Correctly Modelling Reserves, Cost of Funding and Collateral in Monetary Circuit Theory

This post clarifies the treatment of bank reserves and ‘excess reserves’ in the MCT banking model in response to feedback from Steve Keen. Hopefully this approach will be persusive in understanding the interbank role of reserves in transmitting economic expansion, contraction and risk.

1) Where the Power to Lend Comes From

The past series of posts, especially here and here, have looked to develop the double entry monetary circuit approach to endogenous money by extending it to consider equity and other factors such as ‘excess reserves’. The aim was to explain how banks can create money from a starting position of a blank balance sheet. Banks can create money but not from an empty balance sheet. The solution was to introduce equity and use that to feedstock ‘lending power’ a term I am trying to revive from early 20th century banking theory which refers to the ‘intangible asset’ of the ability to create profits from money creation – an issue highlighted by Neil Wilson and now adopted by Steve Keen,

Fig 1 How Equity Contributes to Lending Power in Start Up Bank

Assets Liabilities Equity
Operation Lending Power Value Bank Working Capital Safe
Grant Equity for Lending +Equity -Equity
Grant Lending Power +Equity -Equity

I expected the treatment of reserves to be controversial although I had only one serious challenge in  a new model and the comment below appear to refer to my proposed approach

[One] way to involve reserves and try to make them part of the system is to argue that banks lend from liabilities rather than assets, and that one of its liabilities is a working capital reserve–the banking sector’s own liabilities to itself. Then you can derive a system which appears to show that banks lend from reserves …the bottom line here is that eliminating “Fractional Reserve Banking” does nothing to eliminate the capacity for banks to create money: that will exist in a purely free market system just as much as it does today.

I agree but that is not the issue, the point being made is that fractional reserve banking increases lending power, but that power exists as my model shows when a bank starts up has no deposited reserves, only equity. . Private correspondence from Steve Keen on the basis that all endogenous money creation must come from the liability side – I agree – and my preliminary response was published here. This approach was inadequate though, reserves and excess reserves pop up from the model emerging from the black box within. This revised model explicitly models fractional reserves banking as a series of double entries between liabilities and from my enquiries mirror real world bank operations.

2) Fractional Reserve Banking

In modern form fractional reserve banking arose in renaissance Italy (the earliest recorded example is from Venice) when banks realised that they had more reserves on hand then their day to day demand for reserves from depositors required, and hence they could lend it out at interest. This was greatly aided by the ‘venice system’ the discovery of double entry bookkeeping. We know however that Roman banking (preserved in Byzantine and transmitted to Venice) operated on a fractional reserve basis.

The earliest monetary circuit theory double entry models have assumed that all deposits are held as a liability under working capital and therefore 100% of the reserves are added to lending power. This is unrealistic a bank must keep a reserve amount to deal with anticipated daily withdrawl levels and to meet any regulatory demands. Lets model this for simplicity as before only modelling firms which are also equity holders in the bank. What the model does is to split liabilities through internal transfers between required reserves and working capital.

Fig 2 How Required Reserves Contribute to Lending Power

Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Bank Working Capital
Firm Deposits Safe
Grant Equity for Lending +Equity
Grant Lending Power +Equity
Deposit & maintain required reserves +Deposits
Transfer Excess Reserves +Deposits *(1-reserve ratio) -Deposits *(1-reserve ratio)
Increase lending power from
Excess Reserves
+Deposits *(1-reserve ratio) -Deposits *(1-reserve ratio)
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 Interest and Loan -Loan Repayment
-Interest Charge
-Loan Repayment
-Interest Charge
Record Interest and Loan +Loan Repayment +Interest Charge -Loan Repayment -Interest Charge
Pay Dividends
-Dividends +Dividends
Transfer Dividends to Deposits
+Dividends -Dividends
Increased Deposits From Dividends Used for Asset Purchase +Dividends-Asset Purchase*(1-reserve ratio) -Dividends-Asset Purchase
Increased Deposits from Loan Used for Asset Purchase +(Lend Money-Asset Purchase)*(1/reserve ratio) -Lend Money-Asset Purchase
Increased Working Capital from Excess Reserves +(Lend Money-Asset Purchase)*(1/reserve ratio)
+Dividends-Asset Purchase*(1-reserve ratio)
-(Lend Money-Asset Purchase)*(1/reserve ratio)
-Dividends-Asset Purchase*(1-reserve ratio)
Transfer Working Capital to Lending Power +(Lend Money-Asset Purchase)*(1/reserve ratio)
+Dividends-Asset Purchase*(1-reserve ratio)
-(Lend Money-Asset Purchase)*(1/reserve ratio)
-Dividends-Asset Purchase*(1-reserve ratio)

The formulas and approach is the same as in the previous model with the model taking into account the geometrical reduction of excess reserves through multiples banks only with the explicit modelling of required reserves and the correction for the topping up of lending power via working capital.

