Interconnections of the Industries in the
Economy: a Network Approach
Evgeniya Goryacheva a,∗
a Economics Discipline Group, Business School, University of Technology Sydney,
Australia
Abstract
This paper uses a network approach to investigate the interrelation between industries in the economy. I consider the economy as a network of
the industries connected with each other through the product flows. I propose dynamic directed weighted network formation model. According to
the model industry’s position in a network and productivity level affect its
probability of a new link adoption. I apply a empirical methodology to
the data obtained from the input-output tables in order to identify the key
factors affecting the changes of the technological network.
Keywords: Network; Input-Output Analysis; Intersectoral Linkages.
∗
E-mail:
[email protected].
1
1
Introduction
I use a network approach to describe U.S. economy. I build a network using U.S.
input-output tables. Observing the U.S. input-output tables in different years, we
can conclude that this network is not stable. The product flows and inputs’ shares
are changing over time. New links are created between industries, some old links
disappear, and the weights of the links are also changing over time. The main
research question of this paper is how the industries’ network changes over time.
Which factors affect the network formation process?
I propose the rules of the industries’ network evolution that have economic
interpretation and test their validity empirically. One of these rules is that industries’ positions in a network are closely related to economies of scale. Industries
with high centrality have many consumers. They have cost advantages compared
to other industries, because their fixed costs are spread out over more product
flows. Lower costs lead to the lower prices of the outputs, this attracts new consumers and also increases existing product flows. As a result, these industries
become even more influential over time.
Obtained empirical results support this idea. The U.S. panel data estimation shows that the industry’s eigenvector centrality affects its probability of a new
link creation and its share in intermediate inputs of other connected industries.
I propose the hypothesis that the industry’s productivity influences the
industry’s position in the network. The network evolves in the following way. More
productive industries have low costs and as a result low prices of their outputs.
Many other industries adopt these industries as suppliers for this reason. At the
same time industries increase the product flows from the productive industries
because of the low costs. This makes productive industries more influential over
time. I test this hypothesis using empirical data and obtained results show that
more productive industries become more central over time.
The growth of the industry’s productivity also increases the industry’s
indegree in the period between 1972 and 1992. Because of the competition, industries try to improve their products. As a result innovations lead to the changes in
their production functions and to the adoption of new suppliers. For example, at
some point the car manufacturing industry started using plastic instead of steel
for some car parts. The car manufacturing adopted plastic manufacturing as its
new supplier because of the technological innovation.
I propose a dynamic weighted network formation model which is a modification of the model introduced in Barrat, Barth´elemy, and Vespignani (2004a).
This model captures above evolution rules and leads to the power-law distribution
2
of the industries’ weighted outdegree.
It is important to investigate the process of the network formation, because the structure of the network affects stability of the whole system. As was
shown in Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012), weighted outdegree of the U.S. industries have a power-law distribution.12 This means that
even small shocks can lead to the large system volatility.
The structure of the network can help predict how shocks will propagate in
the economy. Many models try to predict the shocks’ propagation in the network.
It is worth mentioning that the input-output analysis was popular for
investigating effects of different kinds of shocks on the economy in the previous
century. The main advantage of the input-output analysis is its simplicity. It is a
clear mathematical procedure to calculate multipliers and then to use them to get
an impact of the change in one industry on the economic activity of another industry. But at the same time there is a limitation of this approach, because it is valid
only for short-term prediction. Because it makes prediction under an assumption
that the network is static, which is not true in the long run. Many models that use
a network approach to describe shocks’ propagation in the economy also assume
that industries’ network is fixed.
In reality, the structure of the network is changing over time, and if these
changes are large the models with network stability assumption can not be used for
long-term predictions. In this case it is necessary to take into account the evolution
of the network’s structure; otherwise, the prediction of the shocks’ influence on
the economy would be incorrect. Therefore I investigate how industries’ network
is changing over time and what causes these changes.
Using data of the U.S. input-output tables I build a network, where nodes
are industries and links represent product flows between them. Each industry uses
a part of other industries’ outputs as inputs for its own production. The weights
of the links represent the size of the product flows.
For example, the aircraft manufacturing industry uses inputs from different industries: rubber, iron and steel, electronics, metalworking machinery, space
vehicles, motor vehicle parts manufacturing industries. At the same time some of
these industries such as electronics, metalworking machinery, space vehicles and
motor vehicle parts manufacturing industries also use part of the output produced
by the aircraft manufacturing as inputs in their production. This interconnection
ck− β , where P (k)
- the empirical counter-cumulative distribution function, k - a weighted outdegree, c, β - the
constants and β > 1.
