## Wednesday, 15 October 2014

### What's OK and What's Not on Loanable Funds and the Natural Rate of Interest

I've read various things recently on the theory of loanable funds and the natural rate of interest, so I thought I'd say something on it.

I want to start by looking at how we might illustrate a market of loanable funds in a typical demand and supply graph, with quantity on the horizontal axis and some benchmark rate of interest on the vertical axis.  The supply curve then shows the amount that people wish to save at each interest rate, other things being equal.  The demand curve shows how much people wish to borrow at each interest rate, other things being equal.

I think this graph makes a kind of sense.  However, we have to be careful.  Normally, we might use such a graph to show how a change in either demand or supply would lead to a change in price (the interest rate) so as to restore equilibrium.  Let's suppose that this graph showed demand and supply for apples instead.  Then, if the demand curve shifts to the right say, we might expect a rise in the price of apples, changing quantities supplied and demanded until they were equal again.

Bear in mind here the assumption that all other things are equal.  In fact this is an assumption that is almost certainly incorrect.  An increase in demand for apples requires changes in demand and supply in some other market.  You can't just demand more apples; you have to demand more apples instead of something else - bananas say (or leisure time).  So the demand curve for bananas will also move, with implications for the price of bananas.  That in turn will impact on the demand for apples.  So clearing in the apple market is not brought about exclusively by a change in the price of apples, but by changes in all markets.

This is particularly important when thinking about the loanable funds market.  Critically, one of the things assumed constant is the level of income.  So the supply curve shows the amount people wish to save at any given level of income.  Now we need to consider what happens if people wish to save more.  On the face of it, this would lead to a shift in the supply curve to the right.  However, like with the apples, you can't just save more - there has to be some counterpart, which in this case must mean spending less.  And spending less results in lower incomes.

This means that if we want to consider an increased desire to save, we cannot simply represent this as a rightward shift in the supply curve leading to a fall in the rate of interest.  In fact, the income implications of an increased desire to save may result in both the demand and supply curve shifting leftward.

So we need to be careful about applying the standard story to an interest rate clearing the market for loanable funds.

However, if that were all, there would still be some value in drawing a demand and supply graph for loanable funds.  We might show curves that represented demand and supply on the assumption that all other markets were clearing, including in particular the employment market.  This would then tell us what level of interest would prevail in that situation.  It would not tell us how that level of interest came about (and we know to be suspicious of the idea that it arises from supply and demand pressures in that market), but we would know that if every market was clearing, then that must be the rate that would hold.

This rate would then be the natural rate of interest - the rate of interest at which planned savings equals planned borrowing, under conditions of full employment.  You might want to invoke rates of time preference or marginal efficiency of capital, but this is not really necessary for a natural rate to exist.

Nevertheless, it is not clear that such a rate does exist.  If we make certain assumptions about household preferences or production functions, we can certainly show that there is a rate which meets this condition.  But these assumptions are completely ad hoc, and there is no reason to believe they reflect the real world better than some different assumptions.  It is entirely possible that when we draw out the demand and supply curves for loanable funds, that we find that there is no rate for which demand equals supply under full employment.  For example, the graph may look like this.

If that were the case, then full employment would be impossible.

Much of the current consensus approach in economics relies on the idea that full employment (and price stability) can be achieved by setting the market interest at the natural rate.  It may not matter how such a rate is determined, but is clearly essential for this that such a rate does in fact exist.  It is far from clear to me that it does.

On the whole, I find objections to loanable funds and the natural rate of interest overdone.  As theoretical concepts, I think they have their place, if used correctly.  However, I am very sceptical of the idea that the monetary policy is all about matching the market rate to the natural rate.  This is mainly because I have doubts about the stability of the relationships involved.  But at a more basic level, it's also because I don't think we can take it for granted that there is in fact any interest rate that can achieve clearing in all markets.

1. Nick,

For phrasing, I'd say "loanable funds model" is better than simply "loanable funds" because in some sense all funds are loanable.

1. Yes, or maybe "loanable funds theory". I would normally try and make that distinction, but I didn't bother here because I was hoping it was clear enough from the post what I meant.

