Here we add reserve requirements to
Example 1. To see the effects of capital requirements also, see
Example 3. Reserve requirements are regulatory requirements which stipulate that if a bank holds demand deposit liabilities (e.g. customer checking accounts), then it must hold at least some fraction of the dollar amount of these deposits as reserve assets. In the US this
fraction varies, but 10% is typical. Some countries, such as Canada, don't have reserve requirements (i.e. this percentage is 0). Reserve requirements have nothing to do with loan assets, thus you sometimes hear that "bank lending is not reserve constrained."
Regulatory capital requirements, however, do factor in the loan assets on a bank's balance sheet.
Setup: one central bank (CB), two commercial banks A and B, and one person x. Reserve requirements are 10% of deposits, but there are no capital requirements and everyone's balance sheet is initially clear (empty).
Initial balance sheets (for CB, A, B, and x):
CB, A, B, x
| Assets |
Liabilities |
| $0 |
$0 |
Balance sheets after x takes a $100 loan from A (note: I've chosen to show that A borrowed $10 in required reserves from the CB here):
Central Bank
| Assets |
Liabilities |
| $10 reserve loan to A |
$10 reserve deposit for A |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$100 deposit for x |
| $10 required reserves |
$10 reserve borrowing from CB |
Person x
| Assets |
Liabilities |
| $100 deposit at A |
$100 borrowing from A |
Balance sheets after x transfers deposit from Bank A to Bank B:
Central Bank
| Assets |
Liabilities |
| $10 reserve loan to A |
$100 reserve deposit for B |
| $90 reserve overdraft for A |
--------------------------- |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$90 reserve overdraft at CB |
| $0 reserves |
$10 reserve borrowing from CB |
Bank B
| Assets |
Liabilities |
| $100 reserves ($10 required) |
$100 deposit for x |
Person x
| Assets |
Liabilities |
| $100 deposit at B |
$100 borrowing from A |
Balance sheets after Bank A borrows $90 of reserves from Bank B and repays CB overdraft by the end of the day (note: Bank A could have borrowed from any other bank, or even the Central Bank's discount window, but I've chosen to show the case where it borrows from Bank B):
Central Bank
| Assets |
Liabilities |
| $10 reserve loan to A |
$10 reserve deposit for B |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$90 reserve borrowings from B |
| $0 reserves |
$10 reserve borrowings from CB |
Bank B
| Assets |
Liabilities |
| $10 required reserves |
------------------ |
| $90 loan of reserves to A |
$100 deposit for x |
Person x
| Assets |
Liabilities |
| $100 deposit at B |
$100 borrowing from A |
Note that instead of a deposit transfer we could easily modify this example to instead have person x purchase $100 worth of goods or services from another person with an account at Bank B as in
Example 1.1. In fact this would probably be more realistic since most loans are taken with the intention of making a purchase. This happens, for example, every time you swipe your credit card: your deposit is created and then transferred in one process. If buyer and seller use the same bank, then this deposit transfer does not require that any reserves be transferred (unlike what's illustrated in Example 1.1): instead one account is debited and the other credited.
Also note that Banks A and B can make money off of the spreads on their balance sheets. Bank A, if it receives more in interest from its loan to x than it pays to borrow reserves, and Bank B if it makes more from lending $90 of reserves than it pays on x's $100 deposit. Also, Bank B could potentially make interest on reserves (IOR) (if the CB pays that) on the remaining $10. Currently in the United States IOR > 0 (it's 0.25%). Again note that reserve requirements are not requirements on bank lending, but instead on the demand deposits held, thus they affect Bank B in this example (the ultimate deposit holder), rather than Bank A. Also in order for the CB to be willing to loan funds through its discount window, it requires collateral. It's possible that certain loans could be used for this collateral, but probably at a discount.
Suppose now that we continue to up the required reserves (RR) percentage beyond 10%. The money making potential for the lending bank doesn't fundamentally change as long as the CB continues its policy to meet the demand for reserves from the private banks. It's clear, however, that there is some effect on spreads for the deposit holding bank. In particular as the RR % rises, it may become more and more difficult for Bank B to make money on the spread, particularly if IOR isn't paid. In the extreme case (100% required reserves) we have the following resulting balance sheets:
Central Bank
| Assets |
Liabilities |
| $100 reserve loan to A |
$100 reserve deposit for B |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$100 reserve borrowing from CB |
Bank B
| Assets |
Liabilities |
| $100 required reserves |
$100 deposit for x |
Person x
| Assets |
Liabilities |
| $100 deposit at B |
$100 borrowing from A |
In this case, if Bank B doesn't earn IOR then it will need to charge x a fee to hold his deposit in order to have a money making spread on its balance sheet. As all banks would face similar circumstances, they would probably all have to charge a fee on deposits, unless they found that offering a free checking account was worthwhile for other reasons (e.g. as a convenience for customers). Also, since reserve requirements only affect demand deposits, a bank could also escape reserve requirements by convincing demand deposit holding customers to convert their demand deposits to time deposits (e.g. savings accounts or CDs).
The point is that a 100% reserve requirement does not necessarily stop the growth of private credit as long as the CB continues to meet the demand for reserves in the private banking system*. This is fundamentally why the "fractional reserve lending" concept and the related "money multiplier" concept don't really apply in a fiat money system where the CB is chartered with the responsibility to support the private banking system and defend an overnight interest rate**. It's even conceivable that the RR ratio could be greater than 100% in such a system. It's not that upping the RR ratio doesn't have any effect, it's that it doesn't necessarily preclude private credit growth. In order for that to be the case there'd have to be a fixed amount of reserves, such as was essentially the case under the gold standard. Also the requirement would have to apply to all deposits, rather than just demand deposits.
For an interesting discussion of what banks with 100% capital requirements might be like, look at
this Nick Rowe article.
*The CB may not be willing, however, to meet the demand for reserves if the collateral offered for discount window loans of reserves isn't adequate. Thus either large amounts of bank capital may be required, or extremely safe bank assets may need to be available for this collateral. This is a practical reason why a 100% RR would be difficult on the banks.
**Also note that the CB conceivably might NOT be attempting to defend an overnight interest rate, but that's a whole other ball game! In the US the Fed has been defending an overnight rate for some decades now, even thought that rate may be changed every few weeks for
various reasons. Prior to 2009, the target rate was adjusted every six weeks or so. Since then the rate has been essentially fixed by the presence of excess reserves and a fixed interest on reserves (IOR) rate.
