Headquarters Gravity∗
Zi Wang†
Pennsylvania State University
November 3, 2015
Abstract
This paper develops a general equilibrium model in which multinational firms
(MNEs) transfer both productive knowledge and connections with international markets to their affiliates. The key feature of this model is that it allows a MNE’s export
cost to each market to depend on how close this market is to its production locations
(gravity) and to its headquarters location (headquarters gravity). The model provides
a framework that can estimate headquarters gravity consistently in Chinese firm data.
The estimates suggest that MNEs in China face substantially lower export costs to
markets closer to their headquarters. Consequently, their iceberg export costs are on
average 28 percent lower than those of Chinese firms. This difference in export costs
account for about a quarter of Chinese manufacturing exports in 2001.
Keywords: Multinational Firms; Export; Welfare
JEL classification: F12, F23, O19.
∗
This version: Oct 2015. First version: Aug 2015. I am grateful to Steve Yeaple for his continuous
guidance and support. I thank Jonathan Eaton and Felix Tintelnot for extensive discussions and in-depth
comments. I also thank James Tybout, Kala Krishna, Pol Antras, Eduardo Morales, Kamran Bilir, Michael
Peters, Ferdinando Monte, Sam Asher, Fernando Parro, Jianpeng Deng and seminar participants at the
Penn State University (Sept 2015), for helpful comments. All errors are my own.
†
Department of Economics. Pennsylvania State University, University Park, PA, 16801. Email address:
zxw120@psu.edu
1
Introduction
Recent studies have emphasized that by directly controlling factors of production in
foreign countries, multinational firms (MNEs) transfer knowledge across borders .1 But
what kinds of knowledge do MNEs transfer? Previous studies have focused on productive
knowledge.2 In this paper, by carefully investigating MNEs in micro trade data, I argue
that MNEs transfer not only their productive knowledge, but also their connections with
international markets to host countries.
This paper is motivated by a regularity in Chinese firm data: controlling for the destination market size and the destination distance from China, MNEs in China are more likely
to serve markets closer to their headquarters. This regularity is consistent with the idea
that MNEs have better connections with markets closer to their headquarters and some of
these connections are transferable to their affiliates. These connections include their prior
trade experience, their brand names, and their marketing networks. By transferring these
connections, MNEs provide their affiliates better access to export markets. In contrast, the
majority of local firms in host countries lack connections with international markets. Without foreign MNEs, many developing countries will lose most of their connections to export
markets.
This paper aims to quantify the connections with international markets transferred by
MNEs. To achieve this, I develop a general equilibrium model with trade and multinational
production. The key feature of this model is that it allows a MNE’s export cost to each
market to depend on how close this market is to its production locations (gravity) and to
the location of its headquarters (headquarters gravity). Previous models of MNEs’ exports
have assumed that MNEs face the same export costs as local firms (Arkolakis et al., 2015,
Tintelnot, 2014). By doing this, they attribute the MNEs’ outstanding export performances
solely to their productivities. In contrast, in my model headquarters gravity allows MNEs
to be more export-oriented than local firms even if they are equally productive. As a consequence, my model allows me to decompose MNEs’ advantage in export into their export
1
See Keller and Yeaple (2013) for a review of this topic.
Productive knowledge transferred by MNEs is regarded as either technology capital (MacGrattan and
Prescott, 2009) or firm management know-how (Burstein and Monge-Naranjo, 2009)
2
2
costs and their productivities.
Headquarters gravity has profound implications for trade and trade policies. First, headquarter gravity implies that MNEs’ exports cannot be fully explained by previous models
with firm heterogeneity. Trade theories have to take foreign ownership into account. Second,
for governments that are seeking to promote exports, headquarters gravity suggests that an
effective policy is to attract MNEs from large markets.
I estimate my model using Chinese firm data from 2001 which contains information on
firms’ nationalities and their exports by destination. The key empirical challenge is that
the MNEs’ export performances are driven both by their productivities and by their export
costs. I deal with this identification problem by utilizing the model implication that the
firm’s productivity affect its sales in all markets but its export costs affect only exports to
certain destinations. I calibrate the remaining parameters by matching the model-generated
trade and MP flows to aggregate data.
The estimates suggest that headquarter gravity is strong. The iceberg export cost of
a MNE in China to its headquarters country is, ceteris paribus, 32 percent lower than to
any other country. Doubling the distance between the headquarters and the destination will
increase the MNEs’ export costs by 5 percent. Moreover, the shared language and the similar
GDP per capita between the headquarters country and the destination are quantitatively
important for MNEs’ export costs. As a consequence, MNEs in China face substantially lower
export costs than Chinese firms. On average, the iceberg export cost of MNEs in China is
28 percent lower than that of Chinese firms. These results imply that the MNEs in China
do indeed act as trade intermediaries bridging Chinese workers with foreign consumers.
I then turn to quantify the impacts of knowledge transferred by MNEs on Chinese exports
using counterfactual analysis. The result suggests that both productive knowledge and
connections with international markets transferred by MNEs are quantitatively important
for Chinese exports. Shutting down MNEs in China will decrease Chinese manufacturing
exports by 49 percent, about half of which is due to MNEs having lower export costs than
Chinese firms. Moreover, forcing MNEs in China to have the same export costs as Chinese
firms would decrease Chinese manufacturing exports to OECD countries by about a third but
increase Chinese manufacturing exports to non-OECD countries by about 30 percent. Hence
3
headquarters gravity plays an important role in shaping both the scale and the direction of
Chinese manufacturing exports.
The general equilibrium model also allows me to examine the implications of MNEs on
income distribution and welfare in China. I find that both productive knowledge and connections with export markets brought by MNEs can substantially raise the wage of Chinese
workers but decrease the profits of Chinese firms. Intuitively, knowledge transferred by
MNEs can be viewed as a specific factor of production. Increasing this specific factor in
China would increase the demand for Chinese workers but decrease the returns of Chinese
specific factors.
However, productive knowledge and connections with export markets transferred by
MNEs have different implications on Chinese price. Imposing the same export costs on
MNEs as those faced by Chinese firms would decrease the Chinese price index by 6.2 percent
while shutting down MNEs in China would only decrease it by 1.8 percent. The low export
costs of MNEs increase Chinese price by driving out Chinese firms who have advantage in
serving the Chinese market. In contrast, MNEs’ high productivities lower Chinese price by
serving the Chinese market with low cost. Consequently, Imposing the same export costs on
MNEs as those faced by Chinese firms decreases Chinese welfare by only 0.1 percent while
shutting down MNEs in China decreases Chinese welfare by 9.7 percent.
I apply my model to evaluate the welfare implications for Chinese subsidies to MNEs in
China. Before 2008, Chinese corporate income tax rate is 33 percent for Chinese firms but
15 percent for MNEs in China. I re-calibrate my model with corporate income taxes and
conduct counterfactual analysis by changing the tax rate for MNEs. I find that increasing
subsidies for MNEs can increase Chinese exports and the real wage of Chinese workers but
decrease the real profits of Chinese firms. Taking the cost of subsidies into account, China
will experience a welfare loss by subsidizing foreign MNEs.
This paper is related to several strands of the literature. First, this paper contributes to
a growing literature about the MNEs’ home market advantage. Head and Mayer (2015) find
that in auto parts industry it is more difficult to make sales in markets farther away from
brand’s headquarters. This paper departs from their study by focusing on aggregate trade
patterns instead of one industry. Moreover, my model endogenizes the MNEs’ choices on
4
production sites and export destinations, whereas in Head and Mayer (2015) these decisions
are taken as given. These margins are shown to be important for trade and welfare. Cosar
et al. (2015) emphasize the MNEs’ disadvantage in selling outside the home market. This
paper complements their study by emphasizing that the MNEs’ home bias can be transferred
to their affiliates.
Second, this paper builds on and contributes to quantitative studies of trade and multinational production. Tintelnot (2014) allows firms to build export platforms at the expense
of fixed costs. Ramondo and Rodriguez-Clare (2013), Alviarez (2013), and Arkolakis et al.
(2015) aim to quantify the gains from openness in a world with both trade and multinational
production. All of these papers assume that MNEs face the same export costs as local firms
in host countries. Consequently, they cannot capture the MNEs’ advantage in serving markets close to their headquarters. This paper is the first attempt to quantify headquarters
gravity in a general equilibrium model.
Third, this paper contributes to papers about across-border knowledge transfer led by
MNEs. Previous papers focus on productive knowledge in terms of either technology capital
(MacGrattan and Prescott, 2009) or firm management know-how (Burstein and MongeNaranjo, 2009). This paper complements these papers by emphasizing that MNEs transfer
not only productive knowledge but also connections with international markets to their
affiliates.
Four, this paper is related to empirical evidence on MNEs’ exports (Arnold and Javorcik,
2009, Hanson et al. ,2005, Ekholm et al. ,2007, and Guadalupe et al. ,2012). These studies
find that MNEs are more export-oriented than local firms in host countries. This paper
quantifies the MNEs’ advantage in export in a structural model and evaluate the welfare
implications of this advantage.
The rest of the paper is organized as follows. In Section 2, I describe the data I use and
document stylized facts about the exports by MNEs in China. In Section 3, I introduce my
model, define the equilibrium, and deliver structural equations for estimation. In Section
4, the headquarters gravity is identified and estimated from Chinese firm data. Section 5
calibrates the general equilibrium model. Section 6 presents counterfactual exercises. Section
7 concludes.
5
2
Data and stylized facts
2.1
Data Description
The cross-sectional data of essentially all manufacturing firms located in China in 2001
is created by merging the balance sheet data and trade data for all manufacturers and the
registration information of foreign manufacturers.
The balance sheets come from the Annual Survey of Chinese Manufacturing (ASCM)3
which contains the firms’ total sales, employment, and capital stocks. The firm exports
come from the Chinese Customs Records (CCR) which contains the export value of each
firm by destination4 . The registration information of foreign manufacturers in China comes
from Foreign-Invested Enterprise Survey in China (FIESC) which contains the nationality
of a firm’s primary foreign investor. The details on data construction are presented in the
appendix.
Figure 1 illustrates the structure of my data. For each manufacturing firm in China I
observe its nationality and its sales by destination. From this example we can see that MNEs
in China sell to China (the host country), to their headquarters countries, and to the third
countries. In particular, the MNEs’ exports concentrate around their headquarters. I show
below this example is not an exception.
Table 1 shows some summary statistics for MNEs in China by headquarters country. Foreign firms account for 27% of Chinese manufacturing production but strikingly for 68% of
Chinese manufacturing exports. Their exports are extremely concentrated in their headquarters countries. For example, Japanese firms in China account for less than 20% of Chinese
manufacturing exports but for more than 50% of Chinese manufacturing exports to Japan.
