A Spatial Analysis of Migration Choices

A Spatial Analysis of Migration Choices Alice Milivinti and Giacomo Benini January 22, 2018 Abstract The amount of migration between two countries is determined not only by the push and pull factors connecting the two nations, but also by the accessibility of alternative destinations. The influence second-best options exert is called multilateral resistance to migration. Its mathematical derivation comes either from the distribution of the unobserved part of the agent s utility or from the sequential nature of the migration decisions. However, its origin is often treated as a "black-box". In order to understand which sources of attractiveness cause the biggest correlation between alternative destinations, the current paper disentangles the concept of multilateral resistance into a series of exogenous interaction effects which are weighted using geographical, linguistic, economic, institutional and networks proximity. Empirical results, obtained from OECD bilateral flows, suggest that all the contiguity definitions employed generate some sort of inertia, but the largest effects are engendered by immigration laws. Keywords: International Migration, Spatial Panel Model, Spatial Autocorrelation, Multiple Origins and Destinations. JEL Classification: F22, C21, O15, J61. Faculté de Sciences de de la Societé, Institut de Démographie et Socioéconimie, Bd du Pont-d Arve 40, 1205 Genève, alice.milivinti@unine.ch, +41 32 718 39 50. NCCR on the move: NCCR - Swiss National Centre for Competence in Research the Migration-Mobility Nexus. 1

1 Introduction Migration is a double dimension phenomenon. Individually people chose weather to move according to their utilities. Globally these decisions tend to be interdependent. This interplay between a micro and a macro dimension generates theoretical as well as empirical difficulties. From a modelling point of view, it becomes harder to justify traditional discrete choice frameworks which rely on the Independence of Irrelevant Alternatives (IIA). From a practical point of view, it becomes necessary to collect data on bilateral flows as well as on socio-economic variables for all the countries involved in the migration. In recent years researchers have tried to address both these complications. The first step in this direction was the gradual abandonment of traditional random utility models (RUM) (Clark, Hatton, & Williamson, 2007; Pedersen, Pytlikova, & Smith, 2008; Lewer & den Berg, 2008; Hanson, 2010; Mayda, 2010; Grogger & Hanson, 2011), specifically designed to describe independent and mutually exclusive choices, in favour of more flexible frameworks where decisions are interconnected (McFadden, 1978). This novelty sprang out the relevance of outside options showing how the elimination of any non-chosen destination could affect the selection process. Such interrelation, normally referred as multilateral resistance to migration (MRtM), captures the influence exerted by third nations in determining the migration flows between a give pair of states (Bertoli & Moraga, 2013). The second step was the progressive construction of longitudinal datasets able to record origin-destinations matches over time which allowed to control for cross-sectional spill-overs while capturing the dynamic nature of migration. For example, Ortega and Peri (2013) included a set of origin-time dummies in order to account for MRtM, while Bertoli and Moraga (2013) and Bertoli, Brücker, and Moraga (2016) achieved the same result using the Common Correlated Error estimator (Pesaran, 2006). Regressions derived from these more general models acknowledge the effect exercised by the MRtM, while statistical expediences correct the bias resulting from its omission. However, in virtually all cases, the origin of the MRtM is unclear. Recent attempts to overcome this limitation are Bertoli et al. (2016) and Marchal and Naiditch (2016) who respectively explained its genesis by the sequential nature of the migration decisions and by the budget constraint faced by the migrants. Moving in 2

the same direction the current paper tries to deepen our understanding of the MRtM implementing a spatial econometric technique which allows us to (1) identify which are the characteristics shared by different countries that made them perceived as true alternatives; (2) understand how such peculiarities matter and in which ways they are impacting migration dynamics; (3) disclose why they are important in migration decisions. To accomplish these purposes, we propose a spatial analysis which would, not only allow to capture cross-sectional relationship between migration rates, but also to test different definitions of alternative destinations. From the theoretical point of view this translates into a spatially correlated logit (SCL) (Bhat & Guo, 2004) and empirically into a spatial lag of exogenous variables model (SLX). The SLX model permits to introduce weighting matrices specifically designed to capture the migrants preferences towards geography, language, institutions and networks. Therefore, (1) and (2) are empirically explained by estimating which weighting matrices deliver significant results and observing how the spatial interaction coefficients change in terms of sign and magnitude for different exogenous effects. Finally, the analysis reaches a deeper level by understanding the rational (why) lying behind the obtained results. For example, let suppose we want to test if language proximity matters as a source of correlation between locations, so that we define as alternative destinations two French-speaking states: France and Belgium. First, when a shock happens in Belgium, we would like to see if it significantly impacts migration to France and vice versa. If the answer is positive it would mean that language proximity is a source of MRtM, otherwise it is not. Second, we want to observe if there exist differences in migration choices to France in response to a change in employment conditions with respect to a change in GDP per capita in Belgium. The existence of such differences would reflect that the importance of languages in designing alternative destinations differs for distinct shocks. Using the OECD data on bilateral flows, the results show that shocks in countries with similar immigration law frameworks generates the largest inertia effects, especially in response to changes in GDP per capita. Said differently, the biggest deterrent on the migration rates between a pair of states is represented by the increase of the GDP per capita differentials of an alternative destination similar in terms of migration laws. Other significant, but less pronounced, restraining effects are 3

