The Transmission of Lending Power between Banks in Endogenous Monetary Theory

This post sets out an extension of the ‘lending power’ approach to endogenous money I out forward in a previous post which involves equity creating that lending power and subsequent bank profits and excess reserves extending (or contracting) that lending power. The extension is to consider multiple banks.

Stock flow consistent modelling of banks has so far adopted a single bank model for simplicity. However in looking into the historical reasons why economics (or at least the economics of banking) seemed to drop an endogenous model of money – the decisive shift occurring with the rise of monetarism in the 1960s – seemed to be because of an error in the endogenous model – i.e. treating the banking sector as a single bank, and the misinterpretation of the meaning of the mathematical resolution of this error. Has Monetary Circuit Theory fallen into a similar trap and how might it be fixed?

  1. The Multiple Banks Problem

The treatment of multiple banks has been a problem of banking theory for over 200 years. The definitive history of the problem is set out in Thomas M. Humprey’s article ‘The Theory of Multiple Expansion of Deposits: What it is and Whence it Came’. The nature of the problem is set out by Llyod Mints in A History of Banking Theory (1945)


“The problem of the manner in which the banking system increases the total volume of the circulating medium, while at the same time the lending power of the individual banks is severely limited, has proved to be one of the most baffling for writers on banking theory”

I had not read Mints when conceiving of the term ‘Lending Power’ used in the previous article. However I am very reassured that it was used before in the now almost forgotten high period of endogenous money banking theory.

Humphrey sets out the issue in simple terms as follows:

Let the reserve-to-deposit ratio be, say, 20 percent and the system can, by making loans, create $5 of deposit money per dollar of reserves received. By contrast, the individual bank receiving that same dollar on deposit can lend out no more than 80 cents of it. How does one reconcile the banking system’s ability to multiply loans and deposits with the individual bank’s [relative] inability to do so?

This issue is today treated in exogenous money terms. The solution is seen as being through use of a ‘money multiplier’ which through geometrical expansion leads to expansion of an original addition to reserves through a state created monetary base – high powered money – named because of its presumed ability to power the expansion of bank money. This approach seems to have become embedded from Samuelsson’s textbooks and his interpretation of a key concept of endogenous money banking theory set out by Davenport (see next section). Most Post-Keynesians however reject the concept of a money multiplier, or argue its derivation is not as set out in the exogenous theory. The key argument being that banks can endogenously lend without prior access to state money created reserves. However just because Samuelson misappropriated Keynesianism doesn’t not mean we should allow him to misappropriate banking theory. The concept of the geometric expansion of money through reserve relationships between banks originally arose as a solution to a problem posed wholly within the terms of endogenous money theory.

We saw in the previous post’s model that lending power relies on more than state money created reserves. This liberates us to look again at this problem without an a-priori rejection of the concept of geometric expansion of money.

Humprey

Far from understanding how loans generate deposits, bankers throughout the nineteenth and early twentieth centuries insisted that banks lend only the funds entrusted to their care and therefore could not possibly multiply deposits. Economists, on the other hand, often went to the opposite extreme, arguing that individual banks were simply small-scale versions of the banking system at large and thus could multiply deposits per dollar of reserves just as the system does. Both views were wrong. Not until the 1820s did a more plausible view start to emerge. And not until the 1920s was it finally stated in a way that fully convinced the economics profession and thus enabled the theory to gain widespread acceptance.

The originators of the classical endogenous approach such as Law, Berkeley and Hamilton all observed that bank deposits were several times larger than the amount of specie in circulation and therefore inferred that banks must be creating deposits. (O’Brien 11, P15).

The key insight was made by James Pennington in 1826 who first conceived of the concept that the process of deposit multiplication occurs through the successive lending and redeposit of excess reserves. We are using excess reserves in the sense used in the previous post, as reserves in excess of the banks own set minimum reserve ration notwithstanding any regulatory requirements. (So if a bank has a reserve requirement of zero any new deposit is an increase in excess reserves and vice versa).

he argued that if banks receive a cash deposit of which half must be held in reserve the rest will go to purchase earning assets (loans and investments). The sellers of these assets will, upon receiving the cash, redeposit it in their banks thus increasing the volume of deposits. At the end of this first round of the expansion process, the cash reserves of the banks will be the same as before, but the sum total of deposits-including the initial cash deposit plus the additional deposits created by loan-will already be increased by fifty percent… as one bank expands its loans it either recovers the proceeds in the form of redeposits or else it loses reserves to other banks so that they too can expand. Either way, deposits increase.

