The Money Multiplier

Arnold Kling has a post about whether the money multiplier exists.   Scott Sumner commented.      Sumner points that that the money multiplier exists, because it is simply the ratio of some measure of the quantity of money and the monetary base.     Sumner then presents some simple algebra, so that the money multiplier equals (1+c)/(c+r), where c is the ratio of currency to deposits and r is the ratio of reserves to deposits.   He states that these ratios depend on utility maximization.   

Sumner's claim is true enough, though I think most economists studying banking would use something like maximizing expected profit to relate the demand for reserves by banks to the deposits they supply.    Further, I don't think a the ratio of reserves to deposits is the best framing for the banks' relationship, though of course a ratio  exists between the profit maximizing quantity of deposits and the profit maximizing demand for reserves.   Neither do I think that most people optimize a ratio between currency and checkable deposits.   I know I don't.   I do think that both the demand for currency and deposits are positively related to spending on output.

The paper Kling cites appears to focus more on reserve requirements and emphasizes that a substantial portion of M2 has no reserve requirement.   Their approach assumes that the central bank offsets currency drains, making the quantity of currency endogenous, and instead controls the quantity of reserves.   The reserve requirement then creates a fixed ratio between reserves and bank deposits.    To read Kling's discussion, the purpose of controlling deposits would be to control bank lending.   And so, showing that there is no close relationship between bank lending and reserves proves that there is no money multiplier.   A dollar of additional reserves does not create a more than proportional increase in bank loans.

Kling goes on to argue that the Fed supposedly is impacting the economy by purchasing bonds, which lowers long term interest rates.   He argues that since the Fed's purchases or sales of bonds are so small compared to the world supply and demand for bonds, it can have no more than a minimal impact on world long term interest rates, and so has no impact on anything.    While I think there is an element of truth in Kling's argument, a central bank in a small economy with completely open capital markets would impact spending on output and inflation through changes in the exchange rate.    If the central bank is pegging the exchange rate, then sure enough, it has no effect on much of anything else.

Of course, neither traditional monetarists nor market monetarists were much interested in what, if any, effect  central banks might have on long term interest rates or the quantity of bank loans.   While Sumner has long given up on worrying about any measure of the quantity of money broader than the base, most market monetarists focus on the quantity of the medium of exchange relative to the demand to hold it.   The medium of exchange is made up of a variety of financial instruments, and the day in which most of them were issued by commercial banks is long past.  

Kling expressed surprise that retail mutual money market funds are included in M2.   He says that he thought that M2 was M2.   What would that be?   Currency, checkable deposits, and savings accounts?   I am not really sure.    My concern with M2 was primarily the inclusion of small certificates of deposits.   What sense does that make?    In world where other nominal magnitudes are growing, can a $100,000 limit make any sense?    I had no trouble with the addition of retail money market funds.   As they came into existence, adding them to the measure of the quantity of money made perfect sense.   But how can a $50,000 cut off make sense?   Why not all of them?

Fortunately, MZM has existed for years, and it supposedly included all financial instruments with a zero term to maturity.   No certificates of deposit and all money market mutual funds.   Unfortunately, my personal experience always left me a bit troubled.   My savings account balance is subject to restrictions on withdrawals.   More important, I don't count it as part of my ready money balances.    Further, when I did have a money market mutual fund account, the restrictions on using it were more burdensome than a saving account.   Of course, I am just a small retail customer.

Years ago, Eurodollar accounts and repurchase agreements were included in M3, but both overnight and term instruments were included.   And then, M3 was no longer measured.   Overnight repurchase agreements, which have served as a monetary instrument for years, was never included in M2, but was not added to MZM.    As the shadow banking system developed, repurchase agreements became a progressively larger portion of the quantity of money.   Of course, those held by money market mutual funds were included in MZM indirectly, but any directly held by corporate treasurers or financial institutions were an unmeasured portion of the quantity of money, a portion whose quantity collapsed in 2008.   The Divisia measures of the quantity of money did capture that effect.    The M3 and M4 Divisia measures collapsed during that period.

These other monetary instruments have become more and more entwined with checkable deposits.   The development of sweep accounts has allowed liquid funds to be held, or at least reported as being held, in a money market account, a money market mutual fund or as a repurchase agreement, while always being available to cover checks, or electronic payments.     The existence of sweep accounts is at least partly motivated on the prohibition of interest payments on demand deposits, or in other words, for the transactions accounts held by business customers.   They can earn interest by having excess funds swept into interest bearing accounts.   

However, there is another impact of sweep accounts.   Banks sweep funds out of transactions accounts before they report the quantity to the Fed, and it is that reported quantity that determines the amount of required reserves.   By convincing customers to use sweep accounts, banks can reduce their required reserves to something below what they find it profitable to hold.    Since vault cash counts as reserves, and at least some banks need vault cash to meet the needs of their retail customers, the banks' desired reserve ratio remains positive.   And there is little reason to believe that the banks required reserves were much different.  

Of course, with the payment of interest on reserves, and the very low interest rates on other money market instruments, there is little reason to use sweep accounts to reduce required reserves.   The level of reserves banks find it profitable to hold is much larger than the requirements.   The reserve requirements are ineffective under current conditions.  

Given what amount to scams aimed at getting around unnecessary and undesirable regulation, is there any surprise that reserves have no fixed relationship to incomplete measures of the quantity of money?  

Free banking theorists, like George Selgin, have developed the theory of the precautionary demand for reserves.   It doesn't have a fixed relationship to the quantity of deposits.   Selgin argues that it depends on spending on output.   The argument runs through the volume of gross payments and so the variance of net clearing balances.   In particular, if the demand to hold bank deposits rise, the demand for reserves falls, leading to a lower equilibrium reserve ratio.  Selgin emphasizes the argument that the reduced reserve ratio causes an increase in the quantity of deposits, accommodating the increased demand to hold deposits.

One key element of the status quo that is very different from the regimes Selgin describes is that banks cannot issue hand-to-hand currency.    Holding reserves in the form of vault cash is necessary to meet customers' routine demands for hand-to-hand currency.

Further, consider the role of inter-day overdrafts.     Do banks have to hold sufficient reserve balances to cover all claims, or can they maintain negative balances at the central bank/clearinghouse as long as they are covered later?    That rule will influence the demand for reserves.  

More importantly, if there is a central bank that is targeting the interbank clearing rate, then the incentive to hold reserve balances is greatly reduced.    One reason to hold reserve balances is that if there is a shortage of reserves in the system, excess reserves can be lent at higher interest.  And, of course, banks with a need for reserves in such a scenario avoid high borrowing costs.   They have the reserves they need.

My answer to these issues is not to develop some regulatory scheme that keeps the true measure of the quantity of money proportional to base money.   The tie between base money and the broader monetary aggregates is redeemability.    Those other instruments are redeemable for base money.   While there is no guarantee for any kind of proportional relationship between the aggregates, control over the base is sufficient to prevent an excess supply of the other aggregates.    And what about excess demand?   In the end, base money is part of the quantity of money, and by expanding it enough, decreases in the quantity of other monetary instruments can be offset.

Like Sumner, I think the answer is to a money multiplier that can shift is to adjust the quantity of base money according to the demand to hold it.  Unfortunately, that begs the question of what is the nominal anchor.   If the quantity of base money adjusts to the demand to hold it, it cannot serve as nominal anchor.   In my view, a growth path for spending on output, in particular, nominal GDP, is the least bad approach.