence of selection into offshoring, all firms buy inputs from all markets according to
the same market shares χij in (7) with Ji (ϕ) = J for all ϕ.
When fixed costs of sourcing are large enough to generate selection into importing, changes in
variable trade costs will not only affect firm-level sourcing decisions conditional on a sourcing strategy,
but will also affect these same sourcing strategies. As a result, the aggregate elasticity of bilateral
trade flows to bilateral trade frictions no longer coincides with the firm-level one, given by θ. In the
plausible case in which a reduction in τij enhances the extensive margin of imports from country j,
the aggregate trade elasticity will thus tend to be higher than θ.
A general proof of this magnification result for arbitrary parameter values of σ and θ, and for a
general distribution of productivity Gi (ϕ), is intricate due to the difficulties in the characterization
of Θi (ϕ) and due to industry equilibrium effects. For the special case in which σ − 1 = θ, notice
however that Λij reduces to
Z
∞
Λij =
ϕσ−1 dGi (ϕ) = Λij (ϕ̃ij ) .
ϕ̃ij
Thus, to the extent that a reduction in bilateral trade costs between i and j generates an increase
in the measure of firms from i sourcing in j (i.e., a reduction in ϕ̃ij ), it is clear that the elasticity of
bilateral trade flows with respect to τij will now be higher than the firm-level one. Furthermore, as
13
The ideal manufacturing price index in country i is given by Pi1−σ = Ni
16
R∞
ϕ̃i
pi (ϕ)1−σ dGi (ϕ).
we show in the Online Appendix (section B.2), if we assume that firms draw their core productivity
from a Pareto distribution with shape parameter κ (assumed to be higher than σ − 1 to ensure a finite
variance of sales), we can express aggregate manufacturing imports from country j by firms based in
i as
Mij =
(Ei )κ/(σ−1)
P
Ψi
Qj
(Ek )
k
Ψk
κ/(σ−1)−1
where Ψi = fei ϕ−κ
Pi−κ wi
i
κ/(σ−1)
(τkj )
−θ
(fkj )
1−κ/(σ−1)
(τij )−κ (fij )1−κ/(σ−1) ,
(18)
/Li . Notice that equation (18) is a well defined gravity equation
in which the ‘trade elasticity’ (i.e., the elasticity of trade flows with respect to variable trade costs)
can still be recovered from a log-linear specification that includes importer and exporter fixed effects.
But notice that this trade elasticity κ is now predicted to be higher than the one obtained when the
model features no extensive margin of importing at the country level (since κ > σ − 1 = θ).14
The knife-edge case σ − 1 = θ is useful in illustrating why one should expect the aggregate trade
elasticity to be larger than the firm-level one. Yet it masks the fact that whenever σ − 1 6= θ, Λij in
(16) will be a function of Iij (ϕ) Θi (ϕ) for ϕ > ϕ̃ij , and will thus depend on which other countries
are included in the sourcing strategy of firms from i sourcing from j and those other countries’
characteristics. In such a case, equation (17) becomes an extended gravity equation – to use the term
in Morales et al. (2014) – featuring third market effects. Holding constant the sourcing strategy of
all firms (and thus ϕ̃ij and Iij (ϕ) in equation (16)), it appears that the sign of these third-market
effects depends crucially on whether σ − 1 > θ or σ − 1 < θ. Nevertheless, changes in trade costs
naturally affect the extensive margin of sourcing and also lead to rich industry equilibrium effects,
thereby thwarting a sharp characterization of these extended gravity effects in our model.
Interestingly, our model suggests a relatively simple way to control for these extended gravity
forces. In particular, defining the importer-specific term Ξi = Ti (τii wi )−θ (σ − 1) γ (σ−1)/θ Ni Bi , note
that we can express
Λij =
1
× (σ − 1) Ni Bi γ (σ−1)/θ
Ξi
Z
∞
Iij (ϕ) ϕσ−1 (Θi (ϕ))(σ−1−θ)/θ Ti (τii wi )−θ dGi (ϕ) ,
ϕ̃ij
where the second term on the right-hand-side corresponds to the domestic input purchases aggregated
over all firms based in i that import inputs from j. In section 5.2, we show that when including this
bilateral aggregate measure of domestic input purchases into a standard gravity specification, the
resulting estimate of the trade elasticity θ becomes much lower, in line with the one we estimate at
the firm level.
14
It may be surprising that the Fréchet parameter θ, which was key in governing the ‘trade elasticity’ (i.e., the
elasticity of trade flows to variable trade costs) at the firm level, is now irrelevant when computing that same elasticity
at the aggregate level. To understand this result, it is useful to relate our framework to the multi-country versions of
the Melitz model in Chaney (2008), Arkolakis et al. (2008) or Helpman et al. (2008), where an analogous result applies.
In those models, firms pay fixed costs of exporting to obtain additional operating profit flows proportional to ϕσ−1 that
enter linearly and separably in the firm’s profit function. Even though in our model, selection into offshoring increases
firm profits by reducing effective marginal costs, whenever σ − 1 = θ, the gain from adding a new market is strictly
separable in the profit function and also proportional to ϕσ−1 . Hence, this effect is isomorphic to a situation in which
the firm obtained additional revenue by selecting into exporting. It is thus not surprising that the gravity equation we
obtain in (18) is essentially identical to those obtained by Chaney (2008) or Arkolakis et al. (2008).
17
4
Data Sources and Descriptive Evidence
In the theory sections, we provide a parsimonious model that characterizes the margins of firms’
global sourcing decisions. When there are complementarities in the firm’s extensive margin sourcing
decisions, the model is consistent with the strong, increasing relationship between firm size and
the number of source countries depicted in Figure 1. The model also provides a framework for
distinguishing between country-level fixed costs and country sourcing potential – two key dimensions
along which Table 1 suggests that countries differ. Before turning to the structural estimation,
we describe the data used in the paper and provide several novel empirical facts that support the
theoretical framework.
4.1
Data Description
The primary data used in the paper are from the U.S. Census Bureau’s 1997 and 2007 Economic Censuses (EC), Longitudinal Business Database (LBD), and Import transaction database. The LBD uses
administrative record data to provide employment and industry for every private, non-farm employer
establishment in the U.S. The ECs supplement this information with additional establishment-level
variables, such as sales, value-added, and input usage.15 The import data, collected by U.S. Customs
facilities, are based on the universe of import transactions into the U.S. They contain information on
the products, values, and countries of firms’ imports. We match these data at the firm level to the
LBD and the EC data.
The focus of this paper is on firms involved in the production of goods. We therefore limit the
analysis to firms with at least one manufacturing establishment. Because we envision a production
process entailing physical transformation activities (manufacturing) as well as headquarter activities
(design, distribution, marketing, etc.), we include firms with activities outside of manufacturing.16
We also limit the sample to firms with positive sales and employment and exclude all mineral imports
from the analysis since they do not represent offshoring. Firms with at least one manufacturing plant
account for five percent of firms, 23 percent of employment, 38 percent of sales, and 65 percent of nonmineral imports. In terms of explaining aggregate U.S. sourcing patterns, it is critically important
to include manufacturing firms with non-manufacturing activities. They account for 60 percent of
U.S. imports, while manufacturing-only firms account for just five percent. The import behavior of
the firms in our sample is consistent with patterns documented in past work on heterogeneous firms
in trade. About one quarter of U.S. manufacturing firms have positive imports in 2007. Additional
15
The Census of Manufactures (CM) has been widely used in previous work. The other censuses are for Construction,
Finance, Insurance and Real Estate, Management of Companies, Professional and Technical Services, Retail Trade,
Transportation and Warehousing, and Wholesale Trade. The variables available differ across these censuses. This
coverage ensures that we provide a more complete depiction of the entire firm compared to studies that rely solely on
the CM.
16
We recognize that focusing on firms with positive manufacturing activity will miss some offshoring, for example by
factoryless goods producers (FGPs) in the wholesale sector that have offshored all physical transformation activities (see
Bernard and Fort, 2015, for details). Unfortunately, there is no practical way to distinguish all FGPs from traditional
wholesale establishments. Furthermore, data on input usage, which is crucial for our structural estimation, is less
complete for firms outside manufacturing. We also note that we cannot identify manufacturing firms that use inputs
imported by intermediaries.
18
details on the sample and data construction are in the Online Data Appendix.
The model predicts an important role for country characteristics in determining country-level
fixed costs and sourcing potential. We compile a dataset with the key country characteristics in
2007– technology and wages, as well as other controls– from various sources. Country R&D data and
the number of private firms in a country for 2007 are from the World Bank Development Indicators.
Wage data are from the ILO data described by Oostendorp (2005). Distance and language are from
CEPII. Physical capital is based on the methodology in Hall and Jones (1999), but constructed using
the most recent data from the Penn World Tables described by Heston et al. (2011). Control of
corruption is from the World Bank’s Worldwide Governance Indicators. We also obtain years of
schooling and population from Barro and Lee (2010).
4.2
Descriptive Evidence
We use the 2007 data to assess the model’s assumptions and predictions. First, we provide information
on the number of products imported by U.S. firms, and the number of countries from which they
source. Second, we show that firms generally source each input from a single location. Finally, we
document the extent to which firm sourcing decisions follow a hierarchical pattern.
Two key assumptions that drive our theoretical approach are that firms source multiple inputs
and that they may source these inputs from multiple countries. While the Census data do not provide
detailed information about the total number of inputs used by a firm, the linked import data can
shed light on the number of foreign inputs firms use. We define a product as a distinct Harmonized
Schedule ten-digit code, of which there are nearly 17,000 categories in the U.S. import data. The data
show that importers source an average of 12 distinct products from about three foreign countries.
The median number of imported products is two, while the 95th percentile is 41. The median number
of source countries is two, and the 95th percentile is 11.
One feature of our model is that it delivers a closed-form solution for the share of inputs a firm
sources from a particular country. This solution comes from an Eaton and Kortum (2002) selection
process in which a firm sources each input from the single, lowest cost location. Table 2 shows that
this feature of our model is consistent with the data. The table presents statistics on the firm-level
mean, median, and maximum number of countries from which a firm imports a particular product. We
report the mean, median, and 95th percentile of these firm-level measures. The median firm imports
each distinct product from an average of only one country. The median number of countries per
product for firms is always one, even for the 95th percentile of firms. Finally, the maximum number
of countries per product for the median firm is still just one, while firms in the 95th percentile import
the same product from a maximum of four countries.17
Before turning to the structural estimation, it is useful to assess the extent to which firms follow
17
In the Online Appendix (section C.10) we show that this pattern is still evident when the sample of importers is
limited to firms that source from at least three countries. We also show that this pattern is not driven by sparsity in
the data, since the same firm-level statistics on the number of products per country are always greater than 1. We also
provide the statistics at the HS6 level, and we show that every statistic on the number of countries from which a firm
sources a given product is equal to or lower than the comparable statistic for the number of countries to which a firm
exports a given product.
19
Table 2: Firm-level statistics on the number of source countries per imported product
Firm-level
Mean
Median
Max
1.11
1.00
1.61
1.03
1.00
1.00
1.78
1.00
4.00
Mean
Median
95%tile
Notes: Table reports on the number of
countries from which a firm imports the
same HS10 product.
a hierarchical pecking order in their sourcing behavior. To do so, we follow Eaton et al. (2011)
and count the number of firms that import from Canada (the top destination by firm rank) and
no other countries, the number that import from Canada and China (the top two destinations) and
no others, and so on. We calculate these statistics irrespective of firm sourcing outside the top ten
countries. Columns 1 and 2 in Table 3 show that over 21 thousand firms, or 36 percent of importers,
follow a pecking order. To assess the significance of this share, we calculate the share of firms that
would follow this hierarchy if firms selected into countries randomly. Specifically, we use the share of
importers from country j as the probability that any given firm will source from j, and we assume
that each probability is independent. Column 5 shows that fewer than 20 percent of firms would
follow a pecking order under random entry –just over half the share observed in the data.
Table 3: U.S. firms importing from strings of top 10 countries
Data
String
CA
CA-CH
CA-CH-DE
CA-CH-DE-GB
CA-CH-DE-GB-TW
CA-CH-DE-GB-TW-IT
CA-CH-DE-GB-TW-IT-JP
CA-CH-DE-GB-TW-IT-JP-MX
CA-CH-DE-GB-TW-IT-JP-MX-FR
CA-CH-DE-GB-TW-IT-JP-MX-FR-KR
TOTAL Following Pecking Order
Random Entry
Firms
% of Importers
Firms
% of Importers
17,980
2,210
340
150
80
30
30
50
160
650
29.82
3.67
0.56
0.25
0.13
0.05
0.05
0.08
0.27
1.08
6,760
3,730
1,030
240
50
10
0
0
0
0
11.21
6.19
1.71
0.40
0.08
0.02
0.00
0.00
0.00
0.00
21,680
36.0
11,820
19.6
Notes: The string CA means importing from Canada but no other among the top 10; CA-CH means importing from
Canada and China but no other; and so forth. % of Importers shows percent of each category relative to all firms that
import from top 10 countries.
The results here are similar to those in Eaton et al. (2011) where the authors show that 27
20
percent of French exporters follow a pecking order for the top seven destinations, which is more
than double what would be predicted under the same random entry calculation. While our findings
are certainly suggestive of a pecking order in which country characteristics make some countries
particularly appealing for all U.S. firms, they also point to a high degree of firm-specific idiosyncrasies
in the selection of a firm’s sourcing strategy. We will incorporate this feature of the data in our
structural analysis by extending the theory to allow for firm-country-specific fixed costs.
5
Structural Analysis
In this section, we use the firm-level data in conjunction with country-level data to estimate the
key parameters of the model. In doing so, we distinguish country sourcing potential from the fixed
costs of sourcing and quantify the extent to which the latter depend upon source-destination-specific
country characteristics. The parameter estimates obtained here are also critical for performing the
counterfactual exercises in the next section.
The structural analysis is performed in three distinct steps. First, we use a simple linear regression
to estimate each country’s sourcing potential Tj (τij wj )−θ from a U.S. perspective (i.e., i = U.S.). In
the second step, we estimate the productivity dispersion parameter, θ, by projecting the estimated
sourcing potential values on observed cost shifters and other controls. We also measure the elasticity
of demand, σ, from observed mark-ups. In the third and final step, we estimate the fixed costs of
sourcing and other distributional parameters via the method of simulated moments. To make the
firm’s problem computationally feasible, we apply the technique in Jia (2008), originally designed to
estimate an entry game among chains and other discount retailers in a large number of markets.
Because we use data on the sourcing strategies of firms from a single country, in what follows,
we often drop the subscript i from the notation, with the understanding that the unique importing
country is the U.S. We also denote a firm by superscript n. To facilitate the estimation, we include
only those countries with at least 200 U.S. importing firms. This criterion leaves us with a total of
67 countries, including the U.S.
5.1
Step 1: Estimation of a Country’s Sourcing Potential
The first step in our structural analysis is to estimate each country’s sourcing potential. To do so, we
take the firm’s sourcing strategy J n as given and exploit differences in its share of sourcing across
countries. Recall from equation (7) in the model that a firm’s share of inputs sourced from country j,
χij , is simply that country’s contribution to the firm’s sourcing capability, Θni . Country j’s sourcing
potential – from the perspective of country i – is therefore summarized by the term ξj ≡ Tj (τij wj )−θ .
Rearranging equation (7) by taking logs and normalizing the share of inputs purchased from country
j by the firm’s share of domestic inputs leads to
log χnij − log χnii = log ξj + log nj ,
21
(19)
where n denotes the firm. In order to turn the model’s equilibrium condition (7) into an empirical
specification, note that this equation includes a firm-country-specific shock nj . When normalizing by
the domestic share, we set domestic sourcing potential to 1.
The dependent variable in equation (19) is the difference between a firm’s share of inputs sourced
from country j and its share of inputs sourced domestically. We measure these shares using data on
a firm’s total input use, production worker wages, and total imports from each country from which
it sources. We include firms that import from countries with fewer than 200 U.S. importers in the
estimation, adjusting their total input usage by subtracting their imports from any of the excluded
countries. Additional details on our measure of input shares are in the Estimation Appendix.
Intuitively, this specification allows us to identify a country’s average sourcing potential ξj by
observing how much a firm imports from that country relative to the same firm’s domestic input
purchases, restricting attention to countries included in the firm’s sourcing strategy. For this measurement strategy to be consistent, it is important that there is no selection based on the errors in the
regression. This condition will be satisfied if firms only learn their country-specific efficiency shocks,
nj , after their sourcing strategy is selected, or if the term nj simply represents measurement error. It
is also consistent with firm-country-specific shocks to the fixed costs of sourcing. In what follows we
treat nj as measurement error.18
We estimate equation (19) via Ordinary Least Squares (OLS), using country fixed effects to capture
the ξj terms. The estimated coefficients on these fixed effects represent each country’s sourcing
potential, which we note is simply the average share difference by country. By estimating sourcing
potentials via OLS, however, we also calculates standard errors, which show that all the sourcing
potential fixed effects are significant at the one percent level. We have also estimated these sourcing
potential measures controlling for industry effects. The estimates are highly correlated (0.996) with
our baseline results and retain their statistical significance.
Figure 2 plots the estimated sourcing potential fixed effects against the number of firms importing
from that country. Our parameter estimates suggest that China has the highest sourcing potential
for U.S. firms, followed by Canada and Taiwan. More firms import from Germany and the United
Kingdom than from Taiwan, however, and more firms import from Canada than from China, suggesting that fixed costs of sourcing are likely to differ across source countries. The variation in this
figure is helpful for understanding how the structural estimation will identify country fixed costs. For
instance, the fact that more firms import from Canada than China, despite the fact that China has
the highest estimated sourcing potential, suggests that the fixed cost of importing from Canada are
lower than the fixed costs of importing from China.
Our estimates of the sourcing potential of a country enable us to calculate the extent to which the
P
sourcing capability of a firm Θn = j∈J n ξj is higher if it imports from all countries as opposed to
sourcing only domestically. Since domestic sourcing potential is normalized to one and the summation
of the foreign sourcing potential terms is 0.193, these results imply that the sourcing capability of a
18
Note that this assumption rules out measurement error related to a firm’s global sourcing strategy. In other words,
we assume that the set of countries from which the firm imports is correctly observed and that a firm has positive
imports from all countries for which it has paid a fixed cost of sourcing. Online Appendix Section C.5 discusses the
robustness of these estimates.
22
Figure 2: Country sourcing potential parameters and the extensive margin
firm that purchases inputs from all 67 countries is 19.3 percent larger than that of a firm buying inputs
only domestically. The impact of a firm’s sourcing capability on its marginal cost in turn depends on
the dispersion parameter θ of the intermediates productivities, as seen in equation (9). The effect of
sourcing capability on firm sales also depends on θ, as well as on the elasticity of substitution, σ. We
now turn to estimating these two parameters.
