Now there's at least one obvious problem with this approach to happiness. To quote my psychologist cohort Chelle, "[t]he main problem with self report is that people are big fat liars." A more thorough survey would look at physiological and other objective measures. But of course, happiness and other emotional state are subjective experiences, so self-reporting is not an unreasonable measure. It should also be noted that 1) the Wolfers-Stevenson paper is titled "...Subjective Well-Being..." and 2) any criticisms of self-reporting apply just as much to the classic Easterlin study.
What about the main questions, which ask variations on 'how do you rate your life?' or 'how happy are you with your life?' Maybe we're placing too much weight on that one form of question?
Well one of the interesting things here is that the Gallup surveys include a whole range of other questions related to happiness, from "did you experience sadness yesterday?" to "did you have tasty food yesterday?" The relationship in most cases is pretty weak, but in every case increased income improved people's lives (or so they said). (See here.)
Have a look at depression, for example. I know I would have said that rates of depression are higher in rich countries; there's all this angst about unfulfilling consumerist lifestyles, suburban anomie, lack of social support and so-on. It turns out, though, that if you ask people "have you experienced feelings of depression" that's not what you find.
Lon asks another sensible question, "If money can buy happiness, shouldn't that mean the majority of the world would have committed suicide by now?"
To start with, I haven't found any international rates for depression, but there is data for suicides (see here). On the whole it seems more people kill themselves in rich countries (though China and India are major mid-liers and stats for Africa are almost non-existent). Suicide is a pretty puzzling phenomenon and I don't think it's one that relates to other factors in a clear way. Depression, and other mental illnesses, it's harder to say, but depression is a global burden - I think the WHO rates it something like #4 in its list of problem-causing diseases. We're much more aware of it in the rich world partly because we have resources for diagnosis. And, to give the professionals some credit, that may also be why we report lower rates.
That aside, if you trace the best fit line back, it hits 0 on the x-axis with a happiness score not far below Togo(?) and Benin. That's roughly how happy cavepeople might have been... It doesn't seem horrifyingly unhappy.