Consider an immigrant who settles in a new country. To find a job, he or she needs assistance in his/her job search. A large number of studies have shown that social networks, i.e., friends and family, play a major role in job searches. The empirical evidence reveals that also in the advanced economies such as the U.S., the informal search methods are a key deterrent of labor prospects (for a survey, see Ioannides and Loury, 2004). Moreover, Kahanec and Mendola (2007) examined the effect of social networks on labor market status and show that the role of social networks may be especially pronounced for an immigrant minority group. Thus, it is assumed that the immigrant can find a job using two different methods: by investing efforts in creating networks with migrants who arrived before he or she did, *c*, and by investing efforts in creating networks with the natives, *e*.

The strength of the immigrant's social networks is a function of both the immigrant's personal contacts and his or her identification with the culture, norms, and values of the group. The level of the group's commitment to the individual increases with the individual's similarity to that group's members. Thus, the level of efficiency of the immigrant's investments, *c* and *e*, depends on the extent of the relationship between the immigrant and the members of the group. This relationship is affected by the migrant's language acquisition and adaption to the culture and values of the group, among others. Therefore, the immigrant's investments, *c* and *e*, represent his or her ethnic identification with the source society and the new society, respectively. It is assumed for simplicity that the immigrant's leisure time, *T*, is fixed. The immigrant therefore allocates part (or all) of his/her leisure time to creating social networks with immigrants as well as natives. The time required to create social networks with immigrants can differ from that required to create social networks with natives. Let *β* (*β* > 0) denote this difference. Clearly, creating social networks with migrants requires less investment than creating them with the local population (*β* < 1).

The probability of finding a job, *p*, depends on the immigrant's level of social networking and satisfies: \( \frac{\mathit{\partial}p\left(e,c\right)}{\mathit{\partial}e}>0,\frac{\mathit{\partial}p\left(e,c\right)}{\mathit{\partial}c}>0,\frac{{\mathit{\partial}}^2p\left(e,c\right)}{\mathit{\partial}{e}^2}<0,\frac{{\mathit{\partial}}^2p\left(e,c\right)}{\mathit{\partial}{c}^2}<0 \).

Let *w* denote the potential wage that the immigrants can receive in the host country. This wage depends on pre-immigration characteristics such as gender, education, religion, economic status, etc.

We normalize the cost of investing in the migrants' self-network to unity and the cost of investing in the natives' network by *α* (*α* > 1). *α* depends on the cultural distance between the host country's and source country's societies. Denote this distance by *d. α* also depends on the immigrant's different characteristics, such as age and gender. We denote these characteristics by *α*.

The expected utility of the immigrant is given by:

$$ \mathrm{E}\ \left(\mathrm{u}\right)=\mathrm{p}\ \left(\mathrm{e},\mathrm{c}\right)\cdot \mathrm{w}-\mathrm{c}-\alpha \left(\mathrm{d},\mathrm{a}\right)\cdot \mathrm{e} $$

(1.1)

s.t.

$$ \mathrm{c}+\beta \mathrm{e}\le \mathrm{T} $$

(1.2)

Below, we assume that the time constraint is not bounding, i.e. *c* + *βe* < T. We develop the results for a bounding time constraint in the appendix and show that the main results do not change.

The optimal investment in the migrants' network, *c*
^{*}, and the optimal investment in the natives' network, *e*
^{*}, satisfy:

$$ \begin{array}{l}\frac{\partial \mathrm{E}\left(\mathrm{u}\right)}{\partial \mathrm{e}}=\frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{e}}\cdot \mathrm{w}-\alpha \left(\mathrm{d},\mathrm{a}\right)=0\\ {}\frac{\partial \mathrm{E}\left(\mathrm{u}\right)}{\partial \mathrm{c}}=\frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{c}}\cdot \mathrm{w}-1=0\end{array} $$

(1.3)

From (1.3), in equilibrium, it must hold that:

$$ \begin{array}{l}\frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{e}}=\frac{\alpha }{\mathrm{w}}\\ {}\frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{c}}=\frac{1}{\mathrm{w}}\end{array} $$

(1.4)

We assume that the migrants have a relatively smaller population than the local population, and there is therefore a higher return for being part of the natives' network than for being part of the migrants' network. In addition, the type and the quality of the jobs provided by immigrant networks is different than the jobs provided by the native networks (see Kahanec and Mendola, 2007). Let *λ*(*λ* < 1) denote the efficiency of investing in the migrant network vs. the native network. Thus:

$$ {\left.\frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{c}}\right|}_{\mathrm{e}=\mathrm{c}}={\left.\lambda \frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{e}}\right|}_{\mathrm{e}=\mathrm{c}} $$

(1.5)

Moreover, as the stock of immigrants in the host country, *N*, increases, the effectiveness (efficiency) of investing in the migrants' network increases: \( \frac{\partial \lambda }{\partial \mathrm{N}}>0 \).

