Random Graph Models Utilization for Economics Purposes

Jan Panus and Andrea Dymakova

Faculty of Economics and Administration, University of Pardubice, Studentska 95, Pardubice, Czech Republic

Keywords: Social Networks, International Trade, Strategy Research.

Abstract: This paper explores the usability of random graph models from the field of social network analysis for

selected topics in the field of economic sciences. Specific examples are given in the field of international

trade and strategic research as part of international research analysis. At present, there is an increasing need

to connect individuals or organizations to increasingly complex networks, and as the complexity of such

structures grows, the need for understanding how such structures are created and what they actually mean.

The method of random graphs used in the paper serves as an appropriate method for such analysis.

1 INTRODUCTION

From a historical point of view, trade is more

common within nations themselves than between

each other (Helliwell, 2000, McCallum, 1995). As

(Eaton and Kortum, 2002) estimated that areas that

do not have geographical boundaries are able to

have five times more trade than those with borders.

The lack of trade between countries can often be

explained by various formal trade barriers such as

poor enforcement of international contracts with the

help of governments (Anderson and Marcouiller,

2002), or inadequate information on possibilities for

international trade (Portes and Rey, 2005). Business

and social networks that operate between countries

can help to break down these barriers. Researchers

can then help to look at how to overcome these

barriers. Research can serve as documents and is

able to quantify the existence of such barriers.

While transnational networks are primarily

researched as a means of overcoming barriers to

trade, much of the research on the impact of

domestic networks on international trade is rather

motivated by the view that they are an informal

barrier to trade, with network members colluding to

increase their market power by restricting foreign

competition. There is also a line of work that

measures the effects of domestic networks on the

composition of international trade.

The aim of this paper is to highlight the

possibility of analyzing international trade between

countries in terms of social network analysis. The

paper brings some definitions of economic networks

and international trade as outlined in the following

chapters. Many publications deal with the field of

international trade analysis but few of them deals

with social network analysis as a tool to analyze

international trade. We discuss the possibility to

utilize social network analysis to international trade.

We use random graph model to analyze some basic

international trade characteristic.

2 SOCIAL NETWORK ANALYSIS

Social networks and the analysis of relationships is

an important concept in many sorts of areas, from

public administration, sociology, management, and

even within international trade analysis. Social

network analysis focuses on the structure of

relationships between individuals or organizations

where the network is perceived as a set of actors

linked by social bonds. Some analyses focus on

organization theory. Over the last few years, there

have been many studies that deal with relationships

between organizations. There are studies that focus

on key factors and indicators of inter-organizational

relationships, and this phenomenon has a growing

importance as the links from dyads (organizational

sets) to networks are gradually shifting. In the

academic sphere, there is a view that both business

relationships and non-profit sectors are trying to

make any cooperation within the framework of the

growth alliances as one of the possible ways to be

more effective and competitive. It is clear that in the

current globally interconnected world, such

Panus J. and Dymakova A.

Random Graph Models Utilization for Economics Purposes.

DOI: 10.5220/0006578102300234

In Proceedings of the International Conference on Computer-Human Interaction Research and Applications (CHIRA 2017), pages 230-234

ISBN: 978-989-758-267-7

cooperation is an important element among those

organizations that seek to take on the global market.

Such behaviour is not entirely possible in the

traditional market environment.

There are several well-known techniques to

measure the properties of networks (Snijders, 2001),

actors, or relationships. These techniques help to

understand certain features of the network that relate

to research questions.

1) Social behaviour is a complex process, and

stochastic modelling allows us to capture both

regularity in the processes that take place across the

network and variability, and we can then model

them in detail and detail. Adding a small amount of

randomness to an otherwise regular process can

significantly change the output of the entire process.

Researchers usually try to capture stochastic

process if they believe their model best reflects real

world problems. It is very important to design the

stochastic model well to allow them understand

uncertainty of the observation of real world

problems. Researches usually wants to learn

something new about the distribution of the possible

output.

Researchers need to create such statistical model

that allow them to create judgment about certain

structure in the network. This structure occurs in the

model or occurs in the network with some

probability. Researches establish a specific

hypothesis about social processes.

The more complex data structures are in the

network the more useful model is achieve for data

representation.

