Diamond-Dybvig and the Monetary Circuit

One of the main models of the role of banks is Diamond-Dybvig (DD).  This seeks to explain how banks might be able to provide valuable intermediation between:

a) savers who are uncertain when they might want their money back, and

b) entrepreneurs who need funds for a minimum period of time in order to generate returns.

In this model, entrepreneurs can only pay an interest return if they can borrow for the time required.  If required, they can repay early, but with zero interest.  Savers can lend to entrepreneurs directly, but they face an uncertain return, because they don't know when they might want to realise their investment.

Instead, savers deposit with the bank, which lends to entrepreneurs.  The bank deposit contract pays interest, even on an early withdrawal.  The bank can do this because the deposit contract also provides that, in the event the deposit is held for the full term, it pays less than the saver would get from lending directly.  The bank subsidises early withdrawers at the expense of late withdrawers, and can do this because it knows that not everyone will be an early withdrawer.  In the model, savers prefer the deposit contract to direct lending, because they are risk averse and it offers less uncertainty in returns.

This is a model of banking where deposits seem to precede loans.  Savers place deposits with the bank, which lends them out.  In fact, there isn't even any money in the model, just goods.  Loans and deposits are loans of goods and deposits of goods.  So it is physically impossible for the bank to make a loan, before it has taken a deposit.

This is not necessarily a problem for the model, but it seems at odds with the story where "loans create deposits".  So I thought it would be interesting to construct a version of DD that looked a little like something a circuit theorist might identify with.  There's no great message here - I just like thinking about the connection between different ideas.

So, as with DD we imagine there is a single good that can be consumed or used in production.  Entrepreneurs have productive projects that take two periods to generate a non-zero return.

Both savers and entrepreneurs open accounts with the bank.  The account balances all start at zero.  The bank agrees to provide the entrepreneurs with overdraft credit.  Overdrafts must be repaid after two periods with interest at 6.25% per period (simple interest, so 12.5% in total).  The bank may require early repayment, but no interest is then payable.

The bank pays interest on positive balances at 4% per period (again simple interest, with no compounding).  All interest is paid simply by debiting and crediting the appropriate accounts.

There is no provision for positive balances to be "withdrawn".  They can only be used for payments.  However, the bank undertakes to try and maintain the real value of such deposit balances, by targeting the dollar price of goods.  (We might then think of this bank as a whole banking system, with the central bank trying to maintain price stability by influencing the volume of lending).

Having got their credit agreed, the entrepreneurs then buy goods from the savers for $100.  This involves the entrepreneurs instructing the bank to debit $100 from their accounts and credit it to the accounts of the savers.  The entrepreneurs, as a group, then has a negative balance of $100 on their accounts (they are in overdraft) and the savers, as a group, have positive balances of $100.

In period 1, the bank credits the accounts of all savers at 4%, so total deposit balances are $104.   

Now, savers want to realise half their savings ($52 in total).  They can only do this through buying goods from entrepreneurs.  To maintain the value of the dollar, the bank must create demand for dollars (and prompt supply of goods).  It does this by calling in $52 of the entrepreneurs' overdraft.  Entrepreneurs terminate 52% of their projects and sell the goods they were using to savers.  Appropriate debits and credits reduce both savers' and entrepreneurs' balances by $52.  Deposits are now $52 and loans (overdrafts) are $48.

In period 2, entrepreneurs' investments are realised.  The bank credits a further 4% interest to the remaining balance of savers accounts taking them to $54.  It debits 12.5% interest from the remaining overdraft balances of $48, taking these also to $54.

Entrepreneurs sell goods to savers for $54.  The bank makes the appropriate debits and credits, leaving all balances at zero.

By arranging things this way, the bank has provided savers with a certain return of 4%, regardless of when they want their money, rather than an uncertain return of either 0% or 6.25%.

