Multinational Production and Comparative Advantage∗
Vanessa Alviarez
†
Sauder School of Business
University of British Columbia
September 14, 2016
Abstract
This paper assembles a novel industry-level dataset of bilateral foreign affiliate sales to
document two new empirical regularities: 1) the sectoral dispersion patterns of multinational
activity are significantly heterogeneous across countries; and 2) multinational production (MP)
is disproportionately allocated in industries where local producers are relatively less productive.
To account for these facts, this paper incorporates a sectoral Ricardian framework into a
general equilibrium model of trade and MP in order to show analytically and quantitatively, the
extent at which the dispersion of relative sectoral productivities—measured by the Atkinson
inequality index—as well as the barriers to MP, accounts for the magnitude, sectoral allocation
and the welfare impact of multinational production. The paper shows that by ignoring sectoral
heterogeneities, one-sector models systematically understates the welfare gains from MP and
openness. In particular, gains from openness are three times higher in a multi-sector model
compare to a one-sector framework; and 14 percent higher compared to a counterfactual
scenario without differences in relative productivity across sectors. This paper also shows that
gains from trade are decreasing in the sectoral dispersion of MP shares, as MP erodes sectoral
level Ricardian comparative advantages and therefore inter-industry trade. In a counterfactual
scenario in which MP does not affect relative differences in effective productivities, gains from
trade are almost 12 percent lower than in equilibrium. Finally, the paper shows a significant
welfare impact of MP in the non-tradable sector. In particular, when MP is prohibitively
costly in non-tradable goods, real income decreases by 8 percent and gains from openness
decline by 35 percent. Moreover, losing access to non-tradable intermediate inputs produced
by foreign affiliates causes an increase of 2.45 percent in the price index of tradables and an
increase in the overall price index of 5.7 percent.
Keywords: Multinational Production; Comparative Advantage; Sectoral Productivity;
Welfare
JEL Classification Numbers: F11, F14, F23, O33.
∗
I would like to thank my advisors Andrei Levchenko, Alan Deardorff, Linda Tesar, and Kyle Handley for invaluable guidance, suggestions, and encouragement. I am also grateful to the seminar participants at the University of
Michigan, the University of British Columbia, Penn State University, Minneapolis Fed, the Federal Reserve Board,
TIGN and WCT for useful comments and suggestions.
†
Email: [email protected].
1
1
Introduction
A striking feature of multinational activity is its sectoral heterogeneity. In the United Kingdom
for instance, 72 percent of the Transportation and Equipment sector is produced by affiliates of
foreign multinationals, while 70 percent of its Metals production is done by British owned companies. An even more salient characteristic is how distinctive these patterns are across countries. In
France, instead, 74 percent of output in the Transportation and Equipment sector is produced by
French owned companies while almost 50 percent of the Metals production is at hands of foreign
affiliates. These examples highlight two levels of heterogeneity: first, within a country the shares
of multinational production (MP) in total output are heterogeneous across sectors; and second,
this sectoral dispersion of multinational activity is significantly heterogeneous across countries.
In order to take a closer look to these patterns, this paper assembles a novel dataset of bilateral
foreign affiliate sales, employment and number of affiliates that, for the first time, incorporates
the sectoral dimension into a multi-country framework to uncover an empirical regularity: the
observed uneven allocation of MP across sectors is significantly related to differences in sectoral
productivity. In particular, multinational production is disproportionately allocated to industries
where local producers are relatively less productive.
This paper shows that omitting MPs sectorial dimension leads us to ignore channels that significantly affect the magnitude, sectoral allocation and the welfare impact of MP. One-sector models
of trade and multinational production account for the aggregate effects of increasing openness—
trade and MP liberalization—however, they can not account for the impact that reductions on
MP and trade barriers have on the sectoral dispersion of MP and trade shares, leading them to
underestimate the welfare gains from MP and openness. This paper fills this gap by estimating a
Ricardian general equilibrium model of trade and MP that captures the impacts of MP barriers
and differences on relative productivity across sectors in a multi-country framework. Furthermore, this paper estimates the importance of sectoral MP dispersion in accounting for the gains
from trade. In particular, we show that gains from trade are decreasing on the sectoral dispersion of MP, as it erodes industry level Ricardian comparative advantages and, as a consequence,
inter-industry trade.
To evaluate these channels, this paper assembles a multinational production dataset for a
significant number of countries that distinguishes the sector of operations, the country where
production takes place (location), and the country where the parent firm is located (source).
This tri-dimensional dataset—sector-location-source—provides detailed information on production, employment and the number of foreign affiliates for 32 countries, 9 tradable sectors, and
4 non-tradable sectors for the period 2003–2012. The dataset is used to show that (i) for each
source-host country pair, the share of MP on output is significantly heterogeneous across sectors;
(ii) there are significant cross-country differences in the sectoral heterogeneity of multinational
production; and (iii) MP activity is disproportionately allocated in industries where local producers exhibit comparative disadvantage. The intuition behind the later fact relies on competition
1
forces: facing similar prices for intermediate inputs and factors of production, local and foreign
affiliate firms differ primarily in their productivity levels. This implies that foreign affiliates are
more likely to succeed in sectors where local producers are relatively less productive. Further, we
show that this negative and significant relationship between sectoral MP shares and sectoral productivities is robust to different samples, specifications, estimation methods; as well as alternative
measures of productivity and multinational activity.
To capture these stylized facts, analytically and quantitatively, this paper incorporates differences in productivity across industries into a benchmark Ricardian model of trade and multinational production developed by [Ramondo and Rodrı́guez-Clare, 2013] (henceforth RRC). Using
a simplified version of the model and constructing a measure of productivity dispersion based on
the Atkinson inequality index, we develop six analytical predictions. First, and in line with our
stylized facts, we show that the dispersion of MP shares across sectors increases with the sectoral
dispersion of relative productivities, with less-productive sectors receiving the largest fraction of
MP relative to output. Second, we show that there is a systematic relationship between MP
barriers and the sectoral heterogeneity of multinational production. In particular, we show that
the lower the MP barriers, the higher the dispersion of MP shares across sectors, since a reduction in MP costs makes MP shares more responsive to differences in relative productivity across
countries, increasing the sectoral heterogeneity of MP shares.
The next analytical predictions focus on the implications of different sources of sectoral heterogeneity of MP shares on gains from trade (GT), gains from MP (GMP) and gains from openness
(GO). We show that gains from MP are higher in multi-sector models—relative to one-sector
frameworks; and the difference in GMP is larger (i) the higher the dispersion of productivity
across sectors, (ii) and the lower the MP barriers. Next, we show that GT in multi-sector models
can be expressed as the product of the sectoral dispersion of trade shares, measured by the Atkinson inequality index, and the aggregate trade share in the economy. In addition, we show that
a reduction in MP barriers affects the sectoral heterogeneity of MP and trade shares in opposite
directions. In particular, freer MP increases the dispersion of MP shares across sectors and the
gains from MP, but it reduces the heterogeneity of trade shares, which ultimately reduces the gains
from trade. Finally, we show that GO are higher in multi-sector—relative to one-sector—models;
and the difference in GO is larger (i) the higher the dispersion of productivity across sectors, and
(ii) the lower the MP barriers. The use of the Atkinson inequality index—which is calculated by
comparing the geometric and arithmetic mean—is particularly convenient in an analytical framework in which welfare gains are expressed as a multiplicative function of the model’s objects.
Measuring sectoral dispersion through the Atkinson index facilitates the discussion of many of
the analytical predictions of the model by helping us to summarize and uncover the interaction
of different sources of heterogeneity and their welfare implications.
In order to test the implications of the model, our quantitative framework features asymmetric
MP and trade barriers; multiple factors of production (labor and capital); different factor and
2
intermediate input intensities across sectors; a realistic input-output matrix between sectors; interand intra-sectoral trade; and a non-tradable sector. By combining these features into an unified
framework, and with the use our novel dataset, we estimate the models parameters in order to
test it’s main analytical predictions. For each country-sector pair, we estimate the productivity
of local producers—or fundamental productivity—as well as the productivity of all producers in
the economy, including local and foreign affiliate firms—or effective productivity. Distinguishing
productivity by ownership allows us to observe that the dispersion of sectoral productivity is
lower for the overall economy than when it is estimated only considering local producers. These
differences are explained by the larger inward MP shares in sectors where local producers are
relatively less productive. As a result, the productivity enhancement due to MP is uneven and
biased towards sectors in which local firms exhibit comparative disadvantage, reducing the sectoral
productivity dispersion of the overall economy.
Using the estimated parameters, we calculate the gains from MP, trade and openness in our
multi-country, multi-sector model of trade and MP, and compare them with the welfare gains
delivered by one-sector frameworks. On average, in our model gains from MP are 18 percent,
and gains from openness 32 percent, compared to 6.9 and 10.4 percent in one-sector models, respectively. The differences in welfare arising between these two models can be interpreted as the
additional gains coming from diverse sources of heterogeneity all combined. We concentrate our
attention on our first set of counterfactuals, by focusing on one particular source of heterogeneity:
the sectoral dispersion of relative productivities. To isolate the effects that Ricardian comparative advantages have on the dispersion of MP and trade shares, and ultimately on the gains from
openness, we construct a counterfactual exercise in which we “remove comparative advantage”
while keeping other country-sector specific model’s parameters (e.g. trade and MP costs) unaltered. To pursue this exercise, we adjust the methodology developed by [Costinot et al., 2012],
in which the comparative advantage of each country is removed, one at the time, by imposing
the structure of the sectoral productivity differences of each “reference” country to the rest of
the economies. This is done by adjusting countries’ absolute advantage, while preserving relative
nominal income to avoid any indirect terms of trade effects on the reference country. Our results
show that gains from openness are 14 percent higher compared with a counterfactual scenario in
which there are not relative differences in productivity across sectors, with a reduction on real
income of 1.4 percent. Although these differences on welfare gains and real income are considerable, they are partially muted by the interplay between Ricardian productivity differences and
other sources of heterogeneities, such as differences across sectors and countries of MP barriers.
In fact, in a second set of counterfactuals exercises, we find that GO will be more than 30 percent
higher in a scenario where there are no differences in productivity across sectors and there is no
heterogeneity in MP costs.
The effects of the counterfactual changes of relative productivities or MP barriers, can be decomposed into two parts: a first component due to changes in aggregate MP and trade shares,
and a second component due to changes in their sectoral dispersion. Our quantitative framework
3
allows for multiple sources of heterogeneity, and therefore, the comparison with one-sector models
is not longer valid to fully account for the aggregate effects of a change in the model’s parameters.
Instead, we extend [Ossa, 2015] for the case of MP and trade with multiple sectors to express welfare gains as a function of aggregate shares, which allows us to easily adjust the “counterfactual”
aggregates to meet their equilibrium values. The adjusted effect takes away the impact on welfare
created by changes in the aggregate MP and trade shares, isolating the effects due to changes in
their sectoral dispersion.
In our third counterfactual, we calculate the consequences for trade flows and gains from trade
of the lower dispersion of effective productivities caused by an uneven allocation of MP across
sectors.1 To this end, we construct a counterfactual scenario in which multinational activity
only affects the average productivity of the host economy, while keeping relative productivity
differences intact, finding that gains from trade are almost 12 percent higher than in equilibrium.
In the last counterfactual, we explore the impact of allowing MP in the non-tradable sector on
welfare gains and the price index of tradables. The empirical relevance of this counterfactual
is supported by three facts: (i) the non-tradable sector represents a large fraction of the world
economy; (ii) MP shares are relatively large in non-tradables; and (iii) most tradable sectors have
a high input requirement of non-tradable goods. Our results show that when MP is prohibitively
costly in non-tradable goods, real income decreases by 8 percent and gains from openness decline
by 35 percent. Moreover, losing access to non-tradable intermediate inputs produced by foreign
affiliates causes an increase of 2.45 percent in the price index of tradables and an increase in the
overall price index of 5.7 percent.
This paper is closely related to recent efforts in quantifying the impact of multinational production and trade in a general equilibrium framework. [Ramondo and Rodrı́guez-Clare, 2013]
develop a general equilibrium model that measures the gains from openness associated with the
interaction of trade and MP in a one-sector framework; while [Shikher, 2012b] measures the extent
of aggregate technology diffusion across countries that takes place due to multinational production
and quantifies its welfare effects.[Arkolakis et al., 2013] develop a general equilibrium model of
monopolistic competition in which the location of innovation and production is endogenous and
geographically separable. This paper builds upon this literature by exploring the analytical and
quantitative implications of adding sectoral heterogeneity to a model of trade and MP. By omitting the sectoral dimension, one-sector models are by design silent with respect to how MP costs
and sectoral differences in relative productivity can affect the aggregate and sectoral allocation
of MP. In addition, a sectoral framework allows us to capture the role that MPs heterogeneous
allocations has on shaping the observed sectoral trade patterns and their welfare gains. Our paper
is also related to [Neary, 2007], who shows how, in an oligopoly framework, the pattern of crossborder mergers resulting from a market integration is such that low-cost firms acquire high-cost
foreign rivals. Our paper contributes to this literature by uncovering a negative relationship be1
We call effective productivities to the ones corresponding to all producers in the economy–local and foreign.
In addition, we refer as fundamental productivities to those corresponding only to local producers.
4
tween sectoral MP shares and comparative advantage, and by showing the underlying mechanism
in a rich perfect competitive model of trade and MP.
Our paper is also related to the literature that computes gains from trade in multi-sector frameworks and compare them with the GT obtained using one-sector models [e.g., Costinot et al., 2012,
Costinot and Rodrı́guez-Clare, 2014, Caliendo and Parro, 2015, Levchenko and Zhang, 2013, Ossa,
2015, Shikher, 2012a]. However, there are two main differences between those papers and ours.
First, we extend the structure of these models by expanding the set of firm’s choices to allow for
the possibility of serving a country through multinational production. By recognizing the interactions between multinational activity and countries comparative advantage, we are able to study
the impact of MP in the observed sectoral dispersion of trade shares, and therefore, on the gains
from trade. Second, we aim to understand the welfare impact of key sources of heterogeneity,
such as changes in MP cost or sectoral relative productivity differences. To this end, we decompose the effects of such changes in the different sources of heterogeneity into two components: 1)
those coming from their impact on aggregate shares of MP and trade, and 2) those exclusively
attributed to changes in the sectoral dispersion of MP and trade shares.
This paper also pays close attention to the role of comparative advantage on welfare, like
[Levchenko and Zhang, 2016] and [Costinot et al., 2012], who study the effects of Ricardian comparative advantage on gains from trade. Our paper aims to contribute to this literature by
quantifying the importance of Ricardian comparative advantage in a model of MP and trade.
Similarly to [Costinot et al., 2012], we investigate how much of the cross sectional variation in
trade and MP flows as well as the GT, GMP and GO can be explained by differences in relative
productivities across sectors, in a model that also includes intermediate inputs, inter-sectoral linkages, and a non-tradable sector. In particular, we isolate the effects that removing comparative
advantage have on aggregate MP and trade shares from its effects on the sectoral dispersion MP
and trade shares, allowing us to compute welfare changes from these two channels.
The rest of the paper is organized as follows. Section 2 discusses the patterns of multinational
production at the sectoral level. Section 3 and 4 lays out the theoretical framework and derives
analytical results on the impact of sectoral dispersion in MP on gains from trade and gains from
multinational activity. Section 5 sets up the quantitative framework and estimates the parameters
of the model. Section 6 presents a series of counterfactual exercises to quantitatively measure the
effects of multinational activity; and section 7 concludes.
2
Data and Empirical Facts
This section uses a novel industry-level dataset of bilateral foreign affiliates’ sales to establish
two key empirical regularities of the sectoral patterns of multinational production.2 First, MP as a
2
In contrast to bilateral trade data, which is available for many countries at different levels of sectoral disaggregation, there is no systematic dataset of bilateral MP sales broken down by sectors. [Fukui and Lakatos, 2012]
5
fraction of total output is sizable and significantly heterogeneous across sectors within a country.
Moreover, there are substantial cross-country differences in the heterogeneity of sectoral MP
shares. Second, the observed allocation of MP across sectors are shaped by Ricardian productivity
differences. In particular, we show that (i) the fraction of output produced by foreign firms, from
source (s), at location (l) in sector (j), is inversely related to the productivity gap between location
and source country in that sector; and (ii) within a location country, on average, the sectors where
the fraction of output produced by foreign affiliates is relatively higher are also those with lower
relative productivity.
2.1
Data Description
The dataset assembled in this paper contains information about the activity of foreign affiliates—
employment, sales and the number of establishments—for each location country, distinguishing
the sector of operations and the source country where the parent company is located.3 This enables us to do a sectoral breakdown of the domestic employment and production done by foreign
and domestic own firms. Each observation in the dataset is a source-location-sector triplet, averaged over the period 2003–2012; containing information for 32 countries, 9 tradable sectors, and
4 non-tradable sectors.4
Five sources of information are used to construct our dataset: 1) OECD (International Direct
Investment Statistics); 2) Eurostat (Statistics on Measuring Globalisation); 3) ORBIS; 4) BEA
(Operations of U.S. and Foreign Multinational Companies); and 5) UNCTAD (Country Profiles).
Each of these dataset varies in terms of country coverage, dimensionality, and level of sectoral
disaggregation. Combining them allow us to expand the number of triplet observations (sourcelocation-sector) and to minimize the number of missing values that can be mistaken as zeros.
In the construction of this dataset, we have overcome two main challenges. First, the original
dataset cover 70 sectors and sub-sectors for agriculture, mining, manufacturing, and services;
however, due to disclosure and confidentiality issues, the bulk of triplet observations are only
available at higher levels of aggregation.5 Therefore, to maximize the accuracy and coverage of our
dataset, we aggregate the information at roughly 1-digit level ISIC. Second, because the dataset
is an exception, who introduces a sectoral dimension to bilateral data on foreign affiliate sales. The methodology
used in constructing the dataset for the present paper differs substantially from theirs with respect to the primary
sources of information used and the methods implemented as explained in detail in Section B.1.
3
The activities of foreign affiliates are measured by their real operations rather than by their direct investment
(FDI). Tracking the activity of multinationals has several advantages. First, it considers only majority-owned
foreign affiliates—those in which 50 percent or more of the control is exerted by a parent firm located in a foreign
country, whereas FDI data considers all affiliates in which 10 percent or more of their equity capital is foreign-owned.
Second, having majority-owned affiliates ensures that the source country is where the parent company is located,
while FDI statistics register only the country of the immediate investor, even when the capital is passing through
a third country.
4
See table B.9 and table B.10 in the Appendix for the list of countries and sectors in our sample.
5
In some source-location-sector triplets there are only a few foreign affiliates, for which its disclosure could
reveal confidential information for individual firms.
6
combines information from different sources, it is important to assess its quality and consistency.
To this end, we rely on two pieces of information that because of their lower dimensionality are
wider available: i) total manufacturing MP sales for each source-location pair (ignoring sectoral
breakdown), and ii) MP sales for each location-sector pair (ignoring source country breakdown).6
We compare the total bilateral manufacturing MP sales and the total MP sales in each locationsector pair reported directly by OECD, Eurostat, and UNCTAD with the aggregates calculated
from our dataset by summing them up across the nine manufacturing sectors and across all
source countries, respectively.7 Section B in the Appendix provides a detailed explanation about
the construction and external validation of our assembled dataset.
To measure the relevance of MP, we rely on three indicators: 1) the foreign affiliate sales for
each source-location-sector triplet, 2) the sum of multinational sales across all foreign countries for
each location-sector pair (inward MP ), and 3) the sum of multinational sales across all location
countries for each source country-sector pair (outward MP ). Inward MP sales are normalized by
the total output of location country l in sector j to account for differences in sector size across
countries. Similarly, outward MP sales are normalized by the total output of source country s.
j
Let Ils
denotes the sales of source country s at location l in sector j; and Ilj denotes the production
in sector j at country l regardless of the producers’ nationality.8 Then, inward and outward MP
P
P
j
j
/Isj .
/Ilj and (M Poutward )js = l6=s Ils
shares are given by: (M Pinward )jl = s6=l Ils
In our sample, all 32 countries serve simultaneously as source and location country in tradable
and non-tradable sectors. Out of 992 potential source-location country pairs, there are 789 and
903 pairs with positive bilateral MP relationships, for tradables and non-tradables respectively.
There are 4,236 source-location-sector triplets—out of 8,928—in tradable sectors, where a positive
fraction of the output is produced by foreign owned firms. Moreover, the median location country
in the sample receives foreign production from 23 source countries while has operations in 27
locations. Multinational production across countries is patently sizable. For the median location
country, affiliates of foreign parents account for 34 percent of production in tradables and 37
percent in non-tradables. There are important variations in the presence of MP across countries,
though. In economies, such as Austria, Canada, Poland, and the United Kingdom, the presence
of multinational firms is significant, with more than 35 percent of their aggregate output carried
out by foreign affiliates. In contrast, in Japan the presence of foreign multinational corporations
is rather limited, with foreign affiliates’ sales reaching less than 3 percent of the country’s total
output. This is despite Japan being an important source of MP, with outward sales that account
6
Notice that these series aggregate information along one of the three dimensions of our dataset. The first
dataset aggregates across sectors, while the second aggregates across source countries.
7
Figure B.13 and B.14 in the Appendix compares the distribution of our dataset with the distribution of more
aggregated external sources. Performing a two sample nonparametric Kolmogorov-Smirnov test for equality of
cumulative distributions, we cannot rejected the null hypothesis that they are statistically the same, for sales and
employment.
8
Note that MP does not include the production of domestic multinationals, but only the output produced by
foreign affiliates of multinational parents based abroad.
7
Figure 1: Sectoral dispersion of inward MP shares (selected countries)
(a) Share of inward MP on output
Canada
Czech Republic
Finland
Transport
Transport
Minerals
Machinery
Transport
Chemicals
Food
Textiles
Machinery
Chemicals
Metals
Furniture
Wood
Food
Food
Textiles
Metals
Metals
Wood
Furniture
Chemicals
Machinery
Furniture
Textiles
Wood
France
Italy
Machinery
Transport
Machinery
Chemicals
Chemicals
Food
Furniture
Machinery
Transport
Minerals
Minerals
Wood
Metals
Transport
Furniture
Food
Minerals
Wood
Food
Metals
Furniture
Textiles
.2
United Kingdom
Chemicals
Metals
0
Minerals
Minerals
Wood
Textiles
.4
.6
.8
1
0
Textiles
.2
.4
.6
.8
1
0
.2
.4
.6
.8
1
(b) Inward MP share deviations to the world mean
Canada
Czech Republic
Transport
Finland
Transport
Food
Wood
Furniture
Machinery
Textiles
Textiles
Minerals
Metals
Food
Wood
Transport
Minerals
Machinery
Metals
Chemicals
Chemicals
Metals
Furniture
Food
Wood
Chemicals
Furniture
France
Machinery
Italy
United Kingdom
Metals
Chemicals
Wood
Furniture
Furniture
Machinery
Machinery
Wood
Textiles
Chemicals
Metals
Chemicals
Food
Textiles
Food
Wood
Furniture
Minerals
Textiles
Transport
Transport
Metals
Minerals
−.05
Transport
Food
Machinery
−.1
Textiles
Minerals
0
.05
.1
−.1
Minerals
−.05
0
.05
.1
−.1
−.05
0
.05
.1
Notes: Panel (a) shows the fraction of output in sector j produced by affiliates of foreign parents (M P/output)lj for
a group of selected countries and nine manufacturing sectors. Panel (b) shows per sector and country, the difference
P
j
j
s6=l (Ils /Il )
between the normalized share of inward MP on output in country l and the world economy, P P
−
j
j
I
/I
j
s6=l ( ls
l)
j
j
Iworld,l /Iworld
.
P j
j
j Iworld,l /Iworld
Positive (negative) values of this measure reveal those sectors in which the economy host
relatively more (less) foreign production compared to the world sectoral distribution.
8
for 13 percent of its total production.
2.2
9 10
Fact 1: MP Shares are Heterogeneous Across Sectors and Countries
Two levels of heterogeneity characterize the sectoral allocation of MP shares: 1) foreign sales,
as a fraction of output, exhibit substantial heterogeneity across sectors within a country; and
2) there are significant cross-country differences in the degree of heterogeneity of MP shares
across sectors. Figure 1a depicts the sectoral composition of MP, normalized by each sector’s
production, for six selected host countries and nine manufacturing sectors, and it shows that
the level of heterogeneity of MP shares across sectors is significant. In the United Kingdom, for
instance, the share of output produced by foreign affiliates in the Transport Equipment sector is
four times higher than in Textiles; whereas in Finland, the fraction of output in hands of foreign
multinationals is 11 times higher in Minerals compare to the Wood and Paper sector.
Next, we explore cross-country differences in the sectoral dispersion of MP shares by comparing
the sectoral distribution of MP shares in each country to the one corresponding to the world
economy, our reference group. Figure 1b shows for six selected countries the difference between
the normalized MP share for each of the nine tradable sectors and its counterpart for the world
economy. Sectors for which this measure takes positive (negative) values are those whose relative
importance—compared to other sectors in the economy—are higher (lower) than the relative
importance of that sector for the world economy. In Canada, for example, foreign multinational
firms in the Transport Equipment sector are relative more important as a fraction of output,
compared to the world in that sector. Conversely, the presence of foreign affiliates in the Chemicals
sectors—relative to the overall economy—is lower than the world average. This situation is
reversed for Italy, country for which the relative production of foreign affiliates in the Transport
Equipment sector is low compared with world average, but relatively high in Chemicals.11
Similar to what happens in the case of inward MP, the production of affiliates of local multinationals in foreign countries–outward MP—as a fraction of total output in the source country,
varies significantly across sectors, and different source countries show different sectoral patterns
in their foreign activity. Similar to the case of inward MP, outward MP is heterogeneous across
sectors as well as relative to the world average.12
9
See Table A.1 and A.2 in the Appendix.
[Head and Ries, 2001b] show that among the 25 largest Japaneses investors abroad, most of them operating
in Electronics and Automobiles industries, offshore workers constitute on average 30% of these firms worldwide
employment.
11
Differences across countries within a sector are directly compared in Figure A.2 in the Appendix, for four
selected sectors.
12
See Figure A.1 in the Appendix.
10
9
2.3
Fact 2: MP and Comparative Advantage: A Negative Relationship
In this section, we show that inward MP shares are relatively higher in comparative disadvantaged sectors. This section establishes this relationship by showing that (i) within a sourcelocation country pair, the fraction of output produced by foreign firms in a given sector is inversely
related to the differences in sectoral productivity between location and source country;13 and (ii)
within a location country, the fraction of output produced by foreign firms is relatively higher in
sectors with lower relative productivity.
Figure 2 shows the sectors in which the economy host (source) relatively more (or less) foreign
production when compared to the world sectoral distribution. With a first look at the data, a
clear pattern emerge: most sectors in which countries relatively host more MP are also sectors in
which they source relatively less multinational production as a fraction of output—compared with
the world economy. Next, we show that differences in relative sectoral productivity can explain
the observed patterns. In particular, inward MP shares are high in sectors where local producers
are relatively less productive.
To explore the relationship between bilateral MP and sectoral productivity differences, we use
the following baseline regression:
ln
j
Ils
Ilj
!
= αs + κl + µj + β ln
T F Plj
T F Psj
!
+ δXl,s + γXlj + ǫjs,l
j
where Ils
/Ilj denotes the share of MP from source country s in location country l in sector j;
and ln(T F Plj /T F Psj ) measures the percentage productivity differences between location country
l in sector j and source country s in the same sector; and Xs,l includes a set of bilateral specific
variables that proxy for trade costs and Xlj are other location-sector specific factors, such as
Hecksher-Ohlin (HO) forces and effective tax rates. In our baseline estimates, the effects of
market size in providing incentives for sourcing and hosting multinational activity are absorbed
by the source and location fixed effects, αs , κl ; while µj captures specific sector characteristics
that are common across countries.
Table 1 shows the ordinary least square estimates for different specifications using three different measures of relative productivity and three different measures of multinational production.
Columns (1)-(3) use productivity estimates from a Ricardian trade model à la ([Costinot et al.,
2012]);14 column (4)-(6) use the multi-factor productivity provided by the Productivity Level
Database available for eighteen OECD economies.15 Finally, columns (7)-(9) use the revealed
13
This relationship holds not only for relative productivity but also for productivity in levels. In particular, we
show that within a source-location country pair, the fraction of output produced by foreign firms in a given sector
is positively related to the productivity level of the source country and negatively related to the productivity level
of the location country.
14
These productivity estimates come from a trade gravity specification interpreted through the lens of a multisector EK model.
15
The Groningen Growth and Development Centre Productivity Level Database ([Inklaar and Timmer, 2009])
10
Figure 2: MP share deviations from the world mean (selected countries)
Canada
Czech Republic
Transport
Transport
Textiles
Food
Minerals
Wood
Furniture
Minerals
Metals
Textiles
Machinery
Textiles
Food
Transport
Wood
Machinery
Minerals
Chemicals
Chemicals
Metals
Furniture
Food
Wood
Furniture
France
Italy
United Kingdom
Chemicals
Metals
Transport
Food
Wood
Furniture
Machinery
Furniture
Machinery
Machinery
Chemicals
Wood
Metals
Textiles
Chemicals
Food
Textiles
Wood
Furniture
Food
Textiles
Transport
Minerals
Transport
−.1
Machinery
Chemicals
Metals
−.2
Finland
Metals
Minerals
0
.1
.2
−.2
−.1
Minerals
0
Inward
.1
.2
−.2
−.1
0
.1
.2
Outward
Notes: In this figure, the blue bars represent the difference between the normalized share of inward MP on output
P
j
j
j
j
I
/Iworld
s6=l (Ils /Il )
. Positive
− P world,l
in country l and the world economy, in each country-sector pair, P P
j
j
j
j
I
/I
I
/I
)
(
j
s6=l ls
j
l
world,l
world
(negative) values of this measure reveal those sectors in which the economy host relatively more (less) foreign
production compared to the world sectoral distribution. Similarly, the green bars represents the difference between
the normalized share of outward MP on output in country l and the world economy, in each country-sector pair,
P
j
j
j
j
I
/Iworld
l6=s (Ils /Is )
. Positive (negative) values of this measure reveal those sector in which the
− P world,s
P P
j
j
j
j
j
l6=s (Ils /Is )
j Iworld,s /Iworld
economy source relatively more (less) foreign production than the world average.
11
comparative advantage index (RCA) from the CEPII database and available for Austria, Canada,
France, Germany, Italy, Japan, Mexico, Netherlands, Russia, Spain, Turkey, U.K. and U.S..1617
Panels (a), (b) and (c) in Table 1 measure MP shares by sales, employment and number of foreign
affiliates, respectively. Regarding the set of controls, columns (1), (4) and (7) have location fixed
effects, source fixed effects and sector fixed effects, along with a set of gravity bilateral variables
such as: log of distance between location and source country, existence of common border, whether
countries share common language, whether countries have colonial ties and whether they are part
of a regional trade agreement (RTA). All specifications control for Hecksher Ohlin forces, as captured by the interaction between factor endowments in country l and sector j factor intensities
ln(K/L)l × ln(K/L)j .
The specifications in columns (2), (5) and (8) replace the source fixed effects and the location
fixed effects by a source×location country fixed effect to further control for factors that are specific
to the bilateral relationship and that are not captured by any of the bilateral gravity variables.
Finally, columns (3), (6) and (9) include effective tax rates at the country-sector level and replace
the RTA dummy by bilateral-sector tariffs.18 Notice that the last set of controls attempt to
address the potential concern that the size of foreign affiliate sales might be influenced by the tax
strategies followed by the parent firm [Desai et al., 2003]. This could bias the results, for instance,
in cases where the tax regime is location-sector–specific and therefore not controlled by the set
of fixed effects included in our specifications. To alleviate this concern, we explicitly control for
the effective tax rates. We also use the share of employment as an alternative measure of MP
activity, since this should be less subject to manipulation for tax reasons.
In all regressions in Table 1, we obtain a negative coefficient (β < 0) on the relationship between bilateral MP and relative productivities, all statistically significant at 1% level.19 Given
the relatively large number of zeros that characterize bilateral-sector level MP data, Table A.3 in
the appendix shows the estimates using the Poisson Pseudo Maximum Likelihood approach suggested by [Silva and Tenreyro, 2006]. The results are robust to different specifications, estimation
reports levels of multi-factor productivity relative to the U.S for 12 manufacturing sectors and 18 OECD countries.
The gross-output based multi-factor productivity takes into account labor, capital and intermediates inputs.
16
An alternative measure of productivity can be computed based on the OECD Structural Analysis (STAN)
database, which provides information on total output, employment, capital stocks, and intermediate input usage,
by sector and in real terms. However, the set of countries and sectors for which this measure of TFP can be
computed is very limited. Information for at least some sectors is only available for nine OECD countries.
17
To correct for trade-driven selection, the measures of TFP were multiplied by the relative openness between
j
any two pairs of countries i and i′ , πii
/πij′ i′ , raised to the power of the inverse of the trade elasticity, which has
been set equal 6 in the baseline estimates.
18
Effective tax rates are only available for a subset set of countries, limiting the number of observations available
in the regressions corresponding to columns (3), (6) and (9) (see Appendix B.4 for further details). The applied
tariff data reported at the bilateral-sector level is from WITS/TRAINS dataset. A detailed explanation of the
aggregation at 1-digit level ISIC level is done in the Appendix B.3.
19
To avoid cases where few observations could influence the sign and significance of our results, given the potential
presence of outliers, all regressions were calculated by dropping those observations that were identified as highly
leverage, measured by the difference between the regression coefficient of the relative technology calculated for
the whole sample and the regression coefficient calculated with the outliers deleted. Observations for which this
√
difference was above 2/ n were deleted of the sample. In all cases, the sign and significance of the results remain
unchanged.
12
methods and alternative measures of multinational activity and sectoral productivity.20
Next, we replace the relative productivity measure used in our previous specifications with the
productivity level of the source (location) country, including source (location) fixed effects and
location-sector (source-sector) fixed effects. The specification is as follow:
ln
ln
j
Ils
Ilj
j
Ils
Ilj
!
!
= κs + αjl + β ln T F Psj + δXl,s + γXlj + ǫjs,l
= κl + αjs + β ln T F Plj + δXl,s + γXlj + ǫjs,l
Table 2 shows, using different measures of MP and different specifications, that the share of
MP is positively related to the productivity of the source country and negatively related to the
productivity of the location country.
Finally, we also test the negative relationship between MP shares and productivity at the
sectoral level using an alternative aggregation of multinational activity. For each location-sector
pair, we aggregate the foreign production from all source countries in the sample and normalize it
by the total output of country l in sector j. The negative coefficient on the productivity of country
l in sector j suggests that the share of multinational activity is higher in sectors in which local
producers exhibit relative lower productivity. Panel (a) in Figure 3 depicts the correlation between
the share of MP on output in sector j and the location country’s productivity, after netting out
all the effects exert by the included control covariates.21 Panel (b) in Figure 3 shows a negative
correlation when the extent of MP activity is measured by the number of employees working
in foreign affiliates in a given location-sector pair instead of using aggregate foreign sales. The
negative and significant relationship between relative productivity and the cross-sector variation
of MP shares constitutes preliminary evidence supporting the analytical predictions that emerge
from the model presented in next section.
Although the mechanism highlighted in this paper is based on an horizontal perspective of
multinational activity, both horizontal and vertical MP sales coexist in reality.22 Even when is not
possible to disentangle horizontal from vertical MP, it is possible to make some inferences based on
the commercial international transactions of multinationals. Subtracting foreign affiliate exports
from total MP sales in a given country-sector pair gives us the part of MP sales that take place in
the location market, which is likely to be driven by an horizontal motive. Unfortunately, while the
dataset assembled in this paper has information on sales, employment, and number of affiliates per
source-location-sector triplet, it does not have information on international trade transactions by
foreign affiliate firms. To address concerns about the influence of vertical MP on the relationship
20
Note that, as we move across columns to the right of the table, the number of source-location-sector observations
changes. This is due to differences in the country coverage of the different productivity measures used in the analysis.
21
These controls include: location and sector fixed effects, HO forces and effective tariffs. See the regressions’
results in the Table ?? in the Appendix.
22
More than two-thirds of foreign affiliate sales occur in the host market, [Ramondo et al., 2013].
13
between sectoral productivity and MP activity, we explore the correlation between MP sales and
sectoral productivity using the non confidential Bureau of Economic Analysis (BEA) data for U.S.
multinationals operating abroad. The BEA dataset contains information about foreign affiliates’
sales, value added, imports, and exports, from which we can construct domestic sales of foreign
U.S. affiliates abroad. Despite the lower number of sectors (five rather than nine) and countries
for which data is available, we still find a negative relationship between MP shares and sectoral
productivity.
3
MP and Comparative Advantage: Analytical Results
In this section, we present a simplified multi-sector model of trade and multinational production
to illustrate the role of sectoral heterogeneity in determining the gains from MP (GMP), Trade
(GT) and Openness (GO).23 To this end, we rely on a measure of inequality (to capture relative
productivity dispersion) that nicely fits with the structure of the model: the Atkinson inequality
index.24
Allowing countries to interact through trade and MP in a multi-sector environment has a series
of important analytical and quantitative implications when compared with a one-sector MP-trade
model developed by [Ramondo and Rodrı́guez-Clare, 2013]. The first set of implications can be
summarized in the following analytical predictions: 1) the dispersion of MP shares across sectors
increases with the dispersion of sectoral relative productivities; 2) MP shares are disproportionately higher in comparative disadvantage sectors, which is in line with our stylized facts; and 3)
the lower the MP barriers, the higher the dispersion of MP shares across sectors.25
23
Although our main goal is to unveil the quantitative effects of MP heterogeneity on welfare through a full-fledge
multi-sector model of trade and MP. See section 5.
24
In Section 5, these simplifying assumptions are removed and the model is generalized to make it quantitatively
informative by including asymmetric MP barriers, multiple factors of production (labor and capital), differences in
factor and intermediate input intensities across sectors, a realistic input-output matrix between sectors, inter- and
intra-sectoral trade, and a non-tradable sector.
25
A reduction in MP costs makes MP shares more responsive to differences in relative productivities, increasing
the sectoral heterogeneity of MP.
14
Table 1: Relationship Between Bilateral Sectoral MP and Relative Productivity
Dep.
Variable ln M P sharejls
ln T F Plj /T F Psj
Observations
R2
15
ln T F Plj /T F Psj
Observations
R2
ln T F Plj /T F Psj
Observations
R2
Controls (I)
Controls (I and II)
Source FE
Location FE
Source-Location FE
Sector FE
Gravity Based
Relative Productivity Measures
GGDC
RCA
Productivity
Index
Productivity
(1)
(2)
(3)†
−0.341a
−0.315a
−0.435a
−0.995a
−0.976a
−0.699a
−2.274a
−2.835a
−2.520a
(0.0264)
4,015
0.51
(0.0241)
3,839
0.69
(0.0430)
1,592
0.64
(0.1340)
1,837
0.46
(0.1339)
1,669
0.69
(0.1843)
993
0.64
(0.3667)
868
0.62
(0.3571)
853
0.73
(0.4849)
546
0.71
−0.338a
−0.294a
−0.456a
−0.755a
−0.868a
−0.606a
−1.809a
−2.117a
−2.020a
(0.0246)
3,847
0.61
(0.0230)
3,782
0.77
(0.0393)
1,488
0.69
(0.1242)
1,801
0.57
(0.1270)
1,644
0.76
(0.2041)
1,009
0.64
(0.3383)
787
0.64
(0.3136)
772
0.76
(0.4377)
517
0.76
−0.288a
−0.306a
−0.359a
−0.527a
−0.547a
−0.522a
−1.385a
−1.380a
−1.480a
(0.0141)
3,750
0.83
(0.0136)
3,716
0.90
(0.0229)
1,533
0.84
(0.0737)
1,764
0.78
(0.0730)
1,579
0.88
(0.1026)
968
0.83
(0.1678)
818
0.83
(0.1584)
811
0.88
(0.2663)
519
0.88
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
(4)
(5)
(6)†
(7)
(8)
(9)†
Panel (a): Sales
Panel (b): Employment
Panel (c): Number of firms
Notes: This table presents the results of a linear regression model between the share of MP—measured by sales, employment and number of firms—and the ratio
of productivities (T F Pl /T F Ps ) for different specifications and productivity measures. All productivities are corrected for trade-driven selection. Controls (I)
include bilateral distance; dummies for common language, common border, colony ties and belonging to a regional trade agreement (RTA); and the interaction
between factor endowments and sector factor intensities: ln(K/L)l × ln(K/L)j . Controls (II) include effective tax rates at the country-sector level and
bilateral-sector tariffs, instead of the RTA dummy. Standard errors, origin-location clustered, in parentheses. Significance: c p < 0.1, b p < 0.05, a p < 0.01. †
Sample size drops due to lower country coverage of effective tax rates.
Table 2: Relationship Between Bilateral Sectoral MP and Productivity
Productivity Measure: Gravity Based
Dep.
Variable ln M P sharejls
j
ln T F Psource
Observations
R2
Source FE
Location-Sector FE
16
j
ln T F Plocation
Observations
R2
Location FE
Source-Sector FE
Controls (I)
Controls (I and II)
Sector FE
Sales
(1)
Employment
(2)†
(3)
No. of firms
(4)†
(5)
(6)†
Panel (a): Source’s Productivity
0.382a
0.774a
0.300a
0.587a
0.157a
0.242a
(0.0343)
3,983
0.58
Y
Y
(0.0614)
2,156
0.61
Y
Y
(0.0345)
3,824
0.67
Y
Y
(0.0573)
2,071
0.71
Y
Y
(0.0158)
3,774
0.87
Y
Y
(0.0291)
2,046
0.89
Y
Y
Panel (b): Location’s Productivity
−0.250a
−0.584a
−0.324a
−0.680a
−0.394a
−0.627a
(0.0359)
3,983
0.61
Y
Y
(0.0748)
1,560
0.73
Y
Y
(0.0324)
3,824
0.69
Y
Y
(0.0637)
1,454
0.76
Y
Y
(0.0193)
3,774
0.86
Y
Y
(0.0398)
1,519
0.89
Y
Y
Y
–
Y
–
Y
Y
Y
–
Y
–
Y
Y
Y
–
Y
–
Y
Y
Notes: This table presents the results of a linear regression model between the share of MP—measured by sales, employment and number of firms—and the
productivity of the source and location country measured by gravity based productivity. Controls (I) include bilateral distance; dummies for common language,
common border, colony ties and belonging to a regional trade agreement (RTA); and the interaction between factor endowments and sector factor intensities:
ln(K/L)l × ln(K/L)j . Controls (II) include effective tax rates at the country-sector level and bilateral-sector tariffs instead of the RTA dummy. Standard errors,
origin-location clustered, in parentheses. Significance: c p < 0.1, b p < 0.05, a p < 0.01. † Sample size drops due to lower country coverage of effective tax rates.
Figure 3: Sectoral MP and Productivity
−1
−.5
Inward MP Share
0
.5
1
(a) Sales
−1.5
−1
−.5
0
.5
1
Productivity
coef = −0.537, (robust) se = 0.0775
−1
−.5
Inward MP Share
0
.5
1
(b) Employment
−1
−.5
0
Productivity
.5
1
coef = −0.5891, (robust) se = 0.0720
Notes: This figure displays the partial correlation of ln(M P sharejl ) against the location country’s productivity
ln(T F Pl ), after netting out location fixed effects, Hecksher Ohlin forces, as captured by the interaction between
factor endowments and factor intensities ln(K/L)l × ln(K/L)j ; and effective tax rates at the country-sector level.
MP share is measured as the output produce by affiliates from source country s in location country l in sector j
relative to total production of country l in sector j. Productivity is measured by the gravity based productivity.
The figure in the top panel uses MP share by sales and the bottom panel uses employment.
17
The implications for GT, GMP and GO can be summarized as follows: 1) gains from MP are
higher in multi-sector models—relative to one-sector frameworks26 ; and the difference in GMP
is larger (i) the higher the dispersion of relative productivity across sectors, (ii) and the lower
the MP barriers. 2) GT in multi-sector models can be rewritten as a function of the aggregate
level and the sectoral dispersion of trade shares. This allows us to show that the higher the
sectoral dispersion of MP shares—due to lower MP barriers—the lower the sectoral dispersion of
trade shares, and therefore the lower the gains from trade. In particular, in a multi-sector model,
frictionless MP eliminates sector-level Ricardian comparative advantage and inter-industry trade,
which decreases gains from trade. 3) GO are higher in multi-sector models—relative to one-sector
frameworks; and the difference in GO is larger (i) the higher the dispersion of relative productivity
across sectors, and (ii) the lower the MP barriers.
The framework developed in this section abstracts from several complexities, while the basic
intuition regarding the role of various model’s parameters carries to the general case. To solve the
model explicitly, we concentrate on the case of countries (h, s, n) = {1, 2}, and two EK sectors,
j = {a, b}, which are the same size and exhibit symmetric inter-sectoral differences. Equal size
and symmetry imply that countries have the same endowments; the same tastes; and technology
distributions that are “mirror images” of each other.27 Each country is endowed with one unit of
the only factor of production, labor, L1 = L2 = 1; and expenditure shares are equal across sectors,
under Cobb-Douglas preferences; allowing us to obtain analytical results under endogenous factor
price determination.
On the production side, as in EK, each sector is a composite of a continuum of varieties [0, 1]
that do not overlap across sectors, and each country can produce each infinitesimal variety at
home or abroad with a productivity that is drawn independently across goods, countries, and
sectors, from a multivariate Fréchet distribution, with a common dispersion parameter, θ, and
a country-sector specific productivity, Tlj , that satisfies a mirror image assumption (T1a =T2b and
T1b =T2a ).28 Given the multi-sector nature of the model, productivity differences are characterized
by: (1) differences in relative productivities across industries
T1a
T2a
6=
T1b
—or
T2b
Ricardian comparative
advantage at the industry level; and (2) intra-industry heterogeneity, which is governed by θ.29
26
Our goal is to measure the additional gains that cannot be pick up by a model that only considers aggregate
trade shares. In the simplified analytical framework, this is equivalent to compare our results to the welfare gains
in one-sector models.
27
Where s denotes the country source of the technology, l denotes the country where production takes place,
and n denotes the country where consumers are located. Notice that when s = l the country source of technology
is the same as where goods are produced; and when l = n goods are sold in the country where they are produced.
28
The distribution of productivities in a country-sector pair, is given by:
n
h
io
j −θ
j −θ
Fsj (z) = exp −Tsj (z1s
) + (z2s
)
.
j
j
where zjs (ω) ≡ z1s
(ω) , z2s
(ω) is a vector in which each element represents the source country’s productivity in
j
each location country l (zls ). Notice that a higher Tsj leads to a larger productivity draw on average, at home and
abroad, thus regardless of the location of production, the average productivity that matters is the productivity of
the source country s.
29
In this stochastic model, a higher T1a (T1a > T2a ) captures the idea that country 1 is relatively better at
a
producing zl1
goods in any location country l—including its own market. This does not imply, however, that
18
Notice that producers incur in a penalty in the form of a discount in productivity (g), when
producing in a location different from the home country. Barriers to trade across countries (d),
and barriers to produce in a foreign location (g), are also assumed symmetric across countries and
a = gb = ga = gb ,
sectors, and they are modeled as iceberg costs: da21 = db12 = da12 = db21 , and g21
12
12
21
j
j
with no barriers to domestic consumption or local production: dj11 = dj22 = g11
= g22
= 1, ∀
j = a, b.
To serve any given market at the lowest possible price, a firm in sector j chooses between
(1) producing at home s = l and exporting to the destination market n; and (2) building up an
affiliate at the destination market n to produce and sell locally (l=n).30
Therefore, the price at which country s can supply
variety ω in sector j to country n, while
j
cjl gls
j
j
producing in country l, equals pnls (ω) =
dnl . Then, a producer from country s will
j
zls (ω)
choose
him to reach out country n with the lowest possible price, pjns (q) =
n location l that allows
o
min pjn1s (ω) ; pjn2s (ω) . Finally, conditional on each provider being at the cheapest possible
location, consumers in marketnn will choose toobuy from the source country s that offers them
the lowest price pjn (ω) = min pjn1 (ω) ; pjn2 (ω) . Hence, the probability that country n imports
variety ω in sector j from country l, using technologies from country s, is given by:
j
πnls
−θ
j
j j
dnl wl gls
=
−θ −θ −θ −θ j
j
j
j
j
j
j
j
j
j
T1 dn1 w1 g11
+ dn2 w2 g21
+ T2 dn1 w1 g12
+ dn2 w2 g22
Tsj
(1)
j
where πnls
represents the share of total expenditure in country n on goods coming from location
country l, produced with technologies from source country s.
With this at hand, we can calculate the bilateral MP shares, defined by the fraction of
total output being produced by foreign affiliates from country s located in country l, by summing
foreign affiliate sales over all destination markets n.31 Thus, total MP in sector j by affiliates
from country s located in country l is given by:
j
j
j
Ils
= π1ls
X1j + π2ls
X2j
∀j = {a, b}, and ∀l, s = {1, 2}
where Xn = pjn Qjn . Therefore, the share of goods produced in country l with s technologies—or
country 1 should only produce varieties from sector a in any given location l, but instead that all else equal, in
equilibrium, it will produce relatively more of these goods. Whatever the magnitude of T1a , country 2 may still
have lower labor requirements for some varieties. Finally, the mirror image assumption on sectoral productivity
and symmetry in the utility function ensure that wages are equal in the two countries, w1 = w2 = 1, which we set
as numeraire.
30
Section 5 presents the full model where there is a third possibility in which a country establishes foreign
affiliates on a third country l 6= n used as an export platform to ship goods to a final destination n.
j
31
Note that for a given location and source country pair (l, s) πnls
is not mutually exclusive across destination
countries n, given that some foreign affiliates could serve more markets than others.
19
sectoral MP share—is given by:
j
Ils
j
=P
yls
j
i Ils
=
j
Ils
Ilj
=
−θ
j
Tsj gls
Telj
.
(2)
f
f
j −θ
j −θ
where, Tlj = T1j gl1
+ T2j gl2
. Notice that Tlj denotes the productivity of country l in sector
j regardless of whether production is being produced with local or foreign technologies.32 For
f
simplicity, we call Tlj effective technologies to distinguish from the fundamental technology, which
correspond to the average productivity of producing sector j goods in country l using only techf
nologies developed in country l, Tlj . The functional form for Tlj indicates that the set of available
technologies in each country is enlarged by the possibility of foreign activity. This is, each countrysector pair has an effective productivity that equals the local productivity plus the productivity of
j
foreign affiliates producing at home, properly discounted by MP barriers, gls
, which limit the host
economy’s capacity to absorb foreign technologies, so as to enhance their overall productivity.33 .
In the model, the probability that country n will buy a sector j variety from country l—or
trade shares—is calculated by summing up the probabilities of importing goods produced in
j
j
j
country l using technologies from every source country s, including itself: πnl
= πnl1
+ πnl2
.
j
πnl
−θ
f
Tlj wl djnl
=
−θ
−θ ,
fj
fj
j
j
T1 w1 dn1
+ T2 w2 dn2
(3)
Notice that what determines the trade shares are the differences in effective relative productivities
across sectors, which summarize the productivity of all producers in the economy regardless of
ownership; delivering the familiar trade share formula from the EK framework.
3.1
A Simplified Measure to Summarize Productivity Dispersion: the Atkinson Inequality Index
In this section, we devote our attention to uncover the relationship between the heterogeneity
of MP shares across sectors and the strength of Ricardian comparative advantage. In particular,
32
Substituting equation 1 into the former expression, we get:
j
Ils
=
j j −θ
Tsj gls
cl
Ξjl ,
j −θ
pl
−θ j
Xl
djnl pjl /pjn
Xn = Il X
.
ll
f
j
33
Note that technology Tl is not available to all—local and foreign— producers in country l. Instead, each firm
producing in location country l uses technology from its own source country Tsj . Therefore, the model does not
internalize the potential knowledge spillovers that may take place from foreign to local producers. This implies that
in our model the productivity in the location country is enlarged as a result of the coexistence of local and foreign
producers with different levels of technology, and not because local producers become more productive by learning
from their foreign counterparts.
where Ξjl =
P2
m=1
20
we show that the dispersion of MP shares increases with the strength of the relative dispersion
of sectoral fundamental productivity, and decreases with the level of MP barriers. Further, we
show that the share of output produced by foreign firms is relatively higher in sectors where
relative fundamental productivities are lower. Finally, we show that reductions in frictions to
multinational production reduce the dispersion of trade shares. Indeed, at the limit, with no MP
barriers, each variety ω will be produced only by the world best producer, eroding the relative
differences in relative sectoral effective productivities.
In this section, we adopt a measure of inequality that summarizes productivity dispersion across
sectors through a single parameter. This measure, known as Atkinson inequality index, is usually
applied in the literature of income inequality and it can be defined as the complement to one of the
ratio of the geometric mean (g) to the arithmetic mean (µ): A = 1− µg .34 The Atkinson inequality
index has a number of advantages to measure sectoral productivity dispersion. First, it satisfies
mean independence (ie. if all technologies are multiplied by a positive constant, the productivity
dispersion remains unchanged). Second, the Atkinson index is subgroup-decomposable, which
allows the use of data from different sectoral classifications or different digits of disaggregation
and yet yielding same results. Third, the Atkinson index is non-negative, and it is equal to zero
only if all productivities are the same. In the next sections, we use the Atkinson inequality index
to measure the dispersion of several model objects, such as, fundamental (ATl ) and effective (ATel )
productivities, MP shares (Amp ), and trade shares (Aπll ).
3.2
Relationship Between Sectoral MP Shares and Sectoral Productivities
Dispersion
In this section, we show that the share of MP is larger in sectors with relatively lower fundamental productivities. To show this, we proceed in two stages. First, we show that the heterogeneity
of MP shares across sectors, Amp , is positively related to the sectoral dispersion of fundamental
productivities, AT , as well as to the easiness of producing across borders g−θ using the source
country’s technologies. Second, we show that the sectoral dispersion of MP caused by relative
differences in fundamental productivity is such that the largest shares of MP are allocated to
comparative disadvantage sectors.
Proposition 1. The dispersion of MP shares across sectors increases with the dispersion of
∂disp(y a ,y b )
∂A
relative sectoral productivities. This is ∂Amp
= ∂disp Tlla ,Tllb > 0.
T
( l l)
The proof of proposition 1 as well as all subsequent proofs can be found in the Appendix C.
To lay out some definitions, let’s start by showing the dispersion of MP shares in country 1, can
34
In its general form, the Atkinson inequality index is defined as A = 1 −
1
µ
1
N
PN
i=1
x1−ǫ
i
1/(1−ǫ)
, for all
0 ≤ ǫ < 1, where ǫ is the level of inequality aversion. When the level of inequality aversion equals 1 (ǫ = 1), then
Q
1/N
N
the Atkinson index is given by A = 1 − µ1
. Through the paper, it is assumed that ǫ = 1.
i=1 xi
21
be measured by the Atkinson index as:
Amp
a y b 1/2
y11
11
=1−
a +y b
(y11
11 )
(4)
2
where
a
y11
=
T1a
T1b
b
and
y
=
11
T1a + g−θ T2a
T1b + g −θ T2b
Substituting the former into equation 4, and using the definition for AT , we have:
Amp = 1 −
i1/2
h
2
(1 − AT ) (1 − AT )2 1 − g −θ + 4g−θ
(1 − AT )2 (1 − g −θ ) + 2g−θ
;
(5)
2
where the last equality comes from the fact that T1a T1b = [(1 − AT ) χ]2 , and (T1a )2 + T1b =
h
i
(T a +T b )
4χ2 1 − 21 (1 − AT )2 ; where χ is the arithmetic mean of sectoral productivities, χ = 1 2 1 .
As shown in the Appendix C, any increase in the dispersion of relative productivities AT is followed
by an increase in the dispersion of MP shares Amp , this is,
∂[Amp ]
∂AT
> 0. Notice that the increase
in dispersion of MP shares is not random, but rather MP shares are higher in sectors for which
average productivity is relatively lower. The former is summarized in the following proposition:
Proposition 2. Let’s define ã = T1a /T1b . Then, MP sales are higher in comparative disadvantage
b /y a
∂ (y11
11 )
< 0.
sectors. This is
∂ã
Therefore, the stronger the comparative advantages of country 1 in sector a, the larger the
a = y b whenever the
share of MP in comparative disadvantage sector b relative to a. Notice that y11
11
productivity across sectors is the same T1a = T1b . The basic idea is very simple, more pronounced
differences in relative sectoral fundamental productivities increase the proportion of multinational
production in sector b carried out by country 2′ firms. This analytical prediction finds empirical
support in the negative and significant relationship between productivity differences and MP
shares at the sectoral level, as discussed in the previous section. Similar to what happens with
imports, inward MP is relatively higher in relatively less productive sectors. But, unlike imports,
by bringing foreign technologies into the domestic market, MP enhances the country’s overall
productivity that, as we just showed, privileges relative low productive sectors.
Proposition 3. The lower the MP barriers, g, the higher the sectoral dispersion of MP shares.
This is,
∂Amp
∂g −θ
> 0.
The degree at which fundamental differences in productivity across sectors can affect the
heterogeneity of sectoral MP shares depends on the levels of MP barriers between the investing
and host countries. To see this, think about a limit case with prohibitively costly MP barriers,
g → ∞. In this scenario, MP shares across sectors will be the same and equal zero. Conversely,
22
Figure 4: Illustration of Analytical Results
0
.2
Atkinson (Amp)
.4
.6
.8
1
(a) MP share dispersion (Amp ) and fundamental productivity dispersion
(AT ), for a given g
0
.2
.4
.6
.8
1
Atkinson (AT)
g=1.1
g=2
g=1.5
g=2.5
0
.2
Atkinson (Amp)
.4
.6
.8
(b) MP share dispersion (Amp ) and MP barriers (g), for a given AT
1
2
3
4
g
A=0.1
A=0.6
A=0.3
A=0.8
Notes: The top panel depicts how the heterogeneity of MP shares across sectors increases with the dispersion of
technologies, for different values of g. The bottom panel displays how the heterogeneity of MP shares across sectors
decreases with g, for different values of AT .
23
with free MP, g = 1, foreign technologies operating in the local country will not be discounted
and the MP shares will solely reflect differences in fundamental productivity across countries.
Therefore, any positive level of MP barriers will partially erode the dispersion in MP shares
induced by the sectoral dispersion of fundamental productivities.
In summary, we have shown that the dispersion of sectoral MP shares are (1) positively correlated with the dispersion of sectoral fundamental productivities; and (2) negatively correlated
with MP frictions, as illustrated in Figure 4a and Figure 4b, respectively. Notice that these results
resemble what happens in trade-only models, where the dispersion of trade shares increases with
the strength of effective comparative advantage and decreases with the level of trade barriers.35
It is noteworthy that lower MP barriers have opposite effects on the dispersion of trade and MP
shares. On the one hand, as showed above, a lower g increases the dispersion of sectoral MP
shares by allowing them to be primarily affected by differences in fundamental productivities
across sectors. On the other hand, as it will be shown below, a lower g decreases the dispersion
of trade shares across sectors, by eroding the effect that MP has on the sectoral differences in
effective productivities.
4
Gains from MP, Trade and Openness in a Multi-sector Model
In this section, we derive the welfare implications of a multi-sector model of trade and multina-
tional production. In particular, we assess the role that sectoral heterogeneities have on the gains
from MP, trade and openness. In order to isolate the effect of productivity dispersion across sectors from any impact on aggregate trade or MP, we present our results relative to those obtained
in models of trade and MP in one-sector frameworks [Ramondo and Rodrı́guez-Clare, 2013].
4.1
Gains from MP in a Multi-sector Model
The increase in welfare that takes place when a country moves from a counter-factual equilibrium with trade but no MP—when barriers to foreign investments are prohibitively costly—to
the actual equilibrium with positive MP and trade flows is given by:
GM Pl
multi
=
l
l
Wg>0
/Wg→∞
− 1 π a π b − 2θ1
2θ
a b
ll ll
= yll yll
,
a b
π̄
| {z } | ll π̄{z
ll
}
term 1
(6)
term 2
where π̄llj is the domestic trade share in the counterfactual equilibrium with no MP, and where
the domestic MP shares are given by: yllj =
Tlj
.
Tej
As shown in the Appendix C, term 1 and term
l
2 react in opposite directions to an increase in the dispersion of MP shares. On the one hand,
35
The proof of the relationship between trade shares and relative sectoral productivities dispersion in multi-sector
models can be founded in the Appendix C.
24
higher heterogeneity of MP shares increases the gains from MP, as ylla yllb
− 1
2θ
increases. On the
other hand, higher dispersion of MP shares reduces the heterogeneity of trade shares, decreasing
− 1
− 1
πlla πllb 2θ relative to the dispersion of trade shares as g → ∞, π̄lla π̄llb 2θ , which reduces term 2.
The former results contrast with those obtained in a one-sector framework under symmetry,
− 1
1
1
θ
in which the gains from MP are given by GM Pl uni = (ynn )− θ π̄πllll
= (ynn )− θ , given that
− 1
θ
πll
= 1. With only one sector and under symmetry, MP does not facilitate or impede trade;
π̄ll
instead, MP affects all countries equally, having no effects on aggregate trade shares.36 But, with
sectoral heterogeneity, MP acts as a substitute for trade by adding a competing alternative to serve
other markets. The heterogeneous sectoral allocation of MP towards comparative disadvantage
sectors, diminishes the differences in effective productivities, limiting the heterogeneity of domestic
trade shares across sectors. This implies that in a multi-sector model, MP shrinks sector-level
Ricardian comparative advantage and inter-industry trade, decreasing the dispersion of trade
shares, as we move from the counterfactual equilibrium with no MP to the actual equilibrium
with MP. Despite the mentioned counteracting effects, the next proposition shows that there is
a net positive effect of an increase on the sectoral dispersion of MP shares on the gains from
MP, whether the higher dispersion is due to an increase in the sectoral dispersion of fundamental
productivities or to a reduction of MP barriers.
Proposition 4. Gains from MP are higher in multi-sector models—relative to one-sector frameworks; and the difference in GMP is larger (1) the higher the dispersion of productivity across
(GM P multi −GM P uni )
(GM P multi −GM P uni )
sectors, ∂
> 0; 2) and the lower the MP barriers: ∂
> 0.
∂AT
∂g −θ
By comparing the gains from MP in multi-sector and one-sector models, we net out the effect
that changes in the dispersion of sectoral fundamental productivities, AT , and MP barriers, g,
have on aggregate domestic MP shares, yll , allowing us to derive an expression that only reflects
the role of sectoral heterogeneity. The former takes care of the fact that an increase in the
Atkinson index of the fundamental productivities—or a reduction in g−θ , not only increases the
heterogeneity of domestic MP shares across sectors, but also increases the aggregate domestic MP
share in the economy.37 Therefore, a clear comparison, requires to calculate the welfare effects of
higher heterogeneity net of any effect on the aggregate MP share.
Let’s the GMP and the aggregate domestic MP shares (yll ) be written in terms of the model’s
36
In one-sector models and under symmetry, MP is trade independent (see [Ramondo and Rodrı́guez-Clare,
2013]). This result is explained by the fact that a reduction in the cost of producing abroad will increase MP in all
countries. This implies that even when all countries are bigger, relative sizes remain the same, and therefore trade
shares do not change.
37
Notice that the MP share is the complement of the domestic MP share, yll .
25
fundamentals: g, d, and AT .
 1
P j
−θ − 2θ
"
#− 1
2
Y  i Ti (ci d) 
(1 − AT )2 1 − d−θ + 4d−θ 2θ
=
GM Pl =

