Download Diffusion of ideas and centrality in the trade network

Diusion of Ideas and
Centrality in the Trade Network
PRELIMINARY AND VERY INCOMPLETE DRAFT
Magali Pinat
∗
July 31, 2015
Abstract
My work is rooted in the literature of technology's diusion through bilateral
trade and its eects on sustained growth. In the literature of diusion of ideas,
the amount of imports from trade partners determines the probability of learning
in the importing country. My contribution lies in, rst, using a System GMM to
show that trading with central countries matters for economic growth. Central
countries are connected to many countries, show high-intensity ows, and are
also strongly connected to other central countries. I estimate that an increase
in the trade with the top-3 most central countries generates a non negligible
supplement of growth of a 0.4 percentage point. Second, I build a theoretical
model to present the mechanism through which the centrality of trade partners
matter for economic growth. The mechanism is the following: trade leads to
the diusion of technologies embedded in the goods. Countries learn technology
from the partners they trade with, at a certain cost. Everything else equal,
the model predicts that countries have an economic interest of trading with the
most central partners because of clustering eects: adopting the technology of
the most central partners will facilitate their insertion in a popular cluster where
all of the partners are more likely to use the technology. Countries, however,
could face a trade-o when the partner centrality is high but its technology is
not the highest in the trade network or the cost of obtaining the technology is
important. In a third part, I estimate the accuracy of the model's prediction
with an empirical analysis following the methodology of Comin et al. (2012).
Keywords: International Trade, Economic Growth, Technology Diusion,
Network Analysis.
JEL Classication:
F14, F43, O40, D85.
∗ Université Paris I-Sorbonne - Maison des Sciences Economiques, 106-112 boulevard de
l'Hôpital, 75647 Paris Cedex 13, France. e-mail address: [email protected]
1
Introduction
For most of the 20th century, global trade activity was concentrated among
developed countries. Since the dawn of the 21st century, however, developing
countries, led by China and other large emerging economies, rose with surprising
speed, becoming major players in the global trade network. The developing
countries' participation in global trade rose from 20 percent in 1970 to 32 percent
in 2000, and it jumped to 49 percent by 2013 (see Figure ??). This impressive
change was associated with major transformations in the structure of world
trade network.
Figure 2 shows the global trade network in 1980 and 2012. Each node represents a country, and each link corresponds to an active bilateral between two
countries measured as the exports from one country to its partner as a share of
its own exports. All the countries in the network have then all 100 percent of
exports to allocate across its partners. An algorithm of principal component is
then applied to the matrix of share of exports in order to determine the position of each country in the trade network. Two sets of interpretations can be
extracted. First, along the horizontal axis are distributed the centrality of the
countries. More a country is positioned on the right, more relevant it is to the
rest of the network, i.e. he is an important trade partner for a large number of
countries. Further a country is situated on the right of the plot, more central
it is to the trade network. Second, the gure gives also pieces of information
on the similarity of the trade structures. Smaller is the distance between two
countries, the more similar is the structure of their trade connections in terms
of exports to the rest of the world and in term of their relative importance to
the rest of the partners.
Figure 2 panel a presents the results of the algorithm for 1980 data. Only
advanced economies are located to the right; note that they are also very close.
In economic terms, it can be implied that only advanced economies used to
be central to the trade network. Moreover those countries were similar in the
way they were trading, creating a clear cut in the trade network between core
countries and the periphery. Panel b of Figure 2 presents some very dierent
features for 2012. First, some developing countries are moving toward the right
of the picture, meaning they got more central to the trade network. Moreover,
those central countries are not any more closely located. Roles have changed
and cluster of countries begun to appear. Nowadays, the world appears to be
multipolar. The right side of the gure resembles to a star with the apparition
of cluster s of countries. Japan, India and the republic of Korea forms one,
Western Europe another one.
In this paper, I wonder if the centrality of trade partners matter for economic
growth and what are the mechanism that play a role. I take a macroeconomic
approach of diusion of technology at the country level. My contribution lies in,
2
rst, using a System GMM to show that trading with central countries matters
for economic growth. Central countries are connected to many countries, show
high-intensity ows, and are also strongly connected to other central countries. I
estimate that an increase in the trade with the top-3 most central countries generates a non negligible supplement of growth of a 0.4 percentage point.Second, I
build a theoretical model to present the mechanism through which the centrality
of trade partners matter for economic growth. The mechanism is the following:
trade leads to the diusion of technologies embedded in the goods. Countries
learn technology from the partners they trade with, at a certain cost. Everything else equal, the model predicts that countries have an economic interest of
trading with the most central partners because of clustering eects: adopting
the technology of the most central partners will facilitate their insertion in a
popular cluster where all of the partners are more likely to use the technology.
Countries, however, could face a trade-o when the partner centrality is high
but its technology is not the highest in the trade network or the cost of obtaining the technology is important. In a third part, I estimate the accuracy of the
model's prediction with an empirical analysis.
The reminder of this paper is as follow. In Section 2, I present a System GMM
showing evidence of the inuence of the trade with central partner on growth
and on the diusion of technology. In Section 3, I revise the four strands of the
literature that my work will be based on: the endogenous growth literature, the
diusion of ideas or idea ow literature, the literature linking trade openness
and growth and network analysis. In Section 4, I develop a theoretical framework that include the role of the centrality of trade partners in the diusion of
technology. Section 5 presents the empirical estimation of the model. Section 6
concludes.
