I wonder if that direct adjustment is actually the proper way to do it. That's implying a hypothesis that the money-happiness relationship varies due to COL, but is constant once adjusted for purchasing-power parity. But it seems at least plausible that the relationship is a different one. I'd be interested if anyone's directly studied what the money-happiness correlation is in NYC versus, say, Omaha. I wouldn't be surprised to see a deviation in either direction; perhaps New Yorkers need
more than the COL-adjusted equivalent to be happy, or perhaps they need less. May even vary among sub-groups.
In my own case, I've found that the amount of money I need to be satisfied with my income tends to scale less than linearly with COL. In higher-COL places I spend a bigger proportion of my income on rent, and do more low-cost entertainment, in part because more low-cost entertainment is available. For example, I've lived in both Houston and Santa Cruz, and I was quite happy doing a lot of free and cheap things in Santa Cruz, with its great beaches, hiking, etc. In Houston, I had to spend money for entertainment.