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Introduction

International migration becomes the issue of high importance in recent time. The boost in globalization and the increase in human mobility accelerated the growth in international migrant population so that it became to grow faster than the population worldwide. There were 244 million international migrants worldwide or 3,3% of the global population in 2015 [37]. However, international migration influences the origin and destination countries not only by growth in absolute numbers of migrants, but through processes that it touches societies. Migration has impact on economic and demographic situation, as migrants send remittances to their home countries and change the demographic structure in destination country. The recent influx of refugees in Europe is changing its ethnic and demographic composition. According to the recent survey of Pew Research Centre only few citizens of 10 EU countries think that growing diversity makes their country a better place to live [50]. In this way, migration theories are needed to be studied and new approaches to be developed to propose relevant migration policies.

Migration theories have developed in different directions since the first model in eighteenth century [31]. Main causes and consequences of the process were extensively studied by the literature. However, data on international migration improved significantly from that time. The data on international migration is typically presented in the form of bilateral flows or stock of migrants. This fact makes it possible to apply various economic and mathematical models to this field. Precisely, network and gravity models can be applied to this type of data and help to build the complex understanding of the process.

Our work is aimed to study international migration process in the integrated approach. First, it is devoted to find the countries with the highest influence in international migration process with the application of network analysis to international migration flows data. This idea is realized by evaluation of classic centrality indices and new centrality indices, which have certain advantages compared to classic one. Second, international migration process is explored by the main factors that determine bilateral migrant stock. For this purpose, the econometric model is analyzed and influence of economic and political factors is explored by gravity model.

The paper is organized as follows. Chapter 1 provides a survey of the literature of international migration analysis including classic theories, models from network analysis and econometric models. Chapter 2 is devoted to the network analysis, precisely to evaluation of influence of countries in international migration network using centrality indices. In Chapter 3 the determinants of bilateral migrant stock are studied by econometric model.

Chapter 1. Review of literature on classic migration theories, econometric and network models

Introduction

This chapter is aimed to build a connection between the fundamental theories, econometric models and network analysis of international migration. First, early fundamental works on migration theory are reviewed in order to form the understanding of basic motives of migration and main characteristics of the process. Second, econometric models are introduced with the gravity models, which are based on Newton's law of gravitation between two bodies and devoted to study main factors of country to country (bilateral) migration flows. Third, the analysis of international migration as a bilateral process is brought to a new level by network theory, in which all international migration flows (or stocks) are interconnected and influence between them can be studied in this framework. Existing literature on international migration is mainly focused on economic factors as main determinants of the process. However, later works show the importance of migrant communities, cultural and linguistic characteristics of countries. Networks of international migration present the most central countries in the process, established connections of countries and the evolution of the international migration.

1.1 Classic theories

Migration and its fundamental aspects were studied since early times. Remarkably, one of the first scientists who began to study the process of migration was Adam Smith. The main cause of migration flows between the rural and urban areas according to the hypothesis of A.Smith is that in these areas the wage difference is greater than difference in goods' prices. Additionally, A.Smith compared migration flows to the trade flows and came to a conclusion that trade flows were more intense than migration flows, because migration had more barriers: “man is of all sorts of luggage the most difficult to be transported” [31].

The theory developed after Adam Smith was presented in the “Laws of migration” by [29] based on the British population census, migration statistics and vital statistics. All empirical observations E.Ravenstein formulated in 11 Laws of migration, which explain the migration flows. The most relevant for our research statements are 1) The majority of migrants move on short distances, 2) Huge migration wave generate the compensating counter wave of migrants, 3) Cities with fast growing population are inhabited with migrants from the close rural areas, and the migrants from more distant areas populate the shortage generated in rural areas.

Several works explore the phenomenon of migration from the prospect of motives to migrate. The push-pull factors theory has a great importance for the analysis of causes of migration flows [25]. According to that work, there are 4 groups of factors that influence the level of migration between two countries: pull and push factors which characterize both the country of origin and destination, personal factors and intervening obstacles. The examples of the pull factors of the destination country are high wage, high demand for the labor force, considerable amount of social allowance, stable political situation and favorable climate conditions. On the contrary, low wage, unemployment and the conflicts in the country of origin are the push factors for migrants. Personal factors can be different and are defined for each migrant individually. The intervening obstacles can be the huge distance between two countries or strict migration laws.

