There has been a fair amount of research suggesting that beyond some low threshold, additional money does little to increase a person’s happiness.
Here’s a research report (see also here) indicating that the effect of money has sometimes been underestimated because researchers use income as a measure of money, when wealth has a higher correlation with happiness.
There’s probably more than one reason for this. Wealth produces a sense of security that isn’t achieved by having a high income but spending that income quickly. Also, it’s possible that people with high savings rates tend to be those who are easily satisfied with their status, whereas those who don’t save when they have high incomes are those who have a strong need to show off their incomes in order to compete for status (and since competition for status is in some ways a zero sum game, many of them will fail).