Sports and happiness

We investigate the relationship between participation in physical activity and self reported happiness in the United States. IV estimates based on data from the Behavioral Risk Factor Surveillance System between 2005 and 2009 and County Business Patterns indicate that individuals living in a county with greater access to sports facilities are more likely to participate in physical activity and also report higher life satisfaction. Both men and women gain happiness from participation, and men appear to benefit more from participation than women.

That is from the paper "Sports participation and happiness: Evidence from US microdata," by Huang and Humphreys (Journal of Economic Psychology, August 2012).  

Obviously this has policy implications. But, does building a gym create more happiness than building a hospital?