P j
(1 − AT )2 (a − b)2 + 4ab
Te (ci d)−θ
j=a,b
i
yll =
(7)
i
(1 − AT )2 (a − b) 1 − d−θ + 2 b + ad−θ
(8)
(1 − AT )2 (a − b)2 + 4ab
where a = 1 + g−θ d−θ and b = g −θ + d−θ .38
In order to show that changes in GMP attributable only to an increase in productivity dispersion are larger the higher levels of AT , we proceed to compare the GM P multi with the GM P uni .
Notice that the level of aggregate MP used to compute the GM P uni corresponds to the one
obtained in a multi-sector model for each level of AT .39
∂ GM P
multi
− GM P
∂AT
uni
=
∂GM P multi
−
∂AT
∂GM P multi 1
+
∂AT
θ
where GM P
uni
∂yll
∂AT
∂GM P
∂yll
(yll )−
1−θ
θ
uni
×
∂yll
∂AT
>0
>0
(9)
1
= (yll )− θ .40 Notice that different values of sectoral dispersion, AT , and MP bar1
riers, g, are associated to different levels of yll , and therefore different levels of GM P uni = (yll )− θ .
Therefore, for each level of sectoral productivities dispersion, the second term in equation 9,
reflects the GMP that will be calculated if a one-sector model is used instead.41
Likewise, changes in gains from MP caused by a reduction of MP barriers are higher, the higher
g−θ .
multi
This is given by ∂ GM∂gP−θ
−
∂yll
+ 1θ ∂g
−θ (yll )
1−θ
θ
> 0. Figures 5a and 5b illustrate these results
by depicting the gains from MP in multi-sector and in one-sector models, as well as the difference
between them, which increases with the dispersion of technologies AT (top panel), and with lower
MP barriers g−θ (bottom panel).
38
Notice that the share of aggregate output produced with country 1′ technology is given by:
y11 =
b
Yb b
Y a + Y11
Y1a a
a
b
y11 + 1 y11
= 11a
= Y11
+ Y11
Y1
Y1
Y1 + Y1b
j
where the last equality holds because Y1 = Y1a + Y1b = wL = 1. In addition, the expression above Y11
is given by:
h
i
L
1 j
j
j
j
j
Y11
= π111
X1j + π211
X2j = [π111 + π211 ] =
π + π211
2
2 111
j
=
where π111
39
j
T1
j
aT1a +bT2
j
and π211
=
j
T1 d−θ
j
j
bT1 +aT2
.
Notice that we do not need to know the underlying parameters that comply with a given aggregate MP share
in a one-sector model. The aggregate domestic MP share yll already summarizes all information we need, as the
GM P uni are only function of yll and θ.
40
41
Appendix C shows that (1)
∂yll
∂AT
< 0; and (2)
∂GM P multi
∂AT
> − θ1
∂yll
∂AT
(yll )−
1−θ
θ
.
Notice that when the underlying process is multi-sector, changes in AT will have effects on yll .
26
Figure 5: Illustration of Analytical Results
.02
Gains MP
.04
.06
.08
(a) GMP in multi-sector vs. one-sector models and fundamental productivity dispersion, AT
0
.2
.4
.6
.8
1
AT
GMP multi−sector
GMP uni−sector
0
.1
Gains MP
.2
.3
(b) GMP in multi-sector vs. one-sector models and MP barriers, g
0
.2
.4
−θ
.6
.8
1
g
GMP multi−sector
GMP uni−sector
Notes: This figure depicts how the Gains from MP in multi-sector and one-sector models, as well as the difference
between them, increases with the dispersion of technologies AT (top panel), and with lower MP barriers g −θ (bottom
panel).
27
Figure 6: Proposition 4: Gains from MP
(a)
∂ (GMP
multi
− GMP
uni
) / ∂A
T
0.25
0.2
0.15
0.1
0.05
0
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
g−θ
0.2
A
T
(b)
∂ (GMP
multi
− GMP
uni
)/∂g
−θ
0.3
0.25
0.2
0.15
0.1
0.05
1
1
0.8
0.8
0.6
0.6
0.4
−θ
g
Notes: The top panel depicts
displays
uni
∂ GM P multi −GM P
∂g −θ
0.4
0.2
0.2
A
T
uni
∂ GM P multi −GM P
∂AT
for different combinations of AT and g −θ . The bottom panel
for different combinations of AT and g −θ .
28
As can be observed in Figures 6a and 6b, the difference between the gains derived in multi-sector
and one-sector models (welfare gap) increases with lower MP barriers and with the dispersion of
fundamental productivities, as the derivative is always above zero. These figures show how the
different sources of heterogeneity interplay with each other. For instance, a reduction in MP
barriers towards free MP magnifies the effect of changes in the dispersion of fundamental productivity on the differences in the gains from MP between multi and one-sector models. Similarly, a
lower Atkinson of relative fundamental productivities magnifies the effect that a reduction in MP
barriers has on the additional gains from MP implied by multi-sector models. As expected, the
impact of MP barriers on the welfare gap is lower the freer MP already is. Likewise, the impact
of fundamental productivity dispersion on the welfare gap becomes more modest the higher the
starting level of AT .
4.2
Gains from Trade in a Multi-sector Model
In order to explore the effects of the dispersion of trade and MP shares on gains from trade,
1
h /W l
a b − 2θ , as a function of the dispersion of
we define gains from trade Wd>0
d→∞ = GTl = πll πll
domestic trade shares across sectors and the aggregate domestic trade share.
Proposition 5. In multi-sector models of trade and MP, gains from trade can be expressed as a
function of aggregate domestic trade share and the sectoral dispersion of domestic trade shares.
− 1
2θ
GTl = πlla πllb
=
1
(π )− θ
| ll{z }
1
(1 − Aπll )− θ
{z
}
|
(10)
aggregate
dispersion of sectoral
domestic trade share domestic trade shares
Equation 10 clearly separates the effect of aggregate domestic trade share from the effect
of domestic trade shares’ dispersion across sectors. It shows that the higher the dispersion of
domestic trade shares, measured by the Atkinson index Aπll , the higher the gains from trade.42
Notice that when Aπll = 0, equation 10 collapses to the gains from trade in one-sector models.43
But, our focus here is on understanding how, in a multi-sector framework, MP affects observed
trade flows and therefore gains from trade. It is noteworthy that, in a symmetric one-sector model,
even frictionless MP has no effect on trade flows, and therefore, no effect on gains from trade.
However, in a multi-sector model this is not longer the case. In particular, in a multi-sector model,
frictionless MP eliminates sector-level Ricardian comparative advantage and inter-industry trade,
42
A well established result in the literature is that gains from trade are higher in multi-sector frameworks (See
[Costinot et al., 2012], [Levchenko and Zhang, 2013], [Ossa, 2015]).
43
The proof of the relationship between domestic trade shares and relative productivities dispersion in multisector models can be founded in the Appendix C. Notice that this is a formalization for a case with MP and trade
barriers of the relationship between productivity dispersion and GT presented in [Levchenko and Zhang, 2013].
From equation 10, it can be observed that the gains from trade derived from trade-only and trade-MP models, both
in multi-sector frameworks, are identical. Nonetheless, this is true based solely on observables, and it is explained
by the fact that, in the model, MP shares are unresponsive to changes in trade barriers. Therefore, MP shares are
the same in the counterfactual and the actual equilibrium.
29
decreasing gains from trade.44 The next proposition shows that the gains from trade are affected
by the reduction in effective productivity differences that is induced by multinational production.
Proposition 6. The higher the sectoral dispersion of domestic MP shares—due to lower MP
barriers— the lower the sectoral dispersion of domestic trade shares, and therefore the lower the
gains from trade,
∂GTl multi
∂g −θ
< 0; and, these losses in GT caused by a reduction in MP costs are
(GT multi −GT uni )
larger in multi-sector models—relative to one-sector frameworks: ∂
< 0.
∂g −θ
1
∂GTl
∂(1 − Aπll )− θ
− 1θ
=
(π
)
×
ll
∂g−θ
∂g−θ
Let’s decompose
∂GTl
∂g −θ
into two components. The effect of MP barriers in the dispersion of effective
sectoral productivities and the effect of the later on the heterogeneity of sectoral domestic trade
shares.
1
∂AT̃
∂GTl
∂(1 − Aπll )− θ
− 1θ
=
(π
)
× −θ
×
ll
−θ
∂g
∂AT̃
∂g
In the Appendix C, we show that ∂
∂AT̃
∂g −θ
< 0. Therefore,
∂GTl
∂g −θ
(1−Aπll )
−1
θ
∂AT̃
> 0, given that
∂Aπll
∂AT̃
> 0. We also show that
< 0.
The relationship between the dispersion of sectoral trade shares, MP barriers and the sectoral
dispersion of fundamental productivities can be summarized in equation 11.
1 − AT̃
2
=
−θ 2
2 1−g
+
(1
−
A
)
2
| {z T } 1 + g−θ
(1 + g−θ )
|
{z
}
| {z }
term 2
4g−θ
(11)
term 3
term 1
As can be observed, with frictionless MP (g = 1), the dispersion of effective productivities are
completely erode, and AT̃ = 0. Similarly, when MP is prohibitively costly, g = ∞, the dispersion
of effective and fundamental technologies are the same (AT̃ = AT ). Notice that term 1 is positive
for any positive and finite level of g, contributing to the observed heterogeneity in effective technologies AT̃ . Also, through term 2, the dispersion in fundamental productivities, AT , positively
affects the dispersion in effective productivities, AT̃ .45 However, notice that term 3 is lower than
one, and therefore, any positive level of MP busted by a positive and finite level of g, will offset
−θ 2
1−g
the dispersion in T̃ induced by a higher AT by a factor of 1+g
. The former is summarized
−θ
in Figure 7 below.
As can be observe from Figure 8, a reduction in MP barriers lowers GT. This is true for both,
one-sector and multi-sector models, but the magnitude of the GT losses are larger in multi-sector
44
As mentioned before, aggregate domestic trade shares do not change due to the assumption of symmetry, and
the dispersion of domestic trade shares across sectors is affected by changes on MP costs.
45
Of course, this only holds for non-zero values of AT .
30
0
.2
(ATilde)
.4
.6
.8
Figure 7: Illustration of Analytical Results
0
.2
.4
.6
.8
1
AT
g=1.1
g=2
g=1.5
g=2.5
Notes: This figure depicts the relationship between AT̃ and AT for different values of MP barriers, g.
Figure 8: Proposition 6: Gains from Trade
0
∂ (GT multi − GT uni) / ∂ g−θ
−0.01
−0.02
−0.03
−0.04
−0.05
−0.06
1
1
0.8
0.8
0.6
0.6
0.4
−θ
d
Notes: This figure depicts
uni
∂ GT multi −GT
∂g −θ
0.4
0.2
0.2
g−θ
for different combinations of g −θ and d−θ .
31
frameworks.46 The intuition behind this result is that multi-sector models capture two types of
losses: those derived from lower aggregate trade shares (higher πll ), and the losses generated by
the reduction in the dispersion of sectoral domestic trade shares, Aπll .
4.3
Gains from Openness in a Multi-sector Model
The gains from openness, GO, defined as the change in welfare when we allow countries to
exchange goods as well as to produce with their own technologies overseas, is given by the following
expression in multi-sector models.47
GOl =
ylla yllb
− 1 2θ
πlla πllb
− 1
2θ
which as a function of trade and MP barriers, as well as the Atkinson index of sectoral fundamental
and effective productivities, can be re-written as:
"
2
GOl =
1 − g−θ +
4g −θ
(1 − AT )2
·
1 − d−θ
2
+
4d−θ
1 − AT̃
!# 1
2θ
2
(12)
Interestingly, as stated below in proposition 7, gains from openness increase as g−θ approaches
to one. This is due to the fact that when MP barriers are relaxed, the dispersion of MP shares
increases by more than the reduction on sectoral dispersion of trade shares, which implies that
MP has a positive and dominant effect on gains from openness.
Proposition 7. Gains from openness (GO) are higher in multi-sector models—relative to onesector frameworks; and the difference in GO is larger 1) the higher the dispersion of productivity
(GO multi −GO uni )
(GO multi −GO uni )
across sectors, ∂
> 0.
> 0; and 2) the lower the MP barriers: ∂
∂AT
∂g −θ
Notice that the above proposition states that the increase in GO when g −θ increases is larger
in a multi-sector framework.
− 1 ∂y
∂ GO multi − GO uni
∂GO multi 1 θ
ll
1−θ
π
×
y
=
+
>0
ll
ll
−θ
−θ
−θ
∂g
∂g
θ
∂g
1
1
where gains from openness in one-sector models are giving by: GOl uni = (yll )− θ (πll )− θ .
46
Notice that in our model aggregate trade shares are affected by changes in g, and therefore the gains from
trade that will be computed if we use welfare gains formulas as the ones derived in a one-sector framework will also
be affected.
47
The derivation of the gains from openness in a multi-sector framework can be found in the Appendix C.
32
Figure 9: Proposition 4: Gains from Openness
(a)
1.8
∂ (GO
multi
− GO
uni
) / ∂A
T
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
−θ
g
0.2
A
T
(b)
0.4
∂ (GO
multi
− GO
uni
)/∂g
−θ
0.35
0.3
0.25
0.2
0.15
0.1
0.05
1
1
0.8
0.8
0.6
0.6
0.4
−θ
g
Notes: The top panel depicts
displays
uni
∂ GO multi −GO
∂g −θ
uni
∂ GO multi −GO
∂AT
0.4
0.2
0.2
A
T
for different combinations of AT and g −θ . The bottom panel
for different combinations of AT and g −θ .
33
5
Quantitative Framework
In this section, we quantitative estimate a multi-country multi-sector version of the model,
including labor and capital as factors of production, intermediate inputs, and inter-linkages across
sectors. This environment incorporates N countries and J + 1 sectors; the first J sectors are
tradables and the J + 1 sector is non-tradable. Both capital Kl and labor Ll are mobile across
sectors but immobile across countries; while wl and rl represent the wage rate and the rental
return of capital, respectively. Trade and MP costs are location-destination-sector and sourcelocation-sector specific, dnl and gls , respectively. Finally, with N > 2, firms can sell goods to
a final destination either by serving it locally through a foreign affiliate located directly at the
destination market, or by producing on a third country that can be used as platform to export
to country m by incurring in trade cost dnl , in addition to gls . Finally, in order to serve any
foreign market with a variety from sector J + 1, the only option is to locate a firm in the target
market. Therefore, for all non-tradable varieties, the host economy and the destination market
are necessarily the same (l = n).
The main equations of the model are extended in order to incorporate multiple countries,
multiple tradable sectors, a non-tradable sector, capital, intermediate inputs usage, and linkages
across sectors.48
Preferences

