loanable funds

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.

What is the Loanable Funds theory?

I had another stimulating discussion with Noah Smith last week. This time the topic was the ‘loanable funds’ theory of the rate of interest. The discussion was triggered by my suggestion that the ‘safe asset shortage’ and associated ‘reach for yield’ are in part caused by rising wealth concentration. The logic is straightforward: since the rich spend less of their income than the poor, wealth concentration tends to increase the rate of saving out of income. This means an increase in desired savings chasing the available stock of financial assets, pushing up the price and lowering the yield.

Noah viewed this as a plausible hypothesis but suggested it relies on the loanable funds model. My view was the opposite – I think this mechanism is incompatible with the loanable funds theory. Such disagreements are often enlightening – either one of us misunderstood the mechanisms under discussion, or we were using different definitions. My instinct was that it was the latter: we meant something different by ‘loanable funds theory’ (LFT hereafter).

To try and clear this up, Noah suggested Mankiw’s textbook as a starting point – and found a set of slides which set out the LFT clearly. The model described was exactly the one I had in mind – but despite agreeing that Mankiw’s exposition of the LFT was accurate it was clear we still didn’t agree about the original point of discussion.

The reason seems to be that Noah understands the LFT to describe any market for loans: there are some people willing to lend and some who wish to borrow. As the rate of interest rises, the volume of available lending increases but the volume of desired borrowing falls. In equilibrium, the rate of interest will settle at r* – the market-clearing  rate.

What’s wrong with this? – It certainly sounds like a market for ‘loanable funds’. The problem is that LFT is not a theory of loan market clearing per se. It’s a theory of macroeconomic equilibrium. It’s not a model of any old loan market: it’s a model of a one very specific market – the market which intermediates total (net) saving with total capital investment in a closed economic system.

OK, but saving equals investment by definition in macroeconomic terms: the famous S = I identity. How can there be a market which operates to ensure equality between two identically equal magnitudes?

The issue – as Keynes explained in the General Theory– is that in a modern capitalist economy, the person who saves and the person who undertakes fixed capital investment are not usually the same. Some mechanism needs to be in place to ensure that a decision to ‘not consume’ somewhere in the system – to save – is always matched by a decision to invest – to build a new machine, road or building – somewhere else in the economy.

To see the issue more clearly consider the ‘corn economy’ used in many standard macro models: one good – corn – is produced. This good can either be consumed or invested (by planting in the ground or storing corn for later consumption). The decision to plant or store corn is simultaneously both a decision to ‘not consume’ and to ‘invest’ (the rate of return on investment will depend on the mix of stored to planted corn). In this simple economy S = I because it can’t be any other way. A market for loanable funds is not required.

But this isn’t how modern capitalism works. Decisions to ‘not consume’ and decisions to invest are distributed throughout the economic system. How can we be sure that these decisions will lead to identical intended saving and investment – what ensures that S and I are equal? The loanable funds theory provides one possible answer to this question.

The theory states that decisions to save (i.e. to not consume) are decisive – investment adjusts automatically to accommodate any change in consumption behaviour. To see how this works, we need to recall how the model is derived. The diagram below shows the basic system (I’ve borrowed the figure from Nick Rowe).

lf

The upward sloping ‘desired saving’ curve is derived on the assumption that people are ‘impatient’ – they prefer current consumption to future consumption. In order to induce people to save,  a return needs to be paid on their savings. As the return paid on savings increases, consumers are collectively willing to forgo a greater volume of current consumption in return for a future payoff.

The downward sloping investment curve is derived on standard neoclassical marginalist principles. ‘Factors of production’ (i.e. labour and capital) receive ‘what they are worth’ in competitive markets. The real wage is equal to the marginal productivity of labour and the return on ‘capital’ is likewise equal to the marginal productivity of capital. As the ‘quantity’ of capital increases, the marginal product – and thus the rate of return – falls.

So the S and I curves depict how much saving and investment would take place at each possible rate of interest. As long as the S and I curves are well-defined and ‘monotonic’ (a strong assumption), there is only one rate of interest at which the amount people wish to lend is equal to the amount (other) people would like to borrow. This is r*, the point of intersection between the curves. This rate of interest is often referred to as the Wicksellian ‘natural rate’.