This pattern holds for all China’s major FDI sources.
3
ASCM contains all state-owned manufacturing firms and other manufacturing firms whose annual sales
exceed 5 million RMB (about 0.6 million dollars). The omitted firms are small and unlikely to be engaged
with international trade.
4
The original data contains the value, the destination, the 8-digit HS category, and the mode of trade
for each export transaction. Because I am interested in the overall export performance of individual firms,
I aggregate the export value in firm-destination level
6
Figure 1: Data Structure: an Example
(Note: All three firms are household appliance producers located in China. Headquarters
countries are the locations for their primary foreign investors based on their registration information in the Department of Commerce in China. Exports for each firm to each destination
are aggregate export values in 2001. Exports include both ordinary trade and processing
trade.)
2.2
Empirical Regularity
I now turn to describe a new empirical regularity in Chinese firm data.
Fact: Controlling for the firm size, the destination market size, and the destination
distance from China, MNEs in China are more likely to export and export more to the
markets closer to their headquarters.
Following Morales et al. (2015), I measure the distance between headquarters country
i and destination d a vector Ddi which consists of their geographic distance, log(distdi ), a
dummy for common language, langdi , a dummy for similar GDP per capita sgdpdi , and a
dummy for i = d, selfdi . Let xdni (ν) be the sales of firm ν who produce in country n (here
n is China) and whose headquarters is located in country i to destination market d. Then
the export entry is estimated by
1{xdni (ν) > 0} = 1{β0 + f ed + β1 sizen (ν) + β3 Ddi + ud (ν) ≥ 0},
7
d 6= n = CHN,
(1)
Origin
%Firm
%Sales
%Exports
%Sales to HQ Country
AUS
BEL
CAN
DEU
FIN
FRA
GBR
JPN
KOR
SGP
SWE
TWN
USA
.24
.04
.22
.38
.02
.17
.44
2.75
1.11
.83
.06
3.03
2.09
.16
.18
.23
1.82
.6
.33
.94
4.75
1.85
1.54
.34
1.8
4.16
.27
.11
.27
1.71
1.25
.33
2.39
18.71
9.09
3.91
.25
5.84
9.75
3.7
1.9
1.4
14.2
27.0
6.7
4.9
52.1
37.4
14.4
32.4
19.4
15.6
14
27
68
-
All foreign
Table 1: Multinational Firms in China by Headquarters Country
(Note: Firms from Hong Kong and Macau are excluded. % Firm is the share of MNEs in all
manufacturing firms in China in terms of the number of firms. % Sales is the share of MNEs’
sales in Chinese manufacturing sales. %Exports is the share of MNEs’ exports in Chinese
manufacturing exports. %Sales to headquarters country is the share of MNEs’ exports to
their headquarters country in Chinese manufacturing exports to that country.)
where f ed is a destination fixed effect and sizeν is the firm size measured by either the firm
sales in China, log(xnni (ν)), or the firm fixed effect.
The export sales is estimated by
log(xdni (ν)) = β0 + f ed + β1 sizen (ν) + β3 Ddi + ud (ν),
d 6= n = CHN.
(2)
The reduced-form results are presented in table 2. They suggest that the location of
headquarters does matter for MNEs’ exports. Controlling for the standard gravity, multinational affiliates export disproportionately more to their headquarters countries. The MNEs’
exports would decrease by 5% if the geographic distance between headquarters and destination doubles. Furthermore, the shared language and similar GDP per capita between the
headquarters and the destination matter for MNEs’ exports.
The regularity is robust in more disaggregated data and different specifications. Inter-
8
estingly, I find that the “home bias” is stronger in differentiated goods than in homogeneous
goods, which is consistent with the idea that the market access is more important in the
exports of differentiated goods. All robustness checks are presented in the appendix.
Dependent Variable
1{xdni (ν) > 0}
log(distdi )
selfdi
langdi
sgdpdi
log(xnni (ν))
Destination FE
Firm FE
R-square
N. of Obs.
-.05***
(.005)
.94***
(.03)
.21***
(.01)
.05**
(.02)
.04***
(.002)
Yes
No
782775
-.035***
(.01)
.59***
(.08)
.035
(.023)
.24***
(.027)
Yes
Yes
104828
log(xdni (ν))
-.052*** -.033
(.02)
(.02)
1.21*** 1.1***
(.08)
(.12)
-.07
.04
(.05)
(.06)
.04
.21***
(.06)
(.06)
.08***
(.007)
Yes
Yes
No
Yes
.13
.38
30420
17010
Table 2: Extensive and Intensive Margins of MNEs’ Exports
(Note: the sample excludes the firms from China, Hong Kong, Taiwan and Macau. The
extensive margin is estimated by Probit model, which is reported at the left two columns.
The intensive margin is estimated by OLS, which is reported at the right two columns.
The estimation controlling for firm fixed effects excludes all firms with less than 15 export
destinations.)
3
The Model
I present a general equilibrium model with trade and multinational production. There are
two parts in my model. The first part is the firm export entry and sales given their production
sites. This part is set to capture the key features in micro trade data. The second part is
the firm choices of production sites. This part is introduced to close the model and provide
general equilibrium implications. I start with the description of the demand and then turn
to the firm’s problem.
9
I consider a world with i = 1, . . . , N countries, one primary factor of production, labor
Li , and a continuum of horizontally differentiated varieties of goods. In each country the
representative consumer has a Constant Elasticity of Substitution (CES) preference over a
continuum of goods varieties:
Z
Ui = [
qi (ω)
σ−1
σ
σ
dω] σ−1 ,
(3)
ω∈Ωi
where the elasticity of substitution σ > 1, qi (ω) is the quantity of variety ω consumed in
country i, and Ωi is the set of varieties sold in country i.
3.1
The Firm’s Problem
Each variety of is produced by a firm under monopolistic competition. Firm ν originated
from country i draws a productivity ϕi (ν). The measure of firms with ϕi ≥ ϕ is exogenously
given by
Fi (ϕ) = Ti ϕ−θ ,
ϕ > 0,
Ti > 0,
θ > σ − 1.
(4)
After drawing productivity, a firm can replicate its technology in multiple production
sites by building affiliates. Without loss of generality I assume that each firm can at most
build one affiliate in each country. To ensure model identifiability in the data, I make the
following assumption:
Assumption 1 Each affiliate produces a distinctive variety ω, i.e. an affiliate’s pricing does
not affect the demand faced by other affiliates within firm boundary.
Assumption 1 implies that, for example, consumers regard Toyato cars produced in Japan
and in the U.S. as two different goods. This “Armington” assumption has to be enforced
due to data limitation. Note that Chinese firm data contains the nationalities of MNEs in
China and their exports to each market from China. But I do not observe the MP sales of
these MNEs in other countries. Assumption 1 makes my model identifiable in Chinese firm
data by separating the affiliate’s export decision from the firm’s MP decision.
In the rest of this subsection I will introduce geographic frictions that affect the firm’s
multinational production and sales and then solve the firm’s problem.
10
3.1.1
Frictions Shaping Multinational Sales
There are three types of frictions impeding the multinational activities. First, transferring
productive knowledge ϕi (ν) from headquarters to production sites incurs iceberg and fixed
MP costs. So MP sales would fall in distance from the headquarters. Second, transferring
products from production sites to destination markets incurs iceberg and fixed trade costs.
So export sales would fall in distance from the production sites. These two frictions have
been well-documented in the literature.
Motivated by the regularity in Chinese firm data, this paper introduces a new friction:
selling products to the markets far away from headquarters incurs additional iceberg and
fixed marketing costs. So the MNEs’ exports would fall in distance from the headquarters.
This new friction allows MNE affiliates to face different trade costs with local firms in host
countries.
Figure 2: Spatial Frictions Shaping Multinational Sales
These frictions are illustrated in Figure 2. The spatial structure of frictions illustrated
by Figure 2 is related to the one in Head and Mayer (2015). There are two key differences
that depart my work from theirs. First, they do not allow firms to choose their production
11
sites. So they do not incorporate MP fixed costs. Second, they do not allow fixed trade
costs. Both differences are important for my welfare evaluation.
To build an affiliate in country n, firm ν from country i has to pay a fixed MP cost
fni > 0 in terms of n’s labor. MP also incurs iceberg efficiency losses. The unit cost for firm
ν to produce in country n is
cni (ν) = γni wnβ Pn1−β /ϕi (ν),
(5)
where γni is the iceberg efficiency loss for MP from country i to n, wn is the wage in country
n, Pn is the price index for the composite final good consumed in country n, and β ∈ (0, 1]
is the value-added share.
Firm ν’s affiliate in country n incurs standard iceberg trade cost τdn to serve market d.
It also faces an additional iceberg cost ζdi to destination d far away from its headquarters
country i. These iceberg costs enter the production cost multiplicatively. So the unit cost
for an affiliate from country i located in country n to serve market d is
cdni (ν) = τdn ζdi cni (ν) =
γni τdn ζdi wnβ Pn1−β
.
ϕi (ν)
(6)
Monopolistic competition implies that the price of an affiliate from country i located in
country n to serve market d is
γni τdn ζdi wnβ Pn1−β
pdni (ν) = m̄cdni (ν) = m̄
,
ϕi (ν)
m̄ =
σ
.
σ−1
(7)
Note that all affiliates of firm ν from country i share a common component of export
costs ζdi to destination d. This ζdi characterizes connections with international markets
transferred from headquarters to affiliates. These connections include prior trade experience,
brand names, marketing connections, and distribution networks. In short, MNEs transfer
not only their productive knowledge but also connections with international markets to their
affiliates.
To rationalize the micro trade pattern, I introduce affiliate-destination-specific shocks
as in Eaton, Kortum, Kramarz (2011). Firm ν’s affiliate in country n incurs a fixed cost
12
εdn (ν)Edni to serve market d. The common component Edni captures both standard gravity
that depends on the distance between the destination and the production site and headquarters gravity. εdn (ν) is an affiliate-destination-specific idiosyncratic fixed-cost shock. Furthermore, an affiliate in country n faces an affiliate-destination-specific demand shock ξdn (ν) to
serve market d.
The timing of the firm’s decisions is as follows. First, firm ν draws its productivity
ϕi (ν). Second, firm ν decides where to build its affiliates. Third, the idiosyncratic entry and
demand shocks are realized. Finally, firm ν decides the export destinations and export sales
for each of its affiliate.