5.2
Step 2: Estimation of the Elasticity of Demand and Input Productivity Dispersion
It is simpler to start by discussing how we recover σ from the data. With CES preferences and
monopolistic competition, the ratio of sales to variable input purchases (including intermediates and
basic factors of production) is σ/ (σ − 1). We exploit this relationship to obtain a parameter value for
σ by calculating a measure of average mark-ups from the establishment-level data in the 2007 Census
of Manufactures. Specifically, the mark-up is the ratio of sales to variable inputs, where inputs are
the sum of an establishment’s materials, wages, capital expenditures, and total expenses. The markup for the median establishment is 35 percent, with a bootstrapped standard error of 0.0005. This
implies an estimate for the elasticity of demand, σ, of 3.85. Of course it is impossible to distinguish
perfectly between fixed and variable costs in the data, and there may be certain costs that simply
are not measured well, but we view this as a plausible estimate that is similar to previous findings.19
Given the potential issues that may affect the accuracy of our estimate of the demand elasticity, we
include a sensitivity analysis in section 6.3, in which we consider alternative values for the elasticity
of demand, as well as other parameters.
A second key parameter of our model is the dispersion of the productivity shocks of the interme19
For example, Broda and Weinstein (2006) estimate a mean elasticity of 4 and a median of 2.2 at the SITC-3 level for
1990-2001. At the SITC-4 level, Feenstra and Romalis (2014) estimate a higher median elasticity of 6.2 for 1984-2011.
Our estimate falls within this range.
23
diate inputs. Conditional on the firm’s sourcing strategy, θ represents the firm-level trade elasticity
in our model. We use data on wages to identify this elasticity. Recall that the sourcing potential ξj ,
which we estimated in the previous section, is a function of a country’s technology parameter, trade
costs, and wages. We thus project the estimated sourcing potential on proxies for all these terms,
including R&D stock, capital per worker, a measure of control of corruption, wages, distance, and
common language. Specifically, we estimate the following equation:
logˆ ξj =β0 + βr log R&Dj + βk log capitalj + βF log number of firmsj − θ log wj
− θ log βc + βd log distanceij + languageij log βl + βC control of corruptionj + ιj ,
(20)
so that iceberg trade costs are proxied by log distance, common language, and control of corruption.
Equation (20) shows that the parameter θ can be recovered from the estimated coefficient on wages.
In theory, one could also identify θ using tariffs, but, as we show in the Online Data Appendix, there is
not enough variation in U.S. tariffs to do so. A potential issue with the use of country wage data is the
fact that variation in wages partly reflects differences in worker productivity and skill across countries.
Since firms’ sourcing decisions are based on the cost of an efficiency unit of labor, we follow Eaton and
Kortum (2002) and use a human-capital-adjusted wage. Even adjusting for skill differences across
workers, there are other country-level factors that are likely correlated with the average wage, such as
infrastructure, that will lead to an upward bias on the wage coefficient. To address this issue, as well
the potential for measurement error, we instrument for a country’s wage using its population. The
first stage results, presented in the Estimation Appendix, show a negative and statistically significant
coefficient on the log of country population. One concern with using population as an instrument
is that it may violate the exclusion restriction if high population countries are also technologically
advanced countries. To address that possibility, we include country R&D stock, a level measure of
technology, in all specifications. Country population may also indirectly affect sourcing potential since
it could be correlated with the number of potential suppliers in a country, a concern that leads us to
control for the number of private firms in the economy. These country-level variables are available
for 57 of the 66 foreign countries included in the structural estimation.
The first column of Table 4 presents the results from estimating equation (20) via OLS. Column 2
provides the analogous IV estimates, using population as an instrument for wages. As expected, the
IV estimate for θ (1.789) is larger than the OLS estimate. In line with the discussion in section 3.4, the
data on firm-level trade flows suggest a much larger dispersion in productivities across countries than
is typically obtained with aggregate trade data. For example, Eaton and Kortum (2002) estimate
a coefficient of 3.60 using data on wages. Column 4 shows that we obtain a similar coefficient of
4.544 when estimating the same specification as in equation (20), but using aggregate imports as
the dependent variable. In the Online Data Appendix we also provide robustness tests in which we
control for GDP and tariffs, and in which we constrain the coefficient on wages and tariffs to be the
same.
Motivated by our discussion at the end of section 3.4, in column 5 we present estimates from
a specification that includes the log of domestic input purchases aggregated over all U.S. importers
24
Table 4: Estimation of firm and aggregate trade elasticities
log ξ
log HC adjusted wage
log distance
log R&D
log capital/worker
common language
control corrupt
log no. of firms
log aggregate imports
OLS
IV
OLS
IV
IV
-0.537
(0.184)
-0.341
(0.197)
0.352
(0.068)
-0.184
(0.175)
0.105
(0.223)
0.156
(0.151)
0.108
(0.086)
-1.789
(0.696)
-0.621
(0.294)
0.524
(0.125)
0.425
(0.390)
0.146
(0.289)
0.621
(0.312)
-0.020
(0.130)
-0.643
(0.390)
-0.859
(0.418)
0.763
(0.144)
-0.264
(0.370)
0.354
(0.471)
0.365
(0.319)
0.031
(0.183)
-4.544
(1.844)
-1.733
(0.779)
1.298
(0.332)
1.633
(1.033)
0.479
(0.764)
1.816
(0.826)
-0.369
(0.345)
-7.250
(0.922)
-11.068
(2.323)
14.499
(1.952)
2.600
(6.156)
-1.268
(0.768)
-0.650
(0.333)
0.251
(0.176)
0.308
(0.421)
0.137
(0.317)
0.414
(0.350)
-0.062
(0.142)
2.392
(0.327)
-37.389
(6.573)
57
57
57
57
57
log domestic purchases
Constant
Observations
Notes: Standard errors in parentheses. In the IV specifications, the human-capitaladjusted wage is instrumented by population. HC adjusted wage is country wage adjusted
for differences in human capital. Domestic purchases is total purchases of U.S. inputs by
firms sourcing from a country. First-stage F-statistic on the excluded instrument is 6.49.
First-stage regression results are in the Appendix.
from country j. To the extent that this term controls for the term Λij in (15), one would expect this
specification to deliver a lower estimate of θ that is in line with the estimate in column 2. Indeed,
the resulting estimate of θ (1.268) is lower than the one in column 4 and quite close to our preferred
estimate from the firm-level data presented in column 2. This result is reassuring, but should be
interpreted with caution for two reasons. First, the orthogonality condition which ensures that our
firm-level estimate of θ in column 2 is consistent, does not guarantee that the estimate in column
5 is consistent as well (see our Online Data Appendix for details). Second, and perhaps relatedly,
the coefficient we obtain on log domestic purchases is higher than the theoretically-predicted value of
1.20 For these two reasons, we henceforth treat our column 2 coefficient θ = 1.789 as our benchmark
estimate of θ.
With estimates for country sourcing potential, the firm-level trade elasticity, and the elasticity
of demand in hand, we can calculate how global sourcing affects firm costs and size. Our estimates
imply that a firm sourcing from all countries faces around nine percent (1.193(−1/1.789) ) lower input
costs than a firm sourcing purely domestically, and consequently its sales are made around 32 percent
(1.193(2.85/1.789) ) larger by sourcing inputs from all countries.21
20
21
When constraining that coefficient to be 1, we estimate a somewhat larger θ = 3.175.
These calculations are based on an ‘average’ firm importing inputs from all countries. In the data, there is of course
25
Across various specifications, including the additional robustness tests included in the Estimation
Appendix, we find that the ratio of elasticity of demand, σ − 1, to the dispersion of intermediate good
efficiencies, θ, is always larger than one. Furthermore, for our benchmark estimate θ = 1.789, we can
reject the null hypothesis that θ > σ − 1 = 2.85 at reasonable significance levels (the p-value for this
test is 0.06). As shown in section 2, this implies that the profit function has increasing differences in
the firm’s sourcing strategy. In the third step of our estimation, we exploit this feature to solve the
firm’s problem numerically and thereby estimate the fixed costs of sourcing from different markets.
5.3
Step 3: Estimation of Fixed Costs of Sourcing
In this section, we estimate the fixed costs of sourcing via the method of simulated moments. As
is common in the literature that estimates trade costs, we allow the fixed cost of sourcing from a
country to depend on the gravity variables distance and language as well as on a measure of the source
country’s control of corruption. Thus far, the model features fixed costs that differ across countries,
but not across firms. This implies that the number of importing firms will be identical to the number
of firms that source from the most popular country. In contrast, the data show that around 64,600
firms import, while only about 37,800 import from Canada – the most popular sourcing country. For
the remainder of the structural analysis, we therefore enrich the model by allowing the fixed costs of
sourcing to vary by firm-country combinations. Specifically, we model firm-country-specific fixed costs
f
and
of sourcing, fijn , which are drawn from a lognormal distribution with dispersion parameter βdisp
f
control of corruptionj .22 Since by
scale parameter log βcf + βdf log distanceij + log βlf languageij + βC
definition active manufacturing firms must use some domestic inputs (at least in terms of production
worker services), we cannot identify the fixed costs of domestic sourcing, so we set them equal to zero
(fiin = 0).
In a setting with a large number of countries, the firm faces an enormous discrete choice problem
when solving for its optimal sourcing strategy. If there are 66 foreign countries, the firm selects among
266 , which is roughly 1020 , possible sourcing strategies. Clearly, calculating the profits for each of
these strategies for every firm is infeasible. To reduce the dimensionality of the firm’s problem, we
rely on Proposition 2 and adopt an algorithm first developed by Jia (2008). The specifics of the
algorithm are as follows. Given a core productivity ϕ and a guess J for the firm’s sourcing strategy,
J n , define the marginal benefit of including country j in the sourcing strategy J as:


ϕσ−1 γ (σ−1)/θ B Θi (J ∪ j)(σ−1)/θ − Θi (J )(σ−1)/θ − fijn


if j ∈
/J


 ϕσ−1 γ (σ−1)/θ B Θ (J )(σ−1)/θ − Θ (J \ j)(σ−1)/θ − f n
i
i
ij
if j ∈ J .
variation in spending shares across firms, even conditional on their sourcing strategy. In Online Appendix Table C.4,
we present statistics on the distribution of total foreign sourcing shares. Using the ‘sufficient statistic’ formula in Blaum
et al. (2017) and our estimate of θ, we can compute the cost savings associated with importing for firms in the 90th
percentile. These firms import 47 percent of their input purchases, which implies 30 percent cost savings, and a 176
percent increase in their sales due to global sourcing.
22
n
Analogous to the core productivity level, ϕ, the firm learns about its fixed costs of sourcing, fij
, after having paid
the fixed entry cost, fei , which is homogeneous among potential firms in country i.
26
As in Proposition 2, we define a mapping, Vjn (J ) that takes a value of one if this marginal benefit
is positive, and takes a value of zero otherwise. Under the empirically relevant condition σ − 1 > θ,
Proposition 2 shows that this mapping is an increasing function of J . Jia (2008) shows that when
starting from the set J (which contains no country), an iterative application of the V-operator that
adds each country to the set one-by-one leads to a lower bound of the firm’s sourcing strategy. That
is, the optimal sourcing strategy contains at least those countries for which the marginal benefit of
adding a country is positive when that country is added individually. Similarly, when starting from
the set J (which contains all countries), and removing individual countries one-by-one, the iterative
application of the V-operator leads to an upper bound for the optimal sourcing strategy. Should the
two sets not perfectly overlap, it is only necessary to evaluate the profits resulting from all possible
combinations contained in the upper but not the lower bound set.
In the presence of a high degree of complementarity, there is the potential for this algorithm to
lead to a large number of possible choices between the two bounds, hence rendering this approach
infeasible. Intuitively, the iterative process might stall too quickly if it is optimal for firms to add
or drop countries from the set J only in pairs (or larger groups). Fortunately, in our application,
this approach leads to completely overlapping lower and upper bound sets in the vast majority of
simulations. In addition, the two sets only differ by a small number of countries in those cases in
which the sets are not identical (see Appendix Table A.4).23
Turning to the practical implementation of our structural estimation, we follow Melitz and Redding
(2015) and assume that firms’ core productivities are distributed Pareto. As in their paper, we set
the shape parameter κ of the Pareto distribution equal to 4.25. We do not estimate κ to ease the
computational burden associated with estimating non-linearly the other parameters of the model, but
we discuss sensitivity results withh alternative values for iκ in section 6.3. This leaves the following
f
f
.24 To do so, we simulate a large number
, βdisp
six parameters to estimate: δ = B, βcf , βdf , βlf , βC
of U.S. firms. That is, for each firm we draw a core-productivity shock from a uniform distribution
(which, given κ, can be inverted to yield the Pareto-distributed firm core productivity level), and
a J-dimensional vector of fixed cost shocks from a standard normal distribution (which, given a
parameter guess δ, can be used to calculate the lognormal distributed firm-country specific fixed cost
level).25 Note that there is no relationship between the number of simulated firms and the number of
actual firms in the data. The model assumes that we have a continuum of firms whose core efficiency,
fixed cost draws, and country-specific efficiency shocks follow particular distributions, and we use the
simulated firms as evaluation points of these distributions.
23
In principle, the algorithm could still be useful even if a sizable number of location sets need to be evaluated; for
example, one could assume that the firm evaluates the lower and upper bounds and a random vector of alternative
sourcing strategies that are contained in the two bounds.
24
We set γ 1/θ ϕUS = 1, as it scales input purchases equivalently to an increase in B.
25
We use a stratified random sampling technique to simulate the Pareto draws, in which we simulate many more
points in right tail of the distribution (in total 12 intervals with 10 random draws each). For the fixed cost draws we
use a Hybrid-Quasi-Monte-Carlo procedure, in which we generate a vector of 18,000 quasi-random numbers from a van
der Corput sequence in one dimension (which have better coverage properties than usual pseudo-random draws), and
then for each country we use this vector, but with independent random permutations of elements of this vector. Each
core productivity draw is then interacted with a vector of fixed cost draws, which together represent a firm. In total,
the interaction of fixed cost and core productivity draws yields S = 2, 160, 000 simulated firms.
27
We use the simulated firms to construct three sets of moments. The first set of moments includes:
a) the share of importers for all manufacturing firms (about a quarter of all firms); and b) the share
of importers with firm sales below the median (8.4 percent). This is simply a 2 × 1 vector, which we
label as m1 in the actual data and as m̂1 (δ) for the simulated data. The second set of moments is
the share of firms that imports from each country. We label this (J − 1) × 1 vector of moments in the
data as m2 and the simulated moment vector as m̂2 (δ). These two sets of moments are informative
about the overall magnitude of the fixed costs of sourcing, as well as on how they vary with distance,
language, and control of corruption. In addition, the share of importing firms from the most popular
country relative to the total share of importers is indicative of the fixed cost dispersion parameter.
The intuition here is that if there were zero dispersion in fixed costs across firms, the total share
of importers would be identical to the share of importers from the most popular sourcing country.
Similarly, the share of importers among firms with sales below the median firm is informative about
the dispersion parameter. For example, even in a model with i.i.d. fixed cost draws across firms, but
common draws across countries, an increase in the dispersion of fixed cost draws will lead to more
importers in that size bin of firms compared to the share of importers in the full set of firms. Finally,
the last moment included in the estimation is the share of firms whose input purchases from the U.S.
are less than the median U.S. input purchases in the data. This is a scalar, and we label the moment
in the data as m3 and the simulated moment as m̂3 (δ). The information from this moment helps pin
down the scale parameter B, as B governs the level of input purchases.
We describe the difference between the moments in the data and in the simulated model by ŷ(δ):

m1 − m̂1 (δ)



ŷ(δ) = m − m̂(δ) =  m2 − m̂2 (δ)  ,
m3 − m̂3 (δ)
and the following moment condition is assumed to hold at the true parameter value δ0 :
E [ŷ(δ0 )] = 0.
(21)
The method of simulated moments selects the model parameters that minimize the following
objective function:
δ̂ = arg min [ŷ(δ)]> W [ŷ(δ)] ,
δ
(22)
where W is a weighting matrix. We weight the moments equally, hence the weighting matrix is the
identity matrix.26
The parameter estimates are displayed in Table 5 below. We find that the fixed costs of sourcing
are increasing in distance with an elasticity of 0.19, and that sourcing from countries with a common
language reduces fixed costs by about 13 percent. The fixed costs of sourcing also seem reasonable in
magnitude. The median fixed cost estimate ranges from 10,000 to 56,000 USD, though the assumption
26
We use the identity matrix instead of the inverse of the estimated variance-covariance matrix of the 69 moments
as the weighting matrix, since the former leads to a better fit of the import shares of the most popular countries, in
particular China, which are most relevant for the counterfactuals below (at the expense of a worse fit of the shares of
less popular importing countries).
28
of a lognormal distribution means they can be substantially larger for some individual firm-country
combinations. Out of the total variance of fixed cost draws across firms and countries, the countrylevel variation explains about 9 percent of the total variance, with the remainder explained by firmcountry-level variation.
Table 5: Estimated parameters
B
βcf
βdf
βlf
f
βC
f
βdisp
0.122
(0.004)
0.022
(0.002)
0.193
(0.018)
0.872
(0.024)
-0.393
(0.012)
0.934
(0.018)
Notes: Table reports coefficients and standard errors from estimating the model via simulated method of moments Standard errors
based on 25 bootstrap samples drawn with replacement.
In Figure 3, we show the estimated sourcing potential and median fixed costs by country. It is
clear that Canada has one of the highest sourcing potentials, but the lowest fixed costs. Mexico
has both higher sourcing potentials and higher fixed costs than Germany and the United Kingdom.
These differences in sourcing potentials and fixed costs help reconcile the variation in a country’s
rank in terms of the number of importing firms and the import values displayed in Table 1. They
also highlight the importance of heterogeneous fixed costs in matching the model to the data. We
conclude this section by describing the estimated model’s fit of the data, and by assessing the need
for heterogeneous fixed costs for a good fit.
