4.1. Benchmark Regressions

In our benchmark regressions, we do not differentiate between education levels and assume that the coefficients (μ^s_i, μ_j^s, δ^s, α^s, β^s) are identical across different education groups. The dependent variable N_ij in (5) measures the total migration flow from origin country i to US metropolitan area j between 1990 and 2000. As explained above, the PPML estimator addresses the issues created by the presence of large number of zeroes in the migration flows. We use robust estimates, important with the PPML estimator, since failure to do so often leads to underestimated standard errors and unrealistic t-stat above 100. Regression results are presented in Table 2. The standard errors are not reported to save space since they usually lead to estimates of δ^s, α^s, and β^s with t-stat higher than 10.

Table 2. Overall network effects – per sub-samples

Notes: PPML estimates of equation (5). All parameters significant at the 1 percent level except if (a): five percent level; robust estimates. (b) Computed as the difference between the total network and policy effects. Estimation carried out on migrants aged 15 years and over, on the 1990–2000 period; threshold in terms of the size of the total diaspora at destination (across all US metropolitan areas).

The use of the full sample involves the inclusion of small origin countries with idiosyncratic migration patterns. In particular, the coefficients δ^s, α^s, and β^s could be different from the ones for larger countries. Furthermore, many of these countries have fewer than a total of 500 migrants in the US, and their distribution across the US cities is not properly captured in the census data due to imperfect sampling.Footnote ¹⁴ We adjust the initial sample and leave out micro states which we define in terms of the total size of their migrant stock in the US in the year 1990. We use different threshold values: 1040, 2900, 7300, and 10000 migrants in the US. Depending on the threshold, the number of source countries included in the sample equals 135, 113, 104, or 99, respectively. These samples account for 99.9 to 98.9 percent of all immigrants and the respective regression results are reported in columns 1 to 4 of Table 2.

The estimate of the total diaspora effect (given by α + β) is reported on the first line of the table and is consistent with existing literature. The key parameters are quite stable across subsamples which is mainly due to the fact that we capture almost all of the migrants in the US, although we leave out a number of very small source countries. We find that 1 percent increase in the initial network size in 1990 approximately leads to a 1 percent increase in the bilateral migration flow between 1990 and 2000. The results further suggest that one fourth of the network effect, i.e. β/(α + β), is due to the national policy channel, and the rest, i.e. α/(α + β), is due to the assimilation channel. In other words, despite the fact that β can be taken as an upper bound, the magnitude of the policy channel is around 0.25 only. This is slightly lower than the 10-year sponsorship rates obtained by Jasso and Rozenzweig (Reference Jasso and Rosenzweig1986, Reference Jasso and Rosenzweig1989) because observed sponsorship rates capture the joint effect of networks on migration aspirations and realization rates. We identify only the “realization” part of it in this estimation. The elasticity with respect to distance is around − 0.5 regardless of the sample size.

Results in columns 1 to 4 were based on the flows of immigrants aged 15 years and over at time of arrival, regardless of their current age and gender. Next, we use alternative definitions of migration flows and show that, overall, the results are fairly robust to the choice of alternative measures. In column 5, the immigrant sample is restricted to ages 15 to 65 years at the time of arrival. Excluding elderly immigrants slightly reduces the magnitude of the policy channel as expected. In columns 6 and 7, we distinguish between male and female migrants above age 15 years at arrival. The main difference is that the national policy effect is found to be slightly greater for men than for women, while the assimilation effect is greater for women.

Our identification strategy relies on the definition of metropolitan areas used by the US census bureau, which defines the location of our local network/diaspora. In other words, we assume the migrant and his local network are located within the same US metropolitan area. In order to test the robustness to this particular assumption, we modify the definition of the geographic area corresponding to the local network.

In column 7, we now consider that the M_ij variable is composed of the number of migrants from country i living in metropolitan area j as well as in neighboring metropolitan areas that are located within 100 miles from the center of j.Footnote ¹⁵ In about 50 percent of the cases, this modification leads to a sizeable increase in the network mass. Changing the definition of the geographic area in column 8, we find that both effects are roughly similar to the estimates of the regressions presented in columns 1 to 4. The assimilation effect is similar and the policy effect is slightly smaller than in the benchmark regressions.

4.2. Education Level

The existing literature has shown that the magnitude of the network effect on future migration flows tends to decline with the skill levels of immigrants (Carrington et al., Reference Carrington, Detragiache and Vishwanath1996; Winters et al., Reference Winters, de Janvry and Sadoulet2001; McKenzie and Rapoport, Reference McKenzie and Rapoport2010; Beine et al., Reference Beine, Docquier and Ozden2011). It is usually argued that low-skilled migrants face higher assimilation costs and policy restrictions at destination countries. Hence, they rely more on their social networks to overcome these barriers.