Now, consider what happens if the collective impatience of society decreases. At any rate of interest, consumption as a share of income will be lower and desired saving correspondingly higher – the S curve moves to the right. As the S curve shifts to the right – assuming no change in the technology determining the slope and position of the I curve – a greater share of national income is ‘not consumed’. But by pushing down the rate of interest in the loanable funds market, reduced consumption – somewhat miraculously – leads to an automatic increase in investment. An outward shift in the S curve is accompanied by a shift along the I curve.

Consider what this means for macroeconomic aggregates. Assuming a closed system, income is, by definition, equal to consumption plus investment: Y = C + I. The LFT says is that in freely adjusting markets, reductions in C due to shifts in preferences are automatically offset by increases in I. Y will remain at the ‘full employment’ rate of output at all times.

The LFT therefore underpins ‘Say’s Law’ – summarised by Keynes as ‘supply creates its own demand’. It was thus a key target for Keynes’ attack on the ‘Law’ in his General Theory. Keynes argued against the notion that saving decisions are strongly influenced by the rate of interest. Instead, he argued consumption is mostly determined by income. If individuals consume a fixed proportion of their income, the S curve in the diagram is no longer well defined – at any given level of output, S is vertical, but the position of the curve shifts with output. This is quite different to the LFT which regards the position of the two curves as determined by the ‘deep’ structural parameters of the system – technology and preferences.

How then is the rate of interest determined in Keynes’ theory? – the answer is ‘liquidity preference’. Rather than desired saving determining the rate of interest, what matters is the composition of financial assets people use to hold their savings. Keynes simplifies the story by assuming only two assets: ‘money’ which pays no interest and ‘bonds’ which do pay interest. It is the interaction of supply and demand in the bond market – not the ‘loanable funds’ market – which determines the rate of interest.

There are two key points here: the first is that saving is a residual – it is determined by output and investment. As such, there is no mechanism to ensure that desired saving and desired investment will be equalised. This means that output, not the rate of interest, will adjust to ensure that saving is equal to investment. There is no mechanism which ensures that output is maintained at full employment levels. The second is that interest rates can move without any change in either desired saving or desired investment. If there is an increase in ‘liquidity preference’ – a desire to hold lower yielding but safer assets, this will cause an increase in the rate of interest on riskier assets.

How can the original question be framed using these two models? – What is the implication of increasing wealth concentration on yields and macro variables?

I think Noah is right that one can think of the mechanism in a loanable funds world. If redistribution towards the rich increases the average propensity to save, this will shift the S curve to the right – as in the example above – reducing the ‘natural’ rate of interest. This is the standard ‘secular stagnation’ story – a ‘global savings glut’ has pushed the natural rate below zero. However, in a loanable funds world this should – all else being equal – lead to an increase in investment. This doesn’t seem to fit the stylised facts: capital investment has been falling as a share of GDP in most advanced nations. (Critics will point out that I’m skirting the issue of the zero lower bound – I’ll have to save that for another time).

My non-LFT interpretation is the following. Firstly, I’d go further than Keynes and argue that the rate of interest is not only relatively unimportant for determining S – it also has little effect on I. There is evidence to suggest that firms’ investment decisions are fairly interest-inelastic. This means that both curves in the diagram above have a steep slope – and they shift as output changes. There is no ‘natural rate’ of interest which brings the macroeconomic system into equilibrium.

In terms of the S = I identity, this means that investment decisions are more important for the determination of macro variables than saving decisions. If total desired saving as a share of income increases – due to wealth concentration, for example – this will have little effect on investment. The volume of realised saving, however, is determined by (and identically equal to) the volume of capital investment. An increase in desired saving manifests itself not as a rise in investment – but as a fall in consumption and output.

In such a scenario – in which a higher share of nominal income is saved – the result will be weak demand for goods but strong demand for financial assets – leading to deflation in the goods market and inflation in the market for financial assets. Strong demand for financial assets will reduce rates of return – but only on financial assets: if investment is inelastic to interest rate there is no reason to believe there will be any shift in investment or in the return on fixed capital investment.

In order explain the relative rates of return on equity and bonds, a re-working of Keynes’ liquidity preference theory is required. Instead of a choice between ‘money’ and ‘bonds’, the choice faced by investors can be characterised as a choice between risky equity and less-risky bonds. Liquidity preference will then make itself felt as an increase in the price of bonds relative to equity – and a corresponding movement in the yields on each asset. On the other hand, an increase in total nominal saving will increase the price of all financial assets and thus reduce yields across the board. Given that it is likely that portfolio managers will have minimum target rates of return, this is will induce a shift into higher-risk assets.