Fig. 1 Eastern-Western European divergence.

Global trends in cross-border collaboration by international region: 1996–2014. Source: SCImago Journal and Country Rank based on Scopus (40). Notably, the curves for Western (W.) Europe and Eastern (E.) Europe are, before 2004, characterized by a roughly constant offset, thereby satisfying the prior equal slope condition of the DiD framework.

So, why have Western and Eastern Europe followed different paths of cross-border integration in science? To provide insight into this divergence phenomena, we constructed a longitudinal data set for 32 European countries over the 17-year period 1996–2012 by aggregating data from four different sources: (i) publication count, citation count, and international collaboration rate data from SCImago Journal and Country Rank (disaggregated across 14 research subject areas indexed here by s, for example, s = 1300: “biochemistry, genetics, and molecular biology”); (ii) government investment in R&D data from the World Bank; (iii) official country-country pairwise counts of incoming/outgoing European Union (EU) high-skilled labor mobility from the EU Single Market Regulated Professions Database (14); and (iv) global migration data from Abel and Sander (15). See Materials and Methods for further description of these data sets.

We then used these data to compare the levels of cross-border collaboration before and after the 2004 EU enlargement, thereby illuminating the complex relations between the integration of European labor markets, “brain drain” (16–22), and the arrested development of the ERA (8, 9). A hypothetical mechanism connecting these three elements is rather intuitive, following from the dynamic interpersonal nature of scientific collaboration (23): We hypothesize that Europe experienced a significant loss of cross-border integration because as mobile academics pursued international career paths, likely by following their previous collaboration channels, the cross-border links that they previously mediated between their home country and their destination country were subsequently eliminated. Thus, in addition to demonstrating how policy shifts can inadvertently spur high-skilled migration (24), we also demonstrate additional negative externalities on subsequent cross-border activity here. Because high-impact research is more likely to occur in multicountry collaborations (5), our findings show how migration imbalance can negatively affect the convergence of scientific competitiveness across Europe.

RESULTS

To measure the impact of the EU enlargement on the rate of international collaboration in Europe, we implemented two causal inference methods (25)—the synthetic control method (SCM) (26) and a difference-in-difference (DiD) panel regression model. In each method, we use the EU enlargement—10 entrants in 2004 (CY, CZ, EE, HU, LT, LV, MT, PL, SK, and SI) and 2 entrants in 2007 (BG and RO)—as a multicountry two-stage policy intervention corresponding to the (“treatment”) years t* = 2004 and 2007, respectively (for a list of the expanded forms of the abbreviated European country names used in this study, see Countries analyzed in Materials and Methods). Hence, we separated the European countries into two groups, the first comprising the incumbent 2004 EU members and the second comprising the 12 entrant countries.

The dependent variable in our analysis is a country’s level of cross-border activity, operationalized using SCImago’s cross-border counting scheme, which is derived from the affiliation information listed in each publication’s author byline. Specifically, if a publication includes author affiliations from more than one country, the publication is counted as “cross-border” for all countries involved in the publication. Thus, for each country i and year t, SCImago reports the fraction f_i,t of the total publications (D_i,t) involving cross-border collaboration. Then, we calculated the total number of publications χ_i,t = f_i,tD_i,t. Although there may be other cross-border counting schemes, which account differently for the total number of authors, countries, and even the number of affiliations per author, we lack comprehensive publication-level information from Scopus required to implement a sensitivity analysis along these lines; see Publication data in Materials and Methods for a discussion of this and alternative counting schemes. Note that, among alternative counting schemes, the one implemented by SCImago is particularly amenable to statistical analysis because it reduces the interdependency between the observations at the country level. That is, a country receives the same cross-border credit for an international publication, independent of the details of author affiliations and the other countries involved.

SCM estimates

We start by framing our SCM analysis in potential outcomes notation (27). Let the outcome variable Y_i,t(1) = f_i,t(or χ_i,t) correspond to the cross-border activity of a country directly affected by the EU enlargement and Y_i,t(0) = f_i,t(or χ_i,t) correspond to the cross-border activity of a non-European country. Thus, we consider the treatment (or intervention) as the enlargement of the EU, with EU membership status providing unique access to the EU’s large funding programs and the “freedom of movement” for persons and workers, which are fundamental tenets of EU policy. The set of units in our SCM analysis is divided into three subsets: (i) a balanced panel of 26 non-European countries (those with nonzero publication counts in each s for all t), (ii) the 10 countries entering in the 2004 enlargement, and (iii) 15 incumbent EU countries along with 4 close EU affiliates (CH, IS, LI, and NO), which have special trade and mobility agreements with the EU. To simplify the demonstration of the SCM, we collected and averaged the countries in the second and third groups. The result is an averaged representative unit for each group, which from here on we refer to as the “EU entrants” and “EU incumbents,” respectively.

