In some simplified expositions, the monetary multiplier is presented as simply the reciprocal of the reserve ratio, if any, required by the central bank.
Historically, some central banks have tried to conduct monetary policy by targeting the money supply and its growth rate, particularly in the 1970s and 1980s.
The results were not considered satisfactory, however, and starting in the early 1990s, most central banks abandoned trying to steer money growth in favour of targeting inflation directly, using changes in interest rates as the main instrument to influence economic activity.
As controlling the size of the money supply has ceased being an important goal for central bank policy generally, the money multiplier parallelly has become less relevant as a tool to understand current monetary policy.
It is still often used in introductory economic textbooks, however, as a simple shorthand description of the connections between central bank policies and the money supply.
The money multiplier is normally presented in the context of some simple accounting identities:[1][2] Usually, the money supply (M) is defined as consisting of two components: (physical) currency (C) and deposit accounts (D) held by the general public.
As the relation is an identity, it holds true by definition, so that a change in the money supply can always be expressed in terms of these three variables alone.
[1] If, however, one additionally assumes that the two ratios C/D and R/D are exogenously determined constants, the equation implies that the central bank can control the money supply by controlling the monetary base via open-market operations: In this case, when the monetary base increases by, say, $1, the money supply will increase by $(1+C/D)/(R/D + C/D).
In some textbook applications, the relationship is simplified by assuming that cash does not exist so that the public holds money only in the form of bank deposits.
[4] Generally, the currency-deposit ratio C/D reflects the preferences of households about the form of money they wish to hold (currency versus deposits).
[10][11] The insight that banks may adjust their reserve/deposit ratio endogenously, making the money multiplier unstable, is old.
For in the middle of a deep depression just when we want Reserve policy to be most effective, the Member Banks are likely to be timid about buying new investments or making loans.
Moreover, the public’s choice of the currency/deposit ratio depends negatively on market rates of return on highly liquid substitutes for currency; since the currency ratio negatively affects the money multiplier, the money multiplier is positively affected by the return on these substitutes.
[13] An alternative interpretation of the direction of causality in the identity described above is that the connection between the money supply and the monetary base goes from the former to the latter: Interest-rate-targeting central banks supply whatever amount of reserves that the banking system demands, given the reserve requirements and the amount of deposits that have been created.
[16] Whereas used in many textbooks, the realism of the money multiplier theory is questioned by several economists, and it is generally rejected as a useful description of actual central bank behaviour today, partly because major central banks generally have not tried to control the monetary supply during the last decades, hence making the theory irrelevant, partly because it is doubtful as to how large an extent the central banks would be able to control the money supply, should they wish to.
[19] In the United States, short-term interest rates became fourfould more volatile during the years 1979-1982 when the Federal Reserve adopted a moderate version of monetary base control, and the targeted monetary aggregate at the time, M1, even increased its short-term volatility.
[1] Starting in the early 1990s, a fundamental rethinking of monetary policy took place in major central banks, shifting to targeting inflation rather than monetary growth and generally using interest rates to implement goals rather than quantitative measures like holding the quantity of base money at fixed levels.
[1] Also David Romer notes in his graduate textbook "Advanced Macroeconomics" that it is difficult for central banks to control broad monetary aggregates like M2, causing central banks generally to assign the behaviour of the money supply an unimportant role in policy, focusing instead on adjusting nominal interest rates to stabilize the economy.
[22] Gregory Mankiw, author of one of the widely read intermediate textbooks (Macroeconomics) that present the money multiplier theory, notes in its 11th edition that even though the Federal Reserve can influence the money supply, it cannot control it fully because households' decisions and banks' discretion in the conduct of their business may change the money supply in ways unanticipated by the central bank.
The Federal Reserve in 2021 launched several educational resources to facilitate teaching the conduct of current monetary policy, recommending teachers to avoid relying on the money multiplier concept, which was described as obsolete and unusable.
[26][21][27] Jaromir Benes and Michael Kumhof of the IMF Research Department, argue that: the "deposit multiplier" of the undergraduate economics textbook, where monetary aggregates are created at the initiative of the central bank, through an initial injection of high-powered money into the banking system that gets multiplied through bank lending, turns the actual operation of the monetary transmission mechanism on its head.
The authors therefore argue that private banks are almost fully in control of the money creation process.
; suppose the demand for funds is unlimited; then the theoretical superior limit for deposits is defined by the following series: .
The process described above by the geometric series can be represented in the following table, where This re-lending process (assuming that no currency is used) can be depicted as follows, assuming a 20% reserve ratio and a $100 initial deposit: Note that no matter how many times the smaller and smaller amounts of money are re-lended, the legal reserve requirement is never exceeded - because that would be illegal.