I’ve been distracted from fleshing out my two good model by the work on consumption by Christopher Carroll, specifically buffer-stock savings models, consumption concavity, and the equivalence of credit constraints and prudence. I’m going to post a few notes on this work here.
But in this blog let’s take a look at his beautiful paper “Why do the rich save so much?”
Carroll first points to data that the wealthy continue to accumulate until they die. There is no possibility that they are saving in an attempt to smooth consumption or dissave as they grow older. Neither is it possible to explain the wealth levels by increased patience.
Now, you can argue that they are saving to leave bequests to their children — the extremists would argue that they are saving to offset future taxation.
Unfortunately the elderly wealthy without children save more than the elderly wealthy with children.
So what are they saving for?
Carroll proposes a “Capitalist Spirit” model, in which they save in order to accumulate wealth. It doesn’t matter if the purpose of this accumulation is status, fame, the desire to fund an endowment, etc. Their goal is to die with a lot of money left over. Carroll introduces a utility function that is the sum of utility from consumption and utility from the ending endowment. Unlike the utility of consumption, there is not negative infinite disutility from leaving no endowment. The endowment is a luxury good. Those with less money save for precautionary purposes as well as income smoothing. But once the marginal utility of consumption falls below a certain level, you receive more utility from accumulation of wealth than you do from consuming an additional good, in which case acquisition of the luxury good takes precedence over acquisition of the normal good (e.g. consumption). In the limit as wealth goes to infinity, 100% of income is saved.
I like this model because it mirrors a hierarchy of needs, with higher goals of status, power, or philanthropy addressed once the needs of consumption are fulfilled. Utility does not only come from consumption. In this model, it is not that the rich are different from the rest of us — it’s hard to think of a more impatient or childish persona than Larry Ellison, for example — or have different preferences, but because they have so much money, they receive greater marginal benefit from accumulation than from consumption. The rest of us do not get to climb so far up the hierarchy of needs that our utility is improved more by not spending than by spending, but if we did have that much wealth, then we would also accumulate just as they do.
We don’t need to point out the impossibility of Bill Gates or Larry Ellison consuming even their interest income, let alone their wealth — note that buying yachts and paintings is not consumption, as these can be resold. Only the wear and tear or depreciation of the paintings and yachts constitutes consumption.
We can go back throughout history and look at figures such Marcus Licinius Crassus, who even after accumulating a wealth equal to 200,000,000 sesterii (1 sesterii could buy about one ass), and was given the province of Syria to milk, still didn’t have enough, and decided to invade Parthia, where he was killed in battle. The Parthians cut off his head and filled his mouth with molten gold.
It’s difficult to try to explain this behavior in terms of intertermporal utility optimization, unless you acknowledge non-consumption based sources of utility. It seems perfectly plausible that as wealth increases, the non-consumption factors come to dominate decision making.
Updated: Added some pics and fixed some typos.