In line with the existing literature, we first differentiate between migrant flows based on their education levels to identify different skill categories. There is a certain level of imperfection in the census data since the education level is given by the number of years of completed schooling as reported by the migrants who come from different countries with different education systems. Comparison across origin countries is difficult. Nonetheless, we aggregate new immigrants into three different categories, as it is usually done in the literature (Docquier et al., Reference Docquier, Lowell and Marfouk2009). These categories are (i) low-skilled immigrants with less than 11 schooling years (labeled as “Primary”); (ii) medium-skilled immigrants with more than 11 schooling years up to high school degree (labeled as “Secondary”); (iii) the high-skilled immigrants who have at least one year of college education (labeled as “Tertiary”).

We separately estimate equation (5) for these three education levels. Results are presented in columns 1 to 3 of Table 3. Note that we only record immigrants who completed their education prior to migration and did not receive any further education in the United States. This distinction allows us to separate out migrants who entered as children with their families or who entered for education purposes under special student visas. In line with existing literature, we find that the total network effect (α + β) decreases with the education level of migrants, from 1.146 for the low skilled to 0.884 for the college educated. In addition, we find the local assimilation effect, given by α, is greater for low-skilled migrants (0.763) than for college graduates (0.655). The difference in the policy effect is, however, more pronounced (0.383 for the less educated, 0.149 for the medium skilled, and 0.229 for college graduates). These results indicate that the network effect is greater for the less-educated migrants, mostly because it helps them to overcome the national policy restrictions. Moreover, low-skilled migrants are much more sensitive to distance as seen from the sharp decline in the coefficient of distance as education level increases.

Table 3. Results – education level and quality

Notes: PPML estimates on countries with less than 7300 migrants All parameters significant at the 1 percent level, otherwise mentioned; robust estimates. (b) Computed as the difference between the total network and policy effects.

Our educational breakdown does not account for the heterogeneity in the quality of education across origin countries. Migrants from different countries might have similar degrees on paper but different skill levels and human capital. For example, a university degree obtained in a high-income OECD country might imply a higher level of human capital than a degree obtained in a low-income country.Footnote ¹⁶ Such disparities in educational quality matter as our sample only includes immigrants who have completed their education at home. If the quality of education differs significantly among immigrants with the same education levels, the ability to migrate outside family reunification programs or other legal channels might also be different. In the case of poorer countries with lower educational standards, one would expect the policy component of the total network effect to be stronger.

There is no official measure of quality of education by origin country. In a highly innovative paper relevant for us, Coulombe and Tremblay (Reference Coulombe and Tremblay2009) showed that the skill-schooling gap is highly correlated with the level of GDP per capita in the origin country. Based on their results, we estimate (5) distinguishing between three types of source countries. These groups are (i) low-income countries, (ii) middle-income countries, and (iii) high-income countries. We follow the World Bank income classification and, for each group of countries, we use the same thresholds in terms of size of the US diaspora. Obviously, income levels of the origin countries capture many other effects such as the level of development of financial markets, domestic political conditions, quality of economic institutions, etc.

Results of these additional regressions are reported in columns 4 to 6 of Table 3. We find that the overall network effect decreases with income level from 1.905 for low-income countries to 0.968 for high-income countries. In line with the previous estimates of columns 1 to 3, we find that most of the variation is driven by the national visa/policy effects. The policy effect equals 0.211 for high-income countries; it declines to 0.439 for middle-income and, finally, to 1.173 for low-income countries. These results imply that networks play an important role in providing legal access to the US to migrants from low-income countries. On the other hand, the assimilation effect shows almost no variation. We obtain an elasticity of 0.732 for low-income countries and 0.757 for high-income countries. Finally, we see that migrants from developing countries are more sensitive to distance as we would expect. On a final note, the diaspora is also composed of members with different education levels and they might differential impact on migration patterns. We have performed the estimation with multiple diaspora variables, differentiated according to education levels. The results were not different.

4.3. Flows in the 1990’s vs 1980’s

Our analysis in the previous sections focused on the effect of the diaspora size in 1990 on immigration flows to the US between 1990 and 2000. Our dataset includes similar variables for the migration stocks and flows in the 1980’s. Hence, we can conduct the same regressions on the flows observed in the 1980’s to investigate whether there has been any important changes in the migration patterns and the relative size of network effects. An alternative strategy would have been to combine observations from the 1980’s with those from the 1990’s and use a panel approach by pooling the data from the two cross-sections. Since we expect network effects to vary over time, we prefer the present approach.