Sometimes, different social processes can have

similar quality assumptions about network

structures, and can only be determined by

quantitative modelling. For example, clusters in

networks can be made from endogenous (self-

organizing) structures or from homophily. If

researcher want to decide which of the processes is

created, then we need to create a model and find out

from the results what suits us.

Some problems about social network analysis is

to deal with how structures and processes in

networks affect forming of global pattern of the

network. It is very complicated to understand

without any kind of model or modelling. Sometimes

it is well understandable due to quality modelling

and simulations.

2.1 Random Graph Model

Random graph model (Erdos and Renyi, 1966,

Albert et al., 1999, Molloy and Reed, 1995) is usable

tool for creating some models and simulation of real

world problems. Many scientific applications is used

by helping of this model. We should follow these

steps for using random graph model.

1) Each network connection is perceived as a

random variable. This step involves a stochastic base

with a set of fixed points. The combination of these

points is then perceived as a relationship that arises

with a certain probability. It is not possible to

perceive this as the principle of creating a

relationship based, for example, on fashion, etc.

We'd rather determine that we do not know much

about the network and that we do not know much

about forming relations, that our model is not

capable of creating perfect deterministic predictions,

and that the results will contain some noise that we

cannot explain.

2) Eventualities are defined by hypothesis

dependence. Hypotheses represent local social

processes that are capable of networking.

Consequently, connections can be independent of

each, as people create social connections

independently of their previous connections.

3) Researcher should create a hypothesis for

introducing the particle formation into the model.

Each parameter corresponds to a network

configuration, a subset of possible network

connections. Such configurations refers some

structural characteristic of interest. The model

represents the distribution of a random graph. The

configuration is usually created by simple

connection between two actors.

4) It is recommended to simplify parameters.

This simplification is provided by using of

homogeneity and other restriction. Model is defined

by better way if the researcher limits the number of

parameters. The researcher equate some of the

parameters to unify or link other parameters in

different way.

5) Design and interpretation of the model and

its parameters. The focus for modelling is the

emphasis on designing and interpreting the model.

However, this approach usually requires the

completion of the previous four points. This last step

is very complex if the model structure is

complicated, as the real world problems usually are.

Researchers often use the benefits of statistical

models for networks in case of parameter estimates,

as well as an estimate of the uncertainty of the

model.

Creating a random graph is done by taking a

number of N nodes and interconnecting each other

so that each pair i,j has a connection with an

independent probability of p. However, if we want

to examine models that are close to the real base, we

have to accept it. That such a simple model has some

weaknesses. One of them is the distribution of

degrees in the graph, which is to be calculated as in

the real world.

Consider a node in a random graph. With a

certain probability, p is linked to each of the N-1

other nodes in the graph, and hence the probability

that is assigned to node k with a binomial division

3 INTERNATIONAL TRADE AND

SOCIAL NETWORKS

Many authors highlight as a positive feature the

transmission of information from the network can

serve as a source of information about the

possibilities of the business itself or of the

investments possibilities. Literature often uses the

notion of characteristic knowledge as a network

definition. The key is basic characteristic knowledge

of the agents that tend to create a network or

business in the future. Transnational networks can

facilitate such interconnection through commissions

of marketing operations that let potential traders

know that there are customers who are interested in

the product in another country (Chin et al., 1996).

Within a given market, these networks can help find

a suitable distributor of goods for specific customers

(Weidenbaum and Hughes, 1996).

Empirical analyzes point to the positive effect of

international trade on the creation of conditions for

trade between groups operating between borders and

for immigrants. Immigrants know the characteristics

and properties of buyers and sellers in their

homeland, and carry this knowledge to new

countries as well. However, it is often difficult to

predict the extent to which the impact of

transnational cooperation works by providing market

information or using official information. Often

customers' desire for goods from their homeland is

apparent rather than having any effect of being part

of any network (Gould, 1994). Gould estimates

separate import and export equations and the impact

of immigrants' influence on bilateral trade between

the United States and its partners during the 1970-

86. Gould also shows that for the two different rates

of immigration, the estimated coefficients are

positive and significant for both export and import.

Long-term elasticity for preferred goods shows that

there is a 10 percent increase in exports from Canada

to the countries of origin of immigrants by 1.3

percent and the increase in imports to Canada from

these countries by 3.3 percent.