The period before t* = 2004 corresponds to the pretreatment period, for which we assume there to be no difference between Y_i,t<t*(0) and Y_i,t<t*(1); that is, anticipation of the enlargement had no impact on characteristic levels of cross-border activity before 2004. We then use the 2004 enlargement to estimate the counterfactual difference δ between Y_i,t≥t*(1) and Y_i,t≥t*(0), which is the unit-level causal effect of EU enlargement on Y_i,t. Because the entrant and incumbent data are averages, we are actually estimating the mean causal effect for each collection of units, which has been established as an unbiased estimator of the average unit-level causal effect (27).

Of course, in reality, we only observe the potential outcome Y_i,t≥t*(1) for the EU entrants and incumbents. However, the power of the SCM is to estimate the alternative potential outcome Y_i,t≥t*(0)—that is, the counterfactual scenario corresponding to no EU enlargement—by extrapolating synthetic and for t ≥ 2004 using a basis set of countries for which we assume that Y_i,t≥t*(1) = Y_i,t≥t*(0). More specifically, our SCM approach estimates and using a panel data set composed of four covariates (which are used as matching variables) as input: (i) the total number of publications (), (ii) the normalized citations (), (iii) the per-capita gross domestic product (GDP) (log₁₀GDPpc_i,t), and (iv) government expenditure on R&D as a percentage of GDP, e_i,t. Provided these data, the SCM estimates an optimal set of weights using the data for t < 2004, thereby allowing for the extrapolation of for the EU entrant countries based on their projection onto the subspace of covariate data for the 26 non-European control countries [see the study of Varian (25) and the Supplementary Materials for further SCM details]. Note that the extent to which the individual covariates explain the dependent variable is not the aim of the SCM; instead, we use a panel regression in the following section to infer the quantitative relations between the covariates and the trends in f_i,t.

Figure 2 (A and B) shows the empirical curves (f_t and χ_t) measuring the cross-border activity for both the EU incumbents and the EU entrants. In terms of R&D investment and scientific output, the representative entrant county is medium sized (that is, between SG and RU), and the representative incumbent country is large (for example, CA). For this reason, we divided the incumbent χ_t curves by a factor of 10 in Fig. 2 (A and B) to facilitate visual comparison. Along with the real data (indicated by solid lines), each panel also shows the SCM estimates and (indicated by dashed lines).

 

 

Fig. 2 Comparing synthetic (counterfactual) and real cross-border collaboration after the 2004 EU enlargement.

(A) SCM results for the fraction f_t of cross-border publications and (B) the total number χ_t of cross-border publications. The solid curves represent the real data, whereas the dashed curves represent the estimates, and , measuring the counterfactual scenario of no 2004 EU enlargement. Estimates are made using the SCM (26), implemented using a control group of 26 non-EU countries to best fit χ_t (f_t) for t < 2004 and then to extrapolate () for t ≥ 2004 (see the Supplementary Materials). Note that the χ_t that represent the incumbent pre-2004 EU countries are divided by 10 to facilitate visualizing all the curves on the same scale. δ and δ(%) represent the difference between the real and synthetic curves after 2004, providing estimates of the “2004 EU entry” effect on cross-border European integration. (C and D) Estimation of the significance level of the SCM results using the permutation test (25). (C) For the intensive variable f_t, each curve represents the absolute difference ; dash-dotted red and blue curves correspond to the entrant and incumbent EU curves in (A), respectively. Of the 24 curves, the (red) EU entrant curve has the largest positive net difference after 2004. (D) For the extensive variable χ_t, each curve represents the percent difference . The four countries that exceed the average EU entrant curve are peripheral countries bordering the EU. (C and D) The additional colored curves correspond to the SCM difference calculated for each of the non-European control countries. Only the control country curves that passed SCM goodness-of-fit criteria for t < t* based on the mean squared error between the synthetic and real curve are shown (that is, to eliminate control countries with synthetic estimates that are either unreasonably noisy or not estimable).

