The Money Multiplier

The money multiplier is the ratio between base money and some broader measure of the quantity of money. Base money is the sum of currency held by the nonbanking public and reserves. Reserves are made up of vault cash, which is currency held by banks, and reserve balances. Reserve balances are funds that banks hold on deposit at the central bank, the Federal Reserve in the U.S. The nonbanking public is households and firms other than banks.

There are a variety of measures of the quantity of money. The M1 measure of the money supply is made up of checkable deposits, currency held by the public and travelers checks. The M1 money multiplier is the M1 measure of the quantity of money divided by base money.

Simple algebra shows that the M1 money multiplier is equal to (1+c)/(c+r), where c is the currency deposit ratio and r is the reserve deposit ratio. "Deposits" are understood as checkable deposits. Since those ratios can change, there is no reason to assume that the M1 money multiplier, or any of the other ones, such as the M2 money multiplier or the MZM money multiplier, are fixed.

Still, the algebra is interesting. For example, if households and firms choose to hold more currency or the banks choose to hold more reserves, the resulting increase in the demand for base money, will result in a decrease in the broader measures of the quantity of money unless offset by an increase in base money.

Old fashioned monetarists favored targeting some measure of the quantity of money. The rule of thumb was that any change in the relevant money multiplier should be offset by an inversely proportional change in base money. Since money statistics are generated weekly, monetarists generally saw little problem with making these adjustments in real time.

Monetarists were quite aware that this approach was inconsistent with having the central bank target interest rates. For example, if there was a increase in the demand for bank loans, then banks would have to raise interest rates charged on those loans. To some degree, this would reduce the quantity of the loans demanded, but it could also allow banks to obtain funds from some source not included in the target. For example, if M1 were being targeted, and banks increased the interest rates paid on time deposits and attracted additional funds they could expand the amount of bank loans without increasing M1.

Monetarists recognized that banks might choose to reduce their reserve balances to fund the additional loans. If higher interest rates could be earned on loans, this would provide an incentive to economize on reserve holdings. That would raise the money multiplier, and as explained above, the rule would require a contraction of base money to offset that, keeping the quantity of money on target.

It is even possible that those holding currency would choose reduce those holdings and instead hold interest bearing deposits. This could be checkable or not. Regardless, this would reduce the ratio of currency to checkable deposits, and so raise the money multiplier. Again, a target for the quantity of money would require that base money be reduced.

Monetarists have long been aware of interbank lending. And so, along with a higher demand for loans causing banks to seek to attract additional deposits to fund the loans, any one bank can fund its loans by borrowing from other banks. Not all banks can do this at once, and what happens is that the interbank loan rate rises along with interest rates on deposits.

Suppose that the demand for bank loans were to fall. If the quantity of money is targeted, then the interest rate on loans must fall too. This will increase the quantity of loans demanded, and so limit the decrease in the quantity of bank loans. However, with banks earning less on loans, they would pay less on deposits as well. If M1 is targeted, and the decrease in the interest rate paid on time deposits resulted in less funds being deposited in them, then both bank loans and time deposits would contract. Banks could also purchase securities like government bonds with funds that would have used for bank loans, lowering those interest rates as well.

Finally, banks would be more interested in lending to other banks overnight, and less interested in borrowing. This would result in a lower interest rate on the interbank loan market.

It is quite possible that because of low interest rates on deposits, people would choose to hold more currency. It is also possible that banks would choose to hold more reserves. These two effects would tend to lower the money multiplier. With a target for the quantity of money, the central bank would need to expand base money enough to offset that decrease.

For many years now, the Federal Reserve has targeted the Federal Funds rate. Monetarists have been quite aware that when an increase in the demand for bank loans results results in a shortage of funds on the interbank loan market, then if the Fed is targeting that rate, it expands base money. The quantity of money then rises above target.

Similarly, if there were a decrease in the demand for bank loans, and this results in a surplus on the interbank loan market, if the Fed is targeting that rate, it will decrease reserves, and prevent the interest rate from falling. The quantity of money would fall below target.

Monetarists never argued that the quantity of base money should be fixed. But they did say that it should not be changed to keep any interest rate, including the interbank loan rate, from changing. It was never the case that monetarists were unaware that the Federal Reserve adjusted the quantity of reserves to keep the interest rate on interbank loans at a targeted level. It is rather that they opposed that policy. They favored changing the quantity of base money according to a different principle--keeping some measure of the quantity of money on a targeted growth path.

Now, most economists do favor having central banks target interest rates. Traditionally, they argued that if there is a change in the demand to hold money, the liquidity effect would tend to change interest rates. For example, if there is an increase in the demand to hold money, then at least some of those short of money will sell securities, raising their yields. By targeting interest rates, the central bank would expand the quantity of money, by purchasing securities, dampening and reversing the increase in interest rates. The Fed would have increased the quantity of money enough to match the increase in the demand to hold money.

Because the interbank loan rate is tied to other interest rates, stabilizing the interbank rate tends to simultaneously adjust the quantity of money to the demand to hold money. Also, if there is some change in the desire to hold currency or reserve balances at any given interest rate, those changes will tend to cause changes in the interbank loan rate. For example, an increase in the demand for currency would draw down bank reserves and create a shortage on the interbank loan market. By expanding the quantity of reserves, the central bank automatically offsets the change in the money multiplier, leaving the quantity of money unchanged.

These arguments in favor of targeting interest rates are completely consistent with the monetarist account of the money multiplier. They just are inconsistent with the monetarist policy goal of keeping some measure of the quantity of money on target by adjusting base money according to changes in the money multiplier. By the way, the monetarist response to these arguments in favor of targeting interest rates is that changes in the demand for bank loans should result in changes in interest rates and not changes in the quantity of money. As I repeat over and over, an increase in the demand to borrow money from banks is not at all the same thing as an increase in the demand to hold money.

