Dennis Coates (Professor of Economics at University of Maryland, Baltimore County and President-Elect of the North American Association of Sports Economists) provides a nice survey of the academic literature on the economic impact of sports stadiums in The American.

The most basic question about stadiums, arenas, and sports franchises is the extent to which they contribute to the vitality of the local economy. Supporters of publicly financed stadiums argue that the benefits are substantial, while opponents say they are small and highly concentrated among the wealthiest citizens. To buttress their case, supporters mostly use economic impact studies that predict how the local economy will be affected by the stadium, while opponents compare the economy before and after the facility is constructed. Supporters tend to imply that redistribution of economic activity from the suburbs or outlying areas of a city to the downtown is desirable, while opponents generally oppose this sort of redistribution and focus instead on job and income creation.

The typical economic impact study gathers data on all aspects of spending related to a stadium, including the money spent to build it and the money spent by fans in connection with the stadium (including on tickets, at restaurants, and at hotels). The impact of this spending ripples outward into other areas of the economy through a multiplier. By linking spending to employment, the study then calculates how many jobs a stadium has created. It does not perform a cost-benefit analysis, which would address the opportunity costs of raising taxes to pay for a stadium and consider alternative uses of those funds.

Academic researchers have examined the prospective economic impact studies and found a variety of methodological errors in them, all of which raise doubts about the magnitude of the predicted spending and job increases. Other scholars use data from multiple years before and after stadium construction to measure the impact of the stadium. These ex post studies reject stadium subsidies as an effective tool for generating local economic development.

My own research, conducted with economist Brad Humphreys (who is now at the University of Alberta), has used perhaps the most extensive data, incorporating yearly observations on per capita personal income, employment, and wages in each of the metropolitan areas that was home to a professional football, basketball, or baseball team between 1969 and the late 1990s. Our analysis tried to determine the consequences of stadium construction and franchise relocations while controlling for other circumstances in the local economy. Scholars Robert Baade, Allen Sanderson, Victor Matheson, and others have taken slightly different approaches, but the results are fairly constant from one analysis to another. There is little evidence of large increases in income or employment associated with the introduction of professional sports or the construction of new stadiums. (Emphasis added)