found by using a spatial weighting matrix accounting for networks. Furthermore, special mechanisms seem to apply when the alternative destination is one of the first fifteen European Union members (EU15) where we detect boosting, rather than inertial, effects of the MRtM. We observe, in fact, that an increase in the the GDP per capita differentials of an EU15 country rise the migration rates towards its geographically neighbour states while a grow in the employment differentials raises the migration rates towards states with similar labour immigration legislations. Since EU15 neighbour countries according to labour migration policies, as well as geography, are most likely to be others EU15 states, such result underlines expected spillover or temporary migration effects peculiar to the European Union area, which once entered, guarantee free movement of people. 2 Theoretical Framework Migration decisions consist either in staying or moving, discrete outcomes which make the traditional marginalist techniques developed to analyse consumers behaviour inapplicable. Probabilistic discrete choice models are a possible alternative, where a rational agent i decides, according to her utility, whether to move from her country of birth j to a possible destination k. Assuming that the utility function is composed by a deterministic satisfaction index V jk, which captures the particular characteristics of the choice j k, and an unobserved stochastic random error component ɛ ijk, which captures the unmeasured psychological factor involved in the decision, the probability to choose k over a set alternatives l L is Pr(U ijk U ijl ; l L) = Pr(ɛ ijk ɛ ijl V ijl V ijk ; l L). (1) Under the assumption that the deterministic component of the model is linear with respect to a set of explanatory variables, such that V jk = β x jk, and that the error terms are independently identically distribute (iid) as an extreme value distribution (EV) of Type I, the probability for person i to choose alternative k is Pr ijk = exp(β x jk ) 1 + L l=1 exp(β x jl ), (2) 4

where l L is the set of possible alternatives (McFadden et al., 1973). In order to achieve this elegant closed-form solution, it was crucial to assume that the errors were iid and that the response was homogeneous across individuals. The combination of these hypothesises leads to the independence of irrelevant alternatives (IIA) (McFadden, 1978). This means that if alternative j is chosen given a set L, if individual i has to chose from a subset S L with j S, then she must choose again j. In the context of migration theory, this means that given a set of possible destinations eliminating the non-chosen ones does not alternate the decision of the mover. So for example, if a migrant from Italy has among her possible destinations Switzerland, Germany and France and she chooses Switzerland, than the same migrant must choose Switzerland when the choice sets are Switzerland-Germany and Switzerland-France. Despite useful, this simplification does not take into account the influence of third countries in determining the flows between a given pair of states. In other words, the IIA neglects the cross-sectional dependence arising, for example, from the effects national immigration policies have on other countries flows. A possible solution to this shortcoming is to assume that the errors follow a generalized extreme value distribution (GEV). For example, Bertoli and Moraga (2013) grounded migration choices into a cross-nested logit model based on a simplified version of the generating function proposed by Wen and Koppelman (2001), τ G j (Y j1,..., Y jn ) = m (α jlm Y jl ) 1/τ, (3) l b m where Y jl = exp(v jl ), τ (0, 1] is the dissimilarity parameter and b are the destinations nests indexed by m. In the context of international migration, nests are groups of countries sharing unobservable sources of attractiveness. As a result, there could be one nest for each unobservable source of attractiveness m and, at the same time, one destination could belong to different nests where, the degree of this "belonging" depends upon the allocation parameter α jlm. The resulting allocation matrix can vary across origins. Therefore, migrants from different countries can have different preferences due to the stochastic component of the utility function which can follow originspecific patterns across any pair of destinations (Papola, 2004). One of the main advantages of this 5

Figure 1: Correlation Structure Nested Logit Migrant from j Migrant to k Not Migrate Migrate Not Migrate Migrate α jj α jln l b m α kk α hnk j b m U jj U jl1 U jl2 U jl3 U kk U h1 k U h2 k U h3 k type of formulation is its ability to replace group-wise relations with pair-wise similarities (Vovsha, 1997). This property implies that the cross-sectional dependence among the error terms works as a mirror of the opportunities as well as the barriers that migrants face in order to move to a destination different from the preferred one. Said differently, multilateral resistance to migration becomes the direct result of the impact that alternative destinations have on the migrants choices (Bertoli & Moraga, 2013) see Figure (1). The left hand side of the picture depicts the correlations among migration rates from one origin (j) towards various destinations (l n ) belonging to a single nest (b m ). The right hand side, instead, illustrate the correlations among migration rates towards a single destination (k) from various origins (h n ) belonging to nest (b m ). The dotted lines are the correlations within a nest. 2.1 Spatially correlated logit (SCL) A regression derived from a nested logit could potentially correct the bias originating from the omission of the influence that third parties have in determining the flows between a given pair of countries. However, it does not explain the origin of the nests and, more in general, of the multilateral resistance to migration. Important questions such as: why is a certain country part of a nest? or where does multilateral resistance to migration originate from? remain unanswered. In order to overcome this shortcoming, it is necessary to explain the origin of α. We propose space as a way to associate alternative destinations. In particular, using a GEVbased structure, we accommodate the cross-sectional correlation in the utility of the migrants using 6

