Skip to main content
← Back to M Definitions

Money multiplier

What Is Money Multiplier?

The money multiplier is a concept in monetary economics that illustrates how an initial deposit in a banking system can lead to a larger overall increase in the total money supply. It demonstrates the theoretical maximum expansion of the money supply in an economy due to a change in the monetary base. This process is primarily facilitated by fractional reserve banking, where commercial banks hold only a fraction of their deposits as reserves and lend out the rest. The money multiplier helps explain the relationship between the central bank's actions and the broader economy's money supply.

History and Origin

The concept of the money multiplier is rooted in the historical development of banking, particularly the evolution of fractional reserve banking. This practice emerged centuries ago when goldsmiths, who held gold for safekeeping, realized that not all depositors would demand their gold back at the same time. They began lending out a portion of the gold deposits, generating income through loans and effectively expanding the amount of money in circulation beyond the physical gold held.29, 30

As financial systems matured, the role of a central bank became crucial in regulating this process. In the United States, for instance, the National Bank Act of 1863 formalized reserve requirements for nationally chartered banks, mandating them to hold a certain percentage of deposits in reserve.28 While these initial requirements aimed to protect depositors and ensure convertibility, they also inherently established the framework within which the money multiplier could operate. The theoretical understanding of how banks could "multiply" money through sequential lending and redepositing became a cornerstone of classical monetary theory, often taught in introductory economics to illustrate the mechanics of money creation.26, 27

Key Takeaways

  • The money multiplier describes the potential for an initial increase in the monetary base to generate a larger increase in the overall money supply.
  • It operates within a fractional reserve banking system, where banks lend out a portion of their deposits, leading to new deposits and further lending.
  • The simplified money multiplier formula is the reciprocal of the reserve ratio, highlighting the inverse relationship between reserves and money creation.
  • While a foundational concept, the real-world application of the money multiplier has diminished, especially since the 2008 financial crisis, due to factors like excess reserves and changes in central bank monetary policy frameworks.
  • It provides a theoretical framework for understanding the potential impact of central bank actions on money supply, but its predictive power in modern economies is limited.

Formula and Calculation

The simplified formula for the money multiplier ((m)) is based on the reserve requirements set by a central bank. It is calculated as the reciprocal of the reserve ratio ((RR)):

m=1RRm = \frac{1}{RR}

Where:

  • (m) = Money Multiplier
  • (RR) = Reserve Ratio (the fraction of deposits that banks are required to hold in reserve)

This formula suggests that for every unit of initial deposit, the money supply can theoretically expand by a factor of (m). For example, if the reserve ratio is 10% (0.10), the money multiplier would be (1 / 0.10 = 10). This implies that an initial deposit of $100 could lead to a total money supply expansion of $1,000 within the banking system.

Interpreting the Money Multiplier

The money multiplier serves as a theoretical measure illustrating the maximum potential expansion of the money supply given a certain reserve ratio in a fractional reserve banking system. A higher money multiplier indicates that a given change in the monetary base can lead to a larger change in the overall money supply, suggesting greater leverage for central bank actions aimed at influencing economic growth or controlling inflation. Conversely, a lower multiplier suggests a more limited expansion.

However, the interpretation must account for real-world complexities. The simple formula assumes that banks lend out all of their excess reserves and that all loaned money is redeposited within the banking system. In reality, banks may choose to hold more reserves than required, and individuals may hold cash outside the banking system, which reduces the actual multiplier effect.

Hypothetical Example

Consider a simplified banking system where the central bank sets a reserve ratio of 10%. Suppose an individual deposits $1,000 in cash into Bank A.

  1. Initial Deposit: Bank A receives a $1,000 deposit.
  2. Required Reserves: Based on the 10% reserve ratio, Bank A must hold $100 in reserves ((10% \times $1,000)).
  3. Excess Reserves & Lending: Bank A now has $900 in excess reserves (($1,000 - $100)) that it can lend out. It approves a loan of $900 to a business.
  4. Second Deposit: The business uses the $900 loan to pay a supplier, who then deposits this $900 into Bank B.
  5. Bank B's Action: Bank B receives a $900 deposit. It keeps $90 in reserves ((10% \times $900)) and lends out the remaining $810.
  6. Continuing Cycle: This process continues. The $810 loan becomes a deposit in another bank, which then holds 10% in reserves and lends out 90% of that amount, and so on.

The total increase in the money supply from the initial $1,000 deposit can be calculated using the money multiplier: (1 / 0.10 = 10). Therefore, the initial $1,000 deposit has the potential to expand the total money supply by up to $10,000. Each step of lending and redepositing creates new deposits, thus expanding the money supply.

