The Lending Power of Banks in Monetary Circuit Theory – Adding Treatment of Bank Capital

I was pondering a question Neil Wilson posted on his blog in April – which I have now only gotten around to reading.

The debate over reserves is over and I think its pretty clear now that banks are not constrained by their reserves in any system with a floating exchange rate where the central bank is trying to maintain an interest rate…Up to now the majority of models and writings mention capital in passing. The constraint is acknowledged, but not really described in depth (certainly not to my satisfaction). So now we need to understand what the capital constraint means and whether the current control mechanism – the ratio of loans to capital – is adequate for the task.

In have previously argued on this blog that banks are profit constrained and not equity constrained. The causation is from profitability and anticipated profitability and not vice-versa. One response, from Scott Fullweiller in comments, has been – so what – MMT thinkers in his view have consistently argued this. Yet the distinction is not always made and neither from the MCT perspective has been the puzzle of how banks ability to lend can expand in SFC consistent models when there is no expansion in capital, (examples being Godley and Lavoie in Monetary Economics and Steve Keens latest model). The problem here is the lack of a full elaboration in double entry bookkeeping and mathematical terms of the relationship between the scope for banks to expand lending and the capital stock of the bank.

  1. Adding banking capital to the banking licence model

In January of this year Neil Wilson made a correction to the accounting of Steve Keen’s Circuit model. In retrospect we may see this as a breakthrough as Steve Keen, in fully accepting the correction, became reconciled to the quadruple accounting approach and hence able to avoid the criticism of Scott Fullwiller and others that ‘you must have made a double entry mistake’.

banks have a ‘licence to print money’ that the firms don’t … The value of the licence to create money will vary over time depending upon the terms of the licence, the amount of outstanding loans and various other factors. And, like the intrinsic goodwill of the firm or its ‘human resources’, you don’t usually see the value on a bank balance sheet.

The relationship between the ability of a fiat bank to create money and the accounting concept of goodwill has been noted before. If the price of a bank is in excess of its tangible assets minus liabilities there must be a source of value in their in the form of an intangible asset (whether of course this should be included in regulatory capital requirements is a separate issue). An intangible asset must be a commodity with a price. What is that commodity?

Fiat banking is essentially a depositor saying to a bank – I am letting you hold my money – I have goodwill in your ability to pay me on demand. This deposit, though a liability to the bank, can be rented out at interest.

(Note: see my earlier posts on the ‘four factor’ model where money is a factor of production earning a factor return – the income stream of loan repayment plus principal Part I (corrected), Part II, Part III, Part IV Note there has been some confusion in comments about my treatment of money as a commodity as it is a fundamental postulate of the Credit theory of money that it is not a commodity –see Graziani or Ingham. Money however has non commodity functions, as a means of exchange, and commodity forms, as a store of value and as a means of attracting interest – it is the latter commodity forms – the money commodity form M-M’ that Marx stressed, with which we are concerned here.)

The capitalisation of the returns on this rent of money is the intangible asset adding to the banks valuation. An objection I have seen many times is as deposits are a liability of banks – so this can’t be true. There is no double entry mistake if modelled correctly. You simply have to model a liability from to the deposit account matched by an asset to the ‘banking licence’ account in the Neil/Keen model (part of this rental stream can be shared with the depositor of course if the bank offers interest on deposits). I much prefer the term ‘lending power’ account however as ‘licence’ has regulatory overtones. I also prefer ‘working capital’ to vault – vault sends the wrong message as if money somehow had to be saved in a vault before it could be lent. We shall model this in the next section however first we need to model a bank starting out with no deposits and now future income stream from loans as it has made none. All the bank has is its initial equity.