2
Motivation: the empirical importance of centrality on economic growth
In order to motivate the construction of the theoretical model I will begin by
presenting two sets of regressions on how the centrality of the trading partners
inuence the economic growth and the total factor productivity.
2.1 Whether trading partners centrality matter for
growth
In order to assess whether the centrality of trading partner matter for economic
growth I estimate the following regression specication:
yc,t − yc,t−1 = β0 + β1 Cc,t + β2 Altc,t + β3 T Oc,t + β4 HKc,t
+β5 yc,t−1 + µt + ηc + c,t
3
(1)
where yc,t is GDP per capita for country c at time t, Cc,t is the share of trade of
trade with most central partners, Altc,t share of trade with an alternative set of
countries, T Oc,t is trade openness, HKc,t is human capital, yc,t−1 is the initial
GDP, µt are (unobserved) time-specic eects, ηc are (unobserved) countryspecic eects, and c,t is the error term.
While the growth regression specications presented above poses some challenges for estimation, empirical papers in the growth literature have typically
used the system generalized method of moments (S-GMM) procedure developed, in Arellano and Bover (1995) and Blundell and Bond (1998) 1 . To assess
whether the centrality of the partners aect the trade-income nexus with an SGMM framework, I analyze an unbalanced panel dataset covering 122 countries.
Within each panel, the dataset includes at most 10 observations consisting of
non-overlapping 5-year averages spanning the 1960-2010 period2 .
In order to obtain the share of trade with most central partners, I use network
analysis and particularly the random walk betweenness centrality measure to
rank the most central countries in the global trade network. This measure
takes into account each country's share in world trade, their number of trading
partners, and the position of their partners in the global network. Based on this
ranking I construct a proxies to characterize the centrality of countries' trading
partners by using the share of trade with the top-3 most central countries in the
network 3 . I also constructed an analogous proxies to characterize countries'
composition of their main trading partners by the share of trade with its top3 trading partners. All these measures are time-varying variables and then
constructed for every 5-year window in my sample.
Table 1 reports the estimations associated with the share of trade with the
top-3 countries in the global trade network. To contrast the eect of trading
with these center countries with simply concentrated trading relations, I also
include in the regressions the countries' share of trade with their 3 main partners
. Column 1 of Table ?? reports the estimations associated with the share of
trade with the top-3 countries in the global trade network. To contrast the
eects of trading with these center countries with simply more concentrated
trading relations, the regressions also include an analogous proxy to capture
countries' share of trade with their main partners. The coecient on the share
of trade with the most central countries in the global trade network is positive
and statistically signicant, but that on the share of trade with a country's main
trading partners is actually negative and statistically signicant. The dierential
eect is economically large - about 0.7 percentage points. An increase of 10
1 See for example Dollar and Kraay (2004), Loayza et al. (2005), and Chang et al. (2009)
in the trade-growth literature, and Beck and Levine (2004), Beck et al. (2000), and Rajan
and Subramanian (2008) in the nance-growth literature. More details on the methodology
in Appendix A.1
2 More details on the data inA.2
3 robustness check for top-1 and top-5 partners are presented in annex
4
percentage points in the share of trade with the top-3 most central countries
is associated with an increase in growth rates of about 0.1 percentage points,
whereas a similar increase in the share of trade with the top-3 main partners
leads to a decline in growth rates of about 0.6 percentage points.
Column 2 and 3 of Table 1 report the results of the same regression with
alternative denition of the centrality measure, namely share of trade with top1 and top-5 most central countries. In those regressions, the regressions also
include trade with the main partner and the top-5 trade partners, respectively.
Again, the coecient associated with the share of trade with the most central
countries in the global trade network is positive and statistically signicant, but
that on the share of trade with a country's main trading partners is actually
negative and statistically signicant.
2.2 Whether trading partners centrality matter for tfp
growth
As for economic growth, I evaluate the eect of the centrality of the trade
partners on the TFP growth.
tf pc,t − tf pc,t−1 = β0 + β1 Cc,t + β2 Altc,t + β3 T Oc,t + β4 Pc,t + µt + ηc + c,t
where yc,t is GDP per capita for country c at time t, Cc,t is the share of trade of
trade with most central partners, Altc,t share of trade with an alternative set of
countries, T Oc,t is trade openness, HKc,t is human capital, Pc,t are the number
of patent applications of 100 millions workers, µt are (unobserved) time-specic
eects, ηc are (unobserved) country-specic eects, and c,t is the error term.
Unlike with GDP growth regression, data of TFP are not as widely available as
GDP. As a consequence, the number of observations do not allow to estimate
the equation with GMM methodology. I proposed a simple x-eect estimation
to get a sense of a clean correlation between the centrality of partners and the
total factor of productivity.
Table ?? reports the estimations associated with the share of trade with
the top-3 countries in the global trade network on the TFP growth estimates.
Column 1 reports the estimates associated with Equation 2. The coecient on
the share of trade with Top-3 most central countries in the trade network is
positive , while the share of trade with the 3 main partner is negative. Both
coecient are statistically signicant. The magnitude of the coecient is also
interesting. Without being able to refer to causality, an increase of 10 percentage
points in the share of trade with the most central countries is associated with
an increase in tfp growth of about 0.8 percentage points.
5
3
Litterature Review
Most of the cross-country income dierence is based on productivity dierence
(Hsieh and Klenow (2009)). Dierence in productivity across countries can be
analyze through two lenses: from a microeconomic point of view, rms have
large and persistent productivity which lead to an aggregate dierences at the
country level; from a macroeconomic point of view, global dierences across
countries lead to TFP dierences (such as dierences in institutions, in business
environment, in economic context, in education? ). While my work is based
on the second strand of the literature, let?s revise briey the arguments of the
micro-rm level literature.
