Unfortunately, I missed the exchange in the comments section of this Interfluidity post. It raises some issues on the measurement and interpretation of savings ratios and inequality that I found rather interesting. I thought it would be useful to go through some of these points
The issue is to do with whether the rich save more than the poor and it should be seen in the context of the question of whether the distribution of income affects overall consumption. Much of the difficulty arises over whether capital gains should be included in household income when looking at this.
For the purposes of this discussion, I am going to treat gains as being the increase in the value of net assets, regardless of whether or not they are realised. I am going to use the term disposable income to refer to what is normally treated as disposable income in the NIPA accounts, i.e. wages, benefits, interest, dividends, etc.. I will use the term HS income to refer to Haig Simons income, which is disposable income plus gains.
So first of all I want to assume a simple consumption function based on disposable income and gains. I am going to assume that households have the same consumption function whatever their income, but that richer households have a greater proportion of their HS income in the form of gains. So our consumption function is:
Ci = αy . YDi + αa . Ai
where C is consumption, YD is disposable income and A is gains, for each household i. The difference is that the rich have a greater ratio of A to YD. What happens if we assume that households do not spend any of their gains (i.e. αa = 0)? Then, we will find the following:
- The aggregate savings rate of the economy (being 1 - C / YD ) will be equal be equal to 1 - αy
- If we measure the savings ratios of rich and poor as for the aggregate (i.e. using disposable income) their savings ratios will both be the same as the aggregate measure, 1 - αy
- If we measure savings ratios by reference to HS income (i.e. using 1 - C / [ Y + A ] ), then the savings ratio of the rich will be higher than the aggregate savings ratio and higher than that of the poor.
- Neither a transfer of earned income, nor of gains, from rich to poor will change the aggregate savings ratio of the economy (conventionally measured), nor the level of consumption.
Because the savings ratio is conventionally measured by reference to disposable income, we must do the same (ignoring gains) for individual households if want to get comparable measures. And in this special case, that is consistent with the result that redistribution of income and gains has no effect on consumption. However, I think this misses some important points.
So far we have just looked at the household consumption function based on income and gains that accrue directly to households. But we need to be aware that this is not equivalent to GDP. In the simplest case (ignoring flows with public and foreign sectors), disposable income will differ from GDP to the extent of earnings retained by firms. This part of GDP is accruing to the benefit of shareholders, but is not part of their disposable income as it is not paid to them. It is likely that retained earnings will increase the gains of households owning those shares, but this is certainly not a one-for-one relationship.
However, it is important to take this into account, because it is relevant to the issue of how income distribution is affecting consumption expenditure. If we find greater profit retention by corporations, we are likely to find less consumption, even though households may still be benefiting in the form of gains. But it is important to recognise that the effect here shows up as a fall in household disposable income rather than a rise in the savings ratio. Furthermore, on our original assumed consumption function, it still makes no difference if we transfer income or gains from rich to poor. The only thing that is making a difference is the earnings retention level.
Given our assumed consumption function, it is true to say that the rich save more, at least if we consider HS income. However, this is really just a consequence of our assumptions that everybody saves more of their gains than their disposable income and that the rich have more gains. That is why, on this assumption, re-distribution has no effect.
We might alternatively consider a consumption function where the propensity to spend out of gains is non-zero but that the rich have a lower propensity to spend out of disposable income. So the rich may be consuming the same amount as with our previous assumption, but based on different inputs. We could assume different functions for rich and poor, so the function for the rich is:
Cr = αry . YDr + αra . A
and for the poor:
Cp = αpy . YDp + αpa . A
So even with αry < αpy, we might still find that the savings ratio of the rich (measured as 1 - C / YD ) is the same as that of the poor, because they are also spending partly out of gains. And as before, we have to measure individual savings ratios that way if we want the ratios to be comparable to the aggregate savings ratios, simply because that is the way the aggregate savings ratio is measured.
However, we now find that a redistribution of disposable income between rich and poor will change that aggregate savings ratio. This is due to the fact that there is a different propensity to spend out that type of income. The difference with our previous result is due to the distinction between average and marginal rates.
All I have intended to do here is highlight some of issues involved in measurement and interpretation. I am not suggesting that actual household behaviour is actually like any of the scenarios I have used here. On the whole, I believe there is useful truth in the proposition that the rich save more, but I think under-consumption theories are more problematic. I think growing inequality, particularly wealth inequality is a big problem, but not necessarily for reasons of under-consumption.
It's still something I'm grappling with though, and hope to return to later.
(Ramanan also has a good post on this, put up after I wrote this but before I got round to posting it.)