 η ξn
η−1
J
1
X
η−1
1−ξn
η
j η 

Yn =
ω j Yn
YnJ+1
Production
cjl
=
wlj
#1−βj
"
αj 1−αj βj J+1
Y γkj
j
k
rl
pl
Fsj (z)
j
πnls
Price Index
pjn
48
= Γj
= exp
"
−Tsj
X j −θj
zls
l
!#
(15)
−θj
−θj
j
Tsj ∆jns
δnls
=
·
P j j −θj P j −θj
∆
T
k k
n δnls
nk
(14)
k=1
Technology
Market Structure
(13)
j=1
f
∆jn
− 1
θj
= Γj
X
s
Tsj
−θ
∆jns j
(16)
!− 1
θj
This extension follows [Levchenko and Zhang, 2016], but for a multi-sector model of MP and trade.
34
(17)
Goods’ Market Clear
pjl Qjl = pjl Ylj +
J+1
X
k=1
(1 − βk ) γj,k
N X
N
X
m=1 s=1
k
pkn Qkn
πnls
!
∀j = {1, ..., J + 1}
(18)
Where ξn denotes the Cobb-Douglas weight for the tradable sector composite good and YnJ+1
is the non-tradable sector composite good. The elasticity of substitution between the tradable
sectors is denoted by η, and ωj is the taste parameter for tradable sector j. Note that the
consumer’s utility is CES on tradable sectors, allowing η to be different from one. Moreover, in
the quantitative exercise, ξn will vary across countries, in order to capture the positive relationship
between income and the consumption share of non-tradables observed in the data. The valueadded-based labor intensity is given by αj , while the share of value added in total output is given
by βj —both of which vary by sector.49 The weight of intermediate inputs from sector k used by
j
sector j is denoted by γkj . Any firm gets a productivity draw zls
(ω) in each of the N possible
location countries l, which is assumed to be independent across location countries. Also as stated
in equation 18, the market value of total demand in sector j, pjl Qjl , is used as (i) final consumption
pjl Ylj ; and (ii) intermediate inputs for domestic production in all sectors. Notice that the demand
for intermediate inputs in country l for sector j depends on the per unit input requirement that
each sector k has on intermediates from sector
on the world
demand of sector k goods
P j, and
PJ+1
N PN
50 The rest of the section
k
k
k
produced in country l’s:
k=1 (1 − βk ) γj,k
n=1
l=1 πnls pn Qn .
j
focuses on the estimation of three main parameters of the model, Tlj , gls
, and djnl , while details
of the estimation of the remaining model’s parameters can be found in the Appendix E.
5.1
j
Estimating the Model’s Parameters: Telj , Tlj , gls
, and djnl
In this section, we use two steps to estimate the sector-level technology parameters for local
producers (Tlj ) for 32 countries, 9 tradable sectors, and a non-tradable sector. First, the effective
technology parameter (Tej ) is estimated by fitting the structural trade gravity equation implied
l
by the model, using trade and production data.51 In this step, we also estimate the bilateral
trade cost at the sectoral level. Then, we proceed to estimate the corresponding MP barriers at
49
We have re-estimated the parameters of the model by allowing for αl,j , βl,j and γl,kj to vary at the countrysector level by using World Input-Output Database from [Timmer, 2015].
P
PN
J +1
50
Notice that N
n=1
s=1 πnls = 0, whenever n 6= l.
51
The gravity equations are derived from the model under the assumption that productivity draws are uncorrelated across location countries. [Ramondo and Rodrı́guez-Clare, 2013] uses aggregated multinational production
data to calibrate the productivity parameter, and MP and trade barriers assuming two alternative values for ρ,
ρ = 0 and ρ = 0.5. The goodness of the model measured by how it matches the patterns of the data is extremely
similar in both cases. The only variable that performs better when ρ = 0 is the exports of foreign affiliates. As
pointed out by [Ramondo and Rodrı́guez-Clare, 2013] and more recently by [Tintelnot, 2016], this is a consequence
of the limitations of a model of MP that excludes the fixed cost of operating an affiliate overseas. However, this
simplifying assumption buys us the tractability of using the gravity equation for trade and MP, which is directly
comparable to previous works that have focused on the estimation of the average productivity parameters using
trade data at the sectoral level.
35
the sectoral level by fitting the structural MP gravity equation implied by the model using data
j
on foreign affiliate sales at the bilateral-sector level.52 Finally, using our estimates of Tsj and gls
,
we calculate the effective technology parameters for each country-sector pair in a way that are
consistent with both trade and MP gravity equations.53
The effective productivity estimates that emerge from the gravity equation reflect the average
productivity of all producers in a given sector of the economy. Controlling for factors of production
and intermediate inputs prices, as well as for trade barriers, a country that produces a larger
share of its domestic demand exhibits a high effective productivity. However, a high effective
productivity could be the result of highly productive local producers, or could also be explained
by the access to better technologies available to foreign affiliates operating in the location market.
Intuitively, a country that produces a larger share of its output using domestic technologies has
a higher relative fundamental productivity. Conversely, if the share of foreign affiliate production
is high, the country has a relatively low fundamental productivity in that sector. Therefore, the
average absolute difference between Tlj and its effective counterpart T̃lj for each sector is a measure
of the absolute transfer of technology generated by MP, while the difference in the dispersion of
effective and fundamental sectoral productivity is a measure of the effect of MP on comparative
advantage.
5.1.1
MP and Trade Gravity Equations
In order to relate the model to observables in our dataset, we calculate the bilateral sectoral MP
j
j
shares by summing πnls
across all source countries s: πnls
=
j
Xnls 54
j .
Xn
We obtain country l’s trade
shares, reflecting the probability that country n will import sector j goods that are produced
P j
j
in country l, regardless of the source of the technology used in production: πnl
=
s πnls =
j
j
P Xnls
Xnl
j
j =
j . Substituting equation (16)) into this expressions for πnl , we have:
s
Xn
Xn
j
Xnl
Xnj