a spatial logit model (SCL) K 1 G j (Y j1,..., Y jn ) = k=1 K l=k+1 [(α jk,kl Y jk ) 1/τ + (α jl,kl Y jl ) 1/τ ] τ, (4) where every choice j k is valued given the paired nested alternatives (k, l) (Bhat & Guo, 2004). In this context, the allocation parameter α jk,kl is the element of a row standardized matrix which takes positive values if country k and l are neighbours and zero otherwise, such that l α jk,kl = 1. Intuitively, the larger α jk,kl the greater the correlation between alternative k and l (i.e. the smaller the dissimilarity parameter τ). Such a definition reflects the idea that the fewer the contiguous units are, the larger the correlations between destination k and the alternatives l are. As in Bertoli and Moraga (2013), the allocation matrix α j reflects different preferences across different origins, but this time its origin is defined. The GEV structure of the SCL takes the form of a paired generalized nested logit (PGNL) with equal dissimilarity parameters across paired nests, where each bifurcation contains two neighbour units. In order to see how this formulation works in practice it is sufficient to consider a simple example. Suppose that the entire world is composed by Portugal, Spain, France and Belgium, which are all potential destination for a migrant which comes from country j. In this case the PGNL sees the world as a series of bivariate nests, see Figure 2. BEL BEL FRA FRA FRA FRA ESP PRT PRT PRT NLD BEL LUX BEL ITA FRA CHE FRA LUX FRA BEL FRA FRA ESP ESP PRT ESP PRT ESP PRT Figure 2: Paired Nested Structure 7

60 DNK Allocation Matrix BEL FRA ESP PRT 55 IRL GBR NLD BEL 0 0.6 0.25 0.15 50 BEL LUX DEU FRA 0.4 0 0.4 0.2 lat CHE AU ESP 0.2 0.4 0 0.4 45 FRA PRT 0.15 0.25 0.6 0 ITA 40 PRT ESP 35 10 5 0 5 10 long The previous spatial structure can now be translated into an allocation matrix where every cell contains the allocation parameter α jk,kl defining the geographical distance between countries and l α jk,kl = 1, see Table (2.1). If the random components follow the spatial CDF (4), then the probability of moving the k th spatial unit is: p jk = p jk kl p j,kl = k l(α jk,kl e V jk ) 1/τ [(α jk,kl e V jk ) 1/τ + (α jl,kl e V jl ) 1/τ ] τ 1 k l K 1 f=1 K (5) g=k+1[(α jf,fg e V jk ) 1/τ + (α jg,fg e V jl ) 1/τ ] τ Therefore, the log odd-ratio between the possibility of moving from j to k given alternatives (k, l) over the alternative to stay given the alternatives (j, k) 1 becomes ln ( P jk,kl ) = 1 P jj,jk τ V jk V jj + ln ( 1 k l(α jk,kl ) τ [(αjk,kl e V jk ) 1 τ + (αjl,kl e V jl ) 1 τ ] τ 1 j k (α jj,jk ) 1 τ [(α jj,jk e Vjj ) 1 τ + (α jk,jk e V 1 ). (6) jk ) τ ] τ 1 Contrary to (Bertoli & Moraga, 2013), in this setting the multilateral resistance to migration, r jkl = ln ( k l(α jk,kl ) 1 τ [(αjk,kl e V jk ) 1 τ + (αjl,kl e V jl ) 1 τ ] τ 1 j k (α jj,jk ) 1 τ [(α jj,jk e Vjj ) 1 τ + (α jk,jk e V 1 ), (7) jk ) τ ] τ 1 1 Note that we assume a symmetric denominator such that P jj,jk = P jj,jl, so that ln(p jk,kl /P jj,jk ) = ln(p jk,kl /P jj,jl ). 8

Figure 3: Correlation Structure Spatially Correlated Logit Migrant from j Migrant to k α jln,jl 1 α jln,l 1 l 2 α hnk,h 1 k α hnk,h 1 h 2 Not Migrate Migrate Migrate Migrate Not Migrate Migrate Migrate Migrate U jj U jl1 U jl1 U jl2 U kk U h1 k U h1 k U h2 k has a direct interpretation: r jk is a function of the origin effects α jj, of the origin-destination explanatory variables V jk and of origin-alternative destination explanatory variables V jl. Like in the case of (3), it is possible to use a tree diagram to visualize the correlations implied by (4), see Figure (2.1). The links described in (2.1) imply that every migrant i from country j faces the possibility to stay or to move to destination l 1. Nevertheless, l 1 is just one of the alternatives, since there are other states sharing similar features, i.e. l 2, which make them belonging to the same nest. This would mean that the multilateral resistance to migration generates from the countries which are spatially linked to the first choice l 1. Thus, the characteristics of the countries next to l 1 are crucial in determining the magnitude of r jkl. The same is true for migrants going to k. 3 Estimation Strategy Subsection 2.1 relates the multilateral resistance to migration to a series of log-odds ratios. In this section we average equation (6) over time t = 1, 2,..., T, generating a panel regression, y jkt = 1 τ x jkt x jjt + r jklt + ε jkt, (8) where, y jkt is the logarithm of the migration rate from origin j to destination k at time t, x jjt and x jkt are respectively the vectors of origin and origin-destination specific variables contained in the satisfaction indices V jjt and V jkt, r jklt is the multilateral resistance to migration and the stochastic random error component ε jkt is the result of the measurement errors originated from the averaging of the log odd-ratios. 9