Lets model this in double entry terms (with a more realistic reserve ratio expanding the model we had before. For simplicity we shall initially only consider intra-firm spending. For simplicity again we shall only consider a loan not investment banking. Consumer spending and wages we shall consider in a future post.

Rather than the C19 process of discounting bills of exchange we will have a firm banking with bank A receiving a loan and purchasing an asset from a firm banking with Bank B. Again for simplicity we shall model the assets and liabilities of the banks and not of the firms. Additional journal entries are highlighted.

Fig1. Effect of a Excess Reserve from Bank A on Deposits from Sellers of Financial Assets Depositing in Bank B


Bank A
Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital FirmsA Safe
Grant Equity for Lending +EquityA -EquityA
Grant Lending Power +Lending Power ValueA -Lending Power ValueA
Lend Money +Lend MoneyA -Lend MoneyA
Record Loan -Lend MoneyA +Lend MoneyA
Charge Interest +Interest ChargeA  -Interest ChargeA
Record Interest -Interest ChargeA +Interest ChargeA
Repay Loan and Interest -Loan RepaymentA -Interest ChargeA +Loan RepaymentA +Interest ChargeA
Record Loan and Interest Repayment +Loan RepaymentA +Interest ChargeA -Loan RepaymentA Interest ChargeA
Pay Dividends  -DividendsA +DividendsA
Increased Firm Deposits +Excess ReservesAI
-Excess ReservesAI
Firm Asset Purchase +Asset PurchaseA -Asset PurchaseA
Unspent Loan Reserves used as Excess Reserves +(Lend MoneyA-Asset PurchaseA)*(1/Reserve Ratio) -(Lend MoneyA-Asset PurchaseA)*(1/Reserve Ratio)

Bank B
Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital FirmsB Safe
Firm Asset Sale used as Excess Reserves +Asset PurchaseA
*(1/Reserve Ratio)
-Asset PurchaseA*(1/Reserve Ratio)

Loans are generally made to be spent, all the time they remain in reserves they are attracting interest, so the expansion to bankA’s own lending power from its own loans is likely to be small. However it is also unlikely to be zero unless all loans are immediately used to purchase assets at one. There are also cases such as overdraft facilities and standing bank lines of credit where there will be systemic additional excess reserves to the bank itself. In most cases however the increase in lending power will transmit to bank B. This case, and Pennington’s approach, only considered the first instance of the series, not the expansion of lending power by bank B etc.

Throughout here for simplicity we consider if a bank has increased lending power it lends. It might not as it might not be profitable when considering risk etc. Later we shall consider the implications when banks do not fully deploy their lending power.

Torrens built on Pennington’s concept by being the first to specify the limits to deposit expansion.

Whatever sums they may advance on securities in the morning, the same sums will be returned to them in the evening, in the form of new deposits; and in this way the amount of their deposits must continue to increase, until they bear that proportion to the fixed amount of the returning cash, which the experience of the bankers may suggest as safe and legitimate [19, p. 16]…. in ordinary times, one-tenth, or even one-twentieth, of the money deposited with a banker, is a sufficient rest [reserve] for meeting occasional demands; and that ninetenths, or even nineteenth-twentieths, of the sums deposited with a bank may be lent out on securities [19, p. 18]

That is, expansion proceeds via the successive lending and redeposit of excess cash reserves until the desired deposit/reserve ratio is attained.

Humphrey

Torrens focused on the lending redeposit mechanism of the banking system as a whole; he did not trace the expansion process from bank to bank. He merely stated that banks as a group expand loans, then recoup the proceeds in the form of redeposits, and then expand again and again until the limit is reached. He did not identify individual banks nor did he mention the distribution of reserves among them.

Thomas Joplin in his 1841 book The Cause and Cure of Our Commercial Embarrassments explained how expansion proceeds from one bank to the next,. Each Bank lending out its excess reserves and losing it to another bank which also expands and so on until excess reserves are eliminated achieving the reserve ratio desired by bankers.

  1. Inclusion of Dividends in Interbank Deposits

But the model above is not complete in that it assumes that dividends are withdrawn from Bank A and disappear from the circuit. Let us assume that Bank A Equity Holders (those enjoying the factor return on the rent of money) deposit into bank B.