−θj
−θj fj j j −θj
j
j j
j
c
d
T
T
c
d
g
X
s
l nl
l
l nl
ls

=
=

P
−θ
−θ
P fj j j −θ
j
j
jP
j
s
cjk djnk
s Ts
k gks
k Tk ck dnk

(19)
−θj
f
f P
j
. This implies that the effective technology (Tlj ) employed by a country
where Tlj = s Tsj gls
in order to produce and compete on the international markets is a combination of the average
productivity of the local producers in sector j and the average productivity of the foreign affiliates
operating in the domestic market. However, notice that the local economy has a limited capacity
to absorb foreign technologies, which is reflected by the costs that foreign affiliates incur when
For every country l and sector j, the production of local producers Illj is calculated by subtracting the
production of foreign affiliates from total production.
53
See Section 5.1.2 below and Section F in the Appendix.
j
54
Note that πnls
is independent across source countries. This is because source country s would not set operations
in two different location countries l in order to serve a given market n.
52
36
j
producing in the local market (gls
).
To get the specification that will be taken to the data, equation (19) is divided by country
n’s normalized import share. Taking logs to both sides of the equation, and assuming djnl is
a linear function of distance as well as whether countries share a common border bjnl , common
j
language lanjnl , regional trade agreements RT Ajnl , and colony ties colonynl
, we get the following
specification for the gravity equation:
ln
j
Xnl
j
Xnn
!
fj j −θ
fj j −θ
− ln Tn cn
= ln Th ch
{z
}|
{z
}
|
exporter fixed effect importer fixed effect
(20)
j
j
.
−θdistancejnl − θbjnl − θlanjnl − θcolonynl
− θRT Ajnl − θexjl −θνnl
{z
} | {z }
|
error term
bilateral observables
where bilateral trade cost djnl is computed based on the estimated coefficients:
j
j
j
dj + colony
\ nl + bbj + lan
\ nl + RT
[
dbjnl = exp{distance
xjl + µ
bjnl }.
Anl + ec
nl
nl
where the asymmetric specification of the trade barriers in equation (20) follows [Waugh, 2010],
who includes an exporter effect, exjl to reflect the extra costs to country l of exporting a good to
country n in sector j.55
j
Next, we derive a MP gravity equation to identify MP barriers (gls
) and the state of technology
of local producers (Tlj ) for every country l and sector j in our sample. The volume of bilateral
foreign affiliate sales from country s in location country l depends on: (i) the size of the markets
foreign affiliates can access from each location country; and (ii) the probability that foreign
affiliates from country s, located in market l, offer the lowest possible price to consumers in
destination market n (πnls ). Therefore, bilateral MP sales are given by:
j
Ils
=
X
m
j
πnls Xm
−θ
−θ
j j
j −θ
Tsj gls
cl
d
×
pjl
X nl
· Xnj
=
−θ
P P j j −θ j j −θ
j
n
pn
ck dhk
s
k Ts gks
(21)
j
Dividing Ils
in (21) by its counterpart in the location country (Illj ) and taking logs at both sides
55
Notice that similar to [Waugh, 2010], in our dataset, the price of tradables is unresponsive to a country’s GDP.
37
of equation, we get our preferred normalization for estimation.56
ln
j
Ils
Illj
!
=
ln Tsj
| {z }
−
source fixed effect
ln Tlj
| {z }
location fixed effect
(22)
j
−θdistancejls − θbjls − θlanjls − θcolonyls
− θRT Ajls − θsourcejs −θµjls ,
{z
} | {z }
|
error term
bilateral observables
j
j
j
j
j
j
\ ls + bbj + d
\ ls + RT
[
bjls }.
\s+µ
lanls + colony
Als + source
gbls
= exp{distance
ls
Notice that the specification for MP barriers includes a source effect, which represents the extra
costs to source country s of producing sector j goods in country l. This will allow less developed
countries to face systematically higher cost to produce overseas. Notice that the inclusion of
a source effect produces estimates that are consistent with the observed patterns of prices and
income data. Three empirical observations are highlighted in this regard. First, there is home
bias for all countries regardless of their level of development. This means that countries with
relative higher income produce slightly more of their output with local technologies, but the
difference in magnitude is small. Second, there is a systematic correlation between bilateral MP
shares and relative level of development: the larger the difference in relative income, the larger
the disparity in bilateral MP share between two countries. Third, the model estimated with
source effects delivers a flat relationship between tradable prices and GDP per-capita, matching
the data pattern documented in [Waugh, 2010]. By contrast, the model estimated with location
effects instead implies a negative and significant relationship between tradable prices and GDP
per-capita. Section D.2 in the Appendix presents evidence to support the chosen specification in
equation 22.
5.1.2
Estimated State of Technology: Tlj and Telj
j
This section has the goal of getting a set of estimates for Tlj and gls
consistent with the trade
and MP gravity equations previously derived. Through the structural gravity equations and the
model’s derived relationship between Tej and T j , the model offers two independent measures of
l
l
effective productivities. On the one hand, the effective technology parameters Telj can be recovered
through the importer fixed effect in the trade gravity equation, after properly discounted for factor
56
The gravity equations are estimated using Pseudo Poisson Maximum Likelihood (PPML), as suggested by
[Silva and Tenreyro, 2006], to alleviate any bias from log-linearizing in the presence of heteroskedasticity and the
omission of zero trade flows. Notice that results are not much different when compared with the ones obtained by
ordinary least squares; although, as expected, the OLS overestimates the elasticity of trade and MP flows to distance
and other resistance variables. When computing the equilibrium, we set trade and MP cost to be arbitrarily large
j
j
for the instances in which Xnl
and Ils
are zero.
38
trade
prices and prices of intermediate inputs;57 which we refer as Telj
. On the other hand, we can
j
also construct Telj from the gls
and Tsj estimated trough
MP gravity equation,58 by calculating
the
mp
the following system of equations, which we refer as Telj
.
mp X
j −θ j
Telj
=
(gls
) Ts ∀j = 1, ...J + 1,
(23)
i
Although the estimates of effective productivities obtained trough these two procedures are highly
correlated,59 they have been estimated independently. To overcome this challenge, we develop a
tournament process that involves the trade and MP gravity equations anda transition between
mp
P j −θ j
j
them trough equation (23). The idea is to re-estimate gls
and Tlj until Telj
) Ts is
= i (gls
arbitrarily close to the effective productivity estimates obtained from the trade gravity equation
trade
trade
mp
Telj
.60 The procedure starts by comparing the initial gap between Telj
and Telj
mp
and updates the value of Telj
by adding to it a small fraction of the observed gap.61 Next, we
mp
use our updated Telj
and solve for the J vectors of Tlj from the system of equations below:

  j
j
g11 g12
Te1j
 ej   j
j
 T2   g21 g22

 
 ..  =  ..
..

 

 
..
 ..   ..
j
j
j
gN 1 gN 2
TeN
.. ..
j
g1N



j 
g2N
 
 

.. ..
.. 
×
 
.. ..
..  
j
.. .. gN N
.. ..
T1j


T2j 

.. 
.