 

The difference between and f_i,t is an estimate of the country-level causal effect, δ ≡ Y_i,t≥t*(0) − Y_i,t≥t*(1). Because the fraction f_i,t is an intensive variable, whereas the total publications χ_i,t is an extensive variable, we measure δ slightly differently for each variable. For f_t, we estimate δ using the mean annual difference between and f_t for t ≥ 2005. For χ_t, we instead measure the percent difference between and ; that is, . Hence, the summary statistics δ and δ(%) represent the total impact of EU enlargement on the scientific integration and the international competitiveness of the EU in terms of scientific output.

For the 2004 entrants, the SCM results indicate a δ = 0.062 decrease in f_t and a 9% decrease in χ_t relative to the counterfactual (alternative potential outcome). In other words, the positive values indicate that cross-border activity would have been higher had they not entered the EU. In the case of f_t, this corresponds to roughly a 14% decrease over average pre-enlargement levels of f_t ≈ 0.45. The incumbent EU countries also suffered a 15% decrease in χ_t; however, we also calculated a marginally negative value (δ = − 0.013) for the per-publication rate f_t. This discrepancy calls for a closer look at the statistical significance of the SCM results.

To estimate the likelihood of obtaining these results due to random statistical fluctuations, we also applied the SCM to each of the control countries individually. Figure 2 (C and D) summarizes the results of this “permutation test” (25) by showing the differences between the real and synthetic outcome curves after applying the SCM to each country in our analysis—entrant, incumbent, and the controls. For example, the red (blue) dash-dotted curve in Fig. 2C represents the difference between the corresponding red (blue) curves in Fig. 1A. Similarly, the red (blue) dash-dotted curve in Fig. 2D represents the percent difference between the red (blue) curves in Fig. 2B. The other curves represent the individual countries from the control set (see the legend in fig. S1 to identify individual countries by their color).

By comparing the magnitude of posttreatment difference among all permutations of control units, we are able to estimate the statistical significance of the observed SCM result for the entrants and incumbents. To operationalize this comparison, we define the posttreatment difference as the net difference, or , over the 8-year period 2005–2012. Hence, under the null hypothesis that there should be no difference in δ_i,> or δ_i,>(%) among the units, one can estimate the likelihood that the ordered configuration of SCM outcomes could be driven by chance alone. For the case of f_t, the largest δ_i,> = 0.54 belongs to the EU entrants, which exceeds the value of the next two largest δ_i,>values (for Colombia and China) by 16%. Thus, we can assign a false-positive rate of 1/24 = 0.042 to the observed configuration, meaning that it is rather unlikely, just by chance alone, that the SCM produced such a large effect for the entrants. For the case of χ_t, neither the entrants nor the incumbents have the largest net difference, as several peripheral European countries (Ukraine, Belarus, Russia, and Turkey) show an even larger difference between the real and counterfactual outcome, suggesting that the EU enlargement may have even affected external countries as well. As an additional robustness check, we again applied the permutation test, but we used a “placebo” enlargement year t* = 2002 instead. In this case, fig. S1 (C and D) shows that the entrant and incumbent curves are not distinguished in any way among the control countries. Thus, we can conclude that 2004 is a significant intervention year and that we do not find evidence of preexisting factors that might have driven our result.

To further investigate variation in the SCM results due to disciplinary factors, we repeated our procedure for two disaggregated highly collaborative disciplines, biology and physics, with the latter being the most collaborative of all the subject areas analyzed. High collaboration rates in these two domains can be attributed to the increasing prevalence of large collaborations (1) representing multinational consortiums organized around grand scientific challenges, international facilities, and even transnational clinical trials (3). Figure S1 (A to D) shows the SCM estimates for these two subject areas, which can be compared directly to the results shown in Fig. 2 (A and B) calculated by pooling all the subject areas together. For the case of f_t, the results are consistent for each subject area, both in sign and in magnitude. For the case of χ_t, the signs of δ(%) are consistent; however, the magnitude for the biology entrants indicates a negligible difference, δ(%) = 1.2%. We leave the exploration of discipline-dependent variations, as well as their potential causes, for future research.

To demonstrate the robustness of our results at the country level, we show in figs. S2 (for f_i,t) and S3 (for χ_i,t) the analogous SCM time series calculated for the 10 individual 2004 entrant countries along with the two 2007 entrants. The country-level SCM results support the overall results observed at the aggregate level while further identifying some caveats. For example, CY is distinguished as the only country that benefited from the enlargement with both δ < 0 and δ(%) < 0, most likely because of its strategic tax laws, which we will discuss later in terms of high-skilled mobility.

