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Zombie Concepts: The Money Multiplier

The money multiplier is a theory on the link between the quantity of base money (central bank reserves) to the quantity of broad money (bank deposits, currency) in the financial system. In this theory, the central bank adjusts the level of base money in the system, which gives commercial banks greater room under their reserve ratios to lend, which then increases the quantity of broad money. This sounds reasonable, but is inaccurate because commercial banks (and the banking system as a whole) are never constrained by reserves in their lending – they can always borrow more reserves, manage their liabilities differently, or evade regulations by moving their activity off-shore. In this post I’ll show why there is no such thing as a money multiplier.

Carpenter and Demiralp (2012)

What is the Money Multiplier?

The textbook version of the money multiplier taught in undergraduate courses suggest that increasing central bank reserves gives commercial banks more room under their reserve ratios to lend. If banks are required to hold 10% of central bank reserves against their deposits, then increasing the reserves held by commercial banks by $100 would increase the money supply by $1000 as those reserves were multiplied through fractional reserve banking.

But as clearly shown from the first chart (excerpted from an excellent paper on the subject by Carpenter, a former Fed Official who is now Chief U.S. Economist at UBS) – M2 money supply appears to have little relation to reserve levels (Note: reserve requirements can be met with reserves or vault cash. That is why there is a gap between required reserves and total reserves). In the post-QE world, where reserves are in the trillions, there also does not appear to be a boom in bank lending. The money multiplier is clearly non-existent. But why?

Banks Can Avoid Reserve Limitations by Borrowing from Another Bank

If a bank were ever to find it self in need of reserves, it can easily go to the market and borrow reserves from another bank. The market where banks take out an overnight loan of reserves from another bank is called the Federal Funds market. In the pre-QE and pre-Basel III era that market was deep and robust (it is now a dead market because Basel III regulations discourage banks from borrowing from each other). There is no good public data on the Federal Funds market back then, but the interbank loan chart above is a good proxy that shows volumes to be in the hundreds of billions. In an emergency, the bank can also borrow from the Fed via the Discount Window.

A bank deciding to make a loan would never be limited by reserves, but it could be limited by the cost of the borrowing reserves. For example, if a borrower is only willing to borrow from a bank at 5%, and the Federal funds rate is 4%, then it may not make sense for the bank to make that loan. Monetary policy controls credit via the cost of money (interest rates), not through the quantity of reserves.

Banks Can Avoid Reserve Limitations through Liability Management

Banks have many different types of deposits on their balance sheet, and some of them are not subject to reserve ratios. Reserve ratios are designed to make sure that a bank is able to meet withdraws, so it tends to be applied to deposits that can be withdrawn at any time, like checking account deposits. On the other hand, time deposits such as long term CDs to institutional investors cannot be withdrawn by the depositor at any time, but only when the CD matures. The bank is not required to hold reserves against those deposits.

In the example above the Bank A and Bank B each make $900 in loans, but Bank A is required to hold $100 in reserves against its $1000 in checking deposits (assume a 10% reserve ratio). On the other hand, Bank B only needs to hold $50 in reserves because it only had $500 in checking deposits. The rest of the loan is funded by issuing long term CDs issued to institutional investors, which it is not required to hold reserves against. Note Bank B will likely have to pay a higher interest rate on the 1 year CD than the checking account deposit.

Banks Can Avoid Reserve Limitations by Moving Deposits Off-Shore

Dollar deposits held in off-shore branches of U.S. banks (“Eurodollars”) have historically been subject to lower reserve requirements than on-shore deposits. Note that the reserve ratios for Eurodollars have been adjusted through time, but have been 0 for U.S. banks since 1990.

The tables below shows how booking deposits off-shore can change the liability profile of a U.S. bank. In the first table, the bank has $100 million in deposit liabilities, in the second table it reduced those deposit liabilities by moving $10 million in deposits to its London branch, and then borrowing it back. Overall, the bank’s balance sheet size hasn’t changed. The bank simply reshuffled its liabilities to take advantage of lower reserve requirements for off-shore deposits.

from The Euro-Dollar Market: Some First Principles, Milton Friedman 1971

This off-shore/on-shore regulatory arbitrage was one of the drivers in the growth of the off-shore dollar banking system in the 1960-70s. (Note: Exemption from Regulation Q was also a major driver of moving dollars off-shore. Regulation Q put a ceiling on the interest rates banks could pay their on-shore deposits. In response, banks simply began moving their deposits off-shore where they could pay market rates. Reg Q restrictions ended in 2011 ).

Reserve Ratios Don’t Even Exist Anymore

On March 15, 2020, the Fed announced that they would reduce reserve ratios to 0. Under the money multiplier theory an infinite reserve ratio would imply infinite amount of lending, but of course nothing like that happened. Banks tightened their credit standards amidst the prospect of a recession.

Reserve ratios were not just about the making sure banks could meet withdraws, but also an important part in the Fed’s former “scarce reserve” monetary framework. In the pre-QE low reserve world, the Fed controlled interest rates by adjusting the quantity of reserves in the system. The demand for reserves was largely inelastic and determined by the reserve ratio. The Fed could move the Federal Funds rate by adding or subtracting a few hundred million in reserves every day to influence the Federal Funds rate. In the post-QE world the Funds rate is controlled by adjusting the offering rate of the Reverse Repo Facility, and the interest rate offered on reserves.

By setting the reserve ratio to 0, the Fed acknowledges that the ratio has no role to play in the modern banking system. Banks have huge amounts of reserves and thus there is no fear of them unable to meet withdraws. The Fed also does not control rates by adjusting the quantity of reserves anymore.

The money multiplier never existed at all, but a 0 reserve ratio should put the idea completely to rest.


  1. TB

    “The Fed also does not control rates by adjusting the quantity of reserves anymore.”
    Should this not be read as:
    “The Fed also CAN not control rates by adjusting the quantity of reserves anymore.”?

    There are so many reserves in the system now that the average price (under the old system) is effectively zero, but the FED doesn’t want to show it has lost control?

    • Fed Guy

      You are correct. It is no longer possible for the Fed to control rates by adjusting the quantity of reserves. But that does not mean it has lost control – just that overnight rates are controlled using a different system. Note that each time the Fed funds rate was too low or too high over the past few years the Fed was able to move it by simply adjusting interest on reserve by a few basis points.

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