.. 
TNj
Then, we use these fundamental productivity estimates, Tlj , and run a constrained MP gravity
j
j
equation, where the location and origin fixed effects are replaced by Tbl and Tbl both of which are
restricted to have coefficient of one (β0 = α0 = 1), and from which we update our estimates for
MP barriers (c
gls ).62
ln
j
Ils
Illj
!
c
= β0 ln Tsj
c
− α0 ln Tlj
− θ ln (gls ) − θµjls
j
Using the updated estimates for Tbl and (c
gls ), we calculate
mp
P j −θ j
Telj
= i (gls
) Ts and repeat
the procedure until the difference between the effective productivity parameters from the trade
57
j
Isolating Tem
from the estimated importer fixed effect entails a two-step procedure, as proposed by [Shikher,
2012a]. See section D.1 in the Appendix for details.
58
The fundamental productivities, Tsj , are recover by exponentiating the estimated location fixed effect
59
See Appendix A.6 for further details.
60
I thank Andrés Rodrı́guez-Clare for suggesting this procedure.
61
This fraction is set to be five percent in our baseline estimates, but the final estimates are the same if we chose
one percent instead.
62
To estimate (c
gls ), we follow equation (21), where MP barriers are modeled as a function of distance, colony
ties, RTA and common border.
39
trade mp
and MP equations is negligible, ∆ = Telj
− Telj
≈ 0.63 More details of this estimation
procedure can be found in Appendix F.
5.2
Multinational Production and Sectoral Productivity
This section describes the basic patterns of how estimated sector-level productvity varies across
local and foreign producers for all countries in our sample. In particular, it compares the technology of local producers—excluding foreign affiliates, Tsj —with the state of technology of all
producers in the economy, Tesj .
First, we reproduce the negative relationship between productivity and MP shares across sec-
tors presented in Section 2.3, but this time, using the estimated fundamental productivities, Tlj ,
by using the following specification:
ln
Illj
Ilj
!
= κl + µj + β ln Tlj + ǫlj
Figure 10a shows that when all countries and sectors are pooled, after controlling for countryand sector-specific characteristics, the overall correlation is negative and significant at the one
percent level. Second, to shed further light on whether sectors in which local producers show
greater disadvantage are the ones that receive the biggest boost from MP, weregress the inward
MP share with the estimated technological upgrade for country l in sector j, Telj /Tlj .
ln
Illj
Ilj
!
= κl + µj + β ln
Telj
Tlj
!
+ ǫlj
Figure 10b shows a positive and significant relationship between these two variables, suggesting
that, on average, the technology boost due to the operations of multinational affiliates in the
location country is larger in comparative disadvantage sectors, which are sectors where the share
of inward MP is larger. This is also reflected in Figure A.3 in the Appendix, which shows that,
for most countries, the dispersion of Tej is lower than the dispersion T j . This is, the heterogeneity
l
l
and magnitude of the MP barriers is such that allowing MP reduces the dispersion of effective
productivities across countries.
The described patterns of the data are illustrated with some examples for selected countries.
Figure 11 presents scatter plots of the productivity of the tradable sector for both local producers
(red circles) and for the overall economy (blue circles). On the x-axis, sectors are placed in order
63
The comparison of the distribution for (c
gls ) in the first and last iteration shows that they are very similar.
The smooth updates generated through the presented algorithm do not change the moments of the distribution of
the MP barriers. Similarly, the location of the distribution of our Tlj estimates slightly changed to ensure complete
consistency between the trade and the gravity equation, nonetheless other moments of the distribution are almost
mp
trade
unaltered. This is not surprising given the closed tight we documented between Tej
and Tej
, when they
l
are independently estimated.
40
l
Figure 10: Multinational Production and Sectoral Productivity
−2
−1
Inward MP Share
0
1
2
(a) Inward MP shares and Tlj
−2
−1
0
Fundamental Productivity
1
2
coef = −−0.2761, (robust) se = 0.0465, t = −−5.93
ej
T
l
j
Tl
−2
−1
Inward MP Share
0
1
2
(b) MP Shares and Productivity Upgrade
−.5
0
.5
Efffective Productivity / Fundamental Productivity
1
coef = 1.3238, (robust) se = 0.1457, t = 9.08
Notes: Panel (a) displays the partial correlation of inward MP share ln
j
Ill
j
Ill
against the productivity of local
producers in country l, Tlj , after netting out the
fixed effects, and the sector fixed
effects. Panel (b) shows
location
j
j
e
Ill
T
l
the relationship between inward MP shares ln j and the productivity upgrade ln
. Productivity Telj and
j
Ill
Tl
Tlj are estimated as explained in Section 5.1.2
41
Figure 11: Effective Telj and Fundamental Tlj Productivities
France
United Kingdom
1.3
Relative Productivity
Relative Productivity
1.3
1.2
1.1
1
0.9
0.8
0
2
4
6
8
Sectors Sorted by Fundamental T
1.2
1.1
1
0.9
0.8
10
0
Slovakia
Relative Productivity
Relative Productivity
1
0.9
0.8
0.7
0.6
0
2
4
6
8
Sectors Sorted by Fundamental T
0.9
0.8
0.7
0.6
0.5
10
0
Estonia
10
1.2
Relative Productivity
Relative Productivity
2
4
6
8
Sectors Sorted by Fundamental T
Japan
0.9
0.8
0.7
0.6
0.5
10
Poland
1
0.5
2
4
6
8
Sectors Sorted by Fundamental T
0
2
4
6
8
Sectors Sorted by Fundamental T
1.1
1
0.9
0.8
10
0
2
4
6
8
Sectors Sorted by Fundamental T
10
Notes: This figure displays the tradable-sector effective and fundamental productivities for selected countries,
expressed as the ratio to the U.S productivity, for the overall economy (red circles) and for local producers exclusively
(blue circles). The x-axis labels sectors in descending order of local producers productivity, such that sectors where
local producers are relative more productive are on the left.
42
of their distance from the U.S. productivity, such that the local producers’ comparative advantage
sectors are furthest to the left.64 Although there are variations across countries in how MP affects
effective technology across sectors, it can be noticed that: (i) in all countries except Japan, the
productivity for all producers—including multinationals—is larger than the productivity of local
producers only; and (ii) the gap between the fundamental and effective productivity tends to be
larger in the sectors where local producers are less productive.
5.3
Evaluating the Model’s Fit
Before proceeding with the counterfactual exercises of the next section, we evaluate the goodness of our calibrated model by showing how closely it matches the actual relative income differences as well as the MP and trade patterns.65 Table A.7 in the Appendix reports the mean,
median, and the correlation between the model and the actual data for wages, return of capital, manufactured imports as a share of output, and inward and outward MP shares. Figures A.4, A.5, A.6, and A.7 present the comparison between the model and the data for each of
these variables. The ability of the model to replicate income differences across countries is shown
by the close match it achieves of the wages and return of capital relative to the United States
for most countries in our sample. Second, the model slightly underestimates the share of total
output produced by foreign affiliates—the median of the manufacturing Inward MP to output
ratio is 0.31 in the model while this ratio is 0.34 in the data— however, their correlation is high
(0.94). The calibrated model replicates the fact that the distribution of outward MP to output
is left-skewed, with the mean of the outward MP share (0.20) being considerably higher than
the median (0.10). In the following section, we use the calibrated model to construct a number
of counterfactuals exercises that allow us to understand the different mechanisms underlying the
relationship between MP, comparative advantage and the gains from openness.
6
Welfare Analysis and Counterfactual Experiments
In this section, we aim to achieve three goals. First, we calculate the gains from MP, trade and
openness in our calibrated multi-country, multi-sector model of trade and multinational production, and compare them with the welfare gains delivered by one-sector frameworks. Differences in
welfare arising between these two models can be interpreted as additional gains coming from the
different sources of heterogeneity altogether, such as: (i) cross-country differences in preferences
across sectors, (ii) sectoral inter-linkages in production, (iii) sectoral trade elasticities, (vi) differences in relative technology across sectors, and (v) country pair-sector specific MP and trade
costs; all of which manifest themselves in the observed sectoral dispersion of MP and trade shares
64
Results are similar if instead we normalize the productivity of each country sector pair by the global productivity frontier.
65
Section G in the Appendix presents the algorithm that solves for the equilibrium of the model.
43
that are critical in accounting for the welfare gains captured by multi-sector models.
Second, from all possible sources of heterogeneity, we start by focusing our attention to one
in particular: sectoral differences in fundamental productivities. Our goal is to understand how
the dispersion in sectoral technology differences affects the allocation of MP across sectors as well
as the gains from MP and openness. We also decompose the effects of shutting down relative
differences in productivity across sectors into two parts: a first component due to changes in the
aggregate level of MP and trade shares, and a second component due to changes in their sectoral
dispersion. We call “total effect” the welfare impact of joint changes in the aggregate level as
well as in the dispersion of trade and MP shares across sectors. In addition, we call “adjusted
effect” to the welfare impact that can be exclusively attributed to changes in the dispersion of
MP and trade shares—measured by the Atkinson inequality index, while keeping aggregate shares
unaltered. In addition, we explore how the effects of eliminating Ricardian comparative advantage
interplay with other sources of heterogeneity (e.g. MP costs). In particular, we run a conterfactual
scenario in which MP costs are muted, in order to check whether it enhances or offsets the effect
of eliminating comparative advantage on welfare.
Third, we present two additional set of counterfactuals to explore the implications of a multisector model of MP and trade. First, we ask how gains from trade will look like in a counterfactual
scenario in which MP only improves the country’s absolute productivity while keeping the country’s comparative advantage unchanged (AT = ATe ). The idea behind this counterfactual is
that multinational activity could affect the gains from openness by affecting the heterogeneity
of trade shares, since MP modifies the relative dispersion of the effective productivities (Te) used
by countries to produce and compete on international markets. More MP in the economy has a
differentiated impact on sectoral (Te), because MP flows are heterogeneously distributed across
sectors, and on average, they go towards sectors with comparative disadvantage. Second, we ex-
plore the effects that allowing MP in the non-tradable sector has on the overall welfare gains. The
relevance of this counterfactual lies on three well known empirical facts: (i) non-tradables represent a large fraction of the world economy; (ii) MP shares are relatively larger in non-tradables;
and (iii) there is a high production requirements of non-tradable for most tradable sectors.
6.1
Gains From Trade, MP and Openness: A Comparison with One-sector
Models
In this section, we calculate the gains from MP, trade and openness in a multi-sector model
and compare them with those from a one-sector framework. Columns (1)-(3) in Table 3 show the
welfare gains in a multi-sector model with CES preferences and capital as an additional factor of
production, also including intermediate inputs, inter-sectoral linkages and cross country differences
in preferences across sectors; while columns 4-6 correspond to the welfare in a one-sector model.66
66
[Costinot and Rodrı́guez-Clare, 2014] the value of the elasticity of subsitution across tradable sectors has large
effects on the magnitude of the gains from trade. In particular GT are lower for higher values of (η) since consumers
44
Table 3: Welfare Gains from Trade, MP and Openness (%)
Multi-sector
Model
Country
One-sector
Model
GMP
GT
GO
GMP
GT
GO
Australia
Austria
Belgium
Bulgaria
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Lithuania
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Romania
Russia
Slovakia
Spain
Sweden
Turkey
Ukraine
United Kingdom
United States
13.6
13.8
24.5
16.4
13.1
43.7
8.0
25.6
8.7
10.0
10.5
4.9
25.7
6.7
0.8
31.7
4.8
12.3
8.1
11.7
21.8
12.9
34.2
13.1
34.4
9.4
12.5
3.2
14.9
19.0
3.6
4.2
9.6
32.6
14.6
10.2
12.4
12.1
17.6
8.5
4.7
6.2
4.9
14.6
4.4
1.1
20.1
7.3
14.4
7.4
8.5
7.8
9.2
9.0
4.5
14.5
4.3
9.6
4.2
6.7
5.5
1.8
19.2
26.2
76.7
34.7
25.5
68.2
20.9
50.1
18.8
15.3
17.7
9.8
51.7
11.5
2.0
60.8
12.6
28.4
17.0
22.2
32.3
25.4
48.8
21.5
55.7
14.8
24.1
7.3
23.6
25.9
5.4
6.0
6.7
11.9
7.7
6.4
18.1
3.6
11.0
3.9
4.6
4.9
2.1
9.8
2.9
0.3
12.1
2.3
5.6
3.4
5.2
9.6
5.4
13.5
4.4
14.7
4.3
5.7
1.3
6.3
8.5
1.7
1.5
3.4
6.2
4.5
3.5
4.5
4.0
5.1
2.8
2.0
2.4
1.8
4.7
1.8
0.5
5.8
2.7
4.5
2.4
3.1
2.8
3.2
3.2
1.7
4.8
1.8
3.4
1.6
2.4
2.2
0.8
7.8
10.3
18.5
12.4
10.2
23.8
7.7
17.3
7.0
6.8
7.5
3.9
16.0
4.8
0.9
18.9
5.0
10.4
6.1
8.5
12.9
8.9
17.7
6.7
20.3
6.2
9.4
2.9
9.1
11.0
2.5
Mean
Median
18.0
13.0
9.7
8.5
32.0
23.9
6.9
5.6
3.1
3.0
10.4
9.0
Notes: This table reports the changes in real income resulting of moving from autarky to the calibrated levels of
1
trade and MP frictions. Results under “One-sector” are computed using aggregate formulas GT uni = 1 − (πnn )− θ ,
P
− 1
P
1
θ
l6=n Xnl
P
GM P uni = 1 − ynn ππ̄nn
= 1−
,
; and GOuni = 1 − (ynn πnn )− θ ; where πnn = XXnn
l6=n Xnl
nn
n
l Xnl
P
Inn
is measured as total imports and
l Xnl is measured as country n’s total expenditure. Also, ynn = In =
P
P
P
I
ns
s6=n
P
1−
, where
s6=n Ins is measured as total inward MP and
s Ins is measured as country n’s total
s Ins
output. The value of θ is 6.
45
Table 3 shows that multi-sector models deliver higher gains from MP and gains from openness,
and that these differences are sizable in magnitude.67 The implied gains from MP in our multisector model are on average 18.0 percent, which is almost three times the gains derived in onesector frameworks. Similarly, gains from openness are substantially larger in a multi-sector model
(32.0 versus 10.4 percent). These average effects masks a fairly deal of heterogeneity in the
differential gains across countries, though. Lowering MP costs from infinity to their calibrated
values while keeping trade cost unchanged, has a sizable impact on relative small economies such
as Belgium, Estonia or Slovakia; but only has smaller effects for large countries like the U.S.
or Japan, which are countries with large shares of outward MP and smaller shares of inward
MP. Notice that in our perfect competitive environment, outward MP reduces exports and, as a
consequence, it also reduces home production without generating profits, worsening the terms of
trade and the welfare gains; effects that can be offset through higher aggregate inward MP shares
and a more heterogeneous allocation of MP shares across sectors.
6.2
The Impact of Sectoral Productivities Differences on Welfare
The differences on welfare and real income between one-sector and multi-sector models, presented in Table 3, measure the impact coming from eliminating all sources of heterogeneity present
in our model; including, differences in relative sectoral productivities, MP costs, trade barriers,
among others. Comparing the welfare results derived from rich quantitatively frameworks with
the ones delivered by one-sector formulas can be misleading if we want to isolate the welfare
impact of a particular source of heterogeneity. This is because, by design, welfare measures of
one-sector models shut down all sources of heterogeneity at once, making impossible to evaluate
the individual impacts of different model’s parameters on welfare.68
In this section, we aim to understand the additional welfare gains arising only from relative
differences in sectoral productivities. To isolate the effect that Ricardian comparative advantages
has on the dispersion of MP and trade shares, and ultimately on the gains from openness, we
construct a counterfactual exercise in which we “remove comparative advantage” while keeping
other country-sector specific model’s parameters (e.g. trade and MP costs) unaltered. To pursue
this exercise, we follow the methodology developed by [Costinot et al., 2012], in which the comparative advantage of each country is removed, one at the time, by imposing the structure of the
sectoral productivity differences of each “reference” country to the rest of the economies. This
can more easily substitute consumption alleviating the adverse effects of autarky on real income. The elasticity of
substitution has been set to 2 in our baseline scenario. To evaluate the sensitivity of our results to this parameter,
Figure A.8 in the Appendix displays the average welfare gains for different values of (η) in our estimated model,
showing a modest variations in the GT, GMP and GO.
67
Gains from trade are also higher in multi-sectoral models [e.g., Costinot et al., 2012,
Costinot and Rodrı́guez-Clare, 2014, Caliendo and Parro, 2015, Levchenko and Zhang, 2013, Ossa, 2015, Shikher,
2012a].
68
Notice that we did such direct comparison in section 4 to evaluate the effect of a higher dispersion in relative
productivities. In that context, this was a valid procedure because the only source of heterogeneity in the model
was coming from relative technology differences.
46
is done by adjusting countries’ absolute advantage, while preserving relative nominal income to
avoid any indirect terms of trade effects on the reference country.69 Section H in the Appendix
explains in detail this procedure, providing the algorithm that solves for the absolute productivity
adjustments.70
In the analytical results derived in Section 3, we show that changes in the dispersion of fundamental productivities affect not only the aggregate but also the heterogeneity of MP and trade
shares. Therefore, we breakdown the effects on welfare into two components: “total effect” and
“adjusted effect”. The adjusted effect takes away the impact on welfare created by changes in the
aggregate MP and trade shares, isolating the effects due to changes in the sectoral dispersion of
MP and trade shares. To clearly contrast scenarios that imply different levels of aggregate trade
and MP shares, we follow [Ossa, 2015].71 In practice, this implies multiplying each counterfactual sectoral share by the ratio of the “equilibrium” and “counterfactual” aggregates ( π̂πllll ,
ŷll 72
yll ).
In this fashion, we are able to keep the aggregate share constant, while capturing the sectoral
heterogeneity implied by the counterfactual exercise.
Table 4 shows the effects of removing the countries’ comparative advantage on gains from trade,
MP and openness, as well as on real income. Columns (1)-(3) report the total effect on GMP,
GT and GO, measured as percentage change relative to their equilibrium values. The median
country in our sample experiments a decrease of 10 percent and 14 percent in GMP and GO,
respectively. Nonetheless, there is substantial variation across countries. For example, Sweden
and Estonia only decrease their GO by less than 10 percent; Portugal and Finland have a decrease
on GO of more than 25 percent; while Canada, Poland and the United Kingdom experiment an
increase on their GO, when there is no differences in relative sectoral productivity across countries.
The comparison between column (1) and (2) shows that there is more dispersion in the response
of GMP compare to GT—in terms of sign and magnitude—to the removal of the comparative
advantage. This higher sensitivity is related to the fact that MP only takes place in about half of
the location-source-sector triplets in our sample (Section 6.2.1).73 Finally, column (7) of Table 4
shows that most countries are worse off in the counterfactual scenario, with the real income of
the average country being 1.4 percent lower than in equilibrium, representing 9.1 percent of the
69
Notice that in this counterfactual exercise is carry on tradable sectors only.
Notice that there are important differences between the exercise by [Costinot et al., 2012] and the one presented
here. Our model allows for multinational production, and it also features intermediate inputs, a non-tradable sector
and input-output inter-linkages across sectors.
71
[Ossa, 2015] presents a formulation of the welfare gains of a multi-sector model in terms of the aggregate shares.
In this paper, we extend this work to the case of multi-sector MP and trade, and Table A.8 in the Appendix shows
the adjusted formulas for GT, GM and GO. Notice that we use model’s base formulas in our counterfactuals. In
particular, we use a version of the formulas developed in [Costinot and Rodrı́guez-Clare, 2014] adapted for the case
of multi-sector MP and trade, which is entirely based on observables. It features Cobb-Douglas preferences and
no-capital, while having intermediate inputs, a non-tradable sector and a full input-output matrix, as shown in the
top panel of Table A.8 in the Appendix.
72
This allows us to easily adjust the “counterfactual” aggregates to meet their values prior to the counterfactual
exercise, which are set to be at the initial equilibrium levels (π̂ll , ŷll ).
73
For location-source-sector triplet where there is no MP, the MP barriers are set to be prohibitively costly.
70
47
Table 4: Change in Welfare Gains of Removing Comparative Advantage (percentage change)
GT
GMP
GO
GT
Total
Country
GMP
GO
Real
Income
Adjusted
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)†
Australia
Austria
Belgium
Bulgaria
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Lithuania
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Russia
Slovakia
Spain
Sweden
Turkey
Ukraine
United Kingdom
United States
-21.2
-9.3
-11.5
-9.0
-4.5
-2.1
-10.8
-3.2
-28.3
-1.2
-8.6
-17.0
-37.1
-5.2
-26.6
-1.1
6.8
-5.4
-34.3
-13.4
-3.4
-10.1
-31.7
-0.1
-2.1
-11.5
-19.5
-15.7
-0.9
2.2
23.6
-7.9
-22.8
-41.4
21.2
-19.1
-9.5
-10.3
-12.0
-13.6
27.2
-26.2
-7.4
-24.3
-34.4
18.8
-35.1
22.6
12.6
21.7
13.2
-22.4
-66.0
18.8
-13.4
6.0
-32.6
3.2
37.1
-12.4
-5.1
-17.2
-20.9
-24.2
4.3
-20.8
-11.2
-9.1
-30.6
-9.2
3.6
-20.8
-45.5
-16.9
-32.8
5.5
-3.4
2.5
-28.4
-9.2
8.4
-24.9
-63.6
7.8
-16.0
-8.4
-24.5
-16.7
19.6
-7.0
-8.6
-9.9
-21.1
-15.9
-5.6
-1.0
-10.7
-5.6
-21.4
0.8
-6.9
-8.5
-26.2
0.0
-9.0
-7.5
-5.6
-7.1
-22.0
-8.9
-4.0
-9.1
-12.8
-4.3
-0.6
-10.7
-7.5
-9.9
0.4
-0.2
-6.8
2.0
32.4
8.8
8.3
-5.7
-3.8
-8.1
-13.7
-2.4
4.8
-9.2
-25.6
-7.8
-5.0
25.5
9.2
11.6
-21.6
-1.0
11.5
-9.8
-36.7
11.3
-7.2
-1.0
-12.1
3.4
9.4
-2.8
-12.7
-15.0
-21.1
-13.5
-2.2
-14.0
-9.1
-8.6
-24.3
-1.0
-4.2
-8.1
-38.7
-4.6
-8.7
-0.4
-6.2
-2.6
-28.0
-10.9
5.4
-18.9
-36.7
0.9
-11.5
-9.7
-8.5
-10.3
4.8
-2.0
-0.3
-1.8
-3.6
-2.9
0.5
-4.0
-1.0
-2.3
-2.7
-1.0
0.7
-1.4
-9.5
-1.4
-0.5
3.2
-0.1
0.7
-2.7
-0.9
1.5
-3.1
-8.8
2.2
-1.3
-0.7
-1.3
-0.9
2.2
-0.2
-3.1
-10.5
-7.1
-11.6
3.0
-12.9
-6.2
-7.3
-20.5
-9.3
6.0
-19.5
-28.0
-16.4
-25.7
10.3
-1.0
3.4
-21.1
-7.2
7.6
-17.1
-51.5
7.6
-12.7
-4.2
-22.5
-7.8
17.6
-5.1
Average
Median
-11.2
-9.2
-6.2
-9.9
-13.8
-13.6
-8.6
-8.0
-1.4
-2.6
-10.7
-8.9
-1.4
-1.0
-9.1
-7.6
Notes: This table reports changes on GT, GMP and GO, as well as on real income of comparing the equilibrium
levels with a situation without Ricardian comparative advantage at the industry level for tradable sectors. Following
[Costinot et al., 2012], we start by fixing a reference economy and make all other countries to have the same relative
productivity across sectors as this reference country, while adjusting their absolute level of productivity Zn , in such
a way that relative wages around world are held constant. See Section H in the Appendix for further details.
†Percent change in real income relative to the total gains from openness.
48
GO (column (8)).74
Two important questions emerge regarding these results. First, how much of the total effect
is explained by changes in the aggregate MP and trade shares, and how much is only due to
changes in their sectoral dispersion after the elimination of relative differences in fundamental
productivities. Second, to which extent the magnitude of these effects are affected by the interplay
between the sectoral dispersion of relative productivities, and other sources of heterogeneity, such
as MP costs. In Section 6.2.1, we answer this last question by exploring how the welfare losses of
removing comparative advantage change for different values of MP costs.
In order to isolate the welfare reduction coming exclusively from a lower sectoral dispersion
of MP shares, columns (4)-(6) in Table 4 control for the welfare effects due to changes on the
aggregate share of goods produced with foreign technologies. Results show that, on average, more
than 2/3 of the reduction of GO are due to the lower dispersion of sectoral trade and MP shares
alone. Notice that countries such as Canada, Australia and New Zealand experiment a decline in
their adjusted gains from MP (column (5)), even when their total effect is positive (column (2)).
This is explained by the fact that in a scenario where comparative advantage has being removed
these countries receive more inward MP, although the sectoral dispersion of their MP shares is
lower. Conversely, Austria and Bulgaria experience a total negative effect, but a positive adjusted
effect, reflecting lower levels of aggregate MP in these economies in the counterfactual scenario
but with a higher dispersion in their sectoral MP shares.
As expected by the close connexion between welfare gains and the sectoral dispersion of MP
and trade shares derived in Section 3, Figure A.9 in the Appendix displays the Atkinson index
of trade and MP shares, in the baseline versus the counterfactual scenario with no Ricardian
productivity differences. The fact that almost all observations lie below the 45 degree line implies
that the removal of comparative advantage significantly reduces the sectoral dispersion of MP
shares. Finally, we explore the quantitative implications of Proposition 4 according to which the
adjusted gains from MP are larger, the higher is the dispersion of relative productivities across
sectors. Figure A.10 in the Appendix shows a negative and significant correlation between the
GMP losses and the Atkinson index of the relative fundamental productivities. This is, on average,
countries with stronger Ricardian comparative advantage experiment larger losses on gains from
MP in the counterfactual scenario where differences in relative fundamental productivities are
eliminated.
74
Finding a relative modest response of real income and gains from openness to the removal of comparative
advantage is in line with [Costinot et al., 2012], who found that other sources of heterogeneity muted the effect of
removing Ricardian comparative advantages for the case of trade. The main differences between [Costinot et al.,
2012] and our results are coming from the fact that our model has MP and trade, and from the inclusion of
intermediate inputs, a non-tradable sector and inter-industry linkages. Another important difference is that we
remove relative differences in Tn —rather than Ten which still have some sectoral dispersion given the structure of
MP barriers. Section 6.2.1 explores how the welfare losses of removing comparative advantage change for different
values of MP costs.
49
6.2.1
Cross Derivative Effects
The welfare effects of eliminating relative sectoral productivity differences can be affected by
the existence of other important sources of heterogeneity. Differences on MP and trade cost across
countries and sectors also shape relative differences in sectoral autarky prices, and therefore, the
countries’ comparative advantage. In order to understand how changes in relative sectoral productivity differences interplay with MP barriers,75 we repeat the previous counterfactual exercise,
j
but this time applying consecutive reductions or “discounts” to the calibrated MP (gls
) costs,
diminishing their ability to shape the patterns of trade and MP flows.
Figure 12 displays the adjusted average effect on GMP, GT and GO of removing Ricardian
j 76
comparative advantages for different levels of gls
. Panel (a) of Figure 12 shows that effects of
removing differences in sectoral productivity on GMP negative and larger for lower “levels” of MP
barriers. At the limit, where there is no cost associate with foreign investment, the “adjusted”
losses on GMP increase to 4.5 percent—from 1.4 percent in the baseline calibration. In contrast,
under free MP (panel (b) of Figure 12), the GT losses due to the elimination of difference in Tnj
almost disappear.77 Finally, panel (c) of Figure 12 shows that the real income losses of removing
sectoral productivity differences increase to 5.4 percent, when countries do not differ in their MP
j
costs gls
.
6.3
j
Effect of MP (gls
) on Aπnn and Aynn :
In this section, we use our estimated model to explore the quantitative implications of Propoj
