Leaving (Modern) Money (Theory) On The Table

Paul Krugman has recently offended the Modern Monetary Theorists.

He argues that having the government create more money is more inflationary than having the government create more bonds. There is a good argument and a bad argument for his case.

The Bad Argument

The bad argument is the reserve-multiplier fallacy, otherwise known as the money supply multiplier, money multiplier, etc. In this argument, by supplying more reserves to the banking system, banks will go on a lending spree, creating as much inside money as outside money times a multiple, given by the required reserve ratio.

But people are slowing abandoning this belief (hat tip MoslerEconomics).

Don Kohn (Former FRB Vice Chair):”I know of no model that shows a transmission from bank reserves to inflation”.

Vitor Constancio (ECB Vice President): “The level of bank reserves hardly figures in banks lending decisions; the supply of credit outstanding is determined by banks’ perceptions of risk/reward trade-offs and demand for credit”.

Charlie Bean (Deputy Governor BOE): in response to a question about the famous Milton Friedman quote “Inflation is always and everywhere a monetary phenomenon”: “Inflation is not always and everywhere a monetary base phenomenon”

The main flaw here is not understanding how inside money is created. Banks lend money when it is profitable for them to do so. They do not lend money automatically as a result of an increase in aggregate reserves.

Here is a suggested replacement for the money supply multiplier:

Suppose banks must set aside $1 of capital for making $10 of loans (the amount will differ based on the risk characteristics of the loan as well, but let’s ignore that). Suppose that their funding costs for equity are 6%, and their marginal borrowing costs are 4%. In that case, what rate can they charge on a 10$ loan to break even?

10*r = 1*(.06) + 9*(.04)
r = (.06)*(1/10) + (9/10)*(.04)

And then banks will continue to lend as much as borrowers want to borrow at the break-even rate. The quantity of loans made is demand determined, and the cost of lending is set by the government. The quantity of loans made is not set by the government.

Now really you would want to include other terms in this weighted average. Suppose that banks fund themselves with 10% capital at the reserve rate plus 2%, 30% intermediate term loans at reserve rate plus 1%, 30% with short term loans at the reserve rate, and 30% with deposits at a rate of 1%.  Then the weighted average of these will determine the break-even rate. However much borrowers demand to borrow at that break even rate will be the quantity of loans made. By adjusting the reserve rate up, the government can raise the break-even rate.

Notice that nowhere do the quantities of reserves come into play — all that matters is the bank cost of funds and the quantity of loans demanded at the weighted average.

Now you can argue that the marginal cost of reserves will be determined by quantity. But it isn’t. When a bank lends or pays reserves to another bank, then total reserves remain fixed.  The banking system as a whole cannot increase or decrease the total quantity of reserves.

If there is just a small excess of reserves, then the marginal cost of reserves is driven to zero, and a small shortage of reserves drives the marginal cost of borrowing reserves to infinity.

So there is no smooth relationship between the quantity of reserves and the marginal cost of reserves. The relationship between the level of reserve interest rate and the level of reserves is trinary — there are either too few reserves, in which case the equilibrium price is infinite, too many reserves, in which case the equilibrium price is 0, or just the right amount of reserves, in which case the equilibrium price is any non-zero number.

This is why the central bank can increase the cost of reserves by withdrawing a small amount of money and adding it back a few days later. When it withdraws money, banks keep bidding up the price of reserves until the they hit the level that the CB wants, at which point it can reverse the transaction, and the same quantity of reserves is now lent out at a higher rate.

If you want to put this into a model, you can imagine that there is some quantity of reserves demanded, Q_d, which is primarily a function of the price level and technology, as banks are no longer required to hold a proportion reserves against deposits. Required reserves are basically zero in the modern world.  Q_d = f(P). The quantity of reserves supplied is determined by the central bank. and the rate of change of the reserve interest rate is proportional to the difference between the quantity of reserves demanded – the quantity of reserves supplied.

dr/dt = k(Q_d - Q_s)

If Q_d > Q_s, then the borrowing rate keeps going up. If Q_d < Q_s it keeps dropping (until it hits zero). That means that you can achieve any stable rate provided that Q_d = Q_s, by, on the margin, withdrawing a bit and then adding it back. This is a very crude model, but if I were to have to make a simple model about reserve demand,  then this would be it.

But even if Q_d < Q_s, the government can still impose fees or pay interest on reserves so that the break-even rate for lending remains high. For example, if the government paid interest on reserves of 4%, then the cost of reserves would be 4% regardless of quantity. Better yet, if the government taxed assets at 4%, then banks would need to charge more than 4% in order to break even, so the lending rates could be hiked without needing to decrease the quantity of reserves.

