Prof. Bryan Caplan

Econ 918

Spring, 1998

Week 11: Privatizing Money, II: Free Banking

  1. Free Banking: A Working Definition
    1. We now turn from privatization of the monetary base to full deregulation and privatization of banking. Unless stated otherwise, it will be assumed that free banking is combined with a privatized monetary base. Either probably base is highly inelastic, so base money elasticity will generally be ignored.
      1. Gold
      2. Frozen stock of fiat dollars
    2. The "free banking" label has been applied to a wide variety of historical banking systems, many of them highly regulated. To clarify discussion, let "free banking" for the present discussion is stipulated to have the four following characteristics:
    3. Characteristic #1: Freedom of banknote issue. Banks are able to issue not only checks, but bearer-notes (imagine traveler's checks that don't need to be endorsed by anyone). In historical banking systems, private banknotes have circulated widely, and usually disappeared only when subject to discriminatory taxation or simply banned.
    4. Characteristic #2: Unregulated reserves. Banks alone determine what their reserve ratio will be, regardless of the type of account.
    5. Characteristic #3: Unregulated portfolios. Banks alone determine what kinds of assets they want in their portfolios.
    6. Characteristic #4: Uninsured banks. The government does not bail out or otherwise insure banks that can't pay their depositors. An insolvent bank is subject to the general law of bankruptcy, so depositors may lose principal upon liquidation.
  2. The Determinate Reserve Ratio
    1. Helpful approach: think of bank's demand for reserves as a derived demand.
    2. Two reasons a bank needs base money.
      1. Customers' net deposits of base money.
      2. Interbank clearings.
    3. Expected value of net deposits + clearings must be zero in equilibrium. But this does not mean that a bank actually wants zero reserves because this would leave it illiquid half of the time. Instead banks will always want to hold more base money than they expect to need in order to handle some magnitude of above-average clearings.
    4. More formally, banks are trading off two costs, one of which increases in expected value as reserves increase, while the other increases in expected value as reserves decrease. Assuming - as is standard - that businesses are risk-neutral gives a unique optimum.
      1. Expected return foregone increases as reserves increase.
      2. Expected illiquidity/financial embarrassment costs increase as reserves decrease.
      3. Question: Is it a necessary truth that uninsured banks will want to reduce their reserve ratio when interest rates rise?
    5. Two shifters of equilibrium base money demand (can you name the disequilibrium sources?):
      1. SD of customers' net deposits of base money.
      2. SD of interbank clearings.
  3. Free Banking when the Public Holds No Base Money
    1. A frequently-used assumption in the free-banking literature is that the public holds no base money.
      1. This is fairly easy to justify if the base money is a precious metal, but harder if the base money is a frozen stock of dollars.
    2. If the public has no base money, then the sole shifter of equilibrium base money demand is the SD of interbank clearings.
    3. Important advantage of free banking when the public holds no base money: shift in desired currency/deposit ratio does not contract the money supply. (Still important during e.g. Christmas; probably more important in agricultural economy).
    4. Proofs:
      1. Under traditional banking, B=R+C and M=D+C. Let c=C/D and r=R/D. Then B/R=r+c and M/R=1+c, and M/B=(1+c)/(r+c), and M=B(1+c)/(r+c). Thus under traditional banking, increases in the currency/deposit ratio reduce the money supply (holding the base constant).
      2. Under free banking, B=R, not R+C; furthermore, M=D+N, where N is the quantity of non-base banknotes held by the public. Finally, by definition R=r(D+N) under free banking, so M/B=1/r, and M=B/r. Thus under free banking, the broad money supply is independent of the currency/deposit ratio.
    5. Intuitively, under traditional banking, if a customer who wants to start holding an additional $1000 in currency closes an account for $1000, the bank has to fork over $1000 in base money and slightly contract its loans (and if the customer doesn't re-deposit the currency, no other bank can expand as a result. In fact, there's a multiple contraction of the money supply).
    6. In contrast, under free banking, if a customer wants to start holding an additional $1000 in cash, the bank just closes the customers account and hands over $1000 in the bank's own banknotes. It's a swap of one bank-created liability for another, no different than a move from checking to savings.
  4. Banks' Optimal Response to Shifts in Money Demand: the MV Stabilization Theorem
    1. What happens to banks' derived demand for base money when there is a shift in overall money demand (i.e., not just a shift in the desired currency/deposit ratio)?
