Thursday, March 11, 2010

Fractional Reserve Banking 1

The Cobden Center is a think tank devoted to social progress through honest money, free trade, and peace. Unfortunately, one of the writers associated with the Cobden Center, Tony Baxendale, considers ordinary banking to be dishonest. See this article here.

The term "Fractional Reserve Banking" is misleading. Bank reserves are made up of vault cash and balances held in deposit accounts at the central bank. "Fractional Reserve Banking" means that these reserves are a fraction of something. What exactly? And why is that a relevant criterion?

To explore this issue, I am going to describe two very different conjectural histories of banking. Both begin without banks, and with all money being tangible, hand-to-hand currency. It could be gold coins, but I will stick with the more familiar government fiat currency.

The first history has banking develop out of money warehouses. To avoid theft, people pay to have money stored. The second history instead has banking develop out of financial intermediation. Banks borrow money and then lend it out.

Again, the first history begins without banks. People make all payments using tangible paper fiat currency.

Because of fear of theft, a business opportunity exists. Money is fungible, so there is no need to have individual safety deposit boxes. The bank, or "money warehouse," as Murray Rothbard calls it, opens up and begins taking deposits. Accounts are kept for each depositor and the funds are stored in the safe. Depositors can claim their money that they have stored at the bank at any time.

The banks charge people a monthly storage fee. The nominal interest rate on these bank deposits is slightly negative, reflecting storage costs.

In order to make ordinary payments, people still have to keep currency at the home, leaving them targets for burglary and worse, home invasion and robbery. And they must carry currency to actually make purchases.

This creates a further business opportunity. The banks begin to allow payments by check or electronic equivalent.

Because retailers want the business of customers, they accept checks drawn on all banks in payment. Because banks want the business of retailers, they accept checks drawn on all banks for deposits.

The banks organize a clearinghouse to settle net clearing balances. Each bank initially deposits currency at the clearinghouse. As a bank receives checks drawn on other banks for deposit by its customers, it in turn deposits those checks at the clearinghouse. The clearinghouse adds the funds to the clearing account of the bank making the deposit and debits the balances of the banks against whose customers the deposited checks were drawn.

The electronic payments system signals a shift in those clearinghouse balances between banks, reducing the balance of the buyer's bank and adding to the balance of the seller's bank. Then the buyer's bank decreases the buyer's account. And the seller's bank increases the seller's account. All of these payments operations are costly, and so, presumably they are covered by fees for each check or electronic payment.

The money that has been deposited into each bank is matched by that bank's reserves. Some of those reserves are held as vault cash and some is held as a balance at the clearinghouse. The funds banks have deposited at the clearinghouse is matched by the clearinghouse's vault cash.

This scenario is central to understanding the concept of "Fractional Reserve Banking." Of course the amount of reserves these "banks" hold is a variety of fractions of various things, but the key fraction is that reserves are equal to 100 percent of deposits. Because 100 percent is greater than or equal to one, this is not fractional reserve banking.

This account of banks is still very thin. There has been no discussion of bank capital. There has been no discussion of bank leverage. There has been no discussion of bank profit or loss. Presumably, those organizing these peculiar banks would need funds to purchase the building, the vault, and so on. The owners could put up money--equity. And the bank could sell bonds, and fund some of its operations by debt. The capital ratio would be capital divided by assets and leverage would be debt divided by equity.

If the funds deposited are treated as being owned by the depositors (and how that works with some reserves deposited at the clearinghouse is a bit of a puzzle,) then reserves are not bank assets and deposits are not bank liabilities.

Of course, if the bank is robbed, it is possible that it would just apologize to the depositors and say that it was unsuccessful in guarding their funds. Or, perhaps it would have to use the bank's remaining assets to make good on the deposits as best it can--selling the vault and the building. If that is the situation, then the deposits are liabilities of the bank and reserves are assets. The result would be a much thinner capital ratio and much higher leverage than otherwise.