Migration from the prospect of human capital approach was studied in [30]. It was the first application of the idea of human capital to the field of migration studies [11]. The key logic behind this theory is that a migrant chooses a location that maximizes the net return on migrant's human capital. In this case, the problem lies to the maximization of the individual's profit from migration from region to in each period. It is assumed that there are wage differences between the regions and that a migrant will retire within periods. Hence, in discrete time the profit from migration from to is

and in continuous time

where and - wages in destination and origin countries accordingly, and - costs of living in region B and A, and - the interest rates, - costs of migration from A to B, which depend on the distance between regions and any other factors influencing on costs . In both discrete and continuous time models an individual is willing to migrate from A to B only if his/her profit will be positive, i.e., .

The human capital model of migration became fundamental for many modern models aimed to study migration from different aspects. The later works take into account more factors influencing the migration: the influence of kinship and migrant network [38], introducing a family as a decision-making unit [27] studying migration decision in a life-cycle context [28], and imposing remittances as another factor influencing migration [14]. For more detailed review of migration theories see [11]. The theories reviewed above apply different levels of analysis of human migration: the macro-level (migration between countries and regions) and micro-level (individual). They form the basis of theories on migration. The recent improvement in data on international migration made it possible to empirically test the theoretical assumptions proposed in these works. On the one hand, the determinants of country to country migration flows can be explicitly studied by the gravity models. At the same time network theory can bridge the gap in the existing literature and provide the analysis of migration flows in the integrated way.

1.2 Gravity models

Gravity models occupy an important place in the economic science. They are widely used in analysis of trade, capital and transportation flows. The improvement of data on international migration made it possible to apply gravity models to bilateral (i.e. country to country) migration flows. These models are used to find the determinants of international migration. The simplest models include only population and distance. However, modern works study also various economic, cultural and linguistic factors. Below the basic specifications of gravity models is examined, then the influence of income is reviewed and the role of diaspora, cultural and linguistic proximity is considered as well.

1.2.1 Core factors influencing migration

Gravity model of international migration originates from the hypothesis of [39] stating that the level of migration between two regions is directly proportional to population of them and inversely proportional to the distance between them.

, (1.3)

where - population of country of the origin, - population of the destination country, and - the distance between origin and destination countries.

The interpretation of this hypothesis is quite straightforward. First, it is expected that each region has a constant share of population with intention to migrate and when the origin population grows, the amount of potential migrants is rising correspondingly. The destination region is characterized with the constant share of employment opportunities for migrants. Thus, when the destination population increases, the potential to attract new migrants also enlarges. Finally, inverse relation to distance is related to the fact that longer journey for migrants involves higher migration costs. These factors are fundamental for understanding the idea of gravity model.

The basic model of [39] was further extended by [32] with application to international trade flows. After that work gravity models became widespread in the field of spatial economics and were generalized to the following regional interaction model [15].

(1.4)

where is the interregional flow that can be either migration, trade, transportation or any other flow. represent the sizes of regions and , respectively, that are expressed in country GDP, population or income, characterize the potential of interaction between the regions (potential to generate or attract flows), distance between the regions, influence of distance, proportionality constant.

The application of gravity models to international migration became possible after publication of bilateral flow datasets by different international organizations: World Bank, United Nations, OECD and others. Data on international migration is usually represented with bilateral migrant stock or migration flows. Bilateral international migrant stock is studied in [19]. The gravity model of international migration is analyzed to explain international migrant population. The original gravity equation is proposed in a multiplicative form, i.e. bilateral migration stock is the product of explanatory variables in each period. The model is studied with the data for 226 countries for each decade from 1960 to 2000. The following equation is estimated.

 , (1.5)

where the stock of migrants from country living in country () is explained with the population of origin () and destination countries (, distance between them (), relative GDP per capita () and by origin and destination country dummies () and explanatory variable dummies (), i.e. common border, language, religion, colony past and also dummy variables that account for south-south, south-north and north-north migration.

In that work the two-stage estimation technique is applied. First, the probability of migrant stock existence is predicted by the logit model using the same explanatory variables as in original model. The literature on gravity models of trade [15] suggests to follow this strategy to distinguish between three kinds of intercountry flows. First, there are countries with no potential for intercountry trade and, therefore, having zero trade flow. Second, countries could not have the trade flow in current period, but there is a potential for intercountry trade flow due to geographical proximity or trade agreements. Thus, these countries have non-zero probability of trade flow existence. Finally, there is a group of countries already trading with each other.