2Industry’s weighted outdegree is a sum of the industry’s shares in intermediate inputs of
other industries.
1The network has a power-law weighted outdegree distribution if P (k) ∼
3
Figure 1: Industries-suppliers and industries-consumers of the aircraft manufacturing industry
is illustrated in Figure 1.
Figure 2 illustrates the U.S. economy in 2014 as a network. This directed
graph includes the most important links (with large product flows) between aggregated sectors. The size of the node reflects the importance of the industry’s
position in the network. The sectors with a higher eigenvector centrality have a
larger size of the nodes that represent them.
In reality this network is not fixed over time. Industries start to use inputs
from new industries-suppliers, while some industries may lose their industriesconsumers. These changes can be described as new links’ adoption and links’
destruction in the network. At the same time the size of the product flows between
industries is also changing, which again can be described as a change of the links’
weights in the network. I describe the rules of the industries’ network evolution
and their economic interpretation.
4
Figure 2: Aggregated Input-Output Network of the U.S. industries in 2014
5
1.1
Related literature
This paper relates to the two branches of literature, namely, the network formation
models and work that combines the network approach and input-output tables.
Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) relate the idea
of the effect of the power-law distribution on the aggregate fluctuations in a system with a network approach. They show that if nodes’ degrees in a network
have a power-law distribution then a small idiosyncratic shock can create a large
system volatility. This means that the structure of the industries’ network influences aggregate fluctuations. In asymmetric system, where intersectoral linkages
are not uniformly distributed the rate at which aggregate volatility decays is quite
low. Using the U.S. input-output tables they show that the weighted outdegree
of the industries follow the power-law distribution. For this reason I propose theoretical model with evolution rule that leads to the power-law weighted outdegree
distribution.
The networks in which degrees of the nodes behave as a power-law are
called scale-free networks. There are theoretical models of the network formation
that explain how a scale-free network may occur. All of them are based on a
preferential attachment mechanism, which I also use in my model. According to
this mechanism the probability that existing node will be connected to a new node
is proportional to a number of its links. Nodes with many connections become
even more influential over time. The first such model was introduced in Baraba´si
and Albert (1999).
A further extension of this original model is a fitness model introduced
in Bianconi and Baraba´si (2001). Fitness network formation model uses the same
preferential attachment mechanism, but also includes a node-specific parameter
that affects the probability of adoption. I also include a industry-specific parameter related to industry’s productivity level.
Barrat, Barth´elemy, and Vespignani (2004b) build a undirected weighted
network formation model that considers the basic evolution of the system as driven
by the weight properties of the links and nodes. They allow a dynamical evolution
of weights during the growth of the system. A new link creation affects the weights
of existing links. I use their model as a basis for my model and modify it to consider
a directed weighted network formation process.
Atalay, Hortacsu, Roberts, and Syverson (2011) use a scale-free framework
to model indegree distribution of the connected firms in an economy. According
to this model, firms are born, create links with each other and die with certain
probability. Using the U.S. firm level data they estimated parameters of the model.
Their model is close to my model, but the main difference is that they consider
6
unweighted network’s evolution, while I focus on weighted network’s formation
process.
There is some recent literature that also considers the input-output tables
of the industries as networks. For example, Fadinger, Ghiglino, Teteryatnikova,
et al. (2015) build a multi-sector general equilibrium model with IO linkages,
sector-specific productivities and tax rates. Using a statistical approach they show
that an aggregated income depends on the distribution of IO multipliers, sectoral
productivities and sectoral tax rates. They also find the difference in distributions
of IO multipliers for rich and poor countries. Rich countries have more sectors
with intermediate multipliers, while poor countries have many sectors with low
multipliers and just a few sectors with high multipliers.
Magalha˜es, Oso´rio, and Ant´onio (2016) use the U.S. input-output tables
to study the influence of the changes in the inter-sector network structure on
the process of technology adoption. According to the obtained results there are
global (but not local) network structure effects in the intensity of the technology
adoption.
Acemoglu, Akcigit, and Kerr (2015) build a model of the shocks’ propagation through an input-output network under an assumption that this network
is fixed. They show that in the economy with the Cobb-Douglas production function and perfect competition supply-side shocks (productivity shocks) propagate
downstream and affect the consumers but not the suppliers. Demand-side shocks
propagate upstream and affect only industry’s suppliers, but not the consumers.