Figure 3: Estimated sourcing potential and median fixed costs by country
−1
10
BGD
RUS
IDN
VNM
PHL THA PAK
EGY
VEN UKR
ECU
SAU
Median Fixed Cost
PAN
TTO
ARG
LKA
BGR
DOM HND
GTM
PER
ROM
TUR
BRA
COL
MYS
SLV
GRC POL
CZE
SVK
ZAFMAC
IND
ITA
KOR
HUN
CRI
SVN PRT
ESP
ARE
ISR
CHN
MEX
TWN
JPN
CHL
BEL
FRA
DEU
LUX
NOR
AUT
IRLAUS NLD
CHE
NZLFIN SWE SGP
HKG
GBR
DNK
CAN
−3
−2
10
10
Sourcing Potential
29
5.4
Fit of the Model
Overall, the model fits the data reasonably well. We start by comparing the predictions of the model
for the moments it was targeted to fit. First, in both the data and baseline model, around 26 percent
of U.S. firms import (25.8 in the data and 26.8 in the baseline model). For U.S. firms with sales below
the median, around 8 percent import (8.5 in the data and 7.3 in the model). For the second set of
moments on the share of importing firms by country, the correlation coefficient between the actual
and simulated data is 0.98. Figure 4a depicts this relationship by country. Finally, in both the data
and in the parameterized model, the median firm’s input purchases from the U.S. are approximately
equal (568,000 in the data and 572,000 in the model). The model also does a good job at matching two
sets of moments we did not target directly in the estimation. As shown in Figure 4b, the correlation
between the actual and simulated import shares by country is very high (the correlation coefficient is
0.78). In Table 6, we also show that the estimated model does a good job of matching the hierarchal
sourcing patterns of firms. While the model does well in all these dimensions, it overpredicts domestic
sourcing by about 18.25 percent.27
Figure 4: Model fit: share of firms and aggregate sourcing
(a) Share of importers by country
(b) Share of aggregate foreign sourcing by country
0
0
10
10
−1
10
−1
10
−2
data
data
10
−2
10
−3
10
−3
10
−4
10
−4
10
−5
−4
10
−3
10
−2
10
model
−1
10
10
0
10
−4
10
−3
10
−2
10
model
−1
10
0
10
It is important to emphasize that our model fits the data substantially better than a model with
common fixed costs across countries, but with idiosyncratic variation in fixed cost draws across firms.
Such a model would be much simpler to estimate, and would not require our adoption of Jia’s (2008)
algorithm to solve the firm’s problem. This simplification, however, comes at a large expense. For
example, in the common fixed costs model only 17 percent of firms import, as opposed to 26 percent
in the baseline model and data (in the common fixed cost model, the share of importing firms equals
the share of firms importing from the most popular country). The correlation between the common
27
This is not apparent from Figure 4b because the figure plots each country’s share in foreign (and not overall)
sourcing. There are two possible reasons for this overprediction of the domestic sourcing share. First, as discussed
above, we set the fixed costs of domestic sourcing to zero. Second, our sourcing potential estimates, which represent
the (geometric) average ratios of firms’ sourcing from a given foreign country relative to the US, may understate the
importance of foreign inputs for selected large importers, and therefore lead to an under-prediction of aggregate imports
(see Online Appendix section C.5 for a detailed discussion of these sourcing potential estimates).
30
fixed cost model’s predictions and the data is only 0.68 for the share of importers by country and
only 0.67 for import shares by country. Furthermore, while the baseline model does a good job at
fitting the hierarchies in firms’ sourcing patterns, the common fixed costs model does poorly, since
– given the estimated sourcing potentials – it predicts, for instance, that China, not Canada, is the
number one source of inputs.28
Table 6: Hierarchies in sourcing patterns: data and model
Data
Baseline
model
CA
CA-CH
CA-CH-DE
CA-CH-DE-GB
CA-CH-DE-GB-TW
CA-CH-DE-GB-TW-IT
CA-CH-DE-GB-TW-IT-JP
CA-CH-DE-GB-TW-IT-JP-MX
CA-CH-DE-GB-TW-IT-JP-MX-FR
CA-CH-DE-GB-TW-IT-JP-MX-FR-KR
29.82
3.67
0.56
0.25
0.13
0.05
0.05
0.08
0.27
1.08
28.66
3.42
0.58
0.14
0.09
0.02
0.03
0.07
0.12
0.66
TOTAL Following Pecking Order
36.0
33.8
String
Notes: This table depicts the percentage of importers following a particular sourcing pattern. The first row shows the percentage of firms only
importing from Canada; the second row shows the percentage of firms
only importing from Canada and China; and so forth (irrespective of
firm sourcing outside these top 10 countries). The ranking of countries is
determined by the number of firms sourcing from these countries in the
data.
6
Counterfactual: An Increase of China’s Sourcing Potential
In this section, we use the parameter estimates from section 5 to assess how firm-level import decisions,
the firm size distribution, and aggregate sourcing by country respond to a shock in China. We
focus on China not only because it is one of the biggest U.S. trade partners, but also because its
accession to the WTO in 2001 provides an actual shock in the data against which we can compare
the model’s predictions. The aggregate U.S. employment effects of this shock have been studied in
several contexts (e.g., Autor et al., 2013, 2014; Pierce and Schott, 2016), but with a focus on import
competition rather than offshoring opportunities. Our results highlight the empirical relevance of
interdependencies inherent in firm-level sourcing decisions, and show that these interdependencies
28
In Appendix Table A.2 we also illustrate the superior fit of the statistics described in Table 1 by the baseline
model compared to the model with common fixed costs. Note that one important point about the comparison of the
heterogeneous versus homogeneous fixed cost models is that the former has two sources heterogeneity: country and
firm-country-specific variation. A model with common mean fixed costs across countries, but with firm-country-specific
variation in the fixed costs, would still require our algorithm in order to solve the firm’s problem, since for a given firm,
fixed costs would again be heterogeneous across countries.
31
lead to significant heterogeneity in the firm-level implications for domestic employment.
We model the China shock as a change to China’s sourcing potential that is large enough to
explain the observed 178 percent increase in the Chinese share of US manufacturer’s imports between
1997 and 2007. Specifically, when multiplying the Chinese sourcing potential estimate for 2007 by
a factor of 0.46, and holding all other exogenous variables fixed – but re-solving for the price index
and the mass of firms – we can match the observed increase in aggregate imports from China.29 Our
baseline specification uses the estimated parameters for 2007, but with the lower 1997 Chinese sourcing
potential. We then analyze the changes our model predicts from increasing Chinese sourcing potential
to its actual estimated value in 2007. Although it might have been more natural to re-estimate our
model for the year 1997, data limitations (particularly the poor coverage of U.S. importers from
Canada) preclude us from doing so in a proper manner. Throughout the counterfactual exercises we
solve for the new equilibrium price index and let the mass of firms adjust such that the free entry
condition is satisfied.30 While firms in our static model are only one-period lived, we can nevertheless
compare firms with the same productivity levels and fixed cost draws before and after the China
shock.
For the first part of the analysis, we do not take a stance on the underlying cause of the shock
to China’s sourcing potential, but when mapping our counterfactuals to reduced-form evidence, we
will attempt to isolate a shock to Chinese productivity in the production of intermediate inputs. It is
important to emphasize that we are not able to trace the responses of final-good producers in foreign
countries to this China shock. As long as wages are pinned down by a non-manufacturing sector,
these foreign responses are irrelevant for the quantitative implications of the shock for the sourcing
decisions of U.S. final-good producers. Even with endogenous wages, the qualitative implications of
the shock would also be unaffected by the decisions of final-good producers abroad. Nevertheless,
the aggregate implications of our model for overall sales of U.S. intermediate-input producers and for
overall U.S. manufacturing employment could well be affected by these foreign responses.
29
This counterfactual sourcing potential value still implies that China was the number one country for cost savings
in 1997, with Taiwan as the next best country. Of course, the increase in the share of firms sourcing from China may
have been triggered by both an increase of the Chinese sourcing potential and a reduction of the fixed costs of sourcing
from China. Since one of our goals is to compare our model’s predictions with those from a model with common fixed
costs across countries, we focus on a change to only the sourcing potential. In Online Appendix C.8, we alternatively
consider a shock only to fixed costs that achieves the same increase in the Chinese import share. If Chinese sourcing
potential had not changed, the fixed costs of sourcing from China in 1997 would have needed to be almost nine times
larger than their estimated size in 2007. The observed price index change would have been similar to the findings under
the sourcing potential shock, though the counterfactual underpredicts the share of firms importing from China in 1997,
and obviously it cannot generate an expansion in U.S. and third-market sourcing by continuers (a feature of the data
we will document in section 6.4).
30
Given our parameter estimates and the counterfactual parameter change, the calculation of the counterfactual price
index and mass of firms works as follows. We set total expenditure, E, equal to the the total sales of firms in the data.
We then use our estimate of B together with equation (3) and the ideal CES price index associated with (1) to back out
the mass of firms, N , in the equilibrium associated with the estimated parameters. Using the free entry condition (13),
we set the fixed costs of entry to the average profits of firms implied by the estimated model. In our counterfactual,
after changing the Chinese sourcing potential, we solve for the new level of B such that the free entry condition (13),
is again satisfied and – given the new level of B – use (14) to determine the new mass of firms. The new equilibrium
price index then follows from the standard formula.
32
6.1
Baseline Predictions
Table 7 (Panel A) documents how the China shock affects sourcing in various markets for different
sets of firms. We find that the shock induces 5.3 percent of firms to start importing from China,
which is around 80 percent of the actual entry rate observed in the data (6.6 percent). These entrants
account for about a third of Chinese imports after the shock. Consistent with the complementarities
highlighted by our model, these new China importers increase their sourcing from the U.S. and from
third countries by 0.8 and 1.5 percent, respectively. Firms that continue sourcing from China comprise
2.7 percent of firms, and they also slightly increase their domestic and third country sourcing. The
expansion of these new and continuing China importers is associated with these firms’ being able to
sell their products at lower prices, which in turn leads the aggregate price index and the mass of active
firms to adjust. As a result, firms for which the shock is not large enough to induce importing from
China face tougher competition, which leads their sourcing from the U.S. and other foreign countries
to contract by 0.5 and 1.3 percent, respectively. The responses in sourcing from other foreign countries
are generally larger than for domestic sourcing, since the former involves both intensive and extensive
margin adjustments (i.e., firms selecting into or out of particular countries). The extensive margin
adjustments are quantitatively important. The addition of new source countries accounts for 50
percent of the aggregate change in third country sourcing by Entrants, 29 percent of the change by
Continuers, and 58 percent of the change by Others. Sourcing responses are also necessarily larger
for new China importers, since these firms’ extensive margin sourcing change leads them to grow
relatively more.31
Figure 5: Changes in the size of firms
(a) Baseline
(b) Fixed Sourcing Strategies
−3
−3
x 10
x 10
10
10
8
8
6
6
Growth in Sales
12
Growth in Sales
12
4
2
4
2
0
0
−2
−2
−4
−4
−6
0
10
20
30
40
50
60
Percentiles size distribution
70
80
90
100
0
10
20
30
40
50
60
Percentiles size distribution
70
80
90
100
Figure 5a depicts the percent growth in sales by firm size percentile. Firms are ranked according to
their sales before the China shock. Large firms increase their sales by about 1.5 percent. While these
magnitudes may seem small, this is partly driven by the fact that fixed costs are firm-country-specific
31
It is important to note that continuing Chinese importers need not necessarily increase their domestic and third
market sourcing. If the price index decline were sufficiently large, the interdependencies in their extensive margin
sourcing decisions which lead them to grow could be swamped by the increased competitive pressure that leads all firms
to shrink.
33
Table 7: Third country sourcing effects of Chinese sourcing potential shock
Chinese
import status
Change in
sourcing from
U.S.
Change in
sourcing from
other countries
Change in
sourcing from
China
Share
of firms
Share of
imports from
China
1.015
1.001
0.987
∞
2.148
-
0.053
0.027
0.920
0.334
0.666
0.000
2.150
-
0.000
0.027
0.973
0.000
1.000
0.000
∞
2.116
-
0.053
0.027
0.920
0.343
0.657
0.000
2.976
-
0.000
1.000
0.000
0.000
1.000
0.000
Panel A: Baseline model
Entrants
Continuers
Others
1.008
1.001
0.995
Panel B: Baseline model, fixed sourcing strategies
Entrants
Continuers
Others
1.002
0.996
1.002
0.996
Panel C: Independent entry decisions model (θ = σ − 1 = 2.85)
Entrants
Continuers
Others
0.997
0.997
0.997
0.994
0.996
0.992
Panel D: Universal importing model (no fixed costs)
Entrants
Continuers
Others
0.987
-
0.987
-
Panel E: Common fixed costs across countries model (heterogeneous across firms)
Entrants
Continuers
Others
1.006
0.999
0.993
∞
2.249
-
0.999
-
0.108
0.066
0.826
0.328
0.672
0.000
Notes: The table groups firms by Chinese import status. Entrants are those firms (i.e. bundles of productivity levels and fixed cost draws) that begin sourcing from China. Continuers are firms that source from China
before and after the shock. Others are firms that do not source from China before or after the shock. As described in the main text, the shock to the Chinese sourcing potential is calibrated so that the Baseline model
matches the observed 178 percent increase in the Chinese import share from 1997 to 2007. For the Panels
C, D, E we re-calibrate the shock to the Chinese sourcing potential so that the respective models can match
the same 178 percent increase in the Chinese import share. Columns 1, 2, and 3 contain the ratio of the total sourcing by each group of firms before and after the shock. Figures in this table do not include changes
in sourcing due to changes in the mass of firms after the counterfactual shock. Changes in sourcing due to
changes in the overall mass of firms are included in the figures in Table 8.
and hence not all firms within a certain size category import from China. Firms below the 86th
percentile of the size distribution see their sales shrink on average in response to the China shock.
Overall, aggregate imports from China increase by 222 percent, while aggregate sourcing from
the U.S. falls by 0.53 percent (see Table 8).32 The net change in U.S. sourcing masks a substantial
32
The increase in aggregate imports from China is larger than the calibrated 178 increase in the Chinese import
share. These numbers differ because an increase in aggregate imports from China raises both the denominator and the
numerator of the Chinese import share.
34
amount of domestic churn. As shown in Table 8, new and continuing importers from China increase
their domestic sourcing by 4.41 billion USD (or 0.11 percent of total sourcing). Comparing this figure
to the total decline in domestic sourcing accounted for by contracting or exiting firms (i.e., 25.04
billion USD) implies that every dollar reduction in domestic sourcing is thus partly offset by a 18 cent
increase in domestic sourcing from expanding firms. Since in our model this spending represents jobs
in the intermediate goods sector, we predict a substantial amount of employment churn in response to
an increase in Chinese sourcing potential. We also find that an increase in China’s sourcing potential
lowers the price index in the manufacturing good sector by 0.19 percent. Consumers are therefore
better off since they enjoy lower prices for the goods they buy.
Table 8: Gross and net U.S. sourcing effects
Fixed sourcing
strategies
Baseline
Difference in
sourcing in
billion USD
Change in
percent of total
U.S. sourcing
Difference in
sourcing in
billion USD
Change in
percent of total
U.S. sourcing
4.41
-13.93
0.11
-0.36
1.97
-12.86
0.05
-0.33
-11.11
-0.28
0
0
-20.63
-0.53
-10.88
-0.28
Increase in domestic sourcing
Decrease in domestic sourcing
by firms that continue to operate
Decrease in domestic sourcing
by firms that shut down
Total
Notes: We use the model’s predictions for the U.S. sourcing pre and post the shock to China’s sourcing potential in order to calculate percentage changes in U.S. sourcing. We then use aggregate U.S. sourcing purchases in the data and the
percentage differences predicted by the model to calculate the predicted USD change in sourcing in response to the shock.
6.2
Fixed Sourcing Strategies
An important emphasis of our model is the role of the extensive margin in firms’ sourcing strategies.
To assess the importance of this margin on aggregate trade patterns and welfare, we consider the
same shock to Chinese sourcing potential as in Section 6.1 but hold firms’ extensive margin sourcing
strategies fixed. In the exercise, we recompute the equilibrium price index and the mass of firms. As
expected, when firms’ sourcing strategies cannot change, the aggregate response to the China shock
is substantially smaller. U.S. sourcing decreases by 0.28 percent (see Table 8), and aggregate sourcing
from China increases by 115 percent (see Table 7, Panel B), with these responses being about half
as large as those under flexible strategies. The implied growth in the Chinese share of US imports
between 1997 and 2007 is also much lower than in our baseline model (98% versus 178%).
The micro effects by firm type are helpful to understand these differences. In the baseline, the
large number of new importers from China drives most of the aggregate Chinese sourcing increase.
This increase leads the price index to fall significantly, which reduces aggregate sourcing from both the
35
U.S. and other countries. In addition, in the baseline analysis the increase in firms’ extensive margin
sourcing decisions results in higher expenditures on fixed costs. Given constant expenditure in the
manufacturing sector, this leads ceteris paribus to lower expected profits, which in turn are brought
back to zero by a decrease in the number of firms. In contrast, under fixed sourcing strategies, the
number of firms remains the same in equilibrium (despite free entry), and consequently there is no
decrease in U.S. sourcing from firms that shut down (see Table 8).33 Firms that source from China
slightly increase their sourcing from the U.S. and other countries, while all other firms reduce their
sourcing from the U.S. and other countries (see Table 7, Panel B).
The responses of the size distribution are also quite different (see Figure 5b). When firms’ sourcing
strategies are fixed, the only firms that grow are those that previously imported from China, which on
average tend to be the larger firms. Firms of all other sizes contract. Under fixed sourcing strategies
the price index declines by 0.15 percent, which is about 78 percent of the impact of the shock when
firms can adjust their extensive margin decisions.34
6.3
Comparison with Alternative Models and Sensitivity Analysis
As discussed in Section 3.4 when describing the model’s predictions for aggregate trade flows, our
framework nests two canonical frameworks of the last decade: the Melitz (2003) heterogeneous firms
model and the Eaton and Kortum (2002) Ricardian trade model. In order to demonstrate the qualitative differences between our baseline model and these other models, we modify the parameters
such that these canonical models emerge as special cases. We also compare our baseline model’s
predictions to those from a model in which fixed costs are heterogeneous across firms, but common
across countries. For each of these alternative models, we re-calibrate the change in the Chinese
sourcing potential to match the 178 percent increase in the Chinese share of US imports between
1997 and 2007.35 In the Estimation Appendix, we assess the baseline model’s predictions under a
range of alternative parameter values. An important caveat to the model comparisons and robustness
analyses is that, because these exercises require changing parameter values, it is clearly not possible
to hold all else equal. We therefore focus on the qualitative differences in the predictions and caution
that quantitative differences may reflect several changing factors.
We first consider a scenario similar to the Chaney (2008) multi-country Melitz model in which
firms’ import decisions are independent across markets, which occurs in the knife-edge case of θ = σ−1
in our model. To do so, we increase the value of θ to 2.85 so that it is equal to σ − 1. We re-estimate
fixed costs under these parameter values in Step 3, leading to a similar model fit as in the baseline.
To minimize the number of moving parts, and to account for the empirical fact that the number of
importing firms is much larger than the number of firms importing from the most popular sourcing
country, we continue to include firm-country-specific fixed costs, although these are not present in
33
The number of firms does not change since total expenditure on manufacturing is constant, and aggregate expenditure on fixed costs is unchanged (due to the lack of extensive margin adjustments), so that the free entry condition is
satisfied with the same mass of firms as prior to the counterfactual.
34
Given fixed wages, free entry, and a constant share of income spent on manufacturing, the decline in the manufacturing price index captures the full effect of the shock on aggregate real income.
35
In Online Appendix Tables C.6 and C.7, we report various targeted and untargeted moments for each of these
variants of the model.