A common element of the microeconomic literature is that the income dierence across countries is based on dierences of productivity across in rms that
may be explained by a suboptimal allocation of resources across rms (Hsieh
and Klenow (2009), Alfaro et al. (2008), and Midrigan and Xu (2010)). Based on
the idea that more productive rms are in theory larger than small ones (Melitz
(2003)), empirical literature has shown that it is not the case and the main
reason is the imperfect mobility of resources. Syverson (2004) demonstrates
this point by showing that biggest rms produce more with the same input,
and, comparing with the US, the ratio is worse in China and India. Bartelsman
et al. (2013) calculate covariance between eciency and labor allocation across
rm, and nds that the US are doing 50% better than in a random distribution
while some countries from Western Europe only 20%. One reason of this dierence may be explained by policy-induced distortion (argument also provided by
Banerjee and Duo (2005)).
Closer to my work, macroeconomic literature mainly explains the dierences
of productivity by a dierent access to technology (among mainly others Aghion
and Howitt (1992)). Two main reasons for that: rst, it is too costly for poor
country to access to the latest technology, and second even if they could access
it, poor countries may not have the suitable human capital (Banerjee and Duo
(2005)). My work is based on four strands of the economic literature: the
endogenous growth literature, the diusion of ideas or idea ow literature, the
literature linking trade openness and growth and network analysis.
One important strand of my work focuses on the endogenous mechanism of
generating long-term growth in the economy. In most endogenous growth theory
the source of growth is either knowledge spillovers that reduce the relative cost
of entry in an expanding varieties framework (Romer (1990)) or productivity
spillovers that allow entrants to improve the frontier technology in a quality
ladders framework (Aghion and Howitt (1992)).
Another important strand of this work focuses on the diusion of ideas and
technologies of production. The idea ow literature generally modeled the evolu6
tion of eciency to produce by the meeting of an agent with another agent with
higher productivity. Earlier papers on the diusion of ideas and technologies
modeled as a stochastic process can be found in Jovanovic and Rob (1989) and
Jovanovic and MacDonald (1994). In a closed economy model, Kortum (1997)
develops the process of diusion of ideas drawn from an exogenous distribution
of potential technologies. He obtains the 'technological frontier' which is the
most ecient process to produce a good at time t. The number of techniques
for producing good j discovered between time t and s has a Poisson distribution with parameter K(s) and K(t) and derived the stationary distribution of
productivities is Fréchet. At the dierence of my model, there is no long term
growth unless there is population growth and there is no insight from trade
partners. Alvarez et al. (2008) builds on Kortum (1997) a note paper focused
on diusion of technologies in an open economy. Technology of an economy is
described by a dierential equation: when a producer receives a cost idea better
than the one he is now producing they adopt it and this new cost becomes his
state. If he receives a higher cost idea, or no idea at all, his cost state remains
unchanged. The mathematics of diusion of ideas is similar to my framework.
It allows an endogenous growth process based on the research intensity parameter and the distribution of productivities across countries. Nevertheless, at the
dierence of their framework, arrival of ideas will not be fully stochastic.
A third strand of the literature that matters for my work is the one studding
the relationship between trade openness, growth and development. Keller (2004)
review this large literature that is on balance nding some positive spillover.
Comparative studies by Ben-David (1993), Sachs and Warner (1995), and Lucas
(2009) have documented the empirical connections between openness to trade
and growth rates. Coe and Helpman (1995) present a model that treat commercially oriented innovation eorts as a major engine of technological progress.
They nd that a country's total factor productivity depends not only on domestic RD capital but also on foreign RD capital. Coe et al. (1997) rene those
results nding that developing countries benet from developed countries' RD,
particularly from the United States. Developing countries can boost their productivity by importing a larger variety of intermediate products and capital
equipment embodying foreign knowledge, and by acquiring useful information
that would otherwise be costly to obtain. Acharya and Keller (2009) shows that
the productivity impact of international technology transfer often exceeds that
of domestic technological change, more so in high-technology industries. From
a more theoretical point of view, multiples papers from Helpman and Grossman
on the subject are a fundamental basis. In particular, Helpman and Grossman
(1991) models in a small open economy framework, researchers that develop
new varieties of intermediate inputs. Technology is transferred from the rest
of the world as an external eect. Nevertheless, at the dierence of my model,
the pace of technology transfer is assumed to be proportional to the volume of
trade. I add the inuence centrality of the country.
7
At the intersection of these three strands of the literature, four papers are
particularly close to my work. Eaton and Kortum (2002) and Alvarez and Lucas (2007) are two model based on a perfectly competitive Ricardian model of
international trade. In Eaton and Kortum (2002), insights are drawn from the
distribution of potential producers in each country according to exogenous diffusion rates which are estimated to be country-pair specic, although countries
are assumed to be in autarky otherwise. Therefore changes in trade costs do
not aect the diusion of ideas. Alvarez and Lucas (2007) expands this model
to establish the existence and uniqueness of an equilibrium with balanced trade.
Those two models are nevertheless integrating only static eects. Alvarez et al.
