Does the rise in the unskilled employment rate explain the fall in labour productivity in the euro zone?

The argument is often put forward that it is because the unskilled employment rate has risen that labour productivity gains have fallen in the euro zone. We have our doubts about the relevance of this argument: The employment rate among the medium- and highly-skilled has also risen, and the structure of employment by level of education has not changed much; In the United States, the unskilled employment rate has also risen, significantly more than that of the higher-skilled, and yet productivity gains have not fallen .