3.1.2
Export Entry and Sales
I solve the firm’s decision by reverse order. I start with the scenario in which firm ν from
country i has created an affiliate in country n. Monopolistic competition implies that the
potential sales of an affiliate from country i located in country n to destination market d is
given by
xdni (ν) = ξdn (ν)pdni (ν)1−σ Pdσ−1 Xd ,
(8)
where pdni (ν) is its individual price derived in Equation (7), Pd is the price index of destination market d, Xd is the total absorption of destination market d, and ξdn (ν) is the
affiliate-destination-specific idiosyncratic demand shock.
The potential sales in Equation (8) will be realized if and only if the profit from this sales
exceeds the fixed export cost wd εdn (ν)Edni . Monopolistic competition implies that the profit
has a share of
1
σ
in sales. So the affiliate will serve market d if and only if
1
xdni (ν) ≥ wd εdn (ν)Edni .
σ
(9)
Export entry and sales are driven by the unit cos cdni (ν), and the idiosyncratic demand
shock ξdn (ν) and fixed-cost shock εdn (ν). Combining Equation (9) with Equation (8) and
(7), an affiliate from country i located in country n will serve market d if and only if
cdni (ν) ≤ c̄dni (ηdn (ν)),
13
(10)
where
c̄dni (ηdn (ν)) := (ηdn (ν)
1 Pd
Xd
) σ−1 ,
σwd Edni
m̄
(11)
and
ηdn (ν) =
ξdn (ν)
εdn (ν)
(12)
is the idiosyncratic entry shock given by the ratio of the demand shock to the fixed-cost
shock.
Conditional on cdni (ν) ≤ c̄dni (ηdn (ν)), the sales in Equation (8) is given by
xdni (ν) =
ξdn (ν)
cdni (ν) −(σ−1)
[
]
σwd Edni .
ηdn (ν) c̄dni (ηdn (ν))
(13)
I assume that the demand shock ξdn (ν) and the entry shock ηdn (ν) are realizations of
affiliate-destination-specific shocks drawn from a joint c.d.f. G(ξ, η) that is identical and
independent across affiliates and destinations. I further assume that G(ξ, η) is a bivariate
lognormal distribution:
(log(ξ), log(η)) ∼IID

  
2
0
σξ
ρξη σξ ση
),
N (  , 
0
ρξη σξ ση
ση2
(14)
where σξ is the standard deviation for log ξ, ση is the standard deviation for log η, and
ρξη ∈ [−1, 1] is the correlation between log ξ and log η.
To save notations, I denote ξdn = ξ and ηdn = η for all d and n. Moreover, I denote the
vectors of demand and entry shocks an affiliate face in destination markets as, respectively,
˜ η̃) is denoted
ξ˜ := (ξ1n (ν), . . . , ξN n (ν))0 and η̃ := (η1n (ν), . . . , ηN n (ν))0 . The joint c.d.f. of (ξ,
˜ η̃).
as G̃(ξ,
Equation (10) and (13) characterize, respectively, the export entry condition and the
export sales. These two equations, after transformation, will be used to estimate the parameters of headquarters gravity, ζdi and Edni , from Chinese firm data.
14
3.1.3
Production Sites
Since a firm chooses its production sites before the realization of idiosyncratic shocks, it
will build an affiliate in country n if its expected operating profit in country n exceeds its
fixed MP cost. By Equation (13) and (10), the operating profit of an affiliate from country
i located in country n is its profits from exporting to all destinations net of fixed export
costs:5
˜ η̃, cni ) =
πni (ξ,
1
ξ
[ ξ[m̄τdn ζdi cni ]1−σ Pdσ−1 Xd − wd Edni ],
σ
η
X
(15)
d∈Λ(ξ̃,η̃,cni )
where the set of export destinations is derived by Equation (10) as
˜ η̃, cni ) = {d : cdni ≤ c̄dni (η)}.
Λ(ξ,
(16)
Firm ν will establish an affiliate in country n if and only if its expected operating profit
˜ η̃)) exceeds MP fixed cost. By Equation (15), firm ν will create an
(with respect to (ξ,
affiliate in country n if and only if
cni ≤ ĉni ,
(17)
where ĉni is the solution to
Z Z
π̄(cni ) :=
ξ̃
3.2
˜ η̃, cni )dG̃(ξ,
˜ η̃) = wn fni .
πni (ξ,
(18)
η̃
Aggregation
In this section I will add up firms’ trade and MP decisions into aggregate trade and MP
flows. In my model the firm heterogeneity comes from heterogeneity in productivity as well
as the idiosyncratic demand shocks ξ and entry shocks η. Aggregation is done by summing
firms over these three dimensions. Note that if the fixed MP cost fni = 0, my model is
isomorphic to Eaton, Kortum, and Kramarz (2011). The introduction of the fixed MP costs
complicates aggregation.
Note that for each affiliate it draws a demand shock ξ and an entry shock η in each
5
To save notations I omit the firm index ν.
15
destination market from a joint c.d.f. G(ξ, η). I denote the vectors of demand and entry
˜ η̃). The joint c.d.f. for (ξ,
˜ η̃) is
shocks faced by each affiliate in all destination markets as (ξ,
˜ η̃).
denoted as G̃(ξ,
By Equation (4) and (5), the measure of affiliates from country i in country n with the
unit cost in cni ≤ c is given by
µ̃ni (c) = Ti [
γni wnβ Pn1−β −θ
] .
c
(19)
By Equation (4) and (6), the measure of firms from country i serving market d by affiliates
in country n with the unit cost cdni ≤ c is given by
µdni (c) = Ti [
γni τdn ζdi wnβ Pn1−β −θ
] .
c
(20)
I derive the measure of firms from country i building affiliates in country n. It depends
on the distribution of unit costs in Equation (19) and the MP entry condition in Equation
(17):
Z
ĉni
Jni =
cdµ̃ni (c).
(21)
0
Then I derive the price index in country d. It depends on individual prices of all varieties
served in country d. Note that if a firm from country i wants to serve market d from its
affiliate in country n, it must be profitable for this firm to build an affiliate in country n and
for its affiliate in country n to export to country d. By Equation (10) and (17), the firm has
to satisfy
cdni ≤ min{c̄dni (η), τdn ζdi ĉni }.
(22)
By preference in Equation (3) and entry condition in Equation (22), the price index in
country d can be given by
Z Z X
N X
N Z
Pd = {
[
ξ̃
η̃ n=1 i=1
min{c̄dni (η),τdn ζdi ĉni }
ξ(m̄c)
σ−1
σ
σ
˜ η̃)} σ−1 .
dµdni (c)]dG̃(ξ,
(23)
0
By firm sales in Equation (13), the aggregate exports by affiliates from country i and
16
located in country n to market d is given by
min{c̄dni (η),τdn ζdi ĉni }
Z Z Z
Xdni =
ξ
η
0
ξ
c
[
]−(σ−1) σwd Edni dµdni (c)dG(ξ, η)
η c̄dni (η)
(24)
By export entry conditions in Equation (20), the measure of affiliates from country i,
located in country n, and serving market d is given by
min{c̄dni (η),τdn ζdi ĉni }
Z Z Z
Jdni =
cdµdni (c)dG(ξ, η).
ξ
η
(25)
0
By definition the aggregate fixed export costs paid by affiliates from country i and located
in country n to serve market d is given by
Z Z Z
min{c̄dni (η),τdn ζdi ĉni }
Mdni =
ξ
η
0
ξ
cdµdni (c)dG(ξ, η).
η
(26)
The net profit earned by firms in country i is their operating profits net of fixed trade
and MP costs:
N
N
N X
X
X
1
( Xdni − Mdni ) −
wn fni Jni .
Πi =
σ
n=1
d=1 n=1
(27)
Now I get all income flows in this economy. The total labor income in country i is the
sum of wage incomes of production workers, the wages for workers as fixed trade costs, and
the wages for workers as fixed MP costs:
N
wi Li =
N
1 XX
(1 − )β
Xdik
σ d=1 k=1
|
{z
}
+
N X
N
X
Mink +
n=1 k=1
Wage Income of Production Workers
|
{z
N
X
wi fik Jik .
(28)
k=1
}
Fixed Trade Costs
|
{z
}
Fixed MP Costs
Finally, the total absorption of country i is the sum of labor income, the firms’ net profit,
and the expenditure on the intermediates.
Xi =
X
1
+ Πi + (1 − )(1 − β)
Xdik .
|{z}
σ
d,k
Wage Income
Profit
|
{z
}
wi Li
|{z}
Expenditures on Intermediates
17
(29)
3.3
Equilibrium
Definition 2 Given (Li , fni , γni , τdn , ζdi , Edni ), Fi (.) and G(., .), the equilibrium is (wi , Xi , Pi )N
i=1
such that (i) c̄dni is defined by Equation (10) and ĉni is defined by Equation (17), (ii) the
sales of affiliates in n from i to d is given by Equation (24), (iii) the current account balance conditions, Equation (28) and (29), hold, and (iv) the aggregate price index satisfies
Equation (23).
The equilibrium outcomes (wi , Xi , Pi )N
i=1 can be computed by solving equation (23), (28),
and (29). I develop the an iterative algorithm to compute the equilibrium outcomes. The
details of this algorithm are presented in the appendix.
4
Estimating Headquarters Gravity
There are four groups of parameters in my general equilibrium model. They are sum-
marized in Table 3. I take two parameters from the literature: the elasticity of substitution
σ = 4 from Arkolakis et al. (2015) and the value-added share β = 0.35 from Johnson and
Moxnes (2013).
My empirical implementation consists of two parts. In this section I estimate headquarters gravity parameters and shock parameters from Chinese firm data. In the next section I
calibrate the remaining parameters in aggregate data.
The main objective of this section is to estimate the headquarters gravity parameters ζdi
and Edni in Chinese firm data. To achieve this, I follow the Heckman two-step approach
developed by Irarrazabal, Moxnes, and Opromolla (2013). This approach controls for the
firms’ productivities by their sales in China. The identification for {ζdi , Edni } comes from the
fact that firm export entry depends on both ζdi and Edni while firm export sales (conditional
on entry) depends only on ζdi .