2. What are the "funds" that you are referring to . Deposits are liabilities of banks and can not be lent.

1. This would be financial assets, where there is a holder and also someone for whom that asset is a liability. So by saving here, I mean the net acquisition of financial assets (note this is not quite what saving normally means) and by borrowing, I mean that the net accumulation of financial liabilities.

I agree you cannot lend deposits. However, here an increase in the quantity of deposits would constitute saving on the part of deposit holders and borrowing on the part of deposit-takers (i.e. banks).

2. Aside from the bond market the concept of loanable funds is spurious. The creation of Financial assets is endogenous. As you say the quantity of deposits is created by borrowers, and therefore it is not the other way around . There is no "loanable funds" involved in that.

3. I don't think there's anything about loanable funds theory that says that the quantity of loanable funds is not endogenous.

3. Nick, to be sure, I assume that you refer to a case in which people save by lending money to others, not putting money in socks?

In that case, assuming a constant money stock, and assuming that people take loans to spend them, it seems to me that if people start to save more (implying that other people take an equivalent amount of extra loans), that, other things being equal, spending and thus income remain unchanged.

Furthermore, it seems to me that if people decide to save more, they do this because they start to feel less certain about the future. And if so, it seems quite plausible to me that people who consider to take loans also start to feel less certain about the future, and therefore start to take less loans. In other words, the demand curve would shift to the left and the supply curve to the right.

The effect of both shifts, it seems to me, would be that the volume of loans would not change very much, but the interest rate would decrease. In that case there would not be something like a natural level of interest, but something like a natural volume of loans (relative to the money stock).

Anton

1. No, saving money by putting it in socks would count as well. If I spend less dollar notes than I earn and keep the difference, I have increased my holding of dollar notes and this is saving (meaning here a net acquisition of financial assets). This requires that someone else has dissaved a corresponding amount. That might mean someone else has reduced their holding of dollar notes, or it may mean that the supply of dollar notes has increased, which means that the state (including the central bank here) has dissaved.

I do not agree with what you are saying about how the supply and demand curves move. In fact, this is the very thing that I am saying we can't use these graphs to do. I'm saying that if people want to save more, the supply curve does not shift to the right, because the immediate impact of less spending (which is the necessary counterpart to more saving) is to give the supply curve a leftwards impulse.

4. It seems to me that we have TWO savings situations:

1) Savings coupled with borrowing. Here one actor satisfies his desire to save. From his standpoint, the flow of money comes to a stop. A second actor borrows the funds and spends. From the standpoint of the economy-as-a-whole, the money never stops (savings has been coupled with borrowing).

2.) Savings without borrowing. Here one actor saves but there is no corresponding act of borrowing.

Savings without borrowing can occur when money goes under the pillow. It can also happen when money is placed into a warehouse (for safe and convenient keeping) when the warehouse carefully keeps the money safely available for delivery upon demand.

Government can act as a borrower-of-last-resort. When private borrowers vanish (moving the economy into situation 2), government can step up and borrow to keep money moving.

One unanswered question is whether government can CONTINUOUSLY act as a borrower-of-last-resort? The history of about 50 years of near-continuous American borrowing speaks to this question.

Now the unanswered question evolves to whether CONTINUOUS government borrowing does more than simply perpetuate the status quo?

Now we need to weave the two situations in the loanable funds theory. We notice that money continues to move no matter whether government or the private sector is doing the borrowing. The combined total of both government and private borrowing determines whether or not money is coming to a stop.

Finally, we need to ask whether money can increase in total quantity (a bigger measured amount) while at the same time labor is in excess supply? It seems to me that this can occur.

1. See my coment to Anonymous (Anton) above.

If someone saves by putting money under the pillow, there must still be someone else who is dissaving an equivalent amount, either by borrowing or by reducing their saving.

If the amount of dollar bills under my pillow has increased, that means either a) someone else has reduced their holding of dollar bills or b) the total stock of dollar bills has increased. The former is dissaving by that person; the latter means that the government has spend more dollar bills than it has received, which is borrowing by the government (in the sense we mean here).

But I do agree that it can have a very different impact between simply hoarding and offering funds to potential borrowers who are credit constrained.