If all lent money is used to purchase assets there is no net creation of excess reserves. There will be from dividends.

3) Modelling The Cost of Funding

The above model assumes a business model of banking. That is the profit of a bank is the cost of the loan minus the revenue from the loan at net present value. What if a bank has lent up to its lending power but still finds that there are additional profitable loans to be made? If the cost of funding the additional lending power still maintains an acceptable level of profit the bank will if it can borrow short to extend its lending power for long term loans. Before long any positive profits will restore lending power meaning short term funding will be the principle requirement. This is the underlying dynamics behind the nostrum that banks make money through borrowing short and lending long. This is known as the reserve window. Lets model this.

Fig 3 Inclusion of the Cost of Funding

Assets Liabilities Equity
Operation Lending Power Value Bank Working Capital
Firm Deposits Safe
Grant Equity for Lending +Equity
Grant Lending Power -Equity
Cover Reserve Window -Short Term Funding +Short Term Funding

It would be a great mistake to assume that from the viewpoint of the system as a whole as opposed to a single bank the funding costs of one bank are the income of another and this cancels. This would be to make a classic ‘loans=deposits’ mistake. Correct yes in terms of anticipated capitalisation of future income but that income is radically uncertain. In terms of very short terms loans yes for all intents and purposes they will cancel but we also have to consider the impact of collateral.

4) Modelling Collateral

Those who lend without collateral are making a risk that the loan will default. This may add to the cost of the loan by adding an interest premium. If the cost is high then collateral may be required.

Collateral acts as insurance. Lets say there is a 5% risk of a loan then this sum, discounted to NPV is the additional insurance required at the granting of the loan. This is typically taken as cash. Lets model this from the perspective of the banking system as a whole.

Assets Liabilities Equity
Operation Lending Power Value Loan Ledger Bank Working Capital
Firm Deposits Safe
Deposit Collateral +Lend Money*Default Risk -Lend Money*Default Risk
Add Collateral +Lend Money*Default Risk -Lend Money*Default Risk
Record Collateral -Lend Money*Default Risk +Lend Money*Default Risk
Adjust Required Reserves - (Lend Money*Default Risk)*Reserve Ratio - (Lend Money*Default Risk)*Reserve Ratio
Reduce Lending Power - (Lend Money*Default Risk)*Reserve Ratio + (Lend Money*Default Risk)*Reserve Ratio

So we can see from the perspective of the system as a whole collaterals effect in increasing lending power is offset to a very large degree by the reduction in excess deposits in the system. What this means is changes to collateral requirement effect the change in debt – a well observed phenomenon noted by Minsky. As collateral requirements increase so the change in debt reduces.

We may modify our formula as follows

Where C=Collateral

Interesting extensions to this approach would be to model recollaterolisation and collateral chains

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25 thoughts on “Correctly Modelling Reserves, Cost of Funding and Collateral in Monetary Circuit Theory

  1. Where collateral is re-used (rehypothecated), its value declines on each re-use – this is represented by the “haircut”, or amount of extra collateral required to achieve the same risk reduction. Therefore the “flow” of rehypothecated collateral behaves much like the recycling of deposits in the traditional money multiplier – the amount of debt that can be supported reduces with each rehypothecation. Is that helpful?

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  4. Accounting’s definition of working capital is different than the definition used above. Please consider looking it up.

    Working capital = current assets – current liabilities

    So, one should also look up current assets and liabilities. Basically, the “current” part means an assets or liabilities that have a duration of less than a year. { If the asset or liability lasts more than a year it would be called “long term asset” or “long term liability.”}

    Examples of current assets and liabilities can be found on balance sheets. Please see a balance sheet. Assets and Liabilities are both divided into accounts that are “current” and accounts that are “long term”. The current assets are above “Total Current Assets” on the balance sheet. Like wise for the current liabilities. They like to put the more liquid or current assets at the top and the less liquid long term assets afterword.

