3.1. Data

Our sample consists of 23 EU Member States: Austria, Belgium, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden and the United Kingdom.² The data used for our estimations on the examined determinants of migration flows cover the 2000–19 period, while data on the dependent variable, net migration flows, covers the 1995–2019 period, as we include the lagged dependent variable in our estimations.³

To measure the degree of labour migration, we utilize the newly available data set on international bilateral immigration flows prepared by Abel and Cohen (2022). The data set reports the data over 5-year periods and consequently all the variables used in the estimations are adjusted to this format – that is, all the regressors considered are constructed over 5-year period intervals. The data reported in the data set pertain only to EU citizens and exclude refugees and other non-citizens. We scaled the net migration flows using the sum of the working-age population in each pair of countries using data from Eurostat.⁴ Consequently, the net migration per 1,000 inhabitants of working age (15–64) between any pair of countries is calculated as:

$MIG{R}_{ijt}\text{=}\frac{\left|NetMIG{R}_{ijt}\right|}{\frac{1}{5}{{\displaystyle \sum }}_{z\text{=}0}^4\left(Po{p}_{it\text{+}z}\text{+}Po{p}_{jt\text{+}z}\right)}$        (1)

where |NetMIGR_ijt| is net migration between countries i and j at time t = 1995, 2000, … , 2015, denoting the first year of the 5-year period in question. Pop_it+z and Pop_jt+z represent the working-age populations in country i and j, respectively, and z = 0,1, … , 4.⁵

The first explanatory variable that we consider is lagged migration (MIGRlag ≡ MIGR_ijt–1), which can be used as a proxy for well-established formal and informal migration channels: immigrants already living in each country are able to facilitate inflows of their relatives, friends and acquaintances by helping them find housing, jobs and introducing them to the new culture. As an alternative proxy for the “friends and relatives” effect (Boyd 1989), we used the stock values. However, since the database did not include the data on stock variables, we constructed a variable that reflects the accumulation of migration flows between two countries over the examined period. The variable is defined as:

$CumMI{G}_{ijM}\text{=}{\displaystyle {\displaystyle \sum }_{m\text{=}1}^M}MIG{R}_{ijm}$        (2)

where M = 1,2,3,4 is a time index. In other words, we summarize all available past migrations to account for the “friends and relatives” effect.

In line with previous research, our evaluation of net migration flows between EU countries investigates both push and pull factors, analysing the disparities in the intensity of these factors within each pair of countries. For instance, low real wages or high unemployment serve as push factors that encourage economic agents in one country to migrate and seek employment abroad. Conversely, high wages and low unemployment rates can be considered to be pull factors that attract workers from abroad. To assess the net push-and-pull effect for a given pair of countries, we construct independent variables as the absolute values of the differences between push or pull factors in the examined pair of countries.

The two drivers of labour migration that we are most interested in for this research are the pair-wise country differences in earnings and unemployment. We calculate the difference in the level of earnings as:

$EAR{N}_{ijt}\text{=}\frac{1}{5}{\displaystyle {\displaystyle \sum }_{z\text{=}0}^4}\left|NetEAR{N}_{it\text{+}z}–NetEAR{N}_{jt\text{+}z}\right|$        (3)

where NetEARN_it+z and NetEARN_jt+z are average after-tax earnings expressed in purchasing power parity (PPP) euros in country i and j, respectively, at time t = 2000, 2005, 2010, 2015, and z = 0, 1, … , 4.

Similarly, the difference in the level of the unemployment rate is calculated as:

$UNEM{P}_{ijt}\text{=}\frac{1}{5}{\displaystyle {\displaystyle \sum }_{z\text{=}0}^4}\left|U{N}_{it\text{+}z}–U{N}_{jt\text{+}z}\right|$        (4)

where UN_it+z and UN_jt+z are the unemployment rates in country i and j, respectively. The data on net earnings and unemployment rates are annual and come from Eurostat.

The percentiles and median of the distribution of the differences in unemployment rates and in net earnings are depicted in figure 1. The unemployment rate differentials demonstrate an upward trend during periods of economic expansion (e.g. the dot-com bubble) and recession (e.g. the dot-com bubble burst, global financial crisis and sovereign debt crisis). During tranquil periods, they exhibit a tendency towards unemployment rate convergence. The net earnings differentials, in contrast, do not display any convergence pattern. The percentiles below the median remain relatively stable, while those above the median manifest a slow evolution towards greater disparity. Unlike unemployment rates, tendencies in the behaviour of net earnings differentials remain roughly stable during times of crisis, expansion or tranquillity.