In [19] logit model has helped to obtain the matrix that indicates the presence of migration stock for each country pair. Second, weighted matrix with migrant stocks is predicted with the Poisson Pseudo Maximum Likelihood estimation. The logit model has accurately predicted 78,7% of observations. The observed migrant stock has also been successfully predicted (pseudo R²= 0,6477) with all the included variables being significant at the level 1 per cent, except common religion and north-north dummy.

It turns out that migrant stock is positively related to the population of origin and destination countries, inversely with distance between them and with difference in GDP per capita. If countries have common border, religion, language or share a colonial past, it increases the migrant stock between these countries. This work applies basic specification of the gravity model of international migration. However, there are various factors that can influence international migration.

1.2.2 Influence of income

Economic factors in origin and destination countries play the fundamental role in shaping international migration. Income gap is the necessary condition for existence of migration flow between the two countries [16]. The main stimulus for migrants is high income at destination country. Adam Smith [31] included the difference in wages as an economic factor, higher income prospects at destination are significant pull-factor according to [25]. Higher wages are also in line with the human capital model of migration [30], as individual can maximize the return on his/her skills by migrating to more economically prosperous country.

On the other hand, huge income gap with low income at country of migrant's origin does not contribute to large migration flows [16]. Migration is the form of investment and it becomes unaffordable for the most part of potential migrants from poor countries. Income at origin plays the role of credit constraints for migrants and stimulates the outflow of migrants only starting from a certain level [10]. Even though the role of income in migration decisions is already explicitly studied in literature, it does not diminish its significance.

The role of income in the gravity model of international migration is studied in [33] by including the GDP per capita of origin and destination countries. The work is based on the dataset of OECD countries and focuses only on migration flows within these countries. It proposes panel data regression model of bilateral international migration flows. Here to original gravity model of migration log-log transformation is applied. Therefore, the dependent variable is logarithm of bilateral migration flow from country to country at time t. Study period is from 2000 to 2009 (annual data).

The explanatory variables are the following. GDP per capita of origin and destination countries are included separately, accounting for different effects on migration flow. Also, origin and destination countries are characterized by the level of education. Interestingly, in this model the share of youth population (between the age of 15 and 29) in the origin country is included as a push factor. The level of education in origin and destination countries is proxied by the number of graduates from tertiary institutions in these countries. The distance between countries is measured in kilometers between the country capitals. Also, the set of dummy variables describes country dyads: the presence of common border, common official language, common region and former colonial ties. The preference for panel data regression with random effects is given, because of the presence of time invariant variables (all dummy variables and distance).

First, the regression with all variables at the same period is modeled. It is shown, that GDP per capita in destination country has a strong positive effect, and GDP per capita at origin has a weak effect on migration outflow. Distance has a strong negative effect. A significant push factor is the share of young population at origin, representing a huge share of potential emigrants. Common border and language have a small positive significant influence, as well as colonial relationship.

Second, the regression with lagged explanatory variables and with inclusion of stock of migrants in the destination country in 1995 has been made. The first motivation is to overcome possible endogeneity problems, as growth of GDP per capita at destination may depend on the inflow of immigrants. Second, if country is a well-known destination for migrants from particular countries, it will attract even more migrants. Thus, migrant stock in previous decade has been added. It turned out that migrant stock has significant positive effect and for other lagged variables results are almost the same as in the previous regression.

This work is useful because of the analysis of effect of GDP on bilateral migration flow, suggested panel data regression specification, ideas about solving endogeneity problem by adding lagged explanatory variables and inclusion of existing migrant stock.

1.2.3 Diaspora and cultural proximity

Research on international migration focuses on various factors to explain the migration flows between the countries. Apart from traditional economic and demographic variables, i.e. GDP per capita, unemployment rate, population, researchers examine the influence of social factors and cultural differences between the countries on the international migration rate. The role of diaspora, cultural and linguistic differences will be examined in more detail.

In [16] the international migration is studied in the integrated way. Most importantly, he provides the mechanism of interaction between diaspora and cultural difference and the level of migration between the countries. Diaspora is assumed to be the migrant population of particular country living in the destination country. Based on this definition he evaluates the effects of existing migration policy in European countries and proposes his own model of managing international migration.