5. I really wonder whether the loan market works anything like that proposed concept where lenders will be induced to lend only if the prevailing "base" interest rate is high enough but not if it isn't. As far as I can see, if lenders think they will be paid back (ie that the loan won't default) then they will want to lend regardless of the interest rate.
People don't in reality decide between saving and consuming on the basis of whether interest rates are enticing enough to make foregoing current consumption a good deal. Rather those who lend or have savings just put up with whatever the interest rate is. If it is high then they are happy, if it is low then they are unhappy but have to put up with it regardless. I think this reality is revealed by the Gibsons paradox. If interest rates were set by what would satisfy savers, then real interest rates during the gold standard period would have been linked to inflation. That was very much not the case (hence Gibsons paradox).

I wrote an embryonic draft of a blog post about it:
Gibson’s paradox was the name that Keynes gave to a phenomenon that occurred during the gold standard period of 1821 to 1913. During that time, interest rates were not correlated to inflation but were tightly correlated to the price level. Economists have viewed this as paradoxical because they considered that savers would demand an interest rate that made up for the inflation rate. Gibson’s Paradox reveals a crucial reality about interest rates. Savers might be more pleased when interest rates are above inflation and upset when they aren’t (and conversely for borrowers) but they will always get the best interest rate they can -no more and no less. Interest rates are not determined by what will satisfy savers but by what rent savers are able to extract due to the scarcity of bank reserves. If the price level is lower, then a given stock of bank reserves will be sufficient such they have little scarcity value. If however the price level is higher but the stock of bank reserves has not increased, then settlement of payments between banks will become strained. Banks will then offer higher interest rates in a competitive effort to obtain enough reserves to settle payments.

The gold standard period was marked by cycles of credit growth with consequent inflation. As credit was extended, the price of goods, services and wages became higher even though gold of course maintained parity with the currency. However once the price level was high, a “tight money” scenario developed because banks struggled to secure enough reserves and offered higher interest rates in an effort to do so. The constraint of maintaining a fixed rate of exchange to gold precluded the Bank of England from providing more bank reserves except at a high discount rate. Higher interest rates tamped down credit growth and that then tamped down inflation. With high interest rates and no inflation, real interest rates became unbearable for debtors leading to a wave of bankruptcies, foreclosures, fire-sales, unemployment and retrenchment with an exacerbating deflationary spiral. Once the price level had fallen enough, the same stock of bank reserves no longer was insufficient, so banks had no cause to offer savers high interest rates and so the cycle started again.

1. sorry for a typo above. I wrote "real interest rates would have been link to inflation".
I just meant nominal interest rates.

2. I largely agree. In my view, substitution between current and future consumption is fairly inelastic in response to relative price - in other words, people don't change the timing of their consumption much in response to interest rate changes.

When you say lenders, I'm not sure whether you mean actual savers, or intermediaries like banks that lend out of borrowed funds. Certainly, the decision to lend to a particular person is not the same as the decison to save, and this distinction is pretty important.

3. I think by "lender" I was meaning whoever takes the risk of not being paid back. So for bank lending I guess I meant the bank as an intermediary would lend as much as they thought would be paid back irrespective of the interest rate. For bond lending it would be the bond holders. Does that make any sense?

4. Well, in theory a lender will lend when the expected profit (the spread of the loan interest over the funding cost, say) exceeds the expected loss (being the probability weighted possible recovery levels on the loan), with some adjustment for risk aversion. In practice, I think some lenders are more averse to losses because they fear it will be percieved by investors as indicative of poor lending judgement.

6. "So by saving here, I mean the net acquisition of financial assets (note this is not quite what saving normally means) and by borrowing, I mean that the net accumulation of financial liabilities."

"Loanable funds" is an idiosyncratically strange expression.

It could only have come from economics (as opposed to finance).

The core economic concept equates saving and investment, doesn't it?

And in that sense, intended or not, it has nothing directly to do with financial intermediation.

And given that investment creates saving (that includes inventory investment) as a matter of tautology, there's a fundamental problem with the nature of the supply/demand graph - which is that only the intersection (or at best the full "demand" curve) has any real meaning. All other points are nonsense.