36
the original Chaney (2008) paper.
The counterfactual predictions from this version of our model in which firms’ import entry decisions are independent across markets are quite different from the baseline results (despite the share
of firms in each category being virtually identical in the two counterfactuals). Our baseline model
predicts substantial differences between net and gross changes in sourcing, with some firms expanding their sourcing from other countries and the U.S. and other firms contracting. In contrast, under
independent entry decisions, the only effect on sourcing from other countries comes from a general
equilibrium effect (a fall in the aggregate price index), which leads all firms to reduce their sourcing
from the U.S. and other countries except China. All active firms reduce their sourcing from the U.S.
by the same amount: -0.3 percent (see Table 7, Panel C). Sourcing from third markets also declines.
Most notably, the aggregate net effects are exactly equal to the gross effects under these parameter
values. One might be concerned that this conclusion rests on our simplifying assumption that wages
are unaffected by the China shock. Inspection of equation (12) – after plugging in the restriction
θ = σ − 1 – reveals, however, that changes in wages would necessarily lead all firms to change their
sourcing from the U.S. by the same proportion. In sum, when entry decisions are independent, there
is no scope for domestic churn and reallocation following the China shock.36
We next follow Eaton and Kortum (2002) and assume that there are no fixed costs to import,
which results in universal importing by all firms. In this exercise, we re-do the quantification of
the scale parameter, B, in Step 3 of the estimation, while restricting the fixed cost parameters to
be zero. Under these conditions, all firms decrease their sourcing from the U.S. and from all other
countries except China by 1.3 percent (see Table 7, Panel D). Furthermore, as in the case with no
interdependencies in firms’ entry decisions across markets, net changes in import flows are identical
to gross changes in flows.
An important contribution of our paper is to present a new framework for analyzing extensive
margin sourcing decisions when the fixed costs to import differ across countries. To assess the importance of this fixed cost heterogeneity, we revisit the case first described in section 5.4 in which
fixed costs are identical across countries, but heterogeneous across firms. This model predicts a perfect pecking order of firm sourcing in which firms select into countries based solely on the potential
marginal cost savings. Panel E of Table 7 shows that this prediction strongly limits firms’ extensive
margin sourcing responses. China is the number one sourcing potential country in 2007 and also 1997,
even with the lower calibrated potential. As a result, the common fixed cost model predicts that firms
that do not import from China will never find it profitable to import from any other country. This is
evident in the Others row, which shows that non-China importers do not change their sourcing from
other countries. In addition, the Entrants row also shows that new China importers do not change
their third-market sourcing. Under the common fixed cost assumption, new China importers cannot
have intensive margin changes in third market sourcing (since they did not import from anywhere in
1997), and the degree of complementarity we estimate is not powerful enough to induce them to add
third markets. The latter stands in sharp contrast to our baseline model, where half of the change
36
In a Melitz-Chaney model of exporting, domestic sales of all surviving firms change by the same percentage; larger
firms grow and small firms shrink only because the latter only sell domestically, while the former also export. Focusing
on sales in a particular market (not just the domestic one), all firms scale up or down proportionally.
37
in Entrants’ third-market sourcing was driven by extensive margin changes. In the next section, we
will also show that Entrants’ extensive margin changes are also key features in the actual US data.37
A key takeaway from these counterfactual exercises is that the interdependencies in firms’ extensive
margin sourcing decisions lead to significant differences between the gross and net changes caused
by the shock. Although the China shock is associated with a sizable decrease in domestic sourcing
in the U.S., some firms increase their domestic input purchases considerably following the shock.
More generally, the third-market effects – that is how a shock to one country (in this case China)
affects sourcing from other countries – are quite different for both firm and aggregate outcomes in
the presence of interdependencies in the extensive margin.
Before turning to a comparison of our counterfactual predictions to actual data, we test the
sensitivity of our results to specific values of the key structural parameters. To do so, we re-estimate
the fixed costs of sourcing using alternative values of the shape parameter of the core productivity
distribution, κ; the elasticity of demand, σ; and the dispersion parameter of intermediate input
efficiencies, θ. We summarize the main results here, with detailed results presented in Appendix
Table A.3. The estimates for the effects of language and control of corruption on the fixed costs of
sourcing are remarkably robust across alternative parameters. The estimated range of fixed costs
across countries varies, but not dramatically. With respect to the counterfactual predictions, as
expected the price index changes are decreasing in the firm-level trade elasticity θ. The amount of
churning attributable to changes in sourcing from the U.S. increases for a lower value of θ = 1.3. In
that case, for every dollar decrease in U.S. sourcing, a 38 cent increase in U.S. sourcing takes place.
The amount of churning is lower for larger values of θ and for lower values of κ, since more weight is
given to the large firms that are already incumbents of sourcing from China.
6.4
Comparing Counterfactual Predictions to Actual Changes
We conclude this section by comparing the counterfactual predictions from the model to actual
changes in U.S. firms’ sourcing from 1997 to 2007. We analyze changes from 1997 to 2007 since
data on firm sales and input purchases are available only in years ending in 2 and 7, and these years
conveniently span China’s accession to the WTO. Table 9 presents an analog to Table 7 in which we
use the data, deflated to 1997 dollars, to calculate the relative changes in domestic sourcing, sourcing
from other countries, and sourcing from China. We use an unbalanced panel of firms in this exercise
to ensure that the observed patterns are not driven by selection of more productive firms that are
more likely to survive over this period.38
While the counterfactual predicts that firms will grow or shrink their sourcing by small amounts,
37
Another difference between Panel E and our baseline results in panel A, is that continuing China importers are
predicted to shrink in both domestic and third markets. On the other hand, the common fixed costs model is successful
in delivering gross increases and decreases in sourcing from U.S. suppliers, though to a lesser extent than the baseline
model.
38
This selection does not occur in the model since the core productivities of firms are unchanged by the counterfactual.
The share of new China importers (Entrants) in the unbalanced panel is eight percent. This is slightly higher than the
6.6 percent entry rate mentioned earlier, which is the difference between the 1997 share of China importers (1.9 percent)
and the 2007 share of imports (8.5 percent). These numbers do not perfectly coincide because, in reality, not all firms
that import from China in 1997 continue to do so in 2007, and there some firms that enter and exit over the period also
import from China.
38
Table 9 shows that in the data, all types of firms changed their sourcing significantly. This is not
surprising since the counterfactual holds all else constant, while in reality many factors change over the
ten-year period. Nevertheless, one can still compare relative changes in sourcing across Chinese import
status to assess whether the qualitative predictions of the model are evident in the data. Consistent
with the counterfactual predictions, firms that begin sourcing from China grow both their domestic
sourcing and their sourcing from other countries relatively more than continuing China importers and
non-China importers. Table 9 also shows that continuing importers grow their domestic sourcing and
sourcing from other countries more than non-importers. In fact, as in the counterfactual predictions,
aggregate domestic sourcing by firms that never source from China shrinks over this period. The main
qualitative difference from the model is that sourcing from third markets by non-China importers
grows, but this growth is substantially smaller relative to foreign sourcing growth of both new and
continuing China importers.
Table 9: Observed changes in third country sourcing from 1997 - 2007 by firms’ 2007
Chinese import status
Chinese
import status
Entrants
Exiters
Continuers
Others
Change sourcing
from U.S.
Change Sourcing
from other countries
Change Sourcing
from China
Share
of firms
2.68
0.15
1.03
0.74
5.93
0.02
1.32
1.03
0.00
5.75
-
0.08
0.00
0.01
0.91
Notes: This table is based on an unbalanced panel of manufacturing firms from 1997 and 2007. Exiters
(entrants) are those firms that stop (begin) sourcing from China. Continuers are firms that source from
China in 1997 and 2007. Columns 1, 2, and 3 contain the ratio of total sourcing in 2007 deflated dollars
relative to 1997 dollars by each group of firms. The share of firms in column 4 is the number of 2007
firms in each China import status category over total active firms in 2007.
The fact that both the model and data show China importers growing their domestic and third
market sourcing relatively more than non-China importers provides support for the empirical relevance
of the interdependencies highlighted in the model. As shown in both Panels D and E of Table 9, we
would not expect to see increased domestic and third market sourcing by U.S. firms sourcing from
China if entry decisions were independent across markets, or if there were no fixed costs of sourcing.
While the common fixed cost model would still lead to increased domestic and other sourcing by
new China importers, it also makes the extreme prediction that all new importers would necessarily
source from China –a prediction clearly at odds with the empirical evidence presented in Table 1.
A potential concern with this comparison to the data is firms may change their Chinese imports
in response to positive (or negative) demand, productivity, or technology shocks over the period. To
make a cleaner comparison of the counterfactual predictions of our model to the observed evolution
of sourcing in the data, we exploit the significant productivity growth within China and its accession
to the WTO in 2001 to construct a firm-specific, plausibly exogenous shock to Chinese sourcing
potential. In the spirit of Autor et al. (2013) and Hummels et al. (2014), we instrument for changes
39
in U.S. firms’ imports from China using changes in Chinese export shares to other developed countries
in a firm’s 1997 input industries.39 We then estimate the relationship between predicted changes in
sourcing from China and firm sourcing from domestic and third markets according to
∆yn = β0 + βCh ∆Chinan + εn ,
where ∆Chinan =
Ch
ImportsCh
n2007 −Importsn1997
Ch )/2
(ImportsCh
+Imports
n2007
i1997
(23)
is a Davis-Haltiwanger-Schuh (DHS) growth rate of
firm n’s imports from China that captures changes in firms’ intensive and extensive margin sourcing.
We estimate the relationship between China sourcing and five dependent variables (all represented by
a DHS growth rate unless otherwise noted): domestic input purchases, imports from other countries,
the log difference in the number of countries from which the firm sources (excluding China but
including the U.S.), and firm-level employment.40 All dollar values are deflated using NBER industry
deflators.
Table 10 presents results from estimating equation (23) via OLS and two-stage least squares for
the balanced panel of manufacturing firms present in both 1997 and 2007.41 Standard errors are
clustered at the industry level to match the same level of aggregation as the China shock variable.
The OLS estimates presented in columns 1-4 are all significant at the one percent level and suggest
that a ten percentage point increase in firm-level sourcing from China was associated with a 0.6 point
increase in domestic sourcing, a 2.6 percent increase in the number of countries from which the firm
sources, and a 3.6 point increase in sourcing from other foreign countries. Columns 5-7 show that
IV estimates are larger and still significant at the one percent level.42 Given the considerable focus
in the literature on the employment effects of Chinese imports, we also estimate the relationship
between changes in China sourcing and firm-level employment. While the OLS estimate shows that
10 point increase in the growth rate of Chinese imports is associated with a one point increase in the
firm’s U.S. employment, the IV estimate is negative but statistically insignificant. This result is still
consistent with our framework since the model predictions relate to changes in a firm’s total domestic
input/employment use, and not to employment at the firm itself. The bottom panel of Table 10 also
presents first-stage statistics, which show a positive and significant coefficient on the instrument and
39
Unlike Autor et al. (2013) who use changes in the levels of Chinese imports across industries in other high-income
countries as an instrument, we use changes in Chinese market shares in the original 15 European Union countries. We
choose market shares rather than levels to address the potential for correlated demand shocks between those countries
and the U.S., which are a more serious concern in our framework. All our results are also robust to using the same
high-income countries as in ADH, but our first stage is stronger using EU15 countries, especially in the robustness test
in which we instrument for both firm-level sourcing and import competition. Additional details are in the Estimation
and Online Data Appendices.
40
We use DHS growth rates as a simple way to account for both intensive and extensive margin adjustments. Our
results are qualitatively similar when using an indicator equal to one for firms that begin sourcing from China over
the period. They are also similar when using log differences in firms’ domestic input use and employment as outcome
variables. We do not obtain significant results for the log difference in firms’ third-market sourcing – a result consistent
with the model’s predictions about the importance of changes in firms’ extensive margin sourcing decisions.
41
Here we focus on a balanced panel since we require a 1997 firm industry to construct our instrument. The results
are significantly stronger if we used an unbalanced panel and assigned shocks to new firms based on their initial industry.
We do not present those results since they may be biased by firms’ endogenous entry and exit decisions.
42
The difference in magnitude between our OLS and IV estimates are similar to those in Hummels et al. (2014), and
consistent with offshoring being a firm-level response to negative shocks, as documented in Monarch et al. (2017) and
Bernard et al. (2017).
40
a Kleibergen-Paap F-statistic of 28.25.
Table 10: Estimates of the impact of the China shock on firm-level sourcing
Dependent variable is firm-level change from 1997 to 2007 in:
Domestic
inputs
No. of
countries
Foreign
inputs
Firm
empl.
Domestic
inputs
OLS
China, DHS
Constant
N
No. of
countries
Foreign
inputs
Firm
empl.
IV
0.064
(0.010)
0.054
(0.019)
0.255
(0.007)
0.144
(0.013)
0.362
(0.013)
0.315
(0.026)
0.097
(0.007)
-0.075
(0.014)
0.758
(0.214)
-0.054
(0.039)
0.551
(0.080)
0.098
(0.017)
0.670
(0.198)
0.267
(0.044)
-0.092
(0.162)
-0.046
(0.032)
127,400
127,400
127,400
127,400
127,400
127,400
127,400
127,400
First Stage Statistics
Coeff (se) 2.685 (0.505)
KP F stat 28.25
Notes: All variables are changes or growth rates from 1997 to 2007. China, DHS is a Davis-Haltiwanger-Schuh growth rate
in firm imports from China. Domestic inputs, foreign inputs, and firm employment are a DHS growth rate. No. of countries is the log difference in the number of countries (excluding China, but including the U.S.) from which the firm sources
inputs. Foreign inputs exclude China. Standard errors are in parentheses and clustered by 439 NAICS industries. In the IV
specifications, firm-level sourcing from China is instrumented by the change in Chinese market share in EU15 countries of a
weighted average of the firm’s inputs. KP F-stat is the Kleibergen Paap F-statistic. N is rounded for disclosure avoidance.
There are two potential concerns with this reduced form analysis. First, the exclusion restriction
might be violated if industries in which China gained market share in EU15 countries are also industries that faced greater competition from China in final-good markets. Although we instrument with
a shock to a firm’s inputs rather than outputs, input and output shocks may still be correlated. In
the Online Data Appendix, we show that the results are robust to controlling for import penetration
from China, and to instrumenting for import penetration from China with a shock to a firm’s output
industries. Another concern with our approach is that the exclusion restriction could be violated
because the multilateral nature of the China shock may have indirectly affected firm sourcing from
third markets by affecting input suppliers in those markets.43 Unfortunately there is no clean way to
control for shocks to a firm’s suppliers in these data, but this could be a fruitful avenue to explore
with richer information on supply-side firm-level networks.
The results in Tables 9 and 10 provide strong support for the empirical relevance of our theoretical
mechanism. First, they show that firms sourcing from China increase their domestic and third market
sourcing substantially more than firms that do not import from China. This is inconsistent with the
predicted responses in a world with independent entry decisions since, as shown in Panel D of Table 7,
under this scenario all firms decrease their domestic sourcing by the same amount. Second, they show
that increased domestic and foreign sourcing occurs not just across, but also within firms. Third, they
rule out firm-specific demand or productivity shocks as drivers of these changes. Most importantly,
the results show that increased firm-level imports from China do not decrease domestic and third
market sourcing –as might be expected in a world with no interdependencies in sourcing decisions–
but instead are associated with increased firm-level sourcing from other markets.
43
To the extent that the China shock displaced input suppliers either in the U.S. or other foreign countries, these
indirect effects might bias our estimates of βCh down (e.g. Hanson and Robertson, 2010). Alternatively, the China
shock may have led to wage decreases or productivity increases among suppliers that in turn led U.S. firms to increase
sourcing from them. To the extent that these changes disproportionately affect industries in which a firm’s inputs were
shocked (e.g., Torres-Ruiz and Utar, 2013), our estimates might be biased up.
41
7
Conclusion
This paper provides a new framework in which to analyze the global sourcing decisions of firms in a
multi-country world where production combines multiple inputs. Our model nests the two canonical
models of the extensive margin of exporting, the Eaton and Kortum (2002) Ricardian competitive
model and the Melitz (2003) monopolistic competition with heterogeneous firms. These special cases
highlight the fact that in a general setting, sourcing decisions interact through the cost function, so
that determining the extensive margin of importing must involve solving a 2J -dimensional discrete
choice problem (where J is the number of countries), rather than solving J binary problems as in
canonical models of exporting.
A key contribution of this paper is to overcome these challenges by showing that –under a simple
parametric restriction that is consistent with the data– a firm’s decision to source from one country is complementary to its decision to source from other countries. These complementarities in a
firm’s extensive margin sourcing decisions underpin our new methodological approach to reduce the
dimensionality of the firm’s problem and solve it. By extending the pioneering work of Jia (2008) to
a multi-firm environment, we recover the key parameters of our model from confidential U.S. firmlevel data on the sourcing decisions of U.S. firms in 67 countries. Armed with these estimates, we
explore the quantitative bite of the key novel features of our framework by studying how a shock to
the potential benefits of sourcing from a country (namely, China) differentially affects the sourcing
decisions of U.S. firms depending on their core productivity and their pre-shock sourcing strategies.
A distinctive characteristic of our framework is that a sectoral import competition shock that does
not simultaneously increase export opportunities may still lead to intraindustry reallocation effects
by which firms sourcing from the shocked country may expand, while firms not sourcing from that
country shrink. We show that a ‘China shock’ calibrated to match the growth in U.S. foreign sourcing
from China between 1997 and 2007 generates qualitative effects consistent with the observed evolution
of U.S. firms’ domestic and third-market sourcing.
Our theoretical framework is necessarily stylized, but it can flexibly accommodate various extensions. As shown in the Online Appendix and further explored in Bernard et al. (2016), it can easily
be extended to include the joint determination of the extensive margin of importing and exporting.
It is also straightforward to incorporate fixed costs of sourcing costs at the input level (see the Online
Appendix) and also at the supplier level. This latter approach is explored by Bernard et al. (2015)
and Furusawa et al. (2016) in their studies of buyer-seller relationships in Japan. Similarly, we have
abstracted from the type of contractual frictions inherent in global sourcing transactions, but as outlined in Antràs (2016), these contractual aspects can also be incorporated in our framework, thus
permitting a multi-country analysis of the choice between intrafirm versus arm’s-length global sourcing, along the lines of Antràs and Helpman (2004). Finally, we believe that the methodological tools
we have developed in this paper, and particularly our application of Jia’s (2008) iterative algorithm
for solving single-agent entry decisions with interdependencies across markets, could be fruitfully
adopted in alternative environments, such as in exporting models with non-constant marginal costs
or in the presence of demand linkages across markets.