By approximating the multilateral resistance to migration using a first order Taylor approximation around the time average Ṽjl = V jlt T t=1 V jlt /T, it is possible to rewrite r jklt as, r jklt = r jkl + τ 1 τ k l ( α jl,kl eṽjl ) 1 τ k l ( α jl,kl ) 1 τ [( α jk,kl eṽjk ) 1 τ + ( α jk,kl eṽjl ) 1 τ ] (V jlt Ṽjl), (9) where r jkl and Ṽjl are time-invariant components which can be included into (8) as a fixed effects j k, 2 while V jlt is a time-varying regressor, which translates the estimation equation into a spatial lag of the exogenous variables model (SLX). The resulting expression becomes, y jkt = βx jkt + λ ω lk x jlt + ι jk + ε jkt, ε jkt = ι jt + ι t + η jkt, (10) k l where x jlt is a vector of origin-alternative destination explanatory variables, ω lk is the k th element of the spatial matrix reflecting the allocation parameter α jk,kl and ι jk is the origin-destination fixed effect. In addition, the error term is further split into a time fixed effect (ι t ) and a origin-time fixed effects (ι jt ) to account for residual variation due to the aggregation from (6) to (8). Equation (10) has the advantage to allow to control for spatial spillover effects (λ) while keeping the coefficients easily interpretable (Halleck Vega & Elhorst, 2015). In particular, its spatial nature allows to investigate the causes of multilateral resistance to migration using different weighting matrices which can been time dependent (ω jt ), time independent (ω j ), connect all possible destinations or only a sub-group. The alternative weighting matrices are described in the next subsection. The aim of the weighting matrices is to shed light on the rationales behind the perception of two destinations as alternatives. In general, we could expect all spatial effects (λs) to take opposite sing with respect to the βs. Let us consider, for example, the impact of an increase in the GDP per capita differentials between j and k, which usually has a boosting effect on migration rates between the two (β > 0). By the same token, a relative larger increment in the differentials between j and l should redirect the flows j k towards j l. However, since k and l are linked by a definition of proximity enclosed 2 Note that being our dependent variable (y jkt ) the number of people moving form origin j to destination k, it is impossible to include an origin-alternative destination fixed effect any time k has more than one neighbouring country l. 10

in a spatial weighting matrix, the relevance of the impact of l on the j k flows will depend upon the validity of such formalization that can be traced in the significance of λ. Said differently, if ω kl > 0 reflects geographical contiguousness and λ turns out to be non-significant, it will mean that destinations k and l are not perceived as substitutable just because located in the same area. 3.1 The Weighting Matrices The multilateral resistance to migration is the phenomenon for which migrants decide to move to destination k after considering not only the utility deriving from such choice, but also comparing the potential utility drawn from alternative destinations l. What makes two different destinations to be defined as alternatives would depend upon which are the sources of attractiveness according to migrants preferences. In order to better understand the unobserved migrants preferences, we aim to uncover what is behind the concept of multilateral resistance to migration by employing different weighting matrices ω in the estimation. In fact, in our model the definition of "neighbour", which allocate a country k to a particular paired nest, could be arbitrary decided (geographical, economic proximity,... etc.) while remaining subject to l ω jk,kl = 1. Among different possibilities we build weighting matrices controlling for geographical distance, common language, presence of networks, commercial relations and immigration law tightness across destinations. The geographical distance matrix (ω geo ) is calculated from states average latitude and longitude 3. A language matrix is inferred by referring to the CEPII gravity database (Head, Mayer, & Ries, 2010; Head & Mayer, 2013) which reports common official (ω language ) languages spoken across destination by at least the 9% of the population. A network matrices, constructed with OECD (2016) data, define as neighbours states with similar stocks of origin-nationality (ω network ) population 4. An economic weighing matrix takes into account the trade flows between origins and destinations (ω trade ) and it is based on the CEPII TradeProd database (De Sousa, Mayer, & Zignago, 2012). It is constructed to reflect higher correlations among destinations which have more similar commercial relations with a specific origin. Concerning the the similarity of migration laws we used the IMPIC database (Helbling, Bjerre, Römer, & Zobel, 2016), which includes indicators 3 Source: https://opendata.socrata.com/dataset/country-list-iso-3166-codes-latitude-longitude/mnkm-8ram 4 Origin-nationality population stock have been tested and they have delivered the same results 11

for asylum, family reunion and labour migration policies (ω asylum, ω family, ω labour ). As a rule of thumb, the closer two destinations are, in terms of geography, languages spoken, immigration laws, etc., the higher the correlation (ω jk,kl ) between them is. While the geographical weighting matrices, as well as the language, are time-invariant, the others are time dependent. All matrices have row sums standardized to one and zero on the diagonal. 4 Data and Summary Statistics Different data sources have been use to build the dataset employed in the empirical exercise. Data on bilateral migration flows stem from the OECD database (OECD, 2016). Our dependent variable, i.e. the migration rate, is obtained by dividing the flows between the country of origin and destination by the total population in the origin 5. The latter is drawn from the Penn Table 9.0 (Feenstra, Inklaar, & Timmer, 2015), which also represents the source of the two of the classical migration drivers, which are real GDP per capita differentials and employment differentials. The value of the real GDP, expressed in millions of 2005 US dollars at chained purchasing power parity (PPP), is divided by the total country population. The GDP per capita differential is simply obtained by dividing the destination and the origin country s real GDP per capita. The variable of the employment differentials is constructed in the same way. The other data sources required to build the weighting matrices (ω j ) have already been outlined in section 3.1. Table 1 reports the summary statistics of the variable used as explanatory or for constructing the weighting matrices. The data time span goes from 2000 to 2014 with the exception of the immigration laws variables whose values are available from 2000 to 2010. 5 Results Table 2 reports the results for the SLX models for different definitions of neighbours from column 2 to column 8 and for the simple model without spatial interactions in column 1. The endogene- 5 The migration rates are log-transformed using the formula: ln(migration rates jkt ) = ln (1 + number of migrants jkt total population jt ) 12