They assume that the inputs’ shares are stable over time and only industries’ outputs are changed. I argue that productivity shocks also propagate through the
system by creating new links.
The empirical literature that considers the factors that affect the network
formation process is very poor. Carvalho and Voigtla¨nder (2014) use the dynamic
network formation model described in Jackson and Rogers (2007) as a base for
the hypotheses. According to the model each new firm in first period randomly
chooses its suppliers, but in the next period it forms the links with the suppliers
of its suppliers. Using the U.S. input-output data for the period 1967-2002 they
show that a technological distance between industries affects the probability of
a new link creation between them. My paper is closely related to this paper. I
use the same data, but test a different hypotheses. I test whether the industry’s
position in the network affects its probability of new link adoption and weights of
the links to the other connected industries.
7
Figure 3: The U.S. industries’ indegree and outdegree in different years
Number of industries
150
1972
1977
1982
1987
1992
100
50
0
0
50
100
150
200
250
Outdegree
300
350
400
450
Number of industries
40
1972
1977
1982
1987
1992
30
20
10
0
20
40
60
80
100
120
Indegree
140
160
180
200
Number of industries
60
1997
2002
2007
40
20
0
0
50
100
150
200
250
300
350
Outdegree
Number of industries
30
1997
2002
2007
20
10
0
80
100
120
140
Indegree
8
160
180
200
Table 1: Data on the numbers of formed and disappeared links in the U.S. industries’ network
Y ear
Number of new links
Number of disappeared links
1977
1982
1987
1992
5896
5459
2614
2987
4123
3387
4162
7649
Number of industries
318
318
2002
2007
6108
1746
6487
2376
Number of industries
219
219
1.2
Empirical observations
The network of the U.S. industries is changing over time. In each period some
new links are formed, while others disappear. Table 1 provides data on changes
in numbers of formed and disappeared links in the U.S. industries’ network. In
some years the number of new links is greater than the number of the disappeared
links, in other years it is right the opposite. The size of the gap between these two
numbers is changing over time.
I consider two periods from 1972 to 1992 and from 1997 to 2007 separately, because there were two different industries’ classifications during these
periods (SIC and NAICS). These classifications differ in the levels of aggregation;
therefore, they have different numbers of manufacturing industries for these two
periods.
The number of new links halved in both 1987 and 1992 compared to 1977
and 1982 respectively. There was a large drop in the number of new links between
2002 and 2007, this number decreased threefold.
One may think that these changes in the number of new links are related
to the fact that industries buy some inputs every few years. For example, an
airline does not buy new airplanes every year. However, we consider the links not
between the firms but between the industries. Each industry consists of many
9
firms and all these firms buy their inputs in different periods. Therefore, it is
unlikely that no firm buys the input from the regular industry-supplier. Let’s
consider the same example of the aircraft manufacturing and airlines. There are
more than 120 airlines in the U.S. and at least one of them buys a new airplane
every year.
Table 2 provides data on an average indegree, outdegree and weighted
outdegree of the U.S. industries in different years. An average indegree shows
an average number of suppliers that the U.S. industries have. An average outdegree is an average number of industries-consumers that industry has. An average
weighted outdegree is an average sum of the industry’s shares in intermediate
inputs of other industries.
Figure 3 illustrates the outdegree and indegree of the U.S. industries in
different years. Most of the U.S. industries have a low outdegree. The mode for
the indegree is always higher than for the outdegree. This means that there is a
small number of industries that have many consumers. I define these industries as
”universal” suppliers, because they provide inputs to many other industries. The
indegree and outdegree distributions are changing each year. These changes are
related to differences in the numbers of formed and disappeared links in each year.
Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) using the U.S.
data showed that the industries’ weighted outdegrees have a power-law distribution
and got an estimation of the power. Figure 4 illustrates the empirical distribution
function of the weighted outdegree.
The U.S. industries’ network is not fixed and it is constantly changing.
Moreover, the structure of the network demonstrates the power-law properties. I
propose a model that can properly describe the evolution of the industries’ network
below.
2 Theoretical framework
I propose the model of the weighted network formation that is a modification of
the model introduced in Barrat, Barth´elemy, and Vespignani (2004a). The main
difference between their model and my model is that I consider a directed network,
while they consider an undirected network.