42
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A
A.1
Estimation Appendix
Measuring Firm-Level Offshoring Shares
We measure a firm’s total inputs using production worker wages from the Census of Manufactures (CM), total
cost of materials from the Economic Censuses of manufacturing, construction, and mining, and merchandise
purchases from the Census of Wholesale. Inputs from any foreign country j are simply the firm’s total imports
from j. Domestic inputs are the difference between total inputs and imports. A firm’s share of inputs from
country j, χij , is computed as imports from j divided by total input purchases. Additional details are in
described in the Online Data Appendix.
A.2
Estimation of the Trade Elasticity
Table A.1 presents the first stage regressions for the IV estimates of θ, where we instrument for country wages
using population. As expected, the estimated coefficient on population is negative and significant at the five
percent level. The F-statistics for the excluded instrument is 6.49. In unreported results (available in our
online replication files), we verify that the Anderson-Rubin F test and χ2 test of significance of the endogenous
regressors are statistically significant at the five percent level.
Table A.1: First stage regressions for trade elasticity estimates
Dependent variable is log HC adj. wage
log population
log distance
log R&D
log KL
Common language
Control of corruption
log no. of firms
Constant
R2
Observations
-0.32
(0.12)
-0.20
(0.14)
0.32
(0.09)
0.14
(0.17)
-0.05
(0.17)
0.22
(0.12)
-0.04
(0.07)
-1.48
(0.81)
.883
57
Notes: First stage regressions for the IV estimates
presented in Table 4. Wage is the log of the human
capital-adjusted wage. Population is the excluded
instrument.
A.3
Estimation Results and Counterfactual Predictions
In this Appendix, we provide three additional tables related to our structural estimation and counterfactuals.
Table A.2 compares the share of imports and importers in the data (as in Table 1), in the baseline model, and in
the model with common fixed costs across countries. Table A.3 reports our estimation and counterfactual results
for various alternative parameter values. Table A.4 contains details on the performance of our application of
Jia’s (2008) algorithm.
A.4
China Shock Measure for Reduced Form Estimates
We instrument for changes in firm-level sourcing from China using changes in a novel measure of Chinese
comparative advantage in a firm’s inputs. Specifically, we measure Chinese comparative advantage in the
46
Table A.2: Share of imports and importers: data and models
Canada
China
Germany
UK
Taiwan
Italy
Japan
Mexico
France
South Korea
Share of Importers
Data Baseline C.F.C.
Model
Model
0.585
0.554
0.304
0.333
0.297
1.000
0.201
0.191
0.207
0.178
0.134
0.117
0.163
0.158
0.356
0.132
0.059
0.159
0.124
0.133
0.207
0.121
0.137
0.315
0.094
0.068
0.090
0.087
0.081
0.191
Share of Imports
Data Baseline C. F. C.
Model
Model
0.163
0.094
0.055
0.137
0.201
0.244
0.070
0.047
0.036
0.034
0.027
0.019
0.019
0.066
0.067
0.015
0.025
0.026
0.126
0.041
0.036
0.141
0.057
0.058
0.026
0.017
0.014
0.023
0.032
0.032
Notes: This Table depicts for the 10 most popular importing countries the share of importers that buy from that country and the share of import volume.
inputs of industry h and year t as
Chinainput
ht
=
X
m∈h
smh
EU 15importsChina
mt
W orld/U S
!
,
EU 15importsmt
where smh is the expenditure share of inputs from industry m in industry h from the 1997 BEA input-output
table. The terms in parentheses are China’s share of imports in the original 15 European Union countries in
industry m and year t, excluding imports from the U.S., measured using bilateral trade data from the UN
Comtrade database.44 We use Chinese market shares in these countries since it is unlikely that demand or
supply shocks for U.S. firms will drive changes in their aggregate import shares. Since firms often span multiple
industries, we assign changes in these input shocks as the weighted average of firm manufacturing sales across
industries in 1997. All time-series variation in this shock is therefore driven by changes in Chinese market
shares in EU15 countries in a firm’s inputs.
Our approach is similar to Hummels et al. (2014), who construct firm-level shocks to Danish importers’
sourcing decisions by focusing on transport cost shocks to the set of countries and products the firm imported
in a pre-period. We do not use pre-period imports since it is critical for our instrument to identify firm-level
extensive margin decisions to start importing from China. The spirit of our identification strategy is most
similar to Autor et al. (2013), who instrument for Chinese imports per worker in the U.S. using Chinese
exports to eight high-income countries. There are two important distinctions between our approaches. First,
we construct shocks to inputs, while their focus is on shocks to final goods. Second, we use changes in Chinese
market shares, rather than changes in the levels of Chinese exports. Using Chinese market shares helps to
address a potential concern with their identification strategy–namely that correlated industry demand shocks
in other high-income countries and the U.S. may have increased imports from China in both places. Unlike the
Autor et al. (2013) measure, our instrument does not capture any industry growth, but instead relies solely on
changes in Chinese imports’ relative importance in an industry. We use EU15 countries since we do not face the
same data constraints as ADH who need trade data back to 1990. All our results are robust to using the ADH
countries, but our first stage statistics are somewhat weaker, especially for the results in Online Appendix
Table C.11, where we instrument for both firm-level Chinese imports and Chinese import penetration in a
firm’s industry.
As discussed in section 3, changes in market demand (Bi ) may have a significant impact in industry
equilibrium. A key component of market demand is the price index, which was significantly affected by
changes in Chinese productivity. To the extent possible, we control for price changes by deflating firm inputs
and imports from other countries using the NBER industry deflators. The first-stage estimates and additional
details on the variables’ construction are in the Online Data Appendix.
44
The EU15 countries are Austria, Belgium, Luxembourg, Denmark, Finland, France, Germany, Greece, Ireland,
Italy, Netherlands, Portugal, Spain, Sweden, the U.K. In addition to excluding U.S. imports in the denominator, we
also exclude all trade among EU15 countries in the calculation.
47
Table A.3: Sensitivity of parameter estimates and counterfactual predictions to alternative values for
θ, κ, and σ
Variation in θ
Variation
in σ
σ = 2.79 σ = 5
Variation in κ
Baseline
θ = 1.3
θ=2
θ = 2.85
κ=3
κ=4
κ=5
0.122
0.023
0.192
0.871
-0.394
0.939
0.121
0.030
0.209
0.939
-0.434
0.935
0.123
0.020
0.188
0.868
-0.395
0.932
0.124
0.014
0.187
0.872
-0.394
0.927
0.103
0.040
0.414
0.778
-0.393
1.312
0.118
0.024
0.224
0.856
-0.389
0.989
0.132
0.020
0.118
0.901
-0.415
0.819
0.237
0.017
0.002
0.944
-0.468
0.633
0.072
0.039
0.421
0.768
-0.393
1.318
10
56
14
82
9
50
7
35
19
175
11
65
9
42
5
29
19
175
-0.189
1.5
-0.268
3.6
-0.167
0.9
-0.113
-0.6
-0.430
0.1
-0.215
1.3
-0.134
2.0
-0.072
-0.3
-0.408
1.5
0.113
0.345
0.053
0.000
0.011
0.090
0.141
0.000
0.096
-0.527
-0.554
-0.519
-0.497
-0.854
-0.571
-0.433
-0.307
-0.885
Parameter estimates
B
βcf
βdf
βlf
f
βC
f
βdisp
Median fixed cost range across countries
Minimum (in tsd USD)
Maximum (in tsd USD)
Counterfactual predictions
Price index change (in percent)
Change in third country sourcing by
new importers from China (in percent)
Gross increase in U.S. sourcing
(in percent of total U.S. sourcing)
Net change in U.S. sourcing
(in percent of total U.S. sourcing)
Notes: This table presents Step 3 estimation results and counterfactual predictions for alternative parameter values for the firm-level trade elasticity θ,
the shape parameter of the Pareto distribution κ, and the elasticity of substitution σ.
Table A.4: Cardinality of differences in bounds
Cardinality of differences
in bounds
Baseline
Variation in θ θ = 1.3
θ=2
θ = 2.85
Variation in κ κ = 3
κ=4
κ=5
Variation in σ σ = 2.79
σ=5
0
1
2
3
4
5
6
7
8
9
10 - 25
≥ 26
11220190126
12359440019
12073844987
12897360000
12343521037
12786062392
11792382315
13145760000
12304230446
0
0
0
0
0
0
0
0
0
918094
3682595
515622
0
801134
1034458
1107735
0
2885568
84695
600585
36813
0
72030
94304
101502
0
476715
6693
98164
2342
0
5290
7843
7671
0
72738
376
15680
233
0
477
902
719
0
12206
16
2474
3
0
25
99
49
0
1947
0
444
0
0
5
2
9
0
353
0
26
0
0
2
0
0
0
27
0
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Notes: This table displays the number of firm (productivity and fixed cost draws) and parameter combinations for which the cardinality of the
differences in the bounds reached a particular value. While the productivity and fixed cost draws are held fixed during the estimation process,
the parameter vector, δ, varies through the iterations of the estimation process. We allow the differences of the bounds to be less than 26, before
we would revert to evaluating the objective value of the firm’s problem at the bounds and a small number of random values for the countries in
the bound. Since this cardinality of the differences in the bounds is never very high, we always solve accurately the problem of the firm.
48
The Margins of Global Sourcing: Theory and Evidence from U.S.
Firms by Pol Antràs, Teresa C. Fort and Felix Tintelnot
B
Online Theory Appendix (Not for Publication)
B.1
Proofs of Main Propositions
Proof of Proposition 1
Proof of part (a):
Consider two firms with productivities ϕH and ϕL , with ϕH > ϕL . Denote by Ji (ϕH ) = {j : Iij (ϕH ) = 1}
and Ji (ϕL ) = {j : Iij (ϕL ) = 1} the optimal sourcing strategies of these firms, and suppose that Ji (ϕH ) 6=
Ji (ϕL ) (when Ji (ϕH ) = Ji (ϕL ) the result in the Proposition holds trivially). For firm ϕH to prefer Ji (ϕH )
over Ji (ϕL ), we need
X
X
(σ−1)/θ
(σ−1)/θ
ϕσ−1
(γΘi (Ji (ϕH )))
Bi −
fij > ϕσ−1
(γΘi (Ji (ϕL )))
Bi −
fij ,
H
H
j∈Ji (ϕH )
j∈Ji (ϕL )
while ϕL preferring Ji (ϕL ) over Ji (ϕH ) requires
X
(σ−1)/θ
(σ−1)/θ
ϕσ−1
(γΘi (Ji (ϕH )))
Bi −
fij < ϕσ−1
(γΘi (Ji (ϕL )))
Bi −
L
L
j∈Ji (ϕH )
X
fij .
j∈Ji (ϕL )
Combining these two conditions, we find
i
σ−1
h
(σ−1)/θ
(σ−1)/θ
ϕH − ϕσ−1
Θ
(J
(ϕ
))
−
Θ
(J
(ϕ
))
γ (σ−1)/θ Bi > 0.
i
i
H
i
i
L
L
Given ϕH > ϕL , this necessarily implies Θi (ϕH ) > Θi (ϕL ).
Proof of part (b):
As noted in the main text, when (σ − 1) /θ > 1, the profit function in (11) features increasing differences
in (Iij , Iik ) for j, k ∈ {1, ..., J} with j 6= k. Furthermore, it also features increasing differences in (Iij , ϕ)
for any j ∈ J. Invoking Topkis’s monotonicity theorem, we can then conclude that for ϕH ≥ ϕL , we must
have (Ii1 (ϕH ) , Ii2 (ϕH ) , ..., IiJ (ϕH )) ≥ (Ii1 (ϕL ) , Ii2 (ϕL ) , ..., IiJ (ϕL )). Naturally, this rules out a situation
in which Iij (ϕH ) = 0 but Iij (ϕL ) = 1, and thus we can conclude that Ji (ϕL ) ⊆ Ji (ϕH ) for ϕH ≥ ϕL .
Proof of Proposition 2
Consider first the case, j ∈
/ J . The mapping Vij (ϕ, J) defined in the Proposition, is such that Vij (ϕ, J) = 1 if
(σ−1)/θ
(σ−1)/θ
ϕσ−1 γ (σ−1)/θ B Θi (J ∪ j)
− Θi (J )
> fij
and Vij (ϕ, J) = 0, otherwise. Because of increasing differences (see the proof of Proposition 1), the term
(σ−1)/θ
(σ−1)/θ
Θi (J ∪ j)
− Θi (J )
is increased by the addition of elements to the set J . As a result, for
0
J ⊆ J , we cannot possibly have Vij (ϕ, J ) = 1 and Vij (ϕ, J 0 ) = 0. Instead, we must have either Vij (ϕ, J ) =
Vij (ϕ, J 0 ) = 0, Vij (ϕ, J ) = Vij (ϕ, J 0 ) = 1, or Vij (ϕ, J ) = 0 and Vij (ϕ, J 0 ) = 1.
Second, consider the case j ∈ J . The mapping Vij (ϕ, J) defined in the Proposition, is such that Vij (ϕ, J) =
1 if
(σ−1)/θ
(σ−1)/θ
ϕσ−1 γ (σ−1)/θ B Θi (J )
> fij
− Θi (J \ j)
(σ−1)/θ
(σ−1)/θ
and Vij (ϕ, J) = 0, otherwise. Similarly to above, the term Θi (J )
− Θi (J \ j)
is increased by
the addition of elements to the set J . As a result, for J ⊆ J 0 , we cannot possibly have Vij (ϕ, J ) = 1 and
Vij (ϕ, J 0 ) = 0. Instead, we must have either Vij (ϕ, J ) = Vij (ϕ, J 0 ) = 0, Vij (ϕ, J ) = Vij (ϕ, J 0 ) = 1, or
Vij (ϕ, J ) = 0 and Vij (ϕ, J 0 ) = 1.
Thus, we can conclude that Vij (ϕ, J 0 ) ≥ Vij (ϕ, J) for J ⊆ J 0 , as stated in the Proposition.
1
Proof of Proposition 3
Remember from equation (8) that Θi (ϕ) ≡
P
−θ
Tk (τik wk )
and thus Θi (ϕ) corresponds to the sum of
k∈Ji (ϕ)
sourcing potentials of the countries belonging to the set Ji (ϕ). The (weakly) positive effect, holding Bi
−θ
constant, of any sourcing potential Tk (τik wk )
on input flows when (σ − 1) /θ ≥ 1 is then obvious from
inspection of equation (12). The positive effect of a reduction of any fixed cost fk on firm-level input flows
follows from the fact that, holding constant Bi and when σ−1 ≥ θ, a reduction in a fixed cost fk cannot possibly
reduce the profitability of any firm selecting into importing from any country j, but it may well increase it
directly if k = j or indirectly if selecting into k enhances the profitability of importing from j (remember that
the profit function features increasing differences whenever σ − 1 > θ).
Proof of Proposition 4
Given a vector of wages, equations (13) and (14) determine the equilibrium values of Bi and Ni . Notice that
the firm-level global sourcing problem depends only on Bi , wi and exogenous parameters, and not directly on
Ni . As a result, if a unique solution for Bi exists, all thresholds ϕ̃ij for any pair of countries (i, j) will be
pinned down uniquely, given wages. Hence, if a unique solution for Bi in equation (13) exists, we can ensure
that there will be a unique value of Ni solving (14). Let us then focus on studying whether (13) indeed delivers
a unique solution for Bi .
For given wages, the equilibrium condition (13) can be rearranged as follows
Z ∞
Z ∞
X
(σ−1)/θ σ−1
wi fe = Bi
(γΘi (ϕ))
ϕ
dGi (ϕ) − wi
fij dGi (ϕ) ,
(B.1)
ϕ̃iϑ(i)
ϕ̃iϑ(i) j∈J (ϕ)
i
where ϑ (i) denotes the location from which the least productive active firm in country i sources its inputs, or
formally, ϑ (i) = {j ∈ J : ϕ̃ij ≤ ϕ̃ik for all k ∈ J}. Note that ϑ (i) satisfies
ϕ̃iϑ(i)
σ−1
−θ (σ−1)/θ
Bi γTϑ(i) τiϑ(i) wϑ(i)
= wi fiϑ(i) .
(B.2)
P
−θ
Remember also that Θi (ϕ) ≡ k∈Ji (ϕ) Tk (τik wk ) , and Ji (ϕ) ⊆ J is the set of countries for which a firm
based in i with productivity ϕ has paid the associated fixed cost of offshoring wi fij .1
Computing the derivative of the right-hand-side of (B.1) with respect to Bi , and using (B.2) to eliminate
the effects working through changes in ϕ̃iϑ(i) , we can write this derivative as simply
!
P
(σ−1)/θ
σ−1
(γΘi (ϕ))
Bi − wi
fij
Z ∞ ∂ ϕ
j∈Ji (ϕ)
dGi (ϕ) > 0.
(B.3)
∂Bi
ϕ̃iϑ(i)
The fact that this derivative is positive follows directly from the firm’s global sourcing problem in (11). In
particular, holding constant the firm’s sourcing strategy Ji (ϕ) – and thus Θi (ϕ) –, it is clear that an increase
P
(σ−1)/θ
in Bi will increase firm-level profits ϕσ−1 (γΘi (ϕ))
Bi − wi j∈Ji (ϕ) fij . Now such an increase in Bi
might well affect the profit-maximizing choice of Ji (ϕ) – and thus Θi (ϕ) –, but firm profits could not possibly
be reduced by those changes, since the firm can always decide not to change the global sourcing strategy in
light of the higher Bi and still obtain higher profits.2 We can thus conclude that the right-hand-side of (B.1)
is monotonically increasing in Bi .
It is also clear that when Bi → ∞, all firms will find it optimal to source everywhere and the right-hand-side
1
To be precise, it could be the case that the least productive active firm in country i might source inputs from more
than one location. In such a case, the left-hand-side of equation (B.2) would incorporate the other location’s sourcing
potential, but equation (B.3) below would remain unaltered.
P
2
Following the same steps as in the proof of Proposition 1 we can show that both Θi (ϕ) and j∈Ji (ϕ) fij are actually
non-decreasing in Bi . This result is immaterial for the proof of existence and uniqueness in the case of free entry, but
can be used to prove the same result for the case of an exogenous number of firms Ni .
2
of (B.1) becomes
X
Bi γ
k∈J
Tk (τik wk )
−θ
(σ−1)/θ Z
∞
ϕσ−1 dGi (ϕ) − wi
ϕ
X
fij
j∈J
i
and thus goes to ∞. Conversely, when Bi → 0, no firm can profitably source to any location, given the positive
fixed costs of sourcing, and thus the right-hand-side of (B.1) goes to 0.