Table 1: Summary Statistics Statistic N Mean St. Dev. Min Max Origins Destinations Migration_rate 40,400 119.051 578.241 0.000 20,267.930 171 28 GDP p.c. differentials 40,400 9.963 15.425 0.191 255.949 171 28 Employment differentials 40,400 24.474 155.389 0.001 5,620.245 171 28 Geographical Distance 40,260 8,482.534 4,671.123 0.000 20,036.860 168 28 Official Languages 40,260 0.175 0.380 0 1 168 28 Economic Globalization 35,007 77.360 11.554 44.140 99.150 171 28 Asylum Laws Index 29,664 0.311 0.106 0.118 0.683 171 28 Family Laws Index 29,664 0.280 0.224 0.019 1.000 171 28 Labour Laws Index 29,664 0.406 0.161 0.187 1.000 171 28 Foreign Nationals Network 18,643 10,867.550 55,486.550 0.000 1,764,041.000 171 20 Trade flows 33,796 5,379,552.000 25,021,438.000 0.007 666,543,292.000 134 28 Note: Table formatted using stargazer (Hlavac, 2015). ity threat is treated using lagged, instead of contemporaneous, exogenous variables. Since time dependency, as well as possible residual cross-sectional dependency, might persist, standard errors computed following Driscoll and Kraay (1998). At first sight, all the coefficients of the real GDP per capita and employment differentials have the expected positive sign and they range from 1.142 to 0.433 and from 0.468 to 0.113 respectively. They are all highly significant except for the employment differential of the regression using the official languages as weighting matrix (ω language ). Moreover, significant spatial interaction coefficients are found, in general, for all different definitions of neighbours used. With respect to the geographical coefficients, an increase in GDP, but especially in employment differentials in a geographically near alternative destination l would also augment the migration rate between the pair j k. Even though this might seem in contrast with our first expectations, it might just reflect how geographical distance plays a role in temporary migration. Let suppose that the rise in the differentials made the alternative l to become the first-best desired destination for an individual from j, but before reaching the final destination l the migrant might decide to go to a neighbour country k where is, for any reason, easier to enter first. The columns 3 to 5 show the results for the immigration laws weighting matrices. Whether it comes to asylum, family reunification or labour laws, the GDP per capita interaction coefficients are always negative and significant, even if its magnitude is comprehensibly greater for labour and family laws rather than for asylum. This means that an increase in the GDP per capita of an 13

alternative destination l converts into a decrease in the migration rate from j to k, which might be due to a shift of the migrants from k to l. On the other hand, different results are obtained for the employment differentials interaction term. In this case the coefficient is negative, as expected, for ω family and positive for ω asylum and ω labour. For the asylum one this result might be due to the fact that refugees are usually not immediately entitled to work when they enter a country with asylum visas. Therefore, in this scenario, if GDP could still be an important aspect in electing two destinations as alternative, employment differentials are not. More surprisingly is, instead, the results for the labour laws. The official languages (column 6) plays a role in making two destinations similar only when interacted with the employment differentials, but not with the GDP per capita differentials. When it comes to what we call networks effects (column 7), i.e. the stock of the origin-nationality population in alternative destination l, both spatial effects are negative and significant. Interestingly, this regression shows a far better R-squared with respect to the others. The economic weight also deliver interesting results. With respect to trade (column 8) positive spatial effects are found especially for the GDP interaction, but also for the employment one. However, despite the significance of the coefficients, the goodness-of-fit of this model drops, with respect to the non-spatial one, from 0.066 to 0.008. A deeper discussion of the results just presented, as well as some insights about the unexpected signs of some of the coefficients, are introduced in the next section. 14

Table 2: Regression Results Dependent variable:log(migration rate) ω = 0 ωgeo ωasylum ωfamily ωlabour ωlanguage ωnetwork ωtrade (1) (2) (3) (4) (5) (6) (7) (8) log(gdp p.c. differentialt 2) 0.701 0.830 0.572 0.433 0.568 0.814 0.609 1.142 (0.049) (0.050) (0.071) (0.076) (0.083) (0.055) (0.071) (0.073) log(employment differentialt 2) 0.280 0.344 0.229 0.220 0.200 0.105 0.113 0.468 (0.063) (0.064) (0.082) (0.082) (0.082) (0.068) (0.046) (0.068) ω(log(gdp p.c. differentialt 2)) 1.809 3.327 6.902 10.343 0.107 0.616 6.957 (0.233) (1.362) (1.506) (1.949) (0.070) (0.072) (1.113) ω(log(employment differentialt 2)) 4.156 1.384 1.286 2.012 0.608 0.108 0.439 (0.379) (0.786) (0.211) (0.441) (0.156) (0.045) (0.251) Observations 34,982 34,892 29,614 29,614 29,614 34,892 16,021 29,415 Years 2000-2014 2000-2014 2000-2010 2000-2010 2000-2010 2000-2014 2000-2014 2000-2014 R 2 0.192 0.197 0.178 0.179 0.180 0.194 0.337 0.144 Adjusted R 2 0.066 0.072 0.034 0.036 0.037 0.069 0.146 0.008 Note: p<0.1; p<0.05; p<0.01. Standard errors computed following Driscoll and Kraay (1998). Table formatted using stargazer (Hlavac, 2015). 15