Fig2. Corrected Model with Deposit of Dividends


Bank A
Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital FirmsA Safe
Grant Equity for Lending +EquityA -EquityA
Grant Lending Power +Lending Power ValueA -Lending Power ValueA
Lend Money +Lend MoneyA -Lend MoneyA
Record Loan -Lend MoneyA +Lend MoneyA
Charge Interest +Interest ChargeA  -Interest ChargeA
Record Interest -Interest ChargeA +Interest ChargeA
Repay Loan and Interest -Loan RepaymentA -Interest ChargeA +Loan RepaymentA +Interest ChargeA
Record Loan and Interest Repayment +Loan RepaymentA +Interest ChargeA -Loan RepaymentA Interest ChargeA
Pay Dividends  -DividendsA +DividendsA
Increased Firm Deposits +Excess ReservesAI
-Excess ReservesAI
Firm Asset Purchase +Asset PurchaseA -Asset PurchaseA
Unspent Loan Reserves used as Excess Reserves +(Lend MoneyA-Asset PurchaseA)*(1/Reserve Ratio) -(Lend MoneyA-Asset PurchaseA)*(1/Reserve Ratio)

Bank B
Assets Liabilities EquityB
Operation Lending Power Value Loan Ledger Working Capital FirmsA Equity Holder A Safe
Grant Equity for Lending +EquityB -EquityB
Grant Lending Power +Lending Power ValueB -Lending Power ValueA
Lend Money +Lend MoneyB -Lend MoneyB
Record Loan -Lend MoneyB +Lend MoneyB
Charge Interest +Interest ChargeB  -Interest ChargeB
Record Interest -Interest ChargeB +Interest ChargeB
Repay Loan and Interest -Loan RepaymentB -Interest ChargeB +Loan RepaymentB +Interest ChargeB
Record Loan and Interest Repayment +Loan RepaymentB +Interest ChargeB -Loan RepaymentB -Interest ChargeB
Pay/Recieve Dividends +DividendsA *(1/Reserve Ratio)  -DividendsB +DividendsA *(1/Reserve Ratio) +DividendsB
Increased Firm Deposits
Firm Asset Sale -Asset PurchaseA
+Asset PurchaseA
Increased Excess Reserves +Excess ReservesAI
-Excess ReservesAI – Dividends A *(1/Reserve Ratio)
Increased Lending power from unspent loans +(Lend MoneyA-Asset PurchaseA)*(1/Reserve Ratio)
-(Lend MoneyB-Asset PurchaseB)*(1/Reserve Ratio)

This is important as it shows that although a bank loses lending power to itself by granting dividends its expands the lending power of the banking system by an amount equal to the residual of the deposited dividends not held as reserves expanded throughout the banking system.

Let us assume all banks are homogeneous.

Let D be the proportion of the banking surplus paid as dividends (0 to 1)

Let r be the minimum reserve ratio (0 to 1)

Then through geometrical expansion we get the convergent series.

We may therefore modify our formula for systemic change in debt as follows:

2. ΔLP=ΔEQ+ ΔP + ΔI + ΔE + ΔDrM

Where

LP    Lending Power

EQ    Equity

R    Principal repayments

I    Interest

E    Excess Reserves

M    Money leant

We also need to do a correction for excess reserves. The next sections deals with this.

  1. The Davenport/Phillips Geometrical Expansion Solution

The key step was the formalisation/mathematisation of this process. H.J.Davenport set out a fairly comprehensive approach to entrepreneurship, endogenous money, credit and demand, including a credit cycle theory of the business cycle in his 1913 text Economics of Enterprise. The work is largely forgotten now because of a misconceived attack by Fetter in a review (Davenport had criticised Fetter in the book and the Fetter in essence criticised Davenport for not using the same definitions of Credit and Capital as him). Where it was influential was via those influenced by the work, including Knight, Fisher, Schumpter, Hawtry and Keynes. Indeed Knight remarked that parts of the 1913 text were ‘indistinguishable from Keynes’. One concept from the book which did enter the textbooks – which overall took a very heterodox approach to some classical and emerging neoclassical concepts – was over the correct modelling of deposit multiplication.