(2013) is based on Eaton and Kortum (2002) and Alvarez and Lucas (2007)
where freerer trade replaces inecient domestic producers with more ecient
foreign producers. They add a theory of endogenous growth in which people
get new, production-related ideas by learning from the people they do business
with or compete with. Trade has then a selection eect of putting domestic
producers in contact with the most ecient (respect to trade cost) foreign and
domestic producers. They use a continuous arrival of ideas (not Poisson, which
is more traditional). More advanced technologies used for one good are adapt to
other ones. One particularly interesting result is the fact that long term growth
depend on the search of new ideas eorts and the concentration of high productivities in the economy. Buera and Obereld (2014) allow for a more general
distribution of productivities. Diusion of ideas across countries in which the
distribution of productivities in each country is Fréchet, and where the evolution
of the scale parameter of the Fréchet distribution in each country is governed
by a system of dierential equations.
The main innovation of this paper is to add to this framework notions of
centrality of the trade partners. The fourth strand this paper relies on is
then network analysis. In this paper, I will use theoretical as well as empirical
inputs from network analysis literature. Jackson (2008) oers a comprehensive
introduction to network concepts. Newman (2010) has an important discussion
on measurement and modelisation of network, as well as important insights on
how to resolve dynamic systems on networks. The importance of the network in
theoretical economics has been traditionally seen through the lense of spillover
and contagion of shocks. Typically, the most central countries have a bigger
propenstion to diuse shocks, as Newman (2010) and Easley and Kleinberg
(2010) shows it in a model inspired by epidemics/ contagion diseases models.
Later I will talk about centrality measure in a the trade network. Borgatti et al.
(2013) consider direct and indirect centrality measures. They nd an increasing
inuence of Asian countries in the trade network but when the data is weighted,
the US and Europe remain the more central.
8
4
Model
My theoretical framework is based on work is based on Alvarez et al. (2013)
and Buera and Obereld (2014). Section 4.1 gives the main equations of those
models; section 4.2 brings the innovation
4.1 Framework
4.1.1 in a closed economy
Consumers have identical preferences over a [0, 1] continuum of goods. I use
c(s) to denote the consumption of an agent of each of the s ∈ [0, 1] goods for
hR
iη/(η−1)
1
each period t. The period t utility function is C = 0 c(s)1−1/η ds
so
goods enter in a symmetrical and exchangeable way. Each consumer is endowed
by one unit of labor which he supplies inelastically.
Each good s can be produced by many producers, each using the same laboronly linear function y(s) = l(s)z(s) where l(s) is the labor input and z(s) the
productivity associated with product s. All the producers of good s behave
competitively.
Using the symmetry of the utility function and the competitive framework,
I group the product by their productivity and write the time t utility Ct =
iη/(η−1)
hR
1−1/η
where c(z) is the consumption of any good s that
c(z)
dF
(z)
t
R+
has the productivity z and Ft (z) the CDF of distribution of productivity.
In a competitive equilibrium, the price of any good z will be p(z) = w/z and
i1/(1−η)
hR
Real per capital GDP equal
the price index p(t) = R+ p(z)1−η dFt (z)
R η−1
1/(1−η)
real wage, y(t) = w/p(t) = R z
dFt (z)
4.1.2 in an open economy
In this section I move from the autarky model to a world of n countries. I
use icebergs trade costs 4 and populations as given and construct a static trade
equilibrium under the assumption of continuous trade balance.
The model is an adaptation of Eaton and Kortum (2002) and builds on the
way Alvarez and Lucas (2007) builds the diusion of ideas. It is closely related to
Alvarez et al. (2013) and (Buera and Obereld, 2014). Each country under autarky is identical to the closed economy described in Section 4.1.1. I use the same
notation here, adding the country subscript i to the variables ci (s), zi (s), yi (s),
4 Trade
κij = κji .
cost between country i and j are assumed to be κij ≥ 1 and are symmetric so
Note that κii = 1
9
and li (s). I group goods s which have the same prole z = (z1 , ..., zn ) of productivities across the n countries; production technology for goods with productivity z is yi = zi li . I assume that
Qnproductivities are independently distributed
across countries, and let f (z) = n=1 fi (zi ) denote the joint density of productivities. With this notation I can write the period utility as 5
Z
n
Ci =
c(z)
1−1/η
η/(η−1)
f (z)dz
(2)
R+
where c(z) is the consumption of country i of goods that have the cost prole
z.
I use wi wage rates. Each good z = (z1 , ..., zn ) is available in i at the unit
wn κin
w1 κi1
, ...,
which replace both production and transportation costs.
price,
z1
zn
I solve for equilibrium prices,
given
wages. Let pi (z) be the prices paid for good
wj κij
z in i, so pi (z) = minj
since agent i buy the good at the lowest price.
zj
Given prices pi (z), the ideal price index is the minimum cost of providing one
unit of aggregate consumption Ci to buyers in i:
p1−η
i
=
n
X
j=1
(wj κij )
1−η
Z
∞
z
η−1
fj (z)
0
Y
k6=j
Fk
wk κik
z dz.
wj κij
(3)
The minimum cost of providing one unit of aggregate depends on the cost of
production (wages and iceberg cost) of j times the probability that j is providing
the product of productivity z at the lower cost (i.e. the probability that any
other k is producing it at a lower cost).
With the prices determined, given wages, I turn to the determination of equilibrium of wages. Consumption of good z in country i equals:
η
η
pi
pi
wi Li
ci (z) =
(4)
Ci =
pi (z)
pi (z)
pi
where the rst equality follows from individual maximization and the second
follows from the trade balance conditions pi Ci = wi Li .
4.2 Diusion of ideas and centrality of the partners
The main idea of this paper is that the diusion of what Alvarez et al. (2013)
calls 'productivity-related ideas' depends on the trade partner centrality in the
network, weighted by the share of trade with those partners.
