Did the European Union policy response to the large-scale movement of people from the Middle East and Africa introduce pull-factors that encouraged new and/or continued movements from these regions?
It would be a mistake to think of one "wave" of migrants. There are different groups with different pull and push factors.
- Civil war refugees from Syria and Iraq. Many stayed in the region until the international community slashed aid to the camps. These people were willing to risk death to get away from where they were because staying would mean slow death. Clearly push factors.
- Civil war refugees from places like Afghanistan or Somalia. Probably many of them were not aware that getting to Europe was feasible before 2015, so there might have been pull factors here. But objectively, they had every reason to leave and if Europe lived up to its ideals they should get refugee status.
- Economic refugees from extreme poverty and violence in central Africa. Same as for the refugees from Afghanistan. In previous decades many died in their home countries instead of marching north.
- Economic migrants from relative poverty and political oppression in northern Africa. They could survive where they are, it just wouldn't be a good life. The asylum policies may be pull factors here.
- Economic migrants from within Europe, e.g. from Albania and Kosovo. Not many people talk about them, but look at the EU refugee statistics from 2015 and before. A change in regulations slashed refugee numbers since then.
Short answer is, yes. I'm not even going to argue that the Western countries caused that very wave of migration with actions such as the invasion of Iraq or the support for the "arab spring" movement (that began the civil wars that caused a lot of those migrations), or the completely unjustified action against Khaddafi that transformed Lybia from a stable country to a hive of terrorists and slave traders. But yes, most "refugee boats" leave Africa from Lybia now.