To summarize, we used the SCM to estimate the levels of European cross-border activity in the hypothetical counterfactual scenario corresponding to no 2004 EU enlargement. Before we move to a panel regression framework, which facilitates identifying the role and significance of individual covariates in explaining trends in f_i,t, we first introduce high-skilled mobility data, which are central to our main result connecting cross-border activity and mobility. Because the mobility data are only available for European countries, we were not able to incorporate it into the SCM analysis.

High-skilled mobility networks

We collected and analyzed publicly available official EU records to estimate the intra-European flow of high-skilled labor over the period 1997–2012. These data are derived from the formal request procedure of a certified professional in a given “host country” seeking cross-border validation of their degree certificate in a particular “destination country” and are collected and reported by each European country in the EU Single Market Regulated Professions Database (14). Thus, by aggregating these data across all countries, we constructed a mobility matrix, M_ij,t, capturing the total high-skilled mobility (head counts) from country i to country j in a given year t. The total across any given row i (or column j) of M_ij,t gives the total outgoing mobility (or incoming ) from (or to) country i (j). Similarly, we define the net mobility matrix as Δ_ij,t≡M_ij,t − M_ji,t, when there is positive net mobility from i to j (M_ij,t > M_ji,t) and Δ_ij,t≡0 otherwise. See the Supplementary Materials and figs. S4 to S11 for additional in-depth analysis of the aggregate (European), country, and dyadic (country-country) patterns of high-skilled mobility—before versus after the 2004 enlargement.

Figure 3 shows the mobility matrices before (M_ij,<) and after (M_ij,>) the 2004 enlargement. The patchy asymmetry of both matrices demonstrates the uneven geographic distribution of high-skilled mobility across Europe. Moreover, comparison of the mobility matrices and the corresponding and by country (see fig. S4) together demonstrate the drastic sevenfold increase in intra-European high-skilled mobility after the 2004 enlargement.

 

 

Fig. 3 High-skilled mobility before and after the 2004 enlargement.

(Top) Mobility matrices (M_ij) showing the total mobility (head counts) from country i to j, with black cells indicating 0 observations. The red color scale to the left of each M_ij represents , with black cells indicating Δ_i < 4 for 1997–2004 and Δ_i < 155 for 2005–2012; the green color scale indicates log₁₀M_ij and is split into six equally spaced regimes in logarithmic scale. (Middle) Aggregate mobility by country: total outgoing , incoming , net mobility , and mobility polarization ). (Bottom) MST representation of the mobility networks indicated by the orange links, with green links providing an overlay of the non-MST links. The thickness and opacity of links are nonlinearly related to log₁₀M_ij so that only the most prominent links are visible; color values are not comparable between the two time periods.

 

To account for the variation in the countries that constitute our mobility network, we also calculated country-level and dyadic (country-country) measures. For example, we calculated the Gini index () applied to the distribution of incoming (outgoing) mobility to (from) each country in each year to measure the dispersion of incoming (outgoing) mobility. We also measured the net mobility at the country level in two ways, first as the “absolute” net mobility and second as the mobility polarization or “relative” net mobility, ). To illustrate the differences, we show in Fig. 3 the range of Δ_i and B_i calculated for each country, before and after 2004. Note that all of the mobility matrices in our analysis are shown with the countries ordered according to decreasing B_i (calculated over the entire period 1997–2012). For this reason, most of the entrant countries, with the exception of CZ and CY, appear in the upper left quadrant.

To illustrate additional structural information contained in the mobility matrices, we also produced several network visualizations derived from M_ij,t and Δ_ij,t. Figure 3 shows the minimum spanning tree (MST) representation, indicating that UK and DE were each at the core of the MST network before the enlargement, whereas the UK became the principal root vertex afterward. Figure S5 shows a circular network visualization of M_ij,t, before and after 2004, combining the directionality and magnitude of the mobility flow. Figure S6 shows that the community structure of the mobility matrix M_ij and that of the net mobility matrix Δ_ij are nearly identical. Together, we identify UK and DE as the two countries that have gained the most from high-skilled labor mobility: the former being the main “brain gain” hub for the Western European countries and the latter playing the same role for the Eastern European countries.

