Sunday, January 13, 2013

Private Currency and the Zero Bound

Consider the following monetary regime:

The monetary authority targets a growth path for nominal GDP.

The monetary base solely takes the form of mutual fund claims against the monetary authority's asset portfolio.

The monetary authority charges a management fee, so that the yield on those mutual funds is less than the yield on the monetary authority's asset portfolio.

Banks offer a variety of checkable deposits and interbank claims are settled using mutual fund balances at the monetary authority.

From the point of any particular bank, its deposits are subject to being redeemed with mutual fund balances at the monetary authority.

The sole hand-to-hand currency is issued by banks.     Depositors withdraw currency from ATM machines or teller windows at their banks, hold it or spend it as they choose.   Retailers deposit the currency along with any paper checks they receive at their own banks.   The currency is cleared like the checks.

From the point of view of any bank issuing hand-to-hand currency, the currency is subject to being redeemed with mutual fund balances at the monetary authority. 

Under "normal" circumstances all nominal interest rates are positive other than interest rates on hand-to-hand currency which remains zero.   Banks keep balances at the monetary authority to settle interbank claims.  

They earn a return on those balances equal to the yield the monetary authority earns on its asset portfolio less the management fee.   Banks have no reason to hold balances other than for settlement purposes because by holding the assets directly, they earn a higher yield and the risk is the same.   Any losses on the monetary authority's  portfolio are passed on to the banks because the balances at the monetary authority are mutual funds.

Banks issuing currency are able to fund part of their asset portfolios at a zero nominal interest rate.   This is usually attractive to a bank, but the banking system is competitive, and the result is that the difference between the interest rates paid on deposits and the interest rates charged on bank loans shrinks to compete away all of the profits from issuing currency.   This happens because banks issue their own currency to their depositors (and borrowers, if they want to use currency.)

The monetary authority uses open market operations to adjust the quantity of base money however much is needed to keep nominal GDP growing on its target growth path.

From time to time, interest rates throughout the economy fall substantially.   This is due to a temporary increase in the supply of saving and/or decrease in the demand for investment.   Another way to frame the phenomenon is that there is a temporary increase in the supply of credit and/or a decrease in the demand for credit.  

The yields on earning assets held by banks fall.   In a conventional banking system, this would motivate banks to reduce the quantity of credit supplied and hold more reserves.   However, the yield on the monetary authority's earning assets fall as well, and so does the yield that banks earn on the balances they keep with the monetary authority.

The banks are less willing to supply deposits and hand-to-hand currency.    For the deposits, the result is a decrease in the interest rates banks pay on deposits.   However, that doesn't happen with currency.  The interest rate on currency remains at zero, and so with the lower opportunity cost of holding currency, the demand to hold that currency rises.   The banks, benefiting less from issuing currency, lower  the interest rates on deposits more than in proportion to the decrease in the yields on their earning assets. 

Once the interest rates on deposits are so low that funding earning assets is cheaper by issuing deposits than issuing currency, then banks will cease issuing currency.   However, for those using currency and deposits, as the interest rates on deposits fall, using (and holding) currency becomes more attractive than holding deposits.

The result is a shortage of hand-to-hand currency.

The lower the equilibrium interest rate on deposits, the worse the shortage.   Once all banks are at a point where none of them are issuing currency, it is solely the increase in the demand to hold currency at lower deposit interest rates that exacerbates the shortage.

Assuming banks have call provisions on their currency, the lower the yields on earning assets and the longer this period of low interest rates is expected to last, the more likely banks are too exercise their call option.   As banks call the currency, the quantity outstanding shrinks, further exacerbating the shortage of currency.

Nominal GDP, however, continues on target, with all purchases of goods and services being made by check, either paper or electronic.   There is no shortage of clearing balances, the monetary authority issues them as needed.   There is no shortage of credit, the banks can fund  loans by borrowing using deposits with still lower interest rates.    There is no shortage of money in the form of deposits.   The yields on them fall to a point where the demand to hold them matches the quantity banks are willing to issue.  

The "problem" of low interest rates solely creates a problem of a  shortage of hand-to-hand currency.   Banks stop issuing currency because it is not profitable to issue it.

Suppose that instead of a general increase in saving supply and/or decrease in investment demand, or alternatively, increase in credit supply and decrease in credit demand, there was a change in the willingness to bear risk.   For example, investors sell off corporate bonds and buy short term government bonds--T-bills.