    Working capital is calculation netting short term assets and liabilities. It’s not usually a single account on a balance sheet.

    Double entry bookkeeping and accounting are easy enough to be learned by one self. It is so valuable and ubiquitous I don’t understand why it isn’t an educational requirement. The beginning upward slope on the learning curve is “debit” and “credit” and T-accounts. T accounts are a modern simplification of the ledger accounts. Once the initial learning curve hump is passed with a little practice the rest is much easier.

    It might be a good idea to leave existing accounting definitions in tact. If one wants to make up your own definitions or accounts please consider using different terms and give the your definition of the term or account. One is always free to set up their own chart of accounts or make up their own accounts.

    I think if one really wants to begin to understand basic banking is to learn the beginning fundamentals of double entry bookkeeping and then learn about notes and bills (a bill is a form of note.) Actually, the old bookkeeping books have lots of info on notes and bills of exchange. I think notes and bills are the essentials of how a bank work. Then the “Ah hah!” moment comes.

    But, people don’t need banks to use notes and bills of exchange and the old pedagogical literature examples could lead you conclude that they were in very common use. In fact foreign trade can be done this way reducing the magnitude of specie that has to crisscross the world. My father told me that people went to the grocery store and the store saved up the chits and presented them with a bill after a time (he mentioned methods that indicated how efficient the bookkeeping method was.)

    Historians say that the accepting and giving bills of exchange and notes can actually increase the amount of trade.

      • Then is it and asset instead of a liability? Are “Bank Reserves”, also, an asset?

        Your answer is interesting. That classical economic definition[1] is very similar to the accounting one but not the same. The economic definition of “Working Capital” would be equivalent to the accountant’s current assets which is just part of what the accountants calls working capital. Should it be on the asset side? {If one thought of current liabilities as negative current assets then the definition could be almost the same as an net current assets being working capital in the accounting sense.}

        Accountants’ definition:
        Working Capital = Current Assets – Current Liabilities.

        Classical Economists definition of working capital
        = Current Assets (as defined by accountants)

        Accountants’ definition of Current assets: Assets that will last or be held for < 1 year.

        Looking at the sign used convention above it seems you do mathematically treat that account as an asset even though it is labeled under liabilities. That is because the normal balance increases assets (debit). Usually, the initial entry to an account is the normal balance. Your initial +equity entry to what you called "bank working capital" is + equity. And you subtract the equity term from the equity account. How I get that is as follows.

        I think your mathematically correct convention is to increase assets you add, and to increase liabilities and equity you subtract. And the normal balances would be + for assets and – for Liabilities and Equity. Its fine to mathematically to do it that way.

        Using the accounting equation and manipulating it around:

        Assets – Liabilities = Net Worth = Equity

        Assets – Liabilities – equity = 0
        and further clarifying
        { Change in Assets – change in Liabilities – change in Equity = 0 }

        New transactions add 0 to the equation keeping it still valid.

        Your first transaction + Equity and -Equity sum to 0.

        This indicates to me that your math treats the account you call "Bank Working Capital as an asset in actuality.

        So, in your mathematically correct convention Assets are normal balance + (positive) , and Liabilities and equity are normal balance – (minus) ignoring debit and credit conventions. In this way every double entry has a +(transaction amount) and an equivalent -(transaction amount). Some thing like this.

        Assets + (-Liabilities) + (-equity) = 0
        If the last equation is not evident than the parenthesis terms could have a change of variables.
        where, [A]= assets ; [L] = (-Liabilities) ; [E] = (-equity)
        [A] + [L] + [E] = 0

        I hope that is more clear than vague.

        Using the same reasoning about the first transaction, that affects the account you call required reserves, also, would be more of an asset than a liability. Accounts that comprise a bank's reserves are assets. Like central bank notes (cash), moneys owed from other banks, and deposits at the central bank. I think there is not a specific account labeled reserves. I think reserves are a sum of things that are considered reserves. I think the banks have a checking account with the central bank, which the part of their reserves at the central bank.

        I'm still looking for a really good and complete definition of reserves.