DD use their model to consider bank runs.  We can do the same here.  The more savers try to realise their savings early, the more the bank has to call loans to maintain the value of the deposits.  This reduces returns to those who are saving for the full term, eventually to the point that they lose their entire investment.  There is therefore an incentive not to be the last one holding deposits.

However, in this model this run is more in the nature of a run on the currency, not quite what DD is concerned with.  To look at a run on an individual bank here, we would need to consider a model with more than one discrete banking entity.

Can Outside Wealth be a Burden on Future Generations?

Simon Wren-Lewis has another post on the relevance of government debt for future generations, explaining a point that Nick Rowe has also made in the past.  They both set out clear explanations, but the issue continues to cause much confusion.  It's not hard to see why.  The suggestion that public debt can be a burden on the unborn seems to imply that the future can somehow be drained of resources for the benefit of the present.  Clearly, this is not what it means and Wren-Lewis is in fact careful to avoid using the term "burden" in his post.

Actually, I think the debt aspect can be a little misleading here, as it draws people into thinking that this is all about a requirement for future generations to cover a repayment obligation.  So I thought it would be interesting to look at this issue by focussing purely on the asset side.

Imagine there are two groups of people, wealthy and poor.  The wealthy own $100 of government issued bonds and money.  The poor own nothing.  (These discussions are usually cast in terms of two period overlapping generation models.  The wealthy would then be the old generation and the poor would be the young.  I don't need to be so specific here.)

Each year the economy produces 100 real goods.  Normally these sell for $1 each, so income and expenditure are both $100.  However, there is more potential purchasing power here than there are goods.  In addition to the $100 of income, there is $100 of wealth.  But there are only 100 real goods.

If the wealthy decide not to spend any of their wealth, then there's no problem.  Alternatively, if they do decide to spend some of their wealth, but others decide to save some of their income, that may be OK as well.  So, if the wealthy decide to spend $30 of their wealth and those earning income decide to save $30, that's still only $100 being spend on 100 of goods.  So providing $100 of wealth gets carried into the next year (whether that's with the original holders or new ones), it's fine. 

However, the problem does not go away; it simple gets passed on.  That wealth will always represent purchasing power for which there are no goods.  For there to be surplus goods on which that wealth could be spent would require the economy to produce more goods than it does income.  This is clearly impossible.

But if there aren't enough goods to go around, who loses out?  What would happen in the current year, if the wealthy tried to spend all their wealth and the earners tried to spend all their income? 

As there aren't then enough goods to go around, this would push prices up.  This has different effects on income earners and the wealthy.  If prices go up, income earners (in aggregate) are unaffected, since their earnings go up at the same rate.  If the 100 goods now sell for $2 each, their income is now $200.  But the wealthy have no such protection.  They still only have $100 of wealth which will now only buy 50 of goods.

Ultimately, if income earners want to spend all their income, prices will rise indefinitely and the wealthy will be completely squeezed out.  So if the wealthy want to be able to cash-in their wealth, they rely on income earners wanting to save some part of their income (or have the government save for them by running a surplus).  As long as there are savers, anyone with wealth can use it to claim a share of produced goods, passing the wealth overhang onto someone else.

How does the generation question fit into this? 

People are born with no wealth.  If they're lucky they may get bequests from their ancestors, but otherwise if they want wealth, they have to save.  Which means they have to consume less than they earn today.  This gives the opportunity for the wealthy to spend all their wealth before they die, acquiring and consuming goods.  They will have managed to swap purchasing power for which there is no corresponding production into real consumption.  And they will have done so by passing the wealth onto the young savers.

As long as this continues from generation to generation forever, then this may never matter.  But there will always be more purchasing power than there are goods.  And if, for whatever reason, all that purchasing power goes after the same goods at the same time, someone will lose out.  And it won't be those people that are already dead.  

I find it quite useful to recast the issue this way.  But it is not intended to be an argument that public debt should be reduced because it is a burden on the unborn.  Public debt is not only a liability but also someone's asset.  You can only get rid of the liability, when people are prepared to do without the asset.