Figure 4 facilitates the direct comparison of Δ_ij,< and Δ_ij,>, illustrating the drastic evolution of intra-European mobility imbalance (see also fig. S9). Of principal importance is the marked shift in the east-west mobility following the EU enlargement. Over the 8-year period 2005–2012, we observe 29% of the mobility to be from Eastern Europe (E; defined here as the 2004/2007 EU entrants) to Western Europe (W; defined here as the incumbent EU plus the four non-EU countries CH, IS, LI, and NO, which have notable trade, free movement, and other political agreements with the EU). By comparison, this percentage represents a significant increase, more than the 5% value observed from east to west (E → W) over the 8-year period 1997–2004. Nevertheless, despite the drastic increase in the E → W mobility after 2004, the increasing weight of both the E → W and W → E mobility channels, relative to the intraregion mobility E → E and W → W, represents progress toward brain circulation within Europe, which is fundamental for the competitiveness of its knowledge-based economies (28).

 

 

Fig. 4 High-skilled net mobility networks (Δ_ij), before and after the 2004 EU enlargement.

(Top) Mobility between the 2004/2007 entrant countries (“E”) and the rest of the incumbent European countries (“W”). The networks in each period are calculated from a total of 43,075 head counts (1997–2004) and 272,813 head counts (2005–2012), respectively. Link thickness represents the fraction of the total mobility. (Bottom) Node color represents EU entry year group (g_EU,i); node size is proportional to the mobility polarization, 1 + B_i (with larger values indicating larger mobility out of country i); link thickness is proportional to log(|Δ_ij|)² between countries i and j, with the arrow pointing in the direction of the net flow and link color corresponding to the source node. The size/thickness scales used for both networks are the same, facilitating direct comparison.

 

We use B_i,t as a central explanatory variable in a panel regression model in the following section. Similar to f, mobility polarization is also an intensive variable, thereby facilitating the comparison of countries that range considerably in size. It is also a symmetric variable, centered around the value 0 corresponding to equal incoming and outgoing mobility, meaning that the sign of the corresponding coefficient in our regression model has a clear interpretation. By way of example, consider the mean B_i,t values after 2004 for the incumbent and entrant countries, and , respectively. Comparatively, the countries with significant net immigration (B_i,> ≤ −0.5) were CY, LU, and UK, whereas PT, GR, MT, HU, SK, BG, PL, RO, EE, and LT were the countries with the largest relative levels of emigration (B_i,> ≥ 0.5); for further comparison of B_i,< and B_i,>, see fig. S10A. Thus, combined with additional extensive (for example, and ) and intensive (for example, and ) mobility covariates, these variables provide an additional level of variation among the entrants and incumbent EU members.

Panel data regression model

The dependent variable in our model is —the fraction of publications from country i in subject area s in year t that involve cross-border collaboration. We modeled this variable using a panel regression including country fixed effects (β_i,0) to control for time-invariant, country-level characteristics (for example, national language and geography). We also included a year variable to control for the overall increasing trend in cross-border collaboration. For example, the sharp increase in f_i,t around 2002, within the EU and abroad, may stem from the 6th EU Framework Programme, which was the first to broadly include specific international collaboration criteria in its funding schemes.

In addition to the variables included in the SCM analysis (scientific productivity and impact, R&D investment, and GDPpc), we also include controls for publication subject area and additional covariates that control for cross-border activity, namely, mobility. In compact form, highlighting the two most important explanatory variables, our linear panel model is given by(1)

The binary variable T_EU,i,t represents a country’s EU membership status (equal to 1 if i is an EU member in year t and 0 otherwise), so that a 0 → 1 shift captures the “EU entry effect” quantified by β_T. The coefficient β_B captures the linear response of depending on the inward or outward polarization of mobility. Finally, the inner product represents the rest of the model control variables, and is the white noise capturing country-level shocks. Further details on the high-skilled mobility data and the total migration (high skilled + low skilled) data can be found in the Supplementary Materials; for the full specifications of the panel model, see eq. S4.

Within this DiD framework, which comprises the relative comparison of a control and treatment group before and after the EU enlargement, we ran two models to test the significance of β_T and β_B, the results of which are summarized in Fig. 5. In both models, we leverage the fact that the enlargement occurred in two stages: 10 countries entered in 2004, and another 2 countries entered in 2007. In the first model, we use the incumbent EU countries as the baseline for comparison, and thus, β_T represents the change in relative to countries already within the EU. In the second model, we use the delayed 2007 entry of BG and RO to provide a second estimate of the EU entry effect, whereby the baseline for comparison in this case are these two delayed entrants. Thus, in the second model, β_T represents the change in relative to other non-EU countries whose membership was under consideration.