To the degree that the monetary authority holds T-bills as an earning asset, the decrease in the yields on T-bills results in a decrease in the yields banks earn on their balances.     There is no tendency to build up larger reserve balances.    If anything, there would be a motivation to hold smaller balances as well as to reduce T-bills held directly and instead purchase other sorts of securities and expand lending.    On the other hand, the lower yields on T-bills held either indirectly as mutual fund balances with the monetary authority or directly, would result in a decease in willingness of banks to supply currency and deposits, and so, a lower interest rate on deposits.

More importantly, the lower yield on T-bills would tend to raise the demand for currency and deposits.   The decrease in the supply and increase in the demand for deposits results in lower yields on them, but the yield on currency remains zero.   As long as issuing currency is profitable based upon the yields on earning assets, the banks will issue added currency to meet the demand.

Because bank deposits and currency are the liabilities of commercial banks, it is possible that the desire for safety would drive the yields on T-bills below zero.   While this would raise the demand for currency, it would be mistake to carry over conditions that would apply to a system of government currency rather than private currency.   In particular, when interest rates on T-bills are zero, privately-issued hand-to-hand currency is not a perfect substitute for T-bills.    Assuming the government, with its power to tax, is more creditworthy than any particular bank, then privately-issued currency is inferior to T-bills with a zero yield.   And so, if market clearing requires negative yields on T-bills, then the yields on T-bills will fall below zero.

Now, the lower T-bill yields fall, the greater will be the increase in the demand for the deposits and currency issued by sound banks.   If  banks are typically poorly capitalized or hold risky earning assets, then T-bill yields could become quite negative.   On the other hand, a more conservative banking system would limit the decrease in T-bill yields.

If the increase in the demand for bank deposits and currency is large enough that the interest rates banks can pay on deposits fall low enough, then it will stop being profitable for banks to expand their issues of currency to meet the demand.   They will stop, and a shortage of currency will develop.

If all banks are identical, then all of them would cease issuing currency at the same time.   However, consider a situation where depositors perceive that different banks have different risks.   Those banks perceived as least risky will see an increased demand for their deposits and currency.   As low risk yields are lower, it would be the bank perceived as least risky that would find that it can borrow by issuing deposits at interest rates so low that issuing currency is no longer profitable.  

While there is, of course, a shortage of the least-risky bank's currency, there would remain plenty of currency issued by those banks perceived as relatively risky.   From their perspective, issuing currency at a zero-nominal interest rate rather than the higher deposit interest rates they must pay would be profitable.    While those seeking to substitute bank deposits for T-bills whose yields have been driven to less than zero would hardly find currency issued by relatively risky banks attractive as a safe investment, those using currency for small face-to-face transactions would still have plenty of currency.   Given the small amount of currency held for that purpose, risk is not a major concern.

Of course, if the demand for bank deposits, including those issued by the relatively risky bank is large enough, then no bank will find it profitable to issue currency.   The result is a shortage of currency.

A shortage of currency is an undesirable situation.   However, reductions in nominal expenditure on output are worse.   The advantage of currency privatization is that during occasional periods of  low interest rates, there is no tendency for spending on output to fall.   Instead, there are shortages of hand-to-hand currency.



  1. Hi Bill,

    It is of course possible for central bank base money to be mutual fund shares of some kind. However, the central bank would virtually give up all control on the price-level.

    The average price of the assets in the CB's portfolio would forever be, and by construction, 1. If the relative value of wages vs assets were to fall, you'd see unemployment show up in the presence of price rigidities, regardless of quantity of base money.

    In other words, I think your entire post describes a coherent framework except that these two paragraphs conflict with the rest:

    1: "The monetary authority targets a growth path for nominal GDP."

    2: "The monetary authority uses open market operations to adjust the quantity of base money however much is needed to keep nominal GDP growing on its target growth path."

    Just as "safe assets" are near-perfect substitute to money, real assets (those in the portfolio) are near-perfect substitutes to your proposed money: the public is completely indifferent between holding proposed money or the assets that are backing it => this means that increasing the quantity achieves nothing on the price level/NGDP (unless transactions were previously constrained due to lack of liquidity.) Velocity will move exactly opposite to M in order to keep PY constant.

    It sounds like lately you've been trying to find a way around the zero bound. My personal view at this juncture is that the only way to solve the zero bound problem is to burst right through it (lower rates below zero).

    A couple days back I wrote a post on this exact topic arguing that quantity doesn't matter.

    Also, on the topic of alternative banking system, I'd be interest on your opinion on this one.

  2. I don't favor having the monetary authority hold "real assets," but rather "short and safe" assets, such as T-bills. The banks, who hold these mutual fund shares, don't consider them perfect substitutes for T-bills because they have to pay a management fee. Quite the contrary, from the banks' point of view, it is always better to hold T-bills directly rather than hold these shares. Well, other than a need to hold the balances to settle adverse net clearings.