The same category of problem pertains to ISLM.

And if the concept is reverse engineered or transformed to pertaining to something other than the equivalence of saving and investment, it seems to me it must descend into analytical chaos.

The idea ripples out into a total conflation of income accounting and flow of funds accounting.

Like I said, very strange.

1. Re the bit you quote, I just wanted to distinguish NAFA (or net lending as it's called in SNA) from saving as income less consumption expenditure. So Robinson Crusoe might save and that will be equal to his investment, but he certainly doesn't save in the sense of acquiring someone else's liability. I think loanable funds can only really mean the latter.

However, whether it's saving and investment, or lending and borrowing, the two must necessarily be equal. But of course the same is true of demand and supply in any good. The actual amount bought must be equal to the actual amount sold. The curves show what people might want to buy and sell, which may be different. I think that concept does carry across to "loanable funds".

The real problem, I think, is going from micro to macro. When we look at demand and supply in a micro concept, there is an implicit assumption that demand and supply are independent. If you are looking at a single good, you can get away with this. But you can't with the loanable funds market.

2. Thanks.

My thinking on all this has never been clear. You may be able to help by indulging a few questions here:

a) Do you think that the investment curve in the IS diagram is the same thing as a saving demand curve?

b) Do you think that the saving curve in the IS diagram is the same thing as an investment supply curve?

c) Do you think that the IS diagram is the same thing as either an investment supply demand diagram or a saving supply demand diagram?

I’m tempted to answer all three of these in the affirmative. Maybe it is trivially so or maybe you disagree – I’m interested.

d) Do you think that the IS curve in IS-LM is the same thing as either an II curve or an SS curve?

Again, same thing, and I’m tempted to answer in the affirmative.

I guess my way of looking at this is that an II supply demand diagram is a way of looking at what must turn out to be not only the actual level of investment but the actual level of saving by accounting tautology. And an SS supply demand diagram is a way of looking of looking at what must turn out to be the actual level of saving – but only as the result of corresponding investment opportunities at different interest rate levels and only as the result of a forced accounting tautology between the two.

In other words, the S in an IS diagram and in IS-LM is redundant in the sense that it is only II and I that matter respectively.

(For some time I have thought that the IS curve in IS-LM should be thought of and labelled as simply the I curve, because the S factor is redundant.)

Finally:

Suppose for argument’s sake that I represent the IS diagram as an SS supply demand diagram and I represent IS-LM as SS-LM. What is it exactly about all of this that is inconsistent or incompatible or wrong when compared to a post-Keynesian view of “funds”? Is this in conflict or is it just perceived to be in conflict?

For example, Krugman characterizes the IS curve in ISLM as representative of “loanable funds”. I don’t see how any of this is in conflict with “loans create deposits”, which seems to be Keen’s big bugaboo about it for example.

What exactly is the problem with “loanable funds”? Is it “wrong”, or is it right but just limited in portraying a more dynamic approach?

My own take is that Krugman is more right and Keen is more wrong. I think the “conflict” is not actual but only perceived as a result of conflating income accounting with flow of funds accounting. That’s what I think Keen has been doing all along with his accounting, among other things.

I think the loanable funds perspective and IS as part of IS-LM is about investment interest rate sensitivity, and not about any sort of equilibrium between saving and investment as any meaningful concept. Saving and investment are really the same thing in this context – along the entire length of both curves at all actual and potential points – but just with distinct real and monetary representations for the same quantities throughout.

My view is that there is a fundamental redundancy in the logical framework when one goes about drawing diagrams with I and S intersections or with IS equilibrium points along a curve in IS-LM.

Hence my hang-up with this stuff.

Would be interested in your thoughts.

3. Well I think you have to be careful about overanalysing IS/LM.

But.....

I see the IS curve as just representing the level of expenditure compatible with income, for any given exchange rate (and taking prices as given). So for each agent, we could assume that their expenditure is a function of their income and the interest rate (and some other things): Xi = f(Yi,r,Z). Then we aggregate and impose the (necessary accounting) condition that sum(Xi) = sum(Yi) =Y. This gives a value of Y for each value of r. It is implied in this, of course, that savings and investment are equal, so you could equivalently draw a supply and demand graph for savings.

