Tuesday, 4 November 2014

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.


  1. as the entrepreneurs were able to sell goods and settle half the debt on demand as prompted by the depositors the debt wasn't really a long maturity asset in its actual execution, I think that how the account and the exchanges were able to add up in balance there.

    1. That is a fair point, but it is how DD do it in their model. They look at liquidity by reference to the ratio between an asset's pay-off on an early termination and that at its full term. The lower that ratio, the more illiquid the asset.

      I'm not trying to say anything here about whether I think that's a good way of looking at liquidity or not - I'm just going with the way they look at it.

  2. However, the bank undertakes to try and maintain the real value of such deposit balances, by targeting the dollar price of goods.

    Can you elaborate on this and explain how it relates to this:

    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.

    1. I am assuming here that deposits are not convertible into anything else. A bit like central bank money, or like money issued by the banking sector as a whole. You can convert money issued by one bank into money issued by another bank, but that's all (we have to include central bank money in this).

      So the bank has to have another way to get people to accept its money and to do this it makes clear that it will try to maintain the value of its money, i.e. it will try to ensure a stable rate of exchange between its money and goods. This is what central banks do when they follow an inflation target or something similar. They are trying to maintain the value of the currency.

      So, after period 1, savers want to spend $52 on goods. However, if nothing else happens, there is no reason for anyone to sell them goods. There is therefore excess demand for goods and the price gets bid up, which means the value of dollars falls.

      The only action the bank can take to prevent this is to call in some loans. This means entrepreneurs are now forced to sell goods to obtain dollars to repay their loans. There is now a supply of goods to match demand, which prevents the price rising and maintains the value of the dollar.

    2. If the bank is contractually unable to call in loans early then it seems you are stuck with demand pull price inflation, unless you can offer the savers a further savings period with enhanced terms to encourage them to defer spending for a further time period.

    3. Yes, although this is a very limited model. In reality, there are continually loans falling due and new loans being made, so the rate of change of loans outstanding is not at all set in stone.

  3. Thanks, that makes sense - I think. The value of the dollar is maintained by banks calling in loans so that there are not too many outstanding loans vs. goods on sale. Entrepreneurs are incentivised to sell their goods for new money. The monetary circuits are 'closed'.

    Continuing off topic (sorry): what are the central bank's tools in this? Does it influence the maturity of loans? How exactly? Seems interest rates work mainly to curb demand for new loans, I don't see how they influence the maturity of outstanding loans. Is there even an opposing effect in that higher interest rates make new loans more attractive for banks?

    Personally, I've always found circuit theory interesting but also somewhat outdated in that its base model is no longer representative of modern finance. Most new bank money enters the economy through mortgages nowadays, not through corporate loans. So I've been trying to figure out for myself (not very successfully) how or indeed whether the base model would have to be adjusted to reflect this shift. That requires understanding the base model first....

    Wrt to my questions above I wonder: considering mortages are mostly fixed in maturity, i.e. cannot be called in at will, by which means do / should banks and central banks influence the value of their respective liabilities?

    1. This goes a bit beyond what I'm looking at here, but it wouldn't matter if the central bank was acting through influencing borrowers decisions as opposed to lenders. So, if it raised interest rates, so that borrowers decided to terminate projects and repay loans early, that would have the same effect. And, as I commented to Dinero above, there is a continual process of new loans being made and old ones being repaid and its the net flow that matters. Influencing the rate at which new loans are made is probably more important than influencing the rate at which old ones are repaid.

    2. Yes, thanks. That sounds right.

  4. There is an unstated moral apect to this process. It is unstated, but present all the same. In a period of price infaltion, people who don't allready have money are denied access to credit and the spending power there of, by high interest rates, and simultaneously people , that allready have money , contnue with there spending power unfettered by the policy. I'm not stating that is wrong or right, simply that it is interesting that it is present.

  5. If the economy had a lot more equity financing, and a lot less debt, would inflation be more likely? Do fixed interest and schedule debt repayments drive a lot of what ensures the value of money (rather than there just being the tax driver of money value that MMT people emphasize)?

    Hypothetically it would be possible to avoid a lot of debt wouldn't it? I think I heard somewhere that HSBC even looked into the idea of fully islamic mortgages where the householder payed rent on the portion of the house not yet bought and simply had the option to buy more of the house at a regularly revalued current market rate.

    I guess in the post WWII period, households were less indebted and inflation was more of an issue. The period from 1980 until now saw a massive increase in debt and a drop in inflation.

    QE seems to have caused a further step up in debt issuance. Companies have issued bonds to fund stock buybacks, shifting over from equity financing to more debt financing. Perhaps looking forward, that change to greater indebtedness will actually be deflationary?

    1. "If the economy had a lot more equity financing, and a lot less debt, would inflation be more likely?"

      I'm not sure you could necessarily conclude that. But I do think that an economy with high levels of debt may be more prone to fluctuations in demand. Amongst other things, that may make it harder to target inflation purely with an interest rate lever.

    2. I thought that Bernanke made a case that indebtedness actually made an economy more accessible to control with monetary policy. Indebtedness allows consumer spending to be turned on when interest rates fall such that more debt gets taken on and then choked off when interest rates rise (because when interest rates are high, debt expansion can not be afforded and a lot of wages goes to debt servicing). The hope is that it allows monetary policy to control the spending capacity of consumers without having too much unemployment and still having very sticky wage levels.
      I hope this is the correct link, I haven't checked though -sorry.

    3. I just checked over that link
      "Inside the Black Box: The Credit Channel of Monetary Policy Transmission"
      I guess I was just extrapolating when I thought that Bernanke was directly making the point that greater indebtedness led to monetary policy having greater effectiveness (rate rises being able to curb inflation). But I still think that extrapolation is consistent with the point that Bernanke was making which was that much of the way that monetary policy causes its effects by higher interest rates causing the indebted to suddenly spend less and suddenly become worse prospects for further lending.

    4. I would tend to agree that one of the main way interest rates operate is on the level of borrowing and therefore some degree of indebtedness is needed for this to work. It may also be the case, over some range, that more debt makes interest rate policy more effective. However, I still think that the instability introduced by high level of indebtedness means that manipulating interest rates may not be enough.