Formation of Internal Migrant Networks An Economics Approach

Introduction
We are embedded by our social networks. Social networks or connections has had important role in shaping of agents behavior. “While the importance of embeddedness of economic activity in social settings has been fundamental to sociologists for some time, it was largely ignored by economists until the last decade”.(Zenou, 2016). The role of social networks in shaping behavior and formation of networks has received increasing attention recent years. Some central questions in the area of economics of social networks are as follows. How agents are affected by their social networks’ member? How our connections can improve our output? Why there are different shape of networks? Which factors are important in formation of network? Which networks are efficient and stable? Migration, by nature, is a phenomena that is involved in relationship and contacts. In this regards, migration is an attractive area in economics of social network. While there are several economic theory about migration, from theories of initiation and perpetuationofmigration to theories of migration’s welfare effect, some economists has done research about economic, social and cultural assimilation of migrants. In this line of research, formation of migrants’ network is a new open issue. Which factors are important in formation of network of migrants? Which shape of network would emerge in short run and long run? And so on.
The paper aims to find essential factors which are important factor in shaping network. Moreover, optimal level of effort migrants to link with central migrant is investigated and developed to heterogeneity condition. To do so, a survey among Ardablian who migrated to Rasht is conducted and run dyadic regression based on theoretical background.
Theoretical Background, Method and data
Social network, as an unofficial institution, can improve our understanding from social and economic phenomena. Generally speaking, there are three scopes of research in the field of social networks. Network effect (also known as games on network), network formation, topology and structure if network are the ongoing area of research. The paper is categorized in the network formation scope. Network formation models are modeled by two different approaches: strategic network formation and stochastic network formation. Obviously, economists are more interested in strategic approach. There are different methods of model of strategic network formation. Table 1 shows a comprehensive classification of strategic network formation models.
Table 1- Strategic network formation models

Cooperative and Noncooperative models
Farsighted and Myopic models
Dynamic and Static models
Complete and Imperfect Information model

We followed Brueckner (2006) and Epstein and Heizler-Cohen (2016), which is a complete information, myopic and noncooperative model to as a basis for our econometric model. We applied logit method for dyadic data to detect effective factors on network formation. Based on our theoretical model, several variables such as time of arrival, distance at birthplace are used as explanatory variables as well as variables such as age, education and income as proxy for homophily are employed as control variables.
Finally, equation (1) estimated, following Fafchamps and Gubert (2007) method to correct standard errors to overcome inference problem. 
 
 
L_ij = a+b₁ ¦z_i-z_j¦ +b₂(z_i+z_j)+c ¦d_ij¦ +u_{ij                                                        (1)}
 
 
Where z_j and z_i ,  d_ij and d_ij are nodes’ (migrants) specification (such as time of arrival), specification of link (such as distance at birthplace) and error term, respectively.  L_ij stands for relationship matrix, including 0 and 1. 
Moreover, in order to focus on importance of time of arrival, two another form is specified. Equation (2) is a second degree model and equation (3) is a model with dummy variable for different time of arrival.
L_ij = a+b₁ ¦z_i-z_j¦ +b₂(z_i+z_j)+c₁ ¦d_ij¦ +c₁+d_ij²+u_{ij                                       (2)}
L_ij = a+b₁ ¦z_i-z_j¦ +b₂(z_i+z_j)+c₁ ¦d_ij¦ +δD+u_{ij                                               (3)}
It is noteworthy that, the models are reestimated after adding control variables such as differences in education, age, income as proxy for homophily. In order to gathering data, a purposeful questioner designed and a survey conducted among Ardablian who migrated to Rasht. Finally, 411 members and 400 links are detected.
As mentioned before, optimal effort of migrants to making link is investigated.
Bi=(P(e^s_i,1))u+ P (e^s_i,1)(∑^h=2 P(e^s_h,1)v)-e^s_{i,1                                             (4)}
Where is cost or effort in a star network. P(e^s_i,1 ) stands for the intensity (or strength) of the relationship between i and j depends on the investment e. B_j  , u and v stand for benefit or payoff from the friendship, utility of making direct connection and utility of indirect links, respectively.
The optimal effort of individual i who is invested in the linking with the central agent can be obtained as follows:

δB_i⁄δe^s_{i,1 = 0} →δP(e^s_i,1 )⁄δe^s_{i,1 =} 1⁄u+ ∑^h=N P(e^s_i,1 )v                         (5)

In the formation of a star network, the intensity of the agents’ relationships with the central agent increases in every period not with homogenous utility but also with heterogeneity in direct and indirect utility.
Finding
According to our estimations, distance at birthplace (suggesting that migrants who are born in close by locality are more prone to making link), sum of arrival time and differences between time of arrive have explanatory power (Table 5, Panel a).
Moreover, according our second model estimation, squared arrival time has significant effect in linking. It means that there is significant U-shaped relationship between the probability of linking and time of arrival to destination such that new migrants prone to link with old migrants and also tend to making connection between themselves (Table 5, Panel b). Our final estimation shows that migrants are more likely to connects with their cohort (who migrants less than 5 years) and link with older migrants (who migrated more than 23 years) (Table 5. Panel c).Adding control variable does not have a significant effect on the mentioned results. In other words, although some our control variables are significant, the main finding does not change (Table 6, Panel a, b and c).
Conclusion
Results show that time of arrival, distance at birthplace, age, education and income has significant effect on probability of making link.  Furthermore, there is a U shape relationship between probability of making link and time of arrival, which indicates tendency of migrants for linking to cohort migrant also earlier migrants. Another finding which stems from our contribution is that optimal level of effort increases in each period and this finding hold at special level heterogeneity.