Although we are not aware of a sizeable cultural shift that could affect the assimilation effect in the US, it is well documented that the US immigration policy changed significantly between the 1980s and the 1990s. The main changes are due to the 1990 US Immigration Act and the 1986 Immigration Reform and Control Act, which clearly expanded opportunities for family reunification. The main feature of the 1990 Act is that the number of immediate relatives of US citizens who can migrate is not limited or capped under the law. Therefore, quotas for family reunification can be exceeded in practice if the applications by immediate family members are above the estimated number by the law in a given year. As a result, as more immigrants previous cohorts obtain US citizenship, there is a natural upward trend in the number of people coming under the family reunification scheme sensu lato. The 1986 Act corresponds to the amnesty or legalization programs undertaken. As large numbers of undocumented migrants obtained legal resident status, they also became eligible to bring additional family members through the legal channels. Those who became citizens through the amnesty were even able to bring their relatives through the uncapped channel. Therefore, these policy developments suggest that the estimated β coefficient might have increased between the 1980’s and 1990’s.

Table 4 reports the estimates obtained for the 1990’s and the 1980’s. For each period, we estimate the model on all migrants, on those with college education and on the less educated. Our estimates suggest that the national policy effects were greater during the 1990’s than during the 1980’s for all immigrant categories. The change is more important for less-educated migrants, for whom the policy effect doubled within a decade. This change is likely to capture the joint effects of the 1986 and 1990 Immigration Acts. On the other hand, the assimilation effect (α) remained stable across the two decades at around 0.75 for the low skilled and 0.65 for college graduates.

Table 4. Flows in the 1990’s vs 1980’s

Notes: All = All skill types; LS = low skilled; HS = high skilled. PPML estimates on countries with more than 7300 migrants. All parameters significant at the 1 percent level. (b) Computed as the difference between the total network and policy effects. Robust estimates. Estimation carried out on migration flows of individuals aged 15 years and over.

4.4. Distance Thresholds

Geographic distance is one of the major barrier to migration. Furthermore, distance is a source of positive selection as its effect as a barrier is greater for the less educated. This differential impact of distance was illustrated in Table 3. Even though country fixed effects partly control for bilateral distances in our estimations, the sheer size of the US still leads to significant variations in terms of the distance and accessibility from origin countries to different American cities. For instance, the Caribbean countries that are close to the US are likely to send more migrants to cities in the south-east compared to the north-west. In the subsequent set of estimations, we define remote and close countries on the basis of the minimal distance to the US border with a cut-off of 6,790 kilometers. This is the median distance in terms of pairs of origin countries and US metropolitan areas. We also consider the effect of distance for two educational levels, college graduates, and the less educated. Results are presented in Table 5.

Table 5. Close versus remote countries

Notes: PPML estimates on the flow of migrants aged 15 years and over from countries with more than 10,000 migrants in the US. All parameters significant at the 1 percent level, except those superscripted n (non-significant). (b) Computed as the difference between the total network and policy effects. If not mentioned, robust estimates. Cut-off value to define far and close: 6,790 kilometers.

First, we find that distance plays a much more important role for migrants coming from remote countries (columns 1 and 2). The coefficient of distance is significantly smaller when the origin countries are closer to the US which are the Latin American and Caribbean countries. Second, the total network effect is slightly larger when origin countries are far away but this is not statistically significant. However, there is a difference in terms of composition. The national policy effect is greater for distant countries while the local assimilation effect is more important for closer countries.

We obtain more nuanced results when we compare the importance of distance for different education levels in columns 3 to 6. For low-skilled migrants, distance seems to be a very significant deterrent to the extent that it becomes prohibitive. We find that for the low-skilled migrants from distant countries, the policy effect becomes insignificant. On the other hand, for college-educated migrants from distant countries, the visa effect is much greater when compared to neighboring countries.

Finally, we see that the difference in the local assimilation effect between distant and nearby countries becomes small when we control for education. Hence, differences between columns 1 and 2 are mainly due to the skill composition of migration between close and remote origin countries. Once similar migrants pass the border and enter the US, the local assimilation effect does not vary with distance.

4.5. Dropping Small Cities

In order to assess the robustness of our results, it is also relevant to check whether our findings are driven by the inclusion of small cities, which we define as metropolitan areas with a small number of immigrants. Our source of concern is that small cities have larger numbers of zero observations at the dyadic level for both ln(1 + M_ij) and ln(1 + Π_ij). This may lead to spurious correlation between these two variables. Therefore, we re-estimate equation (5) after dropping small countries as well as small cities. As described in the first two rows of Table 6, we drop countries with less than 7,300 or 10,000 migrants in the US, and we drop small cities with less than 2,900 migrants or less than 7,000 migrants. Combining the two cut-off values yields four alternative regressions with very robust results where the values of the assimilation and the policy channels are barely affected.