 

 

Fig. 5 The impact of EU enlargement and mobility on cross-border collaboration.

(A) Point estimates with 95% confidence intervals. Two variables are particularly important to our analysis: (i) β_T captures the interaction between dummy values for before/after 2004 and a country’s EU membership status—that is, the impact of EU entry; (ii) β_B captures the variation due to mobility polarization, B_i,t. We ran two regression models, each with a different baseline set of countries to demonstrate the robustness of our results. In the first model (magenta data, “full model”), the incumbent EU members serve as the baseline because their EU membership status does not change over the period of the analysis (N_obs. = 4494, adjusted R² = 0.66, and N_c = 31 countries). In the second model (orange data, three-period model), we used the 2007 entrants (BG and RO) as the baseline comparison for the 2004 entrants over three periods from 2001 to 2006 (N_obs. = 504, adjusted R² = 0.60, and N_c = 12 countries). See eq. S4 for the model specification and table S1 for the full set of controls, as well as other partial models demonstrating robustness of our results. Parameters are estimated using country fixed effects and robust SEs implemented by the Huber/White/sandwich estimator, which accounts for cross-sectional heteroscedasticity and within-panel (serial) correlation. As a visual aid, asterisks indicate the level of significance for each coefficient estimate: *P ≤ 0.05, **P ≤ 0.01, ***P ≤ 0.001. (B) The marginal effect of B_i,t on f_i,t, calculated using an interaction term between EU membership status and B_i,t. The main results of this model are two partial coefficients: β_B|E.Eur. for the entrants and β_B|W.Eur. for the other Western countries. Holding all other covariates at their mean value, comparison of the marginal linear predictions indicates that a country in the Western European group with B = 1 still has a higher expected level of international collaboration than a country from the Eastern European group with B = − 1. Shaded interval indicates the 95% confidence interval calculated using the δ method.

 

Starting with the first model, where we compare the entrants and incumbent groups, we find that the entrant countries suffered a decrease in f_i,t upon entry into the EU (β_T = −0.058 ± 0.019, P = 0.004). Moreover, the divergence in f_i,t between the entrant and incumbent EU countries was further exacerbated by mobility polarization (β_B = −0.043 ± 0.013, P = 0.002). In relative terms, comparing the corresponding standardized β coefficients and , we conclude that the EU entry effect is roughly twice as large as the brain drain effect (see table S1, column 2). This β_T value is similar in magnitude to the counterfactual difference δ = 0.062 produced by the SCM, pointing to the consistency of these two methods.

In all, the net difference in f_i,t explained by these two effects is . The actual DiD in the mean collaboration rates before and after is [calculated from the mean f_t curves in fig. S4 (A and B) for the 14 s]. Thus, we estimate that T_EU and B_i,t explain roughly 92% of the European east-west divergence in f_t over the period of analysis.

We report the full list of parameter estimates in the first three columns of table S1, which also contains partial model results in the additional columns, together demonstrating the robustness of our main results. Also, fig. S7 shows the results of our panel model including interaction terms between year and country group, demonstrating that our results cannot be explained by preexisting confounding factors (that is, before 2004) among the new EU entrant countries. This result is further supported by the null results of our placebo test for the SCM model shown in fig. S1 (C and D), which we implemented using the premature enlargement year t* = 2002.

In the second model, we restricted the number of years included in our analysis to the 6-year period 2001–2006 and consider only the 12 2004 and 2007 entrant countries. Over this subperiod, we define the treatment group as the 2004 entrants and the control group as the 2007 entrants, because the countries in the latter group had not entered the EU by the end of 2006. Hence, this model represents a more traditional treatment framework because all countries are initially not EU members, whereas for the final period (2005–2006), RO and BG were still waiting for their membership approval. As in the first model, we find that the effect of EU entry is negative (β_T = − 0.13; P < 0.001), indicating that the 10 2004 entrants suffered a significant decrease in relative to the future entrants (BG and RO) that remained outside the EU in 2005–2006. To put this in perspective, because the average f value during 2002–2004 for the EU entrants is roughly 0.45 (see fig. S4B), then the reduction due to β_T represents roughly a (−0.13/0.45) × 100 = −29 % overall effect. Moreover, the impact of emigration is also negative (β_B = − 0.115; P < 0.001), which is consistent in sign with the estimate from the first model. The full list of parameter estimates is shown in the final two columns of table S1 denoted as the “three-period model (G).”

