❔ Frequently Asked Questions (FAQs)

Note: some of these questions were actually asked during the following lecture when homework was assigned. However, they actually relate to topics from this lecture, so I’ve put them here. Let’s master them now, so we can get ahead!

Can you clarify how the reserve ratios relate to Checking Deposits, Vault Cash, Deposits at the Fed, Required Reserves, Excess Reserves, and Deposits at the Fed?

The reserve ratios are about total reserves and checking deposits. A reserve ratio of 10% means that for every $100 of checking deposits, the bank holds $10 of “reserves.”

These reserves don’t have to be vault cash, because deposits at the Fed (ie the central bank) are also counted as reserves. We count deposits at the Fed as reserves because deposits at the Fed are a great substitute for Vault Cash (they can be withdrawn quickly as cash).

An example may help. Suppose the required reserve ratio is $\text{R} = 0\%$ and the excess reserve ratio is $\text{E} = 12\%$. This means that, for every $100 of money that customers have as deposits at the bank, the bank keeps $12, either as vault cash or as deposits at the Fed. For example, if a bank has $100M of customer deposits, it may keep $3M in its vault and $9M in its deposit account at the Fed.

Note that there doesn’t need to be any correlation between Vault cash and required or excess reserves. Suppose, as above, that a bank has $100M of customer deposits, $3M in it’s vault, and $9M in its deposit account at the Fed. However, suppose that $\text{R}=10\%$. In this case, the bank is required to hold $10\% \times \$100\text{M}=\$10\text{M}$ of total reserves. Because it has $12M in total reserves, it has $2M of excess reserves, above what it is required to hold. These excess reserves account for $\frac{\$2\text{M}}{\$100\text{M}}=2\%$ of its total deposits, so $\text{E}=2\%$. Note that the dollar amount of Vault Cash ($3M), Deposits at the Fed ($9M), Required Reserves ($10M), and Excess Reserves ($2M) are all completely independent.

The Fed sets R and the banks determine how many excess reserves they want to hold (ie they set E).

This is all summarized with the following equations:

$\$\text{Total Reserves} = \$\text{Required Reserves} + \$\text{Excess Reserves}$

$\$\text{Total Reserves} = \$\text{Vault Cash} + \$\text{Deposits At Fed}$

Are reserves held against Savings deposits?

No, but don’t overstress about the distinction because it’s just not that important either in this class or in the financial system.

$\text{R} = \frac{\text{Required Reserves}}{\text{Checking Deposits}}$, the percentage of their transaction deposits that banks are (were) required to hold.

$\text{E} = {\text{Total reserves}} - \frac{\text{Required Reserves}}{\text{Checking Deposits}}$, the percentage that banks hold over and above the percentage they are required to hold.

(From Bruce via email)

Vault Cash on a Bank’s Balance Sheet - that does or does not get included in the calculation of Reserve Requirements?

Yes and no. The amount of reserves a bank is required to hold is calculated by multiplying the bank’s deposits by R:

$\$\text{Required Reserves} = \$\text{Deposits} \times \text{R}$

This makes sense because, as we saw last week, one of the main reasons why banks need reserves is because they have massive amounts of deposits, and those deposits may be withdrawn at any time. Likewise, the owner of the deposit might write a check and then reserves will likely be needed to be sent to the other bank where the check is cashed. Bottom line: keeping 10% of your deposits as reserves is a good heuristic.

Historically, R was 10%, but banks have been holding so many excess reserves that the Fed decided to drop the reserve requirement entirely. This means that, these days, $\text{R}=0\%$.

While Vault cash doesn’t count toward the amount of reserves a bank is required to hold, they do count as reserves themselves. As I emphasized in the last lecture, both vault cash and Deposits at the Fed count as reserves:

$\text{Total Reserves} = \text{Vault Cash} + \text{Deposits at the Fed}$

Does Money Supply include Reserves?

No, the money supply is defined in this class essentially as M1. So whenever he mentions the money supply, you want to recall the following slide:

To be completely clear: $\text{M1} = \text{“The Money Supply."}$

According to the slide, $\text{M1} = \text{Cash in the hands of the public} + \text{deposits}$

$\text{Money Supply} = \text{CHP} + \text{Deposits}$

Suppose the public holds $20 of cash. What is the Money Supply?

$$\begin{aligned} \text{Money Supply} &= \text{CHP} + \text{Deposits} \\ \$20 + \$100 &= \$120 \end{aligned}$$

Are money stock and money supply the same thing?

YES

How do you calculate the new equilibrium money supply?

There are several ways. The most common way is that you are given or can calculate the old money supply and you add the change in the money supply ($\Delta$ MS).

To calculate the old money supply, you can often just calculate the total deposits in the economy and the total cash held by the public.

What does “the public holds no cash” mean?

It means “Cash Held by the Public” (CHP) is $0.

What is going on with the Money Multiplier. I don’t get it!! Also, what are total deposits?

Total Deposits are the total amount of deposits in the entire economy, measured in dollars. The money multiplier explains how when someone deposits a small amount of money, it can cause large changes in the total amount of deposits in the economy.

What happens if all consumers want to withdraw money at the same time?

The bank is shut down and taken over by the FDIC because the bank cannot meet its legal responsibility to allow people to withdraw their money.

The bank’s customers may be terribly inconvenienced by this, because their money could be locked up and hard to access. As a result, many of them may try to withdraw all of their money all at once if they think this might happen. This is known as a bank run.

This process can be so destructive that it can make customers at other banks nervous. When this happens, it is known as a “banking panic.” The good news is that the US (and, I suspect, most developed nations) have been relatively free of banking panics among depository institutions for about 80 years because of reserve requirements and the FDIC. The only exception is the financial crisis of 2007-2009. It had terrible consequences, but the bank runs occurred at some of the most famous Wall Street investment banks rather than depository institutions.

What changes now that $\text{R}=0$?

Not much. If you look at the formulas, what matters is $\text{R}+\text{E}$. In the last several years, R decreased, but E increased to make up the difference. As a result, $\text{R}+\text{E}$ didn’t change significantly, so the total deposits in the economy kept growing at the same pace.

Bottom line: $\text{R}+\text{E}$ is all that ever matters.