First I introduce notation.
wij - weight of the link between industry i and industry j, an amount of
industry i’s output used by industry j in its production.
ki - an industry i’s outdegree, number of its industries-consumers.
The weighted outdegree of the industry i shows the amount of the industry
10
Table 2: The average indegree, outdegree and weighted outdegree of the U.S.
industries
Y ear
Average
indegree
Average
outdegree
Average
weighted outdegree
1972
1977
1982
1987
1992
97.7
104.3
112.6
106
89.2
80.2
87.6
94
89.9
73
0.63
0.63
0.59
0.58
0.58
Number of industries
318
318
318
1997
2002
2007
137.6
132.8
131.4
110.1
105.6
101.4
0.55
0.61
0.68
Number of industries
219
219
219
i’s output which is used as an intermediate input by other industries:
si =
,
wij
(1)
j
An initial network consists of N0 industries connected by links with weights
w0. In each period of time a new industry t is born and it creates m links.
The industry i is chosen as a supplier by a new industry with probability
sis . The probability of adoption as a supplier depends on the industry’s weighted
j
j
outdegree. I define industries with many consumers (with a high weighted outdegree) as the ”universal” industries, which means that they have a high probability
to be adopted by new industries in the future. The weight of each new link is w0.
The new link adoption changes the weights of other links in the following
way. Suppose that an industry t adopts an industry i as a new supplier, then
weights of the links for industry i’s suppliers increase in the following way:
wki → wki + ∆wki,
11
(2)
Figure 4: Empirical counter-cumulative distribution function of the U.S. industries’ weighted outdegree
Source: Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012)
∆wki = δk
wki
,
si
(3)
where δk - a productivity level of the industry k. We assume that δk is an independent random variable taken from a given distribution ρ(δ). A higher level of
productivity induces a higher weight growth. Because a high productivity level
leads to a low price of the output.
At the same time the weights of the links for industry i’s consumers increase in the following way:
wik → wik + ∆wik,
∆wik = δi
wik
si
(4)
(5)
As a result we get the following evolution equation for the industry i’s
weighted outdegree:
dsi = m(w + δ ) si (t) + , mδ sk (t) wik (t)
i ), s (t)
i ), s (t) s (t)
0
k
j j
j j
k∈ V
dt
(6)
(i)
The first term shows the case when industry i is chosen as a new supplier with
some probability, which changes its outdegree by 1 and its weighted outdegree
by (w0 + δi). Further we set w0 = 1. The second term shows how the weighted
outdegree may change if the industry i’s consumer was adopted as a new supplier.
12
Where V (i) is a set of industry i’s consumers.
The evolution equation for industry i’s outdegree is as follows:
si (t)
dki
= m ),
dt
sj (t)
(7)
j
In comparison with the usual degree preferential attachment models nodes
connect more likely to the nodes with the higher weighted outdegree.
),
1
Each new link from industry i to industry t increases j sj by (1+δi +δi ),
),
1
where δi = k∈
δk wskit , H(i) - set of industry i’s suppliers. On the average the
H(i)
total weighted outdegree is increasing in the following way:
t
,
1
where δ is a solution of
[
si(t) c:: m(1 + δ )t,
1
(8)
i=1
dδρ(δ)
= 1 (we assume that ρ(δ) is bounded).
Using the fact, that
k∈ V (i) δiwik = δisi and Eq.(8), I obtain the following
expressions for Eqs.(6) and (7):
(δ1),
− 2δ)
(1 + 2δi)si(t)
dsi
=
,
dt
(1 + δ1 )t
si (t)
dki
=
dt
(1 + δ1 )t
(9)
Using initial conditions ki(t = i) = si(t = i) = m I solve these differential equations:
t
1+2δi
1
1+δ
si(t) = m( )
i
,
ki(t) = si(t) + 2δim
(1 + 2δi)
(10)
(11)
According to Eq.(10) a productivity level of an industry increases its weighted
outdegree, that in turn increases the industry’s adoption probability.
The weighted outdegree of the industry and the number of its consumers
are proportional, with a coefficient depending on δi:
si(t) = (1 + 2δi)ki(t) − 2δim
(12)
The generated networks display power-law behavior for the weight, degree, and weighted outdegree distributions. The obtained results suggest that the
inclusion of weights in the networks modeling naturally explains the diversity of
13
power-law distributions empirically observed in real industries’ networks.
