## Thursday, 20 December 2012

### Money multiplier and other myths

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Policies such as Quantitative Easing which has been in the news lately are predicated on a mistaken belief about the way the banking system operates and how the non-government and government sectors interact. One of the hard-core parts of mainstream macroeconomic theory that gets rammed into students early on in their studies, often to their eternal disadvantage, is the concept of the money multiplier. It is a highly damaging concept because it lingers on in the students’ memories forever, or so it seems. It is also not even a slightly accurate depiction of the way banks operate in a modern monetary economy characterised by a fiat currency and a flexible exchange rate. So lets see why!

Allegedly, the money multiplier m transmits changes in the so-called monetary base (MB) (the sum of bank reserves and currency at issue) into changes in the money supply (M). Students then labour through algebra of varying complexity depending on their level of study (they get bombarded with this nonsense several times throughout a typical economics degree) to derive the m, which is most simply expressed as the inverse of the required reserve ratio. So if the central bank told private banks that they had to keep 10 per cent of total deposits as reserves then the required reserve ratio (RRR) would be 0.10 and m would equal 1/0.10 = 10. More complicated formulae are derived when you consider that people also will want to hold some of their deposits as cash. But these complications do not add anything to the story.
The formula for the determination of the money supply is: M = m x MB. So if a \$1 is newly deposited in a bank, the money supply will rise (be multiplied) by \$10 (if the RRR = 0.10). The way this multiplier is alleged to work is explained as follows (assuming the bank is required to hold 10 per cent of all deposits as reserves):
• A person deposits say \$100 in a bank.
• To make money, the bank then loans the remaining \$90 to a customer.
• They spend the money and the recipient of the funds deposits it with their bank.
• That bank then lends 0.9 times \$90 = \$81 (keeping 0.10 in reserve as required).
• And so on until the loans become so small that they dissolve to zero …
The following table and graphs shows you what the pattern involved is (unfortunately not shown due to technical problem). They are self-explanatory. In this particular case, I have shown only 20 sequences. In fact, this example would resolve at around 94 iterations as you can see on the graphs where the succesive loans, then fractional deposits get smaller and smaller and eventually become zero.