Table 6. Dropping small cities

Notes: PPML estimates. All parameters significant at the 1 percent level; otherwise mentioned; robust estimates. (b) Computed as the difference between the total network and policy effects. Estimation carried out on migrants aged 15 years and over, on the 1990–2000 period; threshold in terms of the size of the total diaspora at destination (across all US metropolitan areas).

4.6. Unobserved Heterogeneity

Another potential econometric issue is generated by the presence of unobserved bilateral factors ν^s_ij influencing the bilateral migration flows N^s_ij. In absence of observations for those factors, their effect will be included in the composite error term given by ν^s_ij + u_ij ^s = η^s_ij.Footnote ¹⁷ If those factors also influence the network size M_ij, this leads to a correlation between the error term and one covariate, invalidating the use of OLS and PPML estimators. This is known as the correlated effect problem (Manski, Reference Manski1993).

A traditional approach to take care of the correlated effect bias is to use instrumental variables to predict value of M_ij using a variable that is uncorrelated with N_ij. Given that we estimate model (5) in a PPML set-up, the solution is not straightforward. Tenreyro (Reference Tenreyro2007) proposes a method to combine PPML estimators with instrumental variables estimator which can be implemented with the Generalized Method of Moments (hereafter GMM). Dropping the s subscript for convenience of exposition and aggregating all explanatory variables c_j, M_i, d_ij, and Π_ij into the x_ij vector, the PPML estimator γ solves the following moment condition:

(7)$$\begin{equation} \sum _{ij}^{n}[N_{ij}-exp(x_{ij}\gamma )]x_{ij}=0. \end{equation}$$

In order to instrument x_ij, one can use the following GMM estimator denoted by ψ as an alternative

(8)$$\begin{equation} \sum _{ij}^{n}[N_{ij}-exp(x_{ij}\psi )]z_{ij}=0. \end{equation}$$

In this expression, z_ij represent the vector of instruments, i.e. variables that are supposed to be correlated with M_ij but uncorrelated with N_ij. We rely on the GMM estimator ψ using two potential instruments which are the variables ln(1 + M_ij) and ln(1 + Π_ij) observed in 1950, i.e. about 40 years before the observed diaspora patterns in the benchmark regression. Relying on an internal instrument is problematic if unobserved heterogeneity is driven by persistent dyadic factors such as cultural proximity or climatic variables. If it is the case, our instruments are likely to be correlated with ν^s_ij, invalidating the exclusion condition.

However, using migration stocks prior to the 1965 Hart–Celler Act as instruments might be an appropriate approach for the US. Indeed, the Hart–Celler Act (or 1965 Immigration and Nationality Act) abolished the system of national-origin quotas that had been in place in the US since 1921. As a result, the origin structure of immigration flows changed rapidly after 1965, with many more migrant arriving from developing regions (Asia, Africa, the Middle East, and Lain America) and much less from Western Europe. In addition, data reveal larger geographic dispersion in 1990 than in 1950 (Durand et al., Reference Durand, Massey and Charvet2000; Funkhouser, Reference Funkhouser2000, McConnell, Reference McConnell2008). For example, Mexican migrants in the 1950’s had obviously a strong preference for nearby metropolitan areas with similar climatic conditions. This is not the case anymore since Mexican migrants have spread out to every city in the US. Another example is that of Puerto Rico migrants who tend to concentrate in New York where the climate is quite different from the one prevailing in Puerto Rico.

Despite the 1965 policy reform, immigration stocks in 1950 are reasonably correlated with those of 1990 (a tiny part of the stock of 1990 was already present in 1950). In contrast, the network and policy effects on the flows during the 1990’s associated with the migrants already present in 1950 are supposed to be quite limited. Shortly, the IV results should be mainly seen as robustness checks since they are valid under the condition that unobserved factors of N_ij should not be too persistent over time. Another drawback of using such an instrument is that it leads to a change in the sample. This is first due to the fact that the definitions of origin countries and US metropolitan areas have significantly changed between 1950 and 1990. A second reason is the independence of many former colonies during the 1950’s and 1960’s as distinct origin countries.Footnote ¹⁸

We first re-estimate the PPML regressions and use those estimates as a benchmark with respect to the IV-PPML (or GMM) estimates. Table 7 reports the estimates of the PPML on the restricted sample in column 1 (without instrumenting), and of the IV-PPML estimates à la Tenreyro in columns 2 and 3. In column 2, we use one instrument only, i.e. ln(1 + M_ij) observed in 1950, while in column 3, we supplement the instrument set with ln(1 + Π_ij), again observed in 1950.Footnote ¹⁹ The results show that our estimates are strikingly robust to the instrumentation procedure. Both the total diaspora effect and the estimated policy effect are very similar across estimation methods. They are also very similar regardless of the inclusion of ln(1 + Π_ij) variable observed in 1950.

