Prof. Bryan Caplan

Spring 2000


Week 11: Privatization of Money, I: Commodity Standards

I.                     Privatization of Money

A.                 From week 3 it has been implicitly assumed that money is under the monopoly control of some government.

B.                 But while true in the modern world, this manner of presentation ignores the alternative of non-government provision of the (?) monetary system.

C.                Next two weeks will consider the several angles on the alternative of private supply of money:

1.                  Theory

2.                  Objections

3.                  Relevant historical experiences

D.                All key aspects of a monetary system will be examined through this lens, so at the end of it should be possible to envision a fully privatized monetary system.

1.                  This week: Private supply of base money.

2.                  Next week: Deregulation of banking and note issue; further topics.

II.                   Privatizing the Monetary Base

A.                 From the outset of the course the monetary base has always been assumed to be:

1.                  A monopoly of the government.

2.                  Costless to create.

B.                 The connection between this two assumptions should be clear: if money is costless to create, then competition driving price down to cost drives the purchasing power of money to zero.

C.                Next week, alternatives that challenge this inference - in particular privately supplied fiat money - will be considered.  For now we turn to the most easily understood and historically relevant solution: commodity standards.

D.                Under a commodity standard, one (or possibly more) commodities are simply used as money.  The price level is finite because real resources must be used to produce the commodity.

1.                  From now on I’ll refer to gold standard and commodity money interchangeably, but note that that is not a necessary equivalence.  Note further that unless stated otherwise, I’m discussing a hypothetical gold standard without a central bank, not the historical gold standard.

2.                  Note: Mint also assumed to be privatized.  (Inefficiencies of government mints; Polish example)

E.                 Assuming that gold is a sufficiently focal commodity, all of the standard results on money demand from week 3 hold.  Any exceptions?

F.                 Main difference: supply of commodity base money is inherently endogenous, even in a closed economy.  Unless gold is irreproducible, a rise in the price level ipso facto implies a lower gross return to mining more gold, and vice versa.

G.                Under CRS in gold mining, and assuming no innovations in productivity or money demand, the market endogenously generates an equilibrium money supply, such that if the price level rises too high, gold mining ceases, and if the price level falls too low, unlimited resources flow into the gold mining sector.

1.                  Under these assumptions, new mining merely replaces wear-and-tear of existing gold stock.

H.                 More realistic assumption: extremely inelastic supply due to increasing ACs.  (World) money stock equilibrates at glacial rates, though flows between regions may still be quite rapid.

1.                  Hume’s specie flow mechanism.

I.                     Questions/puzzles:

1.                  What crucial assumption must one make about elasticities for Hume’s specie flow mechanism to work?

2.                  Does jewelry demand play an extraordinary role under the gold standard?

3.                  Why were Europeans always searching for gold instead of non-monetary commodities during the Age of Exploration?

4.                  Why does the market tend to select commodities with non-monetary uses for monetary purposes, when an inelastically supplied commodity without any non-monetary uses would be more efficient?

III.                  100% Reserves vs. Fractional Reserves

A.                 One variant on commodity standards  - seriously considered not just by Rothbard but also by Friedman and others - combines gold base money with a ban on fractional-reserve banking.

1.                  How would banks support themselves?  With fees - just like safe deposit boxes.

2.                  You could still write checks or use bank notes instead of gold coin, but these would be backed 100% by gold.

3.                  Note currency board analogy.

B.                 Positive analysis: what would the impact of imposing the 100% reserve standard be?  Think of banks as a special kind of mutual fund.  Reserve requirements essentially force banks to hold a fraction of their portfolio in zero-return assets.  This can be seen as a tax on one type of mutual fund.

C.                The consequences of this tax:

1.                  A reduction in the price level.

2.                  A shift from banks issuing “money” to other kinds of mutual funds not subject to the required reserves law.

3.                  What determines the relative size of these two effects?  Which would be larger in e.g. the current U.S.?

D.                Normative analysis: why would anyone want to impose a 100% reserve requirement?

1.                  Definitional complaints about “money.”

2.                  Makes sharp deflations nearly impossible, since banking system is forced to be perfectly liquid.

3.                  Makes absence of deposit insurance credible (similar to narrow banking).

E.                 Legal fractional reserve banking does to a 100% gold standard what abolishing reserve requirements does to the current system:

1.                  Raise the price level.

2.                  Cause an expansion in the banking sector and a contraction in the non-bank financial services sector.