Whether the investment in the migrant network is higher or lower than in the native network depends on the relationship between \( \frac{\alpha }{\mathrm{w}} \) and \( \frac{1}{\mathrm{w}} \) and the relationship between \( \frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{e}} \) and \( \frac{\partial \mathrm{p}\left(\mathrm{e},\mathrm{c}\right)}{\partial \mathrm{c}} \). Thus, whether an immigrant will invest more in one network than the other depends on the relative cost and benefit from these investments such that (see Figure 2):

$$ \begin{array}{l} if\kern0.5em \alpha >\frac{1}{\lambda }\ than\ {c}^{*}>{e}^{*}\\ {} if\kern0.5em \alpha =\frac{1}{\lambda }\ than\ {e}^{*}={c}^{*}\\ {} if\kern0.5em \alpha <\frac{1}{\lambda }\ than\ {e}^{*}>{c}^{*}\end{array} $$

### Comparative statics

Let us try to understand the implications of the above results. As noted, the relative cost, *α*, is affected by cultural distance, *d*, and personal characteristics, *α*. The first component, cultural distance, is created by different languages, ethnicities, religions and social norms (see Ghemawat, 2001, Adsera and Pytlikova, 2012). Clearly, as the cultural distance between the source society and host society increases, the immigrant's need to invest more effort to integrate into the host society also increases; thus, the relative cost, *α*, increases. The second component, personal characteristics, includes the immigrant's age at entry and his or her ability to create social networks. As the immigrant's age increases, his or her ability to acquire the new language and the new social norms decreases, and thus the relative cost, *α*, increases (see, for example, Chiswick and Miller 2005).

Now suppose that the cultural distance between the host society and the source society, *d*, increases or, alternatively, that the immigrant's age at arrival increases such that the relative cost of investment in the native compared to migrant network, *α*, increases. Looking at Figure 3, \( \frac{\alpha_0}{\mathrm{w}} \) increases to level \( \frac{\alpha_1}{\mathrm{w}} \), and thus the immigrant's optimal investment in the native network decreases from \( {\mathrm{e}}_0^{*} \) to \( {\mathrm{e}}_1^{*} \), whereas his or her optimal investment in the migrant network does not change. In other words, cultural distance between the host country and the home country or an older age on arrival decreases the ethnic identity with the host society. In term of the *ethnosizer*, cultural distance between the host country and the home country or an older age at arrival causes *marginalization* (if \( {\mathrm{c}}_1^{*} \) is low) or *separation* (if \( {\mathrm{c}}_0^{*} \) is high).

As shown above, the potential wage that immigrants can receive in their host country depends on pre-immigration characteristics such as gender, level of education, experience, etc. Take two individuals who differ in their gender or education: the first can earn w_{0}, whereas the second can earn w_{1} (w_{0} > w_{1}). Figure 4 shows that the individual with the high potential wage (which derives from college and higher education or vocational training in the source country) increases ethnic identity with the host society as well as the source society. In term of *ethnosizer*, a high potential wage at entry decreases *separation* and *marginalization*.

Finally, suppose that the efficiency level of the relative investment in the immigrant's network, *λ*(N), increases. This can happen, for example, when the stock of migrants in the host country increases, thus enabling immigrants to obtain more information on the job market. It also can happen when the political strength of the minority group increases as result, for example, of the election of a minority member to parliament. It is easy to see from Figure 5 that the immigrant will increase his/her investment in the migrant network from \( {\mathrm{c}}_0^{*} \) to \( {\mathrm{c}}_1^{*} \), whereas the investment in the native network will not change. It is thus expected that when the stock of immigrants in the host country increases or the minority's political strength increases, the ethnic identity with the source society will increase. In term of *ethnosizer*, *separation* or *integration* will be obtained. This is consistent with the findings of Constant et al. (2009a) and Constant et al. (2006b) of differences in the ethnic identity of different groups that can be followed by the size and political strength of the groups in the host country.