Seen in terms of the fundamental accounting equation

  1. Assets = Liabilities + Owners Equity

The initial values in the original Wilson/Keen Model with our revised terminology would be as follows:

Fig 1: Wilson/Keen Model – for bank start up

Assets Liabilities Equity
Operation Lending Power Loan Ledger Working Capital Firms Workers Safe
Grant Lending Power +Lending Power Value -Lending Power Value

But note the problem. The bank starts out with assets of zero, it creates an asset with no entry under equity. The accounting equation (1) does not balance. We have to correct the T Account with an initial capital endowment.

Fig 2: Corrected Model with Equity

Assets Liabilities Equity
Operation Lending Power Loan Ledger Working Capital Firms Workers Safe
Grant Equity for Lending +Equity -Equity
Grant Lending Power +Lending Power Value -Lending Power Value

Note this is no loss to the investor in capital terms as when a firm is wound up all assets remaining after liabilities would be distributed to investors in proportion to their equity shares. Note a bank like a firm has two options here to offer dividends or operate solely (as Apple did until recently) on capital gains. Lets include this as well as the full entries for the lending account.

Fig 3: Corrected Model with full lending Accounts and Dividends


Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital Firms Safe
Grant Equity for Lending +Equity -Equity
Grant Lending Power +Lending Power Value -Lending Power Value
Lend Money +Lend Money -Lend Money
Record Loan -Lend Money +Lend Money
Charge Interest +Interest Charge  -Interest Charge
Record Interest -Interest Charge +Interest Charge
Repay Loan and Interest -Loan Repayment -Interest Charge +Loan Repayment +Interest Charge
Record Loan and Interest Repayment +Loan Repayment +Interest Charge -Loan Repayment -Interest Charge
Pay Dividends  -Dividends +Dividends

Now we can see the relationship between undistributed bank profits (where dividends are not paid) and the intangible asset value of bank lending power.

Early 20C banking textbooks (before they forgot about endogenous money), referred to such undistributed dividends as the ‘banking surplus’ and that is the best way of thinking about it. If the outcome of the  initial endowment is distributed 100% as dividends then in those cases banks are not capital constrained at all they are profit constrained (a point I have made on here from different angles). Of course a stockholder will have an opportunity cost of retaining the surplus to ensure future equity or withdrawing it to invest elsewhere so the rate of profit from banking investments is governed by the rate of profit in the rest of the economy.

2. Excess reserves and the expansion of lending power

We began this discussion with the ‘debate is over’ statement over endogenous money and how banks are not reserve constrained. Two key factors in this argument have been that banks can still lend when there is no reserve limit and that empirically the evidence is that banks create loans and then look for deposits later. Of all of the discussions over this issue, especially in the wake of the Keen v Krugman debate I think Scott Fullwiller’s is definitive.

Is this then the end of the reserves issue? No because somewhere along the line we seem to have missed out the fiat model of banking. If a bank has an expected cash flow in of deposits and loan repayments and an expected cash flow out of withdrawls and loans they can put idle balances to profitable use, and even push reserves to zero or even negative on any overnight position if they have recourse to the discount window and interbank loans.

Lets say a bank has hit its own reserve target whether or not there is any regulatory minimum on reserves. Then lets say a firm depositing with it has a windfall profit. The bank would then enjoy what is generally known as ‘excess reserves’. I am using the old fashioned definition from early C20 banking textbooks of excess reserves rather than the highly contextual modern regulatory definition (which does not explain why banks seek to reduce reserves to maximise profits when there are profitable lending opportunities). The banks own set level of reserves would be the banks liquidity preference, its level of working capital, and money in excess of liquidity preference being a ‘hot potatoe’ the bank would immediately seek to put it to productive use. How do we model this in double entry terms?