5 Since the analysis is static, I temporarly supress the time subscripts. The implied dynamics will be studied in the next section.
10
4.2.1 Process of diusion of ideas
First, let's present the equation of diusion of ideas in an n-country economy
model. Each country i has a cdf of the productivity distribution Fi (., t) at date
t. Technological prole F = (F1 , ..., Fn ) is the function determining the state
variables of the economy. It evolves in function of the productivity distribution.
Fi (., t) is distributed Fréchet, a good way to model extreme event such as the
distribution of productivities. In equation:
Fi (z, t) = e−λi,t z
−θ
(5)
where λi,t is the state variable, country-specic and time-varying, and θ the parameter of concentration, constant across country and over time. As developed
in Eaton and Kortum (2002), λi,t can be interpreted as the eciency of each
countries; higher is λi,t , higher is the probability that country i will produce any
good s eciently. It refers to the traditional concept in the literature of absolute
advantage. θ is the variation across distribution of productivity z . It relates to
the heterogeneity across goods. Lower is θ, higher is the variability of goods in
terms of productivity. The potential eect of the comparative advantage against
trade cost is stronger.
In an open economy, the evolution of the state variable λi,t that determine the
evolution of the technological prole Fi,t in country i depends on the arrival of
new ideas from trade partners countries. The processus is as follow: producers in
i meets producers from other countries with a certain probability and without
any cost 6 . Producers in country i adopts the technology y of country j if
y > z . After such a meeting, all the producers of the same good in country i
use instantaneously the technology y . The cdf of the source of distribution of
country i is labeled Gi (., t).
d
lnFi,t (z) = δi,t ln Gi,t (y)
dt
(6)
.: with δi,t the capacity of country i to learn from other. By denition, the capacity of learning of a country grow over time following the following dierential
equation:
(7)
δi,t = δi (0) ∗ eρt
and Gi,t the foreign source of learning equals to:
Gi (z, t) =
n
X
Cj
j=1
| {z }
Proba of
learning from j
6 Similar
z
Z
|0
1−η
Y
wj κij
wk κik
η−1
y
Fk
y dy
Pi
wj κij
{z
} k6|=j
{z
}
Share of total import
of i from j
to a search and matching process.
11
Proba j exports to i
i.e. j lower cost provider
(8)
I am working on a
cleaner version where
the source
of learning
would be
Domestic +
Foreign
The source distribution of diusion of ideas for i is modeled in function of
the sells from the rest of the world to i. It is composed by, rst the centrality of country j , that will be discussed in the next section; multiplied by the
importance of country j in the basket of imports of country i for goods with
productivity y ; multiplied by the probability a producer j with a productivity
y exports to i while no other producers can lower the price.
4.2.2 Centrality of the partners as the probability of learning
The innovation of this paper resids in the reformulation of the parameter
of diusion of ideas. I believe this parameter is not constant as developed
in Alvarez et al. (2013) and Buera and Obereld (2014), but depends on the
centrality of the partners. The idea behind is that more a trade partner is
central to the trade network more she will be listened by its trade partners and
more she will be able to diuse ideas. The parameter of diusion of ideas should
not be understand as the probability of meeting between two producers but as
the probability of willingness to learn from a partner.
In network analysis, centrality refers to the importance of a node within a
network. In my context, nodes are countries, edges that connect countries in
the network reect the volume of trade ows between them, and paths are
a sequence of nodes and edges connecting two countries. The most simple
centrality measure in a network is the degree of the node, i.e. the number of
other countries to which one is connected to7 . In this context, I decided to use
a value of centrality that could be interpreted as the relevance of a country for
the trade network. Mathematically, the centrality of country j is dened as the
sum of the share of imports from j to all the other countries:
I dene the centrality as the Katz centrality of the adjacent matrix of share
of trade. Be the matrix of share of import of k :


π1,1 π1,2 · · · π1,j
π2,1 π2,2 · · · π2,j 


 ..
..
.. 
..
 .

.
.
.

πj,k = 
(9)
 πj,1 πj,2 · · · πj,k 


 .
..
.. 
..
 ..
.
.
. 
πJ,1 πJ,2 · · · πJ,K
I will use the Katz centrality8 to characterize the role in the trade network
of commercial partners. This measure of centrality allows to take into account
the weight of the direct connection of the countries (direct bilateral trade) but
also the connections of the trade partners it self. The Katz cenrality of country
7 Alternative (and perhaps more accurate) way to modelize centrality are developed in
Appendix B
8 More details on other measures of centrality in Appendix C
12
j is not only dependent of its commercial connection, but depends also ont the
centrality of the nodes it is connected to. The Katz centrality of a node j, also
called prestige, is based on eigenvalue centrality and is formally dened as:
X
Cj = α
πjk Ck
(10)
k
where πj k is the adjacency matrix of the trade network with eigenvalues α. α
controls the inuence of partners' centrality on country j centrality and should
be strictly inferior to λm ax−1 . The probability of learning depends then, among
other factors similar to (Buera and Obereld, 2014), on the centrality in the
trade network of trade partners.
4.2.3 Resolution of the dynamic of diusion of ideas
The state of technology in a country is then dened by:
Fi (z, t) = e−λi,t z
−θ
(11)
1−β β
Cj,t πi,j
λj,t
(12)
with
˙ =
λi,t
1−η
Γ 1−β− θ
δi,t η−1 Γ 1− θ
n
X
j=1
Details of the calculations are in the supplement of the appendix D.