The bank's profits would be the difference between revenue, storage and payments fees, and costs, depreciation on the building and equipment, employees, and the like. If the bank earned profit, its capital would increase and its leverage decrease. If those profits were paid out to the owners, then the capital and leverage would remain the same. Losses, on the other hand, would reduce capital and raise leverage. If losses persist, the institution could fail. It is possible that it would not be able to pay off all of its creditors. For example, those who helped finance the "bank" by purchasing bonds.

Of course, there are other creditors as well--the depositors. They could also share in the losses if the bank failed. A robbery, fire, or other disaster destroying the bank's reserves would be one source of losses, but if the collected fees were too low to cover costs that would also create losses.

Implicit in this model is generally an assumption that deposits are senior to other sorts of debt, and that a bank must be closed down before it touches the "reserves" that "back" the deposits, and pay all of them off. Presumably, this is due to imagining that the depositors own the funds in the bank's vault and on deposit at the clearinghouse and ignoring what happens with theft or natural disaster.

What then, is fractional reserve banking? Rather than store all of the depositors' funds and holding a "reserve" equal to deposits, the bank lends some or all of those funds out.

Starting from a baseline in which banks store deposited funds, any remaining reserves are divided by the amount of deposits. The resulting "fraction" is less than one. "Fractional Reserve Banking" then, starts with a narrative of banks storing money for depositors, thus keeping 100% reserves for those depositors. "Fractional Reserve Banking" is a deviation from that ideal, with banks lending out some of the money, and the "fraction" then, being less than one.

Critics of fractional reserve banking sometimes allege that this is inherently dishonest because the bank is lending out the depositors' money rather than storing it. Or, the critics worry about the possibility of a bank run--that is, the depositors seek to withdrawal their money, and there are insufficient reserves to pay them all off on demand because some of the money remains outstanding. However, nearly always, critics of fractional reserve banking are more worried about the macroeconomic implications of the system. In particular, the impact of fractional reserve banking on the quantity of money and the price level.

With 100 percent reserve banking, the quantity of money is equal to the quantity of tangible hand-to-hand currency. It is possible to divide that into the currency held by the nonbanking public and their deposits in the bank. From the point of view of ordinary households and firms, they have currency that they can use to make payments and they have "deposits" at the bank which they can use to make payments. But since the banks "back" the deposits with currency reserves, either held in their own vaults or in the vault of the clearinghouse, the total amount of money is unchanged whether it is in the bank or out of the bank.

Now, suppose one of those banks makes its first loan. It puts currency in a suitcase and delivers it to a borrower. Immediately, the borrower has the currency. But the depositor still has the money in his or her deposit account. The total quantity of paper currency is unchanged, but both the depositors at the bank and the borrower are using it some of it. This situation is considered inherently fraudulent by some critics of fractional reserve banking. In their view, the two people "own" the same money, which is impossible.

Regardless of this "ownership" issue, money can no longer simply be identified with the quantity of paper currency. The quantity of paper currency held by the nonbanking public--households and firms including the borrower, plus the total of bank deposits held by the nonbanking public is the quantity of money. Since the depositors at the bank still have an unchanged quantity of deposits, and the borrower now has some of the currency that was held at the bank, the loan has increased the quantity of money.

Since banks have access to the payments system, they don't need to make loans by paying out currency. A more reasonable and realistic scenario is for a bank to make a loan by creating a deposit for the borrower. The borrower can then spend the loan by writing checks or making electronic payments.

The impact on the quantity of money is the same. All of the depositors still have their deposits, there is also no change in the currency held outside the banking system that remains in the hands of households and other businesses, but now the borrower has a new deposit. This is new money created by the bank. The total quantity of money increases exactly as before--increased by the amount of the loans.

Rather than some strained interpretation where the "real" money, the currency, is somehow doing double-duty and two people "own" it at the same time, this more realistic scenario points to the real situation, the banking system has created new money. If, for some reason, a bank did lend out currency, then the bank has created an equivalent portion of the deposits.

