States with higher shares of union members in total employment tend to have higher gross domestic product (GDP) per capita.  GDP measures economic productivity.  Using State Data Lab to look across the 50 states from a long-term perspective (the 1997-2012 period, on average), one tends to see that states with low union membership have low GDP per capita, and states with high union membership have high GDP per capita.

Which comes first, the chicken or the egg?

Union advocates tend to believe the economic advantages for members of unions are not just for the members but translate into benefits for society generally.  See for example this compilation of research by the Economic Policy Institute.