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Fractional-reserve banking
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Fractional-reserve banking is the banking practice in which banks keep only a fraction of their deposits in reserve (as cash and other highly liquid assets) and lend out the remainder, while maintaining the simultaneous obligation to redeem all deposits immediately upon demand. Fractional reserve banking is a necessary consequence of bank lending – when banks lend out a fraction of the deposits that they receive.
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Encyclopedia
Fractional-reserve banking is the banking practice in which banks keep only a fraction of their deposits in reserve (as cash and other highly liquid assets) and lend out the remainder, while maintaining the simultaneous obligation to redeem all deposits immediately upon demand. Fractional reserve banking is a necessary consequence of bank lending – when banks lend out a fraction of the deposits that they receive. Hence, this practice is universal in modern banking.
History
Prior to the 1800s, savers looking to keep their valuables in safekeeping depositories deposited gold coins and silver coins at goldsmiths, receiving in turn a note for their deposit (see Bank of Amsterdam). Once these notes became a trusted medium of exchange an early form of paper money was born, in the form of the goldsmiths' notes.
As the notes were used directly in trade, the goldsmiths observed that people would not usually redeem all their notes at the same time, and they saw the opportunity to invest their coin reserves in interest-bearing loans and bills. This generated income for the goldsmiths but left them with more notes on issue than reserves to pay them with. A process was started that altered the role of the goldsmiths from passive guardians of bullion, charging fees for safe storage, to interest-paying and interest-earning banks. Thus fractional-reserve banking was born.
However, if creditors (note holders of gold originally deposited) lost faith in the ability of a bank to redeem (pay) their notes, many would try to redeem their notes at the same time. If in response a bank could not raise enough funds by calling in loans or selling bills, it either went into insolvency or defaulted on its notes. Such a situation is called a bank run and caused the demise of many early banks.
Benefits of fractional reserve banking
According to the United States' Federal Reserve, fractional reserve banking provides benefits to the economy and the banking system:
Thus, fractional reserves are a necessary consequence of bank lending. The fractional reserve system allows banks to act as financial intermediaries – facilitating the movement of funds from savers to investors in a society.
According to many economists, fractional reserve banking benefits the economy by providing regulators with powerful tools for manipulating the money supply and interest rates, which many see as essential to a healthy economy. Additionally, fractional reserve banking provides an easy way for the government to finance its debt, as government debt has historically made up most of the commercial banks' reserves (e.g. in U.S. national and state banks).
How it works
In most legal systems, a demand deposit at a bank (e.g. a chequeing or savings account) or banknote issued by a bank (bank-issued paper money) is considered a loan to the bank (instead of a bailment), repayable on demand, which the bank uses to finance its investments in loans and interest bearing securities. Banks make a profit based on the difference between the interest they charge on the loan they make, and the interest they pay to their depositors.
The nature of banking lending is such that there will be only a fraction of cash reserves available at the bank available to repay all of the demand deposits and banknotes issued. This results because when the bank lends out money deposited, keeping only a fraction of the total money as a reserve, it essentially creates new money in the account balances of its depositors. The reason people deposit funds at a bank or hold banknotes issued by a bank is to store savings in the form of a demand claim on the bank. One important aspect of fractional-reserve banking is that the note holders and depositors still have a claim to repayment of their funds on demand even though the funds are already largely invested by the bank in interest bearing loans and securities.
Holders of demand deposits can withdraw all of their deposits at any time. If all the depositors of a bank did so at the same time a bank run would occur, and the bank would likely collapse. Due to the practice of central banking this is a rare event today, as central banks usually guarantee the deposits at commercial banks, and act as lender of last resort when there is a run on a bank. However, there have been some recent bank runs, the Northern Rock crisis of 2007 in the United Kingdom is an example. The collapse of Washington Mutual bank in September 2008, the largest bank failure in history, was preceded by a "silent run" on the bank, where depositors removed vast sums of money from the bank through electronic transfer. However, in these cases, the banks proved to have been insolvent at the time of the run. Thus, the bank runs merely precipitated failures that were inevitable in any case.
In the absence of crises that trigger bank runs, fractional-reserve banking usually functions smoothly because at any one time relatively few "at call" depositors will make cash withdrawals simultaneously compared to the total amount on deposit, and a cash reserve can be maintained as a "buffer" to deal with the normal cash demands from depositors seeking withdrawals. In addition, in a normal economic environment, cash is steadily being introduced into the economy by the central bank, and new funds are steadily being deposited into the commercial banks.