F.                 Normative analysis:

1.                  Fractional reserve system is potentially vulnerable to sharp deflations - but an important paper by Calomiris and Kahn suggests that this is a largely artificial problem.  Historically, bank runs were not random.  They targeted insolvent banks.  Solvent banks sometimes suffered too, but private clearinghouses distinguished between solvent and insolvent banks and provided liquidity only to the former. 

2.                  (Further observation: U.S. style runs basically don't happen in other countries.  Suggests connection to branch banking laws and other unusual U.S. regulations).

3.                  Unregulated reserves prevents need to artificially shed the “bank” label.

G.                General comment: With well-developed financial markets, 100% reserves would probably provoke massive flight from banking sector.  Non-bank sector might be run-proof, but could still experience sharp crashes that would have the same impact as bank failures now.

IV.               Main Objections to Privatizing the Monetary Base

A.                 Resource waste.  Commodity standards are wasteful because the same function could be served by a money without an alternative non-monetary use.

1.                  Gets small for fractional reserve systems.

2.                  Governments have not generally sold off their gold stocks even after abandoning gold standard, and greater inflation volatility has made gold a more valued hedge.  So paradoxically, dropping the gold standard has restricted industrial and consumer uses of gold more, not less!

B.                 Gresham’s Law.  Among the most popular, but quite weak.  Applies only if:

1.                  Price controls are imposed, as in bimetallism.

2.                  Or, verification of the authenticity of money is more costly for merchants than for customers.

C.                Fraud.  Again quite weak - “Private enterprise has been able to supply an almost infinite number of goods requiring high precision standards; yet nobody advocates nationalization of the machine-tool industry or the electronics industry in order to safeguard these standards.” (Rothbard)

1.                  Analogous to machine tools, or more like designer jeans?

2.                  In any case, less of a problem than bad checks.

D.                Makes discretionary macro policy impossible.  Given the time consistency literature, this almost seems like a benefit, especially since the empirical evidence suggests that countries are still not trading off any real performance when they "buy" lower inflation.

E.                 But: Would the gold standard be vulnerable to severe deflations, supply shocks, etc?  I.e., is there a large class of macro ills that discretionary policy has solved so well they are no longer observed?

F.                 Commodity standard inconsistent with optimal inflation rule.  Depends on which policy is optimal (consider 3 rules discussed in class).

1.                  Normal case under a gold standard is arguably a higher growth rate for real output than for the gold stock, but both tend to be positive, so nominal GDP should still show trend growth.

V.                 Time Consistency and the Gold Standard (from Bordo and Kydland)

A.                 The gold standard provided the primary solution to the time consistency problem in earlier periods.

1.                  Note Bordo and Kydland's revisionist concept of rules.  For B&K, a rule is a way to bind policy over time, rather than anything "impersonal and automatic."

B.                 Even with a weaker gold standard, the need to deflate later to compensate for inflation now removed most of the incentive for opportunism.  One-shot gain balanced out by later need to contract, even without reputational effects.

C.                During gold standard period, defection was more likely to involve inflation for expropriation than inflation for employment-expansion.  But the time consistency problem is analogous.

D.                Gold standard worked as a contingent rule: countries did suspend payment during big wars and similar emergencies, but for over a century there was a credible implied promise to return at parity.  Analogous to allowing limited discretion for supply shocks.

1.                  But isn't there also a "peaceful intentions" credibility problem that a non-contingent gold standard could help solve on the international level?  I.e., if countries precommit to make it difficult to raise war revenue, won't that make mutually advantageous disarmament easier?

E.                 The contingent rule of the gold standard also made emergency finance cheaper, since creditors could anticipate repayment would not be eroded by inflation.