4.1
Export Entry
In the first step I deliver and estimate the condition for an affiliate in China to enter
certain export market. The model implies that an affiliate will export to certain market if
18
Outside the Model
Parameter
Definition
Target/Source
σ
β
θ
Li
Elasticity of Substituion
Value-added Share
Dispersion of Firm Productivity
Manufacturing Labor
Arkolakis et al. (2015)
Johnson and Moxnes (2013)
Dispersion of firm sales
ILO (2001)
Headquarters Gravity Parameters
Parameter
Definition
Target/Source
ζdi
Edni
Iceberg HG term
Fixed HG term
Exports given sales in China
Export entry and exports
Shock Parameters
Parameter
Definition
Target/Source
σξ
ση
ρξη
Standard error for demand shock
Standard error for demand/entry shock
Correlation between ξ and η
Relation b/w sales in China and exports
Relation b/w Sales in China and export entry
Relation b/w export entry and exports
Standard Gravity and Technology
Parameter
Definition
Target/Source
τdn
γni
fni
Ti
Iceberg Trade costs
Iceberg MP costs
Fixed MP costs
Level of productivity
Export as a share of production
Inward MP as a share of production
MP affiliates as a share of total firms
Wage from ILO (2001)
Table 3: The Structural Parameters in the Baseline Model
its operating profit of doing that exceeds the fixed export cost. Hence firm ν’s export entry
in Equation (9) can be re-expressed as
γni τdn ζdi wnβ Pn1−β 1−σ
1
ηdn (ν)m̄1−σ [
] Xd Pdσ−1 ≥ wd Edni .
σ
ϕi (ν)
(30)
The productivity ϕi (ν) in Equation (30) is unobserved. But it can be expressed as a
function of sales in China, xnni (ν). Substituting ϕi (ν) by xnni (ν), Equation (30) can be
rewritten as
∗
log(xnni (ν)) + log(ηdn
(ν)) ≥ Hdni ,
d 6= n = CHN,
(31)
where
Hdni = log σ + log(wd Edni ) + (σ − 1) log(ζdi ) − (σ − 1) log(ζni )
|
{z
}
|
{z
}
Fixed Export Cost
Iceberg Headquarters Gravity
− [log(Xd Pdσ−1 /Xn Pnσ−1 ) − (σ − 1) log(τdn )],
|
{z
}
Export Sales Potential
19
(32)
∗
and ηdn
(ν) = ηdn (ν)/ξnn (ν) is a compound entry shock.
Equation (31) means that an affiliate in China from country i will serve market d if
its sales in China plus an affiliate-destination specific shock exceed an entry hurdle Hdni .
Therefore, the entry hurdle Hdni characterizes how likely an affiliate will export to a market,
given its sales in China.
Hdni consists of three parts. First it increases with respect to the fixed trade cost wd Edni .
Second it increases with respect to the distance between ζdi (relative to ζni ). Third it
decreases with respect to the export sales potential which depends on the destination market
size, the destination price level, and the distance between the destination and China.
∗
(ν)) is drawn from a normal distribution with mean 0 and stanBy construction log(ηdn
q
dard deviation ση∗ = ση2 + σξ2 . Therefore, Θ1 = {Hdni , ση∗ } can be estimated by a ML
estimator with the following likelihood function:
l1 (Θ1 ) =
XXX
d6=n
i
[1−ydni (ν)] log{Φ[
ν
Hdni − log xnni (ν)
Hdni − log xnni (ν)
]}+ydni (ν) log{1−Φ[
]},
ση∗
ση ∗
(33)
where ydni (ν) = 1 indicates that firm ν enters market d and Φ[.] is the c.d.f. of the standard
normal distribution.
The entry hurdle Hdni is estimated as a headquarters-destination fixed effect in Probit
Equation (33). The entry hurdle Hdni is identified by the mean sales in China for those firms
from country i who serve market d. With a higher entry hurdle Hdni , firms from country i
have to be more productive to serve market d. This in turn raises the mean sales in China
for those entrants.
The standard deviation of the compound entry shock, ση∗ , is recovered from the coefficient
of the sales in China in Probit Equation (33). The model implies that the firm with larger
sales in China are more likely to export to all destination countries. However, this firm size
effect is disturbed by compound entry shocks. With ση∗ = 0, the export entry is entirely
decided by the sales in China.
To estimate Equation (33), I restrict the sample by requiring that xnni (ν) > 0 and for
each headquarters-destination pair (d, i) there are at least 20 entrants and 20 non-entrants.
The sample details are presented in the appendix.
20
The estimation on Probit Equation (33) shows that the coefficient of log(xnni ) is 0.203
with with standard error 0.0033. This implies that the standard deviation of the compound
entry shock η ∗ is ση∗ = 4.93.
Figure 3 reports the estimated entry hurdle, Hd,CHN,n , with respect to the distance between the headquarters country and the destination. It shows that MNEs in China must be
larger in terms of their sales in China to serve the markets farther away from their headquarters. Note that Hdni is the headquarters-destination fixed effect in Probit Equation
(33). The patterns in Figure 3 are entirely data-driven since I do not impose any geographic
structure on Hdni .
Without Headquarters = Destination
25
Entry Hurdles
20
20
15
15
10
Entry Hurdles
25
All Country Pairs
4
6
8
10
Distance b/w Headquarters and Destination Countries
6
7
8
9
10
Distance b/w Headquarters and Destination Countries
Figure 3: Entry Hurdles with Distance between Headquarters and Destination
(Note: Entry hurdle Hd,CHN,i is defined in Equation (31) as a cutoff of the sales in China
above which a firm located in China would export to a certain market.)
Figure 4 shows cultural and economic distances beItween the headquarters and destination countries matter to export entry as well. The MNEs in China have better access
to markets using the same language or with similar income level with their headquarters
countries. In particular, the MNEs in China face substantially lower export entry hurdles to
21
their headquarters countries.
Similar GDP
0
1
25
20
Entry Hurdle
10
10
10
15
15
Entry Hurdle
20
25
20
15
Entry Hurdle
Self
25
Shared Language
0
1
0
1
Figure 4: Entry Hurdles with Cultural & Economic Distances
(Note: Entry hurdle Hd,CHN,i is defined in Equation (31) as a cutoff of the sales in China
above which a firm located in China would export to a certain market. Cultural distance
refers to whether the headquarters country and the destination use the same language.
Economic distance refers to whether the headquarters country and the destination have
similar GDP per capita. “Self” refers to whether the headquarters country is the destination
country.)
4.2
Export Sales conditional on Entry
In the second step I estimate ζdi from the export sales conditional on entry. According to
the previous subsection, a firm from country i will serve market d if and only if log(xnni (ν))+
∗
log(ηdn
(ν)) ≥ Hdni . I then define an affiliate-specific entry hurdle as
H̄dni (ν) = Hdni − log(xnni (ν)).
(34)
By definition, an affiliate from country i will export to market d if and only if its com∗
pound entry shock ηdn
(ν) is greater or equal to its affiliate-specific entry hurdle H̄dni (ν).
∗
Conditional on ηdn
(ν) ≥ H̄dni (ν), the export sales relative to sales in China can be given
22
by
xdni (ν)
= − [(σ − 1) log(ζdi ) − (σ − 1) log(ζni )]
{z
}
|
xnni (ν)
Iceberg Headquarters Gravity
+
[log(Xd Pdσ−1 /Xn Pnσ−1 )
|
− (σ −
(35)
∗
1) log(τdn )] + log(ξdn
(ν))
{z
Export Sales Potential
}
∗
where ξdn
(ν) = ξdn (ν)/ξnn (ν) is a compound demand shock.
I parametrize ζdi as a function of observed gravity variables:
log(ζdi ) = ρζ,1 log(distdi ) + ρζ,2 langdi + ρζ,3 sgdpdi + ρζ,4 selfdi := ρζ Ddi ,
(36)
where distdi is the distance between d and i, langdi is a dummy for d and i speaking the
same language, sgdpdi is a dummy for d and i having similar GDP per capita, selfdi is a
dummy for d = i, ρζ = (ρζ,1 , ρζ,2 , ρζ,3 , ρζ,4 ) and Ddi = (log(distdi ), langdi , sgdpdi , selfdi )0 .
Equation (35) can be rewritten as
xdni (ν)
∗
= −(σ − 1)ρζ Ddi + ιni + κdn + log(ξdn
(ν)),
xnni (ν)
(37)
where ιni = (σ − 1) log(ζni ) and κdn = log(Xd Pdσ−1 /Xn Pnσ−1 ) − (σ − 1) log(τdn ).
∗
Note that Equation (37) only holds for firms with ηdn
(ν) ≥ H̄dni (ν).
Therefore if
cov(η ∗ , ξ ∗ ) 6= 0, then the OLS estimator of ρζ from Equation (37) will be biased. It is
straightforward to show that if cov(η ∗ , ξ ∗ ) > 0 then the OLS estimator of ρζ will be biased
towards 0. I leave the details of this proof in the appendix.
To correct the selection bias, I insert the estimated affiliate-specific entry hurdle into
Equation (37) with a general functional form:
log(
xdni (ν)
) = −(σ − 1)ρζ Ddi + ιni + κdn + m(H̄dni (ν)) + udni (ν),
xnni (ν)
(38)
where m(.) is a general-form function and udni (ν) is a measurement error. Then I use
Robinson (1988) semiparametric estimator to estimate Equation (38). The details of this
estimator are presented in the appendix.
The left column of table 4 presents the results of semiparametric estimator. ρζ is sta-
23
Dependent Variable: (log(xdni ) − log(xnni ))
Semi-parametric
OLS
.13***
(.019)
-.1**
(.04)
-.4***
(.15)
-1.2***
(.1)
17814
.2
.033*
(.02)
-.07**
(.04)
.005
(.16)
-.56***
(.08)
17814
.08
(σ − 1)ρζ,1 : log(distdi )
(σ − 1)ρζ,2 : langdi
(σ − 1)ρζ,3 : sgdpdi
(σ − 1)ρζ,4 : selfdi
# obs.
R-sq
Table 4: The Estimates on ζdi : Semi-parametric vs OLS
(Note: Semiparametric results are based on Robinson (1988) double residual estimator for
Equation (38). Fixed effects are not reported.)
tistically significant and with the expected signs. The estimates suggest that the MNEs
have advantage in serving markets closer to their headquarters: the iceberg export cost of a
MNE in China to its headquarters country is, ceteris paribus, 32% lower than to any other
country. If the distance between the headquarters and destination countries doubles, the
MNE’s export cost would increase by 4.4%. The shared language between the headquarters
and destination countries would decrease the MNE’s export cost by 3.4%. And the similar
income level between the headquarters and destination countries would decrease the MNE’s
export cost by 15%.
To show the importance of controlling entry selection, I also estimate Equation (38) by
OLS estimator without controlling for H̄dni (ν). The result is presented on the right column
of Table 4. The OLS estimator without controlling entry hurdles biases the estimates of ρζ
towards 0, which implies cov(η ∗ , ξ ∗ ) > 0.
24
4.3
Fixed Export Costs
With the estimated entry hurdle Hdni and iceberg headquarters gravity term ζdi , I can
compute the fixed export cost Edni directly by
log(Edni ) = Hdni − (σ − 1) log(ζdi ) + ιni + κdn − log σ − log wd ,
(39)
where the wage wd is approximated by GDP per capita in 2001 from Penn World Table.