increases the GMP, even after those
sition 3, according to which a reduction in MP costs, gls
j
are adjusted by the increase in the aggregate MP share that follows a reduction in gls
. The top
panel of Figure 13 displays the adjusted change in GMP, averaged across countries, for different
j
discount levels on MP barriers gls
, from zero discount, to a situation of free MP (from right to
left). As can be observed, GMP increase on average by 3.5 percentage points when there are not
MP barriers, and therefore, they no longer act as a source of heterogeneity. Notice that, this only
accounts for the increase in GMP coming from higher a dispersion of MP shares, since we keep
aggregate MP shares equal to their equilibrium levels. This result is explained by the fact that
j
with lower gls
’s, the dispersion of relative fundamental productivities AT plays a more central role
in shaping MP patterns across countries and sectors, as implied by 1, and as shown at the top
panel of Figure 14. The second implication of Proposition 6 is that a reduction on MP barriers
decreases the heterogeneity of trade shares across sectors (bottom panel of Figure 14), negatively
affecting the gains from trade. This can be observed in the middle panel of Figure 13, which
75
Note that in this section we focus on MP barries, but the same analysis is valid for trade costs.
Notice that in this exercise the lowering MP costs is done by applying an uniform discount to the calibrated
values.
77
Figure A.11 in the Appendix shows the former set of graphs for total changes in welfare gains due to the
removal of Ricardian comparative advantage for different levels of MP barriers, measured in percentage points.
76
50
j
Figure 12: Adjusted GT, GMP and GO losses and MP barriers gls
(Removing Comparative
Advantage)
Adjusted Avg GMP losses
−1
−2
−3
−4
−5
−1
−0.8
−0.6
−0.4
−0.2
0
−0.2
0
−0.2
0
Adjusted Avg GT losses
5
0
−5
−10
−1
−0.8
−0.6
−0.4
Avg Real Income losses
0
−2
−4
−6
−1
−0.8
−0.6
−0.4
g discount
Notes: The top panel of this Figure displays the adjusted change in GMP, average across countries, for different
j
discount levels on MP barriers gls
, from zero discount, to a situation of free MP (from right to left). Positive
(negative) values reflect an increase (decrease) in GMP. Similarly, the middle panel of this Figure display changes
in GT and the bottom panel shows the corresponding changes in real income.
51
shows an average reduction of one percentage points in GT when there is a complete discount on
MP cost or free MP.
j
Figure 13: Adjusted Changes in GT, GMP and GO, and MP barriers gls
Adjusted Avg GMP Change
60
40
20
0
−1
−0.8
−0.6
−0.4
−0.2
0
−0.2
0
−0.2
0
Adjusted Avg GT Change
0
−2
−4
−6
−8
−1
−0.8
−0.6
−0.4
Adjusted Avg GO Change
30
20
10
0
−1
−0.8
−0.6
−0.4
g discount
Notes: The top panel of this Figure displays the adjusted change in GMP, average across countries, for different
j
discount levels on MP barriers gls
, from zero discount, to a situation of free MP (from right to left). Positive
(negative) values reflect an increase (decrease) in GMP. Similarly, the middle and bottom panel of this Figure
display changes in GT and GO.
6.4
Effect of MP Dispersion on Gains from Trade
In order to assess the effect of MP on comparative advantage, this section presents a counterfactual scenario where MP flows only change the average productivity of the economy, while
keeping constant the estimated country’s comparative advantage.
achieve this goal, we calcu To
j
late the geometric mean of the productivity of local producers Tl across sectors as well as all
producers in the economy Telj . The ratio of the two values tells us if the average productivity
has increased due to multinational activity. The counterfactual effective productivity is calcuQ
1/J
( J Telj )
lated by increasing Tlj by the factor Qj=1
1/J on every tradable sector j. Figure (A.12) in the
( Jj=1 Tlj )
52
j
Figure 14: Atkinson of MP (Ayll ) and Trade (Aπll ) shares and MP barriers gls
Average Atkinson MP Change
20
15
10
5
0
−1
−0.8
−0.6
−0.4
−0.2
0
−0.2
0
Average Atkinson Trade Change
0
−0.5
−1
−1.5
−2
−2.5
−3
−1
−0.8
−0.6
−0.4
g discount
Notes: The top panel of this figure displays the change of the Atkinson of MP shares (Ayll ) average across countries
j
for different discount levels on MP barriers gls
, from zero discount, to a situation of free MP (from right to left).
Positive (negative) values reflect an increase (decrease) in the Atkinson index of MP shares. Similarly, the bottom
panel of this figure displays the average of the Atkinson of trade shares (Aπll ) average across countries for different
j
discount levels on MP barriers gls
.
53
Appendix illustrates this exercise.
Tej
l
count
Q
J
ej
j=1 Tl
= Tlj × QJ
j
j=1 Tl
1/J
1/J ∀j = 1, ...J + 1,
Table 5 compares the gains from trade in the actual equilibrium with the counterfactual scenario, showing that differences are relatively modest. Relative to the baseline, the average total
gains from trade in the counterfactual scenario are almost 12 percent higher than in equilibrium,
while the adjusted gains from trade are almost 9 percent above the equilibrium levels.
6.5
Multinational Production in the Non-Tradable Sector
Multinational production is the only option producers in the non-tradable sector have to serve
foreign markets. MP in non-tradables represents a significant share, about 60 percent, of total
MP activity. Moreover, non-tradables are the second most used intermediate input, after the
sector itself.78
A multi-sector model with intermediate linkages and MP provides us the proper framework
to evaluate the importance of multinational activity in the non-tradable sector. We decompose
the impact of multinational production in the non-tradable sector into a direct and an indirect
effect. The direct effect measures the impact of lower prices in the non-tradable sector due to the
access to foreign technologies in the non-tradable sector itself. The indirect effect measures the
increase in competitiveness in tradable sectors, expressed by lower prices of tradables goods, due
the access to cheaper non-tradable intermediate inputs. Table 6 shows that in a counterfactual
scenario in which MP is prohibitively costly in non-tradable goods, real income decrease by 8
percent and gains from openness decline by 35 percent. Moreover, the lack of access of nontradable intermediate inputs produced by foreign affiliates leads to an increase in the overall price
index of 5.7 percent; an increase in the price of non-tradables of 8.4 percent, and an increase of
2.45 percent in the price index of tradables.
78
On average, 40 percent of each dollar produced on tradables come from the non-tradable sector.
54
Table 5: Effect of Sectoral MP on Gains from Trade
∆ GT (%)
Country
Australia
Austria
Belgium
Bulgaria
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Latvia
Lithuania
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Romania
Russia
Slovakia
Spain
Sweden
Turkey
Ukraine
United Kingdom
United States
Average
∆ GT (pp)
Adjusted
∆ GT (%)
∆ GT (pp)
Total
12.22
14.76
18.47
9.47
3.08
29.38
-0.82
0.31
9.31
0.41
3.94
-3.11
30.52
1.35
2.39
7.18
8.30
2.93
-0.82
8.48
9.06
1.54
19.46
3.70
41.40
8.81
19.47
2.82
-0.76
6.48
2.67
1.84
0.52
1.44
6.06
1.37
0.31
3.66
-0.10
0.05
0.82
0.02
0.25
-0.15
5.59
0.06
0.03
1.36
1.70
0.22
-0.12
0.66
0.79
0.12
1.76
0.32
1.92
1.28
0.83
0.28
-0.03
0.45
0.15
0.03
17.18
12.97
15.57
6.74
2.86
29.95
0.26
4.86
13.03
2.91
6.73
-1.97
38.41
5.67
9.26
11.00
11.57
2.51
1.20
13.09
12.43
4.92
19.86
11.61
59.77
8.59
19.45
5.21
1.98
16.47
4.90
2.43
0.73
1.27
5.11
0.98
0.29
3.73
0.03
0.85
1.15
0.14
0.43
-0.10
7.03
0.25
0.11
2.08
2.37
0.19
0.18
1.02
1.08
0.39
1.80
1.01
2.77
1.24
0.83
0.51
0.08
1.15
0.27
0.04
8.57
0.99
11.61
1.22
Notes: This Table shows the changes in GT, in percentage change and in percentage points, when we compare the
equilibrium levels with a counterfactual scenario in which MP changes the average productivity of the economy,
but does not affect the country’s comparative advantage.
55
Table 6: Welfare Gains and Non-tradable Sector
∆Pn
∆PnT
∆PnN T
5.41
5.58
7.83
5.16
5.35
13.11
3.80
7.87
4.32
3.87
4.42
2.92
7.94
3.13
2.22
10.54
10.37
3.48
5.04
3.87
5.69
6.11
4.49
8.70
3.64
10.07
3.88
4.62
2.53
5.97
6.65
2.63
2.45
2.42
2.49
2.45
2.37
2.86
2.35
2.62
2.35
2.31
2.37
2.21
2.57
2.27
2.17
2.98
2.86
2.27
2.38
2.34
2.40
2.50
2.37
2.83
2.31
2.82
2.31
2.38
2.17
2.56
2.51
2.22
7.51
7.36
11.99
7.56
7.11
20.81
4.91
11.99
5.53
4.91
5.91
3.53
12.44
3.83
2.26
19.45
18.52
4.44
7.03
4.87
7.60
9.52
6.35
15.31
4.85
17.44
4.93
6.15
2.91
9.82
9.92
2.91
5.66
2.45
8.43
Country
Australia
Austria
Belgium
Bulgaria
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Latvia
Lithuania
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Romania
Russia
Slovakia
Spain
Sweden
Turkey
Ukraine
United Kingdom
United States
Average
n
∆w
Pn
∆GM P
∆GT
∆GO
-7.45
-7.64
-12.69
-7.31
-6.83
-22.69
-4.16
-12.69
-5.09
-4.14
-5.50
-2.16
-13.39
-2.56
-0.19
-19.27
-18.88
-3.19
-6.94
-4.00
-8.04
-9.73
-5.80
-15.60
-3.89
-18.08
-4.15
-5.85
-1.32
-9.75
-10.51
-1.17
-62.27
-62.55
-64.97
-52.55
-58.74
-74.55
-56.00
-61.29
-63.65
-45.42
-57.58
-45.97
-74.91
-40.55
-23.78
-82.34
-79.15
-69.06
-63.29
-53.82
-76.76
-53.78
-50.50
-60.22
-33.59
-70.08
-48.55
-52.56
-42.12
-73.76
-65.89
-33.27
1.32
0.25
1.18
0.37
1.41
5.19
-0.57
1.65
-0.23
-0.60
-0.39
-1.02
1.37
-1.05
-1.02
4.71
3.67
0.36
0.15
-0.17
0.17
1.15
0.25
4.27
-0.76
3.98
-0.46
-0.14
-1.71
1.62
1.75
-1.29
-45.88
-36.30
-30.00
-28.31
-33.75
-55.55
-23.55
-37.86
-31.49
-31.05
-36.14
-24.19
-37.96
-24.84
-9.34
-52.95
-49.58
-28.27
-30.96
-26.86
-43.77
-39.73
-28.56
-47.52
-21.66
-50.06
-31.97
-29.76
-19.59
-49.96
-50.96
-22.44
-8.15
-57.92
0.79
-34.71
Notes: This table reports changes in the overall price index, the price index of tradables and changes in real income,
GMP, GT and GO, resulting from a move from a situation where MP barriers are prohibitively costly only the
non-tradable sector to the calibrated levels of trade and MP frictions. All results are reported in percent changes.
56
7
Conclusion
This paper shows that by omitting MP sectoral heterogeneities and their relationship with
countries’ comparative advantage, one-sector models of trade and multinational production systematically understate the gains from MP and openness. This paper assembles a unique industrylevel dataset of bilateral foreign affiliate sales for thirty-two countries and documents that sectoral
dispersion patterns of multinational activity are significantly heterogeneous across countries. More
importantly, it shows that this heterogeneity is not random but rather it is related to differences
in relative productivities across sectors. In particular, MP is disproportionately allocated to
industries where local producers are relatively less productive.
In order to account for these facts, this paper incorporates a multi-sector framework into a
Ricardian general equilibrium model of trade and multinational production. Using this analytical
framework and the Atkinson inequality index as a measure of sectoral dispersion, we show that
the heterogeneity of MP shares across sectors increases with the sectoral dispersion of relative
productivities, with less-productive sectors receiving the largest fraction of MP relative to output.
Second, we show that there is a systematic relationship between MP barriers and the sectoral
heterogeneity of multinational production. In particular, we show that the lower the MP barriers,
the higher the dispersion of MP shares across sectors, and the gains from MP. This paper also
shows that a reduction on MP barriers affects the sectoral heterogeneity of MP and trade shares
in opposite directions. Freer MP increases the dispersion of MP shares across sectors and the
gains from MP; but it also reduces the heterogeneity of trade shares, which decreases the gains
from trade.
To the best of our knowledge, this paper provides the first set of estimates for sectoral MP
barriers and sectoral productivities distinguishing by ownership—local and foreign—using a rich
multi-sector, multi-country model of trade and multinational production that includes capital,
intermediate inputs and intersectoral linkages, in order to carry on several counterfactuals excercises. First, we show that Ricardian comparative advantage is relevant in determining the aggregate levels and sectoral allocation of MP and trade, as well as on their welfare gains. Second, we
highlight how previous results are significantly affected by the existing barriers to multinational
production. Third, we show that gains from trade will be 12 percent higher in a counterfactual
scenario in which multinational activity only affects the average productivity of the host economy,
while keeping relative productivity differences intact. This is explained by the fact that, unlike
trade, MP entails a direct transfer of productivity across countries, which we estimate to be larger
in sectors in which MP shares are higher—the comparative disadvantage ones. Finally, we show
a significant welfare impact of MP in non-tradables not only by its direct effect on non-tradables
but also their indirect effects on the competitiveness of tradables.
The results of this paper highlight the importance of incorporating a sectoral dimension in
the analysis of multinational activity. Our analysis distinguishes between the absolute and com-
57
parative advantage effects of MP, which is essential to improve our understanding of the welfare
implications and the mechanism through which the economy responds to multinational production.
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61
Appendix A: Figures and Tables
Table A.1: Summary Statistics
Number with M Plsj > 0
Tradables
Non-Tradables
Source countries
Location countries
Source-location pairs
Source-location-sector triplets
Sectors
32
32
789
4,236
9
32
32
903
903
4
(M Plj /outputjl )
Mean
Inward MP
Median
Outward MP
Mean Median
All Sectors
0.30
0.27
0.31
0.08
Food, beverages
Textiles
Wood and paper products
All chemical products
Non-metallic mineral products
Basic and fabricated metal products
Machinery and equipment
Transportation equipment
Furniture, recycling
Non-tradable
0.28
0.21
0.22
0.32
0.41
0.26
0.33
0.40
0.23
0.38
0.27
0.19
0.24
0.32
0.36
0.25
0.31
0.37
0.21
0.33
0.40
0.30
0.13
0.18
0.57
0.53
0.23
0.36
0.19
0.22
0.07
0.10
0.02
0.07
0.09
0.15
0.05
0.15
0.08
0.10
Note: The top panel shows the number of source countries, location countries, source-location pairs and sourcelocation-sector triplets for tradables and non-tradables sectors. The bottom panel shows the share of inward and
outward MP on output in each sector for the mean (first and third columns) and the median (second and fourth
columns) of the sample. Inward MP represents the foreign affiliate sales from all source countries in a given
location-sector pair and outward MP represents the affiliate’s sales of local multinationals producing abroad. The
non-tradable sector comprises the following industries: electricity, gas and water supply, and construction; trade,
repair, hotels and restaurants; transportation, storage and communications; and finance, insurance, real estate, and
business activities.
62
Table A.2: Multinational Production by Country
Country Name
Australia
Austria
Belgium
Bulgaria
Canada
Czech Rep.
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Lithuania
Latvia
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Romania
Russia
Slovakia
Spain
Sweden
Turkey
Ukraine
United Kingdom
United States
Source Countries
(Number)
MP/output
(Inward)
Location Countries
(Number)
MP/output
(Outward)
20
31
27
33
9
33
26
30
29
33
33
23
33
33
17
29
30
20
30
18
27
33
29
33
33
33
31
28
25
33
33
23
0.31
0.36
0.53
0.35
0.42
0.60
0.20
0.50
0.22
0.27
0.30
0.18
0.79
0.16
0.02
0.56
0.67
0.10
0.31
0.23
0.31
0.44
0.28
0.56
0.16
0.57
0.24
0.32
0.07
0.31
0.47
0.08
31
32
32
18
32
25
31
20
31
33
33
23
19
32
33
19
20
27
33
28
30
28
27
16
27
17
31
32
26
16
33
33
0.16
0.33
0.18
0.02
0.21
0.05
0.30
0.15
0.42
0.32
0.27
0.07
0.05
0.08
0.13
0.11
0.05
0.05
0.82
0.33
0.19
0.03
0.08
0.01
0.08
0.05
0.11
0.45
0.02
0.13
0.33
0.10
Note: Inward MP refers to foreign affiliate sales from all source countries in a given location-sector pair. Outward
MP refers to the sales of foreign affiliates in all location countries for each source-sector pair. The first column
represents the number of foreign countries operating in each country. Similarly, the third column represents the
number of countries in which each country has operations abroad.
63
Figure A.1: Sectoral dispersion of outward MP shares (selected countries)
(a) Share of outward MP on output
Canada
Czech Republic
Transport
Finland
Chemicals
Metals
Furniture
Minerals
Machinery
Wood
Furniture
Wood
Metals
Food
Food
Metals
Chemicals
Wood
Textiles
Minerals
Machinery
Chemicals
Machinery
Food
Minerals
Textiles
Transport
Furniture
Transport
Textiles
France
Italy
Minerals
United Kingdom
Transport
Chemicals
Chemicals
Minerals
Furniture
Minerals
Machinery
Machinery
Metals
Metals
Transport
Food
Wood
Food
Transport
Food
Metals
Machinery
Chemicals
Textiles
Textiles
Furniture
Wood
Wood
Textiles
0
.5
1
1.5 0
Furniture
.5
1
1.5 0
.5
1
1.5
(b) Outward MP share deviations to the world average
Canada
Czech Republic
Metals
Furniture
Machinery
Furniture
Food
Wood
Wood
Metals
Transport
Metals
Chemicals
Textiles
Textiles
Minerals
Food
Machinery
Wood
Furniture
Food
Textiles
Chemicals
Minerals
Machinery
Minerals
Chemicals
Transport
Transport
France
Italy
United Kingdom
Minerals
Transport
Furniture
Chemicals
Metals
Minerals
Food
Metals
Machinery
Minerals
Machinery
Metals
Textiles
Textiles
Food
Food
Wood
Furniture
Transport
Wood
Machinery
Furniture
Chemicals
−.1
Chemicals
Wood
Textiles
−.2
Finland
0
.1
.2
−.2
−.1
Transport
0
.1
.2
−.2
−.1
0
.1
.2
Notes: Panel (a) shows the fraction of output, in sector j and source country s, produced multinationals overseas
or Outward MP (M P/output)sj . Panel (b) shows per sector and country, the difference between the normalized
P
j
j
j
j
Iworld,s /Iworld
l6=s (Ils /Is )
. Positive
share of outward MP on output in country s and the world economy, P P
j
j − P
j
j
I
/I
I
/I
)
(
s
j
l6=s ls
j
world,s
world
(negative) values of this measure reveal those sectors in which the economy source relatively more (less) foreign
production when compared to the world sectoral distribution.
64
Figure A.2: Cross-country differences in the heterogeneity of sectoral MP shares (selected sectors)
Basic and fabricated metals (S27_28)
Machinery and equipment (S29_33)
Bulgaria
Hungary
Portugal
Spain
Turkey
Austria
Italy
France
Australia
Poland
Canada
United Kingdom
Estonia
Slovakia
France
Ukraine
Poland
Finland
Lithuania
Hungary
United States
Germany
Spain
Italy
United Kingdom
Austria
Latvia
Estonia
Slovakia
Czech Republic
Portugal
Canada
Turkey
Australia
Japan
Germany
Japan
Bulgaria
Czech Republic
United States
Finland
Ukraine
Latvia
Lithuania
Transport equipment (S34_35)
Wood, paper, printing (S20_22)
Spain
Ukraine
Portugal
Canada
United States
Austria
Czech Republic
Australia
United Kingdom
Latvia
Australia
France
Slovakia
Hungary
Austria
Poland
Estonia
Latvia
Canada
Bulgaria
Germany
Lithuania
Czech Republic
United Kingdom
Turkey
Slovakia
Finland
Lithuania
Italy
Poland
Germany
Hungary
Bulgaria
France
Italy
Spain
Portugal
Turkey
United States
Finland
Japan
Estonia
Japan
Ukraine
−.2
−.1
0
.1
.2
−.2
−.1
0
.1
.2
Notes: This figure shows per country, the difference between the share of MP on output in country i and the world
economy ((M P/output)jl − (M P/output)jworld ) for selected sectors. Positive values of this measure reveal which
countries host relative more multinational activity compared to the the world average; while negative values reveal
which countries host relative less multinational activity compared to the the world average.
65
Table A.3: Relationship Between Bilateral Sectoral MP and Relative Productivity (PPML)
Dep.
Variable ln M P sharejls
ln T F Plj /T F Psj
Observations
R2
66
ln T F Plj /T F Psj
Observations
R2
ln T F Plj /T F Psj
Observations
R2
Controls (I)
Controls (I and II)
Source FE
Location FE
Source-Location FE
Sector FE
Gravity Based
Relative Productivity Measures
GGDC
RCA
Productivity
Index
Productivity
(1)
(2)
(3)†
−0.175a
−0.173a
−0.380a
−0.439a
−0.466a
−0.648a
−1.634a
−1.667a
−2.034a
(0.0381)
10,098
0.29
(0.0322)
7,101
0.41
(0.0573)
3,795
0.51
(0.1501)
3,078
0.38
(0.1438)
2,637
0.52
(0.2199)
1,764
0.42
(0.4960)
1,404
0.59
(0.4384)
1,242
0.69
(0.6732)
780
0.68
−0.166a
−0.163a
−0.294a
−0.348a
−0.372a
−0.538a
−1.348a
−0.859c
−2.020a
(0.0482)
9,801
0.38
(0.0436)
6,822
0.54
(0.0518)
3,696
0.51
(0.1281)
3,078
0.57
(0.1240)
2,610
0.68
(0.1810)
1,764
0.53
(0.5137)
1,296
0.28
(0.6246)
1,134
0.49
(0.5083)
744
0.77
−0.138a
−0.137a
−0.249a
−0.245c
−0.259b
−0.188
−1.024a
−1.074a
−0.868b
(0.0342)
10,098
0.63
(0.0274)
7,002
0.77
(0.0407)
3,795
0.65
(0.1439)
3,078
0.68
(0.1225)
2,610
0.80
(0.1961)
1,764
0.65
(0.2608)
1,404
0.78
(0.2346)
1,206
0.80
(0.3600)
780
0.84
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
Y
–
Y
Y
–
Y
Y
–
–
–
Y
Y
–
Y
Y
Y
–
Y
(4)
(5)
(6)†
(7)
(8)
(9)†
Panel (a): Sales
Panel (b): Employment
Panel (c): Number of firms
Notes: This table presents the results of a Pseudo Poisson Maximum Likelihood (PPML) between the share of MP—measured by sales, employment and number
of firms—and the ratio of productivities (T F Pl /T F Ps ) for different specifications and productivity measures. All productivities are corrected for trade-driven
selection. Controls (I) include bilateral distance; dummies for common language, common border, colony ties and belonging to a regional trade agreement (RTA);
and, the interaction between factor endowments and sector factor intensities: ln(K/L)l × ln(K/L)j . Controls (II) include effective tax rates at the country-sector
level and bilateral-sector tariffs instead of the RTA dummy. Standard errors, origin-location clustered, in parentheses. Significance: c p < 0.1, b p < 0.05, a
p < 0.01. † Sample size drops due to lower country coverage of effective tax rates.
Table A.4: Relationship Between Bilateral Sectoral MP and Productivity
Productivity Measure: Revealed Comparative Advantage (RCA)
Dep.
Variable ln M P sharejls
(1)
j
ln T F Psource
2.794a
5.018a
2.011a
4.029a
1.122a
1.078a
(0.3545)
2,037
0.58
Y
Y
(0.5303)
1,361
0.65
Y
Y
(0.3028)
1,946
0.69
Y
Y
(0.3992)
1,317
0.76
Y
Y
(0.1507)
1,918
0.88
Y
Y
(0.2512)
1,302
0.89
Y
Y
Observations
R2
Source FE
Location-Sector FE
67
j
ln T F Plocation
Observations
R2
Location FE
Source-Sector FE
Controls (I)
Controls (I and II)
Sector FE
Sales
Employment
(2)†
(3)
(4)†
No. of firms
(5)
(6)†
Panel (a): Source country’s Productivity
Panel (b): Location country’s Productivity
−2.136a
−1.582a
−1.889a
−1.823a
−1.572a
−1.852a
(0.3696)
1,624
0.77
Y
Y
(0.6018)
1,044
0.80
Y
Y
(0.3647)
1,462
0.69
Y
Y
(0.5328)
998
0.83
Y
Y
(0.1854)
1,514
0.87
Y
Y
(0.2872)
1,035
0.90
Y
Y
Y
–
Y
–
Y
Y
Y
–
Y
–
Y
Y
Y
–
Y
–
Y
Y
Notes: This table presents the results of a linear regression model between the share of MP—measured by sales, employment and number of firms—and the
productivity of the source and location country measured by revealed comparative advantage (RCA) productivity. Controls (I) include bilateral distance;
dummies for common language, common border, colony ties and belonging to a regional trade agreement (RTA); and, the interaction between factor endowments
and sector factor intensities: ln(K/L)l × ln(K/L)j . Controls (II) include effective tax rates at the country-sector level and bilateral-sector tariffs instead of the
RTA dummy. Standard errors, origin-location clustered, in parentheses. Significance: c p < 0.1, b p < 0.05, a p < 0.01. † Sample size drops due to lower country
coverage of effective tax rates.
Table A.5: Comparison of welfare gains in one-sector and multi-sector trade-MP models
One-sector
AT = 0
Multi-Sector
AT > 0
Observables
− 1θ
GM P
(yll )
πll
π̄ll
− 1
− 1
ylla yllb 2θ
θ
1
GT
(πll )− θ
GO
[yll × πll ]− θ
πlla πllb
1
a πb
πll
ll
a π̄ b
π̄ll
ll
− 1
− 2θ1
2θ
68
− 1
2θ
ylla yllb × πlla πllb
Model’s Fundamentals
GM P
GT
GO
h
1+
Tl
T1 +g −θ T2
T̃l
T˜1 +d−θ T˜2
2
g −θ
× 1
− 1
θ
− 1
θ
2
+ d−θ
i1
2θ
1−
2
g−θ
2
(1−AT )2 (1−d−θ ) +4d−θ
(1−AT )2 (a−b)2 +4ab
T̃l
T˜1 +d−θ T˜2
+
4g −θ
(1−AT )2
− 1
θ
×
− 1
2θ
1
× (1 − Aπll )− θ
1−
2
d−θ
+
4d−θ
2
(1−AT̃ )
1
2θ
Notes: This table presents the formulas for gains from MP, trade and openness, for one-sector and multi-sector models, as a function of observables and model’s
fundamentals.
Figure A.3: Multinational Production and Sectoral Productivity
0.8
0.7
Atkinson Effective (Tn)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Atkinson Fundamental (Tn)
0.7
0.8
Notes: This figure displays the Atkinson inequality index of the Tlj and Telj , along the 45 degree line.
69
trade
mp
Table A.6: Comparison beteween Telj
and Telj
Panel A: Sector by Sector Rank Correlations
Sector Name
Correlation
Countries
0.63
0.53
0.48
0.33
0.54
0.23
0.51
0.72
0.45
32
32
32
32
32
32
32
32
32
Food and Beverages
Textiles apparel
Wood, paper and printing
Chemical products
Non-Metallic Mineral Products
Basic and Fabricated Metal Products
Computing, Machinery, Communication Equipment
Transport Equipment
Furniture and Other Manufacturing
Panel B: Fixed Effects Regressions
trade
Dep. Var: log Telj
mp
log Telj
Observations
R-squared
Country FE
Sector FE
(1)
(2)
(3)
0.605a
0.570a
0.492a
(0.0721)
(0.0450)
(0.0537)
288
0.20
–
–
288
0.84
Y
–
288
0.88
Y
Y
Notes: This table reports the results of comparing the effective productivity estimates from the trade gravity equa mp
trade
, by combining Tlj
, with the effective productivity estimates using the MP gravity equation Telj
tion, Telj
j
and the MP barriers gls
. Panel A reports the Spearman rank correlations of the two alternative overall productiv mp
trade
. Robust
on Telj
ity measures by sector. Panel B reports the results of a fixed effect regression of Telj
standard errors reported in parentheses. Significance:
c
p < 0.1,
70
b
p < 0.05,
a
p < 0.01.
Table A.7: The Fit of the Baseline Model to the Data
Variable
Statistics
Model
Data
Wages
Mean
Median
corr(model,data)
0.638
0.552
0.926
0.628
0.620
Imports/output
Mean
Median
corr(model,data)
0.356
0.344
0.792
0.364
0.357
Manufacturing
Inward MP/output
Mean
Median
corr(model,data)
0.275
0.269
0.855
0.313
0.283
Outward MP/output
Mean
Median
corr(model,data)
0.209
0.091
0.946
0.183
0.080
All Sectors
Inward MP/output
Mean
Median
corr(model,data)
0.311
0.285
0.936
0.343
0.311
Outward MP/output
Mean
Median
corr(model,data)
0.202
0.103
0.909
0.178
0.131
Note: This table compares the mean and median of wages relative to the U.S., imports as a share of output, inward
and outward MP; both in the model and in the data, along with their correlation. Wages, total output, inward and
outward MP in the data, are calculated as described in Section B.
71
Figure A.4: Wages Relative to the United States
1.5
NOR
1
GBR
CAN
AUS
ESP
NLD DEU
AUT
FIN
USA
SWE
FRA
BEL
ITA
JPN
GRC
.5
NZL
PRT
MEX
HUN
POL
EST
CZE
TUR SVK
LTU
LVA
ROM
RUS
BGR
UKR
0
Wages Relative to U.S (data)
DNK
0
.5
1
1.5
Wages Relative to U.S (model)
.8
Figure A.5: Imports/output
LVA
LTU
.4
CAN
SWE
GBR
UKR
BEL
SVK
BGR
AUT
DNK NLD
ROM
PRT
GRC
CZE
HUN
POL
MEX
FRA DEU
ESP
NZL FIN NOR
TUR
AUS
ITA
.2
Imports/output (data)
.6
EST
RUS
USA
0
JPN
0
.2
.4
.6
.8
Imports/output (model)
Note: The Figure in the top presents the scatter-plot of wages in the data (y-axis) against the model’s counterpart
(x-axis). The bottom panel presents the scatter-plot of imports/output in the data (y-axis) against the model’s
counterpart (x-axis). Imports/output are the average manufacturing imports as a share of total output in the data
over the period 2003-2012. Wages are calculated as described in Section B.2 using UNIDO data. The solid line is
the 45-degree line.
72
.8
Figure A.6: Inward MP/output
Inward MP/output (data)
.2
.4
.6
HUN
BEL
GBR
DEU
CAN
SWE
LTU
AUT
BGR
FRA
ROM
SVK CZE
EST
POL
NLD
ESP
PRT
AUS
LVA
NORNZL
UKR
DNK
ITA
GRC FIN
USA
RUS
MEX
TUR
0
JPN
0
.2
.4
.6
.8
Inward MP/output(model)
Figure A.7: Outward MP/output
Outward MP/output (data)
.4
.6
.8
1
NLD
SWE FIN
GBR
DNK AUT
.2
NZL
FRA
DEU
CAN NOR
USA
BEL
0
AUS
JPN
ITA
EST
GRC
PRT
ESP
MEX
RUS
UKR
POL
HUN
SVK
LVA
LTU
TUR
CZE
BGR
ROM
0
.2
.4
.6
.8
1
Outward MP/output(model)
Note: The Figure in the top presents the scatter-plot of Inward MP/output for manufacturing sectors in the
data (y-axis) against the model’s counterpart (x-axis). The bottom panel represents the scatter-plot of Outward
MP/output for manufacturing sectors in the data (y-axis) against the model’s counterpart (x-axis). In the data,
Inward (Outward) MP are calculated by summing the foreign affiliate production of all possible sources (locations)
for each location (source) country-sector pair, and then is normalized by the total output of the location (source)
country in each sector. The solid line is the 45-degree line.
73
Figure A.8: Sensitivity of GT, GMP and GO to Different Values of η
Average Gains from Trade
10
9
8
7
6
1
2
3
4
5
6
7
8
6
7
8
7
8
Average Gains from MP
14.6
14.55
14.5
14.45
14.4
1
2
3
4
5
Average Gains from Openness
28
26
24
22
1
2
3
4
5
6
Elasticity of Substitution (η)
Notes: The top panel of this Figure displays the GMP for diferent values of the elasticity of substitution across
tradable sectors, η, in the baseline scenario. Similarly, the middle and bottom panel of this Figure display changes
in GT and GO, respectively.
74
Table A.8: Comparison of welfare gains in one-sector and multi-sector trade-MP models
