Although economists love to tell themselves that economics is a highly quantitative, empirical discipline, the reality is that when it comes to money, clear thinking goes out the window. Forcing banks to hold reserves at a below market rate of interest is obviously an imposition -- a tax -- but it is somehow excused as being some form of a free lunch, because reserves are "money."
In "Why Helicopter Money Is A 'Free Lunch'", Biagio Bossone argues:
As such, the elimination of interest payment on excess reserves (or its offsetting through the levy of an explicit charge on commercial banks, as suggested by Bernanke) would only amount to eliminating (or compensating for) the policy-determined price distortion discussed above. Consistently with this, the imposition from the central bank of a non-interest bearing compulsory reserve requirement equivalent to the amount of the monetary expansion under HM (or the levy of a charge to offset the interest net payments to commercial banks) would not represent a form of tax financing.
This argument is at best misleading. If the argument is that a "levy" is not really a "tax," it is just a word game. Otherwise, if the central bank increases the amount of reserves that are required to be held by banks, it is an imposition on the profits of banks, and bank shareholders would correctly regard such "financial repression" as a form of tax. I explain this in further detail below.
The apparent "free lunch" Bossone identifies is what is normally called seigneurage "revenue" -- the amount of interest cost saved by replacing debt by non-interest bearing "money." The annual amount of seigneurage revenue is calculated by multiplying the monetary base by the short rate -- which is the interest savings created by replacing treasury bills/bonds by "money."
If the monetary instrument we are referring to is currency (notes and coins) that are voluntarily held by households, it might reasonably be viewed as a free lunch; the government gets a reduced interest cost as a result of the decision to hold a liquid instrument. However, if banks are forced to hold instruments with a below market rate of return, this will result in an involuntary reduction in bank profits, which is undoubtedly a form of a tax.
In any event, if forcing banks to hold reserves at a below market rate of interest is somehow cost-free, forcing all investors to hold special Treasury bills that pay a below market rate of interest would also be cost free. If the reader believes that this is the case, I would suggest pitching that idea to some institutional investors to see their reactions.
Required Reserves -- A Lunch Paid For By The Banks
Let us assume that the prevailing short-term risk free rate is 2%, and the central bank forces an unlucky bank to hold $100 in non-interest bearing excess reserves.
The bank suffers an annual opportunity cost of $2, as it could have held $100 in Treasury bills that would have paid $2 in interest.
That $2 loss in profits by the bank is exactly equal to the seigneurage revenue that is generated by replacing $100 in Treasury bills by non-interest bearing reserves. That is, the bank is paying for what is allegedly a "free" lunch.
Meanwhile, forcing a bank to hold reserves cannot be construed as doing it a favour (as a result of improving its liquidity position). If a bank is forced to hold $100 million in reserves, that represents $100 million in assets that are utterly immobilised. If it has a liquidity drain, it cannot draw on those reserves, it needs to sell something else (or borrow against something else) in order to keep its reserve levels at $100 million.
The situation is not greatly helped even if the liquidity loss is the result of a reduction of deposits against which reserves are held. (Not all classes of deposits create a reserve requirement.) Reserve calculations are not done in real time, and so reserve requirements are fixed until the next accounting period. (The drop in deposits would apply some relief in the next accounting period; however, required reserves would only drop by the reserve ratio times the deposit loss. For example, if the reserve ratio is 10%, $1 in lost deposits would free up $0.10 in reserves; however, the remaining $0.90 would still have to be raised by selling liquid assets.)
Background On Interest On Excess Reserves
One point which may not be clear to those who are new to this topic is the question of interest on reserves. Since they look like a form of "money," why should they pay any interest?
Since banks are not required to hold these excess reserves, they will attempt to trade them away. They would be extremely likely to buy Treasury bills, which are a liquid short-term instrument. The market rate on Treasury bills will inevitably converge towards the interest rate paid on excess reserves.
If the central bank does not pay interest on excess reserves (like other forms of "money"), the implication is that short rates would be stuck near 0%. There would be no way for the central bank to raise interest rates; that is, they will have lost control of interest rates. (The pre-2008 Federal Reserve was in this position as a result of the prevailing institutional structure, where all reserves did not pay interest. This was changed, bringing the Fed closer to the operational practices of other central banks.)
The Bossone article discusses this loss of control of interest rates, and it explains why he is suggesting to impose additional reserve requirements on banks (to compensate for "helicopter money"). The extra reserve requirements will wipe out the "excess reserves," and so market interest rates can once again be decoupled from the rate of interest paid on required reserves. (I found that parts of his discussion on this topic were somewhat unclear, so I wanted to add some explanatory comments.)
If money were not viewed as some magical substance within economic theory, we would not be having these discussions. It would be obvious that obligatory reserve holdings is a tax on the banking system (which of course is going to be passed on via lending spreads), and we would start asking ourselves whether such a tax makes sense in the first place. After all, economists howl about the "distortionary" effects of taxes; imposing a severe competitive disadvantage on the formal banking system versus the poorly regulated non-bank financial sector is an obvious distortion that one should be concerned about.