The conception of the money multiplier is really as simple as that. But while simple it is also wrong to the core! What it implies is that banks first of all take deposits to get funds which they can then on-lend. But prudential regulations require they keep a little in reserve. So we get this credit creation process ballooning out due to the fractional reserve requirements.
Well that is not at all like the real world. It is a stylised text-book model which isn’t even close to how things actually operate. The way banks actually operate is to seek to attract credit-worthy customers to which they can loan funds to and thereby make profit. What constitutes credit-worthiness varies over the business cycle and so lending standards become more lax at boom times as banks chase market share.
These loans are made independent of their reserve positions. Depending on the way the central bank accounts for commercial bank reserves, the latter will then seek funds to ensure they have the required reserves in the relevant accounting period. They can borrow from each other in the interbank market but if the system overall is short of reserves these “horizontal” transactions will not add the required reserves. In these cases, the bank will sell bonds back to the central bank or borrow outright through the device called the “discount window”. There is typically a penalty for using this source of funds.
At the individual bank level, certainly the “price of reserves” will play some role in the credit department’s decision to loan funds. But the reserve position per se will not matter. So as long as the margin between the return on the loan and the rate they would have to borrow from the central bank through the discount window is sufficient, the bank will lend.
So the idea that reserve balances are required initially to “finance” bank balance sheet expansion via rising excess reserves is inapplicable. A bank’s ability to expand its balance sheet is not constrained by the quantity of reserves it holds or any fractional reserve requirements. The bank expands its balance sheet by lending. Loans create deposits which are then backed by reserves after the fact. The process of extending loans (credit) which creates new bank liabilities is unrelated to the reserve position of the bank.
The major insight is that any balance sheet expansion which leaves a bank short of the required reserves may affect the return it can expect on the loan as a consequence of the “penalty” rate the central bank might exact through the discount window. But it will never impede the bank’s capacity to effect the loan in the first place.
What about open market operations? These are allegedly how the central bank increases or decreases the money supply. So assume the central bank wants to increase the money supply it would purchase bonds in the markets and, accordingly, add reserves to the banking system. The banks in turn will try to lend those reserves out because they don’t want to be stuck with underperforming deposits and competition in the overnight markets will drive the interest rate down. Clearly, if the central bank wants to maintain control over the overnight interest rate it has to then drain the excess reserves which would require it offer the banks an interest-bearing asset commensurate with the overnight rate. That is, it would have to sell bonds in an open market operation. The reverse is true if it tried to reduce the money supply by selling bonds. This drains reserves from the cash system and would probably leave some banks short of required reserves. Given the only remedy for an overall shortage of reserves is intervention from the central bank the attempt to decrease the money supply fails.
It is clear that the central bank then is unable to control the volume of money in the system although it can control the price through its monetary policy settings. The money multiplier is a flawed conception of how things work. The monetary base does not drive the money supply. In fact, the reverse is true. So the reserves at any point in time will be determined by the loans that the banks make independent of their reserve positions.
So when you consider this in the light of the current policy debate you have to wonder what half the commentators are on! For example, it makes no sense to say that the credit crunch is because banks have no money to lend and that Quantitative Easing will provide them with “printed money” that they can then lend. Banks will always lend when a credit-worthy customer walks through the door and the terms are to the bank’s favour.
Endogenous money or Wicksellian myths
Mainstream economists are not the only group who demonstrate a misconception of the way the monetary system operates. Among so-called progressive economists there are many, who while recognising that we use a fiat currency (manifest as worthless tokens) rather than a “commodity money” (where the actual unit has intrinsic value), still fail to consider how the currency gets its value and its role in the non-government sector transactions. So-called Circulation or Wickesellian models of the credit cycle which fail to include a government sector are examples of these flawed approaches. In general, these models reject the money multiplier myth but replace it with another – that you can understand capitalism without understanding the essential role that Government plays in the monetary system.
Accordingly, these models consider economies as being made up of households (who supply productive factors and consume); firms (who produce) and banks (who loan working capital to firms in advance of production). And they then analyse the “circuits of production” whereby firms borrow from banks to hire and pay workers to produce. The workers then use their wages to consume and the firms then are able to pay back the banks. At that point the “credit money” is destroyed (and corresponding and offsetting assets and liabilities). Any household saving is reflected in unpaid bank loans at the end of each circuit unless firms offer “bonds” to the households to soak up their saving.
The Wicksellian view then is that “money” is largely created by banks in response to the demand for credit from economic agents. It is clear that the revolving fund of credit finance can expand to accommodate growth in private sector activity, at a rate related proportionately to the product of provisioning rates for capital adequacy requirements and the percentage of retained earnings available for leveraged lending. For this very reason, the private sector can take up some of the slack created through government fiscal conservatism. However, and this is the crux of the modern monetary view, this growth will become unsustainable because net financial assets are either being destroyed or are not being created in insufficient quantity to meet the net saving needs of the private sector. Private sector debt levels will be rising while the stock of net financial assets declines. But back to the main story!