It thus only remains to show that the right-hand-side of (B.1) is a continuously non-decreasing function
of Bi . This may not seem immediate because firm-level profits jump discontinuously with Bi whenever such
changes in Bi lead to changes in the global sourcing strategy of firms. It can be shown, however, that
Z ∞ ∂ (Θi (ϕ))(σ−1)/θ Bi ϕσ−1
dGi (ϕ)
∂Bi
ϕ̃iϑ(i)
is continuously differentiable in Bi . To see this, one can first follow the same steps as in the proof of Proposition
1 to show that Θi (ϕ; Bi ) must be non-decreasing not only in ϕ, but also in Bi and Bi ϕσ−1 . We can then
(σ−1)/θ
represent (Θi (ϕ))
Bi ϕσ−1 as a non-decreasing step function in ϕ, in which the jumps occur at different
σ−1
levels of Bi ϕ
. This is analogous to writing

1/(σ−1)

θ1 Bi ϕσ−1
if ϕ < b1 /Bi



 θ2 Bi ϕσ−1 if b1 /B 1/(σ−1) ≤ ϕ < b2 /B 1/(σ−1)
i
i
(σ−1)/θ
.
(B.4)
(Θi (ϕ))
Bi ϕσ−1 =
..
..


.
.



1/(σ−1)
θJ Bi ϕσ−1
if bJ−1 /Bi
≤ϕ
Hence, we have
Z
∞
(σ−1)/θ
(Θi (ϕ))
Bi ϕσ−1 dGi (ϕ)
Z
1/(σ−1)
b1 /Bi
θ1 Bi ϕσ−1 dGi (ϕ) +
=
ϕ̃iϑ(i)
ϕ̃iϑ(i)
Z
1/(σ−1)
b2 /Bi
θ2 Bi ϕσ−1 dGi (ϕ) + ... +
1/(σ−1)
Z
b1 /Bi
∞
1/(σ−1)
θJ Bi ϕσ−1 dGi (ϕ) .
bJ−1 /Bi
It is then clear that the derivative of this expression with respect to Bi is a sum of continuous functions of Bi ,
and thus is continuous in Bi itself.3
Using similar arguments we can next show that
!
P
fij
Z ∞ ∂ wi
j∈Ji (ϕ)
dGi (ϕ)
(B.5)
∂Bi
ϕ̃iϑ(i)
is
Bi . First, a simple proof by contradiction can
to show
that
be used σ−1
P also continuously differentiable in σ−1
σ−1
f
is
non-decreasing
in
B
ϕ
.
More
specifically,
suppose
that
for
B
ϕ
>
B
ϕ
we
also
i
i
i
j∈Ji (ϕ) ij
H
L
P
P
σ−1
had j∈JiH fij < j∈JiL fij . Given the non-decreasing dependence of Θi (ϕ) on Bi ϕi , we would then have
(γΘiH (ϕ))
(σ−1)/θ
Bi ϕσ−1
L
−
X
(σ−1)/θ
j∈JiH
fij > (γΘiL (ϕ))
which clearly contradicts JiL being optimal given Bi ϕσ−1 = Bi ϕσ−1
L
Bi ϕσ−1
L
−
X
. With this result,
j∈JiL (ϕ)
P
fij ,
fij can then
j∈Ji (ϕ)
be expressed as a step function analogous to that in (B.4), in which the position of the steps is continuously
differentiable in Bi . This in turn ensures that (B.1) is continuous in Bi and concludes the proof that there
3
The two last expressions assume that there are J − 1 jumps, implicitly assuming that at each jump, only one
country is added to the sourcing strategy. Given the complementarities in our model, and as pointed out in footnote 1,
an increase in Bi might well lead to the simultaneous inclusion of two or more locations. In such a case, there would be
less than J − 1 jumps, but the continuous differentiability of (B.4) would clearly be preserved.
3
exists a unique Bi that solves equation (13).
B.2
Equilibrium in the Complements-Pareto Case
In Proposition 1, we have established that whenever σ − 1 > θ, the model delivers a ‘pecking order’ in the
extensive margin of offshoring. For each country i, we can then rank foreign countries in terms of some index
of sourcing appeal. We shall assume, for the time being, that this ranking is strict in the sense that the set of
firms sourcing from any two distinct countries j and k do not coincide; more specifically, the measure of firms
sourcing from the strictly more attractive country is necessarily larger. This assumption is fairly immaterial,
as we shall show below.
Suppose also for simplicity that ϕ̃i = ϕ̃ii , so that all firms that source a positive amount (i.e., all firms that
are active) do so, at least in part, from Home. Denote by r the r-th least appealing country from which firms
from i source from, so Home is r = 1. Define also
Θir =
r
X
−θ
Tj (τij wj )
.
j=1
Note that Proposition 1 implies that the set of productivity thresholds ϕ̃ir defined in the main text will be
such that any firm with productivity above that threshold ϕ̃ir necessarily sources from country r, or in terms
of the notation in equation (17), Iir (ϕ) = 1 for all ϕ > ϕ̃ir .
In light of the profit function in 10, these thresholds are given by
ϕ̃σ−1
i1
=
ϕ̃σ−1
ir
=
wi fi1
(σ−1)/θ ;
−θ
(σ−1)/θ
γ
Bi Ti (wi )
γ (σ−1)/θ B
i
wi fir
(σ−1)/θ
Θir
(σ−1)/θ
− Θir−1
for r > 1.
(B.6)
Consider now the industry equilibrium. Using the above notation, we can write the free entry condition (13)
as
Z ∞
J
J−1
X
X (σ−1)/θ Z ϕ̃ir+1
ϕσ−1 dGi (ϕ) − wi
fir
γ (σ−1)/θ Bi
Θir
dGi (ϕ) = wi fe .
ϕ̃ir
r=1
ϕ̃ir
r=1
Next, invoking the Pareto distribution, Gi (ϕ) = 1 − (ϕi /ϕ)κ , and solving for the integrals, we obtain:
γ (σ−1)/θ Bi
J−1
X
(σ−1)/θ
Θir
r=1
J
σ−κ−1
κ (ϕ̃ )σ−κ−1 − (ϕ̃
X
ϕi κ
ir
ir+1 )
− wi
fir
= w i fe .
κ ϕi
κ−σ+1
ϕ̃ir
r=1
Plugging the thresholds in (B.6) delivers
κ
κ−σ+1
ϕi
ϕ̃i1
κ
κ
wi fi1 −
κ−σ+1
ϕi
ϕ̃i2
(ϕ̃ )
κ J−1
X (σ−1)/θ ir
+ κ ϕi
Θir
κ
(σ−1)/θ
Θ1
(σ−1)/θ
Θi2
(σ−1)/θ
− Θ1
−κ wi fir
(σ−1)/θ
(σ−1)/θ
Θir
−Θir−1
wi fi2
− (ϕ̃ir+1 )
−κ wi fir+1
(σ−1)/θ
(σ−1)/θ
Θir+1
−Θir
κ−σ+1
r=2
− wi
J
X
fir
r=1
(σ−1)/θ
Expanding the summation involving the terms Θir , canceling the terms in Θir
we finally obtain
κ
J σ − 1 X ϕi
fir = fei .
κ − σ + 1 r=1 ϕ̃ir
4
(σ−1)/θ
−Θir−1
ϕi
ϕ̃ir
κ
= wi fe .
, and simplifying,
(B.7)
It is worth emphasizing that this equation holds regardless of the relative values of σ − 1 and θ as long as these
parameters and the degree of heterogeneity in fixed costs are such that a hierarchy in sourcing decisions exists.
The key insight of Proposition 1 is that σ − 1 > θ is a sufficient condition for this hierarchical structure to
emerge regardless of the values of the fixed costs of offshoring fij .
In deriving equation (B.7), we have assumed that, from the point of view of firms in country i, the ranking
of the appeal of the various source countries was strict. Whenever σ −1 > θ, the complementary in the sourcing
decisions of firms implies, however, that the set of firms sourcing from two distinct countries j and k can in
principle coincide. Intuitively, it could be the case that sourcing from country j can only be profitable when a
firm in i also sources from country k, and vice versa. Fortunately, the above analysis can be readily adapted to
deal with this sort of situations. More specifically, it suffices to define a merged country j ∪ k with a sourcing
potential equal to the sum of j’s and k’s sourcing potential and with a sourcing fixed cost also equal to the sum
of j’s and k’s sourcing fixed costs. This merged country can then be assigned a position r in the ranking of
sourcing appeal across countries, and then it only suffices to be careful to run the summations in the expressions
above replacing J with J − M where M is the number of countries that have been dropped by being merged
with other countries. It is then straightforward to see that one can again find its way to equation (B.7).
Note that equation (B.7) in turn implies that
Z ∞ X
σ−1
+ 1 fei ,
fij dGi (ϕ) + fei =
κ−σ+1
ϕ̃i
j∈Ji (ϕ)
and thus plugging this expression in (14), we can conclude that
Ni =
(σ − 1) ηLi
,
σκfei
(B.8)
as claimed in footnote 12.
Some of the above expressions are useful in deriving the gravity equation in (18) characterizing bilateral
manufacturing trade flows in the case of independent entry decisions (i.e., σ − 1 = θ). To see this, begin with
equation (15) and plug the formula for the Pareto distribution in (16) to obtain
σ−1−κ
−θ
Mij = (σ − 1) Ni Bi γTj (τij wj )
κϕκi
(ϕ̃ij )
.
κ−σ+1
With independent entry decisions, the threshold in (B.6) simplifies to
ϕ̃σ−1
=
ij
wi fij
γBi Tj (τij wj )
−θ
.
Plugging this expression for ϕ̃σ−1
into the previous one for Mij , imposing θ = σ − 1, and manipulating the
ij
resulting expression in a manner analogous to the derivation of the general gravity equation in (17), we obtain
κ
−κ
Mij = Ni (Bi ) σ−1 (τij )
Qj
κ
1− σ−1
ϕκi (wi fij )
P
k
Nk (Bk )
κ
σ−1
−κ
(τkj )
κ
κ
1− σ−1
(ϕ̃k ) (wk fkj )
.
Using (3) and (B.8) and defining
Ψi =
fei −κ −κ κ/(σ−1)−1
ϕ Pi wi
,
Li i
we thus obtain equation (18) in the main text.
B.3
Details on Some Extensions of the Model
Towards the end of section 2, we briefly mentioned three extensions of our theoretical model. In this section of
the Online Appendix we provide more details on these extensions. Because we do not incorporate these features
into the structural estimation and quantitative analysis, we will limit ourselves to discussing the effects of these
extensions on firm behavior, and not on the aggregate implications of the model.
5
A. Tradable Final Goods: Exporting and Importing
In the benchmark model in the main text, we have assumed that final-good varieties are prohibitively costly to
trade across borders. We have done so to focus our analysis on the determinants and implications of selection
into global sourcing. In this section, we briefly relax this assumption and demonstrate the existence of intuitive
complementarities between the extensive margin of exporting and that of importing at the firm level.
X
Suppose then that trade in final-varieties is only partially costly and involves both iceberg trade costs τij
X
as well as fixed costs fij of exporting. Firm behavior conditional on a sourcing strategy is largely analogous
to that in section 3.1. In particular, after observing the realization of its supplier-specific productivity shocks,
each final-good producer will continue to choose the location of production for each input to minimize costs,
which will lead to the same marginal cost function ci (ϕ) obtained above in equation (9). The main novelty
is that the firm will now produce output not only for the domestic market but also for a set of endogenously
chosen foreign markets, which constitute the firm’s ‘exporting strategy’. We can then express the problem of
determining the optimal exporting and sourcing strategies of a firm from country i with core productivity ϕ
as:

max
M
Iij
∈{0,1}J
j=1
X
Iik ∈{0,1}J
k=1
πi ϕ, IM , IX
= ϕ(σ−1) γ
J
X
(σ−1)/θ
−θ 
M
Iij
Tj (τij wj )
j=1
−wi
J
X
M
Iij
fij − wi
j=1
J
X
X
X
Iik
τik
1−σ
Bk
k=1
J
X
X X
Iik
fij ,
k=1
Note that IM and IX denote the vector of extensive margin import and export decisions, respectively. It is
straightforward to see that, whenever
(σ − 1) /θ > 1, this more general profit function continues to feature
increasing differences in IjM , IkM for j, k ∈ {1, ..., J} with j 6= k, and also features increasing differences in
IjM , ϕ for any j ∈ {1, ..., J}. As a result, Proposition 1 continues to apply here and we obtain a ‘pecking
order’ in the extensive margin of offshoring in the complements case.
The key new feature of the above profit function πi ϕ, IM , IX is thatit also exhibits increasing differences
in IjM , IjX for any j, k ∈ {1, ..., J} and increasing differences in IjX , ϕ for any j ∈ {1, ..., J}. This has at
least two implications. First, regardless of whether σ − 1 > θ or σ − 1 < θ, any change in parameters that
increases the sourcing capability Θi (ϕ) of the firm – such as reduction in any τij or an increase in any Tj
– will necessarily lead to a (weak) increase in the vector IX , and thus (weakly) increase the export margin
of exporting. Second, restricting attention to the complements case (σ − 1) /θ > 1, the model delivers a
complementarity between the exporting and importing margins of firms. For instance, holding constant the
vector of residual demand parameters Bi , reductions in the costs of trading final goods across countries will
not only increase the participation of firms in export markets, but will also increase the extensive margin of
X
sourcing, in the sense that vector IM is non-increasing in τik
. Furthermore, as firm productivity increases, the
participation of firms in both export and import markets increases, and at a faster rate than when one of these
margins is shut down.
B. Introducing Value Added in Assembly
In our benchmark model, we assume that the marginal cost of final-good producers consists of the cost of
procuring a measure one of intermediate inputs. Here we consider the case in which final-good producers also
hire local labor to assemble the bundle of inputs. In particular, let the marginal cost for firm ϕ based in country
i of producing a unit of a final-good variety now be
ci (ϕ) =
1
ϕ
Z
1
µ
(1−µ)(1−ρ)
(wi ) (zi (v, ϕ; Ji (ϕ)))
1/(1−ρ)
dv
,
(B.9)
0
which is analogous to equation (5) except for value-added (labor payments) accounting for a share µ ∈ (0, 1)
of the costs of assembly.
It should be clear that the use of labor in final-good production does not affect the location from which
6
inputs are sourced conditional on a sourcing strategy. Following the same steps as in the benchmark model,
we find the same intermediate input import shares as in equation (7), the same sourcing potential as in (8),
and a resulting profit function conditional on a sourcing strategy Ji (ϕ) equal to
X
−µ(σ−1)
(1−µ)(σ−1)/θ
πi (ϕ) = ϕσ−1 (wi )
(γΘi (ϕ))
Bi − wi
fij ,
(B.10)
j∈Ji (ϕ)
which is analogous to equation (10) in the main text. The two main differences are that country i’s wage rate
now directly affects operating profits, and that the elasticity of firm profits to the firm’s sourcing capability is
equal to (1 − µ) (σ − 1) /θ rather than (σ − 1) /θ, as in our benchmark model. The profit function πi continues
to be supermodular in ϕ and Θi (ϕ), but now features increasing differences in (Iij , Iik ) for j, k ∈ {1, ..., J}
and j 6= k, whenever (1 − µ) (σ − 1) /θ > 1. As a result, the main Propositions 1-3 characterizing the optimal
sourcing strategy and firm-level comparative statics continue to hold in this extension, except that the region
of the parameter space in which import entry decisions are complementary is given by (1 − µ) (σ − 1) /θ > 1
instead of (σ − 1) /θ > 1.
Clearly, for large values of µ it is possible that (σ − 1) /θ > 1 but (1 − µ) (σ − 1) /θ < 1. One might then
be concerned that, because in our estimation we back out σ from markup data and θ from the effect of costshifters on the import shares in (9), we might infer that the complements case best describes the data when
in fact (1 − µ) (σ − 1) /θ < 1, and thus import entry decision are substitutes. Nevertheless, as we describe
in Appendix A.1, when constructing our measure of domestic intermediate input purchases, we add a firm’s
total production-worker wage bill in manufacturing to its total expenditures on material inputs. We include
production worker wages in a firm’s input costs because our complete-contracting model does not determine
whether intermediate inputs are sourced from external suppliers or are provided within firm boundaries, thus
constituting value added (which maps to the share µ in this extension).
In sum, our construction of domestic input shares is such that our model interprets some of the domestic
intermediate inputs sourced by the firm as being provided within the firm by production workers. Of course,
these production worker services do not constitute the entire amount of domestic labor services used by the
firm. Yet, this is unlikely to overturn our key condition (σ − 1) /θ > 1 for two reasons. First, the majority of
non-production worker labor in our framework is more likely to constitute a fixed rather than a marginal cost,
and will therefore not affect µ. Second, even if some non-production worker labor relates to marginal costs,
these are likely a small fraction, and our benchmark estimates of σ = 3.85 and θ = 1.79. imply that small
changes in µ will not affect our conclusion.
C. Endogenous Input Variety
Our benchmark model assumes that all final good producers use a measure one of inputs. We next briefly
outline how our results extend and generalize to the case in which the final-good producer is allowed to choose
the complexity of production, as captured by the measure of inputs used in production (see Acemoglu et al.,
2007). As we shall see, this ends up producing an equilibrium essentially identical to the one we have described
above, but with additional implications for how the measure of inputs purchased by firms changes with firm
productivity.
The formal details of this extension are as follows. Final-good production continues to combine inputs
according to a CES technology, but we now let the measure of inputs be firm-specific and given by ni (ϕ).
More specifically, we generalize the marginal cost function in (5) as follows:
ci {j
1
(v)}v=0
1
1/(ρ−1)−λ
, ϕ = ni (ϕ)
ϕ
Z
!1/(1−ρ)
ni (ϕ)
τij(v) aj(v) (v, ϕ) wj(v)
1−ρ
dv
.
0
A higher value of ni (ϕ) enhances productivity via an input variety effect. As in Acemoglu et al. (2007), we
1/(ρ−1)−λ
introduce the term ni (ϕ)
in front of the integral in order to control the importance of variety effects
for productivity via a parameter λ disentangled from the elasticity substitution between inputs ρ. In order to
create a check on the optimal degree of complexity, we assume that firms face a fixed cost equal to wi ni (ϕ) fin
when combining ni (ϕ) inputs in production. As in our benchmark model, in each of the countries in which the
final-good producer incurred the fixed cost of sourcing, there is a competitive fringe of potential suppliers that
can provide differentiated inputs to the firm with a firm-specific intermediate input efficiencies drawn from a
7
Fréchet distribution.
With a continuum of inputs, the equilibrium measure of inputs used in production by a final-good producer
has no implications for the distribution of input prices faced by that producer. Exploiting this feature, we can
use derivations analogous to those in the benchmark model and in Eaton and Kortum (2002), to write the
marginal cost of production as
1
−λ
−1/θ
ci (ϕ) = (ni (ϕ)) (γΘi (ϕ))
,
(B.11)
ϕ
and the firm’s profits conditional on a sourcing strategy Ji (ϕ) as
πi (ϕ) = ϕσ−1 (ni (ϕ))
(σ−1)λ
(γΘi (ϕ))
(σ−1)/θ
Bi − w i
X
fij − wi ni (ϕ) fin ,
j∈Ji (ϕ)
where Bi is again given in (3). It is clear that conditional on a sourcing strategy Ji (ϕ) – and thus a value of
Θi (ϕ) – this profit function is supermodular in productivity and the measure of inputs ni (ϕ).4 Hence, a novel
prediction from this extension is that more productive firms will tend to source more inputs from all sources
combined (domestic and foreign) than less productive firms, even when these firms share a common sourcing
strategy.5 In the complements case with σ − 1 > θ, this variant of the model also predicts that more productive
firms will tend to buy (weakly) more inputs from any source than less productive firms.