3 Hypotheses
Hypothesis 1. More productive industries become more central over time. The
logic of this hypothesis comes from the following reasoning. The industries that
experience growth in their productivity have a lower cost and can be adopted as
suppliers by new industries. A creation of new links makes these industries more
influential. Productivity shock shifts the industry’s supply curve, which leads to
a decrease in equilibrium price and to an increase in equilibrium quantity. This
increase in quantity may occur due to the growth of the existing product flows
and by attracting new consumers.
Hypothesis 2. The higher the industry’s centrality the higher the probability of a new link adoption is. More influential industries have a higher chance to
grow further, because they have more contracts with different industries, through
which they may find new suppliers and consumers. Additionally, industries with
high centrality supply big product flows to many other industries. Their costs per
unit of output decrease with increasing outgoing product flows. This leads to the
lower prices of their outputs. These industries become more attractive suppliers,
which increases their chance of finding a new industry-consumer.
Hypothesis 3. The centrality of the industry increases its product flows
to other industries (the weights of the links). Economies of scale and low prices
of the industries with high centrality may also lead to increased product flows to
existing industries-consumers.
4 Data
I use the panel data of the U.S. 5-year period annual input-output benchmark
tables for 1972-2007 provided by the Bureau of Economic Analysis. The Use table
shows the inputs to industry production and the amounts that are consumed
by final users. The Industry-by-Industry Total Requirements Tables show the
production that is required from each industry to deliver a dollar of output to
final users.
I derived the Direct Requirements tables (DR) from the Total Requirements tables (TR) using the following formula:
DR = (TR − I) ∗ TR − 1
14
(13)
The Direct Requirements table shows the amount of a commodity that is
required by an industry to produce a dollar of the industry’s output.
To get the matrices with shares of the intermediate inputs (W), I divided
each element of the matrix DR by the appropriate column sum.
I also use the NBER-CES Manufacturing Industry Database, which provides information on the manufacturing industries’ total factor productivity (TFP)
and total employment.
I use a matrix W , where wij - a share of the industry i’s input in a
total intermediate input of the industry j. And from the matrix W I derived an
”indicator” matrix A, where each element is determined as follows:
Aij,t =
1,
if wij,t > 0 and wij,t− 5 =
0,
otherwise
0
(14)
Final uses growth rate for each industry is determined as follows:
∆i,t =
Di,t − Di,t− 1
,
Di,t−
(15)
1
where ∆i,t - industry i’s final uses growth rate, Di,t - industry i’s final uses in
period t.
A technological distance between industries i and j in defined in the following way:
dij =
1
w ij
(16)
The higher the weight of industry i’s input in intermediate input of industry j, the shorter technological distance between these two industries is. If
industries i and j are connected indirectly through other industries, then the
technological distance is a minimal sum of the distances between all nodes on
the path. To calculate technological distances between industries I use Dijkstra’s
shortest path algorithm for the weighted graphs.
I consider two datasets for 1972-1992 (Panel 1) and for 1997-2007 (Panel
2) separately, because of a significant change in classification (from SIC to NAICS)
in 1997. There are some changes in classifications even within these two periods.
I transform all the matrices to the unified versions of classification for these two
periods.
Centrality measures identify the most important nodes within graph. The
simplest centrality measure is a degree centrality. Because I work with the directed
15
graph I derive both an indegree and an outdegree centrality for each industry by
16
using the Direct requirement matrix W . An indegree is a number of links directed
to the node and an outdegree is a number of links that originate from the node.
The degree centrality counts every link a node receives equally. But not
all of the links are equivalent, some of them represent large product flows between
industries, other represent small flows.
I also use an extended version of the degree centrality, an eigenvector
centrality. This centrality measure also takes into consideration an importance
of the other nodes linked to the node. The main difference between the degree
centrality and the eigenvector centrality is that a node with a high degree centrality
does not necessarily have a high eigenvector centrality. Because it can be linked
to many nodes, but all of them are not so important. Reverse is also true, a node
with high eigenvector centrality is not necessarily highly linked.
To provide an example I consider centrality measures for the U.S. industries in 2007. The computer terminals manufacturing has a relatively low degree
but a very high eigenvector centrality. Which means this industry does not have
so many consumers, but it is an important supplier for influential industries such
as the telephone apparatus manufacturing, the semiconductor and related device
manufacturing. These industries also have important positions in the network
according to the eigenvector centrality.
An example for the second case is the plastics packaging materials manufacturing. It has a high degree, but a low eigenvector centrality. Many other
industries use product of this industry as inputs, but these inputs do not play
important roles in the production process of the industries.