So the “elephant in the room” which is ignored by these analyses is the question of the currency unit. Why would these transactional circuits use the unit that the Government has legally sanctioned? Why would anyone accept the unit of account? You cannot answer these fundamental questions if you have excluded the Government sector from your analysis. Further models that exclude government clearly cannot say anything about the important fiscal effects on bank reserves?
Modern monetary theorists consider the credit creation process to be the “leveraging of high powered money”. The only way you can understand why all this non-government “leveraging activity” (borrowing, repaying etc) can take place is to consider the role of the Government initially – that is, as the centrepiece of the macroeconomic theory. Banks clearly do expand the money supply endogenously – that is, without the ability of the central bank to control it. But all this activity is leveraging the high powered money (HPM) created by the interaction between the government and non-government sectors.
HPM or the monetary base is the sum of the currency issued by the State (notes and coins) and bank reserves (which are liabilities of the central bank). HPM is an IOU of the sovereign government – it promises to pay you \$A10 for every \$A10 you give them! All Government spending involves the same process – the reserve accounts that the commercial banks keep with the central bank are credited in HPM (an IOU is created). This is why the “printing money” claims are so ignorant. The reverse happens when taxes are paid – the reserves are debited in HPM and the assets are drained from the system (an IOU is destroyed). Keep this in mind.
HPM enters the economy via so-called vertical transactions. Please refer back to Deficit spending 101 – Part 1; Deficit spending 101 – Part 2 and Deficit spending 101 – Part 3 for the details and supporting diagrams.
So HPM enters the system through government spending and exits via taxation. When the government is running a budget deficit, net financial assets (HPM) are entering the banking system. Fiscal policy therefore directly influences the supply of HPM. The central bank also creates and drains HPM through its dealings with the commercial banks which are designed to ensure the reserve positions are commensurate with the interest rate target the central bank desires. They also create and destroy HPM in other ways including foreign exchange transactions and gold sales.
We can think of the accumulated sum of the vertical transactions as being reflected in an accounting sense in the store of wealth that the non-government sector has. When the government runs a deficit there is a build up of wealth (in \$A) in the non-government sector and vice-versa. Budget surpluses force the private sector to “run down” the wealth they accumulated from previous deficits.
One we understand the transactions between the government and non-government then we can consider the non-government credit creation process. The important point though is that all transactions at the non-government level balance out – they “net to zero”. For every asset that is created so there is a corresponding liability – \$-for-\$. So credit expansion always nets to zero! In previous blogs I have called the credit creation process the “horizontal” level of analysis to distinguish it from the vertical transactions that mark the relationship between the government and non-government sectors.
The vertical transactions introduce the currency into the economy while the horizontal transactions “leverage” this vertical component. Private capitalist firms (including banks) try to profit from taking so-called asset positions through the creation of liabilities denominated in the unit of account that defines the HPM (\$A for us). So for banks, these activities – the so-called credit creation – is leveraging the HPM created by the vertical transactions because when a bank issues a liability it can readily be exchanged on demand for HPM.
When a bank makes a \$A-denominated loan it simultaneously creates an equal \$A-denominated deposit. So it buys an asset (the borrower’s IOU) and creates a deposit (bank liability). For the borrower, the IOU is a liability and the deposit is an asset (money). The bank does this in the expectation that the borrower will demand HPM (withdraw the deposit) and spend it. The act of spending then shifts reserves between banks. These bank liabilities (deposits) become “money” within the non-government sector. But you can see that nothing net has been created.
Only vertical transactions create/destroy assets that do not have corresponding liabilities. My friend and sometime co-author Randy Wray puts it this way:
Credit money (say, a bank demand deposit) is an IOU of the issuer (the bank), offset by a loan that is held as an asset. The loan, in turn, represents an IOU of the borrower, while the credit money is held as an asset by a depositor. On this view, money is neither a commodity (such as coined gold), nor is it ‘fiat’ (an asset without a matching liability).
But what gives the unit of account chosen by the Government its primacy. Why do all the banks and customers demand it? The answer is that state money (in our case the \$A) is demanded because the Government will only allow it to be used to extinguish tax liabilities. So the tax liability can only be met by getting hold of the Governments own IOU – the \$A. Further, the only way that we can get hold of that unit of account is by offering to supply goods and services to the Government in return for their spending. The Government spending provides the funds that allow us to pay our taxes! That is the reverse of what most people think.
This process is how the Government ensures it can get private resources in sufficient quantities to conduct its own socio-economic policy mandate. It buys labour and other resources and creates public infrastructure and services. We are eager to supply our goods and services in return for the spending because we can get hold of \$A.
So the private money creation activity that is central to many progressive models misses the essential point – that the credit creation activity is leveraging of the HPM – and is acceptable for clearing private liabilities (repaying loans) only because it is the only vehicle for extinguishing one’s tax liabilities to the state.
References
Graziani, A. (1990) ‘The Theory of the Monetary Circuit’, Economies et Societes.
Mosler, W.B. and Forstater, M. (2002) A General Analytical Framework for the Analysis of Currencies and Other Commodities.

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