As pointed out in the main text, it is important to emphasize that input-specific fixed costs do not serve as
a substitute for country-specific fixed costs of sourcing. By this we mean that, in the absence of the latter type
of fixed costs, our framework would not be able to account for the key facts motivating our benchmark model,
since in such a case, all firms would source inputs from all countries, thus violating the patterns in Figure 1
and Table 1 in the Introduction.
4
For the choice of ni (ϕ) to satisfy the second-order conditions for a maximum, we need to impose that the efficiency
gains from input variety are small enough to guarantee that (σ − 1) λ < 1 holds.
5
Although our benchmark model is also consistent with more productive firms importing more inputs than less
productive firms, with a common measure of inputs, this could only be rationalized by having more productive firms
sourcing less inputs domestically than less productive firms.
8
C
C.1
Online Data Appendix (Not for Publication)
Sample
Table C.1 provides details of all firms in the Economic Censuses with positive sales and employment. The
first row corresponds to firms that consist only of manufacturing establishments (“M” firms). The second row
presents information for all firms with one or more manufacturing establishments and at least one establishment
outside of manufacturing (“M+” firms). Together, these two types of firms comprise our sample.
Table C.1: Sample of firms
Firms
Imports
$millions
Empl
000s
Sales
$billions
Fraction
Importers
238,800
11,500
4,006,400
300,300
7,600
76,020
829,592
100,169
241,077
141,753
5,869
20,581
77,400
3,489
6,365
1,239
9,527
12,620
2,305
2,259
0.23
0.77
0.03
0.31
0.51
4,564,600
1,388,612
113,704
27,950
0.06
Firm Type
Manufacturing Only (M)
Manufacturing Plus (M+)
Other (O)
Wholesale Only (W)
Wholesale and Other (WO)
Total
Notes: Table provides information on firms in the Economic Census with positive sales and
employment. Analysis in paper based on all M and M+ firms. Numbers rounded for disclosure
avoidance. Imports exclude products classified under mining.
C.2
Premia and Decomposition
Following Bernard et al. (2007), we report employment, sales, and productivity premia for firms that import in
2007. To do so, we regress the log each of these variables on an importer dummy and industry controls. Table
C.2 reports the results. The top panel presents results using 2007 values of firm size and productivity and the
bottom panel uses 2002 values. The first column of the table shows that firms importing in 2007 are larger and
more productive than non-importers. In addition, these premia for 2007 import status were present in 2002.
The magnitude of these import premia is similar to those typically found for exporters, with importers being
on average about three times larger and about 6-7% more productive than non-importers.
We confirm the importance of the extensive margins of trade, both in terms of the number of imported
products and the number of importing firms, first documented by Bernard et al. (2009). Following those
authors, we decompose total U.S. imports MU S,j from country j according to
!
OU S,j
MU S,j
f irms
prods
ln(MU S,j ) = ln(NU S,j ) + ln(NU S,j ) + ln
+ ln
,
prods
OU S,j
NUf irms
S,j × NU S,j
where OU S,j is the number of firm-product combinations with positive imports from j. The first two terms
prods
represent the unique numbers of firms (NUf irms
S,j ) importing and products (NU S,j ) imported from country j.
The third term, referred to as the density, captures the fraction of firm-production combinations with positive
import values. The final term captures the intensive margin. It measures the average import value per firmproduct observation, for all combinations with positive imports. Table C.3 presents coefficients from OLS
regressions of the logarithm of each margin on the logarithm of total trade. As is well known, these OLS
coefficients sum to one, with each coefficient representing the share of overall variation explained by each
margin. As in previous work, we find that variation in the extensive margins account for the majority of the
variation in aggregate import volume across countries. The extensive margins account for a total of 65 percent,
while the intensive margin explains just 35 percent of the total variation.
9
Table C.2: Premia for 2007 importers
All
Firms
Non-2002
Importers
2007 Log employment
2007 Log sales
2007 Log value-added per worker
1.552
1.737
0.060
1.269
1.399
0.039
2002 Log employment
2002 Log sales
2002 Log value-added per worker
1.466
1.638
0.074
1.154
1.270
0.052
Notes: All results are from OLS regressions of the variable listed on the
left on an indicator equal to one if the firm imported in 2007. The first
column includes all firms. The second column is based on the subset of
firms that did not import in 2002. Results with 2002 variables are based
only on the subset of firms that existed in 2002. All regressions include
four digit industry controls. All coefficients are statistically significant
at the 1% level.
Table C.3: Extensive and intensive margin decomposition
Log of number
of importing
firms
Log of number of
imported products
Log of
Density
Log of average
import value per
product per firm
0.541
(0.016)
0.85
221
0.535
(0.015)
0.84
221
-0.426
(0.014)
0.81
221
0.350
(0.018)
0.64
221
Adj. R2
Observations
Notes: Each column corresponds to results from regressing the log of each margin on the log
of total import values. The coefficients are a measure of the fraction of variation in aggregate
import volumes across countries explained by that margin. Density represents the fraction of
all possible firm-product combinations with positive import values. The estimated coefficients
sum to one.
C.3
Premia Figures
In the Introduction, we plot the relationship between the log of firm sales and the minimum number of countries
from which a firm sources. To construct the figure, we regress the log of firm sales on cumulative dummies
for the number of countries from which a firm sources and industry controls. The omitted category is nonimporters, so the premia are interpreted as the difference in size between non-importers and firms that import
from at least one country, at least two countries, etc. The horizontal axis denotes the number of countries from
which a firm sources, with 1 corresponding to firms that use only domestic inputs. The introduction figure
controls for firm industry with variables that measure the share of a firm’s employment in four-digit NAICS
industries. (These are simply industry fixed effects for all firms that span only one industry.) Here we show
that the patterns depicted in the introduction are robust when considering a firm’s size prior to importing and
when controlling for the products that a firm imports or exports. Figure C.1 plots the relationship between
a firm’s log sales in 2002 and the number of countries from which it sources in 2007, for firms that did not
import in 2002. Figure C.2 depicts the relationship when controlling for the number of products a firm imports
10
(left panel) and the number of products the firm exports (right panel). In additional undisclosed results,
available upon request, we show similar patterns when using firm employment and the log of value-added labor
productivity.
0
2002 Premium
1
2
3
Figure C.1: Importer premia for firm’s 2002 sales, limited to firms that do not import in 2002,
1
2
3
4
5
6
7
8
9
Minimum number of countries from which firm sources
Premium
10
95% CI
Figure C.2: Importer premia with product controls
(a) Controlling for number of products imported by the firm (b) Controlling for number of products exported by the firm
C.4
Measuring Total and Domestic Input Use
We construct a measure of a firm’s total intermediate input purchases using material input purchases from the
Censuses of Manufactures, Construction, and Mining and merchandise purchases from the Census of Wholesale.
This approach ensures a more complete metric of a firm’s inputs than traditional measures based purely on
manufacturers’ use of materials because it takes into account the input usage of both the manufacturing as
11
well as the wholesale establishments of U.S. firms.6
The model does not take a stance on whether intermediate inputs are sourced within or across firm boundaries. For the purposes of this paper, this is of little relevance for international transactions, but it might lead
to important biases in our measure of overall input use if a significant share of domestic inputs is produced
within the firm and is recorded as value added. For this reason, we add a firm’s total production-worker wage
bill to the firm’s total input purchases. In terms of our model, this corresponds to assuming that the final-good
producer employs production workers to manufacture internally any inputs produced by the firm, while it uses
the other factors of production (nonproduction workers, physical capital, and land) to combine intermediate
inputs and cover all fixed costs. This approach is also motivated by the notion that the services typically
provided by production workers are particularly offshorable. Table C.4 presents summary statistics on foreign
input shares. The mean share of imported inputs is 0.14, with a standard deviation of 0.23.
Table C.4: Summary statistics on firms’ share of foreign input sourcing
mean
std. dev.
median
75 pctile
90 pctile
0.14
0.23
0.03
0.15
0.47
Notes: This table reports statistics on the share of imported inputs for the subset of offshoring firms.
This new measure of total intermediate input purchases is highly correlated with traditional input measures
for manufacturing firms based on reported inputs of materials and parts from only the Census of Manufactures.
A firm’s share of inputs from country j, χij , is computed as imports from j divided by total input purchases.
A firm’s share of domestic inputs, χii , is simply the difference between its total input purchases and imports,
divided by total input purchases. A very small fraction of firms has negative values for their implied domestic
input purchases using this approach. This occurs when a firm’s total input purchases are less than its imports.
Likely explanations for this are measurement error and imports of capital equipment. To address any potential
bias from dropping these firms, we therefore use the maximum of a firm’s implied domestic input use and its
production worker wages as its domestic input usage and adjust total input usage accordingly.7
C.5
Robustness of Country Sourcing Potentials
In this section we further elaborate on our approach to estimating and interpreting country sourcing potentials.
To assess the robustness of our estimates, we re-estimate sourcing potentials using firms that import from one
country, 2 countries, 3 countries, 4-9 countries, 10-19 countries, and 20+ countries. The correlation coefficients
between our baseline estimates and those using the samples of firms that source from just one country, and
those sourcing from just 2 countries are quite low. This seems to be driven by strange selection criteria, since a
firm sourcing only from a non-top country (e.g., El Salvador) is quite different from the average firm, and not
representative of the aggregate patterns our theory seeks to explain. When we limit the set of countries to the
top 10 countries based on number of firms (as listed in Table 1), we find a correlation coefficient of 0.708 for
firms sourcing from just one country. The correlation coefficient between our baseline estimates and the other
6
The wholesale sector includes a significant number of plants that design goods and coordinate production, often
by offshoring, but do not perform physical transformation activities (see Bernard and Fort, 2015, for a description).
Ignoring these plants’ inputs could severely understate multi-sector firms’ total inputs. For example, Feenstra and
Jensen (2012) find that a significant fraction of some manufacturing firms’ imports are not reported as input purchases.
We address this issue by including a firm’s wholesale plants’ inputs. Although there is no way to measure inputs for
establishments outside the manufacturing and wholesale sectors, those plants are much less likely to be involved in
production or importing. An alternative approach would be to use an estimate of the demand elasticity σ and exploit
the CES structure of our model to back out input usage from sales data.
7
This approach leads to a tiny number of firms with zero implied domestic sourcing. In an alternative approach,
we have limited the sample of firms in the structural analysis to firms with at least fifty percent of their sales in
manufacturing. We do not report the numbers from this analysis here to minimize disclosure issues, but note that the
numerical results are very similar and the qualitative interpretations remain unchanged.
12
samples is higher for all other samples (we have not disclosed each correlation due to disclosure concerns). The
correlation coefficient between our baseline estimates and the sample of firms sourcing from three countries is
0.417 across all countries, and becomes substantially higher as the sourcing set grows. As an alternative check,
we also examined the trade-weighted correlation coefficients between our baseline estimates and those based
on each of the samples described above. The trade-weighted correlation coefficients for all subsamples are in
the same range, or substantially higher, as the coefficient for firms sourcing from at least three countries.
When estimating sourcing potentials, we have also noticed that the estimates are somewhat sensitive to
controlling for firm size. Large firms tend to have larger domestic shares, a feature at odds with our theory. On
the other hand, there are certain countries from which some extremely large firms import disproportionately
large shares of inputs (e.g., Mexico). This heterogeneity is beyond the scope of this paper, but suggests there
is substantial scope for exploring this variation in future work.
C.6
Estimation of the Trade Elasticity
We identify the firm-level trade elasticity, θ, using variation in country wages. The wage data are from the
International Labor Organization reported average nominal monthly wages in local currencies for 2007. These
wages were converted to USD using exchange rates from the World Bank. When data for 2007 were missing,
we used data for the next closest year within a two-year range. To address the fact that skill levels differ across
countries, we follow Eaton and Kortum (2002) and use human capital adjusted wages, wiHCadj = (wi )e−0.06Hi ,
where Hi is the years of schooling from Barro and Lee (2010) and 0.06 represents the return to education
estimated in Bils and Klenow (2000).
Table C.5 presents several robustness tests for estimation of the firm-level trade elasticity. We use data on
country GDP from the World Bank Development Indicators (WDI) and country tariffs are the simple average
of country tariffs from the World Bank WITS database. Column 1 shows that our estimate of θ is somewhat
smaller, suggesting greater complementarity, when controlling for GDP. Column 2 shows that it is virtually
unchanged when controlling for tariffs. In column 3 we report the results of constraining the coefficient on
tariffs and wages to be the same. Finally, column 4 shows results when we do not control for the number of
firms in an country.
In section 5.2 of the main text, we claim that the orthogonality condition that ensures that our firm-level
estimates of θ are consistent, does not guarantee that the estimate in column 5 is consistent as well. We now
substantiate this claim. Remember from equation (19) that
χnij
−θ
= Tj (τij wj ) nj ,
χnii
(C.1)
where nj represents measurement error, or a shock that is only observed by firms after their sourcing strategy
−θ
is selected. Under these conditions, we have E log nj | log Tj (τij wj )
= 0. In the main text, we leveraged
−θ
this orthogonality condition to obtain a consistent estimate of log ξj = log Tj (τij wj )
using firm-level data
and then projected this estimate on human-capital-adjusted wages to obtain an estimate of θ in a simple
cross-country regression.
As pointed out in sections 3.4 and 5.2, as a potential alternative way to back out θ, we could have simply
aggregated the import data at the country-level and estimated θ exploiting the relationship:
X
X
−θ
χnii nj .
(C.2)
χnij = Tj (τij wj )
{n:j∈J n }
{n:j∈J n }
In the main text, we note that if nj = 1, this implies that a gravity equation that controls for the domestic
input purchases of firms that source from j should deliver a trade elasticity equal to θ. In the presence of
measurement error, i.e., nj 6= 1, it is not clear however that such a regression would provide a consistent
estimate of θ. To see this, note that we can write equation (C.2) as




X
X
−θ
log 
χnij  − log 
χnii  = log Tj τij
− θ log wj + uij ,
{n:j∈J n }
{n:j∈J n }
13
Table C.5: Robustness estimates for the firm-level trade elasticity
Dependent variable is log ξ
IV R1
-1.31
(0.28)
HC adjusted wage
IV R2
-1.81
(0.71)
log(1+tariff)+ log wage
log distance
-0.49
(0.22)
0.17
(0.24)
0.34
(0.13)
0.23
(0.22)
0.48
(0.18)
0.18
(0.18)
Common language
log R&D
log KL
Control of corruption
log GDP
log (1+tariff)
log no. of firms
0.00
(0.10)
-14.19
(4.75)
57
48.04
Constant
Observations
F-Stat
IV R3
IV R4
-2.08
(0.75)
-0.72
(0.35)
0.24
(0.32)
0.52
(0.13)
0.45
(0.40)
0.61
(0.31)
-1.54
(0.58)
-0.54
(0.26)
0.12
(0.26)
0.49
(0.11)
0.30
(0.33)
0.53
(0.27)
-0.88
(0.36)
0.15
(0.32)
0.50
(0.09)
0.60
(0.45)
0.73
(0.36)
6.75
(9.78)
-0.03
(0.13)
-11.14
(2.36)
57
6.30
0.01
(0.12)
-10.31
(1.96)
57
3.91
-11.76
(2.73)
58
7.36
Notes: Standard errors in parentheses. The human capital-adjusted wage
is instrumented by population. In IV R3, the coefficient on wages and
tariffs is constrained to be identical. For this specification, both population and tariffs are the instruments. F-Stat is the Cragg-Donald Fstatistic for the excluded instrument(s).
where

uij = log 

χnii
X
P
{n:j∈J n }
{n:j∈J n }
χnii
nj  .
−θ
−θ
and nj are uncorrelated, log Tj (τij wj )
and uij may well be
It is then clear that even if log Tj (τij wj )
correlated because the sourcing potential of a country directly impacts the set of firms sourcing from j (i.e., n
such that j ∈ J n ), as well as the share of their spending on domestic inputs (i.e., χnii ). For these reasons, we
treat the estimate of θ in column 5 of Table 4 with caution and consider instead the one in column 2, based
on firm-level data, as our benchmark one.
C.7
Moments and Model Fit - Various Models
In Tables C.6 and C.7 we present the value of the moments used in the estimation for various models at the
estimated parameters.
14
Table C.6: Moments and other statistics at estimated parameters – Various Models
Targeted moments:
m̂1 (δ̂) (first element)
m̂1 (δ̂) (second element)
m̂2 (δ̂): corr(model,data)
m̂3 (δ̂)
Share of firms sourcing from China
Untargeted moments:
Share of imports in total sourcing
Imports by ctr: corr(model,data)
Share of China in aggregate imports
Total following pecking order
Baseline
model
Independent
entry decisions
model
(θ = 2.85)
Universal
importing
model
Common
fixed costs
across countries
model
Data
0.268
0.073
0.984
0.498
0.080
0.268
0.073
0.984
0.498
0.080
1.000
1.000
0.000
0.498
1.000
0.174
0.067
0.681
0.498
0.174
0.258
0.085
0.500
0.086
0.037
0.783
0.201
0.338
0.035
0.784
0.206
0.340
0.162
0.717
0.118
1.000
0.040
0.671
0.244
0.091
0.186
0.137
0.360
Notes: The moments are described in the text above equation (21). The detailed list of m̂2 (δ̂) for the various models is presented in Table C.7 below. One may be surprised to see that the Total following pecking order statistic is not equal to zero
for the Common fixed costs across countries and Universal importing models. We note that for those models, the share of
firms following the pecking order is equal to zero up to row 9 in Table 6.
C.8
Lower Chinese Fixed Costs Counterfactual
As an alternative to an increase in Chinese sourcing potential from 1997 to 2007, we explore the effects of a
change in fixed costs of sourcing from China that is calibrated to explain the growth in the share of aggregate
imports from China from 1997 to 2007 (same target as in the main section of the paper). We find that under
constant sourcing potentials, in 1997 fixed costs of sourcing from China would have needed to be 8.85 times
larger than their size in 2007. Table C.8 is analogous to Table 7 in the main text and illustrates the third
country effects of this shock to the fixed costs of sourcing from China. It is visible that the third market effects
are qualitatively similar to those in obtained for an increase in the Chinese sourcing potential, but compared
to the data, this alternative counterfactual underpredicts the fraction of firms that would have imported from
China in 1997. With respect to the price index, the effects are similar to the Chinese sourcing potential increase
discussed in the main text, also implying about a 0.19 percent fall in the price index. Finally, this counterfactual
fails to generate an expansion in the U.S. and third-market sourcing of continuers.