Multi-Sector
AT > 0
One-Sector
AT = 0
Welfare’s based formulas
−αjn δnk θ1
j
πj
j
ynn
× ¯jnn
π nn
j=1 k=1
N
J
+1 Y
Y
GMP
N
J
+1 Y
Y
GT
j=1 k=1
J
+1 Y
N
Y
GO
j=1 k=1
j
πnn
−αjn δnk
j
j
ynn
× πnn
(ynn )
− β1 θ1
j j
1
θj
−αjn δnk
×
(πnn )
1
θj
(ynn )
− β1 θ1
j j
πnn
π̄nn
−
1 1
βj θj
− β1 θ1
j j
× (πnn )
− β1 θ1
j j
Total Effect
GMP
(ynn )
−
PJ
j=1
ln(ynn ) 1
j
k=1 αn δnk ln(y
) θ
GT
GO
j
PJ
nn
(πnn )
(ynn )
−
PJ
j=1
−
PJ
j=1
j
×
(πnn )
(π̄nn )
−
PJ
j=1
j
ln(πnn ) 1
j
k=1 αn δnk ln(πnn ) θj
PJ
j
P
PJ
ln(π̄nn ) 1
j
− J
α δ
j=1
k=1 n nk ln(π̄nn ) θj
(ynn )
− β1 θ1
j j
j
ln(πnn ) 1
j
k=1 αn δnk ln(πnn ) θj
PJ
j
ln(ynn ) 1
j
k=1 αn δnk ln(ynn ) θj
PJ
× (πnn )
−
PJ
j=1
×
(πnn )
j
ln(πnn ) 1
j
k=1 αn δnk ln(πnn ) θj
PJ
(ynn )
− β1 θ1
j j
πnn
π̄nn
−
1 1
βj θj
− β1 θ1
j j
× (πnn )
− β1 θ1
j j
Adjusted Effect
GMP
(ŷnn )
−
PJ
j=1
PJ
j
k=1 αn δnk
j
ŷ
ln(ynn nn )
ynn
1
θj
ln(ynn )
×
(π̂nn )
ˆnn
π̄
GT
GO
(π̂nn )
−
(ŷnn )
PJ
j=1
PJ
j
k=1 αn δnk
−
PJ
j=1
PJ
j
k=1 αn δnk
j ŷ
ln(ynn nn )
ynn
1
θj
ln(ynn )
−
PJ
j=1
PJ
j
k=1 αn δnk
j π̂
ln(πnn nn )
πnn
1
θj
ln(πnn )
ˆ
j π̄
ln(π̄nn nn )
PJ
P
j
π̄nn
1
α δ
− J
j=1
k=1 n nk
θj
ln(π̄nn )
(ŷnn )
− β1 θ1
j j
j π̂
ln(πnn nn )
πnn
1
θj
ln(πnn )
× (π̂nn )
−
PJ
j=1
PJ
j
k=1 αn δnk
×
(π̂nn )
j π̂
ln(πnn nn )
πnn
1
θj
ln(πnn )
(ŷnn )
− β1 θ1
j j
π̂nn
ˆ nn
π̄
−
1 1
βj θj
− β1 θ1
j j
× (π̂nn )
− β1 θ1
j j
Note: This table presents the formulas for gains from MP, trade and openness in terms of observables in a model
of trade and MP with Cobb-Douglas preferences, intermediate inputs, I-O inter-linkages and no capital, for both
multi and one-sector models.
75
Figure A.9: Sectoral dispersion of trade and MP shares (Removing Comparative Advantage)
(a) Atkinson of trade shares
Atkinson trade shares (No Comaprative Advantage)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Atkinson trade shares
0.35
0.4
0.45
(b) Atkinson of MP shares
0.2
Atkinson MP shares (No Comparative Advantage)
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.05
0.1
Atkinson MP shares
0.15
0.2
Notes: Panel (a) displays the Atkinson of trade shares in the equilibrium (x-axis) versus the one corresponding
to the counterfactual where comparative advantages are removed (y-axis). Panel (b) displays the Atkinson of MP
shares in the equilibrium (x-axis) versus the one corresponding to the counterfactual where comparative advantages
are removed.
76
Figure A.10: Atkinson of Tnj and GMP losses (Removing Comparative Advantage)
−0.4
−0.45
−0.5
GMP losses
−0.55
−0.6
−0.65
−0.7
−0.75
−0.8
0
0.1
0.2
0.3
0.4
Atkinson T
0.5
0.6
0.7
Note: This figure illustrates the relationship between the Atkinson of fundamental productivities and the reduction
in GMP of a counterfactual scenario where there is no differences in relative fundamental productivities across
sectors.
77
j
Figure A.11: Total GT, GMP and GO losses and MP barriers gls
(Removing Comparative Advantage, pp)
Total Avg GMP losses
0
−2
−4
−6
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
−0.3
−0.2
−0.1
0
−0.3
−0.2
−0.1
0
Total Avg GT losses
0
−0.5
−1
−1.5
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
Total Avg GO losses
−2
−4
−6
−8
−10
−1
−0.9
−0.8
−0.7
−0.6
−0.5 −0.4
g discount
Notes: The top panel of this Figure displays the adjusted change in GMP, average across countries, for different
j
discount levels on MP barriers gls
, from zero discount, to a situation of free MP (from right to left). Positive
(negative) values reflect an increase (decrease) in GMP. Similarly, the middle and bottom panel of this Figure
display changes in GT and GO.
78
Figure A.12: Counterfactual 2: Proportional Technology Upgrade
ZĞůĂƚŝǀĞ
dĞĐŚŶŽůŽŐLJ
>ŽĐĂůƐнDW;ĐƚƵĂůƋƵŝůŝďƌŝƵŵͿ
>ŽĐĂůƐнDW ;ŽƵŶƚĞƌĨĂĐƚƵĂůͿ
>ŽĐĂůƐ
^ϭ
^Ϯ
^ϯ
^ϰ
^ϲ
^ϱ
^ϳ
^ĞĐƚŽƌƐ
Note: This figure illustrates a counterfactual exercise in which MP increases the absolute productivity while keeping
intact relative productivity differences.
79
Appendix B: Data Description
B.1
Multinational Production Data
Multinational production data at the country pair-sector level was constructed using three
main sources of information. First, we rely on unpublished OECD data, in particular, International Direct Investment Statistics and the Statistics on Measuring Globalisation. This dataset
contains information concerning the economic activities of multinational firms such as production,
employment and number of affiliates, for 30 reporting countries belonging to the OECD, and the
35 partner countries that are host or source of their MP operations. Nominal data is reported
in the currency of the reporting country, which is converted to U.S. dollars using the average
annual exchange rate sourced from OECD statistics. This dataset contains information about the
activity of affiliates of foreign parents established in the reported country—or inward MP—and
the overseas activities of firms whose parents reside in the reporter country whose activities—or
outward MP.
For those countries that do not belong to the OECD, or for which complete information was not
available in the OECD data, we draw information from the Foreign Affiliate Statistics database
provided by Eurostat. This dataset reports information for 41 source and 22 host countries at the
source-location-sector triplet. A total of 117 sectors and sub-sectors are covered by the original
dataset. Eurostat uses NACE Revision 2, for which we develop a concordance to merge it with the
ISIC, Rev 2 and Rev 4 classification used by the OECD database. OECD and Eurostat datasets
include information for majority-owned foreign affiliates, that is, those in which 50 percent or
more of the control is exerted by a parent firm located in a foreign country.79
We complete the construction of our dataset using ORBIS, a dataset compiled by Bureau van
Dijk, containing financial accounting information from detailed harmonized balance-sheets of more
than a 100 countries worldwide. The most attractive feature of ORBIS is its capacity to link firms
by their ownership structure, providing global coverage of corporate hierarchies. In particular,
it contains detailed ownership information encompassing over 30 million shareholder/subsidiary
linkages, allowing the identification of a significant fraction of the multinational corporations
around the world. Besides listing the set of shareholders of firms in the sample, along with
their direct and indirect participation, ORBIS provides three major ownership measures useful to
identify the international measure of the firm: the Global Ultimate Owner (GUO), the Domestic
Ultimate Owner (DUO) and the Immediate shareholder (ISH). In order to make it consistent
with the ownership threshold followed by the OECD and Eurostat, we chose 50% as the minimum
percentage for the path from a subject company to its Ultimate Owner.80 ORBIS has available
two types of industrial classification NACE Rev. 2 and NAICS 2007, that we translate to ISIC
79
A country secures control over a corporation by owning more than half of the voting shares or otherwise
controlling more than half of the shareholders’ voting power.
80
We classify as multinationals all ultimate owners of at least one foreign subsidiary that has positive employment
and sales above USD 100,000.
80
codes.
For validation proposes, we use the Investment Country Profiles from UNCTAD dataset, which
present systematically, at the country level, inward and outward activities of multinational corporations. Finally, we use the statistics on U.S. multinational companies produced by the Bureau
of Economic Analysis (BEA) which provide data on the assets, employment and sales of foreign
firms controlled by U.S. companies, as well as companies located in the U.S. controlled by foreign
parents.
After all quality controls have been applied, we get positive MP information for 5,139 sourcelocation-sector relationships from a potential of about 9,920 triplets, in tradable and non-tradable
sectors using the ISIC Revision 3 sectoral classification.81 Even when a total of seventy sectors and
sub-sectors are covered in the original data for agriculture, mining, manufacturing, and services;
due to disclosure and confidentiality issues, many observations are only available—non-missing—
at a higher level of aggregation.82 Therefore, to maximize the accuracy and coverage of the data,
we aggregate the information at roughly 1-digit ISIC level, as shown in Table B.10. In order to
ensure that a zero was not mistaken for a missing value in the data, we rely on two additional
measures of multinational activity recorded in the dataset (employment and number of foreign
affiliates) as well as information on revenues reported by ORBIS and BEA. Whenever possible,
inward flows were chosen, given that it is more likely that multinational sales are better reported
by the host country than by the sending country. Moreover, the host country also reports the
ultimate sector of investment, which can be different from the parent firm’s sector in the source
country.
Given the different data sources used on the construction of the dataset, it is important to
assess its consistency and quality. Because of disclosure and confidentiality issues, the accuracy
of reported foreign affiliate sales increases with the aggregation level. This means that we have
better information about the total manufacturing sales of Italian multinationals in France, but
less accurate information about how much of those sales occur in the chemical and textile sectors.
Therefore, we rely on two-dimensional data to assess the quality of our three-dimensional dataset.
The first one is the bilateral MP sales for total manufacturing in a given source-host pair, and it
is used to assess how well the sectoral disaggregation accounts for total manufacturing flows. The
second one aggregates MP sales across all source countries for any given host-sector pair and also
across all host countries for any given source-sector pair. Total manufacturing foreign affiliate
sales are calculated by summing them across the nine manufacturing sectors and then comparing
them with the total manufacturing sales of foreign affiliates reported directly by OECD, Eurostat,
and UNCTAD.
81
Source-location-sector triplets with MP sales below a million dollars are excluded from the final sample.
Because some source-location-sector triplets have only few foreign affiliates, a full disclosure could reveal
confidential information of individual firms.
82
81
Table B.9: List of Countries
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Italy
Japan
Latvia
Lithuania
Mexico
New Zealand
Netherlands
Poland
Portugal
Norway
Romania
Russian Federation
Slovakia
Slovenia
Spain
Sweden
Turkey
United Kingdom
Ukraine
United States
Note: This table reports the 32 countries in our final sample.
Table B.10: Sectors
SIC Code
Sector Name
S15-16
S17-19
S20-22
S23-25
S26
S27-28
S29-33
S34-35
S36-37
S40-45
S50-55
S60-64
S65-74
Food, beverages, and tobacco
Textiles, wearing apparel, leather, footwear
Wood and paper products, publishing, printing
All chemical products
Non-metallic mineral products
Basic and fabricated metal products
Total machinery and equipment; medical and precision instruments
Transportation equipment
Furniture, recycling, and manufacturing n.e.c.
Electricity, gas and water supply, construction
Trade, repair, hotels and restaurants
Transportation, storage and communications
Finance, insurance, real estate, business activities
Note: This table reports the nine tradable sectors (manufacturing) and four non-tradable sectors used in our sample.
82
Figure B.13: Data Comparison for External Validity (By location-source)
0
.05
.1
.15
.2
(a) Bilateral Sales
−5
0
5
External
10
15
Baseline
0
.05
.1
.15
.2
(b) Bilateral Employment
0
5
10
External
15
Baseline
Notes: Panel (a) shows the distribution of bilateral MP sales for total manufacturing as reported by OECD and
Eurostat (External) and compares it with the bilateral sales in total manufacturing
constructed from our data by
P
j
j
summing Ini
for each country-pair across all manufacturing sectors: Ini = Jj=1 Ini
(Baseline). Performing a two
sample nonparametric Kolmogorov-Smirnov test for equality of cumulative distributions, we cannot rejected the
null hypothesis that both distributions were statistically the same with a p-value of 0.941. Panel (b) compares
similar distributions for employment with a p-value of 0.279 for the Kolmogorov-Smirnov test.
83
Figure B.14: Data Comparison for External Validity (By location-sector)
0
.05
.1
.15
.2
(a) Sectoral Sales
4
6
8
10
External
12
14
Baseline
0
.05
.1
.15
.2
.25
(b) Sectoral Employment
4
6
8
10
External
12
14
Baseline
Notes: Panel (a) shows the distribution of MP sales for each location-sector pair as reported by OECD and
Eurostat (External) and compares it with the MP sales for each country-sector
constructed from our data by
P
j
j
summing Ini
for each location-sector pair across all source countries: Inj = N
i6=n Ini (Baseline). Performing a two
sample nonparametric Kolmogorov-Smirnov test for equality of cumulative distributions, we cannot rejected the
null hypothesis that both distributions were statistically the same with a p-value of 0.742. Panel (b) compares
similar distributions for employment with a p-value of 0.134 for the Kolmogorov-Smirnov test.
84
B.2
Trade and Production Data
Production data: gross manufacturing production data at the sectoral level is from the 2012
UNIDO Industrial Statistics Database, which reports output, value added, employment, and the
wage bill at a 2-digit ISIC Revision 3 level of disaggregation. The data was further aggregated
in order to match the classification used in the assembled MP database. Production data at
the 2-digit ISIC level was extensively checked for quality. In cases where a country-year-sector
observation had missing values, or where production was lower than exports, those values were
imputed based on information from previous years as well as information on export patters. The
production dataset is also used to calibrate important parameters of the model, such as the share
of value added in production (βj ) and the share of labor on total value added (αj ), which are
calculated by taking the median of each parameter across countries for each tradable sector.
Note, however, that the UNIDO database does not contain information on the non-tradable
sector. Therefore, to calculate αJ+1 and βJ+1 , we use the 2002 Benchmark Detailed Make and
Use Tables for the United States. Table B.11 lists the sectors along with the key parameters
values for each sector: αj , βj , and the taste parameter ω. More important, we use the production
data to compute the share of output produced by local producers in country l and sector j. This
is calculated by subtracting from the output the total production of foreign affiliates, in every
country-sector pair.
Table B.11: Model’s Parameters
Sector Name
α
Food, beverages, and tobacco
Textiles, wearing apparel, leather, footwear
Wood and paper products, publishing, printing
All chemical products
Non-metallic mineral products
Basic and fabricated metal products
Total machinery and equipment; medical and precision
Transportation equipment
Furniture, recycling, and manufacturing n.e.c.
Non-Tradables
0.351
0.515
0.401
0.303
0.343
0.396
0.424
0.467
0.483
0.54
β
ω
θ
0.256
0.308
0.339
0.241
0.371
0.273
0.276
0.252
0.253
0.64
0.209
0.103
0.025
0.114
0.071
0.014
0.187
0.175
0.065
2.84
5.59
9.50
8.28
3.38
6.58
10.6
1.84
5.00
Note: This table reports the median of the labor share in value added (αj ), the share of value added in total
production (βj ), and the taste parameter for tradable sector j. The values of the dispersion parameter θ correspond
to estimates of Caliendo and Parro (2011).
Trade Shares: Bilateral trade data was drawn from Comtrade (4-digit SITC Revision 2),
and aggregated up to the 2-digit ISIC level, using a concordance that we developed. Then, we
aggregate further to the sectoral aggregation shown in Table B.11 to merge the trade data with
85
production and MP datasets. Note that imports were used for trade values, which were discounted
by a factor
of 1.2,
because transportation cost is included in the value. To calculate the trade
j
j
shares Xnl /Xn at a sectoral level, we first compute a country’s exports in a given sector, by
aggregating bilateral exports across all partners countries. Then, we divide the value
of country
m’s imports from country h by the demand of the importer for sector j goods Xnj ; which is
gross production minus exports, plus imports in sector j, yielding bilateral trade shares. Also
note that imports and exports are calculated using only the countries in the sample.
Bilateral gravity variables: the distance measures used to estimate trade cost, as well as
data on common border and common language, are taken from the Centre d’Etudes Prospectives
et d’Informations Internationals (CEPII). Information on trade agreements comes from the RTA
database maintained by the WTO.
Factor prices: For each country in the sample wages are calculated by dividing the wage bill
aggregated across all manufacturing sectors by the total employment in manufacturing; wages
are then normalized by wages in the U.S.. For the few countries for which information on wage
bill or employment was not available, the income percapita reported by the Penn World Tables
(P W T ) was used. To calculate the return of capital, we rely on the market clearing condition of
the model (rl /wl = ((1 − α) Ll ) / (αKl )), along with the data on labor and capital.83 Total labor
force in each country (Ll ) and capital stock are obtained from the P W T . Total labor force is
calculated as the ratio of real GDP (calculated as the product of real GDP per capita and total
population) and real GDP per worker. Total capital is calculated using the perpetual inventory
method (Kl,t = (1 − δ) Kl,t−1 + Il,t ), where Il is the total investment in country h in period t; the
depreciation rate δ is assumed to be six percent. The initial value of K is equal to Il,0 /(γ + δ),
where γ is the average growth rate of investment in the first ten years for which data is available.
Intermediate input coefficients: The intermediate input coefficients (γkj ) are obtained
from the Direct Requirements Table in the 2002 Benchmark Detailed Make and Use Tables for the
United States, which uses the NAICS classification. Specifically, this data report the intermediate
input in each row (k) required to produce one dollar of final output in each column (j). Then,
we use a concordance to the ISIC Revision 3 classification to build a direct requirement table at
the 2-digit ISIC level, and then further aggregate to the ten-sector level classification used in this
paper. For a given column j, we can aggregate the rows k using the concordance. In order to
further aggregate the columns to the ten-sector level, we compute the weighted average across
columns, with the weights given by the relative importance of each sector. We have re-estimated
the parameters of the model by allowing for αl,j , βl,j and γl,kj to vary at the country-sector level
by using World Input-Output Database (W IOD) from [Timmer, 2015].
Prices of tradables and non-tradables: The price of non-tradables relative to the United
J+1 and the price of non-tradables relative to tradables in each country pJ+1 /pT
States pJ+1
/p
n
usa
l
l
83
Where α is the aggregate share of labor of GDP, which is set to 2/3.
86
are calculated using data from the International Comparison of Prices program (ICP).84
In order to estimate the productivity of each country-sector pair in levels rather than relative
to the United States, we need to estimate the U.S. productivity in every sector. To do this, we calculate the TFP for each tradable sector using the NBER-CES Manufacturing Industry Database,
which reports total output, input usage in production, employment, and capital stock along with
deflators for each sector. The data are available at the 6-digit NAICS classification and they are
converted into the ISIC 2-digit classification using a concordance we have created. Finally, the
share of expenditures of traded goods (ξl ) for each country is sourced from [Levchenko and Zhang,
2016].
B.3
Tariff Data
A bilateral-sector level data of trade costs was constructed using tariff data from World Integrated Trade Solution (WITS/TRAINS), trade values and production data at high levels of
sectoral disaggregation from UN Comtrade and ORBIS, respectively. The trade value data at
sector level is aggregated over each bilateral origin-location-year pair, where the Harmonized System (HS) classification is used. The trade costs data consist of two parts: the most favored nation
(MFN) tariffs and the preferential tariffs. The tariff information is reported in four different revisions of Harmonized System (HS): HS 1988/1992 or H0, HS 1996 or H1, HS 2002 or H2, HS 2007
or H3.
The different HS classifications are match using the series of concordance tables provided by the
World Integrated Trade Solution (WITS), which uniquely matched H1, H2, H3 codes to H0. The
trade data puts together a complete list of countries in each preferential trade agreement. Since
one country can be affiliated with multiple regional trade agreements, there could be multiple
observations for the same origin-location-year-industry pair. In that case, the tariff line with the
lowest binding simple average tariff was kept and the rest of higher tariff were dropped. The same
process described above was done for the most favored nation tariff data.
In order to compare trade patterns with domestic production patterns across industries and
country pairs, we further need to match the different versions of HS classifications with North
American Industry Classification System (NAICS), which is the classification for production data
at 4-digit level. We do a country specific mapping from different versions of HS at 6 digit level to
NAICS at 4 digit level based on Pierce and Schott (2012)85 concordance table between 10-digit
HS codes and 6-digit NAICS codes. After identifying the version of HS codes used, we generate
a one-to-many mapping between 6-digit HS codes and 4-digit NAICS codes.
84
The sectors grouped as tradables are: food and non-alcoholic beverages, alcoholic beverages and tobacco,
clothing and footwear, furnishings, household equipment, and household maintenance. As non-tradables we group
housing; water, electricity, gas, and other fuels; health; transport; communication; recreation and culture; education;
restaurants and hotels.
85
The Pierce and Schott (2012) concordance is based on the US Census data. It links each 10-digits product-level
HS code with 6-digits NAICS code year by year from 1989 to 2009.
87
In order to find out the most important NAICS code when there are multiple NAICS codes
matched, we brings information on domestic production values from ORBIS. The idea is to view
a NAICS code as dominant if a NAICS code has highest share of production value among the
multiple NAICS codes matched. Since the production patterns are different among different
countries, the most important NAICS codes are country specific, which means that countries can
have different dominating NAICS for the same HS code.
The concordance between HS and NAICS with ORBIS country-NAICS code-sales data set
matches 201,363 observations. The criteria for choosing the most important NAICS code are as
follow:
1. When information of sales value is available, choose the NAICS code with the higher sales
value share. 94,979 out of 201,363 mappings from HS to NAICS were dropped, because
those NAICS have lower sales value shares comparing to other NAICS codes matched with
the same HS code for the same country.
2. When turnover is not available, choose the sector with higher employment share. 147
mappings were dropped because those matched NAICS codes have lower employment shares
comparing to other NAICS codes matched with the same HS code for the same country.
3. If one matched NAICS code contains information of sales or employment and others do not,
we keep the matched one. 32,166 mappings were dropped because those matched NAICS
codes do not contain information about the sales value or employment number in that
industry for that country, while other competing NAICS codes have the information.
4. When neither turnover nor employment is available, choose the NAICS with the larger value.
Following the previous criteria, we obtained a country specific one-to-one mapping between
versions of HS and NAICS. Then, weighted average trade costs are calculated for the 9 manufacturing sectors used in the paper. Finally, we take their average across years.
B.4
Effective Tax Rates
The sector-country level effective tax rate is calculated based on the information provided by
professor Prof. Adamodar on his website (http://pages.stern.nyu.edu/ adamodar/). In particular,
he provides the effective tax rate together with other financial variables for about 40,000 individual
companies globally. The effective tax rate is calculated as the ratio of the taxes payable and the
taxable income for each of these companies and it measures the average tax rate paid across all
of the income generated by a firm. To aggregate the firms level information at the country-sector
pair, we calculate the weighted average effective tax rate, using the value of the firm as weights.86
The countries for which this data is available are: Austria, Belgium, Bulgaria, Canada, Denmark,
86
The value of the firm measures the market’s estimate of the value of operating assets.
88
Finland, France, Germany, Greece, Italy, Japan, Netherlands, New Zealand, Norway, Poland,
Portugal, Spain, Sweden, Turkey, the United Kingdom, and the United States.
Appendix C: Proof of Propositions
C.1
Proof of Proposition 1
The dispersion of MP shares across sectors increases with the dispersion of sectoral relative
a ,y b
∂disp(yhh
∂A
hh )
> 0.
productivities. This is ∂Amp
=
a ,T b
T
∂disp(Thh
hh )
Proof. Let’s measure the dispersion of MP shares in country 1 by the Atkinson index as:
Amp
a y b 1/2
y11
11
=1−
a +y b
(y11
11 )
2
Next, we show that any increase in the dispersion of relative productivities AT is followed by an
increase in the dispersion of MP shares Amp . Let’s further assume that MP costs are equal across
a = ga = gb = gb = g
countries and sectors, thus: g12
21
12
21
a y b 1/2
y11
1 − Amp
11
= a
b
2
y11 + y11
a
y11
=
T1a
T1a
=
T1a + g−θ T2a
T1a + g −θ T1b
b
y11
=
T1b
T1b
=
T1b + g−θ T2b
T1b + g −θ T1a
Substituting in the equation of the Atkinson index for MP shares, we have:87
1 − Amp
=
2
"
#1/2
T1a T1b
i
h
2
2
(1+g−2θ )T1a T1b +g−θ (T1a ) +(T1b )
h
i
2
2
2T1a T1b +g −θ (T1a ) +(T1b )
i
h
2
2
(1+g−2θ )T1a T1b +g−θ (T1a ) +(T1b )
Using the definition of At, notice that T1a T1b = [(1 − ATn ) X]2 , where X is assumed to be constant
(T a +T b )
and equal to the arithmetic mean of sectoral productivities X = 1 2 1 ; and therefore (T1a )2 +
87
The last equality uses the mirror image assumption.
89
T1b
h
i
= 4X 2 1 − 12 (1 − ATn )2 Then, the above expression can be rewritten as:
2
1 − Amp
=
2
(1−ATn )2 X 2
(1+g−2θ )(1−ATn )2 X 2 +g−θ 4X 2 [1− 12 (1−ATn )2 ]
2(1−ATn )2 X 2 +g −θ 4X 2 [1− 12 (1−ATn )2 ]
1/2
(1+g−2θ )(1−ATn )2 X 2 +g−θ 4X 2 [1− 12 (1−ATn )2 ]
ii1/2
h
h
2
−2θ + 4g −θ 1 − 1 (1 − A )2
(1
−
A
)
(1
−
A
)
1
+
g
Tn
Tn
Tn
2
1 − Amp
h
i
=
2
2 (1 − ATn )2 + 4g −θ 1 − 12 (1 − ATn )2
i
h
1−Amp
∂
2
<0
∂ATn
h
i
Let’s now denote a = 1 − ATn ; b = 1 + g−2θ ; c = g−θ and e = 1 − 12 (1 − ATn )2 .88 Then the
former equation can be expressed as:
=
=
1/2
a a2 b + 4ce
1 − Amp
=
2
2a2 + 4ce
h
i
1−Amp
∂
2
=
∂ATn
h
i 2
1/2
1/2 1 2
2a + 4ce + 4a2 (1 − c) a2 b + 4ce
(−1) a2 b + 4ce
+ 2 a b + 4ce ]−1/2 2a2 b(−1) + 4ca2
[2a2 + 4ce]2
1
[2a2 + 4ce]2
i
h
1−Amp
∂
2
∂ATn
C.2
1/2
a2 b + 4ce
−4ba4 − 8cea2 b − 8a2 ce + 8c2 ea2 + 4ca4 + 4a4 b + 16a2 ce − 4a4 cb − 16a2 c2 e
2
[a b + 4ce]
= (−1)
1
[2a2 + 4ce]2
1/2
2
a2 b + 4ce
2a e(b − 1) + a4 (b − 1) + 2cea2 9 + 4ce2 < 0
2
[a b + 4ce]
Proof of Proposition 2
Let’s define ã = T1a /T1b . Then, MP sales are disproportionately higher in comparative disadb /y a
∂ (y11
11 )
vantage sectors. This is
< 0.
∂ã
Proof.
b
y11
a =
y11
88
T1b
T1b +g −θ T2b
T1a
a
T1 +g −θ T2a
=
T1a /T1b + g−θ
=
b 2
T1a /T1b + g−θ T1a /T1
Notice that 0 < a < 1, b > 1, 0 < c < 1 and 0 < e < 1.
90
ã + g−θ
ã + g−θ ã2
where ã = T1a /T1b 89
b a
ã + g−θ ã2 − ã + gθ 1 + 2g −θ ã
/y11
∂ y11
=
2
∂ã
(ã + g−θ ã2 )
b a
∂ y11
/y11
−gθ 2ãg−θ + ã2 + 1
<0
=
2
∂ã
(ã + g−θ ã2 )
C.3
Proof of Proposition 3
The lower the MP barriers are the higher the sectoral dispersion of MP shares are. This is,
∂
h
1−Amp
2
−θ
∂g
i
<0
Proof. Notice that when g = 1 multinational activity takes place at a full extent and under
symmetry. Otherwise (with g > 1 reduces the MP heterogeneity)
∂
h
1−Amp
2
−θ
∂g
i
where
"
2 #
(1 − AT )
1
2
4
−θ
−θ
= 2 1/2 2g (1 − AT ) − 8g
1 − (1 − AT )
2
Q Y
1 − Amp
(1 − AT ) Y 1/2
,
=
2
Q
1
Q = 2 (1 − ATn )2 + 4g −θ 1 − (1 − ATn )2 > 0
2
and
1
2
−θ
−2θ
+ 4g
1 − (1 − ATn ) > 0
Y = (1 − ATn ) 1 + g
2
2
Therefore,
∂
h
1−Amp
2
−θ
∂g
i
=
i
(1 − AT ) h −θ 2
(1
−
A
)
−
1
<0
8g
T
Q2 Y 1/2
which holds given that 0 < (1 − AT ) < 1
C.4
Proof of Proposition 4
The gains from MP are higher in multi-sector models—relative to one-sector frameworks; and
this difference in GMP is larger (a) the higher the dispersion of productivity across sectors,
89
Notice that 0 < ã < 1.
91
∂
(GM P
multi −GM P uni
∂AT
)
> 0; b) and the lower the MP barriers: ∂
(GM P
multi −GM P uni
)
∂g −θ
> 0.
Proof.
GM Pl =
Tla
Tela
Tlb
Telb
!− 1
Tela
Tla
2θ
Telb
Tlb
 P
!− 1
 i