6 Discussion The results presented in the previous section, while displaying which are the definitions of proximity characterizing neighbours, they also show how their impacts vary in terms of significance and sign. The whys, important in the better understanding of migration decisions, are summarized hereafter. Networks are not the biggest source of multilateral resistance to migration in terms of magnitude, but they emerge to explain a lot in terms of R-squared. The smaller impact might follow the evidence of networks being the result of an historical process, making them rooted and not quickly changeable. There is almost no uncertainty about how networks would look like in the next period. On the other hand, the multilateral resistance to migration is, by definition, a quick reaction in the migration decisions between two given countries to a shock happening in an alternative destination. Therefore, the inelastic peculiarity of network formation, translates into small, but persistent inertia effects. Differently, the largest deterrence effects, when it comes to GDP per capita, are produced by countries with similar immigration laws. Conversely to what we said about networks, changes in policies are fast and can produce important changes from one legislature to another. Such elasticity reflects in migration intentions which closely follows legislative trends. Migrants who compare destinations according to their policies rely on something extremely mutable and they must have fast reactions since the next period will be uncertain. Our ω geo spatial matrix delivers coefficients with unexpected signs. However, geography seems to be important in temporary migration choices. In fact, a pushing effect, rather than a deterrent, originates from an increase in better opportunities in a geographically close country to the original destination. Beside the spatial spillovers hypothesis, which foresees that the rise in GDP per capita differentials between origin j and alternative destination l might be followed by a subsequent increase in the differentials between j and destination k, the repeated migration intuition is partially supported by the fact that the GDP spatial term become negative from the lag t 5, while the employment spatial term by t 9. Moreover, a refined analysis, which take into consideration how the multilateral resistance effects can be continent-specific (see Tables 3 and 4 in Appendix 8.1), 16

highlights that the belonging of a destination to the EU15 countries 6 delivers positive spatial effects when geographical weights are interacted with GDP (0.711), as well as when labour immigration policies weights multiply employment differentials (1.062). Such outcomes imply that better opportunities in EU15 countries (l) close to the destinations (k), in terms of ω geo and ω labour, produce higher migration rates between the origin-destination pair (j k). Intuitively, since the EU15 closest neighbours are other EU15 states, the important for migrants appears to enter the EU15 and then to move within it once they got the permit to freely circulate in the area. This result is in accordance to the hypothesis of temporary migration, as well as of geographical spillovers, easier justified in a integrated economic area. A crucial role of the official languages as a source of correlation across destinations is detected only when interacted with the employment differentials following the rationale that migrants see linguistic proximity important especially in the optic of work possibilities. Conversely to the ω network regression, whose R-Square outperforms all the alternatives, the trade spatial matrix seems the least appropriate. While delivering significant coefficients, the ω trade regression displays a low adjusted R-squared suggesting that commercial flows characteristic are not making two destinations perceived as alternative. This could be due to the fact that migrants are usually over-represented in non-tradable sectors. Nevertheless, dissecting the spatial terms by continent helps clarifying some less intuitive mechanisms (see Tables 4 in Appendix 8.1). The first result becomes evident in the adjusted R-Squared, which knows the largest rise compared to the other regressions. Moreover, while at the aggregate level the spatial effects are both positive with a larger magnitude of the GDP per capita, at the continent level the only destination area preserving positive effects of the GDP is North America. Let suppose that l and k have similar trade flows with origin j and that the GDP per capita in l increases. If l is located outside the North American continent, such increase provoke a shift of the migration rates from j away from k probably due to a perception of greater chances achievable with l. Contrarily, if l is located in North America, the rise in the GDP augments the migration rates from j to k. Hence, if for the rest of the world goods and people movements seem to be potentially complementary, in the case of North America, 6 The EU15 is the number of member countries in the European Union prior to the accession of ten candidate countries on 1 May 2004. It comprised the following 15 countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, United Kingdom. 17

they appear to be substitutes. A potential explanation to such result might lie in the difference between trade accessibility and migration entry restrictions, which is particularly pronounced in North American countries relatively to the rest of the world 7. 7 Conclusion Traditionally, the economic literature has studied the interdependencies among migration rates relying on random utility models (RUM) hypothetizing the Independence of Irrelevant Alternatives (IIA) assumption to hold. Nevertheless, more recent advancements have tried to relax the IIA assumption (Ortega & Peri, 2013; Bertoli & Moraga, 2013). In particular, Bertoli and Moraga (2013), after having formally derived the multilateral resistance to migration term through a cross-nested logit model, have employed a Common Correlated Error Model (CCE) (Pesaran, 2006) to control for it in the estimation. However, if on the one hand, the CCE allows them "to obtain estimates of the vector of coefficients without having to introduce additional assumptions on the allocation matrix α j " (Bertoli & Moraga, 2013), on the other, it requires a big longitudinal dimension, which is usually only reachable through high-frequency data. Anyhow, the characteristics which make alternative destinations to belong to the same nest remained unobserved. Within a less data demanding framework, this study has tried to disclose the reasoning migrants embrace when electing two states as potential destinations. Theoretically justified by a spatially correlated logit model (SCL), we have empirically implemented a spatial lag of exogenous variables model (SLX) to deal with the endogeneity issue introduced by the MRtM. Such setting permits to investigate the meaning of neighbourhood through the choice of the entries of the allocation matrix α interpretable as a spatial weighting matrix (ω j ). Said differently, the SLX model has allowed us to understand why two destinations are perceived as substitutes by designing a set weighting matrices accounting for geographical, linguistic, commercial, institutional and network proximity. Our model consents, not only to account for cross-sectional dependence, but also to investigate the mechanisms, sometimes contrasting, behind different definitions of alternative destinations. Moreover, the use 7 We refer in particular to the United States of America. 18