Davenport

When the check drawn by the borrowing depositor may be deposited in other banks and collected by them against the lending bank, its granting of credits rapidly draws down its reserves to swell the reserves of its competitors. $100,000 of new reserves may not mean to it an increase of lending power of more than, say, $125,000. For banks in the aggregate, however, this increase of reserves brings its full several-fold increase of lending power, provided that all the reserve efficiency is utilized in whatever bank it rests. As the lending by each bank is depleting its reserves, the lending which other banks are doing is reenforcing these reserves. The aggregate possible extension of credit is not changed. (p295)

Davenport observed that the total lending power of an aggregate of banks was the same as a single monopoly bank.

Davenport

It follows from the foregoing analysis that, in the main, banks do not lend their deposits, but rather, by their own extensions of credit, create the deposits; that these deposits are funds which the deposit-creditors of the bank can lend if they will, and that many men into whose hands these deposits fall through transfer are certain to use them as funds to be lent. In fact, also, even when the deposits in the’ bank are not derived from the lending activity of the bank, but are really funds deposited from outside sources, these funds are commonly used by the bank as a reserve basis on which loans are extended rather than as funds which are themselves loaned out by the bank. Banks are, in truth, mostly intermediaries between debtors and creditors – but not in the sense of borrowing funds from one class of customers in order to lend them to another class, but rather in the sense of creating for their borrowing customers funds which may be used by these borrowers as present purchasing power [to settle with those with such purchasing power]. (p 263)

We can see here the influence on Keynes re investment creating savings, only within a context where it makes sense; an explicit endogenous theory of money.

It is, therefore, a sheer blunder to infer that a bank is rich or strong because of its great total of deposits, or to regard deposits in banking institutions as making part of the aggregate wealth of the community … The solvency of the bank is in its portfolio of securities. Its deposits are not its assets, but its liabilities. These liabilities it has mostly created for the use of its borrowers. The further it may safely go in assuming liabilities, the larger its holdings of borrowers’ notes may be, and the more interest or discount charges it may collect. Essentially, therefore, the business of a bank is a form of suretyship – the guaranteeing of its borrowers’ solvency – an underwriting of the credit of its customers. (p264)

But what if all banks together try to strengthen reserves?

the ultimate difficulty is that the very process by which all the banks at once are trying to strengthen their reserves is an altogether impossible process – a paradox – a death-blow at the very fundamental principle of banking.(P268)

The mathematisation and extension of Davenport’s model was the contribution made by CA Phillips in Bank Credit 1931. (Phillips acknowledged in the book that the treatment was essentially that of Davenport)

Phillips is critical of the traditional theory of deposit expansion that one increment of excess reserves enables that bank to expand its deposits several fold to restore its desired reserve ratio.

if there were only one bank into which all of our banks were merged, doing the loan and deposit business of the entire country and maintaining a reserve-deposit ratio of r, that the net deposit of a given amount of cash or reserve, c, would enable the institution to lend, in addition to its normal amount of loans outstanding,

This is true because the deposit arising from the cash, c, would itself call for a reserve equal to re, leaving c-rc as reserve for deposits arising from additional loans…. The total deposits expansion for the banking system, under the conditions stated, would be

Let the ratio of cash to deposits for the banking system, then, be represented by r, the new cash or reserve, by c, the expansion of deposits traceable to an addition to cash, by D, the loan expansion arising from the same source, by X, and the following equations stand forth:

We have seen that the loan expansion in an isolated bank or in the banking system, as the result of the acquisition of a given amount of reserve, is several times greater than the loan expansion practicable for an individual bank acquiring the same amount. What is true for the banking system as an aggregate is not true for an individual bank that constitutes only one of many units in that aggregate. The sudden acquisition of a substantial amount of reserve by a representative individual bank, other things remaining the same, tends to cause that bank to become out of tune with the banks in the system as a whole. As the individual bank increases its loans in order to re-establish its normal reserve-deposits ratio, reserve is lost to other banks and the new reserve, split into small fragments, becomes dispersed among the banks of the system. Through the process of dispersion it comes to constitute the basis of a manifold loan expansion. (P38-40)

Phillips extended his model to include consideration of loans left in deposits and not withdrawn by the debtor, considering this most likely immediately after a loan is granted and when a repayment is due. We have already considered this in stricter double entry terms.