However, these estimates give me only Edni for n = CHN . To impute Edni for all (d, n, i)
triples, I parameterize Edni as
log(Edni ) = ρE,1 log(Ddi ) + ρE,2 log(Ddn ) + vdni ,
d 6= n, n = CHN,
(40)
where vdni is an exogenous measurement error and Ddn are distance measures described in
previous sections.
I estimate Equation (40) by OLS estimator. The result is presented in Table 5. Similar to
ζdi , the estimates on Edni suggest headquarters gravity being substantial. The fixed export
cost of an affiliate to its headquarters country is, ceteris paribus, 80% lower than to any other
country. Doubling the distance between the headquarters and the destination will increase
the fixed export cost by 10%.
Dependent Variable: log(Edni )
log(distdi )
.1*
(.065)
langdi
-.4
(.12)
sgdpdi
-.95***
(.15)
selfdi log(distdn ) langdn
-1.6***
-.18
-.88***
(.44)
(.11)
(.20)
sgdpdn
.25
(1.1)
R-sq.
.47
N. of Obs
311
Table 5: Imputing Fixed Export Costs Edni : Gravity and Headquarters Gravity
4.3.1
Shock Parameters
The observed export sales (relative to sales in China) are drawn from a truncated lognormal distribution which depends on shock parameters {σξ , ση , ρξη }. I utilize this truncated
lognormal distribution to back out shock parameters. The parameters for demand and entry
25
shocks can be estimated by the following constrained ML estimator:
l2 (Θ2 ) =
XXX
d6=n
i
ydni (ν) log{
ν
log(xdni (ν)) − log(xnni (ν)) − ρζ Ddi + ιni + κdn − µξ∗ (ν)
1
φ[
]},
σξ∗ (ν)
σξ∗ (ν)
(41)
where
σξ2 + ρξη σξ ση
µξ∗ (ν) =
λdni (ν),
ση∗
σξ2 + ρξη σξ ση 2 Hdni − log(xnni (ν))
)[
λdni (ν) − λ2dni (ν)] + 2σξ2 ,
σξ2∗ (ν) = (
∗
∗
ση
ση
φ[(Hdni − log(xnni (ν)))/ση∗ ]
λdni (ν) =
,
1 − Φ[(Hdni − log(xnni (ν)))/ση∗ ]
(42)
ση2∗ = ση2 + σξ2 ,
and Θ2 = {σξ , ση , ρξη }. Note that (Hdni , ρζ , ση∗ , ιni , κdn ) are from the estimates in previous
subsections.
The variance of demand shock σξ2 is identified by the variance of firms’ export sales that
cannot be explained by firms’ sales in China. Given the firm’s sales in China, the firm’s
export sales would be more dispersed if σξ is larger (see Equation (42)). Note this effect
exists even without selection. In contrast, the correlation between demand and entry shock,
ρξη , affects the mean of export sales through selection. Conditional on entry, the mean of
export sales would increase with respect to ρξη (see Equation (42)). This conditional mean
identifies the correlation term ρξη .
The approach in Irarrazabal, Moxnes, and Opromolla (2013) estimates ρζ and (σξ , ση , ρξη )
simultaneously by ML estimator in Equation (41). My approach departs from theirs by first
estimatingρζ by semiparametric regression and then estimating shock parameters by a ML
estimator. The advantage of my approach is that the key parameter ρζ does not depend
on the estimates of shock parameters. In fact, to estimate ρζ consistently I only need the
compound entry shock to be i.i.d. and log-normally distributed. Therefore, my approach is
more robust to model specification errors.
The estimation results are shown in Table 6. It confirms that cov(η ∗ , ξ ∗ ) = σξ2 +ρξη σξ ση >
0.
26
MLE
σξ
3.55***
(.019)
ση
3.42***
(.0002)
ρξη
.94**
(.37)
Table 6: The Estimates on Shock Parameters
Note that ξ is an idiosyncratic demand shock and η is the ratio of ξ to an idiosyncratic
fixed export cost shock ε. The correlation between log(η) and log(ξ) is close to 1, which
implies that the variation of idiosyncratic demand shocks is much higher than the variation
of fixed export cost shock. The Chinese firm data implies that we can almost regard the
idiosyncratic fixed export cost shock ε as a constant and the variation of export entry across
firms is primarily driven by the demand shock. The shock variation estimated from Chinese
firm data is much larger than the estimates in Eaton, Kortum, and Kramarz (2011) from
French firm data but similar to the estimates of Irarrazabal, Moxnes, and Opromolla (2013)
from Norwegian firm data.
4.4
Model fit for Micro Data
In this section I test the fit of my model of firm exports for micro data patterns. To
generate model predictions, I take the sales of each MNE in China as given and simulate
(ξ, η) for all affiliate-destination pairs. Then the export entry and sales can be derived from
equation (31) and (35).
Figure 5 presents the model fit for the number of exporters and export sales in Chinese
data. The model fits the number of exporters by destination and the number of exporters to
headquarters countries pretty well. The fits in intensive margins shown in the right column
of Figure 5 are not as tight as those for extensive margins shon in the left column of Figure
5. But they are still reasonably good.
To shed light on the importance of headquarters gravity on the model fit, I eliminate
headquarters gravity by forcing MNEs in China to have the same export costs as Chinese
firms. The simulation results are shown in Figure 6. Eliminating headquarters gravity
would make my model severely underestimate the number of exporters and export values
27
Exports by Destination (Model)
10
15
25
20
GTM
ROU
2
4
6
8
# Exporters by Destination (Data)
JPN
USA
SGP
KOR
GBR
MYS
DEU
AUS
TWN
NLD
FRA
CAN
BRA
ITA
THA
MEX
ESP
IDN
BEL
ZAF
VEN
IND
ISR
CHL
SAU
RUS
DNK
NZL
CHE
GRC
SWE
NOR
FIN
IRL
ARG
POL
AUT
TUR
PRT
COL
HUN
LBN
CZE
CRIURY
IRN
GTM
ROU
10
15
20
25
Exports by Destination (Data)
Exports to HQ Countries (Model)
15
20
25
# Exporters by Destination (Model)
2
4
6
8
# Exporters to HQ Countries (Model)
6
3
4
5
7
JPN
USA
KOR
TWN
SGP
DEU
GBR
AUS
CAN
MYS
THA
ITA
NLD
FRA
IDN
ESP
BEL
IND
ZAF
SWE
NZL
ISR
BRA
MEX
CHE
SAU
DNK
CHL
ARG
FIN
GRC
NOR
POL
TUR
RUS
CZE
PRT
IRL
VEN
AUT
HUN
COL
LBN
URY
IRN
CRI
JPN
KOR
USA
TWN
SGP
DEU
GBR
FRA
NLD
AUS
MYS
CHE
ITA
THA
CAN
3
4
5
6
7
# Exporters to HQ Countries (Data)
JPN
USA
SGP KOR
DEU
TWN
GBR
NLD
FRA
CAN AUS
MYS
ITA
THA
CHE
16
18
20
22
24
Exports to HQ Countries (Data)
Figure 5: Model Predictions on Chinese Exports
(Note: The model predictions are generated by simulating demand and entry shocks for all
MNEs in China, taking their sales in China as given.)
to headquarters countries. Therefore, headquarters gravity is the key for my model to fit
patterns in micro trade data.
4.5
The Magnitude of Headquarters Gravity
The estimates of ζdi and Edni show how the MNEs’ export costs depend on their headquarters locations. In this section I illustrate the effects of headquarters locations on the
export costs of MNEs in China.
I start with computing the average differences in export costs between MNEs in China
and Chinese local firms. I compute the average iceberg headquarters gravity term weighted
P
X
by export share log(ζ̄M N E ) = d,i6=CHN P d,CHN,i
log(ζdi ). Similarly for Chinese local firm
l,k Xl,CHN,k
P Xd,CHN,CHN
log(ζ̄CHN ) = d P Xl,CHN,CHN log(ζd,CHN ). Then I can compute the average difference by
l
∆ζ =
ζ̄CHN −ζ̄M N E
.
ζ̄CHN
By exactly the same procedure I can get the average difference for the
fixed cost ∆E .
The results suggest the MNEs’ advantage in export is substantial: ∆ζ = 0.28 and ∆E =
0.82. However, this advantage in export is not distributed evenly across destinations. By
28
Exports to HQ Countries (Model w/o HG)
12
16
20
24
# Exporters to HQ Countries (Model w/o HG)
4
0
2
6
8
JPN
USA
SGPKOR
DEU
GBR
THA
MYS
NLD
FRA
AUS
CAN
ITA
JPN
USA
KOR
SGP
DEU
GBR
NLD
FRA
CAN AUS
MYS
ITA
THA
CHE
0
2
4
6
# Exporters to HQ Countries (Data)
CHE
8
12
16
20
Exports to HQ Countries (Data)
24
Figure 6: Model Predictions on Chinese Exports
(Note: The model predictions are generated by simulating demand and entry shocks for all
MNEs in China, taking their sales in China as given.)
the estimates of headquarters gravity, we have known that this advantage is strongly biased
towards headquarters countries. I now turn to summarize the MNEs’ advantage in export by
destination, showing the MNEs’ comparative advantage in exporting to some destinations.
The average iceberg headquarters gravity term by destination can be computed by
P
X
ζ
−ζ̄
P d,CHN,i log(ζdi ). Then ∆ζ,d = d,CHN M N E,d . ∆E,d is derived
log(ζ̄M N E,d ) =
i6=CHN
Xd,CHN,k
ζd,CHN
k
analogously. The results are illustrated by Figure 7. MNEs in China are shown to have
strong advantage in exporting to developed countries such as Japan, Korea, Germany, and
the U.S. Apparently this is due to these developed countries are Chinese major MP sources.
In contrast, Chinese local firms have comparative advantage in exporting to developing
countries such as India and Poland. This comparative advantage, as I elaborate below, has
distributional implications for Chinese manufacturing exports.