of weighting matrices allows the investigation of the impact of time-invariant characteristics while controlling for a bunch of fixed effects. The results have highlighted how the matrices specificities reflect either a time-specific or locallyspecific dimension. Concerning the time aspect we found evidence, on one side, of big impacts played by policies on migration decisions in the very short run since migrants seems to be fast respondents to changes in either the asylum, labour or family legislation. On the other, we remarked smaller, but more persistent effects of national networks. Another interesting evidence, with respect to the regional facet, is found for the fifteen first members of the European Union (EU15), whose degree of institutional homogeneity act as a "hub". Migrants seem to move to an EU15 neighbour country even in presence of better opportunities in others EU15 either in the optic of temporary migration or of spillover effects, both of them facilitated by the EU cohesion. References Bertoli, S., Brücker, H., & Moraga, J. F.-H. (2016). The european crisis and migration to germany. Regional Science and Urban Economics, 60, 61 72. Bertoli, S., & Moraga, J. F.-H. (2013). Multilateral resistance to migration. Journal of Development Economics, 102, 79 100. Bhat, C. R., & Guo, J. (2004). A mixed spatially correlated logit model: formulation and application to residential choice modeling. Transportation Research Part B: Methodological, 38 (2), 147-168. Retrieved from http://www.sciencedirect.com/science/article/pii/ S0191261503000055 doi: http://dx.doi.org/10.1016/s0191-2615(03)00005-5 Clark, X., Hatton, T. J., & Williamson, J. G. (2007). Explaining us immigration, 1971-1998. The Review of Economics and Statistics, 89 (2), 359 373. De Sousa, J., Mayer, T., & Zignago, S. (2012). Market access in global and regional trade. Regional Science and Urban Economics, 42 (6), 1037 1052. Driscoll, J. C., & Kraay, A. C. (1998). Consistent covariance matrix estimation with spatially dependent panel data. Review of economics and statistics, 80 (4), 549 560. 19

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McFadden, D. (1978). Modeling the Choice of Residential Location. Transportation Research Record(673), 72 77. Retrieved from http://onlinepubs.trb.org/onlinepubs/trr/1978/ 673/673-012.pdf McFadden, D., et al. (1973). Conditional logit analysis of qualitative choice behavior. OECD. (2016). International migration database. Retrieved from /content/data/data-00342-en doi: http://dx.doi.org/10.1787/data-00342-en Ortega, F., & Peri, G. (2013). The effect of income and immigration policies on international migration. Migration Studies, 1 (1), 47 74. Papola, A. (2004). Some developments on the cross-nested logit model. Transportation Research Part B: Methodological, 38 (9), 833 851. Pedersen, P. J., Pytlikova, M., & Smith, N. (2008). Selection and network effects migration flows into oecd countries 1990 2000. European Economic Review, 52 (7), 1160 1186. Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 74 (4), 967 1012. Vovsha, P. (1997). Application of cross-nested logit model to mode choice in tel aviv, israel, metropolitan area. Transportation Research Record: Journal of the Transportation Research Board(1607), 6 15. Wen, C.-H., & Koppelman, F. S. (2001). The generalized nested logit model. Transportation Research Part B: Methodological, 35 (7), 627 641. Retrieved from http://www.sciencedirect.com/science/article/pii/s019126150000045x doi: 10.1016/S0191-2615(00)00045-X 8 Appendix 8.1 Robustness Checks It might be argued that the multilateral resistance to migration effects might change depending on the origins. To check if this is the case we interacted the spatial effects with the origin continents (Table 3) and the destination (Table 4). The reference group are, respectively, Africa for the Table 3, North America for Table 4. In general, differences in multilateral resistance to migration are 21

more pronounces across different destinations rather than origins. 22

Table 3: Regression Results: Origins Interactions Dependent variable:log(migration rate) ωgeo ωasylum ωfamily ωlabour ωlanguage ωnetwork ωtrade (1) (2) (3) (4) (5) (6) (7) log(gdp p.c. differentialt 2) 0.708 0.635 0.635 0.634 0.708 0.677 0.815 (0.049) (0.058) (0.058) (0.058) (0.049) (0.080) (0.050) log(employment differentialt 2) 0.274 0.241 0.241 0.242 0.272 0.463 0.261 (0.063) (0.075) (0.075) (0.075) (0.063) (0.103) (0.065) ω(log(gdp p.c. differentialt 2)) 0.021 0.057 0.099 0.049 0.006 0.009 0.085 (0.049) (0.137) (0.148) (0.139) (0.007) (0.027) (0.064) ω(log(employment differentialt 2)) 0.007 0.050 0.075 0.043 0.005 0.009 0.018 (0.019) (0.100) (0.100) (0.103) (0.009) (0.023) (0.037) ω(log(gdp p.c. differentialt 2)): North America 0.123 0.034 0.035 0.022 0.004 0.065 0.096 (0.094) (0.254) (0.275) (0.260) (0.013) (0.062) (0.129) ω(log(gdp p.c. differentialt 2)) : Asia 0.015 0.129 0.147 0.182 0.011 0.003 0.108 (0.068) (0.190) (0.204) (0.192) (0.010) (0.037) (0.088) ω(log(gdp p.c. differentialt 2)) : EU15 0.026 0.058 0.034 0.047 0.006 0.024 0.095 (0.083) (0.244) (0.258) (0.243) (0.012) (0.057) (0.106) ω(log(gdp p.c. differentialt 2)) : Rest of Europe 0.099 0.102 0.086 0.144 0.008 0.110 0.067 (0.079) (0.219) (0.233) (0.219) (0.011) (0.055) (0.096) ω(log(gdp p.c. differentialt 2)) : Oceania 0.202 0.070 0.132 0.0003 0.009 0.246 0.265 (0.190) (0.511) (0.555) (0.520) (0.028) (0.285) (0.222) ω(log(gdp p.c. differentialt 2)) : South America 0.096 0.014 0.024 0.026 0.004 0.007 0.139 (0.104) (0.295) (0.318) (0.298) (0.015) (0.067) (0.125) ω(log(employment differentialt 2)): North America 0.036 0.173 0.211 0.180 0.015 0.084 0.001 (0.037) (0.189) (0.187) (0.194) (0.015) (0.044) (0.075) ω(log(employment differentialt 2)) : Asia 0.011 0.079 0.083 0.140 0.001 0.015 0.082 (0.026) (0.140) (0.138) (0.143) (0.012) (0.032) (0.057) ω(log(employment differentialt 2)) : EU15 0.034 0.043 0.019 0.042 0.001 0.026 0.043 (0.035) (0.183) (0.179) (0.188) (0.014) (0.037) (0.085) ω(log(employment differentialt 2)) : Rest of Europe 0.003 0.261 0.198 0.304 0.030 0.020 0.119 (0.031) (0.162) (0.159) (0.165) (0.013) (0.036) (0.069) ω(log(employment differentialt 2)) : Oceania 0.096 0.077 0.009 0.208 0.009 0.161 0.111 (0.076) (0.399) (0.398) (0.403) (0.031) (0.118) (0.141) ω(log(employment differentialt 2)) : South America 0.036 0.033 0.054 0.014 0.006 0.001 0.022 (0.041) (0.220) (0.219) (0.225) (0.017) (0.050) (0.090) Observations 34,877 24,932 24,932 24,932 34,877 16,427 29,315 Years 2000-2010 2000-2010 2000-2010 2000-2014 2000-2014 2000-2014 2000-2014 R 2 0.193 0.217 0.217 0.217 0.193 0.286 0.193 Adjusted R 2 0.067 0.040 0.040 0.040 0.067-0.012 0.058 Note: p<0.1; p<0.05; p<0.01. Standard errors computed following Driscoll and Kraay (1998). Table formatted using stargazer (Hlavac, 2015). 23