The additional cash or reserve (c);

Overflow cash, i. e., what a bank tends to lose as the result of making the additional loans (c);

Loan power expansion resulting from additional cash (x);

The ratio of cash or reserve to deposits (r);

The ratio of derivative deposits to loans (k) (that is loans not withdrawn)

[Note: k in the double entry terms above is equal to lend money – asset purchase, that is the remaining amount of reserves in the original bank creating the loan after the asset purchase, or prior to the asset purchase the full amount of reserves in the account]

For derivation see Phillips Page 55.

Note also that k is a factor equivalent to the monopoly power of a bank. If K=1 then it is like the whole economy modelled as a single bank and c at unity we have

3. 

Phillips summed up his result as follows:

Writers in the past have assumed that the ratio of loans to cash on hand after the loans were made, as in the case of a representative bank thoroughly assimilated to the system, was an accurate measure of new loans that could be extended on the basis of new reserve. They have overlooked the pivotal fact that an addition to the usual volume of a bank’s loans tends to result in a loss of reserve for that bank only somewhat less on the average than the amount of the additional loans. The reserve retained, what we have called residual cash or residual reserve, is only a fraction, on the average throughout the loan period, of additional loans made. The residual cash supports loans,—and deposits,—several times as great as itself, but the residual cash is only a fraction of the cash accretion, the possession of which prompts the banker to expand his loans. Manifold loans are not extended by an individual bank on the basis of a given amount of reserve. Instead, as a consequence of lending, the reserve of the individual bank overflows, leaving only the equivalent of a fractional part of the additional volume of loans extended, the overflow cash finding its way to other and still other banks until it becomes the “residualized,” yet shifting, foundation of manifold loans and deposits.

Now we can undertake the series expansion.

4. 

Where as before r is the minimum reserve ration and E is excess reserves.

So we can finally correct our formula to account for deposit expansion as follows:

5.

In double entry terms we can correct the ‘single bank’ model to include the systemic effects of interbank lending whilst avoiding having to actually model individual banks, as follows:

Fig3. Corrected System Single Bank Model


Bank
Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Working Capital Firms Equity Holder 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
Transfer Dividends to Deposits -Dividends*Reserve Ratio +Dividends*Reserve Ratio +Dividends -Dividends
Increased Firm Deposits used for Asset Purchase +Excess Reserves*(1-Reserve Ratio) -Excess Reserves*(1-Reserve Ratio) -Dividends
Increased Excess Reserves +(Lend Money-Asset Purchase)*(1/Reserve Ratio)
-(Lend Money-Asset Purchase)*(1/Reserve Ratio)

4 ) Interpretation

Note how loan power expansion is greatest at the beginning of a term. As debt is amortised then principal and interest will fall. So continual debt expansion is needed to maintain bank lending power.

Note also how the lending power contribution of excess reserves and dividends are inversely related to reserve ratios. If profits rise throughout the economy then the lending power of banks increase in proportion to how low reserve ratios are. If banks pay large dividends (or a similar extraction through bonuses) then this is extracted from lending power potential in proportion to the deposit ratio, if the deposit ratio is zero then there is no extraction from lending power.

This shows that the current Basel III rules on rebuilding deposits may be having a doubly negative impact on lending power through expansion of the reserve ratio.

In the next section we will look at the relationship between this endogenous money multiplier and the khan/keynsian multiplier and velocity of money and goods.  In due course we will also look at the impact ofd state money expansion on reserves and the expansion or otherwise of lending power.

The bookkeeping here is tough and my maths have been unused for 20 years so I doubt I havent made a mistake – greatful for comments/corrections.

Tsk Tsk, forgot to add references.  I will add Thursday – bad form

31 thoughts on “The Transmission of Lending Power between Banks in Endogenous Monetary Theory

  1. Interesting post, Andrew – and the previous one too.

    You haven’t taken fully on board the implications of a banks’ power to accept risk. You quote from Davenport regarding the fact that a bank guarantees its borrowers’ solvency, but you don’t then extend that to address the issue you raised in your first post concerning the difference between the price of a bank and its balance sheet valuation. From depositors’ point of view, the value of depositing money in a bank includes that guarantee – which I would therefore suggest is a good candidate for the “intangible asset” that inflates the bank price. Non-bank investments (corporate bonds, for example) generally can’t offer the same guarantee. Any bank that can guarantee borrower solvency from depositors’ point of view is therefore always going to be “worth” more than its balance sheet suggests.