I derive a eigenvector centrality from the Direct requirements coefficients
matrix W . The eigenvector centrality of a node i is determined as follows:
Cent =
i
1,
λ
wij Centj
(17)
j
Or in matrix form:
λCent = CentW,
(18)
where Cent - an eigenvector of the matrix W related to the largest eigenvalue
λ /= 0.
A higher centrality measure means that an industry has more connections
with other industries. A possible explanation of the outdegree measure’s influence
on a probability of a link creation is that if an outdegree of an industry is high
enough, then it is an evidence that this industry is an universal supplier to other
industries. This means that there is a high probability that new industries will
also choose this industry as their supplier. The second centrality measure is the
17
eigenvector centrality that takes into account not only links that an industry sends
but also receiving industries, which captures the whole spread of information about
this industry.
5
Methodology
To test Hypothesis 1 and to check whether the productivity level of the industry
affects its centrality in the future I use U.S. industries’ panel data to estimate the
following equation:
Vi,t = αi + β1Vi,t− 1 + β2∆TFP i,t− 1 + ui,t,
(1)
where Vi,t - different centrality measures (indegree, outdegree, eigenvector centrality) for the industry i in period t and ∆TFP i,t− 1 - a lag of the industry
i’s productivity growth rate. I use different centrality measures, because the
produc- tivity growth may affect in several ways. More productive industries
may have more consumers over time, because the cost of their outputs
decreases. Then I expect a positive and significant coefficient in a regression
where the dependent variable is outdegree. At the same time, an industry that
experience its productiv- ity growth may introduce some innovations. And for a
future development of these innovations it needs new materials and it will start
adopting new suppliers for this reason. Then I can also expect a positive and
significant coefficient in a regression with indegree. While the eigenvector
centrality may capture both of these effects and also an increase of product flows
of the more productive industries.
To test Hypotheses 2 and to verify whether the industry’s centrality and
growth in final uses affect the industry’s probability of a link creation I use the
following fixed effect panel data linear probability model:
Aij,t = αij + β1Centi,t− 5 + β2Centj,t− 5 + β3Empi,t + β4Empj,t + β5∆TFP i,t− 1
+β6 ∆TFP j,t− 1 + β7Distanceij,t− 5 + β8∆FUsei,t− 5 + β9∆FUsej,t− 5 + uij,t, (2)
where Aij,t is a dummy variable, which is equal to 100, if a new link between industries i and j was formed in period t and 0 otherwise; Centi,t− 5 is a 5-years lag of
the industry i’s eigenvector centrality; Empi,t is the industry i’s total employment
in period t in 1000s; ∆F inalU sei,t− 5 is a 5-years lag of the industry i’s growth in
final uses; Distanceij,t− 5 is a 5-years lag of technological distance between industries i and j; ∆T F Pi,t− 1 is a one-year lag of the industry i’s productivity growth
rate; uij,t is an error term.
Similar equation is used in Carvalho and Voigtla¨nder (2014). But they do
not include industries’ centralities, which is important for testing my hypothesis.
18
I use the total employment variable to control for the size of the industries.
Larger industries may have more suppliers and consumers and more possibilities
to create new links. I also include lags of ∆TFP to control for productivity levels.
The estimated coefficients β1 and β2 will clarify how centrality measures
of both industries affect the probability of new link creation between them. Additionally, I include lags for the growth of final uses and expect coefficients β8 and
β9 to be positive and significant. An increase in final uses of one industry may
affect the process of its link creation. For example, if in one industry final uses
are growing then it may attract new suppliers, because now it has a higher ability
to optimize its production.
To test Hypothesis 3 and to check whether the industry’s centrality affects its share in intermediate inputs of other industries I estimate the following
equation:
Weightij,t = αij + β1Centi,t− 5 + β2Centj,t− 5 + β3Empi,t + β4Empj,t + β 5 ∆TFP i,t− 1
+β6 ∆TFP j,t− 1 + β7Distanceij,t− 5 + β8∆FUsei,t− 5 + β9∆FUsej,t− 5 + uij,t, (3)
where Weightij,t - a share (%) of an input from the industry i in a total intermediate input of the industry j in period t, all other variables are the same as in
Equation (2). I also control for the industry’s size and productivity growth. I add
lags of the growth in final uses for both industries to check whether they affect
the link’s weight.