However, if a bank is experiencing a financial crisis, and net redemption demands are unusually large over a period of time, the bank will run low on cash reserves and will be forced to raise new funds from additional borrowings (e.g. by borrowing from the money market or using lines of credit held with other banks), and/or sell assets, and/or call in short-term loans to avoid running out of reserves and defaulting on its obligations. If creditors are afraid that the bank is running out of cash or is insolvent, they have an incentive to redeem their deposits as soon as possible before other depositors access the remaining cash reserves before they do, triggering a cascading crisis that can result in a full-scale bank run.
Money creation
Modern central banking allows multiple banks to practice fractional reserve banking with inter-bank business transactions without risking bankruptcy. The process of fractional-reserve banking has a cumulative effect of money creation by banks, essentially expanding the money supply of the economy.
There are two types of money in a fractional-reserve banking system operating with a central bank:
- central bank money (money created or adopted by the central bank regardless of its form (precious metals, commodity certificates, banknotes, coins, electronic money loaned to commercial banks, or anything else the central bank chooses as its form of money)
- commercial bank money (demand deposits in the commercial banking system) - sometimes referred to as chequebook money
When a deposit of central bank money is made at a commercial bank, the central bank money is removed for circulation, and an equal amount of new commercial bank money is created. When a loan is made using the central bank money from the commercial bank (which keeps only a fraction of the central bank money as reserves), the money supply expands by the size of the loan.
The table below displays how loans are funded and how the money supply is affected. It also shows how central bank money is used to create commercial bank money from an initial deposit of $100 of central bank money. In the example, the initial deposit is lent out 10 times with a fractional-reserve rate of 20% to ultimately create $400 of commercial bank money. Each bank involved in this process creates new commercial bank money on only a portion of the original deposit of central bank money, ensuring that it always has enough reserves on hand to meet the inter-bank business demands, and also ensuring that multiple banks participate in the inflation process so that all banks are inflating at the same rate.
The process begins when an initial $100 deposit of central bank money is made into Bank A. Bank A then takes 20 percent of it, or $20, and sets it aside as reserves and then loans out the remaining 80 percent, or $80. At this point there is actually a total of $180 in the system, not $100; because the bank has loaned out $80 of the central bank money, kept $20 of central bank money in reserve, and substituted a newly created $80 IOU claim for the depositor that acts equivalent to and can be implicitly redeemed for central bank money (the depositor can transfer it to another account, write a check on it, etc.). These checkbook IOUs are termed commercial bank money and are simply recorded in a bank's register as an asset (specifically, an IOU from the loan recipient) next to the reserves. From a depositor's perspective, commercial money is central bank money--it's impossible to tell the two forms of money apart until a bank run happens (at which time everyone wants central bank money). At this point Bank A still holds $100 of central bank money reserves on its books, but $80 of those reserves are soon going to be needed to satisfy the loan recipient. The loan recipient soon spends the $80. The receiver of that $80 then deposits it into Bank B. Bank B demands $80 of central bank money be delivered from Bank A to Bank B in satisfaction of the loan recipient's check. Bank A now only has $20 of central bank money on its books.
Bank B is now in the same situation as Bank A started with, except it has a deposit of $80 of central bank money instead of $100. Similar to Bank A, Bank B sets aside 20 percent of that $80, or $16, as reserves and lends out the remaining $64, creating $64 of IOUs to its depositors. As the process continues, more commercial bank money is created. To simplify the table, a different bank is used for each deposit. In the real world, the money a bank lends may end up in the same bank so it then has more money to lend out.