Possible consequences for economic efficiency

in transnational networks that provide information

on profitable business opportunities are provided by

(Rauch and Casella, 2003). They use a model that

considers the following: the manufacturer needs to

match to his needs if such agreement is acceptable,

then it is possible to employ an internationally

immobile labor force and then to realize the

production. Within its home country, the

manufacturer is able to match his needs (i.e. what he

needs to produce and with which resources he can

find) based on his own experience. Typical needs

and knowledge abroad are not so familiar to

manufacturers from other countries, and they cause

problems. Such international consensus can then

serve to shift labor demand in the form of services to

manufacturers from countries where such labor is

rare in countries where it is enough.

Based on the above information, it goes without

saying that social networks, as an analytical tool is

an appropriate way to describe and understand

networks at international level. There is a large

number of problems in transnational co-operation

where it is necessary to establish relationship with

other producers or employees who know the

environment and are a suitable tool for how to

efficiently use resources in the countries concerned.

The exponential random graph model (ERGM),

which will be described in the next chapter, is then

an appropriate tool for analyzing and modeling a

given situation.

4 ERGM AS AN ANALYTIC

TOOL

Exponential random graphs model is a part of

random graph model has following form:



































(1)

Where X

is a random graph that represents the

connection between actors. X then represents the

element matrix n and x then represents the matrix of

the realized network connections. A then represents

another network of configuration types. Z

(x)

represents a set of dependent variables on the model,

expressing that any set of statistics A calculated on x

affects the probability of creating a given network.

An unknown parameter is represented by µ

coefficient and this parameter estimated and

expresses the effect of network statistics in the

monitored network model. The coefficient k

represents the number of numerators displayed in a

possible network with n number of elements.

Parameters are initially estimated in ERGM

using pseudo-similarity (Strauss and Ikeda, 1990)

but this approach is often not reliable. Instead, it is

more appropriate to use the Markov Chain of Monte

Carlo as a similarity estimate (Geyer and Thompson,

1992). Monte Carlo simulates the distribution of a

random graph using the initial values of the

parameters, and this process is repeated until we

reach the cleaned values that we compare with the

simulated distribution of the given graph with the

observed data (Snijders, 2002). The advantage of

this approach is that with an infinite number of

network configuration distributions, we give an

estimate equivalent to maximum like-hood

estimation and provide a reliable number of standard

errors (Wasserman and Robins, 2005). A series of

other network specifications, called the social circuit

dependence (Pattison and Robins, 2002), have been

developed that significantly reduce cases where the

high level of triads often occurs due to poor model

specification (Hunter and Handcock, 2006, Robins

et al., 2009).

5 DISCUSSION

The possibilities of using the ERGM method on

economic themes have been demonstrated in (Kim et

al., 2016), when the connections between firms and

their boards of directors (Mizruchi, 1996) were

modeled. The number of selected companies were

set on 95. The influence of the independent variables

on the characteristics of various companies was

studied, namely the company characteristics, dyad

co-variates and structural effects. These properties

identifies as important features for establishing a

connection within a multinational network in

international trade. If companies have similar or

even the same company characteristics, or Structural

effects, it is possible with some probability to define

that there is a connection within the network.

The ERGM methodology allows significant

expansion for the development of a strategy to

expand business opportunities or attract new

potential customers and businesses in the field of

transnational trade. ERGM's ability to directly

describe network dependencies allows for a more

accurate analysis of the factors that were examined

in the previous research. The results can be used to

test the formation of connections to create rigorous

empirical evidence for developing models that are

not only attractive but also scientifically valid

(Colquitt and Zapata-Phelan, 2007). Previous

research proves that the influence of organizational

resources on alliance formation is important. Multi-

source companies have more opportunities to build

links, and their higher level of resources makes it

possible to eliminate the need for co-operation

through the alliances.

The promising area where ERGM can be used is

also the area of micro-transactions in the area of

inter-organizational and transnational cooperation.

Various research highlights the important role of

existing links between individuals and their

connection to the creation of links between

organizations (Gulati and Westphal, 1999,

Rosenkopf et al., 2001). Typical examples are new

startups that are founded by people who previously

worked in multinational companies. These people

are then linked to the staff of these large companies

and can be contacted for further cooperation.

In conclusion, ERGM is an important technique

that can be used in various areas of research, be it in

the field of international trade and modeling of

producer and vendor networks, but also in other

economic areas such as strategic research, that can

be taking into account of transnational trade. As the

interconnection between individuals, organizations

or entire communities grows, there is a growing

need to better understand and understand structures

within networks. The ERGM method can build on

the classic foundations of social network analysis

and move them in the next direction to better

understand the organization network genesis.