6 Results
The results for Regression 1 for Panel 1 and Panel 2 are provided in Table 2.
According to the results for Panel 1, an industry’s TFP growth rate affects all
three centrality measures. Coefficients of ∆TFP t− 1 are positive and significant
for all three variables. The change in the industry’s growth rate of TFP by 1%
in previous year increases the industry’s indegree by 25.79 (p-value=0.001), the
industry’s outdegree by 18.6 (p-value=0.0065) and the eigenvector centrality by
0.003 (p-value=0.028) in current year. A change for the eigenvector centrality is
small, because the eigenvector centrality itself takes values from 0 to 0.2531. This
means that industry’s productivity growth affects the process of a new link formation. More productive industries have more industries-suppliers and industriesconsumers over time.It is also possible that the industry’s productivity growth
increases its product flows to other industries.
More productive industries have low costs and low prices for their inputs.
As a result, other industries start to buy inputs from these industries; this means
19
Table 3: Results of Regression 1
Dependent variable
Eigenvector centrality
Centt− 1
0.16
(0.11)
∆TFP t− 1
0.003∗ ∗
(0.001)
Indegree Outdegree
Panel 1
0.22∗ ∗ ∗
(0.26)
25.79∗ ∗
∗
0.125∗ ∗
(0.056)
18.6∗
(10.05)
(7.39)
1268
1268
1268
Centt− 1
0.083
(0.067)
Panel 2
− 0.14∗ ∗
∗(0.043)
− 0.05∗ ∗
∗(0.018)
∆TFP t− 1
0.016∗ ∗ ∗
(0.006)
2.14
(10.96)
− 0.69
(27.66)
Number of observations
436
436
436
Number of observations
an increase in their outdegree. High productivity growth means that an industry
makes some innovations in its technological process. Further innovations need new
inputs and the industry adopts new suppliers. This is reflected in the growth of the
industry’s indegree. The influence of the productivity growth on the eigenvector
centrality captures both of these effects. It also may capture an increase in the
size of product flows within existing connections.
Results for Panel 2 show that the coefficient for ∆TFP t− 1 is only significant in the regression where the dependent variable is the eigenvector centrality.
This means that during the period 1997-2007 the productivity growth only affected the industry’s eigenvector centrality and did not affect its indegree and
outdegree. During this period more productive industries did not have higher
chance to be adopted as new suppliers or consumers. But because there is an
influence of the productivity growth on the eigenvector centrality we can conclude
that the weights of the industry’s links to other connected industries increased.
The industry’s productivity growth increased the size of industry’s product flows.
Results for both panels support our Hypothesis 1 that more productive
industries become more central over time.
20
Table 4: Baseline results for Panel 1 (1972-1992)
Regression 2
Dummy for adoption∗
Regression 3
Weight∗ ∗
Centi,t− 5
27∗ ∗ ∗
(4)
Centj,t− 5
35∗ ∗ ∗
(5.5)
Empi,t
− 0.002∗ ∗ ∗
(0.003)
− 0.007∗ ∗
(0.002)
2.2∗ ∗ ∗
(0.4)
− 0.05
(0.04)
0.0007∗ ∗ ∗
(0.0002)
− 0.00005
(0.00005)
0.05∗ ∗
(0.02)
0.014
(0.015)
− 0.0000006∗ ∗
Dependent variable
Empj,t
∆TFP i,t− 1
∆TFP j,t− 1
Distanceij,t− 5
∆FinalUsei,t− 5
∆FinalUsej,t− 5
Observations
5∗ ∗ ∗
(0.7)
1.2∗
(0.7)
− 0.00007∗ ∗ ∗
(0.00001)
− 0.017∗ ∗ ∗
(0.003)
− 0.014∗ ∗ ∗
(0.003)
291957
∗
(0.00000006)
− 0.00017∗
(0.00007)
0.00005
(0.00006)
291957
The estimated coefficients for Regression 2 for Panel 1 are provided in
Table 4. The estimated coefficients for lags of both industries’ eigenvector centralities are positive and significant. This means that there is a high probability
that an industry with a high eigenvector centrality will be adopted as a consumer
or as a supplier in the future. The coefficient for the industry-consumer is greater
than the coefficient for the industry-supplier. The eigenvector centrality of the
industry-consumer affects the probability of a new link creation stronger than the
centrality of the industry-supplier.