        1. Working capital — This includes the stocks of finished and semi-finished goods that will be economically consumed in the near future or will be made into a finished consumer good in the near future. These are often called inventories. The phrase "working capital" has also been used to refer to liquid assets (money) needed for immediate expenses linked to the production process (to pay salaries, invoices, taxes, interests…) Either way, the amount or nature of this type of capital usually changed during the production process. Then type, {cntrl-f} working capital {return}

      • No bank reserves are a liability, but if you leave your asset, a lawnmower, in my front lawn and I use it to mow my lawn I can gain an economic service from it, same principle.

      • Sorry didnt read full details and thought you were referring to reserves.

        Working cpital is an investment from someone, eith as equity or a loan, hence should be treated as a liability for the firm, then it is simply an issue of how that liability is signed for transactions. Of course in terms of day to day accounting you can create a further liability from this account to an asset account called ‘payroll’ or ‘cash on hand’ or somesuch and this might be easier to follow. Thoughts?

  5. It may come from my ignorance of accounting but trying to understand your model, there’s a few things which seems illogical to me.

    First, I don’t see how a bank could start with no reserves. In order to obtain a banking licence, there’s an initial capital requirement (I know it’s the case in Canada so I assume it’s the same everywhere, maybe not?). For exemple, if I want to start a bank, say Bank A, I’m gonna have to provide the required capital from my own savings. As I see it, I’m gonna have to make a transfert from my deposit account at Bank B to the equity account of Bank A. This transfert gonna have to be matched by an equivalent transfert of reserves from Bank B to Bank A accounts at the central bank. Now, considering reserves as a liability doesn’t make sense to me. Banks are borrowing reserves from each other and it doesn’t make sense to borrow a liability because both the loan and the reserves would add to liabilities. In the landmower example you gave above, the landmower is an asset to it’s owner and it won’t become a liability because it’s lent out. If I borrow a landmower from you, I borrow an asset and “I owe you” a landmower, which is the corresponding liability.

    Now, the first line of your table starts with – equity in the equity account and + equity in the working capital account. It’s weird because the bank starts with no assets and to match the increase in equity, working capital needs to be a “negative” liability. If instead you consider reserves as an asset and the transfert of reserves, you would have – equity in the equity account and + equity in the reserve account on the asset side of the balance sheet, which makes much more sense to me. The bank could then lend directly from equity ( + loan in equity account and – loan firm deposit account) and recording the loan would restore equity (+ loan in loan ledger and – loan in equity account). This wouldn’t require lending power or working capital… It would make things more straightforward and easy to follow and I think more logical.

    It’s hard for me to judge since I don’t know accounting and I never saw what a real bank balance sheet look like. Does it make sense to you?

    • In the model the banks starts with equity (capital). That being lent then becomes reserves. In accounting for banks reserves are always liabilities , as in the initial case to refund the equity account.It has to be a liability as the equity owner must be rapid. There was an earlier version with it as an asset but this drew some criticism from accountants.

      • I can’t agree with reserves beiing a liability. The confusion may come from the fact that reserves are a liability of the central bank, but it’s an asset for a member bank. Looking at this paper from the federal reserve, reserves are an asset for banks and a liability for the central bank. Altought they explain the money multiplier, which I agree with you is wrong, I doubt they would confuse assets and liabilities, they still know the banking system…

        Steve’s earlier models have been criticized for not beiing consistant with accounting, but the critic was that all lines didn’t sum to zero, not that reserves was an asset. Trying to solve that problem, Neil Wilson putted reserves on the liability side and added goodwill (lending power) on the asset side. I think it was a mistake, it didn’t particularily matter in a pure credit economy since it’s hard to define reserves when the bank can just print as much notes as it want, but it create problems when you try to generalize the model by adding fiat money, where reserves are clearly defined as an asset for banks. In fact, just adding an equity column would have solved the problem because the lines summed to equity instead of zero. As I argued above, since equity is assets minus liabilities, it doesn’t make much sense to me to start with equity and no assets. The bank can’t just create equity out of thin air, it has to come from a transfert of already existing money which will be matched by an equivalent transfert of reserves.

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  8. Huge problem with using the term ‘reserves’ as a liability side entry in banking. And that’s because ‘Central bank reserves’ are private bank assets.

    You are right that it is an accounting equity reserve, but you need to come up with another name for it or you will lose your readers.

    And banks are not restricted in their lending capacity unless regulated. And that requires a ‘police force’, and a police force that is able to shut the bank down.

    • This is the terminology used in Banking texts for 200 years – so I don’t see the problem. The problem is how central bank ‘reserves’ are described. Of course an asset to one party on a balance sheet crates a matching liability on another – again what’s the big deal?