Practical Applications

Historically, the money multiplier has been a foundational concept in understanding how monetary policy could influence the money supply. Central banks, by adjusting reserve requirements, theoretically had a direct lever to control the amount of money banks could create through loans. For instance, lowering reserve requirements would increase the money multiplier, allowing for greater credit expansion and aiming to stimulate economic growth. Conversely, raising them would reduce the multiplier, contracting the money supply to combat inflation.

However, the practical application and relevance of the money multiplier in modern monetary policy have significantly diminished. Many central banks, including the U.S. Federal Reserve, have reduced reserve requirements to zero, effectively eliminating this policy tool.25 Furthermore, banks often hold substantial amounts of excess reserves, especially after periods of large-scale asset purchases (like quantitative easing), which complicates the direct link between the monetary base and the broader money supply.24

Modern central banks primarily influence the economy through managing interest rates and providing liquidity to the financial system, rather than relying on strict reserve requirements to control money creation.

Limitations and Criticisms

Despite its pedagogical value in illustrating the principles of fractional reserve banking, the money multiplier model faces significant limitations and has drawn considerable criticism, particularly following recent financial crises. One major critique is that it oversimplifies the complex process of money creation. The traditional model implies that the central bank directly controls the money supply by manipulating the monetary base and reserve requirements. However, in reality, commercial banks create money through lending, and they are not simply intermediaries constrained by pre-existing deposits.21, 22, 23

A key problem arose during the 2008 financial crisis and subsequent periods of quantitative easing. Despite massive increases in the monetary base, the broader money supply did not expand proportionally because banks chose to hold vast amounts of excess reserves.19, 20 This "collapse" of the money multiplier indicated that banks' willingness to lend and borrowers' demand for loans play a more significant role in money creation than the simple multiplier theory suggests.17, 18

Indeed, some argue that the money multiplier, as presented in many textbooks, "turns the actual operation of the monetary transmission mechanism on its head." Research from institutions like the Federal Reserve Bank of San Francisco contends that the tight link between reserves, money, and bank lending suggested by the multiplier "does not exist."16 Central banks, they argue, do not control the creation of money in the way the multiplier implies, nor do they try to.

The Federal Reserve itself reduced reserve requirements to zero in March 2020, further signaling the diminished practical relevance of this concept as a direct tool for monetary control.15

Money Multiplier vs. Quantitative Easing

While both the money multiplier concept and quantitative easing relate to the broader money supply, they describe different mechanisms and operate within distinct frameworks of monetary policy.

The money multiplier is a theoretical construct explaining how an initial injection of funds (part of the monetary base) can be "multiplied" into a larger total money supply through sequential lending and redepositing in a fractional reserve banking system. Its primary focus is on the role of reserve requirements and bank lending in creating money.

In contrast, quantitative easing (QE) is an unconventional monetary policy tool used by central banks to stimulate the economy, typically when traditional interest rates are near zero.14 During QE, a central bank purchases large quantities of financial assets, such as government bonds or mortgage-backed securities, from commercial banks and other financial institutions.12, 13 This action directly injects liquidity into the financial system by increasing the banks' reserves at the central bank.11 The aim of QE is to lower long-term interest rates, encourage bank lending and investment, and support asset prices.9, 10 While QE does increase the monetary base, it does not rely on the simple money multiplier mechanism to expand the broader money supply. Instead, it works by influencing financial conditions, encouraging portfolio rebalancing, and signaling the central bank's commitment to accommodative policy.8 The relationship between increased reserves from QE and bank lending has often been weak, as banks accumulated significant excess reserves rather than lending them out.6, 7

FAQs

How does a central bank influence the money multiplier?

Traditionally, a central bank could influence the money multiplier by setting or adjusting reserve requirements for commercial banks. Lowering the reserve ratio would theoretically increase the multiplier, while raising it would decrease it. However, many central banks, including the U.S. Federal Reserve, have eliminated or significantly reduced reserve requirements, making this direct influence largely theoretical in modern practice.5

What are the main limitations of the money multiplier concept?

The main limitations stem from its simplifying assumptions. It assumes banks lend out all excess reserves and that all money loaned is redeposited. In reality, banks may hold onto excess reserves, and the public may hold cash, which weakens the multiplier effect. Furthermore, it often overlooks the fact that banks create money by making loans, rather than simply lending out pre-existing deposits.3, 4

Does the money multiplier still apply in today's economy?

The theoretical framework of the money multiplier is still taught in some economic textbooks to explain the basics of money creation in a fractional reserve banking system.2 However, its practical relevance as a tool for monetary policy or a precise predictor of money supply changes has greatly diminished, particularly since the 2008 financial crisis and the shift to ample reserve regimes by many central banks.1