4.6
The Value of Connections with International Markets
In the previous section I show that MNEs in China face substantially lower export costs
than Chinese firms. This could be a reason for Chinese firms to acquire MNEs in China. By
29
40
% Difference
20
10
30
0
JP
KON
C R
H
SWE
TW E
D N
E
U U
S
SGA
G P
BR
FR
A
IT
C A
A
AUN
N S
LD
IR
N L
Z
ES L
P
IS
D R
N
K
BE
PR L
T
FI
N
AU
N T
O
G R
R
C
C
R
VE I
N
AR
G
C
H
U L
R
M Y
E
BRX
A
LB
N
C
Z
H E
U
N
PO
L
IN
D
SA
M U
YS
100
% Difference
50
0
-50
JP
KON
C R
H
SWE
U E
S
D A
E
TWU
G N
BR
IR
C L
AN
AU
FRS
SGA
P
N
ZL
IT
A
IS
R
N
LD
ES
D P
N
K
BE
PR L
T
FI
N
AU
N T
O
G R
R
C
C
R
LB I
N
VE
N
IN
AR D
G
C
H
U L
R
M Y
EX
BR
C A
Z
H E
U
N
PO
SA L
M U
YS
Figure 7: Differences in Export Costs between MNEs in China and Chinese Firms
(Note: The upper panel is the percentage differences in iceberg export costs by destination,
ζ
−ζ̄M N E,d
∆ζ,d = d,CHN
. The lower panel is the percentage differences in fixed export cost by
ζd,CHN
destination, ∆E,d =
Ed,CHN,CHN −ĒM N E,d
.)
Ed,CHN
doing this, Chinese firms would get access to MNEs’ brand names and networks in foreign
markets. If a Chinese firm gets access to export markets by acquiring a MNEs in China,
how much will its export expand? With the estimated headquarters gravity, I can calculate
the value of connections with international markets to Chinese exporters.
I consider a Chinese firm acquiring a U.S. multinational affiliate in China. By doing
this the Chinese firm could gain in many aspects. To focus on market access, I do not
allow the Chinese firm to produce the variety that is formerly produced by the U.S. MNEs.
Instead the Chinese firm can sell its own products to market d with iceberg export cost
min{ζd,U SA , ζd,CHN } and fixed export cost min{Ed,CHN,U SA , Ed,CHN,CHN }. I take the Chinese
firm’s sales in China, Chinese wage, and the destination market size as given. Then I simulate
(ξ, η) for all firm-destination pairs. Equation (31) and (35) deliver the export destinations
and export sales for each Chinese firm.
I can then compute how much, on average, the exports of the Chinese firm will expand
if it gets connections with international markets as a U.S. multinational affiliate in China.
Figure 8 shows that the exports of the Chinese firm to the U.S. can increase by about 40
30
percent. Its overall exports can increase by 13 percent. By getting access to brand names
and international networks of the U.S. MNE, the Chinese firm can substantially expand its
U
S
C A
AN
IR
ES L
G P
B
ISR
PRR
NT
C ZL
H
N E
O
D R
N
BEK
G L
R
AUC
FRS
A A
SWUT
FE
N IN
L
D D
EU
IT
M A
E
CX
SGRI
KO P
VER
JPN
CN
H
U L
R
AR Y
BRG
LB A
TWN
CN
Z
POE
H L
U
INN
SAD
ZAU
TU F
THR
R A
U
R S
O
M U
Y
IR S
IDN
G N
T
CM
O
L
0
% Difference
10
20
30
40
market share in the U.S. and other foreign countries.
Figure 8: Export Expansion from Acquisition
(Note: Here I consider a Chinese firm acquires a U.S. MNE affiliate in China. I assume that
by doing this the export costs of the Chinese firm is reduced from ζd,CHN and Ed,CHN,CHN
into, respectively, min{ζd,U SA , ζd,CHN } and min{Ed,CHN,U SA , Ed,CHN,CHN }.)
5
Calibrating the general equilibrium model
In this section I calibrate the rest of the structural parameters in the general equilibrium
model. This enables us to compute the general equilibrium outcomes and to conduct counterfactual analysis in next section. The key remaining parameters include the dispersion
parameter of productivity (θ) and bilateral trade and MP frictions. The world I target to
consists of 28 economies in 2001.6
In the following subsections, I first calibrate θ from the domestic sales of Chinese local
firms. Then I calibrate bilateral trade and MP frictions by matching the model-generated
trade and MP flows to their data correspondents.
6
These economies are Australia, Austria, Belgium & Netherlands, Brazil, Canada, Switzerland, China,
Germany, Denmark, Spain, Finland, France, Britain, Indonesia, India, Ireland, Italy, Japan, Korea, Mexico,
Malaysia, Poland, Portugal, Singapore, Sweden, Thailand, Taiwan, and the U.S.
31
5.1
Calibrating θ and Li
The dispersion parameter of firm productivity, θ, is calibrated from the dispersion of the
domestic sales for Chinese local firms.
Let α =
θ
.
σ−1
The model shows that the domestic sales for Chinese local firms is
log(xnnn (ν)) = ζ̃(ν) + log ξ(ν) + Ξn ,
(43)
where Ξn = An m̄(wnβ Pn1−β )1−σ (ζnmin )σ−1 , ζ̃ follows an exponential distribution with parameter
α, and log ξ follows a left-truncated normal distribution.
For the domestic sales I ignore the selection of exporters, assuming log ξ is symmetrically
distributed7 . The property of exponential distribution gives that
mean(log(xnnn )) − median(log(xnnn )) =
Therefore,
θ
σ−1
1 − log(2)
.
α
(44)
= 1.39. Since σ = 4, θ = 4.17.
Li comes directly from ILO database for 2001. I use the variable “paid employment in
manufacturing” as the measure of country size in the model. There are two reasons for me
to use this measure. First it is a comparable measures for manufacturing employment in
all 28 countries I am interested. Second I will use the manufacturing wage in ILO database
to calibrate the technology levels. This “paid employment in manufacturing” is compatible
with my wage measures.
5.2
Calibrating {τdn , γni , fni , Ti }
I calibrate the general equilibrium model to match aggregate bilateral trade flows and
MP sales. The data moments are summarized in Table 7.
The aggregate bilateral trade flows come from UNCOMTRADE database. Since this
paper is about manufacturing exports, I keep trade flows with 2-digit HS code between 16
and 97 (excluding 25, 26, 27). The bilateral MP sales and numbers of affiliates come from
7
The imputed entry hurdle for local firms in the domestic market, Hnnn , is very low. Therefore assuming
log ξ is symmetrically distributed will not change the result much.
32
Moments
tr
πdn
mp
πni
af f
πni
wi
Definition
Data Source
Export Share
UNCOMTRADE
MP Share
Ramondo et al. (2015)
Affiliate Share
Ramondo et al. (2015)
manufacturing wage
ILO database
Model
P
P
Xdni / d,i Xdni
i
P
P
d Xdni /
d,i Xdni
Jnni /Jiii
wi
Table 7: Data moments for calibrating the general equilibrium model
(Note: All data are for year 2001.)
Ramondo et al. (2015). The manufacturing wages come from ILO database. It will be
targeted in order to back out technology level Ti .
I have normalized bilateral trade flows and MP sales as shares of the total production
of the exporting countries. Moreover, the number of bilateral affiliates is normalized as a
share of total firms in the source countries. Targeting on shares instead of levels prevents
my calibration from dealing with current account imbalance in the data.
Given the estimated (θ, σ, β, ση , σξ , σξη ) and (ζdi , Edni , Li ), I calibrate (τdn , γni , fni , Ti ) by
the following algorithm. This algorithm can be widely used in calibrating gravity models.
0
0
0
, Ti0 ). Compute (wi , Xi , Pi ) using the iterative algorithm described
, fni
Guess (τdn
, γni
mp
af f
tr
above. Then compute the model-generated moments, w̃i , π̃dn
, π̃ni
, and π̃ni
, and their gap
with the data moments. If the gap is below tolerance, stop. Otherwise increase τdn if the
trade share in the model is higher than in data. Similar rules apply for γni and fni . Increase
Ti if the wage in the model is lower than in data. Stop until converge.
Figure 9 shows that the calibrated bilateral trade costs are increasing with the bilateral
distances between import and export countries. Moreover, the calibrated iceberg and MP
costs are increasing with the distance between source and host countries. These patterns are
consistent with the literature. Finally, the calibrated technology levels are in line with the
TFP measures from Penn World Table for 2001.
5.3
Out-of-Sample Predictions
In this section I provide additional validity for my model using the data moments that my
calibration never targets to. OECD database has provided the MNE affiliates’ export share
33
Iceberg MP Cost (in log)
0
.5
1 1.5 2
-.5
Iceberg Trade Cost (in log)
-1
0
3
1
2
4
7
8
9
Distance (in log)
10
6
-6
-1
Fixed MP Cost (in log)
0
1
2
3
Technology Level (in log)
-4
-2
0
2
6
6
7
8
9
Distance (in log)
10
7
8
9
Distance (in log)
10
DNK
AUS
USA
AUT
FIN
ESP
CHE
CAN
SWE
GBR
FRA
ITA
JPN
PRT BEL IRL
KOR
SGP
DEU
POL TWN
BRA
MEX
MYS
IND
CHN
THA
IDN
-1.5
-1
-.5
0
.5
Total Factor Productivity (in log)
Figure 9: The Calibrated (τdn , γni , fni , Ti )
(The parameters are calibrated by the algorithm described above. The distance is the geographic bilateral distance between the importing and the exporting countries (compared
with trade costs) and between the source and host countries (compared with MP costs). The
TFP comes from Penn World Table for 2001.)
34
for 5 OECD countries in 2001. I compute the equilibrium with the calibrated parameters
and compare the moments generated by the model with the data.
To examine how important the headquarters gravity is for out-of-sample predictions, I
re-calibrate the model ignoring headquarters gravity, i.e. ζdi = 1 and Edni = 1 for all (d, n, i)
and re-calibrate the model to match the bilateral trade and MP shares. By construction,
the baseline model and the model ignoring headquarters gravity should generate the same
production share of MNEs. But their predictions for the MNEs’ export shares could be
different.
The outsample predictions are shown in Table 8. The baseline model fits the MNEs’
export shares in several OECD countries. The model ignoring headquarters gravity tends to
underestimate the MNEs’ export shares. Therefore, headquarters gravity is the key for my
model to fit the exports of multinational affiliates.
% Exports
FRA
IRL
ITA
NLD
SWE
Data
40.6
90.6
23.4
64.2
45.1
Baseline model
46.6
89.0
35.7
66.6
57.5
Model ignoring HG
20.9
68.8
13.4
39.7
28.6
Table 8: Model-fit for MNEs’ Export Share in OCED Countries
(Note: %Exports refers to the MNEs’ export share in the host countries. The data shown
in this table come from OECD database. The model ignoring headquarters gravity comes
from setting ζdi = 1 and Edni = 1 for all (d, n, i) and re-calibrating the model to match the
bilateral trade and MP shares.)
6
Counterfactual Analysis
In this section I conduct counterfactual experiments to quantify impacts of knowledge
transferred by MNEs on trade and welfare. In the first experiment I decompose the impacts of
productive knowledge and connections with international markets. In the second experiment
I apply my model to evaluate the welfare implications of Chinese subsides for MNEs in China.
35
Note that in this paper I take China as an example. But apparently my multi-country general
equilibrium model can apply for policy discussions in other countries.