It is assumed that migration is defined by the following core factors: income gap, diaspora, cultural distance between the countries and economic, legal and social obstacles for migration [16]. These factors interact with each other in a multiplicative form. Huge migration flow is formed by significant income gap, not very low level of income in the sending country, huge diaspora and considerable difference in cultures between the host and home countries. While the first two factors are quite straightforward to understand, the diaspora and cultural divergence between the host and home countries are not obviously related with increasing migration level.

The necessary condition for existence of bilateral migration flows between countries is income gap. Migrants come from low income countries to those with successful economy. In this sense migration is an intention to economic effectiveness. Also, migration is the form of investment for migrants and is not affordable to everyone. That is why we do not observe the high levels of migration from very poor countries.

Diaspora plays the key role in the international migration according to this model. Diaspora is defined as foreign population in the host country that is not integrated in the host society, i.e. they still have their own traditions, social norms. Diaspora is the way of immigration of relatives, the source of information and financial support for migrants. As diaspora is the opportunity for potential migrants, it lowers the costs of migration significantly and strong diaspora increases the migration level. In different studies the size of diaspora is often proxied by the size of foreign population, as there is no other statistics on migrants' integration.

The distance between the countries can be represented not only by the physical distance, but also by the difference in cultures of societies. Therefore, it is usually expected that countries with huge difference in cultures should have low migration flow. However, in [16] difference in cultures between the receiving and sending countries is positively related to the level of migration between these countries. The mechanism of this interaction is the following.

Migrants are represented with their existing diaspora in the host country and with the inflow of newcomers. Diaspora is characterized by its size and the pace of absorption into the host country society. Diaspora is attracting new migrants by reducing the costs of migration for them. Pace of absorption of diaspora depends mostly on cultural proximity of migrant community and host country society. The more culturally distant is migrant community, the more time is needed for its absorption. Joint influence of diaspora and cultural distance, therefore, increases the inflow of new migrants. With the presence of huge cultural distance diaspora is attracting new migrants and they assimilate slower, increasing the size of diaspora even more.

As it was discussed above, diaspora and its assimilation to the society can be the key point of successful migration policy. Interestingly, the influence of diaspora, its interaction with cultural divergence, income gap and other relevant characteristics of countries on bilateral migration flows can be analyzed within the gravity model of international migration.

In [17] this theoretical assumption is tested by econometric model. Migration from low and middle income to high income OECD countries is studied in gravity model. While high income OECD countries only account for 15 per cent of the global population, they are the destination of 56 per cent of all global migrants (originating from poor, middle and high income countries).

(1.6)

The change in the stock of migrants over decades () is modeled by migrant stock in the previous decade (diaspora) (), sending () and receiving () country characteristics, country-pair characteristics () and interactions of these variables with diaspora. This change approximates the flow of migrants and equals to the difference between the stock of migrants between the decades. It accounts for mortality of migrants and does not account for return migration. The work is based on the data for 5 decades from 1960 to 2000 for 175 countries.

It is expected that the effect of the country characteristics depends on the size of the existing migrant stock, or the diaspora. Therefore the interactions of the country and country pair characteristics with the diaspora are added to explanatory variables. The explanatory variables are the following. First, the population of sending and receiving countries and distance between them (in logarithms) are included following the main hypothesis of gravity model. Then there are economic and political characteristics of host and home countries and variables for cost of migration. In that work income (GDP per capita) is included separately for sending and receiving countries, as in [33]. Income of destination country represents the pull factor of migration. However, origin country income represents a different incentive. It induces outflow of migrants only after reaching a certain level, as migration is the form of investment and is hardly affordable for very low income countries.

The political factors of origin and destination countries are represented by the degree of political freedom and social disruption. The degree of political freedom is also included separately for origin and destination. Social disruption is proxied by periods of civil and international warfare. The investment costs of migration are modeled by distance between the country dyads, size of diaspora and former colonial relationship. The cultural distance is proxied by the linguistic difference between countries. Time effects are controlled by decade dummies, country effects by country dummies.