Figure 1

Unemployment rate and net earnings differentials

Note: The lilac shaded area denotes the dot-com bubble period, and the grey shaded area denotes the period of the global financial and sovereign debt crises.

Source: Our own compilation based on Eurostat data.

We control for several economic, social and institutional, and cultural factors that can potentially contribute to net migration. A detailed description of these variables and the source of the data can be found in table A1 in the appendix. As regards economic factors, we control for difference in income tax (Tax) and average social benefits per person (Social) between two countries. In this regard, Warin and Svaton (2008) provide an interesting investigation into “welfare migration”. We also examine the impact of the size of government through the variable GOV. The role of government size on international migration flows is advocated by Clemente, Pueyo and Sanz (2008), while that of the quality of government institutions is supported by Ariu, Docquier and Squicciarini (2016). The human capital variable, HC, uses the measure provided by Barro and Lee (2013), based on schooling attainment. Following research on the impact of income inequality on migration flows by Davies and Wooton (1992), we account for the differences in income distribution using the variable Gini.

Moving to social and institutional factors, we first account for the differences in safety and crime through the Crime and Corruption variables. Lage de Sousa (2014) reports that crime rate is an effective impediment of migration flows and Poprawe (2015) indicates that corruption encourages emigration and discourages immigration. We also control for differences in fertility rates through the FER variable. To the best of our knowledge, we are the first to examine the association between fertility rate and migration flows.

The last group of factors that we consider are related to the differences in culture. The first four variables could be seen as proxies for transportation costs; however, they are widely considered as proxies for cultural distance between countries. The dummy variables B and MB, controlling for countries sharing a common border and a maritime border, respectively, are complementary given that countries with shared land and sea borders often have a common history. The dummy variable MA controls for access to the ocean or sea, while LNDGEO is the natural logarithm of the distance between the capitals of a given pair of countries. Gravity variables are the most widely used type of regressors in the literature on international migration flows (Ashby 2007; Kim and Cohen 2010; Etzo 2011).

The variable on the difference in the average annual temperature between two countries (Temp) could be considered a proxy for quality of life, as living in warmer European countries is associated with additional benefits (nicer weather), and those countries are major tourism destinations. On the other hand, especially in the European context, the difference in temperature can also serve as a proxy for cultural similarity. The impact of temperature on migration flows has been widely researched given its bearing on the global warming debate (Minehan and Wesselbaum 2023).

Lastly, OLDEU is a dummy variable for membership of the EU before 2004. L is a dummy variable that controls for common official languages. TRANS is a binary variable that controls for post-communist countries.

3.2. Estimation strategy

We adopt Bayesian model averaging (BMA) as a method of evaluating the robustness of the examined determinants of international migration in Europe. In particular, BMA is based on an estimation⁶ of all possible models that can be assigned based on the set of determinants under consideration. BMA utilizes Bayes’ theorem to provide inferences based on the entire model space, thus accounting for model uncertainty. As demonstrated in the literature (Kass and Raftery 1995; Raftery 1995), methodology based on model averaging outperforms approaches based on the evaluation of multiple model specifications estimated with OLS. The latter fails to adequately account for model uncertainty.

Our baseline regression can be expressed as follows:

$y_{ijt}\text{=}\mathcal{\gamma }\text{+}\alpha y_{ijt–1}\text{+}\beta x_{ijt}\text{+}{\upsilon }_{ijt}$        (5)

where y_ijt is the net migration flow between countries i and j over the period t, defined in equation (1), x_ijt is a matrix of potential bilateral migration determinants, β is a parameter vector, γ is a constant, and υ_ijt is a random disturbance to net migration. All the variables were standardized before estimation to facilitate comparisons of the relative strength of influence among the examined regressors.

The model setup in equation (5) allows for the use of BMA. Given 19 potential regressors (including lagged net migration), indexed by k = 1, … , 19, it is possible to estimate 2^K = 2¹⁹ = 524,288 models. Once estimated, each model is assigned a posterior model probability (PMP) given by Bayes’ rule:

$PM{P}_m\text{=}\frac{L\left(data|M_m\right)*P\left(M_m\right)}{{{\displaystyle \sum }}_{m\text{=}1}^{2^K}L\left(data|M_m\right)*P\left(M_m\right)}$        (6)

where L(data|M_m) is the value of the likelihood function for model m (M_m) and P(M_m) is the prior probability of model m. Using the PMPs as weights allows for the calculation of the posterior mean (PM) and posterior standard deviation (PSD) of the coefficient β_k. The posterior PM of the coefficient β_k is then given by:

$P{M}_k\text{=}{\displaystyle {\displaystyle \sum }_{m\text{=}1}^{2^K}}PM{P}_m*{\widehat{\beta }}_{km}$        (7)

where ${\widehat{\beta }}_{km}$ is the value of the coefficient β_k estimated for the model m and k indexes the regressor. In addition, the PSD is equal to:

$PS{D}_k\text{=}\sqrt{{\displaystyle {\displaystyle \sum }_{m\text{=}1}^{2^K}}PM{P}_m*V\left({\beta }_k|data,M_m\right)\text{+}{\displaystyle {\displaystyle \sum }_{m\text{=}1}^{2^K}}PM{P}_m*{\left[{\widehat{\beta }}_{km}–P{M}_k\right]}^2}$        (8)

where V (β_k|data, M_m) denotes the conditional variance of the parameter in model M_m.

Assuming that each model M_m has a binary vector φ ascribed to it, where 0 signifies exclusion and 1 indicates the inclusion of a variable k in the model, the posterior inclusion probability is calculated as:

$PI{P}_k\text{=}{\displaystyle {\displaystyle \sum }_{m\text{=}1}^{2^K}}1\left({\phi }_k\text{=}1|data,M_m\right)*PM{P}_m$        (9)

The posterior probability of a positive sign of the coefficient in the model, P (+), is calculated as follows:

$P\left(\text{+}\right)\text{=}\{\begin{array}{c}{\displaystyle {\sum }_{j\text{=}1}^{ 2^K}P\left(M_j|y\right)*CDF\left(t_{ij}|M_j\right), \text{if} sign\left[E\left({\beta }_i|y\right)\right]\text{=}1}\\ 1–{\displaystyle {\sum }_{j\text{=}1}^{2^K}P\left(M_j|y\right)*CDF\left(t_{ij}|M_j\right), \text{if} sign\left[E\left({\beta }_i|y\right)\right]\text{=}–1}\end{array}$        (10)

where CDF denotes the cumulative distribution function and $t_{ij}\equiv ({\widehat{\beta }}_i/{\widehat{SD}}_i|M_j)$ .

The application of BMA requires the specification of the model prior, and it is common to use a g-prior on the parameter space. The “benchmark” rule (Fernández, Ley and Steel 2001) dictates the choice of the unit information prior (UIP) (Kass and Wasserman 1995) on coefficients. The combination of UIP with the uniform model prior (equal probabilities of all considered models) is advocated by Eicher, Papageorgiou and Raftery (2011), while Ley and Steel (2009) recommend a binomial-beta model prior (equal probabilities on all considered model sizes). Accordingly, in all the estimations presented here, UIP was combined with uniform and binomial-beta priors on model space.

The robustness of the variables is assessed with the posterior inclusion probability and the absolute value of the ratio of PM to PSD of a given regressor. Raftery (1995) classifies a variable as weak, positive, strong and very strong when the posterior inclusion probability (PIP) is between 0.5 and 0.75, between 0.75 and 0.95, between 0.95 and 0.99, and above 0.99, respectively. He considers a variable robust if this ratio is higher than 1, indicating that the inclusion of the variable improves the power of the model. Masanjala and Papageorgiou (2008) advocate a critical value of 1.3 relating to a 90 per cent confidence interval in the frequentist approach, while Sala-i-Martin, Doppelhofer and Miller (2004) advise using a critical value of 2 corresponding to a 95 per cent confidence interval.

Lastly, we resort to a quantile regression by estimating equation (4) and including all the variables as explanatory factors of migration flows. The main contribution of this approach is derived from the assessment of bilateral migration flows and the above-mentioned variables outside the mean values of the data, at the same time allowing the analysis of possible non-linear relations between the set of explanatory factors and our variable of interest. Therefore, the main goal of this methodology is to disclose heterogeneous impacts of push and pull factors over migration flows. Hence, we split our sample into quantiles, from the lowest (lowest relative migration flows) to the highest quantiles (highest relative migration flows). Quantile regression has the important advantage of distinguishing which determinants are associated with different magnitudes of relative migration flows. Therefore, using this approach, we can assess not only the statistical but also the economic significance of the results. Lastly, it is important to highlight that the country-pair, as well as period composition, of each quantile changes. The period composition of quantiles is presented in table A2 in the appendix and we can see that the time composition of quantiles is relatively stable, while the country-pair composition of quantiles is characterized by far greater variability.⁷