6.1
Implications of Knowledge Transfer by MNEs
In this subsection I decompose the impacts of productive knowledge and connections with
international markets by counterfactual experiments in two scenarios. First, I force MNEs
in China to have the same export costs as Chinese firms, i.e. ζdi = ζd,CHN and Ed,CHN,i =
Ed,CHN,CHN for d 6= CHN .8 Second, I shut down MNEs in China by letting γCHN,i =
∞. Changes between these two scenarios capture the impacts of productive knowledge
brought by MNEs. I start with implications for Chinese exports and then discuss the welfare
implications.
6.1.1
To Promote Export, promote MNEs
Changes in Chinese manufacturing exports from the baseline economy to counterfactual
scenarios are presented in Table 9. According to micro trade data, MNEs in China account
for 68 percent of Chinese manufacturing exports in 2001. The counterfactual experiment
shows that shutting down MNEs in China would decrease Chinese manufacturing exports
by 49 percent. Shutting down MNEs in China would induce the entry of Chinese firms. But
these new entrants are less productive and with higher export costs than MNEs in China.
Consequently, Chinese manufacturing exports would fall dramatically if MNEs exit Chinese
market.
Moreover, imposing the same export costs on MNEs as those faced by Chinese firms will
decrease Chinese manufacturing exports by 23.3 percent. So half of the MNEs’ contribution
to Chinese exports is due to their low export costs. The remaining half is due to their
high productivities. In sum, both productive knowledge and connections with international
markets transferred by MNEs are quantitatively important for Chinese exports.
Furthermore, the impacts of connections with international markets are not evenly dis8
Headquarters gravity implies Chinese local firms having advantage in serving Chinese market. In this
counterfactual scenario I do not allow MNEs in China to incur the same trade cost to China with Chinese
local firms. Otherwise it gives MNEs additional advantage in serving China.
36
tributed across destinations. Table 9 shows that if MNEs in China have the same export
costs as Chinese firms, Chinese manufacturing exports to OECD countries would decrease
by 32 percent while Chinese manufacturing exports to non-OECD countries would increase
by 27 percent. This trade switching effect is mainly due to the fact that most MNEs in
China come from rich OECD countries. In contrast, shutting down MNEs in China would
decrease Chinese exports to both OCED and non-OEDC countries. This is mainly due to
the productivity effect. Unlike those productive MNEs in China, Chinese firms can hardly
export to developing countries which usually have high trade barriers.
% Changes in Chinese Manufactuing Exports
No MP
Total
-49.4
To OECD
-55.9
To non-OECD
-11.6
No HG
-23.3
-31.9
27.4
Table 9: The Impacts of MNEs in China on Chinese Exports
(Note: No HG refers to the counterfactual scenario in which MNEs in China have the same
export costs with Chinese local firms. No MP refers to the counterfactual scenario in which
γCHN,i = ∞. %Change are counterfactual levels relative to the baseline level.)
Figure 10 illustrates impacts of headquarters gravity on Chinese exports by destination.
If MNEs in China lose their advantage in export, China would lose a large fraction of its
exports to developed countries such as Japan, Britain, Germany, and the U.S. Chinese
exporters would then switch into the developing countries such as India, Indonesia, and
Thailand. In short, headquarters gravity does not only affect Chinese export scales but also
shapes the geographical patterns of Chinese exports.
In sum, the counterfactual analysis shows that MNEs in China are responsible for a substantial fraction of Chinese export booms. Both productive knowledge and connections with
international markets brought by MNEs are quantitatively important for Chinese exports.
These results suggest for governments that seek to promote exports, an effective policy is to
attract FDI from large markets.
37
60
% Changes in Chinese Exports
-20
0
20
40
U
S
JP A
G N
B
C R
H
D E
N
D K
E
BEU
L
IR
C L
AN
AU
ES T
P
FI
FRN
SWA
AUE
PRS
T
IT
KO A
SGR
TW P
M N
E
POX
BR L
IN A
M D
Y
THS
ID A
N
-40
Figure 10: The Impacts of Headquarters Gravity on Chinese Exports by Destination
(Note: % Change refers to the percentage change from the calibrated economy to the counterfactual economy. Here counterfactual refers to the case that MNEs’ in China have the
same export costs as Chinese firms. )
6.1.2
Welfare Implications
The general equilibrium model allows me to examine the welfare implications of knowledge transfer by MNEs. Due to the CES preference and the exogenous country size, I can
measure the welfare by real GDP:
Wi =
wi + Π i
.
Pi
(45)
The GDP consists of two parts: the workers’ wage and the firms’ profits. I assume that
the firms’ profits are owned by a unit measure of entrepreneurs. The fundamental difference
between wage and profits is that the wage can only be earned in the country the labor lives
in but the profits can come from multinational production.
Table 10 shows the welfare implications. If MNEs in China have the same export costs as
Chinese firms, the welfare in China would decrease by 0.1 percent. This small welfare effect,
however, is associated with a substantial distributional effects. Forcing MNEs in China to
have the same export costs with Chinese firms would decrease Chinese nominal wage by
8.8 percent. Losing access to international markets would greatly decrease Chinese labor
38
demand, making Chinese workers worse-off. In contrast, eliminating the MNEs’ advantage
in export would shelter Chinese local firms from the MNEs’ competition, increasing their
nominal profits by 1.4 percent. The productive knowledge transferred by MNEs has similar
effects for Chinese wage and profits.
However, two types of knowledge have different price effects for China. Productive knowledge transferred by MNEs decreases Chinese price index by promoting Chinese productivities. In contrast, connections with international markets increases Chinese price because
MNEs drive out Chinese firms that have advantage in serving Chinese markets. As a result,
imposing the same export costs on MNEs as those of Chinese firms would decrease Chinese
price index by 6.22 percent but shutting down MNEs in China would decrease Chinese price
by only 1.8 percent.
%Changes in China
Welfare
Nominal Wage
Nominal Profit
Price
No MP
-9.73
-23.9
26.9
-1.78
No HG
-.10
-8.83
1.39
-6.22
Table 10: Welfare, Distributional, and Price Effects of Headquarters Gravity
(Note: No HG refers to the counterfactual scenario in which MNEs in China have the same
export costs with Chinese local firms. No MP refers to the counterfactual scenario in which
γCHN,i = ∞. %Change are counterfactual levels relative to the baseline level. The results
for all 28 countries are presented in the appendix.)
6.2
Subsidizing Foreign MNEs
MNEs have advanced productive technologies and connections with international markets. As I have shown, the knowledge transfer led by MNEs is crucial for the exports of
host countries. A related policy question is whether the government could subsidize MNEs
to promote exports, and by doing this, what the welfare effect would be.
My model provides a suitable workhorse for evaluating this kind of policies. As an
important component of its “Reform and Openness” policies, Chinese governments provided
substantial subsidies for foreign MNEs. Before 2008, Chinese corporate income tax rate was
39
33 percent for Chinese firms but only 15 percent for foreign firms. My model provides a
suitable workhorse to evaluate the impacts of this subsidy.
I first introduce corporate income taxes into my baseline model. I assume that these
taxes are proportional to the profits of firms in China (33% for Chinese firms and 15% for
MNEs in China). Tax revenues are assumed to be transferred uniformly to all workers and
entrepreneurs in China. I then re-calibrate {τdn , γni , fni , Ti } in the model with corporate
income taxes to match aggregate data. To examine the impacts of subsidies, I compute
the equilibrium in which Chinese corporate income tax rate for MNEs in China is tM N E ∈
[0, 0.33]. The lower tax rate mean higher subsidies.
Figure 11: Welfare Implications for Subsidizing MNEs in China
The results are shown in Figure 11. Subsidizing foreign MNEs do indeed promote exports.
It can also increase Chinese real wage. But it can substantially decrease Chinese real profits.
Taking the costs of subsidy into account, Subsidizing foreign MNEs leads to welfare loss in
China.
40
7
Conclusion
This paper first points out that by directly controlling factors of production in foreign
countries, MNEs transfer not only their productive knowledge but also connections with
international markets across borders. I then quantify connections with international markets
transferred by MNEs in a general equilibrium model. The key feature of this model is that
it allows a MNEs’ export costs to depend on the location of its headquarters (headquarters
gravity). The model provides a framework that can estimate headquarters gravity in micro
trade data. The estimation results show that MNEs in China face substantially lower export
costs to markets closer to their headquarters. As a result, the export costs of MNEs in China
are much lower than those of Chinese firms. My model captures micro data patterns much
better than previous models without headquarters gravity.
With structural parameters in hand, I conduct counterfactual experiments to examine
the implications of knowledge transfer by MNEs on trade and welfare. I find that both
productive knowledge and connections with international markets transferred by MNEs are
quantitatively important for Chinese exports. They both raise Chinese wage but decrease
Chinese firm profits. But productive knowledge tends to decrease Chinese price level while
connections with international markets tends to increase Chinese price. Consequently, China
gains much more from productive knowledge than from connections with international markets. I also apply my model to evaluate Chinese subsidies for foreign MNEs. I find that
subsidizing foreign MNEs can promote Chinese exports but lead to welfare loss.
This paper may be extended in several ways. One possibility is to introduce multiple
sectors in the model. The motivation of this extension is a simple observation that foreign
firms in China produce a very different set of goods with Chinese local firms. Therefore
MNEs in China do not only affect Chinese export scales and directions, but also affect the
composition of Chinese exports. A second direction is to disentangle the demand and supply
factors on headquarters gravity. Headquarters gravity could be driven by lower penetration
costs or by higher demands in markets closer to headquarters. This extension requires
detailed quantity and price data similar to Cosar et al. (2015). A third direction is to
incorporate imports of multinational affiliates into the model. Foreign firms are known to
41
use more imported intermediates than local firms. Combining imports and exports could
give us more precise estimates on MNEs’ welfare implications.
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location on manufacturing quality. NBER working paper (2012).
[36] Tinbergen, J. Shaping the world economy: Suggestions for an international economic
policy. New York: Twentieth Century Fund .
[37] Tintelnot, F. Global production with export platforms. Working paper (2014).
45
Appendix A
A.1
Data Construction
Merging Customs Records with Manufacturing Survey
The balance sheet data in manufacturing survey contains a numerical firm identifier which
is consistent over time. The customs records also includes a numerical identifier for exports.
Unfortunately, two numerical identifiers coming from different systems have no way to be
connected directly. As in the literature (see, for example, Wang and Yu (2012) [?]), a fuzzy
matching algorithm is required. I use the standardized firm name, the manager name, phone
number, and zip code as fuzzy identifiers. Exports are restricted within manufacturing goods
whose 2-digit HS code is above 15 and below 98 (excluding 25, 26, 27).