    2. Continuing to assume that the public holds no base money, notice that an increase in money demand implies a reduction in the total value of purchases, hence a reduction in total bank clearings. And when total bank clearings falls, so does the SD of total bank clearings!
    3. Two polar cases:
      1. If the decline comes purely from the size of transactions rather than the number, the SD declines in exact proportion to the decline in total clearings.
      2. If the decline comes purely from the number of transactions, the SD declines in exact proportion to the square root of total clearings.
    4. What then does the new equilibrium look like? When the SD of clearings falls, banks have more reserves than they want. They are over-secure, holding a quantity of reserves appropriate for a higher SD of clearings. This makes it safe for all banks to reduce their quantity of reserves.
    5. But if the public doesn't hold base money, then the reserves are in a closed system. What has to happen? Social income has to grow. Banks keep reducing reserves until the new influx of money has raised income back to the level necessitating the total reserves in existence. And what income level is that? The original level! Under free banking reserve requirements fluctuate to stabilize MV.
      1. If decline comes from number of transactions, MV fluctuations are dampened but not eliminated. (Why?)
    6. Formal proof: Let Xi~(0,s xi)represent impact of transaction i on bank j's total bank reserves; Xi={-1, 0, +1}. Then X, the sum of all transactions, has impact X~N(0,s ). Then optimization requires that Rj=bs =bs xiT1/2. b=p/r, where p is per-dollar adjustment cost of reserve deficit, and r is per-dollar opportunity cost of reserve holding.
    7. If each transaction is for $P instead of $1, then Rj=Pbs xiT1/2. Then interpret P as the price level, and use the equation of exchange: MVT=PT. (Note: VT is planning-period velocity, and T is number of transactions). Subbing in for P: Rj=bs xMVTT1/2.
    8. Finally, define y=kT, the planning-period value of real income, and note that therefore V, the income-velocity of money, is kVT. Then Rj=bs xMVy1/2k-3/2. Now for the whole banking system, R is fixed, and so too (?) are b, s x, y, and k. Thus, the product of the two remaining variables MV must be constant.
  5. The MV Stabilization Theorem: Some Critical Questions
    1. Are the other variables really constant when V shifts? (Note b=p/r!)
    2. Are V shifts important anyway?
    3. Timing problems: which happens first - the business downturn in response to the velocity fall, or the monetary expansion in response to the velocity fall? If the former, then - due to collateral and similar credit market imperfections discussed earlier - might not banks respond by increasing their reserve ratio instead of decreasing it?
    4. Is this a short-run or a long-run result? In order to be an efficiency advantage, it needs to be short-run, because that is the time horizon that MV stabilization matters over.
    5. Why doesn't MV stabilization happen now? (Are reserve requirements analogous to price controls?)
  6. Advantages of Free Banking
    1. Knowledge problem of central banking - even if you want to stabilize MV, how do you know how to do it? CBs unlike free banks must rely on aggregate statistics rather than the market signals, but:
      1. Knowledge is dispersed and decentralized (as Hayek emphasizes).
      2. Long and variable lags.
      3. No profit and loss test.
    2. Automatic MV stabilization.
    3. Automatic adjustment of currency/deposit ratio without need to seasonally adjust base money.
    4. Runs, panics, and insurance: see earlier weeks.
    5. Hybrid system: combining active fiat money issue with free banking.
  7. Disadvantages of Free Banking
    1. Runs, panics, and insurance - the other side.
    2. MV stabilization rule may not hold at all due to credit market imperfections.
    3. MV stabilization may be a purely long-run result, in which case it isn't particularly helpful.
    4. Can you really expect the public to hold no base money?
    5. Can you expect banks and/or merchants to accept other banks notes at par?
      1. Note-dueling.
    6. If fiat dollars are the base, then why would anyone want banknotes instead?
      1. Serial number lotteries?
    7. The natural monopoly argument:
      1. Variant #1: Under free banking, one bank would ultimately become the sole bank. (Highly implausible).
      2. Variant #2: While the equilibrium number of banks under free banking is greater than 1, the optimum number of banks is 1. (Dissipation caused by zero-profit condition?)
      3. Variant #3: While the equilibrium number of banks is zero, clearinghouse associations and similar inter-bank organizations can effectively cartelize the industry.
    8. Inflation rule arguments (unless productivity norm is your first-choice inflation rule!)
    9. Other externalities, coordination failures, etc.?
  8. Historical Examples
    1. U.S. (not a very good example!)
    2. Scotland
    3. Canada
    4. New England
    5. Many others. Interesting general finding: system-wide runs of the U.S. type hardly ever occur anywhere else.