In order to solve the model, let's rst work on de-trended equation by reρ
moving trends in the model. As λ grow asymptotically at the rate
, the
1−β
detrended equation of the distribution parameter Fréchet is λ̂ = λ/eρ/(1−β)t .
Also the de-trended dynamic of the parameter Fréchet is:
n
X
Γ 1 − β − 1−η
˙
1−β β
θ
ˆ
λi,t = δi,t (0)
Cj,t πi,j
λj,t −
η−1
Γ 1− θ
j=1
ρ
ˆ
1−β λi,t
(13)
˙
The de-trended stock of technology is the result of the equation λˆi,t = 0:
n
1−η
δi,t (0)(1 − β) Γ 1 − β − θ X
1−β β
ˆ
λi,t =
Cj,t πi,j
λj,t
(14)
ρ
Γ 1 − η−1
θ
j=1
I am going to evaluate the inuence of the centrality of trade partners respect
to the case in which all the countries are symmetric, their wages identical and to
simplify equal to 1, the cost to trade is null, kij = kii = 1. In that case, all the
13
obsolete - do
not include
β
countries have the same value of centrality constant over time Cj,t = Ck,t = c̄.
The de-trended stock of ideas is equal to:
λ̂ =
5
1−η
δi,t (0)(1 − β) Γ 1 − β − θ
ρ
Γ 1 − η−1
θ
!β−1 Estimation
Based on the methodology of Comin et al. (2012).
TBW
14
1 + (n − 1)c̄
n1−β
β−1
(15)
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17
Figure 1: Evolution of world trade
18
19
(b) 2012
Source: Pinat (2015) based on de la Torre et al. (2015) and WDI. Note: Each node represents a country, red nodes an OECD member in 1980, blue nodes
the rest of the world. Each link corresponds to an active trade connection between a pair of countries. Arrows at the end of each link capture the direction
of these connections. Trade connections are measured as the share of good exports of the source country. Only shares greater than 1 percent are reported.
Networks are drawn using the principal component layout.
(a) 1980
Figure 2: The rise of developing countries in the world trade
A
Appendix: Econometrics of the empirics
A.1 Methodology S-GMM
The S-GMM procedure estimates a system of equations that combines the regression specication in levels, as described above, and the same specication
in dierences9 . This method allows to deal with both the unobserved countryspecic eects in this dynamic setup and the potential biases arising from the
endogeneity of explanatory variables. Dierentiating the regressions allows us to
control for the unobserved country-specic eects. This creates the additional
problem that the error term of the dierentiated equation is correlated with
the lagged dependent variable. Taking advantage of the panel structure of the
dataset, the so-called internal instruments are then used to address this issue as
well as the potential endogeneity of the explanatory variables. More specically,
for the equation in levels, the instruments are given by the lagged dierences
of the explanatory variables, whereas for the equation in dierences, the instruments are lagged observations of both the explanatory and the dependent
variables.
It is worth pointing out that the set of instruments grows with the number of
explanatory variables and time periods. As the time dimension of my sample
size is rather limited, I use a restricted set of moment conditions in order to avoid
over-tting bias 10 . In particular, I use as internal instruments only the rst
appropriate lag of each time-varying explanatory variable. For the variables
measured as period averages, the instruments correspond to their average in
period t − 2; for the variables measured as initial values within a given period,
the instruments correspond to their observation at the start of period t − 1. In
the estimations of Equation ?? and ?? as well as in higher order, proxies for
the nature of trade connections are interacted one at a time in order to simplify
the interpretation of the results and not to overextend the number of required
instruments (and hence the number of estimated parameters)11 . Moreover, even
with this restricted set of instruments, there are some specications in which
the actual number of instruments is close to or even larger than the number of
countries in the sample. In this case, I use a more restricted sample of control
variables in order to reduce the number of explanatory variables, as suggested
by Roodman (2009).
This S-GMM procedure rely on four key assumptions: (i) the error term is not
serially correlated; (ii) shocks to growth are not predictable given the past values
9 I use the S-GMM instead of the dierence GMM estimator, which relies solely on the
dierence equation, because my explanatory variables are persistent over time and could thus
render my instruments weak. In addition, Bond et al. (2001) show that for relatively small
sample periods, S-GMM performs better than the dierence GMM.
10 See for example Roodman (2009).
11 I do not use instruments for the interacted terms as I already have instruments for each
individual term within an interaction. A similar approach has been followed by Chang et al.
(2009).
20
of the explanatory variables, (iii) the explanatory variables are uncorrelated
with future realizations of the error term; and (iv) the correlation between
the explanatory variables and the country-specic eects is constant over time.
Nonetheless, the method allows for current and future values of the explanatory
variables to be aected by growth shocks -it is exactly this type of endogeneity
that the method is designed to handle.
In addition, the consistency of the S-GMM estimates of the parameters of
interest and their asymptotic variance-covariance matrix depend on whether
lagged values of the explanatory variables are valid instruments in the growth
regression. I consider three specication tests to evaluate these potential issues.
First, I present the Hansen test of over-identifying restrictions on the full set
of instruments. This "Full Hansen" tests the validity of the instruments by
analyzing the sample analog of the moment conditions used in the estimation
process. Second, I also report the Hansen test of over-identifying restriction
on the additional instruments that are introduced in the levels equations. This
"Incremental Hansen" tests the stationarity assumption on which these instruments are based. And third, I test whether the error term is serially correlated
12
. In all three tests, failure to reject the null hypothesis validates the estimated
regression specication.