One complication is the exports through intermediaries. My theory cannot rationalize
the exports of intermediaries since they do not export what they produce. So I exclude
them in the data by dropping exporters whose names contain key words such as “import”,
“export”, “foreign trade”, “service trade”, and so on. This step excludes about 48% of the
export transactions which account for about one third of Chinese manufacture exports in
2001. This result is in line with Manova and Zhang (2012) [?].
Another complication is that the same exporter in the customs records may correspond
to different names and phone numbers. The same occurs in the manufacturing survey. To
address this problem, I first collect all names and other identifiers used by each exporter
over 2000-2006 (the period covered by data), given it exports in 2001. I then do similar
work in manufacturing survey for each firm operating in 2001. Then I merge two sets of
fuzzy identifiers by a matching algorithm based on the weighted average of string distance.
I allow multiple exporters to correspond to the same firm in manufacturing survey, but I
do not allow multiple firms in manufacturing survey to correspond to the same exporter.
For the latter case, I merge two datasets manually. This algorithm matches exporters which
account for about 85% of Chinese manufacturing direct exports to their balance sheet data
in manufacturing survey.
Foreign-invested-enterprise survey shares a unique numerical firm identifier with manufacturing survey. So merging this two datasets is straightforward.
46
The U.S. MNEs in China in 2001
Chinese Data
BEA Data
32255
21808
3418
7029
29578
20419
3066
6094
Total Sales
Sales in China
Sales to the U.S.
Sales to other
Table 11: The U.S. MNEs in China: Chinese data vs BEA data
(Note: All values are in million dollars.)
A.2
Data Quality and Summary Statistics
To examine the quality of Chinese firm database I constructed in the previous section,
I compare the aggregate sales of the U.S. MNEs in China in Chinese firm data with the
records in the BEA database. I take the BEA database “Data on activities of multinational
enterprises” in 2001 which contains information on, for each host country, the total sales of
the U.S. MNEs, the sales to the host country, the sales to the U.S., and the sales to other
countries. Table 11 shows the comparison result. The aggregate statistics of the U.S. MNEs
in China recorded in Chinese firm data is reasonably closed to the records in BEA database.
This result suggests that the quality of Chinese firm data is good for my purpose.
Table 12 presents some summary statistics of MNEs in China. Several patterns are
confirmed. First comparing to Chinese firms a larger fraction of MNEs are exporters. Second,
a large fraction of MNEs in China export to their headquarters countries. Third MNEs in
China are larger than Chinese firms either in terms of total sales, number of employees, or
value-added. Fourth the value-added share of MNEs in China is not significantly lower than
the value-added share of Chinese firms.
47
(a) Japanese MNEs in China
(b) British MNEs in China
Figure 12: The Exports of MNEs in China: by Destination
(Note: The exports of MNEs in China to each destination are normalized by Chinese manuX
facturing exports to that destination, i.e. Xd,CHN,i
where Xd,CHN,i is the exports of MNEs in
d,CHN
China from country i to country d and Xd,CHN is Chinese manufacturing exports to country
d. The darker blue means higher normalized exports.)
48
Origin
#Firms
#Exporters
#Exp to Origin
Sales
Value-added
Employment
Export
Exp. to origin
AUS
AUT
BEL
CAN
DEU
DNK
ESP
FIN
FRA
GBR
ITA
JPN
KOR
NLD
NZL
SGP
SWE
TWN
USA
268
49
40
243
429
25
42
27
191
495
138
3088
1247
163
33
933
67
3400
2341
161
35
26
140
299
17
20
21
130
330
81
2531
1049
122
17
617
43
2374
1515
67
13
13
47
206
10
10
13
62
122
47
2319
889
45
2
336
21
1117
1028
1260
383
1414
1828
14094
571
243
5759
2651
7378
956
37738
14713
5279
243
12155
2815
14312
33415
353
100
359
387
3815
160
65
740
707
2070
253
9375
3136
1045
48
3189
584
3578
9394
45
17
11
41
131
7
9
8
42
196
30
927
456
55
9
294
13
743
630
328
59
118
320
1837
312
41
2449
442
2676
170
20928
10090
2377
83
4387
414
6598
11607
54
1
18
18
611
148
17
172
100
141
36
12631
2558
124
2
460
135
422
3797
CHN
96804
15251
-
588496
147952
33185
37981
-
Table 12: Summary Statistics for Manufacturers in China by Origin
(Note: Sales, value-added, exports, exports to origin are in million dollars. Employment is
in thousands. Firms from Hong Kong and Macau are excluded.)
Appendix B
Robustness for the Reduced-form Evidence
Appendix C
Model Derivation and Computation
C.1
Algorithm for computing general equilibrium
Algorithm 3 (Computing General Equilibrium Outcomes) To compute (wi , Xi , Pi )N
i=1 ,
I normalize XU SA = 1. Then
• Guess initial price indices (Pi0 )N
i=1 .
– Guess initial wages and absorptions (wi0 , Xi0 )N
i=1 .
– Update wages into (wi1 )N
i=1 by Equation (28).
– Update absorptions into (Xi1 )N
i=1 by Equation (29).
1
1 N
– If the distance between (wi0 , Xi0 )N
i=1 and (wi , Xi )i=1 is below the tolerance, stop.
Otherwise repeat until stop.
• Update price indices into (Pi1 )N
i=1 by Equation (23).
1 N
• If the distance between (Pi0 )N
i=1 and (Pi )i=1 is below the tolerance, stop. Otherwise
repeat until stop.
49
1{xdni (ν) > 0}
log(empni (ν))
log(distdi )
selfdi
langdi
sgdpdi
R-squared
N. of Obs.
Ordinary
.14***
(.003)
-.044***
(.004)
.93***
(.02)
.12***
(.009)
.057***
(.02)
Processing
.26***
(.003)
-.011***
(.005)
1.2***
(.03)
.10***
(.01)
-0.001
(.03)
1137780
872014
log(xdni (ν))
Ordinary
0.034***
(0.01)
-.043***
(.02)
.89***
(.07)
.08**
(.04)
-.017***
(.05)
.09
38406
Processing
.52***
(.01)
.02
(.02)
1.3***
(.08)
.11***
(.04)
-.15**
(.07)
.24
31671
Table 13: Headquarters locations and MNEs’ Exports
(Note: Destination fixed effects are not reported. Firms from Hong Kong and Macau are excluded. i refers to headquarter
country and d refers to destination country. dist is geographic distance. lang is a dummy for shared language. sgdp is a dummy
for similar GDP per capita. self is a dummy for i = d.)
1{xdni (ν) > 0}
log(empni (ν))
log(distdi )
selfdi
langdi
sgdpdi
R-squared
N. of Obs.
Apparel
.05***
(.012)
-.12***
(.02)
.87***
(.07)
.23***
(.04)
-.06
(.06)
Machinery
.22***
(.005)
-.003
(.009)
1.12***
(.05)
.07***
(.02)
-.006
(.04)
112704
229824
log(xdni (ν))
Apparel
0.30***
(0.05)
.04
(.06)
1.6***
(.3)
.18
(.15)
-.12
(.16)
.34
2641
Machinery
.62***
(.02)
.06
(.04)
1.5***
(.2)
.03
(.08)
.19
(.13)
.16
9678
Table 14: Headquarters locations and MNEs’ Exports
(Note: Destination fixed effects are not reported. Firms from Hong Kong and Macau are excluded. i refers to headquarter
country and d refers to destination country. dist is geographic distance. lang is a dummy for shared language. sgdp is a dummy
for similar GDP per capita. self is a dummy for i = d.)
Appendix D
D.1
Empirical Implementation
The Sample used in Estimating Entry Hurdles
For each MNE in China I observe its headquarters country i and its exports to each
destination d (include sales in China). Exports to each destination are 0 for non-entrants
and positive for entrants. The original data includes 116 headquarters countries (include
China) and 172 destination countries (include China). Since I focus on MNEs’ exports, I
exclude Chinese firms from the sample. Furthermore, I exclude firms from Hong Kong and
Macau from the sample.
50
1{xdni (ν) > 0}
log(empni (ν))
log(distdi )
selfdi
langdi
sgdpdi
R-squared
N. of Obs.
Homo.
.17***
(0.0034)
.011*
(.007)
0.71***
(.029)
0.11***
(.014)
-0.05
(.016)
Diff.
.17***
(.0019)
-.026***
(0.004)
0.96***
(.02)
0.11***
(.008)
0.07***
(.03)
1206576
1342656
log(xdni (ν))
Homo.
.25***
(.021)
-.011
(0.04)
0.33*
(.17)
0.058
(.09)
-0.072
(.017)
0.05
9805
Diff.
.48***
(.0075)
-0.056***
(0.01)
1.28***
(.061)
0.09***
(.03)
0.03
(.05)
0.23
51025
Table 15: The headquarters gravity equation: homo. vs diff. goods
(Note: the coefficients of industry dummies are not reported. The classification is based on Rauch (1999). The homogeneous
goods include goods with organized exchange and reference priced goods in “liberal” classification.)
To estimate entry hurdles, I have to restrict my sample in two dimensions. First, since I
control for the firm size by sales in China, I have to drop pure exporters which do not sell in
China. These firms, mainly export processors, account for about a quarter of Chinese total
exports.
Second, the identification of Hdni requires that some MNEs in China from country i
export to market d while others do not. Therefore I restrict my sample by requiring that
for each pair of the headquarters and destination countries, (d, i), there are at least 20
firms export while at least 20 firms do not. This restriction leaves me a sample with 10652
MNEs in China from 15 headquarters countries, 48 destination countries, and 311 pairs of
headquarters and destination countries.
D.2
Selection Bias
∗
Conditional on ηdn
(ν) ≥ H̄dni (ν), the export sales can be given by
xdni (ν)
∗
= −(σ − 1)ρζ Ddi + ιni + κdn + log(ξdn
(ν)),
xnni (ν)
(46)
where ιni = (σ − 1) log(ζni ) and κdn = log(Xd Pdσ−1 /Xn Pnσ−1 ) − (σ − 1) log(τdn ).
Without loss of generality, I assume that the coefficient of log(distdi ), ρζ,1 , is greater
∗
than 0. Then log(distdi ) is positively correlated with H̄dni (ν). Since ηdn
(ν) ≥ H̄dni (ν),
log(distdi ) is positively correlated with η ∗ (ν). Since cov(η ∗ , ξ ∗ ) > 0, log(distdi ) is positively
51
correlated with ξ ∗ (ν). So OLS estimator will upbias the estimates of −ρζ,1 . Therefore, the
OLS estimator will bias the estimates of ρζ,1 towards 0.
52