The main results of this model are the following. The interaction of variables allows to broaden the interpretation, as the effect of each variable is the sum of its direct and interaction (with other variables) effect. The effect of diaspora is huge, but mainly because of the interaction with other variables. Interesting finding is that with small diaspora income at origin country is positively related with outflow of migrants, and with large diaspora it reduces the migration flow. In the mean size of diaspora income has a small effect. With the growth of diaspora migration flow grows faster, if distance is huge and slower if it is shorter. Political openness in countries-of-origin is more important, but greater openness increases emigration rather than reducing it.

To sum up, the works by Collier present a beautiful idea behind, and can help to understand better the process of migration. The variables included into his model (diaspora, periods of conflicts, cultural distance and interaction of variables) indicate the importance of influence of new factors apart from economical ones.

1.2.4 Influence of language

The role of language in the development of international migration flows has also been examined with the gravity models [4]. Knowledge of destination country language can be a great opportunity for potential migrants in source country, thus, reducing the costs for migration. In that work it is shown that the effect of linguistic proximity is higher, than common border, shared colonial past and difference in unemployment rates at origin and destination countries (higher at origin and lower at destination). However, traditional pull factors, i.e. GDP at destination and ethnic networks have stronger influence on migration flows, than linguistic proximity.

In [4] the contribution is made by the comprehensive dataset of international migration and construction of new measure for linguistic difference. The destinations are restricted to 30 OECD countries and the origin countries are represented by 223 countries all over the world. The period under study is from 1980 to 2010.

The econometric model includes the dependent variable migration flow from country to country divided by the population of the source country. All the variables in model are expressed in logarithms except linguistic proximity indices and dummy variables. GDP per capita, unemployment rate at origin and destination country are the explanatory variables related to economy. The share of GDP on social expenditures at destination can be interpreted as country's welfare attracting migrants. In some specifications GDP of origin country is included in quadratic form to check the hypothesis of non-linear effect. The idea is the following. When source country income is too low, potential migrants cannot finance their journey, after reaching a certain level it induces outflow of migrants. Then, when it becomes higher, the difference between source and destination country income reduces, and potential migrants will not gain much profit from changing locations, thus migration reduces.

Migrant stock (lagged) divided by source country population is also included as a factor reducing migration costs. Another push factor presented in the model is the degree of political freedom measured by Freedom House, which accounts for the freedom in political rights in each country of origin.

The variables that account for distance between the countries in the model are the following. First, the distance between the origin and destination country capitals in kilometers is included in the model. Second, dummy variables for common border and colony past. Third, the measure of genetic difference between the countries is included. This index takes the value of zero, if the populations of two countries are ethnically similar, i.e. the distribution of alleles is the same and increases with difference in ethnic relations.

The main hypothesis tested in [4] is the negative effect of linguistic differences on migration flows. Linguistic distance is assumed as a factor inducing higher costs of migration by creating barriers for skill transferability of workers and for integration into the host society. Thus, the indices of linguistic proximity are added into the model.

The results obtained in that work are the following. Strong positive effect of per capita GDP at destination is in line with previous works and main hypothesis of gravity model. Also, assumption about migrant stock in previous period as being a strong predictor of future migration flows is confirmed here. Negative influence of squared per capita GDP at origin follows the idea that after GDP at origin reaches a certain level, it reduces the outflow of migrants. Unemployment at origin increases the outflow of migrants and, on the contrary, reduces the inflow in destination country. Public social expenditure is a significant pull factor for migration in that model. Interestingly, bilateral flow of migrants between the countries with the same language increases by 20 per cent, compared to the countries with most distant languages. This effect is higher, than unemployment and lower than GDP per capita and migrant population at destination in that model.

Studies on gravity models of international migration have been improved significantly during the last years. Gravity models are useful instrument to analyze the push and pull factors of international migration flows. The availability of country-pair data on flows and stocks of migrants makes possible the analysis of such important determinants of international migration, as the role of economic factors at destination and origin, diaspora at destination country and cultural and linguistic proximity between countries.

1.3 Network models

Network analysis originates from social science, in fact, from an analysis of social interactions of individuals. Network is presented as a graph, where nodes are agents and edges are relationships between them. In our case the migration process is presented as a weighted-directed graph, where nodes are countries and edges - migrant stocks or flows between them. Therefore, network models help to study the process of migration in the integrated way, i.e. countries are not isolated elements, they are all connected through flows of migrants.