Why is the creation of money by bank a problem? It is because an increase in the quantity of money, ceteris paribus, reduces the purchasing power of money. This means, ceteris paribus, the money prices of goods and services rise. All of those who were holding money will, in the end, have a smaller command over goods and services.

Ceteris paribus means "other things begin equal," and perhaps the most important thing that must be equal is the demand for money, the amount of money people choose to hold. If a bank were to create money, and at the same time, the demand for money had risen the exact same amount, then the purchasing power of money and so, the prices of goods and services would remain unchanged.

However, many critics of fractional reserve banking would correctly point out that the increase in the quantity of money created by banks results in the purchasing power of money being lower than it would have been regardless of what is happening to the demand for money. And if the demand for money happened to be rising as least as much as the bank-instigated increase in the quantity of money, then those holding money are robbed of their rightful real gain from money holdings.

So, money creation by banks creates a problem. And they create this problem by lending out reserves. If the banks don't create the problem, and simply hold the reserves, then they have a 100 percent reserve ratio. There is a currency reserve backing 100% of the deposits. The reserves are 100 percent of deposits. The smaller the fraction (less than one) that banks keep, the greater the problem that banks are creating. So, banks that keep 90 percent reserves create a small problem. Banks that keep 10 percent reserves, create a bigger problem.

Understanding patterns that are the unintended consequence of individual action is the key subject matter of economic science. Economists have long understood that "money warehouses" that start to create money by lending reserves interact in a way that has the unintended consequence of "multiplying" their efforts.

For example, if an individual bank keeps a 50 percent reserve, then it would appear that it would increase the quantity of money by 50 percent of the amount of initial deposits. If all the banks do this, then the total quantity of money should be increased by the banking system by 50 percent of the deposits.

However, this is a fallacy of composition. If banks created money for borrowers, and they simply held it, then this would be true. However, borrowers generally spend what they borrow, and those selling to the borrowers typically deposit the funds they receive in some bank, which creates new deposits for banks to lend out.

If there are more than a handful of banks, any one bank that creates a deposit for a borrower, must expect that the borrower will soon spend the funds. Those selling to the borrower will deposit the funds in other banks. The other banks will deposit the sellers' checks at the clearinghouse, and the clearinghouse will debit the banks' balance there. The individual bank gives up reserves when it makes a loan. With electronic payments, the borrowers payment signals the clearinghouse to decrease the reserve balance of the bank making the loan and increase the reserve balance of the seller's bank--the bank whose customer is selling goods or services to the borrower.

If these sellers' banks keep 100 percent reserves, nothing more happens. But if they habitually lend out part of their reserves, then it is likely that they will respond to the increased deposits by their customers who received payment for added sales, by expanding their lending as well.

If all banks keep the same fraction of reserves to deposits, then very simple algebra can be used to find a deposit multiplier, which is ratio of deposits to reserves (D/R). It is simply 1/r, where r is the reserve ratio.

So, if banks keep 80 percent reserves, and lend out 20 percent of their deposits, then the multiplier will be 1/.8 or 1.25. While each bank directly creates money equal to 20 percent of deposits, their interaction creates 25% additional deposits.

While that isn't too significant of a difference, consider a 50% reserve ratio. Then the multiplier for deposits is 1/.5 or 2. While each bank directly creates new money by making making loans with newly created deposits equal to 1/2 of its existing deposits, which would suggest a new level 1.5 times the initial level, the interactions of the banking system doubles the amount of deposits.

With a 10 percent reserve ratio (the legal minimum in the U.S. today,) then this simple multiplier is 1/.1 = 10. While each bank creates new money equal to 90% of its deposits, suggesting they would slightly less than double the amount of money, the increase is tenfold!

Of course, the problem created by fractional reserve banking is the creation of new money, and deposit money is only one type of money. Given the "power" of thinking about simple ratios, many economists have suggested that perhaps the amount of currency that firms and households keep outside of the banks is a simple ratio of the amount the keep in the banks. In other words, the proportions of currency and deposits people keep remains constant as the total quantity of money, currency plus deposits, change.