 P
2θ
i
Tia (ci d)−θ
Teia (ci d)−θ
Substituting in the gains from MP expression, we have:
P
i
Tib (ci d)−θ
P eb
Ti (ci d)−θ
i
− 1
2θ



2 −θ − 2θ1
d
+ (T1a )2 + T1b
GM Pl = 
2 
T1a T1b [a2 + b2 ] + ab (T1a )2 + T1b

Let’s define χ =
T1a +T1b
.
2
T1a T1b 1 + d−θ
2
Therefore T1a T1b = [1 − AT ]2 χ2 and (T1a )2 + T1b
2
h
i
= 4χ2 1 − 12 (1 − AT )2 ,
where AT is the Atkinson inequality index of the fundamental productivities. Substituting in the
above equation, we have:

GM Pl = 
h
i
− 2θ1
+ 4χ2 1 − 12 (1 − AT )2 d−θ
h
i 
2 2 2
2
1
2
2
[1 − AT ] χ [a + b ] + 4abχ 1 − 2 (1 − AT )
[1 − AT ]2 χ2 1 + d−θ
GM Pl =
C.4.1
Let’s show that
∂GM P
∂AT
"
2
[1 − AT ]2 1 − d−θ
2
+ 4d−θ
[1 − AT ]2 [a − b]2 + 4ab
#− 2θ1
> 0:
"
#
2
2
1 − 1 −1 −2 (1 − AT ) 1 − d−θ Q2 + 2 (1 − AT ) (a − b) Q1
∂GM P
= − Q 2θ
∂AT
2θ
Q22
where Q =
Q1
Q2 ,
with Q1 = [1 − AT ]2 1 − d−θ
2
+ 4d−θ and Q2 = [1 − AT ]2 [a − b]2 + 4ab
2
−2 (1 − AT ) 1 − d−θ Q2 + 2 (1 − AT ) (a − b)2 Q1 < 0
2
1 − d−θ Q2 > (a − b)2 Q1
2 h
i
2
1 − d−θ
[1 − AT ]2 [a − b]2 + 4ab > (a − b)2 [1 − AT ]2 1 − d−θ + 4d−θ
2
1 − d−θ ab > [a − b]2 d−θ
92
The above inequality holds given that:
where
and
C.4.2
1 − d−θ
2
> [a − b]2
1 − d−θ > [a − b] = 1 − d−θ 1 − g −θ
d−θ < ab = 1 + d−θ g−θ g−θ + d−θ = d−θ + g−θ + d−θ g−θ + d−2θ g−θ
Let’s show that
∂GM P
∂g −θ
> 0:
∂GM P
=
∂g−θ
h
2
1 − 1 −1 [1 − AT ]
Q 2θ
2θ
1−
2
d−θ
+
4d−θ
ih
2
2 (1 − AT )
1−
Q22
g−θ
1−
2
d−θ
+4 1+
d−2θ
+
8g−θ d−θ
which holds given that
0 < g−θ < 1, 0 < d−θ < 1 and (1 − AT )2 > 0
C.5
Proposition 5
In a multi-sector model of trade and MP gains from trade can be expressed as a function of
aggregate domestic trade share and the sectoral dispersion of trade shares.90
− 1
1
1
2θ
GTl = πlla πllb
= (πll )− θ (1 − Aπll )− θ
Proof. Gains from trade are expressed as:
− 1
2θ
h
l
.
Wd>0
/Wd→∞
= GTl = πlla πllb
Let’s define the dispersion in trade shares across sectors through its Atkinson index:
Aπll = 1 −
πlla πllb
1
2
a +π b
πll
ll
2
πa πb
= 1 − ll ll
πll
1
2
1
(π a π b ) 2
Notice that the dispersion of trade shares across sectors is given by: Aπll = 1 − llπ ll , where πll =
ll
Notice that the last equality holds because under symmetric Cobb Douglas preferences, Xla = Xlb =
90
therefore, πlla =
a
Xll
Xla
= 2Xlla and πllb =
b
Xll
Xlb
= 2Xllb .
93
a
b
πll
+πll
.
2
1
; and
2
i
>0
Notice that πlla =
a
Xll
a
Xn
= 2Xla and πlb =
b
Xll
Xlb
preferences, Xla = Xlb = 12 . Therefore, πl =
C.6
πlla πllb
− 1
2θ
= 2Xllb ; given that under symmetric Cobb Douglas
Xl
Xl
=
b
Xla +Xll
a
Xl +Xlb
= Xlla + Xllb =
1
1
= (πll )− θ (1 − Aπll )− θ
a +π b
πll
ll
2
and
91
Proposition 6
The higher the sectoral dispersion of MP shares—due to lower MP barriers— the lower the
sectoral dispersion of trade shares, and therefore the lower the gains from trade,
∂GTl multi
∂g −θ
< 0; and,
these losses in GT caused by a reduction in MP costs are larger in multi-sector models—relative
(GT multi −GT uni )
to one-sector frameworks: ∂
< 0.
∂g −θ
Proof.
∂GTl
1
1
− 1θ ∂πnn
− θ1 −1 ∂(1 − Aπ ) ∂ATe
− 1θ −1
− 1θ
(1
−
A
)
(1
−
A
)
(π
)
(π
)
=
−
+
<0
π
π
ll
ll
ll
ll
∂g−θ
θ
∂g−θ
θ
∂ATe ∂g−θ
where we have shown that
∂πll
∂g −θ
> 0;
C.6.1
∂πll
∂g −θ
> 0:
πll =
Let’s show that
1 Q1
2 Q2
and
∂πll
g −θ
=
1 1
2 Q22
h
∂Q1
Q
∂g −θ 2
∂(1−Aπ )
∂ATe
< 0; and
∂ATe
∂g −θ
< 0:
i
∂Q2
> 0 where:
− Q1 ∂g
−θ
1
2
−θ −θ
−2θ
+ 4 1 − (1 − AT )
Q1 = 2 (1 − AT ) 1 + 2d g + g
d−θ + 2g −θ + d−θ g−2θ
2
2
Q2 =
1
2
2
−θ −θ
−2θ
−2θ
−2θ −2θ
+4 1 − (1 − AT )
+d
+d g
(1 − AT ) 1 + 4d g + g
d−θ + g −θ + d−θ g−2θ + g−θ d−2θ
2
1
∂Q1
2
2
−θ
−θ
−θ −θ
+
4
1
−
2d
+
2g
=
2
(1
−
A
)
2
+
2g
d
(1
−
A
)
T
T
2
∂g−θ
1
∂Q2
2
2
−θ
−θ
−2θ −θ
−θ −θ
−2θ
+
4
1
−
4d
+
2g
+
2d
g
=
(1
−
A
)
(1
−
A
)
1
+
2g
d
+
d
T
T
∂g−θ
2
91
Notice that the exponent associated to the number of sectors for the GT is the same needed for the calculation
of the geometric mean of the Atkinson index. This indicates that this proposition holds for any number of sectors
considered.
94
where
1
∂Q1
∂Q2
2
2
−θ
−θ
−θ −θ
+ 4 1 − (1 − AT )
Q2 − Q1 −θ = 2 (1 − AT ) 2d + 2g
2 + 2g d
∗
∂g−θ
∂g
2
1
2
−θ
−θ
−θ −2θ
−θ −2θ
−θ −θ
−2θ
−2θ
−2θ −2θ
d +g +d g
+g d
+ 4 1 − (1 − AT )
+d
+d g
(1 − AT ) 1 + 4d g + g
2
1
2
2
−θ −θ
−2θ
−θ
−θ
−θ −2θ
+ 4 1 − (1 − AT )
− 2 (1 − AT ) 1 + 2d g + g
d + 2g + d g
∗
2
1
2
2
−θ −θ
−2θ
−θ
−θ
−2θ −θ
1
+
2g
d
+
d
(1
−
A
)
=
+4 1−
(1 − AT ) 4d + 2g + 2d g
T
2
i
h
−4 (1 − AT )4 d−θ 1 + d−2θ g−2θ − d−2θ − g−2θ +
2
1
16 1 − (1 − AT )2
2
2
which is positive given that
1
16 1 − (1 − AT )2
2
C.6.2
Let’s show that
2
i
h
d−θ 1 + d−2θ g−2θ − d−2θ − g−2θ
1
= 16 1 − (1 − AT ) + 4 (1 − AT )4 > 4 (1 − AT )4
2
∂(1−Aπ )
∂ATe
< 0:
Let’s measure the dispersion of trade shares in country 1 by the Atkinson index as:
a π b 1/2
π11
11
Aπ = 1 −
a +π b
(π11
11 )
2
Next, we show that any increase in the dispersion of relative effective productivities ATe is followed
by an increase in the dispersion of trade shares Aπ . Let’s further assume that MP and trade costs
a = g a = g b = g b = g and da = da = db =
are equal across countries and sectors, thus: g12
12
21
12
21
12
21
db21 = d.
a
π11
=
b
π11
=
a π b 1/2
π11
1 − Aπ
11
= a
b
2
π11 + π11
Te1a
Te1a + d−θ Te2a
Te1b
Te1b + d−θ Te2b
95
=
=
Te1a
Te1a + d−θ Te1b
Te1b
Te1b + d−θ Te1a
Substituting in the equation of the Atkinson index for MP shares, we have:92
1 − Aπ
=
2
"
#1/2
Te1a Te1b
i
h
2
2
b
a
−2θ
e
e
(1+d )T1 T1 +d−θ (Te1a ) +(Te1b )
i
h
2
2
2Te1a Te1b +d−θ (Te1a ) +(Te1b )
i
h
2
2
(1+d−2θ )Tea T b +d−θ (Tea ) +(Teb )
1
1
1
1
2
1 − ATe X , where X is assumed to be constant
2
(Tea +Teb )
and equal to the arithmetic mean of sectoral productivities X = 1 2 1 ; and therefore Te1a +
h
2
2 i
Te1b = 4X 2 1 − 12 1 − ATe
Then, the above expression can be rewritten as:
Using the definition of ATe , notice that Te1a Te1b =
1 − Aπ
=
2
1 − Aπ
=
2
where Q1 =
h
1 − ATe
∂
1−Aπ
2
∂ATe
1/2
−Q1
2
1 − ATe
"
2
(1−ATe ) X 2 h
i
2
2
(1+d−2θ )(1−ATe ) X 2 +d−θ 4X 2 1− 12 (1−ATe )
#1/2
h
i
2
2
2(1−ATe ) X 2 +d−θ 4X 2 1− 12 (1−ATe )
h
i
2
2
(1+d−2θ )(1−ATe ) X 2 +d−θ 4X 2 1− 12 (1−ATe )
h
2 ii1/2
1 + d−2θ + 4d−θ 1 − 12 1 − ATe
h
2
2 i
2 1 − ATe + 4d−θ 1 − 12 1 − ATe
h
1 − ATe
2
1/2
1 − ATe Q1
1 − Aπ
=
2
Q2
h
h
2 ii
2
1 + d−2θ + 4d−θ 1 − 21 1 − ATe
and Q2 = 2 1 − ATe +4d−θ 1 −
=
h
1/2
−Q1
+ 1 − ATe
1
−1/2 ∂Q1
∂ATe
Q22
2 Q1
i
1/2 ∂Q2
Q2 − 1 − ATe Q1 ∂A
e
T
2
2 1 −1/2 1 −1/2 ∂Q1
1/2
Q1
= −Q1 − 1 − ATe
1 − d−θ < 0
+ 1 − ATe Q1
2
∂ATe
2
2 1/2 1/2 ∂Q2
= 4 1 − ATe Q1
1 − d−θ > 0
− 1 − ATe Q1
∂ATe
92
1/2 ∂Q2
1 −1/2 ∂Q1
Q2 − 1 − ATe Q1
+ 1 − ATe Q1
∂ATe
2
∂ATe
∂ATe
2
2 1 −1/2 2
2
1
1/2
−θ
−θ
= −Q1 − 1 − ATe
Q
1−d
1 − ATe
2 1 − ATe + 4d
1−
2 1
2
2 1/2 +4 1 − ATe Q1
1 − d−θ
∂
1−Aπ
2
1
= 2
Q2
1/2
−Q1
The last equality uses the mirror image assumption.
96
1
2
1 − ATe
2 i
h
i
2
2
2 1
1/2
−θ
−θ
= − Q1
2 1 − ATe + 4d
1−
1 − ATe
− 4 1 − ATe
1−d
2
2 h
2
2 −1/2 2 i
1
−θ
−θ
1 − ATe
− 1 − ATe Q1
2 1 − ATe
+ 4d
1−d
1−
2
h
h
2 ii
2 1/2
= − Q1
2 1 − ATe
1 − d−θ + 4d−θ + 4 1 − 1 − ATe
2 h
2 −1/2 2 i
2
1
−θ
−θ
− 1 − ATe Q1
2 1 − ATe
+ 4d
1−d
1−
1 − ATe
2
2
Which is negative given that 1 − d−θ > 0 and 0 < 1 − ATe < 1
C.6.3
Let’s show that
∂ATe
∂g −θ
< 0:
Let’s express the sectoral dispersion of effective technologies, AT̃ , as a function of model’s
parameters:
1 − AT̃
=
2
T1a
T1b
g −2θ
1+
1
1−AT
2
Let’s define χ =
=
(T1a T1b ) 2
T1a +T1b
AT̃ = 1 −
"
T1a
T̃1b
+ g−θ
T1a
T1b
+ 1 (1 + g −θ )
2
1
2
+1
. Substituting in the equation above, we have:
"
4g −θ
2
(1 + g −θ )
2
∂ATe
1
=−
+ 1 − AT̃
2
−θ
−θ
∂g
2 (1 + g )
4g−θ
+ 1 − AT̃
g−θ
1−
1 + g−θ
2
1 − g −θ
1 + g −θ
2 #1/2
h
i
2 #−1/2 4 1 − g−θ − 1 − A 2 1 − g −θ Te
(1 + g −θ )
Which is negative since
h
C.7
1 − g −θ − 1 − ATe
i h
i
2 2 1 − g −θ = 1 − ATe
1 − g −θ > 0
Proposition 7
− 1 − 1
2θ
2θ
a b
a
b
GOn = ynn
ynn
πnn
πnn
97
3
MP Shares:
− 1
2θ
a b
ynn ynn
=
Let’s again define χ =
T1a +T1b
.
2
T1a
T1b
·
T1a + g−θ T1b T1b + g−θ T1a
− θ1
Therefore T1a T1b = [1 − AT ]2 χ2 and (T1a )2 + T1b
Substituting in the equation above, we have:
a b
ynn
ynn
− 1
2θ

=
2
h
(1 + g−2θ ) [1 − AT ]2 χ2 + 4g−θ χ2 1 −
a b
ynn
ynn
− 1
2θ
1
2
(1 − AT )2
1
2θ
2
−θ
g


=  1 − g−θ + 2 

h
i
= 4χ2 1 − 12 (1 − AT )2 .
− 1
2θ
χ2
[1 − AT ]
2
i
1−AT
2
Trade Shares: Similarly we can express trade share as:
− 1
2θ
a
b
=
πnn
πnn
therefore:
T̃1b
T̃1a
·
T̃1a + d−θ T̃1b T̃1b + d−θ T̃1a
!− 1
2θ
1

2θ
− 1
2
d−θ 
2θ

a
b
−θ
+
πnn πnn
= 1−d
2 
1−AT̃
2
Using the derived relationship between AT̃ and AT :

1
2θ
− 1
2

2θ
a
b
−θ
πnn
πnn
+
1
−
d
=

g −θ
2
1+g
( −θ )
+
d−θ
1−AT
2

2 −θ 2 

1−g
1+g −θ
Therefore, the gains from openness:

 
2
2

g−θ  
−θ
 1 − d−θ +
GOn = 
1
−
g
+
·


2


1−A
2
C.7.1
T
 1
2θ
g −θ
2
(1+g−θ )
+
d−θ
1−AT
2


2 −θ 2 

1−g
1+g −θ
The lower the MP restrictions the higher the gains from openness:
∂GOn
>0
∂g−θ
98
Let’s define Q1 =
Q1
Q2 ,
Q1 =
1−g
Therefore
−θ 2
+
g −θ
1−AT
2
2
!

2
and Q2 =  1 − d−θ +
g −θ
+
(1+g−θ )2
d−θ
1−AT
2
2 1−g −θ
1+g −θ

2 
1
1
∂Q2
∂GOn
−1 ∂Q1
2θ
=
(Q1 Q2 )
Q2 + −θ Q1
∂g−θ
2θ
∂g−θ
∂g
which is positive if
∂Q1
Q
∂g −θ 2
+
∂Q2
Q
∂g −θ 1
>0
Proof. Let’s further define X = g−θ , Z = d−θ and Y =
1−AT
2
∂Q2
∂Q1
Q2 + −θ Q1 > 0
∂g−θ
∂g
2
.
We can rewrite the above condition as:




Z
(1 + X) (1 − X) (1 − 4Y ) 
1 
X 

2
2
−2(1 − X) +
(1 − Z) +
−Z 2  > (1 − X) +
2 
Y
Y
2
X
1−X
X
+
Y
(1
−
X)
+
Z
1+X
(1+X)2
(1 − 2Y (1 − X)) (1 − Z)2 X + Y (1 − X)2 + Z (1 + X)2 > −Z (1 + X) (1 − X) (1 − 4Y )
(1 − 2Y (1 − X)) (1 − Z)2 X+(1 − 2Y (1 − X)) (1 − Z)2 Y (1 − X)2 +(1 − 2Y (1 − X)) Z (1 + X)2 >
Z (1 + X) (1 − X) (1 − 4Y )
which holds given that
(1 − 2Y (1 − X)) Z (1 + X)2 − Z (1 + X) (1 − X) (1 − 4Y ) =
i
h
Z (1 + X) 2X + 2Y (1 − X)2 > 0
C.7.2
The higher the dispersion of fundamental productivity the higher the gains
from openness:
∂GOn
>0
∂AT
Let’s define Q1 =
Therefore
Q1
Q2 ,
Q1 =
1−g
−θ 2
+
g −θ
1−AT
2
99
2
!

2
and Q2 =  1 − d−θ +
g −θ
+
(1+g−θ )2
d−θ
1−AT
2
2 1−g −θ
1+g −θ

2 
1
1
∂Q2
∂GOn
−1 ∂Q1
2θ
(Q1 Q2 )
=
Q2 +
Q1
∂AT
2θ
∂AT
∂TT
which is positive if
∂Q1
∂AT Q2
+
∂Q2
∂AT Q1
>0
Let’s further define X = g−θ , Z = d−θ and Y =
1−AT
2
2
.
∂Q1
∂Q2
Q2 + −θ Q1 > 0
∂g−θ
∂g
We can rewrite the above condition as:




2
2
Z
X  Z (1 + X) (1 − X) 
X


2
2

2  (1 − AT ) > 0
2 + (1 − X) +
3 (1 − Z) +
Y
2
(1 − AT )
X
1−X
X + Y (1 − X)
+ Z 1+X
(1+X)2
which holds given that (1 − AT ) > 0
Appendix D: Estimation
D.1
Effective technology: two-step procedure (Shikher, 2012)
The importer fixed effect recovered from the gravity equation is given by:
Snj
Tenj
= j
Teus
cjn
cjus
!−θ
The share of spending on home-produced goods is given by:
j
Xnn
Xnj
=
Tenj
cjn
pjn
!−θ
Dividing it by the values for the U.S., we have:
j
Xnn
/Xnj
j
j
Xus,us
/Xus
Tenj
= j
Teus
cjn
cjus
!−θ
pjn
pjus
!−θ
= Snj
pjus
pjn
The ratio of price levels in sector j relative to the U.S. becomes
pjn
pjus
=
j
Xnn
/Xnj
1
j
j
Xus,us
/Xus
Snj
!1
θ
Then, cost of the input bundles relative to the U.S can be written as:
100
!−θ
cjn
cjus
D.2
=
wnj
j
wus
!αj βj
rnj
j
rus
!(1−αj )βj
J+1
Y
k=1
pkn
pkus
γk,j !1−βj
Bilateral MP Barriers: A Source Effect
The specification for the investment barriers includes a source effect.93 In this section, we
support our chosen specification in equation 22, where the inclusion of a source fixed effect,
sourcejs , allows for the estimation of asymmetric barriers of foreign production that is consistent
with the pattern of prices and income in the data. There are three empirical observations of
importance. First, there is a home bias for all countries regardless of their level of development.
This means that countries with relative higher income produce slightly more of their output with
local technologies, but the differences in magnitude are small. Figure D.16 shows the residuals of
the equation below:
ln
Ill
Il
= β0 + β1 ln (GDPl ) + µl
where the estimated coefficient for income per-capita is 0.0116, which it is not significantly different
from zero. The second observation is that there is a systematic correlation between bilateral MP
shares and the relative level of development. Figure D.15 shows that the larger the difference in
relative incomes, the larger the disparity in bilateral MP shares between any two countries. The
slope coefficient of the equation below is statistically significant and equal to 3.466.
ln
j
Ils
j
Isl
!
= β0 + β1 ln
GDPs
GDPl
+ ǫsl
Finally, as shown in figure D.17, the model delivers a flat relationship between tradable prices and
GDP per-capita, matching the data pattern documented in [Waugh, 2010] for the case of trade.
By contrast, the model estimated with location effects instead implies a negative and significant
relationship between tradable prices and income.
93
To the best of our knowledge there is no precedent in the estimation of multinational production asymmetric
barriers at the sectoral level. An exception is [Head and Mayer, 2016] who estimate the MP frictions for the
automotive industry using brands level data.
101
−10
−5
log (MP ij / MP ji)
0
5
10
Figure D.15: Bilateral MP shares and Income Differences
−5
0
log (GDP j / GDP i)
5
coef = 0.3463, se = 0.05844, t = 5.93
.5
Figure D.16: Home Bias and MP
TUR
LVA
USA
GRC ITA FIN DNK
NOR
NZL
AUS
ESP
NLD
DEU
FRA
AUT
SWE
CAN
PRT
0
BGR
log Inn/In
CHE
JPN
MEX
RUS
LTU
POL
EST
SVK
CZE
GBR
0
.5
−.5
ROM
−1
HUN
−1
−.5
1
log GDP per capita
coef = 0.1166, se = 0.08438, t = 1.38
.3
Figure D.17: Price of Tradables and Income Per Capita
.2
AUS
.1
EST
CAN
LTU
LVA RUS
DNK
SWE
NLD
FIN
USA
AUT
0
BGR
MEX
ROM
−.1
Price of Tradables: U.S.=1
NZL
CZE
POL
HUN
PRT
ESP
GBR
SVK
GRC
NOR
DEU
JPN
ITA
FRA
TUR
−1.5
−1
−.5
0
.5
1
GDP Per Worker: U.S.=1
coef = −0.011, se = 0.026, t = −.44
Note: The Figure in the top shows the relationship between relative incomes GDPj /GDPi and bilateral trade
shares M Pij /M Pji in the data. The figure in the middle panel shows the relationship between the share of total
output produced with local technologies Inn /In and GDP per worker. The bottom panel shows the relationship
between the model-implied aggregate price of tradables and income per capita.
102
Appendix E: Estimated Parameters
1. Preferences
a) σ, where
1
1−σ
is the inter-temporal elasticity of substitution: takes a value of 4.
b) η, elasticity of substitution between the tradable sectors: takes a value of 2 for the welfare
calculations under CES and capital, while it becomes 1 by definition under a Cobb Douglas
specification.
c) ξn , Cobb Douglas weight for the tradable sector composite good in country n: Section B.2.
d) ωj , weights of each tradable sector in final consumption: Section B.2.
2. Technology
a) ǫj , elasticity of substitution in production across goods in sector j.
b) αj , value added based on labor intensity Section B.2.
c) βj , valued added based on labor intensity: Section B.2.
d) γkj , output industryj requirement from input industry k: Section B.2.
e) θj , dispersion of productivity draws in sector j: a value of 6, common across sectors, is used
in our baseline estimation. We re-do our estimation and welfare analysis using sector level θj ’s
from [Caliendo and Parro, 2015].
f) Tnj , state of technology in country n and sector j: Section 5.1.2.
3. Multinational production and Trade barriers
a) djns , iceberg trade cost of exporting from country s to country n in sector j: Section 5.1
and 5.1.2.
b) hjsi , iceberg MP cost of produce in country s using technologies from country i in sector j:
Section 5.1.2.
4. Labor and capital endowment
a) Ln , stock of labor in each country: Section B.2.
b) Kn , stock of capital in each country: Section B.2.
103
Appendix F: Algorithm to solve for Tsj
j
This section presents in detail the algorithm to get estimates for Tlj and gls
that are consistent
with both the trade and the MP gravity equation previously derived. Through the structural
gravity equations and the model’s derived relationship between Tej and T j , the model offers
l
l
two independent measures of effective productivities. To overcome this challenge, we develop a
tournament process that involves the trade and MP gravity equations as well as the transition
between them through equation 23.
In order to estimate a set of fundamental productivity parameters for each country-sector pair
that are consistent with trade and MP gravity equations, we do the following steps.
94
Step 1: From the trade gravity equation, we estimate the effective productivities for each
trade
sector-country pair Tej
(see Section 5.1 for details).
l
t
Step 2: Estimate the bilateral-sector MP barriers and the first set of fundamental productiv-
ities from the location fixed effect estimated from the gravity equation. Using our estimates of
j
Tsj and gls
, we calculate a set of effective productivities by the following system of equations:
mp X −θ
j
gls
=
Tsj t
Telj
t
t
s
∀j = 1, ...J + 1,
where the subscript t represents the iteration in the algorithm process.
Step 3: Compute the difference between the effective productivities estimated through
the
mp
trade and the MP gravity equations, and update the effective productivities, adjusting Tej
l
by adding to it five percent of the calculated differential.
t
trade mp
∆t = Telj
− Telj
t
Telj
mp
t+1
t
mp
= Telj
+ 0.05 ∆t
t
Step 4: Calculate the fundamental productivities
equations:
mp
X j −θ
Telj
=
gls
Tsj t+1
t+1
t
s
Tsj by solving the following system of
∀j = 1, ...J + 1,
Step 5: Use the estimates for Tsj from the previous step to run a constrained gravity MP
94
mp
trade
Notice that we refer as Telj
and Telj
to the effective technology parameters estimated based on the
t
MP and trade gravity equation, respectively.
t
104
j
equation, with α0 = β0 = 1, in order to estimate MP barriers gls
:
ln
j
Ils
Illj
!
cj
c
j
= β0 ln Ts − α0 ln Tlj − θdjk − θbjls − θlanjls − θcolonyls
− θRT Ajls − θsourcejs − θµjls
mp
Step 6: Update the set of effective productivities Telj
by using equation
mp
X j −θ
=
gls
Telj
Tsj t+1
t+2
∀j = 1, ...J + 1,
t+1
s
Step 7: Repeat steps 3 to 6 until ∆T ≈ 0. This is, when the effective productivities calculated
from the procedure described above is sufficiently close to the effective productivities directly
estimated from the trade gravity equation:
trade mp
≈ Telj
Telj
T
T
Appendix G: Equilibrium Solution
n oJ
Given Ll , Kl , Tlj
j=1
, ξn
N
,
n=1
ε, αj , θ j , βj , {γk,j } ,
n
j
gls
compute the competitive equilibrium of the model as follows:
o
N ×N
,
1. Guess {wl , rl }N
n=1
a) Compute prices from the following equations:
cjl
h
= (wl )
αj
(rl )
1−αj
"
#1−βj
iβj J+1
Y γkj
pkh
k=1
j
δnls
= cl gls dnl
∆jns
"
#− 1
X j −θj θj
=
δnls
h
ej =
∆
n
e J+1
∆
=
n
X
X
s
Tsj ∆jns
s
−θj
−θj
J+1
g
TsJ+1 cJ+1
n
ls
105
n
djnl
o
N ×N
J+1
j=1
, and η, we
− 1
θj
ej
pjn = Γj ∆
n

 1 ξn
1−η
J
X
1−ξn
1−η
pJ+1
Pn = Bn 
ωj (pn ) 
n
j=1
b) Compute final demand, for any country n, as follows:
Ynj = ξn
wn Ln + rn Kn
pjn
1−η
ωj pjn
PJ
1−η
k
k=1 ωk (pn )
YnJ+1 = (1 − ξn )
∀j ∈ {1, ..., J}
wn Ln + rn Kn
pJ+1
n
j
c) Compute probabilities πnls
as follows:
j
πnls
−θj
−θj j
cjl djnl
Tsj gls
=
P P j j −θ j j −θj
cl dnl
l
s Ts gls
d) Total Demand. In this section, we are looking for the Qkh that satisfies the following equation:
pjl Qjl
=
pjl Ylj
+
J
X
N X
N
X
(1 − βk ) γj,k
k
πnls
pkn Qkn
n=1 s=1
k=1
!
+ (1 − βJ+1 ) γj,J+1
N
X
J+1 J+1 J+1
πlls
p l Ql
s=1
e) Compute factor allocations across sectors, for any country n, as follows:
N X
N
X
j
πnls
pjn Qjn =
n=1 s=1
N
X
J+1 J+1 J+1
=
p l Ql
πlls
s=1
wl Ljl
rl Klj
=
αj βj
(1 − αj ) βj
rl KlJ+1
wl LJ+1
l
=
αJ+1 βJ+1
(1 − αJ+1 ) βJ+1
f) Update {wl′ , rl′ }N
n=1 with the feasibility conditions for factors, for any n, as follows:
J+1
X
j=1
Ljl
= Ll ,
J+1
X
j=1
106
Klj = Kl
N
2. Repeat the above procedure until {wl′ , rl′ }N
n=1 is close enough to {wl , rl }n=1 .
Appendix H: Algorithm to solve for absolute productivity adjustment vector Zn
This section provides a detailed explanation of the algorithm used to estimate the absolute
productivity adjustment for each country Zn used in section 6. Following [Costinot et al., 2012],
we start by fixing a reference economy and make all other countries to have the same relative
productivity across sectors as this reference country, while adjusting their absolute level of productivity Zn , in such a way that relative incomes around world are held constant. This aims to
guarantee that changes in fundamental productivity levels from Zn to Zn′ have no indirect terms
of trade effects on the reference country, n0 . Accordingly, the impact of such changes on sectoral
and aggregate trade flows as well as in welfare in country n0 can be interpreted as the impact of
Ricardian comparative advantage at the industry level.
We start with an initial guess for the vector of absolute productivity adjustment parameters.
We use the geometric average of the estimated fundamental productivities as our initial guess.
The productivity of each country is replaced by the productivity of the reference country shifted
by the Zn . We use the equilibrium wages as our initial nominal wages. Although nominal wages
change, the algorithm ensures that the relative wages are preserved at the end of the calibration.
The same happens with the return to capital, for the model specification that has capital and
CES preferences. Here is the description of the algorithm procedure after the introduction of the
initial guess.
Step 1: Given the vector of factor prices, wlt and rlt , employment levels and an initial guess
for sectoral prices, we find sectoral prices through the steps in Appendix G, until they converge.
Step 2: Using the price vector for each country-sector pair, we compute the aggregate price
index, final demand, aggregate demand and the optimal factor allocation across sectors.
j
Step 3: Given the demand, final and intermediate inputs, Qjl , and the matrix of πnls
calculated
above, we use the market clearing condition in order to solve for the vector of Zn , such that relative
wages are unaltered. To do this, we solve for:
N X
N
J+1
XX
j
πnls
pjn Qjn
j=1 n=1 s=1
where
j
πnls
=
=
J+1
X
j=1
J+1
X
wl Ljl
rl Klj
=
αj βj
(1 − αj ) βj
j=1
−θj
−θj j
Zst T0j gls
cjl djnl
Φjn
107
and Φjn =
PN
n=1
−θ −θj
j j
t−1 T j g j
Z
c
d
; and the subscript t represents the number
0
s=1 s
ls
l nl
PN
of the iteration in the algorithm process. Notice that the procedure above solves for Zst while
j
ignores second order effects. This is, on each iteration the values of Φjn and
depend on
t Qn the
j
t−1
and
absolute productivity adjustment calculated in the previous iteration, Φn = f (Zn )
t
Qjn = f (Zn )t−1 , for which Zn is solved through an iterative procedure.
Step 4: Next, to guarantee that Z0t = 1, the vector of absolute productivity Zn is adjusted by
the value corresponding to the reference country Z0 , Znt = Znt /Z0t .
Step 5: Repeat the above steps until the vector Znt converges.
108