    We now know that for the largest banks that guarantee in the last resort is provided by the sovereign: prior to the financial crisis I don’t think that was clearly understood. Various attempts have been made to value that implicit state guarantee: NEF and Positive Money have both had a go at it, as I recall, and this paper from the Bank of England is interesting:

    http://www.bankofengland.co.uk/publications/Documents/fsr/fs_paper15.pdf

    I would expect the fact that the state acts as “guarantor of last resort” for systemically-important banks (and prior to 2007, implicitly for ALL banks – since some were bailed out that weren’t systemically important) both to reduce funding costs and increase net worth, wouldn’t you?

    In my view the main constraint on bank lending is risk appetite, not the availability of either reserves or capital. Ann Pettifor pointed out on one of my posts that when banks have a lot of poor-quality assets (so have high risks on their balance sheets), they don’t want to lend even if they have adequate capital and liquidity. Asset quality is absolutely essential for a bank to maintain its guarantee in a world in which the sovereign guarantee is less comprehensive than it used to be and some lenders to banks may in future take losses in the event of borrower insolvency.

    • I stated in the first post that the assumption is that all capitalisation of future loan income are risk adjusted.

      What these simple models dont do however is examine the systemic nature of risk and how this effects overall bank capitalisation, but so far it they do look at one key aspect of the transmission of that risk, intra bank deposits.

      The models have started out with a base of looking at the potential for loans. So far I havnt considered the propensity to invest and the assessment of risk in whether loans to full lending power are made or not. Neither have I considered yet collaterol or the quality of collaterol.

      I dont disagree with anything in your response its just that its not possible to cover all angles at once the aim being rather some fill in some of the theoretical black holes before building up a systemic model – although risk is one of those areas where neo-classical assumptions have got us in a pickle too.

  2. As the real value of a bank that intermediates funds lies in its ability to mitigate the risks that depositors would face if they tried to lend directly to borrowers, leaving out the value of this risk does weaken your model quite a bit, I think. I’m not talking here about systemic risk, which is largely to do with the funding relationships between banks. I am talking about the basic risks inherent in lending (liquidity risk, credit risk, market risk).

    • Thats v loanable funds

      No its much simpler than that risk has a price and that price is the insurance that the lender needs to take out – collateral – nothing to do with intermediation

      That collateral is a liability and adds to excess reserves

      So can be simply added to model and is the intention of a future post

  3. I think the double entry for the initial recording of the intangible asset “Grant lending power” should be debit the asset (Lending Power Value) ” , credit capital reserves (Equity). Whereas you have recorded the credit as a liability, which it clearly is not. The bank is under no obligation to repay this initial lending power value to anyone, it is simply an internally generated asset, with no inherent liability.

      • Ok agreed, but you have not anwsered the question of why the credit entry is a liability on your table. I think you need to address this point to tighten up your model.

    • Im struggling with your logic here as if a bank started out with no equity it would have no lending power so why debit the asset, for an asset to grow it must be credited not debited.

      • My comments are made as a practising accountant and you make a fundamental accounting error in your reply here. Crediting an asset does not increase it (make it grow). Debiting an asset increases it, crediting it reduces it. This is basic bookkeeping.

  4. I’m struggling with you double entry. Take “Lend money”, the double entry extends over two separate entities, the bank and the firm. This is single entry bookkeeping and the ledgers will not balance.

    Take “Record loan”, debit the asset (loan ledger, ok), but credit the “Lending power value” ? A banking lending money will see a reduction in its cash (or working capital), as the borrow drawdowns the loan.

  5. You answered your own question. As loans are repaid the lending power asset is credited expanding the ability to make future loans. Its a stock that runs down when a loan is first made but which then gradually tops up.

    I should add this element of the model is from Nelil Wilson – he is an accountant and im not. Though I can see the flaw you suggest. Perhaps you should take it up on his website. The link was on the first post.