4.1. BMA results

The results of the BMA under uniform and binomial-beta model priors are presented in table 1. Figure 2 depicts the comparison of PIPs between the results obtained with uniform and binomial-beta models priors. We have identified five variables that are classified as robust according to at least one criterion under both model prior specifications. All the PMs and PSDs are standardized to facilitate comparison of the relative strength among the examined determinants.⁸

Figure 2

Posterior inclusion probabilities obtained with uniform and binomial-beta model priors

The lagged migration (MIGRlag) variable is characterized by the highest PIP and the highest PM to PSD ratio. It also has the highest PMs for uniform and binomial priors, 0.366 and 0.377, respectively, roughly twice the size of the second variable, the border dummy. This effect is relatively strong and demonstrates that past immigration lays the foundation for future migration by facilitating better conditions for the arrival of family, friends and acquaintances. As mentioned above, current immigrants can help them find housing and jobs and introduce them to the new culture and legislation of the hosting country.

Table 2 reports the results obtained using an alternative measure of past migration – cumulated bilateral migration over the examined period, defined in equation (2). In this case, we find that the variable CumMIG (“friends and relatives”) is even stronger, as PMs rise to 0.466 and 0.477 for uniform and binomial-beta priors, respectively, with virtually the same PSDs. This increase in the association between past and current migration demonstrates that the so-called “friends and relatives” effect increases with time as more immigrants integrate into the host country’s culture or create networks and institutions that facilitate the arrival of new immigrants. Interestingly, the increase in the association between past and current migration was accompanied by a drop in the correlation between migration and unemployment differentials. As a result, UNEMPL is fragile in this case. This outcome further illustrates our assertion about the dominant role of differences in earnings over differences in unemployment.

As table 1 illustrates, the variable with the second highest PIP and PM to PSD ratio is the border dummy, B. This outcome reveals that the cultural ties connecting neighbouring countries are strong enough to outweigh the economic incentives expressed in differences in earnings or unemployment rates. The last cultural variable classified as robust is the dummy variable for EU membership prior to 2004, OLDEU. It is ranked above the differences in unemployment, but below differences in earnings. The results thus show that cultural factors dominate economic considerations in terms of the strength of their association with migration flows.

Regarding our main variables of interest, the first economic variable on the list of robust determinants of migration is the absolute value of the difference in net salary expressed in PPP, while differences in the unemployment rate rank as the last variable classified as robust. Their comparison shows that the effect of the difference in earnings is more than twice as strong as the effect of unemployment differences. The standardized PMs for EARN are 0.115 and 0.105, while for UNEMPL they are 0.059 and 0.043, under uniform and binomial-beta model priors, respectively. The relative strength of differences in earnings against differences in the unemployment rate is further substantiated by the fact that EARN passes the robustness checks that we describe in the supplementary online appendix, while UNEMPL fails to do so on several occasions. Still, the results on the impact of unemployment and salary differences on migration are corroborated by average values for net migration for the period.⁹

Three more variables turned out to be weakly robust under the uniform model prior; however, they were found to be fragile under the binomial-beta model prior. The first of these is the difference in human capital (HC), whose positive PM indicates that workers flow from the countries with low human capital to the countries with high human capital. The last two robust variables are proxies for cultural similarity: access to the ocean or sea (MA) and difference in the average temperature (Temp). The case of Temp is especially interesting, as it shows that the difference in temperature is a better proxy for cultural similarity than a common language in the European context. Moreover, a negative PM on Temp shows that there is no evidence for people migrating from colder to warmer countries. The remaining variables turned out to be weaker regardless of the considered robustness criterion. However, the fragility of some variables can be considered an interesting result in its own right. Differences in average tax rates (Tax), the level of social benefits (Social), the government spending share of GDP (GOV) and the Gini coefficient (Gini) are fragile. This result holds even if we drop net earnings from the considered set of regressors.¹⁰ Therefore, the results demonstrate that intra-EU migration is not characterized by the “migration to welfare states” phenomenon. Similarly, differences in the prevalence of crime and corruption do not correlate with migration flows.

We conducted several robustness checks on the BMA results, which are presented and discussed in section B.1 of supplementary online appendix B. These confirm the findings reported in this article.

4.2. Quantile regression results

The results of the quantile regression estimation are presented in table 3.¹¹ The first quantile represents the smallest net migration flows, while the ninth quantile is associated with the highest migration flows. As expected, the point estimates in quantile regression are always higher than their respective PMs. In the case of quantile regression, we do not account for model uncertainty, so the estimated coefficients are biased upward in comparison. Accordingly, point estimates in quantile regression should be interpreted as upper limits of the association. For this reason, in the case of quantile regression, we interpret the results from a qualitative rather than from a quantitative perspective.

