According to a report by the OECD the European Union is not getting its fair share of skilled international workers due to its legal policies.  As skilled migrants are needed to drive innovation and contribute to productivity growth the report concludes that unless comprehensive measures are undertaken the long term competiveness of the EU is at stake.

Whilst a lot of press attention is being given to the migration problem in the EU this is mainly due to younger less educated persons when compared to other OECD countries.
For example, the United States attracts around 57% of highly skilled workers from third country states, a high number indeed when compared to 31% for the EU.  In recognition of this the EU did introduce the blue card system, a work permit programme not dissimilar to the US green card, which is used in the majority of countries except for the UK, Ireland of Denmark.  However, this was criticised as being hard to obtain and was consequently vastly undersubscribed and has not had nearly as much success as the American programme.
On the other hand, the EU on average does attract more international students, but fails to retain many of these after graduation.
The report makes a number of recommendations designed to remove unnecessary obstacles that may be off putting for international workers when choosing the EU, such as simplifying recognition of foreign qualifications.