A Comparison Between Traditional Banking and Market Based Finance

I've been working on a paper using stylised balance sheets to look at the interaction between traditional banking and market-based finance.  The aim is to examine the reasons for shifts between these two intermediation models before and during the crisis and the implications for liquidity and solvency across the sector.  In this post, I just want to give a brief overview of the differences between the two techniques.

The diagram shows some simplified balance sheets.  These are not necessarily supposed to represent distinct entities, so much as different business models.

The assets of traditional banking consist of a loan portfolio and a holding of high quality liquid assets (HQLA).  The liabilities will be short term unsecured deposits with the balance forming capital (there will be other borrowings of a longer term nature, but we can ignore those here).

 The loan portfolio will be long dated assets which will generally be fairly illiquid, in that it is difficult to sell them at short notice for a price close to balance sheet valuation.  Given the short term nature of its deposit liabilities, the traditional bank is therefore running a maturity mismatch risk.

To deal with this mismatch, the bank maintains a holding of HQLA.  This might consist primarily of government securities, but central bank reserves would also be included in this.  In the event that it faced deposit withdrawals in excess of the rate of run-off on its loans, the bank would hope to cover this out of its HQLA holding.

The traditional bank is therefore running a kind of liquidity insurance.  It is offering liquidity to all of its depositors but covering this with a much smaller quantity of liquid assets.  Its risk is that more depositors wish to withdraw their deposits at once than it can cover out of liquid assets.

With market based finance the assets are all marketable instruments.  I have illustrated this here as securitised loans.  The underlying loans may be similar to those held as illiquid assets on the traditional bank's balance sheet.  The process of securitisation transforms these into a standardised tradeable instrument.  This means they can be bought and sold much more easily.  With sufficient market depth, there will be a continual market price for these securities and a holder will expect to be able to sell at close to that price.

Having liquid securities as its assets allows an entity using market-based finance to fund itself using secured financing, for example repo.  The repo funding provided by investors is effectively secured by underlying assets (the securitised loans).  The value of the security provided is slightly higher than the amount of funding and, critically, is adjusted every day for market movement.  This is only possible because the collateral is in the form of marketable securities with a transparent market price.  The level of additional security provided therefore only needs to cover possible day-to-day price movement.

In the market based finance model, all of the assets are used as collateral[1].  There is no pool of unencumbered liquid assets like the HQLA held by the traditional bank.  However, no such pool is needed, because the market based finance model is providing liquidity in a different way.  Rather than rely on a type of insurance as in traditional banking, the liquidity transformation relies on the marketability of the underlying assets.  Whereas a traditional bank would dip into its pool of unencumbered liquid assets to deal with a high level of withdrawals of its funding, an entity using market based finance would simply look to sell down its regular asset base.

Both business models face liquidity risks, but they manifest themselves differently.  The liquidity risk in traditional banking is that the HQLA holding is insufficient to cover withdrawals.  The liquidity risk in market based finance is that the liquidity of the assets fails.  For both models, the robustness of their liquidity strategies may change.

A depositor with a traditional bank is taking credit risk on the bank.  They do not know the intricate details of bank's balance sheet, so they are relying on the skills of the bank's management in making good business decisions.  They will however draw comfort from the level of capital which provides a cushion against loan losses.

A provider of finance in the form of secured funding takes much less risk on the borrower itself, relying instead on the collateral provided.  Some degree of over-collateralisation is needed to meet rating requirements or to cover haircuts, but generally the market based finance model requires lower levels of capital.

A number of developments within the financial intermediation sector in the run-up to the crisis and during it can be traced to the differences between these two business models.   These include changes in liquidity and solvency levels, changes in lending appetite including credit criteria, and changes in credit spreads.

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[1] There will repos with a variety of different counterparties.  Distinct collateral is used for each counterparty; they do not share in the same collateral pool.

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.