Fig 4: Corrected Model with lending of excess reserves


Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital Firms Safe
Grant Equity for Lending +Equity -Equity
Grant Lending Power +Lending Power Value -Lending Power Value
Lend Money +Lend Money -Lend Money
Record Loan -Lend Money +Lend Money
Charge Interest +Interest Charge  -Interest Charge
Record Interest -Interest Charge +Interest Charge
Repay Loan and Interest -Loan Repayment -Interest Charge +Loan Repayment +Interest Charge
Record Loan and Interest Repayment +Loan Repayment +Interest Charge -Loan Repayment -Interest Charge
Pay Dividends  -Dividends +Dividends
Increased Firm Deposits -Excess reserves
Excess Reserves increase lending power +Excess Reserves

3. Determinates of the Change in Debt

From the fundamental accounting equation (1) the value of the asset A=L+OE will be the change will be the change in NPVs of profits from loans plus the change in capital endowment from investors plus the change from any excess reserves (which can be negative if a bank is forced to transfer from its lending account to reserves because of for example regulatory requirements, a bank run or any other negative excess reserve shift). Put formally

(2) ΔLending Power=ΔEquity + ΔLoan Repayments + ΔInterest Payments + ΔDividends + ΔExcess Reserves  ΔMoney Leant

You might object that in the lending power column interest charges cancel account, true for that account but not for the bank as a whole, because assuming that the interest charge is risk adjusted and includes an element to cover the overhead costs of making the loan the business model of banking dictates that

(3) Banking Profits = NPV(Loan Cost-Loan Revenues)

Which is simply the mark up price/surplus approach for any commodity only in this case applied to the rent of money at interest. Banks make a profit from risk adjusted full cost interest and this interest goes to the working capital column and is put bank to use in the grant lending power +lending power journal entry. Like any capitalist firm a bank will accumulate capital and invest it compounding returns.

You may also argue that dividends in not in that column, but in reducing working capital it reduces transfers to lending power.

So bank lending then is constrained by profits but can also be expanded by attracting further capital or excess reserves.

One means whereby banks can attract additional excess reserves is by charging a higher deposit interest rate. Its ability to do so however is constrained by its profitability; it attracts additional capital at the cost of future high liabilities which it must cover through profits on loans. There is a risk as in Northern Rock and the Icelandic banks of banks expanding their lending power by this means above and beyond the fundamentals of future profits on loans – effectively a ponzi scheme.

Another aspect of this equation is it enables us to separate out the issues of bank liquidity from bank solvency – bank lending power represents liquidity, and represents future opportunities for extending loans up to that level – which is part and only part determined by undistributed past profits. If those opportunities exist then a bank may lend up to this level, and expand it, if it can attract capital, even if its profitability is falling.

A stockholder in a bank either can vote for a dividend or vote for retaining profits in the bank and this ‘banking surplus’ can add to future lending power. The opportunity cost of doing so is to sell the equity and invest it in equity at the market rate of profit. This of course is stating Modilani-Miller Theorum in another form, though in this form the equity value of banks is set by the rate of profit on their created loans. As the equity value is based on future profits which aren’t yet realised – what the classical economists called ‘fictitious capital’ – a mispricing of financial assets can cause an systemic increase in risk and overextension of loan as opposed to equity finance and the refinancing and rolling over of debts rather than deleveraging.

4. The Limits of the State Control of the Change in Debt

From equation (2) how many are controllable by the State? Only the interest payments (via interest rates – though I would argue there are long run limits on this especially for non reserve currencies) and through its ability to create forced saving or disaving by banks through central bank operations or regulation of banking reserve ratios. By setting capital adequacy ratios it can also indirectly effect dividend payments as banks are forced to compete for the additional capital. If a bank sees a profitable loan opportunity it may compensate for restrictions in expansion of debt from contraction of some terms (of equation 2) by expanding others, that without these restrictions would not be the lowest marginal cost means of expanding lending power.

All attempts to control the ‘monetary base’ through controlling excess reserves have failed, and here we can see why, the endogenous ability of banks to expand the supply of money through profits from loans will remain whatever. If profitable loans are possible then banks will lend up to the limit of their lending power and then either borrow the remainder (if arbitrage opportunities exist between short and long term lending) or seek further equity which can either be funded by loans or Crusoe like savings. The effect of interest rates is entirely indirect in that in reducing the marginal efficiency of investments reduces the total amount of profitable lending opportunities that come before banks.