Table 4: Regression Results: Destinations Interactions Dependent variable:log(migration rate) ωgeo ωasylum ωfamily ωlabour ωlanguage ωnetwork ωtrade (1) (2) (3) (4) (5) (6) (7) log(gdp p.c. differentialt 2) 0.622 0.601 0.584 0.615 0.629 0.542 0.686 (0.054) (0.068) (0.067) (0.068) (0.054) (0.089) (0.058) log(employment differentialt 2) 0.220 0.272 0.290 0.272 0.203 0.255 0.225 (0.066) (0.087) (0.087) (0.088) (0.066) (0.144) (0.073) ω(log(gdp p.c. differentialt 2)) 0.339 0.641 1.189 0.040 0.080 0.002 0.331 (0.238) (0.480) (0.566) (0.408) (0.088) (0.006) (0.118) ω(log(employment differentialt 2)) 0.832 0.031 0.435 0.619 0.851 0.006 0.098 (0.357) (0.435) (0.457) (0.376) (0.325) (0.004) (0.084) ω(log(gdp p.c. differentialt 2)) : Asia 0.896 1.866 1.904 0.940 0.320 0.595 (0.400) (0.752) (0.857) (0.674) (0.208) (0.164) ω(log(gdp p.c. differentialt 2)) : EU15 0.711 0.452 1.861 0.311 0.274 0.010 0.302 (0.278) (0.500) (0.587) (0.426) (0.099) (0.008) (0.122) ω(log(gdp p.c. differentialt 2)) : Rest of Europe 0.583 0.901 1.036 0.591 0.068 0.372 (0.360) (0.606) (0.617) (0.521) (0.174) (0.141) ω(log(gdp p.c. differentialt 2)) : Oceania 0.729 1.004 1.572 0.805 0.440 0.576 (0.375) (0.688) (0.785) (0.600) (0.137) (0.163) ω(log(gdp p.c. differentialt 2)) : South America 0.265 1.314 1.612 0.952 0.523 0.961 (0.588) (1.044) (1.229) (0.970) (0.195) (0.258) ω(log(employment differentialt 2)) : Asia 1.995 0.560 0.458 0.406 1.128 0.070 (0.578) (0.689) (0.723) (0.600) (0.512) (0.109) ω(log(employment differentialt 2)) : EU15 1.204 0.231 0.924 1.062 1.359 0.004 0.056 (0.399) (0.450) (0.474) (0.390) (0.339) (0.005) (0.087) ω(log(employment differentialt 2)) : Rest of Europe 1.176 0.378 0.364 0.032 0.974 0.175 (0.476) (0.551) (0.511) (0.489) (0.371) (0.097) ω(log(employment differentialt 2)) : Oceania 0.331 0.917 1.245 0.838 0.371 0.070 (0.578) (0.605) (0.619) (0.562) (0.449) (0.119) ω(log(employment differentialt 2)) : South America 1.187 1.734 1.459 0.904 1.181 0.039 (0.888) (1.104) (1.021) (0.853) (0.386) (0.198) Observations 34,877 24,932 24,932 24,932 34,877 16,427 29,315 Years 2000-2010 2000-2010 2000-2010 2000-2014 2000-2014 2000-2014 2000-2014 R 2 0.194 0.215 0.215 0.216 0.195 0.306 0.191 Adjusted R 2 0.067 0.031 0.031 0.032 0.068 0.097 0.037 Note: p<0.1; p<0.05; p<0.01. Standard errors computed following Driscoll and Kraay (1998). Table formatted using stargazer (Hlavac, 2015). 24