Table Sources: | Individual Bank | Amount Deposited | Lent Out | Reserves | | A | 100 | 80 | 20 | | B | 80 | 64 | 16 | | C | 64 | 51.20 | 12.80 | | D | 51.20 | 40.96 | 10.24 | | E | 40.96 | 32.77 | 8.19 | | F | 32.77 | 26.21 | 6.55 | | G | 26.21 | 20.97 | 5.24 | | H | 20.97 | 16.78 | 4.19 | | I | 16.78 | 13.42 | 3.36 | | J | 13.42 | 10.74 | 2.68 | | K | 10.74 |
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| Total Reserves: |
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| 89.26 |
| Total Amount Deposited: | Total Amount Lent Out: | Total Reserves + Last Amount Deposited: |
| 457.05 | 357.05 | 100 |
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| Commercial Bank Money
Created + Central Bank Money: | Commercial Bank Money Created: | Central Bank Money: |
| 457.05 | 357.05 | 100 |
Although no new money was physically created in addition to the initial $100 deposit, new commercial bank money is created through loans. The 2 boxes marked in red show the location of the original $100 deposit throughout the entire process. The total reserves plus the last deposit (or last loan, whichever is last) will always equal the original amount, which in this case is $100. As this process continues, more commercial bank money is created. The amounts in each step decrease towards a limit. If a graph is made showing the accumulation of deposits, one can see that the graph is curved and approaches a limit. This limit is the maximum amount of money that can be created with a given reserve rate. When the reserve rate is 20%, as in the example above, the maximum amount of total deposits that can be created is $500 and the maximum amount of commercial bank money that can be created is $400.
For an individual bank, the deposit is considered a liability whereas the loan it gives out and the reserves are considered assets. The deposit will always be equal to the loan plus the reserve, since the loan and reserve are created from the deposit. This is the basis for a bank's balance sheet.
The creation and destruction of commercial bank money occurs through this process. Whether it is created or destroyed depends on what direction the process moves. When loans are given out, the process moves from the top down and money is created. When loans are paid back, the process moves from the bottom to the top and commercial bank money is canceled out, effectively erasing it from existence.
This table gives an outline of the makeup of money supplies worldwide. Most of the money in any given money supply consists of commercial bank money. The value of commercial bank money comes from the fact that it can be exchanged at a bank for central bank money.
This is a general outline of how it works. The actual increase in the money supply through this process may be lower, as (at each step) banks may choose to hold reserves in excess of the statutory minimum, borrowers may let some funds sit idle, and some borrowers may choose to hold cash, and there may be delays or frictions in the process. It may also be higher if the reserve requirement is lower or if there are no reserve requirements. Government regulations may also be used to limit the money creation process by preventing banks from giving out loans even though the reserve requirements have been fulfilled.
Money multiplier
The most common mechanism used to measure this increase in the money supply is typically called the money multiplier. It calculates the maximum amount of money that an initial deposit can be expanded to with a given reserve ratio.
Formula
The money multiplier, m, is the inverse of the reserve requirement, R:
Example
For example, with the reserve ratio of 20 percent, this reserve ratio, R, can also be expressed as a fraction:
So then the money multiplier, m, will be calculated as:
This number is multiplied by the initial deposit to show the maximum amount of money it can be expanded to.
Reserve requirements
The reserve requirements are intended to prevent banks from:
- generating too much money by making too many loans against the narrow money deposit base;
- having a shortage of cash when large deposits are withdrawn (although the reserve is a legal minimum, it is understood that in a crisis or bank run, reserves may be made available on a temporary basis).
The money creation process is affected by the currency drain ratio (the propensity of the public to hold banknotes rather than deposit them with a commercial bank), and the safety reserve ratio (excess reserves beyond the legal requirement that commercial banks voluntarily hold—usually a small amount). Data for "excess" reserves and vault cash are published regularly by the Federal Reserve in the United States. In practice, the actual money multiplier varies over time, and may be substantially lower than the theoretical maximum.
Financial ratios
In addition to reserve requirements, there are other required financial ratios that affect the amount of loans that a bank can fund. The capital requirement ratio is perhaps the most important of these other required ratios. When there are no mandatory reserve requirements, the capital requirement ratio acts to prevent an infinite amount of bank lending.
Money supplies around the world
Fractional-reserve banking determines the relationship between the amount of central bank money (currency) in the official money supply statistics and the total money supply. Most of the money in these systems is commercial bank money . Fractional reserve banking involves the issuance and creation of commercial bank money, which increases the money supply through the deposit creation multiplier. The issue of money through the banking system is a mechanism of monetary transmission, which a central bank can influence indirectly by raising or lowering interest rates (although banking regulations may also be adjusted to influence the money supply, depending on the circumstances).
Regulation
Because the nature of fractional-reserve banking involves the possibility of bank runs, central banks have been created throughout the world to address these problems.