Further discussion of this issue will require looking at consumer spending and multiple banks, which ill do in a future piece.

Edit:  Ive corrected one aspect of the journal approach thanks to a suggest by Steve Keen that the debit of dividends should come from working capital not lending power – that makes sense – the maths otherwise remains the same.

Ive also corrected the treatment of interest charged on equity, Neil Wilson explained his logic here – see comments below – there was no error on his part.

8 thoughts on “The Lending Power of Banks in Monetary Circuit Theory – Adding Treatment of Bank Capital

  1. There is no error in the charging of interest. You have missed the significance of why I did it that way.

    Charging interest for a bank is the way they gain access to seigniorage. When a bank charges interest the amount of the loan goes up (transfer from lending power to firms/worker loans) and the equity that the bank has goes up (transfer from working capital to profit and loss a/c), which then cycles around and increases the lending power and working capital capacity of the banks instantly at that point due to the ‘capital ratio’ of their banking licence (or the markets perception of the ratio if you’re operating in a fictional unregulated model).

    *There is no requirement for the interest to be paid by anybody before this happens*.

    Whether interest is paid or becomes a bad debt then just rolls into the loan repayment system.

    So you can have a bank that lends entirely roll up loans with no repayment and you’ll still have a bank that can expand its capacity to lend via the interest earning mechanism.

    The size of both sides of the balance sheet changes wrt Interest Earned – Bad Debts written off – Dividends paid

    • Thanks for the clarification. My mistake was treating the left hand equity column as the ‘original’ owners equity – and that all equity owners would have a share of working capital on the profit and loss account if the bank was rolled up.

      If I get your logic if a debt is a bad debt it reduces the equity invested, so you have to have an interest charge on equity. This makes perfect sense so thank you for explaining.

      Im not an accountant so i’ve corrected it.

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  3. A few points.

    1) For the borrower, lending is bringing forward future income. The interest on the loan represents the difference between the present and future value of the income brought forward. Therefore the interest received by the bank is also income brought forward (unless the interest is rolled into bullet repayment at maturity, which would be highly unusual). The same is true for money that the bank borrows (deposits and wholesale borrowing). Banks are only profitable to the extent that borrowers will pay more to banks to bring income forward from the future than lenders demand from banks for deferring income into the future. If that were to change, banks could not make any sort of profit even though they were receiving interest on loans. You are leaving out funding costs at the moment – in effect you assume that loans are self-funding, which is not the case. That means you overstate profits from lending, because you wrongly assume that all interest on lending is profit. It is not.

    2) The money supply is expanded by lending itself, not by interest payments. M4 (broad money) includes all time & sight deposits at UK financial institutions, including those created as a consequence of loan accounting.

    3) I’ve said this elsewhere, but I don’t agree that banks’ lending power is constrained by profits or reserves, and it is only constrained by capital to the extent that regulations make it so. The real constraint is a simple consideration of risk versus return. Banks would make higher profits on higher-risk lending, but they pay a price for that in terms of market perception of their value. You could usefully model the changes in apparent value arising from different risk mixes in bank asset portfolios, though this is of course very affected by externalities.

    • 1) As I stated in the first post I assume throughout a business model of banking and that the interest component includes costs of funding. In this model of course profits =cost of funding minus receipts.

      Though the explicit means of cost of funding is not yet explicitly modelled it can easily be extended to include this. No assumption at this stage is made about the degree of profitability.

      2) No assumption is made that interest expands money supply. Indeed the model shows that only the loan itself expands money supply not interest, which means that growth itself is deflationary unless state money is expanded alongside the growth in bank money – accomodationism.

      3) I think the model demonstrates that profits and reserves matter and the inclusion of risk/collaterol/portfolios in the forthcoming section will demonstrate this more.

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