C.9
Reduced-Form Evidence on Interdependencies
Constructing China Shock Measures
We construct the China shocks using bilateral trade data from the UN Comtrade database, which we map
from six-digit HS codes to six-digit NAICS industries using the concordance from Pierce and Schott (2012).
This concordance does not always map to a six-digit NAICS. In those cases where the concordance maps to a
five-digit NAICS, we aggregate the analysis accordingly. In addition, the concordance implies zero trade for a
number of six-digit NAICS industries. We use the 2007 Census of Manufacturers data to assess the credibility
of zero trade flows. Since plants classified in these industries often have significant exports, we conclude that
the implied zero trade flows are a data measurement issue. We therefore aggregate the trade data as needed to
ensure that every industry has positive imports, though we maintain the disaggregated information whenever
it is available. For example, consider a four-digit NAICS that is an aggregation of four six-digit NAICS codes.
If we have detailed import shares at the NAICS6 level for two of the detailed NAICS6 industries, we use
the six-digit shares for those industries. For the remaining two NAICS6 codes with implied zero shares, we
aggregate to the lowest level of aggregation necessary to ensure non-zero flows for all codes and assign the
aggregate share to the remaining NAICS6 codes that would otherwise have had zero implied shares.
15
This firm-level shock is given by
shockninput =
X
snh Chinainput
h2007 −
h∈n
X
snh Chinainput
h1997 ,
(C.3)
h∈n
where snh is industry h’s share of firm n’s manufacturing sales in 1997. The importance of Chinese imports as
inputs in a particular industry is
Chinainput
=
ht
X
m∈h
smh
EU 15importsChina
mt
W orld/U S
,
EU 15importsmt
where smh is the expenditure share of inputs from industry m in industry h and
EU 15importsChina
mt
W orld/U S
EU 15importsmt
is China’s
share of EU15 country imports in industry m and year t, excluding imports from the US, as well as trade
among the EU15 countries. We measure the expenditure shares of inputs using the 1997 BEA input-output
tables. We measure Chinese market shares using UN Comtrade data. We follow the general approach in
Autor et al. (2013) and use Chinese exports to the following original European Union countries: Austria,
Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal,
Spain, Sweden, and the U.K.8 The underlying shock measure is thus a weighted average of changes in Chinese
market share in these countries for a firm’s inputs, making it unlikely that demand or supply shocks for U.S.
firms drive the variation.
Deflating Inputs and Imports
We deflate all nominal values to 1997 values using industry deflators from the NBER-CES productivity database
for six-digit NAICS 1997 codes. We use the Fort-Klimek NAICS 2002 codes to classify establishments in both
1997 and 2007 on a consistent industry basis.9 There is a one-to-one mapping from NAICS 1997 codes to
NAICS 2002 codes for manufacturing industries. For plants outside of manufacturing, and for firm imports
outside manufacturing, we deflate plant-level variables using the Bureau of Labor Statistics Consumer Price
Index for urban consumers, all items, taken from FRED. This deflator value is 1.292 between 2007 and 1997.
We use the deflator series pimat to deflate plant-level non-imported input expenditures, by industry. Since
the model implicitly treats production workers as substitutable with purchased material inputs, we deflate
their wages using the pimat deflator for the plant’s industry. Wholesale plant input purchases are deflated
+
using the CPI. After deflating, we compute real total inputs as Inputsn = M atP urchn + M erchwhole
n
.
P rodW orkerW agesmanuf
n
We use the deflator series piship to deflate plant sales. We also deflate firm imports by industry using the
piship deflators. Firm imports are reported at the level of HS10, 2007 vintage. We first apply the Pierce-Schott
HS10 to NAICS concordance to convert import values to NAICS 2007. We then concord the NAICS 2007 codes
to NAICS 2002 codes using sales shares we construct from the 2007 CM data.10 We then deflate firm imports
by the industry of the imports themselves, using the piship industry deflators.
Finally, we compute real domestic inputs as deflated total inputs - deflated total imports. We drop a very
small number of firms for which implied deflated domestic input purchases are zero or negative.
Robustness Tests for the Evidence on Interdependencies
Here we present summary statistics for manufacturing firms’ in 1997 by their China import status (see table
C.9). We also show that the evidence presented in section 6.4 is robust to controlling for import penetration
in a firm’s industry and to instrumenting for import penetration in a firm’s industry (see Tables C.10 and
C.11, respectively). We measure Chinese import penetration as total Chinese imports in an industry divided
8
We use EU15 countries since we do not face the same data constraints as ADH who need trade data back to 1990.
All our results are robust to using the ADH countries, but our first stage statistics are somewhat weaker, especially
for the results in Online Appendix Table C.11, where we instrument for both firm-level Chinese imports and Chinese
import penetration in a firm’s industry.
9
See Fort and Klimek (2016) for details on these industry codes.
10
The 2007 CM collects establishment-level data on a NAICS 2002 and NAICS 2007 basis, which allows us to construct
an aggregate sales-weighted concordance.
16
by total US absorption in the industry. We measure absorption using shipments and exports from the CM, and
imports from Comtrade data. We aggregate industries as necessary to ensure a positive measure of imports for
all industries. In undisclosed results (available internally to researchers with access to the data) we also ensure
that the results are robust to excluding Canada and to limiting the treatment group to new China importers.
The former is important since the match rates from the EC data to the import data are significantly lower for
Canada prior to 2007.
First Stage Statistics
Table C.12 presents first-stage estimates for all the specifications.
C.10
Countries per Product Counts
In section 4.2, we show that most firms source most products from a single location. Table C.14 reproduces
these results (right panel), and also shows that in contrast, firms tend to import multiple products from a
particular country. Table C.15 shows that the pattern of sourcing most inputs from one location persists for
firms that source from at least three foreign countries. We also compare these firm-level statistics to the same
numbers for exporting. To make a valid comparison, we must first aggregate to the HS6 level. This ensures
the same number of product categories for imports and exports. Table C.16 shows that, even at the HS6 level,
most firms source most products from one location. This is in contrast to firms’ exporting decisions, where
we see that the median firm sells at least one product to three destinations and the 95th percentile sells to 21
countries.
We conclude by reporting some figures that illustrate the superior performance of importers in our sample. Even though U.S. importers constitute only 25.8 % of U.S. firms that perform some manufacturing, the
sales of these importers constitute 95.6% of the sales of all firms performing some manufacturing, and their
manufacturing sales account for 92.1% of U.S. manufacturing sales. More broadly, when looking at firms in
all sectors of the U.S. economy, the sales of importers are 70.2% of the total sales of all U.S. firms. These
figures are comparable on the exporting side. The sales of manufacturing exporters constitute 93.7% of the
sales of all manufacturing firms, with their manufacturing sales accounting for 90.1% of U.S. manufacturing
sales. Furthermore, the sales of exporters in all sectors account for 61.8% of the total sales of U.S. firms.
17
Table C.7: Moment m̂2 (δ̂) at estimated parameters – Various Models
Baseline
model
’CAN’
’MEX’
’GTM’
’SLV’
’HND’
’CRI’
’PAN’
’DOM’
’TTO’
’COL’
’VEN’
’ECU’
’PER’
’CHL’
’BRA’
’ARG’
’SWE’
’NOR’
’FIN’
’DNK’
’GBR’
’IRL’
’NLD’
’BEL’
’LUX’
’FRA’
’DEU’
’AUT’
’CZE’
’SVK’
’HUN’
’CHE’
’POL’
’RUS’
’UKR’
’ESP’
’PRT’
’ITA’
’SVN’
’GRC’
’ROM’
’BGR’
’TUR’
’ISR’
’SAU’
’ARE’
’IND’
’PAK’
’BGD’
’LKA’
’THA’
’VNM’
’MYS’
’SGP’
’IDN’
’PHL’
’MAC’
’CHN’
’KOR’
’HKG’
’TWN’
’JPN’
’AUS’
’NZL’
’EGY’
’ZAF’
0.149
0.037
0.007
0.004
0.003
0.003
0.000
0.002
0.000
0.002
0.001
0.000
0.006
0.005
0.008
0.002
0.010
0.006
0.007
0.007
0.036
0.007
0.015
0.006
0.001
0.018
0.051
0.008
0.002
0.001
0.002
0.016
0.002
0.003
0.001
0.006
0.004
0.016
0.003
0.001
0.002
0.001
0.004
0.011
0.000
0.001
0.014
0.013
0.002
0.004
0.008
0.012
0.006
0.014
0.006
0.005
0.003
0.080
0.022
0.026
0.042
0.036
0.009
0.006
0.001
0.002
Independent
entry decisions
model
(θ = 2.85)
0.149
0.036
0.007
0.003
0.003
0.003
0.000
0.002
0.000
0.002
0.001
0.000
0.006
0.005
0.008
0.002
0.010
0.005
0.007
0.007
0.036
0.007
0.014
0.006
0.001
0.018
0.051
0.008
0.002
0.001
0.002
0.016
0.002
0.003
0.001
0.006
0.004
0.016
0.003
0.001
0.002
0.001
0.004
0.011
0.000
0.001
0.014
0.013
0.002
0.004
0.008
0.012
0.006
0.014
0.006
0.005
0.003
0.080
0.022
0.026
0.042
0.036
0.008
0.005
0.001
0.002
Universal
importing
model
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Common
fixed costs
across countries
model
0.053
0.055
0.017
0.007
0.007
0.005
0.000
0.005
0.000
0.003
0.002
0.001
0.013
0.005
0.017
0.005
0.005
0.004
0.004
0.003
0.020
0.004
0.008
0.006
0.000
0.016
0.036
0.005
0.004
0.001
0.003
0.009
0.004
0.012
0.003
0.007
0.005
0.028
0.003
0.002
0.004
0.002
0.009
0.012
0.000
0.002
0.032
0.036
0.010
0.011
0.024
0.038
0.014
0.008
0.020
0.016
0.006
0.174
0.033
0.016
0.062
0.036
0.005
0.003
0.003
0.004
Data
0.151
0.031
0.001
0.001
0.002
0.002
0.001
0.003
0.001
0.003
0.001
0.001
0.002
0.003
0.011
0.004
0.012
0.004
0.005
0.008
0.046
0.006
0.016
0.011
0.001
0.024
0.052
0.009
0.006
0.002
0.004
0.017
0.005
0.002
0.001
0.013
0.003
0.034
0.002
0.002
0.002
0.001
0.005
0.009
0.001
0.002
0.020
0.003
0.001
0.001
0.011
0.004
0.010
0.010
0.006
0.006
0.001
0.086
0.022
0.019
0.042
0.032
0.012
0.005
0.001
0.004
Notes: Moment m̂2 (δ̂) is equal to the share of firms that imports from each country.
18
Table C.8: Third country sourcing effects of Chinese fixed costs shock
Chinese
import status
Entrants
Continuers
Others
Change sourcing
from US
1.007
0.994
0.994
Change Sourcing
from other countries
1.012
0.994
0.987
Change Sourcing
from China
∞
0.994
-
Share
of firms
0.077
0.003
0.920
Notes: The table groups firms by Chinese import status. Entrants are those firms (i.e. bundles of productivity levels and fixed cost draws) that begin sourcing from China. Continuers are firms that source
from China before and after the shock. Others are firms that do not source from China before or after
the shock. The shock to the fixed costs of sourcing from China is calibrated to match the observed 178
percent increase in the Chinese import share from 1997 to 2007.
Table C.9: Firm-level means for firm characteristics in 1997, by firms’ Chinese import status in 1997
a) Non-importers
b) China importers
c) Other country importers
Sales
Employment
Domestic
inputs
China
imports
Other country
imports
No. source
countries
4
1071
110
3
307
44
2
398
50
0
2
0
0
74
3
1
7.9
3.4
Notes: This table reports firm-level means by firms’ 1997 China import status, for the 127,400 firms in the balanced panel
used in the regression analyses table 10. No. of source countries includes the US, but excludes China. Inputs and import
inflated to 2007 $ values. Employment rounded to nearest 10 and sales, inputs, and imports rounded to nearest $million for
disclosure avoidance.
Table C.10: Estimates of the impact of the China shock on firm-level sourcing, controlling for import
penetration
Dependent variable is firm-level change from 1997 to 2007 in:
Domestic
inputs
No. of
countries
Foreign
inputs
Firm
empl.
Domestic
inputs
OLS
China, DHS
Import Penetration
Constant
N
First Stage Statistics
0.065
(0.009)
-0.024
(0.150)
0.055
(0.022)
127,400
0.254
(0.007)
0.07
(0.080)
0.141
(0.014)
127,400
No. of
countries
Foreign
inputs
Firm
empl.
0.872
(0.271)
-0.445
(0.247)
0.254
(0.045)
127,400
0.184
(0.258)
-0.610
(0.269)
-0.064
(0.035)
127,400
IV
0.362
(0.012)
0.022
(0.151)
0.314
(0.030)
127,400
0.104
(0.007)
-0.536
(0.115)
-0.055
(0.016)
127,400
Coeff (se) 1.809 (0.498)
1.271
(0.428)
-1.132
(0.517)
-0.088
(0.053)
127,400
0.707
(0.106)
-0.346
(0.109)
0.087
(0.017)
127,400
KP F stat 13.20
Notes: All variables are changes or growth rates from 1997 to 2007. China, DHS is a Davis-Haltiwanger-Schuh growth rate in firm
imports from China. Domestic inputs, foreign inputs, and firm employment are a DHS growth rate. No. of countries is the log
difference in the number of countries (excluding China) from which the firm imports. Import penetration is the change in industrylevel import penetration from China for the sales-weighted average of a firm’s 1997 industries. Standard errors are in parentheses
and clustered by 439 NAICS industries. In the IV specifications, firm-level sourcing from China is instrumented by the change in
Chinese market share in EU15 countries of a weighted average of the firm’s inputs. KP F stat is the Kleibergen Paap F-statistic. N
rounded for disclosure avoidance.
19
Table C.11: Estimates of the impact of the China shock on firm-level sourcing instrumenting for
import penetration
Dependent variable is firm-level change from 1997 to 2007 in:
Domestic
inputs
No. of
countries
Foreign
inputs
Firm
empl.
Domestic
inputs
No. of
countries
OLS
China, DHS
Import Penetration
Constant
N
0.065
(0.009)
-0.024
(0.150)
0.055
(0.022)
127,400
First Stage Statistics
0.254
(0.007)
0.07
(0.080)
0.141
(0.014)
127,400
Foreign
inputs
Firm
empl.
1.381
(0.244)
-1.568
(0.391)
0.220
(0.040)
127,400
0.067
(0.249)
-0.352
(0.366)
-0.057
(0.036)
127,400
IV
0.362
(0.012)
0.022
(0.151)
0.314
(0.030)
127,400
0.104
(0.007)
-0.536
(0.115)
-0.055
(0.016)
127,400
0.859
(0.301)
-0.221
(0.541)
-0.061
(0.045)
127,400
0.931
(0.102)
-0.838
(0.182)
0.073
(0.015)
127,400
Coeff (se) for China, DHS 2.798 (0.670)
KP F stat 7.12
Notes: All variables are changes or growth rates from 1997 to 2007. China, DHS is a Davis-Haltiwanger-Schuh growth rate in firm
imports from China. Domestic inputs, foreign inputs, and firm employment are a DHS growth rate. No. of countries is the log
difference in the number of countries (excluding China) from which the firm imports. Import penetration is the change in industrylevel import penetration from China for the sales-weighted average of a firm’s 1997 industries. Standard errors are in parentheses
and clustered by 439 NAICS industries. In the IV specifications, firm-level sourcing from China is instrumented by the change in
Chinese market share in EU15 countries of a weighted average of the firm’s inputs and import penetration is instrumented by the
same shock in a firm’s output industries. KP F stat is the Kleibergen Paap F-statistic. N rounded for disclosure avoidance.
Table C.12: First-stage regressions for the DHS China growth rate specifications
Dependent variable is change from 1997 to 2007 in firm
Input shock
China
DHS
China
DHS
China
DHS
China
Imp Pen
2.685
(0.505)
1.809
(0.498)
0.720
(0.171)
2.798
(0.670)
0.626
(0.207)
-0.059
(0.145)
0.037
(0.025)
0.01
0.311
(0.064)
-0.034
(0.009)
0.29
Import Penetration
Output shock
Constant
Adj. R2
0.033
(0.029)
0.01
0.044
(0.026)
0.02
Notes: All variables are changes or growth rates from 1997 to 2007.
China, DHS is a Davis-Haltiwanger-Schuh growth rate in firm imports
from China. Import Penetration is the change in import penetration for
the sales-weighted average of a firm’s 1997 industries. Input shock is the
change in Chinese market share in EU15 countries of a weighted average
of the firm’s inputs. Output shock is the change in Chinese market share
in EU15 countries of a weighted average of the firm’s inputs. Shocks are
assigned based on the firm’s 1997 industry. Standard errors are in parentheses and clustered by 439 NAICS industries. N rounded for disclosure
avoidance.
20
Table C.13: Firm-level statistics on the number of source countries and imported inputs
Country Count
Product Count
Mean
Std. Dev.
25th Ptile
Median
95th Ptile
3.26
11.91
5.09
48.88
1
1
2
3
11
41
Notes: The first row reports on the number of countries from which a firm imports. The
second row reports on the number of unique HS10 products a firm imports. Note that data
confidentiality protection rules preclude us from disclosing exact percentiles. Statistics for
all percentiles in the paper are therefore the average for all firms that are within +/- one
percent of the reported percentile.
Table C.14: Firm-level statistics on the number of imported products per source country and the
number of source countries per imported product
Products Per Country
Mean
Mean
Median
95%tile
Firm-level
Median Max
2.78
2.00
8.23
2.18
2.00
5.00
7.21
2.00
25.00
Countries Per Product
Mean
Firm-level
Median Max
1.11
1.00
1.61
1.03
1.00
1.00
1.78
1.00
4.00
Notes: The left panel reports on the number of unique HS10 products
that a firm imports from a particular country. The right panel reports
on the number of countries from which a firm imports the same HS10
product.
Table C.15: Number of countries from which a firm imports the same HS10 product, for firms that
import from at least 3 countries
Firm Level
Mean
Median
95%tile
Mean
1.28
1.19
1.96
Median
1.05
1.00
1.00
Max
3.18
2.00
9.00
Notes: Table reports statistics on the firmlevel mean, median, and maximum of the
number of countries from which a firm imports the same HS10 product.
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Table C.16: Number of countries per HS6 product traded by a firm
Firm Level Imports
Mean
Median
95%tile
Firm Level Exports
Mean
Median
Max
Mean
Median
Max
1.15
1.00
1.93
1.05
1.00
1.00
1.92
1.00
5.00
1.76
1.11
4.26
1.33
1.00
3.00
4.87
2.00
21.00
Notes: Table reports statistics on the firm-level mean, median, and maximum of the number of countries from which a firm imports or exports the
same HS6 product.
22