Our findings indicate that past migration is the best predictor of current migration across all quantiles. The strength of the association between the two increases from the first and the ninth quantile, from 0.542 to 0.875. The value of the point estimate increases successively from quantile to quantile. This finding further highlights the influence of the “friends and relatives” effect, where higher past migration flows contribute to increased flows in the future. The effect is non-linear and the data show that migrants gravitate more strongly towards places where their fellow citizens are already established in vast numbers. We found that differences in unemployment rates and earnings affect nearly all quantiles. We can see that the results for EARN in table 3 are mainly driven by lower quantiles, where the association between migration and differences in earnings is the strongest.

The values of the point estimates for earnings, as depicted in figure 3, are above the values of those for unemployment in all quantiles except the ninth, and here the coefficients are not statistically significant. This outcome corroborates the results obtained under the BMA framework regarding the relative importance of earnings and unemployment differences in driving the net migration flows. It also strongly reinforces the role of past immigration in facilitating future immigration. Relatively, the size of the impact of differences in earnings and unemployment diminishes as the size of the flow increases, while the so-called “friends and relatives” effect takes over.

Figure 3

Point estimates on unemployment and earnings differentials over the migration distribution (standardized coefficients)

The quantile regression results for the variables associated with physical distance and cultural proximity are more diverse. The geographical distance between the countries, LNDGEO, has a negative effect on migration in the first six and in the eighth quantiles. As expected, the greater the distance between the two countries, the smaller the size of the migration flows, indicating the importance of transportation costs, as well as cultural distance proxied by spatial distance. However, transportation cost does not seem to be a major factor for the largest migration flows. Sharing a common marine border, MB, is associated with higher bilateral migration in the top seven quantiles. The presence of a common border, B, is significant in the seventh and eighth quantiles, while a common language is significant in the first, seventh and ninth quantiles. The difference in average temperature, Temp, and access to the sea, MA, are significant in only one quantile. These results demonstrate that unlike past migration and economic considerations, cultural factors tend to be more quantile-specific.

Consistent with the results for the entire sample, we find that past migration is the most important predictor of future migration. Moreover, the strength of the “friends and relatives” effect increases with the magnitude of the relative migration flows. On the one hand, lower quantiles are dominated by economic considerations, including differences in earnings, differences in available job opportunities, as well as travel costs. On the other hand, cultural factors play a greater role in the higher quantiles, where we see that sharing a common border and having a common language are associated with the highest net migration flows, which can even override the purely economic drivers.

Contrary to the results across the entire distribution, the difference in human capital is positively associated with migration in all quantiles. This result demonstrates that variations in the skill level of the population are a good predictor of international migration flows. This outcome is particularly surprising, as differences in human capital are classified as fragile. However, this may be explained by the concept of complementarity of regressors from the jointness literature (Ley and Steel 2007; Doppelhofer and Weeks 2009; Hofmarcher et al. 2018). HC exhibits a complementary relationship with other robust determinants of international migration, such that differences in human capital are statistically significant when included with them. This is reflected by the fact that HC is robust under the uniform model prior. The binomial-beta model prior places greater probability mass on smaller models where the association of international migration with HC is not significant. Another possible explanation for the lack of robustness of HC in the main results is that the data suggest that the relationship is not well modelled by a linear approximation. The quantile regression results indicate that HC has a u-shaped impact across the quantiles, in terms of the estimated magnitude of the effect, the highest degree of association with international migration flows observed in the lowest and highest quantiles.

The difference in the government spending share of GDP (GOV) is negatively associated with international net migration flows, indicating that “migration to welfare states” is not supported by the data. This notion is further reinforced by the results for the difference in income distribution (Gini). The point estimates for this variable are negative and statistically significant in only four quantiles. The difference in the level of corruption (Corruption) exhibits a negative slope in lower quantiles, and coefficients are statistically significant for just two quantiles. However, the estimated coefficient turns positive in the three highest quantiles, with a statistically significant point estimate in the ninth quantile. Therefore, the data do not provide any clear conclusion regarding the association between the level of corruption and the size of migration flows. Lastly, the estimated coefficients for differences in crime rates (Crime) are positive and statistically significant in six quantiles, suggesting that European citizens prefer living in safer countries. However, this effect is limited to relatively high migration flows.