      No banks are restricted in their lending even if completely unregulated – otherwise they soon face a liquidity crunch and potentially a run – see my latest post on the durability gap.

    • No central bank required reserves are liabilities on the central banks balance sheet – see

      The BoE refers to these as ‘rest’ rather than reserves but that is an archaeic term used by no other central bank I have no intention of reviving. In any event the key issue here is the amount of ‘excess’ reserves held about this level of the level of bank desired reserves if higher. The term excess reserves is well used in monetary theory and I think I would lose my readers more if I adopted a different terminology.

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  10. This is to you and your readers.

    Please consider leaning more about double entry bookkeeping for a bit, before learning of more confusing economics.

    Bookkeeping is simpler than economics because it works! It’s not perfect, but it works!

    In the word accounting, is the word “count”. Accountants and bookkeepers know how to count. Economists, well…, do they they know how to count? I’m not so sure, they keep getting it wrong… Accountants are not constantly assuming every thing out of consideration, because they don’t know how to treat those things. Many economists have turned away from accounting or have never had enough exposure to it. We both agree economics delivered to the public and undergraduate level is lacking so much?

    ******** Have you gotten any books or courses on double entry bookkeeping and or accounting? Please consider learning some more, double entry bookkeeping, DEB. The bookkeeping books tend to be shorter and have basic examples. I like them both and began with the simplest.

    Bookkeeping is simpler than economics because it works!

    Bookkeeping doesn’t come with the confusion of the failure of economics. It is the language of business. It is known in depth by more people than economics is. It has real utility. The vocabulary is more precise and understood by more people. It can save you money. It has more educational content. It handles both stocks and flows. You could use it in business. Accountants have a code of ethics. Economics has no code of ethics.

    You use some of it for economics because it shows promise of improving dismal economics. You could easily be much better at it. Why not go in the bookkeeping direction a little while and learn some more of it? It might be more interesting to you than the economics without accounting. It would only take a few days study to start. And you would be able to run circles around most economists. And you would be more aware of them assuming important things away. You may be able to spot more of the ridiculousness of more assumptions and ideas purported.

    Accounting can be self taught. Reading the first few chapters of some books with pencil and paper to do the examples, is a good start. Unless you are blessed with that genius of learning math stuff with out practice you have got to practice it in the beginning because every thing is based on the basics.

    The basics of accounting are the system of using debit and credit. I like the idea of “Normal Account Balances” for explaining debits and credits. So, books with that in the index might be good. I think a few introductory books would work. Also, the concept of Revenue and Expense being sub accounts of Equity (belonging to equity) or them being nominal (or temporary) accounts that are transferred or cleared to equity is good. They are temporary accounts because those accounts are filled for the period to measure the flow of income over that period. Then they are cleared for the next period by transferring the balances to profit & loss, income, or retained earrings (a sub account of equity).

    I have a note to keep in mind when learning accounting. Income statements and balance statements are value based, not cash based. In accounting things are recorded at the value that was paid for them, but are not currency. One could have income but run out of currency. That is why the banks have reserves ready for the demands of depositors’ withdraws. Thus the cash flow statement is actuality is very important. But cash flow statements are treated as a very advanced subject in accounting books. (A cash book is also a good way to keep a tab on cash.) A entity always has to have enough cash, but can be making an accounting profit but run out of cash. Why? If they make all there sales by giving credit that counts as income but they have not gotten the cash yet there could be a problem.

    Here are some videos of the basics done by one of the best teachers I have seen on the web. Each are about 8 minutes. He uses the “Normal Account Balance” concept. I hope you like them too.

    Use pencil and paper to practice to understand faster

    lecture 1: Balance sheets part 1
    lecture 2: Balance sheets part 2
    lecture 3: debits and credits
    lecture 4: recording transactions
    lecture 5: T-accounts
    lecture 6: The accounting cycle

    Some one elses idea:

    Here is a course offered by a lady who seems experienced. I haven’t bought her course but have looked at her free presentations. I thought her treatment of bank reconciliation was very good. She offers a 60 day money back warranty. Real classes might be better because students can learn from each otters.

    Sorry I don’t have a book recommendation of you.

    Do you know of accounting is widely ignored in economics in the West? If that is so, why would accounting be ignored? Is there any good reasons for economist to ignore accounting?

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