F.                 Other important aspects:

1.                  Core vs. periphery countries.

2.                  Inflation (non-)persistence.

G.                Gold standard as a rule was extremely credible (for some countries) for a long period.  Consider:

1.                  Resumption after Napoleonic wars.

2.                  Resumption after WWI.

H.                 Contrast with:

1.                  ABC countries of Latin America.

2.                  Southern European countries.

I.                     Questions

1.                  How does the classical gold standard compare to other solutions to the time consistency problem?

2.                  Why did the gold standard cease to be credible from the inter-war period on?

3.                  How would a non-contingent gold standard compare - in stability and as a solution to the time consistency problem?

4.                  A tale of reverse causality: how could going off the gold standard cause wars?  How could peace treaties become more credible if participants make it difficult to get emergency tax revenue?  (Do you need additional assumptions on conquest and defense technology?)

5.                  Is there an analogy between "dollarized" economies and an economy on a non-contingent gold standard?

VI.               The Gold Standard Era in Perspective (from Bordo, "The Gold Standard, Bretton Woods and Other Monetary Regimes")

A.                 Three caveats:

1.                  Under historical gold standard, central banks held much or most of the monetary gold, and stayed on the gold standard by pegging the price of gold in terms of domestic currency.  So even in its heyday it was a much weaker gold standard than the pure case considered above.

2.                  Pre-WWI CGS differed markedly from post-WWI "gold-exchange" standard.  Will be explored more fully in Week 13; current discussion focuses on pre-WWI CGS.

3.                  Large measurement error for early periods means variances tend to be over-estimated.  (See e.g. Christina Romer's piece "Is the Post-War Stabilization a Figment of the Data?")

B.                 Four major eras - plus several notable sub-periods - in the monetary history of the G-7 countries over the past century or so:

1.                  Classical gold standard: 1881-1913

2.                  Interwar period: 1919-39

a)                 Floating exchange rates: 1919-1925

b)                 Gold exchange standard: 1926-1931

c)                  Managed float: 1932-1939

3.                  Bretton Woods: 1946-1970

a)                 Pre-convertible: 1946-1958

b)                 Convertible: 1959-1970

4.                  Floating: 1971-present

C.                How does the classical gold standard measure up?

D.                Inflation:

1.                  Classical gold standard had the lowest rate of inflation of any period except the interwar period. 

a)                 N.B.  Countries' inflation rates also showed most convergence during CGS era.

2.                  Inflation volatility of CGS beats all other periods (though convertible Bretton Woods sub-period beats inflation volatility of CGS).

E.                 Real output growth (per capita):

1.                  Bretton Woods period beats CGS on both level and volatility.  (Could this be due to greater measurement error in early years?  What kind of measurement error?)

F.                 Money growth:

1.                  CGS had lowest money growth except for interwar period.

2.                  Money growth volatility of CGS actually loses to floating exchange rate regime, but beats Bretton Woods.  (Interwar regime does worst of all).

G.                Interest rates:

1.                  Short-run nominal - CGS level lower than all except interwar period.  Volatility lowest of all.

2.                  Short-run real - CGS second-highest (only interwar higher).  Same for volatility.

3.                  Long-run nominal - CGS mean lowest of all.  Same for volatility.

4.                  Long-run real - Highest level except for interwar; lowest volatility.

H.                 Persistence: Inflation found to be white noise during CGS, highly persistent in other periods.

I.                     Responsiveness: Responsiveness of prices to D and S shocks founds to be much greater during CGS.  (Why?  More flexible labor markets, more restricted suffrage, less understanding of short-run benefits of policy hence less temptation...?)


Prof. Bryan Caplan

Spring 2000


Week 12: Privatization of Money, II: Free Banking and Alternatives

I.                  Free Banking: A Working Definition

A.                 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. 

B.                 Either probable base is highly inelastic, so base money elasticity will generally be ignored.

1.                  Gold

2.                  Frozen stock of fiat dollars

C.                The "free banking" label has been applied to a wide variety of historical banking systems, many of them highly regulated.  To clarify discussion, "free banking" for the present discussion is stipulated to have the four following characteristics:

D.                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.

E.                 Characteristic #2: Unregulated reserves.  Banks alone determine what their reserve ratio will be, regardless of the type of account.

F.                 Characteristic #3: Unregulated portfolios.  Banks alone determine what kinds of assets they want in their portfolios.