The most important parameter estimates are summarized in Fig. 5A for both models. The positive relation between cross-border activity and a country’s scientific reputation (β_R > 0) was significant in both models. Also, the country-level economic covariates—government expenditure in R&D (β_E), per-capita GDP (β_GDPpc), and per-capita researchers (β_Spc)—also played significant roles in explaining the variation in f. For example, in the second model (which only considers EU entrants), increased levels of government R&D expenditure were positively related to levels of cross-border collaboration. This relation was not significant in the first model, likely due to saturation in the impact of R&D expenditure on cross-border embeddedness. Additional covariates that we were unable to include in our model that also may contribute to the divergence between Eastern and Western Europe cross-border collaboration rates are inequality in R&D funding within the EU Framework Programmes, institutions, and the location of central scientific facilities (29, 30).

To estimate the partial effect of mobility on the Eastern versus the Western European countries, we also ran the first model including an interaction term between B_i,t and a binary dummy variable equal to 1 if a country was a member of the EU in 2003 (Western) and 0 otherwise (Eastern). Hence, this model produces a mobility parameter estimate for each region: β_B|W.Eur. = −0.0161 ± 0.0073 (P = 0.029) and β_B|E.Eur. = −0.0265 ± 0.074 (P < 0.001). Figure 5B shows the marginal effects of mobility on f_i,t by region, with all other covariates evaluated at their mean values. Because B_i shifts from B_i < 0 (net immigration) to B_i > 0 (net emigration), there is a significant decline in the international collaboration rate for each country group, with Eastern European countries showing lower levels of f_i,t and a slightly more negative marginal effect (the difference between the coefficients β_B|E.Eur. − β_B|W.Eur. = −0.0104 ± 0.0061; P = 0.088).

We conclude by considering potential limitations and sources of error in our analysis. First, we are limited to using SCImago’s definition of cross-border collaboration rate because we lack the publication-level microdata that are necessary to perform a sensitivity analysis of different affiliation counting schemes. Along these lines, we are also unable to account for variations across authors and across time in the number and type of affiliations per author, which would be difficult even with perfectly annotated author byline metadata. In all, because SCImago data are based on the full Scopus publication corpus, comprising millions of publications from numerous subject areas, we assume that there are no substantial country-level biases induced by their cross-border counting scheme and that year-level statistical errors affect all countries equally.

Second, the high-skilled mobility data are limited to intra-European flow; thus, we were unable to incorporate it into the SCM model analysis, which uses a global set of countries as the control set. Instead, our panel regression approach uses the incumbent EU members as the control set in the first panel model, unlike other studies, which use the rest of the world as the control (8, 9).

Third, the EU mobility data are constructed from official records tracking certificate-based professions, such as law, health, business, and education. As a result, these data do not incorporate the mobility of publishing academics (Academia has its own longstanding system of certifying Ph.D. training and credentials based on the evaluation of publication output and institutional reputation; thus, unfortunately, there was no need for the EU to track this profession). To our knowledge, there is no comprehensive publication database that would provide accurate coverage of academic mobility across discipline and time, namely, due to the author name disambiguation problem and the difficulty in directly linking author names with author affiliations in author byline metadata. Thus, we must assume that the mobility patterns of academics are correlated, and thus substitutable, by high-skilled labor mobility patterns. Because mobility is likely related to underlying patterns of collaboration, this assumption may not apply to all disciplines to the same degree, because collaboration itself can vary widely by discipline. For this reason, we included subject area dummies in our panel regression models.

Fourth, we encountered difficulty in using the SCM to estimate the extensive variable because of the skew in the size distribution of scientific output at the country level. As a result, the SCM was unable to obtain a suitable set of matches for the larger countries in our permutation test across the control countries, and thus, the SCM failed to produce for the largest countries. Thus, the largest countries within the control set (for example, United States and Japan) contributed differently for each of the SCM estimates. Nevertheless, because neither the entrant nor the incumbent unit was within this size regime, the results for and are largely consistent and are not driven by overfitting due to the largest countries. In all, these considerations point to several open avenues for future research to identify the microlevel mechanisms linking mobility and cross-border collaboration.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/4/e1602232/DC1