A.2 Data
To assess whether the centrality of the partners aect the trade-income nexus
with an S-GMM framework, I analyze an unbalanced panel dataset covering
122 countries -13 from North and Central America and the Caribbean, 11 from
South America, 31 from Europe, 32 from Africa, 11 from the Middle East and
Central Asia, 5 from Southeast Asia, 12 from East Asia, and 3 from the Pacic.
As robustness, I also considered a smaller (and perhaps more standard in the
literature) sample of 82 countries. Within each panel, the dataset includes at
most 10 observations consisting of non-overlapping 5-year averages spanning the
1960-2010 period.
As pointed out above, the dependent variable in my empirical analysis is the
average rate of growth in real per capita GDP within a 5-year period. One
of my variables of interest is the degree of trade openness, which is dened as
imports plus exports as a share of GDP, and is also measured as the average
over any given 5-year period. I explore a number of other explanatory variables. As is standard in the literature, I control for the initial condition in an
economy by including its GDP per capita at the beginning of each period as a
regressor. I also include the rate of secondary and tertiary school enrollment
12 In the S-GMM system specication, the test is whether the residual of the equation in
dierences is second-order serially correlated, which would indicate that the original error
term is serially correlated and follows a moving average process of at least order one. In this
case, it would reject the validity of the proposed set of instruments and would call for higher
order lags to be used as instruments.
21
of the active population at the beginning of the period to account for human
capital investment. As additional controls in the regressions, I have the number
of main telephone lines per capita as a proxy for the development of the public
infrastructure in each country and a country's terms of trade to proxy for relative price stability and exchange rate uctuations. Both variables are measured
as averages over 5-year periods.
Using network analysis, I rank the most central countries in the global network using the random walk betweenness centrality measure. This measure
takes into account each country's share in world trade, their number of trading
partners, and the position of their partners in the global network. Based on
this ranking I construct three dierent proxies to characterize the centrality of
countries' trading partners: (i) the total share of trade with the top-3 most central countries in the network; (ii) the total share of trade with the top-1 most
central country in the network (iii) the total share of trade with the top-5 most
central country in the network 13 . I also constructed three analogous proxies to
characterize countries' composition of their main trading partners: by the share
of trade with its top-3, top-1 and top-5 trading partners. All these measures
are time-varying variables, they are constructed for every 5-year window in my
sample.
13 Results
of (ii) and (iii) are presented in annex
22
Table 1: Inuence of the most central countries on economic growth
Initial GDP per capita
Labor Force education
Trade Openness
Sh. Trade w/ Top-3 countries
Sh. Trade w/ Top-3 most central countries
Sh. Trade w/ Top-1 countries
(1)
(2)
(3)
-2.008***
(0.100)
3.036***
(0.152)
0.570***
(0.115)
-0.528
(0.424)
1.870***
(3.222)
-1.954***
(0.084)
3.082***
(0.131)
0.440***
(0.118)
-2.298***
(0.096)
4.007***
(0.175)
0.264**
(0.116)
Sh. Trade w/ Top-1 most central countries
Sh. Trade w/ Top-5 countries
-1.039***
(0.059)
0.335***
(0.059)
Sh. Trade w/ Top-5 most central countries
Constant
5.554***
(1.685)
13.000***
(0.733)
-3.138***
(0.595)
4.591***
(0.268)
6.606***
(1.858)
Observations
873
873
873
# of countries
122
122
122
# of instruments (xtabond2)
109
109
109
Hansen J-test p-value
0.279
0.254
0.236
p-value of AR(2) statistic
0.443
0.406
0.496
Notes: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
The dependent variable is GDP per capita growth.
23
Table 2: Inuence of the Top-3 most central countries on the tfp
(1)
Labor Force education
Initial TFP
Patents
Trade Openness
Sh. Trade w/ Top-3 countries
Sh. Trade w/ Top-3 most central countries
Constant
0.234
(0.455)
-1.933***
(0.481)
0.080
(0.111)
0.392
(0.453)
-3.002***
(0.925)
2.439***
(0.454)
8.183**
(2.318)
Observations
369
Number of c1
99
R2
0.168
Notes: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
The dependent variable is TFP growth.
24
B
Appendix: Centrality
A natural next step to improve the measure of centrality Cj is the weight the
value of πij on how it is constructed by the importance of those countries in the
network.
The the weighted in-degree centrality is calculated as the sum of the rows
normalized by N countries of the share of import matrix:
Cj =
N
X
πjk
N
k
(16)
Betweenness centrality measures captures the extent to which a node lies on
paths between two other nodes. Nodes with high betweenness centrality have a
substantial inuence in the network as they 'control' the ow passing through
them. Betweenness centrality is typically measured as the ratio of shortest paths
between nodes pairs that pass through the node of interest. Mathematically,
the normalized betweenness for country j is dened as:
CjB =
Pj (i, k)/P (i, k)
(N − 1)(N − 2)/2
(17)
where P (i, k) is the number of path between i and k , Pj (i, k) the number of
path between i and k that go through j and N the total number of countries in
the network.
An interesting alternative in very dense network ( as it is the case for trade
network) is the Random-Walk Betweenness Centrality developed by Newman
(2005) and Fisher and Vega-Redondo (2006). In this variant, all the paths
from country i to county k are taken into account -not only the shortest one.
