High-skilled mobility—by profession and geographical region—before and after the 2004 EU expansion. (a) Rank-distribution of the top-100 high-skilled professions over the entire period of analysis, 1997–2014. The colour of each datapoint corresponds to its classification within the five broad profession groups. Dividing any given value by the total number of observations (381 757) gives the frequency, i.e. the top two professions are ‘Doctor of medicine’ and ‘Nurse’, accounting for 20% and 17% of the total observations, respectively. The top-100 professions shown account for 97% of the total observations. (b) Distribution of the observations by profession group—before and after the 2004 EU expansion. Totals within each profession group and within each period are shown. (c) Comparison of the mobility within and between Eastern and Western Europe before (inner ring) and after (outer ring) the 2004 EU expansion. Listed in the centre of each ring chart are the total mobility before (i) and after (ii) 2004. (d) Disaggregation of the east–west mobility flow by year and profession group. Note that the y-axis is shown on logarithmic scale. (Online version in colour.)
High-skilled mobility network: 2005–2014. Each country is represented on the circumference with an arc-length that is proportional to the total incoming and outgoing mobility of each country after the 2004 EU enlargement. The ribbons between each country are proportional to the mobility Mij,t. The mobility direction is encoded in the colour of the ribbon, which is the same as the destination country, as well as the endpoint characteristics of the ribbon, denoted by the gap between the ribbon and the termination arc. The legend provides a schematic example of a country which receives incoming mobility from just a single (yellow) country and provides outgoing mobility to just a single (blue) country. As such, the mobility of each country can be summarized by three histograms shown: the outer-most arc represents the total distribution of mobility by all partner countries, the middle arc represents the distribution of incoming mobility by source country, and the inner arc represents the distribution of outgoing mobility by destination country. For example, approximately 80% of mobility for UK is incoming; of the remaining 20% of outgoing mobility, almost 10% is going to IE. Shown are only the links representing more than 1% of the total flow into or out of a given country; the links shown account for 93% of the total mobility.
Comparative importers and exporters of high-skilled labour. (a) High-skilled mobility: before 2004, and in the periods before and after the 2007 global financial crisis—by profession group. (b) Revealed comparative advantage (RCA) by country and profession. Countries are ordered according to the overall level of high-skilled emigration over the entire period 1997–2014, and are assigned to the subgroup ‘E’ if they are among the 2004/2007/2013 EU entrants and ‘W’ otherwise. Within the RCA matrices, black squares indicate countries with no observed counts for the specified time period. The colour scale splits the range of values into seven groups: six groups of width 0.5 and one group for those extreme values for which RCAi,p > 3. Thus, blue shade values can be considered as significantly below or around the baseline RCAi,p = 1 value, whereas yellow/red values are significantly above RCAi,p = 1. (Online version in colour.)
High-skilled mobility matrices separated by profession group. (a) Shown are the mobility matrices representing net headcount from row country i to column country j over the period 2005–2014. The aggregated matrix (All) is the total across all five profession classes. The colour scale for each matrix visualization represents a partitioning of the log10Mij matrix entries into quartiles to facilitate visual inspection and for identifying the strongest dyadic flows. Below each matrix we also show for each country the total outgoing mobility Oi (red bars), total incoming mobility Ii (green bars) and relative brain drain Bi = (Oi − Ii) / (Oi + Ii). (b) Matrix showing the Pearson's correlation between each of the profession-specific mobility matrices shown in (a); correlation calculated between logarithmically scaled matrices, log10(1 + Mij,t); correlation values are shown in the corresponding lower triangular cells. (Online version in colour.)
Convergence within the European high-skilled mobility network. (a) Centrality time series (ci,t) for each of the incumbent EU members in 2004. (b) ci,t for each of the European countries that were not EU members in 2004. For visual comparison, each panel includes a horizontal dashed line corresponding to the uniform baseline c* = 1 / 32. Panels (a) and (b) include the average (thick grey curve) calculated across the countries in each panel, respectively; the y-axis is plotted on logarithmic scale. (c) Scatter plot of the PageRank centrality of each country representing each country's relative importance within the network, calculated using a standard algorithm for weighted networks applied to the pre- and post-2004 mobility networks. Points above (below) the diagonal dashed line indicate that the country's centrality increased (decreased) between the two periods. (d) Scatter plot of the PageRank centrality of each country using the post-2004 (2005–2014) mobility networks, with the vertical value representing the centrality in a hypothetical ‘extremely hard Brexit’ scenario with q = 1 corresponding to 100% of incoming UK mobility redirected elsewhere. The ci data points in panels (c) and (d) are normalized by c*, and thus we show the baseline (mean) centrality value equal to 1, indicated by the dashed orange horizontal/vertical lines; data plotted using logarithmic axes. (e) Per cent change %(q≡1) in the PageRank centrality under the q = 0.8 and q = 0.2 ‘Brexit’ scenarios. (f) Per cent change % (q) in the PageRank centrality of 2004 incumbent EU members as a function of q, the fraction of redirected incoming UK mobility. (g) Per cent change % (q) in the PageRank centrality of 2004 entrant and non-EU members as a function of q. Thus, as shown in (e), the q = 1 values in (f,g) represent the maximum per cent change values for most countries. Within (e,f), the average %(q) value is indicated by the opaque grey curve. (Online version in colour.)
Comparison of the mobility network community structure: empirical versus hypothetical ‘hard Brexit’ scenario. (a) Community structure for the empirical mobility network (q = 0) characterized by five communities. (b) Community structure for the hypothetical ‘extremely hard Brexit’ scenario (q = 1) characterized by four communities. Larger arrow size and link darkness indicate higher mobility. (Online version in colour.)
Mobility regression model estimates. See equation (3.6) for the model specification and electronic supplementary material, tables S1–S2, for the full set of model parameter estimates for each profession and specification. Significance levels: *(p < 0.05), **(p < 0.01), ***(p < 0.001). (Online version in colour.)