I think the point of it being IS, rather than just II, is that people's saving plans do matter even if the actual quantity of savings is determined by investment. If people decide to try and save more, it has an effect, even though they cannot actually save more.

I would also tend to say that Krugman is more right than Keen. If there are issues with loanable funds and the natural rate of interest, it doesn't have anything to do intermediation and endogenous money. It just comes down to the question of whether, at any point in time, there is a rate of interest which can achieve a zero output gap. If you think there is then you are accepting the natural rate of interest.

I don't know what counts as a post-Keynesian view. (Keen doesn't strike me as very post-Keynesian anyway - a comment others have also made). In the G&L models, it is often the case that interest rate manipulation will impact on demand, so I'd be inclined to say that these models do exhibit a natural rate of interest, at least in the short term.

My own view is this. I do not think it is definitely the case that full employment can be achieved by manipulation of the interest rate alone. But I think it probably can be in the short run. Therefore I think there is some kind of short run natural rate of interest. Probably. But interest rate manipulation works through altering the ratio of balances to flows (rising debt, falling savings). It therefore has long run effects as well as short run effects, and these make it harder and harder to use interest rates as a tool. I think it extremely unlikely that full employment and stable prices can be achieved through interest rate management alone.

This is the topic of my most recent post (on the problem with monetary policy), but see also section 5.7 of G&L.

4. I think I agree with most of what you’re saying.

I realize I’m at risk of overanalyzing this area (although deliberately so) and that it’s not the main subject of your post. But let me just push this IS-LM aspect one notch further, one last time.

“I think the point of it being IS, rather than just II, is that people's saving plans do matter even if the actual quantity of savings is determined by investment. If people decide to try and save more, it has an effect, even though they cannot actually save more.”

I understand the idea, but I don’t think that’s what is incorporated in either IS-LM or a simple I-S graph.

A desire to save may cause aggregate saving to decline due to the paradox of thrift. The desired saving behavior shifts the investment schedule, since excess desired saving slows down aggregate demand. It is the investment change that then causes the actual saving change. But that is a dynamic process over time that is not reflected in an I-S graph or in the IS curve. It happens over a period of time. IS-LM is a static snapshot in time. There is nothing in the IS curve or the underlying I-S graph that suggests that the paradox of thrift is a necessary assumption in order for investment to be interest sensitive. I think this happens outside of the static IS-LM snapshot view.

One of the general criticisms of IS-LM is that it is a static view. But criticizing it for being a static view is analogous to criticizing a balance sheet for not being an income statement. IS-LM attempts to balance a rate of investment/saving flow with a monetary stock (or in an updated version an interest rate set by the central bank) – both of those things captured at a point in time. It is a snapshot of a (“instantaneous”) flow condition and a stock condition at a point in time. You could conceive of a point in time and a balance sheet for the economy and say – there is the ISLM “equilibrium” at the point that balance sheet was constructed.

I think this is the sort of point Krugman makes from time to time about IS-LM. He knows it’s static and he thinks that the criticism that it is static is a straw man, or at least that’s my interpretation of what he is saying.

All that said, I think what IS-LM says is quite trivial at the end of the day and could be said differently in a better way without the graph. In my view, all IS-LM really says is that investment is interest-sensitive, and that monetary policy (whether expressed as an interest rate or as some configuration of “money supply” that magically corresponds to that interest rate) plays the dominant role in setting the actual interest rate to which investment responds. Anything about saving is redundant – at least as it appears in this simple framework.

Anyway, I’ll leave it there for now, given that its off-topic to the main point of your post.

Thanks.

5. I think IS/LM is OK as far as it goes. There is an important idea in a lot of macro to do with the interaction of the financial side (portfolio balancing) and the real side (spending) of the economy. IS/LM captures that quite neatly.

However, it only does so in a very general way. It's difficult to go from that to a more realistic model, even though those realistic models may also exhibit this financial-real interaction. This is partly the static / dynamic question.

I think you're right - what IS/LM says is quite trivial. But as long as we accept that, I think it's OK.