However, paths have dierent probabilities -typically, shorter paths and paths
with a high intensity of trade have a greater contribution to the betweenness
score of country j . Formally,
X j
rik
(18)
CjRW BC =
ik
j
where rik
is a combination of the number of times that the random walk from i to
k passes through j and the weight of each path, averaged over many repetitions
of the random walk. .
Another interesting measure is the prestige centrality, calculated as the Katz
centrality. Katz centrality generalizes the degree centrality, by counting number
the number of direct neighbor but also all other nodes in the network that
25
check the
algorithm
Brandes
connect to the node under consideration through these immediate neighbors.
Nodes are penalized by distance. Mathematically, it is dened as:
CjKatz =
∞ X
N
X
αk Akij
(19)
k=1 j=1
where αk is the attenuation factor of the distant nodes comprised in [0, 1].
Nevertheless, this measure cannot be
26
Supplement of Appendix: Development of equations
27
C
Appendix: from F to G
. A country i has a productivity z distributed Fréchet with parameters λi,t and
θ. Also,
Fi (z) = e−λi,t q
θ
(20)
Let the probability that country i can supply a good to country n at a price
lower or equal to p be:
(21)
P r(Pni ≤ p) = Gni (p)
At the equilibrium, the price equalize the cost of the product over the productivity:
p=
wi kni
q
(22)
Hence,
Gni (q) = 1 − Fi
wi kni
p
(23)
The price aggregate of country n is then:
pn = min{Pn1 , Pn2 , ..., PnN }
Y
P r(pn ≤ p) = 1 −
P r(Pni ≥ p)
i
=1−
Y
[1 − Gni (p)]
i
Y
wi κni
=1−
1 − (1 − Fi
p
i
=1−
Y
−λi,t
e
wi κni
p
!θ
i
=1−
Y
e−λi,t Φn p
θ
i
= Gn (p)
The share of expenditure of a country i in n's country budget expenditure:
Z ∞
(wj κi,j )1−η q η−1
πij =
dFi j(q)
Pi1−η
0
λj (wj κij )−θ
=P
−θ
k λk (wk κik )
28
supplement
must be updated with
addition of β
D
Appendix:
Resolution of the dynamic equa-
tion
Let's begin with the probability of diusion
1−η
Z z
n
Y
X
wk κik
wj κij
η−1
y
Fk
Gi (z, t) =
y dy
Cj
Pi
wj κij
0
j=1
(24)
k6=j
By simplicity, let's dene the probability j is the lower cost provider for i:
Y
wk κik
S ij (y) = Fk
y dy
(25)
wj κij
k6=j
D.1 Determination of the share of trade
Z
∞
πij =
0
1−η
(wij κij )
y η−1
dS ij (y)
1−η
Pi
(26)
To be developed
D.2 Determination of the Price
P i1−η =
X
(wj κij )
1−η
0
j
=
X
∞
Z
(wj κij )
1−η
y η−1 dS ij (y)
∞
Z
−1
y (η−1) e−πij
λj y −θ
λj y −θ−1 θdy
0
j
−1
Let's make the following change variable x = πij
λj y −θ
=
X
1−η
(wj κij )
1−η η−1
πij θ λ θ
Z
X
x−
η−1
θ e−x dx
0
j
=
∞
η−1 η−1 − θ
λ θ Γ 1
(wj κij )1−η πij
−
j
η−1
θ
Using the denition of πij in Equation26
=
X
λj (wj κij )
1−η P
(wj κij )
j
P i1−η =
X
η−1
− θ
k (wk κi k)
λj (wj κi j)
η−1 η−1
θ λ θ Γ
j
29
η−1
λ θ Γ
1−
η−1
1−
θ
η−1
θ
(27)
D.3 Determination of the diusion of ideas
The source distribution is given by the expenditure weighted distribution of
productivity of sellers
Gi (y, t) =
n
X
Cj
j=1
wj κij
Pi
1−η Z
y
0
y η−1 dS ij (y)
and me want to represent the dynamic of the state variable λ
Z ∞
˙
λi,t =
y θ dGi (y, t)
0
Let's develop this expression:
Z
∞
θ
y dGi (y, t) =
0
n
X
Cj
j=1
=
=
n
X
j=1
n
X
Cj
Cj
j=1
wj κij
Pi
1−η Z
wj κij
Pi
1−η Z
wj κij
Pi
1−η Z
∞
0
∞
y θ dS ij (y)
−
P
yθ e
k
wk κik
y
wj κij
λk
!−θ
λj θy −θ−1 dy
0
∞
−1
y θ e−πij
λj y −θ
λj θy −θ−1 dy
0
−1
Let's make the following change variable x = πij
λj y −θ
=
n
X
Cj
j=1
=
=
n
X
j=1
n
X
j=1
Cj
Cj
wj κij
Pi
1−η Z
wj κij
Pi
1−η
wj κij
Pi
1−η
∞
y θ e−x λj θy −θ−1 dy
0
1−η η−1
πij θ λj θ
Z
∞
x
1−η
θ −1 e−x dx
0
1−η η−1 1
πij θ λj θ Γ
30
−η
θ
Including the price equation obtained in Equation 27
Pn
=
P
j
1−η
j=1 Cj (wj κij )
η−1 η−1
λj (wj κij ) θ λ θ Γ 1 −
1−η
η−1
θ
1−η
Γ
n
X
θ
=
Cj λj η−1
j=1
Γ 1−
θ
1−η
Γ
n
n X
n
X
πkj X
θ
=
λj η−1
N j=1
j=1 k=1
Γ 1−
θ
31
η−1 θ Γ 1
πij θ λj
−η
θ