How is it that the quantity of money changes when there is an increase in base money? There is a terribly unrealistic story often told in introductory textbooks. The story starts with a bank having excess reserves. The bank lends those reserves out. The borrower spends the money and the sellers deposit the checks. The checks clear, and the bank that made the loan no longer has the excess reserves, but the bank used by the seller now has the excess reserves. It makes a loan, and so on. Assuming banks' demand for reserves increases with their supply of deposits, then the amount lent each time is smaller. The initial quantity of excess reserves is "multiplied" into many deposits and many bank loans.

Now, there is an element of truth to this account. If there is an excess supply of base money, there will be a tendency for banks to create credit. They don't necessarily have to make loans and instead can purchase existing securities--often government bonds, but possibly corporate bonds as well. With a bank loan, the story is that those borrowing the money spend it, and those selling to the borrowers deposit the check. This does result in shift of reserves between banks, but the total amount of reserves that banks have are unchanged. For the excess supply of base money to clear up, the demand for base money must rise. This could occur because with a higher quantity of deposits, banks demand higher reserve balances. It could be that people like to keep their total money holdings in fixed proportions between deposits and currency, and so more deposits increases the demand for currency.

In my view, by far the most important process is that the increase in deposits results in additional expenditures on output. The growing nominal income results in an added demand for currency and reserve balances.

Also, I often point out to my students that the simple story of banks making loans based upon their existing level of excess reserves is very unrealistic. Do banks put out a sign saying, "excess reserves available today, come get your loans?" In reality, banks set interest rates on both loans and deposits intending to use their deposits to fund their loans. In a growing economy, this generally involves setting interest rates on loans and deposits so that demand for loans from banks is matched by the supply of deposits to banks. The banks then use money market instruments to adjust for any temporary imbalances between the demand for loans and the supply of deposits. Higher loan demand would immediately result in banks selling off government bonds, reducing overnight lending to other banks, or borrowing more overnight from other banks. An increase in the supply of deposits would result in banks buying government bonds, reducing overnight borrowing from other banks, or lending more overnight to other banks.

This suggests that the immediate effect of any excess supply or demand for base money will directly impact money market interest rates. Only if those new rates are expected to persist would the result be changes in the interest rates that banks charge on loans and pay on deposits. And so, only if the change in money market rates are expected to persist would bank loans expand or contract.

With interest rate targeting, both the current level of money market rates and those expected in the future are going to be driven by current and expected future central bank policy. (Of course, I don't favor targeting interest rates or any measure of the quantity of money.)

Anyway, if a central bank wants to expand the quantity of money, it undertakes open market purchases. This creates an excess supply of reserves. Banks use the reserves to purchase money market instruments. The impact on overnight interbank loans just reduces the interest rates on those loans. Further, purchases of government bonds by banks from other banks has no impact on the quantity of money, and only results in lower interest rates on the bonds. However, purchases of government bonds from firms other than banks and households increases the funds in their checkable deposits, as well as lowering the interest rates. The increase in the checkable deposits of those households and firms other than banks is an increase in quantity of money.

Is this effort to increase the quantity of money consistent with keeping short term interest rates on some "target?" No, it is not. Does this effort to increase the quantity of money result in more bank loans? Perhaps not.

Suppose that the banks respond to lower interest rates on government bonds by selling them and instead just hold reserve balances. This is a decrease in the money multiplier, and tends to reduce the quantity of money. How then can a central bank expand the quantity of money? It buys all of the government bonds the banks want to sell, and also buys bonds from households and firms. And the result is an increase in the quantity of money. Base money expands enough to offset the decrease in the money multiplier and increase the quantity of money. Nothing in the process requires that banks make any loans.

What would be necessary for the simple textbook story of the money multiplier to be realistic? First, suppose that bank deposits take the form of hand-to-hand currency rather than interest bearing deposits. If that is true, there is little question of banks adjusting the interest rates they pay to obtain funding for loans. So, the "realistic" story where banks set the interest rates they charge and pay to match deposits and loans doesn't apply. Interest rates only apply to lending. Further, all of the banks' liabilities are monetary.

Second, suppose that usury laws create binding price ceilings on bank loans. At the legal maximum there is a shortage of loanable funds, and banks ration out the funds however they think best. A responsible approach would be to provide them to the best credit risks.

Third, suppose there are no good markets for money market instruments. Communications and transport are primitive. Bank asset portfolios are made up of reserves and loans. Bank liabilities are made up of deposits. And, of course, the bank owners have equity in the bank.

If a bank obtains added reserves, then the only options are to either hold them or else lend them. Because of the usury laws, there is a shortage of funds at the legal interest rate, and so no problem with lending out all the funds. Those borrowing the funds spend them, and the funds are mostly deposited in other banks, which then have excess reserves to lend. And so, there is a multiple expansion in the quantity of money, the banknotes, and in bank loans.

If banknotes are replaced with checking accounts that bear no interest by law, then the account changes little. It is only when we have a system where banks can use money market instruments to manage their reserves, and banks are funding their loans and securities portfolios with a variety of interest bearing deposits, does a quite different approach to understanding the banking business become reasonable. In particular, changes in the interest rates on money market instruments and the interest rates that banks pay and charge become very important for any reasonable account of the banking business.

Still, if there is an excess supply of base money, the result will be increased spending on something--goods, services, or perhaps just financial assets--until the demand to hold base money rises to meet the quantity. Unless, of course, the issuer of base money, the central bank, chooses, to to reduce the quantity of base money to prevent the effects of that expenditure. Interest rate targeting is an example of such a policy.