The application of the network approach to the international migration is presented in [19]. The data is taken from the World Bank international migration database (World Bank, Global Bilateral Migration Database) for each decade of the period from 1960 to 2000. The database contains information about stock of migrant population in 226 countries, i.e. people living in the country other than a country of their origin in a given point of time.

In that study the International Migration Network (IMN) is constructed as weighted-directed graph, where nodes are countries and edges corresponded to stock of migrants. Interesting findings are obtained by analyzing binary and weighted characteristics of the network, clustering based on network structure and gravity modeling.

Weighted-network statistics has power-law distribution, meaning that migrant stock is increasing over time. Additionally, the number of connections also has increased over the period; countries have become more interconnected through migration flows, which corresponds to the trends in international migration [34].

IMN is characterized as a network with high clustering and disassortativity [19]. This result is rather simply interpreted empirically. High clustering relates to connections between countries over time. The following clusters of countries have been formed: Asian and Sub-Saharan African, former Soviet Union, European and American. Disassortativity in IMN means that countries with low migrant stock are likely to be connected with countries with huge migrant population, i.e. there are established countries of migrant origin and destination.

The results of ordinary least squares regression and gravity model outline geographical, political and socio-economic factors as more significant than local network properties for the structure of IMN.

International migration is studied in [18] by constructing the global human migration network. The data on migrant stock for 226 countries are used as in [19]. The data are available for the period from 1960 to 2000 for each decade. Interesting characteristics of the global human migration network, community analysis and the development of the network over the period have been introduced.

In [18] properties of the migration network presented as a weighted-directed graph are analyzed and the following results are obtained. The largest connections have been found within Europe, between Middle East and India, within former Soviet Union countries, from Western Europe, Canada, Eastern Asia and Mexico to the United States of America (USA). The results do not perfectly correspond to the growing issue of “South-North” migration [18]. Communities of countries with intense connections within them and modest inter-community connections are formed and appeared to be very similar to the communities identified by [19]. The global human migration network has turned out to increase in interconnection and transitivity and decrease in average path's length over the period. These results are highly related with the processes of globalization and escalation of human mobility over the past time.

Overall, in [18,19] the fundamental network analysis of the international migration has been proposed with the results having meaningful empirical evidence. The analysis in both papers is based on the migrant stock statistics, which is an accumulative pattern that represents total number of migrants living in a given country in certain period. However, there is another statistics of international migration, which represents the flow of international migrants arriving to a given country or leaving it each year.

One of the most recent and relevant papers which studies migration flows from the network prospective is [33]. The research is focused on the network analysis of international migration flows between countries of the Organization for Economic Co-operation and Development (OECD) (32 countries). The analysis can be divided into the following steps: estimation of the network attributes, community detection in international migration network, and, finally, application of the generalized gravity model to international migration flows that was described previously.

As network attributes several centrality indices (degree, weighted degree, normalized weighted degree) have been estimated for one year period (2000) and some interesting features of the international migration network have been obtained.

Degree centrality characterizes the number of countries connected with the given country through migration flows. The USA, Canada and some European countries (Austria, Finland, Spain, Sweden) have the highest in-degree centrality. In other words, migration flows to these countries are originated in the highest number of different countries. The USA, The United Kingdom (the UK) and Germany have the highest out-degree centrality, i.e. the number of countries-destinations for migrants from these countries is the highest. The USA, Canada and Germany are ranked as top-3 by degree centrality and have the in-flow and out-flow of migrants from and to the largest number of countries.

The next group of centrality indices evaluated in that work are weighted degree centralities, which consider the number of migrants in inter-country migration flows. Weighted in-degree centrality is the number of immigrants and weighted out-degree is the number of emigrants for each country. In addition, the difference between in-degree and out-degree is calculated, which stands for the net migration flow. The USA, Germany and the UK have the highest number of migrant in-flow, Mexico, Poland and the UK are top 3 countries of migrant out-flow, and Germany, the USA and Switzerland have the highest net migrant flow.

Another step in that paper is the normalization of weighted degree centralities by the population of destination country. The normalization is important in the context of understanding the influence of immigration flow on the country of destination: the flows of 5000 people for countries with the population of around 0.5 million people (e.g., Luxembourg) and 300 million people (e.g., the USA) produce completely different effect. For example, Luxembourg, Switzerland and Germany are top 3 countries in ranking by normalized weighted in-degree, which is different from the top 3 countries by weighted in-degree centrality (Germany, the USA and the UK). The population of destination country is an essential network attribute used in our research.

