I guess annual income also hints at annual expenses which should be important for the study. There are people who constantly spend all they make, and probably score low on self assessed happiness. Also income != wage, can be passive.

I think for a study like this, a money-happiness correlation would need a more sophisticated definition of money, to account for peer pressure and spending.

For a given zip code - take p75 of pre-tax income, multiply by 50% - this would be a proxy of how much someone needs to spend per year to be comfortable with local cost of living and their peers. 50% takes taxes and savings out, call it spend/burn. Then someone's wealth could be a ratio of net-worth/burn. The higher the wealthier - people 25 and over essentially not needing to work, and people with < 3 are essentially in indentured servitude, even with high income. Control for age.