    With an open market purchase, the monetary authority purchases T-bills, and creates new mutual fund shares equal in value to the T-bills. These belong to the bank used by the whoever sold the T-bills to the monetary authority.

    That bank now has a larger balance than it prefers. (Assuming it started with the balance it preferred based upon the management fee vs. the transaction costs of offseting the net clearings generated by the business of its customers.) It fixes that situation buy purchasing securities, reducing the interest rate charged on loans, and else reducing the interest rate paid on deposits.

    The purchases of other securities or newly made loans increases the quantity of money (bank deposits) and the lower interest rate on deposits decreases the demand to hold money. Those with the excess money balances spend them on goods, services, or assets. The added spending on goods and services is an increase in nominal GDP.

    It is certainly possible that the initial purchase of T-bills by the monetary authority would tend to drive up their prices and reduce their yields. Under a conventional policy, this would reduce the opportunity cost of holding reserve balances. The difference between the yield on T-bills and the presumed given interest rate on reserve balances (perhaps zero) is smaller. However, with the mutual fund type of base money, the yield on the mutual funds changes exactly like that of the T-bills (lower in this case,) but it is lower still by the management fee.

    If there was an excess supply of these mutual fund shares, lower yields on T-bills does nothing to reduce it.

    If the monetary authority sells T-bills, then it reduces the balance in the mutual fund account of whichever bank was used by whoever purchased the T-bills. That bank has a smaller balance. Assuming that it was holding what it wanted before, then it must rebuild it by selling securities (maybe T-bills it owns,) raising interest rates on loans, or raising the interest rate paid on deposits. The net repayment of loans and sale of securities reduces the quantity of money (deposits) and the higher interest rate on deposits raises the demand to hold money. To rebuild (or build up) money balances, people sell other assets and restrain spending on goods and services. The restraint on spending on goods and services reduce nominal GDP.

    Now, the sale of T-bills and other asset sales should increase their yields. Under a conventional system, this increases the opporunity cost of banks for holding reserve balances. The difference between the assumed fixed interest rates on reserve balances (maybe at zero) and the yields on other assets gets larger. But with the mutual fund type of base money, the interest rate that banks earn on their reserve balances rises with other interest rates (though it remains lower.)

    The monetary authority can use open market operations to control nominal GDP with a mutual fund type of reserve balances.

    Whether banks are issuing hand-to-hand currency or not doesn't make much difference.

    What mutual fund base money does is make it more difficult for a central bank to use liquidity effects to manipulate interest rates.

  3. Ha sorry when you said mutual funds I jumped to a conclusion and assumed a fund with more conventional assets (equities, long term bonds, etc.), not a money-market fund.

    Now, your "management fee" is very interesting and virtually identical to my "liquidity charge" in this setup (i.e. the difference between the cost of sourcing cash, and the return on cash.

    In my setup, the CB "announces" the rate at which it lends reserves and the rate it will pay on reserve and uses those two quantities to target both NGDP and money supply/velocity.

    In your setup, the central bank knobs are the money supply and your management fee. I think those two quantities are highly "colinear" (both knobs are trying to manipulate the same dimension) so there's some kind of issue here: I can't express it so well but consider this example to see the problem:

    There's been a huge drop in NGDP so the CB increases its management fee to 10% per annum to discourage people from hoarding cash.

    Also the CB purchases $10tn of 1-year securities yielding 0% and let's say that's very generous by anyone's standard.

    By the end of the year, the CB takes its 10% cut (and presumable sends it to the treasury?).

    Now it's left with $9tn of T-bills about to mature and $10tn in currency liability. Given the "mutual fund" model, the $1tn of currency should be worth the same as the $900bn of T-bills, but the T-bills are denominated in currency -> this leads to a contradiction.

    Once the T-bills mature, the CB is left with no assets and $100bn of liabilities. Either the treasury recapitalizes the CB or the CB continues to fund the govt with money printing.

    Looking at this from a different angle: the CB can never sell securities once it's started charging a management fee since the market will only purchase them at par and the CB should only be willing to sell them for more than PAR (to be fair to all fund holders).

  4. I disagree that there would be a shortage of currency. What would happen is that currency would trade above face value (and banks would continue to issue currency, but not at face).

    The same thing would happen if the Fed stopped converting reserves into currency. With a negative interest rate, FRNs would trade above face value.

  5. Bill,

    In your opinion, why dont commercial banks make physical currency already right now. I know there are no laws banning them in the USA.

    Also, are there any other benefits to currency privatization besides the zero-bound?

    Bes regards,

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