Assuming that the currency/deposit ratio remains constant, simple algebra shows that the money multiplier, the ratio of both deposits and currency held by firms and households to the total amount of currency plus bank reserves is equal to (1+c)/(c+r), where c is the ratio of currency to deposits and r is the ratio of reserves to deposits.

If the banks keep 100% reserves, then r equals one, so (1+c)/(c+1) = 1. The total amount of money is equal to the currency held by the public plus the reserves of the banks. In the scenario here, that would be their vault cash plus the currency they have deposited at the clearinghouse. The total quantity of money would equal the total quantity of paper currency. By keeping 100 percent reserves, the banks have no impact on the total quantity of money. Other things being equal, they are not creating new money and causing inflation.

Suppose, instead, that households and firms keep $8 of currency for every $10 of deposits, and banks keep a 10 percent reserve. The money multiplier is (1+.8)/(.8+.1) or 1.8/.9 or 2. The result is that the banking system doubles the quantity of money. Other things being equal, fractional reserve banking would half the purchasing power of money and double the price level!

If one imagines going from 100 percent reserves to 10 percent reserves with a step by step process over time, then banks are making loans, and receiving deposits and making new loans. As this expands the total quantity of money (and spending and prices) there is a greater demand for currency and so some currency is withdrawn from the banks and held directly, but most is deposited and lent again. This process looks suspiciously like some kind of "credit bubble," that is liable to burst!

Most concerned about instability of fractional reserve banking are concerned about changes in the money multiplier. If banks keep 100 percent reserves, the money multiplier is one. It is also one if no one keeps any money in banks. The formula is a bit awkward for that scenario, because as people hold more currency and less deposits the ratio grows progressively larger. Unfortunately, when deposits equal zero, then it becomes undefined. However, using limits, (c+1)/(c+r), approaches one as c approaches infinity. So, if no one uses banks, then the quantity of money is again equal to the amount of paper currency. (Of course, that is obvious without appealing to the equation or limits. No banks, and no impact of banking on the quantity of money.)

And so, the story would be that when times are good, people trust banks and the currency deposit ratio falls. Further, banks seeing strong prospects for loans and having little reason to worry that their depositors will pull out their money, they reduce their reserve ratio. With the reserve ratio less than one, (c+1)/(c+r) rises with a lower value for c. More currency is put into the banks, and so, more money created by the banks. With r in the denominator, a lower reserve ratio also results in the banks creating more money. And, of course, the additional money created by the banks is matched by increased lending.

In bad times, everything goes into reverse. The banks, worried about bad loans, may reduce lending and increase reserve ratios. Depositors, worried about their banks failing, withdraw currency, raising the currency deposit ratio. Banks, worried that their depositors might withdraw currency, raise their reserve ratios to have vault cash to pay out. Worse still, since banks only have fractional reserves, and are generally obligated to pay off depositors on demand as long as they have reserves, they may face runs. Depositors, worried about bank losses may try to withdraw money first, before the bank runs out of reserves. All of these various worrisome processes reduce the money multiplier and cause the quantity of money to fall.

The conjectural history by which banks began has money warehouses and then began to lend out part of the money they stored, makes "Fractional Reserves" an important aspect of banking. That banks keep "fractional" rather than 100 percent reserves gives them special macroeconomic import, and changes in the exact fraction of reserves banks hold determine the size of that macroeconomic import.

Does this account of banking make sense in the context of the other conjectural history of banking? Suppose banks begin as financial intermediaries, borrowing money and then lending that money out. Can such banks borrow by issuing monetary instruments? Are fractional reserves and a multiplication processes a useful way to describe the operations of such a system? Those issues will be explored in Fractional Reserve Banking 2.


  1. For a short time, I accepted the Austrian critique of fractional reserve banking, but, given further analysis, it seems quite beautiful.

    When discussing the multiplier effect of fractional reserve banking on the money supply, few critics seem to appreciate that it occurs over time.

    There is a temporal integrity to the spending that ensures that "savings" (i.e. money not currently being spent) are continually redeploying resources to the production of future goods and services.

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