ACKNOWLEDGEMENTS

This paper is supported by project number

SG470022.

REFERENCES

Albert, R., Jeong, H. & Barabasi, A. L. 1999. Internet -

Diameter of the World-Wide Web. Nature, 401, 130-

131.

Anderson, J. E. & Marcouiller, D. 2002. Insecurity and the

pattern of trade: An empirical investigation. Review of

Economics and Statistics, 84, 342-352.

Eaton, J. & Kortum, S. 2002. Technology, geography, and

trade. Econometrica, 70, 1741-1779.

Erdos, P. & Renyi, A. 1966. On Existence Of A Factor Of

Degree 1 Of A Connected Random Graph. Acta

Mathematica Academiae Scientiarum Hungaricae, 17,

359-&.

Geyer, C. J. & Thompson, E. A. 1992. Constrained

Monte-Carlo Maximum-likelihood for Dependent

Data. Journal of the Royal Statistical Society Series B-

Methodological, 54, 657-699.

Gould, D. M. 1994. Immigrant Links to the Home Country

- Empirical Implications for United-States Bilateral

Trade-flows. Review of Economics and Statistics, 76,

302-316.

Gulati, R. & Westphal, J. D. 1999. Cooperative or

controlling? The effects of CEO-board relations and

the content of interlocks on the formation of joint

ventures. Administrative Science Quarterly, 44, 473-

506.

Helliwell, J. F. 2000. How Much Do National Borders

Matter?, Brookings Institution Press.

Hunter, D. R. & Handcock, M. S. 2006. Inference in

curved exponential family models for networks.

Journal of Computational and Graphical Statistics,

15, 565-583.

Chin, K. S., Yoon, I. J. & Smith, D. 1996. Immigrant

small business and international economic linkage: A

case of the Korean wig business in Los Angeles, 1968-

1977. International Migration Review, 30, 485-510.

Kim, J. Y., Howard, M., Pahnke, E. C. & Boeker, W.

2016. Understanding network formation in strategy

research: Exponential random graph models. Strategic

Management Journal, 37, 22-44.

Mccallum, J. 1995. National Borders Matter - Canada-Us

Regional Trade Patterns. American Economic Review,

85, 615-623.

Mizruchi, M. S. 1996. What do interlocks do? An analysis,

critique, and assessment of research on interlocking

directorates. Annual Review of Sociology, 22, 271-298.

Molloy, M. & Reed, B. 1995. A Critical-Point for Random

Graphs with a Given Degree Sequence. Random

Structures & Algorithms, 6, 161-179.

Pattison, P. & Robins, G. 2002. Neighborhood-based

models for social networks. Sociological Methodology

2002, Vol 32, 32, 301-337.

Portes, R. & Rey, H. 2005. The determinants of cross-

border equity flows. Journal of International

Economics, 65, 269-296.

Rauch, J. E. & Casella, A. 2003. Overcoming

informational barriers to international resource

allocation: Prices and ties. Economic Journal, 113, 21-

42.

Robins, G., Pattison, P. & Wang, P. 2009. Closure,

connectivity and degree distributions: Exponential

random graph (p*) models for directed social

networks. Social Networks, 31, 105-117.

Rosenkopf, L., Metiu, A. & George, V. P. 2001. From the

bottom up? Technical committee activity and alliance

formation. Administrative Science Quarterly, 46, 748-

772.

Snijders, T. A. 2002. Markov chain Monte Carlo

estimation of exponential random graph models.

Journal of Social Structure, 3, 1-40.

Snijders, T. A. B. 2001. The statistical evaluation of social

network dynamics. Sociological Methodology 2001,

Vol 31, 31, 361-395.

Strauss, D. & Ikeda, M. 1990. Pseudolikelihood

Estimation for Social Networks. Journal of the

American Statistical Association, 85, 204-212.

Wasserman, S. & Robins, G. 2005. An introduction to

random graphs, dependence graphs, and p*. Models

and methods in social network analysis, 27, 148-161.

Weidenbaum, M. L. & Hughes, S. 1996. The Bamboo

Network: How Expatriate Chinese Entrepreneurs are

Creating a New Economic Superpower in Asia, Martin

Kessler Books.