Central banks
Government controls and bank regulations related to fractional-reserve banking have generally been used to impose restrictive requirements on note issue and deposit taking on the one hand, and to provide relief from bankruptcy and creditor claims, and/or protect creditors with government funds, when banks defaulted on the other hand. Such measures have included:
- Minimum required reserve ratios (RRRs)
- Minimum capital ratios
- Government bond deposit requirements for note issue
- 100% Marginal Reserve requirements for note issue, such as the Bank Charter Act 1844 (UK)
- Sanction on bank defaults and protection from creditors for many months or even years, and
- Central bank support for distressed banks, and government guarantee funds for notes and deposits, both to counteract bank runs and to protect bank creditors.
Liquidity and capital management for a bank
To avoid defaulting on its obligations, the bank must maintain a minimal reserve ratio that it fixes in accordance with, notably, regulations and its liabilities. In practice this means that the bank sets a reserve ratio target and responds when the actual ratio falls below the target. Such response can be, for instance:
- Selling or redeeming other assets, or securitization of illiquid assets,
- Restricting investment in new loans,
- Borrowing funds (whether repayable on demand or at a fixed maturity),
- Issuing additional capital instruments, or
- Reducing dividends.
Because different funding options have different costs, and differ in reliability, banks maintain a stock of low cost and reliable sources of liquidity such as:
- Demand deposits with other banks
- High quality marketable debt securities
- Committed lines of credit with other banks
As with reserves, other sources of liquidity are managed with targets.
The ability of the bank to borrow money reliably and economically is crucial, which is why confidence in the bank's creditworthiness is important to its liquidity. This means that the bank needs to maintain adequate capitalisation and to effectively control its exposures to risk in order to continue its operations. If creditors doubt the bank's assets are worth more than its liabilities, all demand creditors have an incentive to demand payment immediately, a situation known as a run on the bank.
Contemporary bank management methods for liquidity are based on maturity analysis of all the bank's assets and liabilities (off balance sheet exposures may also be included). Assets and liabilities are put into residual contractual maturity buckets such as 'on demand', 'less than 1 month', '2-3 months' etc. These residual contractual maturities may be adjusted to account for expected counter party behaviour such as early loan repayments due to borrowers refinancing and expected renewals of term deposits to give forecast cash flows. This analysis highlights any large future net outflows of cash and enables the bank to respond before they occur. Scenario analysis may also be conducted, depicting scenarios including stress scenarios such as a bank-specific crisis.
Risk and prudential regulation
In a fractional-reserve banking system, in the event of a bank run, the demand depositors and note holders would attempt to withdraw more money than the bank has in reserves, causing the bank to suffer a liquidity crisis and, ultimately, to perhaps default. In the event of a default, the bank would need to liquidate assets and the creditors of the bank would suffer a loss if the proceeds were insufficient to pay its liabilities. Since public deposits are payable on demand, liquidation may require selling assets quickly and potentially in large enough quantities to affect the price of those assets. An otherwise solvent bank (whose assets are worth more than its liabilities) may be made insolvent by a bank run. This problem potentially exists for any corporation with debt or liabilities, but is more critical for banks as they rely upon public deposits (which may be redeemable upon demand).
Although an initial analysis of a bank run and default points to the bank's inability to liquidate or sell assets (i.e. because the fraction of assets not held in the form of liquid reserves are held in less liquid investments such as loans), a more full analysis indicates that depositors will cause a bank run only when they have a genuine fear of loss of capital, and that banks with a strong risk adjusted capital ratio should be able to liquidate assets and obtain other sources of finance to avoid default. For this reason, fractional-reserve banks have every reason to maintain their liquidity, even at the cost of selling assets at heavy discounts and obtaining finance at high cost, during a bank run (to avoid a total loss for the contributors of the bank's capital, the shareholders).
Many governments have enforced or established deposit insurance systems in order to protect depositors from the event of bank defaults and to help maintain public confidence in the fractional-reserve system.
Responses to the problem of financial risk described above include:
- Proponents of prudential regulation, such as minimum capital ratios, minimum reserve ratios, central bank or other regulatory supervision, and compulsory note and deposit insurance, (see Controls on Fractional-Reserve Banking below);
- Proponents of free banking, who believe that banking should be open to free entry and competition, and that the self-interest of debtors, creditors and shareholders should result in effective risk management; and,
- Withdrawal restrictions: some bank accounts may place a limit on daily cash withdrawals and may require a notice period for very large withdrawals. Banking laws in some countries may allow restrictions to be placed on withdrawals under certain circumstances, although these restrictions may rarely, if ever, be used;
- Opponents of fractional reserve banking who insist that notes and demand deposits be 100% reserved.