The important aspect of international migration process is not only the flow of people, but also the integration of migrants into the host country. The level of integration has influence on migrants, host country population and future migration flows, as diaspora can attract new migrants [16]. In [21] migrants' integration in the large metropolises is explored from the perspective of spatial segregation. Spatial segregation in the urban areas is quantified by using the social media data from Twitter.

In this work migrant is defined as a user writing posts in a language other than a local one or in English. Each community is assumed to be fully integrated into the host society, when migrants are spread across the city area. On the contrary, low level of integration corresponds to the concentrated migrants' communities in the city, i.e., Chinatown, Indian neighborhood, etc. The idea is explored by the network with the following structure. There are two types of nodes: languages and cities, which are connected by edges. The edge weight is the degree of integration (). This metric shows how the real distribution of users is different from the random one. Random distribution stands for the case when migrants are spread across the city area, therefore, fully integrated. High values of mean that community is more integrated. It has turned out that London, San Francisco and Tokyo have a high level of integration and Istanbul and Moscow are characterized with lower level of integration. The new approach to measure the level of integration is relevant and may have applications to different data sources.

Recent works on international migration networks show possibilities to identify the influential countries in the network, communities of countries, explore the integration of migrants in the large cities. Literature on network analysis shows that connections in the international migration network have become more intense, certain migration corridors have been formed over the period. International migration is becoming a more complex process and network models can help to provide policy makers with essential information.

Conclusion

Classic theories identify the main incentives of migration on the individual level and determine the core mechanisms and groups of factors influencing migration. These factors are vital for understanding the migration process and theories. With the increase in spatial mobility of people the theory of migration was also improving. Current databases made it possible to explore the international migration flows in the integrated way applying network theory and gravity models. There is a significant number of works that study international migration using network and gravity models. However, there is still quite a few works that combine these techniques in the following way. First, the main trends and patterns of international migration are explored with the techniques from network analysis, then the determinants of network structure are explained with gravity model. These findings will be an essential step to the global understanding of the international migration and will help to develop an appropriate policy with the respect to most influential actors in the network and main stimuli identifying the process of migration.

Chapter 2. Network analysis of international migration flows

Introduction

This Chapter is devoted to the network analysis, in which all countries involved in the international migration are presented as a graph, where nodes are countries and edges - migration flows between them. This approach allows to consider the flows between any two countries integrated into the whole system of countries and shows how the changes in one flow may affect the flows between the other seemingly unrelated countries.

The main purpose of network analysis is to detect the countries with highest level of importance in the international migration network. For this purpose, we evaluate the classical and new centrality indices. Classical centrality indices are the fundamental attribute of the network analysis and are essential for the representation of major migration flows occurred within the network in each period. Nevertheless, there is a necessity to consider indirect connections between the countries and node attributes. We use the Short-Range and Long-Range Interactions Centrality Indices that consider the node attributes - population of the destination country as well as group influence and indirect connections between the countries in the network. Indices have been proposed in [7]. Application to international migration has been published in [8], where more detailed analysis of dynamics is presented.

2.1 Data on international migration flows

Data on international migration is usually presented in two fundamental statistical categories: stock of migrants and migration flows. Migration flow is defined as a number of persons arriving to country or leaving it in a given time period. Migrant stock corresponds to the total number of people living in a country other than the country of origin in a certain moment. The key difference between these two categories is that the stock of migrants is an accumulative pattern, and the flow data represents the fact of immigration or emigration to or from a given country.

We use the data on migrant flow for analysis of the international migration. The high frequency flow statistic is extremely difficult to find. Additionally, it becomes even more challenging when the research is focused not on the analysis of the migration within the certain geographical region or the association of countries, but on the international migration worldwide. The data provided by the United Nations [40,41] is rather helpful, when the purpose is to maximize the number of included countries. Therefore, the UN international migration flow statistics was used. However, international migration flow data usually lacks completeness and is collected by the national statistical agencies for various political purposes. These factors lead to difficulties in possibilities of making cross-country comparisons and inconsistency in data.

Next, we provide the description of the database and the steps accomplished to resolve the problem of inconsistency in data.