  6. I don’t think you can regard the risks to sources of funding as a question of collateralisation (insurance). The fact is that deposits and other sources of funds ARE used to settle deposit drawdowns, so although you may not regard this as direct intermediation of funds, it is still deployment of borrowed money to fund risk ventures. Not all lending is collateralised, but all lending carries risks for the sources of funding – which include depositors, other banks, bondholders, shareholders and central banks. How much risk is borne by each of these categories is determined by the legal nature of the bank’s obligation to them. At present depositors are fully insured up to £85K in the EU and I think $250K in the US. Central banks are fully insured because they demand collateral against borrowings (with a haircut representing the risk inherent in the collateral itself – so over-collateralisation is normal). No other category is necessarily insured at all, although these days other banks may also demand collateral. The insurance for bondholders and uninsured depositors therefore rests on two things: 1) asset quality 2) extent of shareholders’ funds.

    Depositors none-the-less regard banks as a “safe place to put their money”, which enables banks to offer them a lower rate of return in relation to riskier ventures. To the extent that this is a GENERAL perception of banks – for example, because access to lender of last resort facilities eliminates liquidity risk – it also reduces their wholesale funding costs and increases their share price. It is that reduction in cost and increase in value that you may wish to attempt to price in a subsequent post. And you may also wish to consider what the risk parameters are that govern lending.

    One more point – and this is much more serious, in my view. Your model currently gives the impression that lending can be completely divorced from borrowing, because you leave out drawdown (which is separate from loan agreement). The fact is that banks DO borrow to fund drawdown of deposits, including those made as a consequence of lending. You’ve pretty much ignored the whole funding side except for shareholders’ funds – in effect you’ve treated your model banks as 100% equity financed, which is unrealistic. Don’t be fooled by the “loans create deposits” thing – that is true, but it doesn’t mean a bank can fund itself from its own lending. The banking system AS A WHOLE can do this, but individual banks can’t. You appear to be trying to model the whole banking system as if it is a single bank, and in so doing you are introducing a fallacy of composition.

    • As I said ill deal with the whole issue of risk and collaterol in a future update.

      You make a good point about equity/loan funding mix. Id like to know more from your banking background as to how banks determine this. From the Mog/Miller thesis this shouldn’t matter however I dont think this thesis fully tackles the issue of risk.

      I wouls like to know more about deposit drawdown, and why it would outweigh deposit additions

  7. Hi Andrew,

    I just want to make sure I followed your post. Is your argument that in addition to the “money multiplier” that allows the sum of loans to be greater than total reserves, that reserves are themselves increasing as retained banking system profits get added into them ?

    • Not quite, the lending power account must top up working capital – its a payback an internal liability – but the growth of the economy caused by the loan causes a second order effect of creating excess reserves of depositors.

  8. Pingback: Correctly Modelling Reserves, Cost of Funding and Collateral in Monetary Circuit Theory « Decisions, Decisions, Decisions

  9. Andrew,

    Re debt/equity mix:

    Modigliani/Miller does not directly take account of balance sheet risk – they roll it into cost of capital considerations. Equity is nearly always more expensive than debt because the risk to equity holders is greater. The adjusted form of the Modigliani-Miller model takes into account the tax shield caused by the preferential treatment of debt over equity in corporate accounting, which makes equity even more expensive. The tax shield plus the higher risk of equity is sufficient in my view to make preference for high gearing inevitable in optimising capital structure.

    The only type of bank that would finance entirely from capital would be a full reserve bank. Fractional reserve banks always rely on debt financing and they are usually very highly geared. The direction of regulation at the moment is to force them to reduce their gearing, but they still wouldn’t finance entirely with equity or anywhere near it – it would be far too expensive. Regulatory capital is measured against risk weighted assets, remember, not total assets.

    Those who promote full reserve banking never, ever talk about the higher costs associated with financing all lending with equity and subordinated debt.

  10. And re deposit drawdown:

    Deposit drawdowns are the other side of deposit additions. When a loan is created it adds to deposits. When the loan is spent it reduces deposits. But more importantly, drawdown involves physical movement of funds. Up to the point when the loan is drawn, all the entries are virtual funds – balance sheet movements within the same bank. When the loan is drawn, there is a real movement of money. That movement has to be funded, and that’s where reserves come in. Reserves held at the central bank facilitate the movement of money from one bank to another. If a bank does not have sufficient reserves to allow the money to leave it without creating a negative reserve balance at the central bank (or below reserve requirement if the requirement is positive – it is zero in the UK at the moment), then it must borrow to fund its reserve account or face failed payments. The great debate about funding and reserves is really about deposit drawdowns, not lending – the same issues arise when customer deposits (i.e. money physically deposited by customers) are drawn.

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