Loanable funds is not helping

Noah Smith has a Christmas post in which he intervenes in the debate over whether $600 government cheques should be given to rich people or poor people. This is the latest iteration of the age-old debate that stems from the dubious argument that income inequality is good because rich people use resources efficiently and poor people waste them. Noah correctly concludes that this argument is wrong and that cheques should be sent to those on lower incomes. But his argument contains several mistakes.

National Saving

Noah starts by discussing whether the rich or poor are more likely to save their $600 cheque, noting that although the rich have a higher propensity to save than the poor, the effect on “national saving” of windfall gains like a one-off cheque may be hard to predict: “if you want to increase national saving, you might want to give the $600 to Tiny Tim instead of to Scrooge!”

Noah’s assumption, at this point in the argument, is that unspent government cheques will increase “national saving”. Is this plausible?

The official definition of “national saving” is total income, Y, less total consumption expenditure, C, (including government consumption). Since “saving” for each sector is sector income less sector consumption, “national saving” is also equal to private saving plus public saving. Manipulation of accounting definitions demonstrates that S = I + CA, where S is national saving, I is total investment (private and public) and CA is the current account surplus. For a closed economy, CA = 0 and S = I. For “national saving” to increase, either I or CA must increase.

Why would members of the public — rich or poor — depositing government cheques at banks increase national saving?

If the cheques are bond-financed, then private sector financial investors have handed over deposits in return for government bonds, while households have accepted deposits. The overall effect is an increase in bond holdings by the private sector, and a redistribution of private deposit holdings. Since private sector income has increased but consumption has not, private sector saving has increased.

But public sector saving has decreased by an equal amount. National saving is unchanged — as is total income. (The same is true for tax-financed cheques.)

Loanable funds

Noah then poses the question “do we really want to increase national saving?”

On a charitable reading, we can assume that, by “national saving”, Noah means “private sector saving”, and his question should be read accordingly.

To answer the question, Noah uses the loanable funds model. Before going on, we need a brief recap on why this model is incoherent, at least when used without care.

As already noted, S = Y – C = I + CA: “National saving” is just another way of saying “investment plus the current account”. There is no such thing as a “supply of savings”: households can choose to consume or not consume. They cannot decide on the size of S, because it equals Y – C. Households choose C but not Y, therefore they don’t choose S. A macro model which has “supply of saving” as an independent aggregate variable is incorrectly specified.

Noah uses this model to consider what happens when the “supply of saving” increases (which he apparently takes as equivalent to the “supply of” what he calls national saving).

He starts by noting that the usual configuration is such that an increase in the “supply of saving” causes “interest rates or stock returns or whatever” to fall and this in turn raises business investment. He then adjusts the model by asserting, “OK, suppose that the amount of business investment just doesn’t depend much on the rate of return”. (By “rate of return” he means “interest rates or stock returns or whatever”, i.e. the rate paid on loans by business, not the rate of profit on business investment.) This gives a diagram like so:

Now, here comes the punchline:

OK, now suppose that in this sort of world, you give someone $600 and they stick it in the bank. That increases the supply of savings. But it doesn’t do anything to the demand for business investment. Businesses invest the same amount. And the rate of return just goes down … in fact total saving doesn’t even go up!

What’s going on here? The supply of savings has increased yet total saving doesn’t change? To understand what Noah thinks he’s saying, let’s switch to apples briefly. Imagine the same supply-demand diagram as above with a vertical (inelastic) demand curve but this time for apples.

This model says that, assuming the quantity of apples consumed is fixed, if the cost of production of apples decreases (because that’s what the supply curve represents, at least in a competitive market), then the price of apples falls. A similar outcome arises if, instead of the cost of production falling, a magician appears, waves a wand, and a stack of extra apples magically appear all harvested and ready for market. At the marketplace, if nobody knows about the wizard, it just looks like the price of apples has fallen.

This is what Noah is doing with the “increase in supply of savings (apples)” arising from the $600 cheques (magic apples): since the “demand for savings” (apples) is fixed, apple sales (business investment/”national savings”) won’t change, but the price (“the rate of return on stocks or whatever”) falls. On the diagram, it looks like this:

This is incoherent in its own terms because, as already noted, a “supply of savings” doesn’t exist in the same way that a supply of apples does: apples are not one number minus another number.

But even putting this non-trivial issue aside, There is a another problem.

Where did the apples go?

Remember that the “supply of savings” has increased in the sense that the price per unit has fallen. But the actual quantity of “savings” is unchanged, according to Noah.

In apple world, the way this works is that when the magic apples appear, the orchard people, understanding the inelastic demand curve of the marketplace, save themselves some effort, harvest less apples, but take the right amount to the marketplace.

How does it work for the “supply of savings?” Don’t worry, Noah has an answer!

You give the $600 to one person, they stick it in the bank or in the markets, that lowers interest rates or stock returns or whatever, and then other people save $600 less as a result. No change.

Pretty neat. Every time someone banks a $600 cheque, another person responds by spending exactly $600 on consumption! In the aggregate, Noah tells us, every dollar is spent! It’s actually impossible for the private sector to save their cheques!

Conclusion

This kind of incoherence is where you end up when you read results from pairs of lines that do not represent the thing that you are trying to understand. The conclusion that total consumption expenditure increases by an amount exactly equal to the total value of the cheques arises as the result of a sequence of ill-defined concepts and inappropriate assumptions, all bolted together without much thought.

In reality, what will happen is the following. Some cheques will be saved, some will be spent on consumption. Those that are saved will have no effect on national saving and probably little effect on the rate of interest, although they might nudge asset prices up a bit. Higher consumption will lead to higher national income, employment and imports. National income will probably rise by more than the amount spent on consumption because of the multiplier. “National saving” is a residual — income less consumption — and is a priori indeterminate. None of this requires us to go anywhere near a loanable funds model.

Loose use of terminology and hand-waving at poorly-defined graphical models does not constitute macroeconomic analysis.