Most studies that examine the relationship between sports franchises and the economies of their host cities show no significant relationship. It's argued that consumer spending on (or related to) a pro sports franchise simply substitutes for other spending that would have occurred anyway.
Some studies suggest that the existence of a sports team may actually lower wages and employment in host cities, suggesting a small but negative multiplier effect associated with pro sports. A rationale for this negative multiplier is that relative to the businesses that would have received the spending that is replaced, the most of the owners of resources that produce professional sports contests in a home city do not make their permanent residences there (heck, half of the participants in any game usually don't represent the city they are playing in). As a result, more money leaves the home city than if people went, say, shopping instead.
Here is a nice article on Johan Santana, the Cy Young-winning pitcher of the Minnesota Twins. Its focus is on Santana and his offseason in his native Venezuela. But there is a passage in the article more in line with this post. He has filed for arbitration this year and will earn at least $3,400,000 more than he earned last year. What will he do with some of the money?
And now Santana wants to do a lot for them (people in his hometown of Tovar, Venezuela). The fame if not fortune -- Santana, who made $1.6 million last season, is taking the Twins to salary arbitration seeking a raise -- the Cy Young has brought Santana has provided him the platform he says he needs to make his dream of a sports complex in Tovar a reality.
I admire Santana for wanting to improve the quality of life in his hometown. But still, is this the sort of thing that US cities should (indirectly) subsidize?