Table 7. Instrumenting network sizes

Notes: Column 1 : PPML estimates. Columns 2 and 3: IV-PPML or GMM estimates. All parameters significant at the 1 percent level. (b) Computed as the difference between the total network and policy effects. Robust estimates. Estimation carried out on migration flows of individuals aged 15 and over. Instrument for IV estimates in col 2: local network size observed in 1950. Instruments for IV estimates in col 3: local and national network sizes observed in 1950.

4.7. Homogeneity Assumption

Our identification strategy assumes that the functional forms for the local assimilation and the national policy effects of the diaspora networks are identical. In particular, we assume that both effects have log-linear form. It is important to assess whether this homogeneity assumption affects our results. One possibility is to estimate directly α and β in equation (4). Unfortunately, this is not possible if one accounts for unobserved heterogeneity across origin countries via inclusion of the fixed effects (μ^s_i) in the estimated equation. As an alternative, we proceed via a two-step estimation of equation (4). In the first step, we estimate the following equation via PPML estimation:

(9)$$\begin{equation} \ln N_{ij}^{s}=\widetilde{\mu }_{i}^{s}+\mu _{j}^{s}-\delta ^{s}\ln d_{ij}+\alpha ^{s}\ln \left( 1+M_{ij}\right), \end{equation}$$

where the origin fixed effect ($\widetilde{\mu }_{i}^{s}$) now accounts for the national policy component of the network effect.

This first estimation yields the coefficient for α for the 1990’s. Interestingly, using a cut-off value of 7,300 US migrants to exclude small countries, we get an estimated value for the coefficient of α equal to 0.719. This is strikingly close to the value of α in Table 2. The estimation of (9) also yields an estimate for $\widetilde{ \mu }_{i}^{s}$ which can be used in a second step as the dependent variable. More precisely we can estimate the value of β with the following country-level regression based on (4):

(10)$$\begin{equation} \widetilde{\mu }_{i}^{s}=\gamma +\beta ln(1+M_{i})+\rho ^{\prime }X_{ik}+\xi ln(N_{ii})+\omega _{i}, \end{equation}$$

where ω_i is an error term and where X_ik are country-specific time-invariant factors. The inclusion of the X_ik is supposed to account for the variability in the $\widetilde{\mu }_{i}^{s}$ that is unrelated to the policy effect. We consider four potential factors: trade openness captured by the share of export to GDP, GDP per capita in 1990, a dummy variable capturing whether the country speaks English of not, and a regional dummy as defined by the World Bank official classification. In line with Section 4.3., the sign of the GDP/capita variable should be expected to be negative as rich countries are shown to have a lower magnitude for the policy effect. The estimation tends to confirm this expectation. Note also that we include a proxy for N_ii, i.e. the size of native population staying in their origin country between 1990 and 2000.Footnote ²⁰

The following exercise should be nevertheless seen as a sub-optimal procedure, aimed only at guessing the importance of the linearity assumption for both externalities. The reason is threefold. First, the method is a two-step method, which is less efficient that the one step estimation methods like the one used earlier. Second, the inclusion of observable variables and the estimation of country fixed effects lead to small sample sizes. Finally, as reflected by the measure for N_ii, our proxy that are specific to each origin country are likely to be plagued by measurement errors.

Table 8 reports the estimation results. The results suggest that the impact of economic development is, as expected, negative. The estimated value of β ranges between 0.19 and 0.26, which is clearly in line with the estimated β in Table 2. Although the two procedures are quite different, the results are relatively similar and this robustness check confirms that the local assimilation effect tends to dominate the global policy effect. Overall, this exercise suggests that our identification strategy yields sensible results, and that the functional homogeneity assumption does not seem to have a visible influence on the magnitude of the policy effect.

Table 8. A two-step identification strategy (dependent: $\widetilde{\mu }_{i}^{s}$)

Notes: First-step estimation described by equation (9). Cut-off values of inclusion of origin countries: 7,300 migrants. Note that the first-step estimated α is 0.719. a, b, c: significant at 1 percent, 5 percent, and 10 percent level respectively.