2.1.1 Data Description

Two datasets, both collected by United Nations Population Division [40,41] are used for the construction of international migration network. These datasets contain time series dyadic data on migration flows from selected countries.

The 2008 Revision includes data on international migration flows from 29 countries for the period from 1970 to 2008. The 2015 Revision is characterized by the increase in the number of countries to 45 and different period (from 1980 to 2015). The list of countries provided statistics for each database is presented in the Appendix 1. Migration flows for countries not included in the list are accounted by the statistics of the countries presented in each database.

To distinguish international migrants from other categories of movers, countries apply different time criterion - the minimal period of staying abroad. By this criterion countries are divided into the following groups: establishment of permanent residence (abroad), expected stay (abroad) of at least one year, six months, three months, other time criterion or they do not specify it.

The data have been collected through different sources: population registers, border statistics, the number of residents permits issued, statistical forms that persons fill when they change place of residence and household survey.

There are three ways to define country of migrants' origin or destination by

1) residence, 2) citizenship, 3) place of birth.

The distribution of countries from the two databases by this criterion is presented in Table 2.1.

Table 2.1. Distribution of countries by country of origin criteria

Most countries in both 2008 and 2015 Revisions define the country of origin as the country of previous residence. However, statistics differs in both datasets for inflows and outflows.

For 2008 Revision 21 country (Australia, Austria, Canada, Croatia, Czech Republic, Denmark, Estonia, Finland, Germany, Iceland, Israel, Italy, Latvia, Lithuania, New Zealand, Norway, Poland, Slovakia, Spain, Sweden, the United Kingdom) apply residence criterion to define the country of origin or destination. In seven countries (Belgium, France, Hungary, Luxembourg, Netherlands, Slovenia, Switzerland) the country of citizenship is used to classify migrants, and only in the United States the place of birth is used to define the origin of migrants.

There are considerable differences in distribution of countries by this criterion in the 2015 Revision compared to 2008: for 43 out of 45 countries there are data on migration flows based on residence. This list lacks only the USA and Canada, where place of birth and citizenship criteria are used correspondingly.

Additionally, as countries apply different criteria to determine international migrant and the country of origin, collect data through different sources and have various purposes of migration policy, there are some cases of inconsistency in observations. The steps proposed to make data more comparable are presented below.

2.1.2 Data aggregation

There are three key issues in aggregation of the databases: the choice of the most relevant criteria on the country of origin, inconsistency in data on the certain migration flows and the cases of flows with the same country of origin and destination.

The preference is given to statistics on residence, when data for both residence and citizenship have been available. The reason is that, as we can see from Table 2.1, more countries apply this criterion in the 2015 version. Additionally, this principle more accurately reflects the definition of the international migrant by the United Nations: person who changes his or her country of usual residence. Country of citizenship is not mandatory the country of usual residence and country, where migrant lived before (previous residence), that is why data on residence is more representative in terms of migration flows. The preference for the 2015 Reversion has been given as well, when there is the data from both datasets. An exception is the case, when there are data based on residence in 2008 version and no data on residence in 2015 version.

Overall in 5% of observations data is inconsistent: for the same migration flow data from different countries is not the same (8672 out of 173435 observations). In most of these cases the difference is not significant, therefore the average value is estimated. However, there are 21 observations, where simultaneously the minimum value is less than 10 and the ratio . We explain the reason of it by incorrect statistics of country with minimal value and take into consideration only maximum values. For example, for 5 observations the country of destination or origin is one of the former Soviet Union countries. After Soviet Union disintegration migration statistics in these countries was not of the high quality, therefore the maximum value is chosen. List of the observations with inconsistency is provided in Appendix 1.

Another feature of the data is the presence of flows, which have the same origin and destination countries (loops). Total number of loops in aggregated data is 743. The documentation of the 2008 Revision provides the following explanation of them. For Sweden and Spain: the criterion for the country of origin is citizenship and these migrants are returned citizens. These observations are not important for our study, because they do not contain the information about migrant's country of origin. Another case that is explained in the documentation deals with migration flows to and from Australia: “loops” are migration flows between Australia and its external island territories or internal migration. This data is not applicable for international migration flows. Other countries did not provide the information about such cases, thus we assume that the explanation is similar to one of the given above. Therefore, we can conclude that the cases of the same origin and destination countries can be excluded from observations, as they do not have any meaningful interpretation.