The Good Argument

The good argument acknowledges the above, but points out that regardless of how the financial system is regulated, there is still only a finite amount of zero maturity assets that the public can be convinced to hold. This is a “limit to seignorage” argument. Sure, the government can pay interest on reserves and prevent excess credit growth, but in that case why not sell bonds? Well, one reason is that you don’t need to worry about the mythical “bond vigilantes”. You can raise or lower borrowing rates by adjusting the quantity of reserve interest payments or taxes levied on banks without needing to tap the market.

But the real problem with the good argument is that the public does not hold the base, the banking system holds reserves, and the public holds deposits + currency. When determining the limits of seignorage, are those limits determined by the amount of seignorage that can be extracted from supplying reserves equal to Q_d, and the public with currency equal to their currency demand — or are the limits of seignorage determined by the public’s demand for deposits + currency?

The Data

The Fed defines the money stock as MZM, or Money at Zero Maturity. The interest on money is the MZM own rate.

The first thing to notice is that the quantity of MZM held by the public is already roughly equal to the quantity of Federal Debt held by the public, and more often than not, the former exceeds the latter.

Therefore the public is already willing to hold the entire U.S. federal debt as zero maturity money, paying an absurdly low interest rate – on average, a negative real rate:

Therefore there is an inherent tension:

• If we put on our economist hat, then government creating more money will cause inflation as people want to hold bonds and not money, so the government should primarily supply the private sector with bonds instead of money.
• If we put on our banker’s hat, then the non-financial sector is desperate to hold more money, not bonds, and so banks provide a valuable service by supplying the private sector with deposits.

Both views cannot be true.

All seignorage income should flow to the government, not banks.

In the current system, the government is granting almost all seignorage income to  banks. That is why it cannot seize more seignorage income for itself. This is a voluntary constraint to grant gifts of seignorage income to the private sector, and have the government limit its own seignorage income to be a small fraction of the total amount.

With these gifts, the financial sector swells, so that compensation of Finance and Insurance employees is in excess of 20% of gross investment and 80% of net Investment. Even though the majority of business investment is via retained earnings and does not involve intermediation at all. It is becoming very expensive to match borrowers with lenders, if finance requires a 20% cut.

How would one go about seizing seignorage income from banks?

Option 1: Ban The Rents

One (draconian) option is to require banks to borrow from the government rather than from the private sector.

Banks would only be allowed to sell equity to the public.

The government can directly provide deposit services. The banks would borrow from the government at the policy rate, creating a deposit account that pays roughly zero. The government would borrow from the public by supplying them with the zero interest deposit account, and it would receive the policy interest income from the bank.

Now it still may be the case that households have too many deposits, and in that case the government can sell bonds, removing some of the deposits, or alternately it can hike the policy rate so that fewer deposits are created. But even in the former case, the amount of bonds that would need to be sold would be determined by the difference between the public’s demand for MZM and the total government debt. It would not be a function of the deficit at all.

In such an arrangement, as there is only outside money, only a small fraction of the deficit, and typically a negative fraction, should be funded by selling bonds. Whenever the public’s demand for deposits exceeds the (current) quantity of hard money, we should expand money-financed deficit spending so that the two are equal. Whenever the public’s demand for deposits is less than the current stock of hard money, we should either retire money (by increasing taxes) or sell bonds. Note that this model has no reserves at all — it has only deposits backed by outside money. Once money stops being gold coins, then there is no need to have a separate monetary base that is different from MZM.

Option 2: Tax The Rents Away

A less intrusive method would be to levy a tax equal to

(policy) rate*Assets - interest paid on liabilities

Where Assets on the left are any assets that are not liabilities of the central bank, and the interest payments on the right are any payments that are not to bank capital. I.e. dividends on common or preferred equity would be excluded, as would long term subordinated debt. The definition of bank capital would be up to the regulators as part of their capital adequacy requirements.

Simultaneous to that, the government would be willing to lend unconstrained to the banks at the policy rate, and it would offer longer term loans as well, so that banks would have no motivation to borrow at higher rates than the policy rate.

If banks cannot earn seignorage income from deposits, then why would they offer deposit services? There are benefits from data mining customer accounts, and selling additional services to customers. But at the same time, the government should offer basic deposit services to the public at no charge. That is a small price to pay for obtaining an income stream whose net present value is the entire federal debt.

The government, in this proposal, will continue to sell bonds to the public when deficit spending. But in such an arrangement, the taxes paid by banks correspond to a reduction in the base — a massive contraction. And this contraction would need to be offset by the central bank monetizing debt in order to keep the monetary base constant. This monetization corresponds to the full amount of seignorage income that can be extracted. If MZM is growing very rapidly, then this proposal might even force the government to deficit spend more once all the debt has been retired.

The proposal would be functionally equivalent to the “no bonds” and “zero rate” proposals in most cases, even though the government is selling bonds and maintaining positive interest rates throughout. The result of this proposal is that instead of supplying economic rents to the financial sector, the foregone interest relinquished by households in exchange for liquidity is used to fund public works supply public benefits, rather than build mansions in Connecticut.