Example of a bank balance sheet and financial ratios
An example of fractional reserve banking, and the calculation of the reserve ratio is shown in the balance sheet below:
| Example 2: ANZ National Bank Limited Balance Sheet as at 30 September 2007 |
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| ASSETS | NZ$m | LIABILITIES | NZ$m | | Cash | 201 | Demand Deposits | 25482 | | Balance with Central Bank | 2809 | Term Deposits and other borrowings | 35231 | | Other Liquid Assets | 1797 | Due to Other Financial Institutions | 3170 | | Due from other Financial Institutions | 3563 | Derivative financial instruments | 4924 | | Trading Securities | 1887 | Payables and other liabilities | 1351 | | Derivative financial instruments | 4771 | Provisions | 165 | | Available for sale assets | 48 | Bonds and Notes | 14607 | | Net loans and advances | 87878 | Related Party Funding | 2775 | | Shares in controlled entities | 206 | [subordinated] Loan Capital | 2062 | | Current Tax Assets | 112 | Total Liabilities | 99084 | | Other assets | 1045 | Share Capital | 5943 | | Deferred Tax Assets | 11 | [revaluation] Reserves | 83 | | Premises and Equipment | 232 | Retained profits | 2667 | | Goodwill and other intangibles | 3297 | Total Equity | 8703 | | Total Assets | 107787 | Total Liabilities plus Net Worth | 107787 |
In this example the (legal tender) cash held by the bank is $201m and the demand liabilities of the bank are $25482m, for a (legal tender) cash reserve ratio of 0.79%.
Other financial ratios
The key financial ratio used to analyze fractional-reserve banks is the cash reserve ratio, which is the ratio of cash reserves to demand deposits and notes. However, other important financial ratios are also used to analyze the bank's liquidity, financial strength, profitability etc.
For example the ANZ National Bank Limited balance sheet above gives the following financial ratios:
- The (legal tender) cash reserve ratio is $201m/$25482m, i.e. 0.79%.
- The central bank notes/balances reserve ratio is $3010m/$25482m, i.e. 11.81%.
- The liquid assets reserve ratio is ($201m+$2809m+$1797m)/$25482m, i.e. 18.86%.
- The equity capital ratio is $8703m/107787m, i.e. 8.07%.
- The tangible equity ratio is ($8703m-$3297m)/107787m, i.e. 5.02%
- The total capital ratio is ($8703m+$2062m)/$107787m, i.e. 9.99%.
Clearly, then, it is very important how the term 'reserves' is defined for calculating the reserve ratio, and different definitions give different results. Other important financial ratios may require analysis of disclosures in other parts of the bank's financial statements. In particular, for liquidity risk, disclosures are incorporated into a note to the financial statements that provides maturity analysis of the bank's assets and liabilities and an explanation of how the bank manages its liquidity.
How the example bank manages its liquidity
The ANZ National Bank Limited explains its methods as:
| Example 2: ANZ National Bank Limited Maturity Analysis of Assets and Liabilities as at 30 September 2007 |
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| | Total carrying value | Less than 3 months | 3-12 months | 1-5 years | Beyond 5 years | No Specified Maturity | | Assets | | | | | | | | Liquid Assets | 4807 | 4807 | | | | | | Due from other financial institutions | 3563 | 2650 | 440 | 187 | 286 | | | Derivative Financial Instruments | 4711 | | | | | 4711 | | Assets available for sale | 48 | 33 | 1 | 13 | | 1 | | Net loans and advances | 87878 | 9276 | 9906 | 24142 | 44905 | | Other Assets | 4903 | 970 | 179 | | | 3754 | | Total Assets | 107787 | 18394 | 10922 | 25013 | 45343 | 8115 | | Liabilities | | | | | | | | Due to other financial institutions | 3170 | 2356 | 405 | 32 | 377 | | | Deposits and other borrowings | 70030 | 53059 | 14726 | 2245 | | | | Derivative financial instruments | 4932 | | | | | 4932 | | Other liabilities | 1516 | 1315 | 96 | 32 | 60 | 13 | | Bonds and notes | 14607 | 672 | 4341 | 9594 | | | | Related party funding | 2275 | 2275 | | | | | | Loan capital | 2062 | | 100 | 1653 | 309 | | | Total liabilities | 99084 | 60177 | 19668 | 13556 | 746 | 4937 | | Net liquidity gap | 8703 | (41783) | (8746) | 11457 | 44597 | 3178 | | Net liquidity gap - cumulative | 8703 | (41783) | (50529) | (39072) | 5525 | 8703 |
Criticism
The primary criticisms relate to the potential fragility of bank liquidity in a fractional reserve banking environment, the financial risk of bank runs that depositors bear when depositing money with banks, and the impact that demand deposits have on the stock of money, and on inflation (that is, the implicit debasement of the currency and its associated impact on the exchange rate). An alternative to fractional reserve banking is making the practice illegal and classifying the practice as a form of embezzlement, only permitting full-reserve banking. With full-reserve banking, some monetary reformers as such as Stephen Zarlenga of the American Monetary Institute, support the concurrent issuance of debt-free fiat currency from the Treasury, while others such as Congressman Ron Paul and the Ludwig von Mises Institute call for a commodity currency such as was possible under the Gold Standard.
