The Banking System: The Reserve Multiplier

The Reserve Multiplier For the entire banking system, an injection of $8 million in new excess reserves can be used to support a maximum of $40 million in new deposits when the required reserve ratio is 0.2! An individual bank can create no more checkable deposits than the amount of excess reserves it acquires. However, the entire banking system can create new checkable deposits that amount to a multiple of the initial injection of excess reserves into the banking system. Any individual bank is likely to lose the excess reserves it acquires when it creates a checkable deposit for a loan customer. However, except for currency withdrawal, the excess reserves are not withdrawn from the banking system. When the new checkable deposits are deposited in another bank, that bank also acquires reserves of which another 80 percent can be loaned out. Notice that the money creation process is just like the one described for the multiplier effect in the chapter on Keynesian analysis. The maximum amount of new checkable deposits that can result from a new injection of excess reserve dollars into the banking system can be expressed as an infinite geometric progression. After the $8 million in initial deposits created by the initial injection of new excess reserves, the second-round maximum of new deposits that can be created by the Detroit bank is $6.4 million. The $6.4 million can be expressed as (0.8) ($8 million). Similarly, the $5.12 million maximum of new deposits that can be created at the third stage by the New York bank can be expressed as 0.8 [0.8($8 million)], which equals (0.8)($8 million). In the same way the $4.10 million in maximum checkable deposits that can be created at the fourth stage by the Chicago bank, assuming it loans out all its newly acquired excess reserves, can be expressed as (0.8) (S8 million). The infinite geometric progression is: As the sum continues, each successive term becomes smaller, because when any number less than 1 is raised to a higher power it becomes smaller. The maximum possible increase in checkable deposits, and hence the money stock (AM), resulting from the initial increase in excess reserves for the banking system can be calculated by using the following formula to solve for the sum of an infinite geometric progression: where AER is the change in excess reserves for the banking system. In this example, AER is $8 million, which represents the increase in excess reserves resulting from an initial $10 million deposit of currency into the banking system. The maximum increase in the money stock resulting from new checkable deposits that can be created from this amount of excess reserves is therefore When the required reserve ratio is 0.2, each dollar of excess reserves that enters the banking system can support five times as much in new checkable deposits when banks find it profitable to loan out all their excess reserves at each stage of the process. Under these circumstances an injection of $8 million in new excess reserves into the banking system can therefore ultimately support $40 million of new money stock in the form of checkable deposits. The reserve multiplier is the maximum amount of new money stock that can be created from each dollar increase in excess reserves available to the banking system. In the example just given the reserve multiplier was 5. In general the reserve multiplier can be calculated simply by dividing the number 1 by the required reserve ratio: In this case the reserve multiplier is If the required reserve ratio were 0.1 instead of 0.2, the reserve multiplier would be increased to The maximum amount of new checkable deposits, AM, that can result from any increase in excess reserves can also be expressed as: This gives the amount of checkable deposits that the banking system can create from any increase in excess reserves when all excess reserves are loaned out and there is no withdrawal of currency from the banking system. In the previous example the maximum increase in checkable deposits is 5 times $8 million, which is $40 million. Notice that the maximum possible increase in the money stock depends on both the excess reserves injected into the banking system and the required reserve ratio. Other things being equal, the larger the increase in excess reserves or the lower the required reserve ratio, the greater the increase in the money stock. The actual increase in the money stock depends on the willingness of banks to lend out excess reserves they acquire as a result of the money creation process and the amount of loan proceeds that end up in other banks (that is, the public's taste for currency). Thus the preceding equation represents the maximum possible creation of deposits; in reality, the amount of money created will be less than is implied by the formula. As a further illustration of the way to use the formula, suppose the Denver bank borrows $5 million from its district Federal Reserve bank. When it does, the Denver bank's account at the district Federal Reserve bank will be credited by $5 million. This $5 million represents new bank assets in the form of reserves that are balanced by a liability in the form of a $5 million debt to the Federal Reserve. Since no new deposits were acquired, the entire $5 million becomes excess reserves for the Denver bank. Assuming a required reserve ratio of 0.1, the maximum increase in the money stock that can result from the Denver bank's loan from the Federal Reserve is: Assuming that banks find it profitable to loan out all excess reserves at each stage of the money creation process, a $5 million loan to a bank by the Federal Reserve Bank will increase the money stock by $50 million.