These results support Hypothesis 2. More central industries have more
connections to other industries; and through these connections they find new suppliers and new consumers. Also, I consider more central industries as ”universal”
suppliers to many other industries. When a new industry is born it adopts this
”universal” industry as supplier with a high probability.
21
Table 5: Baseline results for Panel 2 (1997-2007)
Regression 2
Dummy for adoption
Regression 3
Weight
Centi,t− 5
32∗ ∗ ∗
(4.6)
24∗ ∗ ∗
(4)
Centj,t− 5
− 4.1
(4.6)
− 0.0045∗ ∗ ∗
(0.0012)
0.0047∗ ∗ ∗
(0.0012)
− 0.9∗ ∗
(0.4)
− 0.00019∗
Dependent variable
Empi,t
Empj,t
∆TFP i,t− 1
∆TFP j,t− 1
Distanceij,t− 5
∆FinalUsei,t− 5
∆FinalUsej,t− 5
Observations
∗
(0.000096)
0.00007
(0.000096)
11∗ ∗ ∗
(1.6)
2.2
(1.6)
− 0.00026∗ ∗
(0.0001)
0.0094
(0.03)
− 0.08∗ ∗ ∗
(0.03)
1∗ ∗ ∗
(0.1)
− 0.065
(0.12)
− 0.43∗ ∗ ∗
(0.009)
0.0059∗ ∗
(0.0024)
0.0009
(0.00244)
47088
47088
I control for the technological distance between industries (to avoid the
effect that industries with higher eigenvector centrality have short distances to
many other industries). The estimated coefficient for the distance is negative and
significant, but very small. This means that the shorter the technological distance
between industries, the higher the probability that these industries will be linked
in the future is. This result is consistent with the results obtained in Carvalho
and Voigtla¨nder (2014). They show that if there is a short technological distance
from the industry i to the industry j then the industry j will adopt the industry
i as a new supplier with a high probability.
The estimated coefficients for the growth in final uses for both industries
are negative and significant, but very small. As a result, I cannot argue that the
growth in final uses increases the probability of a new link adoption.
The estimated coefficients for Panel 1 and Panel 2 support the Hypothesis
22
3. The industry i’s eigenvector centrality increases its input’s share in intermediate inputs of other industries (Table 2). This effect is big enough in Panel 2, but
small in Panel 1. The industry i with the high eigenvector centrality has many
industries-consumers that leads to the cost advantage and low price of the output.
For this reason industries-consumers increase their product flows from this industry. ”Universal” industries have high shares in intermediate inputs of connected
industries.
According to the results for both Panels the shorter the distance between
two industries 5 years ago, the higher the input share of industry i’s product in
total intermediate input of the industry j, but again this effect is very small.
The estimated coefficients for the lags of the industry i’s productivity
growth for both Panels are significant and positive. This means that the higher
the industry’s productivity growth in previous year the higher its input share in
an intermediate input of other industries this year.
7
Conclusion
I consider the U.S. industries as a network, which is changing over time. I propose
a theoretical model that describes a industries’ network formation process and an
evolution of links and their weights.
According to the model, the most productive and central industries have
a higher chance to be adopted as suppliers by new industries. The position of the
industry in the network and its productivity affect the weights of the links. This
means that productive industries with many connections will have large product
flows to other industries-partners. As a result, the evolution rule leads to the
power-law distribution of the industries’ weighted outdegree. This is exactly what
is observed in the U.S. data.
I use the U.S. input-output tables for 1972-2007 to verify whether these
rules of the network formation are implementable for real industries’ network formation process. The obtained empirical results support the hypotheses.
Industries with a higher productivity growth become more central over
time. Three different centrality measures are used for the estimation: the indegree,
the outdegree and the eigenvector centrality. The productivity growth of the
industry affects all three centralities in period 1972-1992. This means that if
an industry experiences a productivity growth and introduces innovations then
it starts to adopt new suppliers. An industry may also attract new industriesconsumers, because of a reduction in its costs that is related to the productivity
growth.
23
I also empirically verified that the industry’s position in the network affects its future expansion. More influential industries in terms of the eigenvector
centrality have a higher probability to create new links with other industries in the
future. Moreover, it also increases the size of its product flows to other connected
industries.
One possible direction for the future research is to build a model that
combines a network formation process and microfoundations, where the evolution
of a network is not simply determined by the proposed rule, but is a result of
firms’ economic decisions. A firm belonging to a particular industry makes a
choice of suppliers and the size of the inputs. Decisions of all the firms determine
the network evolution over time.
23
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