Exacerbation of the business cycle
Some Austrian School economists claim that fractional-reserve banking, by expanding the money supply, will lower the interest rates compared to a hypothetical full-reserve banking system. They argue that this will affect the role of the interest rate as the price of investment capital, guiding investment decisions. In their view, the natural (free of government influence) interest rate reflects the actual time preference of lenders and borrowers. Government's monopolistic control of the money supply through central banks and regulations insuring fractional-reserve banking activities disturbs this equilibrium such that the interest rate no longer reflects the real supply of and demand for investment capital. Austrian School economists conclude that, if the interest rate is artificially low, then the demand for loans will be higher than the actual supply of willing lenders, and if the interest rate is artificially high, the opposite situation will occur. This misinformation leads investors to misallocate capital, borrowing and investing either too much or too little in long-term projects. Periodic recessions, then, are seen as necessary "corrections" following periods of fiat credit expansion, when unprofitable investments stimulated by fiat credit creation are liquidated, freeing capital for new sustainable investment. One of the proponents of aspects of the business cycle theory, Friedrich von Hayek, was awarded the Nobel Prize in Economics,, although Hayek himself accepted that bank credit and fractional reserve banking - even if they contributed to business cycles - were necessary as "the price we pay for a speed of development exceeding" that which would otherwise be possible, and that "financial institutions have never been prohibited from holding fractional reserves." A few Austrian School economists, such as Pascal Salin, also suggest that a full-reserve banking system should not be enforced legally and dispute Murray Rothbard's characterization of fractional-reserve banking as a simple form of recursive embezzlement, and rather advocate the abolition of central banking and suggest that free banking replace the current system.
Effects of an increased money supply
Fractional reserve banking involves the issuance and creation of commercial bank money, which increases the money supply on an exponential basis. According to the quantity theory of money, this increase in the money supply leads to more money "chasing" the same amount of goods, which leads to inflation. Most monetarists and Austrian economists, and indeed economists in general, believe that the exchange rate or purchasing power of the monetary unit is governed by the quantity of money, including demand deposits and notes, and therefore view fractional reserve banking as the main cause of inflation.
Some quantity theorists who criticize fractional reserve banking support minimum reserve ratios or other government controls on the quantity of money created by commercial banks. Some support a gold standard or silver standard to restrain "unfettered", "speculative" fractional-reserve banking activities. Fractional reserve currency has also been characterized as a hybrid of receipt currency and fiat currency, and a form of currency that will eventually become fiat currency.
See also
Further reading
- Huerta de Soto, J. (2006), Money, Bank Credit and Economic Cycles, Ludwig von Mises Institute
- Meigs, A.J. (1962), Free reserves and the money supply, Chicago, University of Chicago, 1962.
- Crick, W.F. (1927), The genesis of bank deposits, Economica, vol 7, 1927, pp 191-202.
- Philips, C.A. (1921), Bank Credit, New York, Macmillan, chapters 1-4, 1921,
- Thomson, P. (1956), Variations on a theme by Philips, American Economic Review vol 46, December 1956, pp. 965-970.
- Parliament of Tasmania, Monetary System, Report of Select Committee, With Minutes of Proceedings, 1935.
External links
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- Federal Reserve Document explaining how money is created.
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