The notion that “cutting the ECB deposit rate into negative territory — that is, charging banks to hold money at the ECB instead of paying them — could push them to lend” is a mistaken, yet popular view.

This is a Q&A on the subject:

How would the ECB set a negative rate?

The ECB could set a negative rate on all banks’ accounts at the ECB above the “minimum reserve” level set by the ECB.

What is the minimum reserve level today?

Minimum reserves are set equal to 1% of all deposits with maturity less than 2 years, not including repos.

Does the ECB remunerate minimum reserves?

Yes, at the “main refinancing operations rate” set by the ECB (today, 0.25%).

Does the ECB normally remunerate accounts in excess of minimum reserves?

No, unless banks move their funds to a special account called “deposit facility” where they get remunerated at the deposit facility rate set by the ECB (though this is now set at zero).

Do Eurozone banks today hold liquidity accounts in excess over minimum?

Yes, since the fourth quarter of 2008, the banking system as a whole does: The sum of total reserves and deposit facility accounts is greater than minimum reserves.

Where do banks hold their excess reserves?

Banks used to keep excess reserves in the deposit facility when the ECB paid interest, but since the interest on the deposit facility accounts has been set at zero, banks are indifferent.

With a negative rate, who will pay the interest rate on accounts in excess of minimum reserves?

Any bank holding reserves in excess over minimum will pay (rather than being paid) an interest rate to the ECB.

Will banks then try to get rid of their excess liquidity to avoid paying the rate?

The banking system cannot reduce its accounts at the ECB unless the ECB takes the¬ initiative of carrying “liquidity absorbing operations” such as reverse repos.

Don’t banks choose the amount of “excess reserves” they hold?

No, the overall (end-of-day) balance of bank reserves depends on the net payments between banks and the public sector (this includes both the central bank and the government) and does not depend on banks’ choices about how to allocate their assets.

What can a bank do when it holds excess reserves it does not need?

It will be willing to loan them out to another bank at interest.

What interest?

The interest that other banks will be willing to bid.

What interest will other banks likely bid?

This depends on whether liquidity needs of those banks that are short of reserves are higher or lower than excess liquidity sitting in those banks that are long on reserves.

What is the case today?

The banking system is net long: This means that no bank will bid more than what the ECB pays on excess reserves (today, as said, zero).

Then, what is the effect on the banking sector of a negative rate on excess reserves?

If the ECB charges banks for holding excess reserves, the interbank rate of reserves will also turn negative: No bank will bid more than the negative rate, and the banking system as a whole will pay the ECB for holding excess reserves.

Will this have an impact upon banks’ net worth?

Yes, the interest paid works like a tax and lowers banks’ net worth.

Would not banks pass this “tax” through to depositors?

Yes, they would partly do that and, if so, what the banks did not lose, the depositors would, creating consequences that would ripple throughout the private sector.

If holding bank accounts becomes more expensive, would depositors hold more banknotes?

Yes, if the negative rate exceeds the cost of holding cash, depositors will cash part of their deposits.

What would be the consequence if bank clients decided to withdraw a significant share of their bank accounts to avoid paying interest (or more fees) on their bank accounts?

Banks would request more banknotes from the ECB, their excess reserves would drop, and they would make fewer interest payments to the ECB.

Does this mean there is a limit on how low a negative rate can be set?

No, but when the negative rate on reserves is big enough, depositors will withdraw such a significant amount of banknotes that banks’ excess reserves will be eliminated, so the negative rate on excess reserves is moot.

OK, so let us go back to the case where the interest rate on excess reserves is negative but not as low as to prompt depositors to withdraw their cash: Would each single bank not be willing to make more loans to get rid of excess reserves on which it pays a “tax”?

No, when there are excess reserves in the banking system, the negative rate does not alter the funding cost of a new loan to the bank: The funding cost is the financial opportunity cost of reserves, no matter what the size of reserves that the bank owns when it decides to make a new loan.

Would not the opportunity cost of holding reserves increase with negative rates?

No, when there are excess reserves, the financial opportunity cost of holding reserves is always zero: This is because the interest rate that banks will charge other banks for lending reserves will settle at the same rate that the ECB pays on reserves.

Isn’t it true, though, that if a bank makes a loan, it will lose reserves?

Yes, it is true: When the borrower uses the loan, the bank will make payments on behalf of the borrower and, assuming payment recipients have accounts at another bank, the bank will settle the borrower’s payments by debiting its account at the ECB.

Then, if the bank has excess reserves, would it not be suitable for the bank to make more loans, lose reserves, and thus lower the “tax” on reserves?

If all banks increased their loans, each bank would lose and at the same time acquire reserves: If all banks made more loans, they would still pay the tax.

What if one single bank increased its lending at a faster rate than any other bank in order to keep its reserve outflows larger than reserve inflows?

That single bank’s excess reserves would drop and the bank would pay less of the tax, yet all other banks would pay more of the tax.

Would not each bank therefore have an incentive to do this?

No, a decision to accelerate the rate of lending is a decision of increasing the bank’s leverage, and this depends on current and desired leverage.

What does a bank’s desired leverage depend on?

Desired leverage depends on bank capital ratio requirements, the quality of potential borrowers, and expected profit from lending.

Could not negative rates be a reason for banks to increase their desired leverage?

No, the fact that banks lose money on their excess reserves has no effect on the quality of potential borrowers or on the expected profit from lending. Negative rates are just contractionary.