G.                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.

II.               The Determinate Reserve Ratio

A.                 Helpful approach: think of bank's demand for reserves as a derived demand.

B.                 Two reasons a bank needs base money.

1.                  Customers' net deposits of base money.

2.                  Interbank clearings.

C.                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.

D.                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?

E.                 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.

III.            Free Banking when the Public Holds No Base Money

A.                 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.

B.                 If the public has no base money, then the sole shifter of equilibrium base money demand is the SD of interbank clearings.

C.                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).

D.                Proofs:

1.                  Under traditional banking, B=R+C and M=D+C.  Let c=C/D and r=R/D.  Then B/D=r+c and M/D=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, designate the quantity of non-base banknotes held by the public as N.  Then under free banking, r=R/(D+N) and M=D+N.  Thus, R=r(D+N), so B=r(D+N).  Substitute in for (D+N) and rearrange to find that under free banking M/B=1/r and M=B/r.  Thus under free banking, the broad money supply is independent of the currency/deposit ratio.

E.                 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).

F.                 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.

IV.            Banks' Optimal Response to Shifts in Money Demand: the MV Stabilization Theorem

A.                 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)?

B.                 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!

C.                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.

D.                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. 

E.                 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?)

F.                 Formal proof: [note mistake in Selgin/White article!]  Let Xi~(0,sxi)represent impact of transaction i on bank j's total bank reserves.  Then X, the sum of all transactions, has impact X~N(0,s).  Then optimization requires that Rj=bs=bsxiT1/2.  b=p/r, where p is per-dollar adjustment cost of reserve deficit, and r is per-dollar opportunity cost of reserve holding.

G.                If each transaction is for $P instead of $1, then Rj=PbsxiT1/2.  Then interpret P as the price level, and use a variant of the equation of exchange: MVT=PT.  (Note: VT is planning-period velocity, and T is number of transactions).  Subbing in for P: Rj=bsxMVTT-1/2.

H.                 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=bsxMVy-1/2k-1/2

I.                     Now for the whole banking system, R is fixed, and so too (?) are b, sx, y, and k.  Thus, the product of the two remaining variables MV must be constant.

V.               The MV Stabilization Theorem: Some Critical Questions

A.                 Are the other variables really constant when V shifts?  (Note b=p/r!)

B.                 Are V shifts important anyway?

C.                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 (see my Monetary Week 8 notes if you're curious)- might not banks respond by increasing their reserve ratio instead of decreasing it?

D.                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.

E.                 Why doesn't MV stabilization happen now?  (Are reserve requirements analogous to price controls?)

VI.            Advantages of Free Banking

A.                 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.

B.                 Automatic MV stabilization.

C.                Automatic adjustment of currency/deposit ratio without need to seasonally adjust base money.

D.                Runs, panics, and insurance (see my Monetary Week 7 notes for more details).

E.                 Hybrid system: combining active fiat money issue with free banking.

VII.         Disadvantages of Free Banking

A.                 Runs, panics, and insurance - the other side.

B.                 MV stabilization rule may not hold at all due to credit market imperfections.

C.                MV stabilization may be a purely long-run result, in which case it isn't particularly helpful.

D.                Can you really expect the public to hold no base money?

E.                 Can you expect banks and/or merchants to accept other banks notes at par?

1.                  Note-dueling.

F.                 If fiat dollars are the base, then why would anyone want banknotes instead?

1.                  Serial number lotteries?

G.                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.

H.                 Inflation rule arguments (unless productivity norm is your first-choice inflation rule!)

I.                     Other externalities, coordination failures, etc.?

J.                  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.

[if running out of time, lecture stops here]

VIII.      Other Approaches to Privatization, I: Multicommodity Standards

A.                 Historical commodity standards typically have only one good serve as the monetary base, but why do this?  I.e., instead of defining $1=1/20 oz. gold, define $1=(1/100 oz. gold + 5 lbs. tin + 3 liters of Coke +...).  Or even $1=$1 in 1997 CPI.

B.                 It is not particularly convenient to redeem $1 worth of the 1997 CPI.  But that is not a problem.  Just pay out $1 worth of the 1997 CPI in the most convenient single commodity - which could even be gold.  No need for banks to keep a bizarre warehouse stocked with finely divided quantities of every good on the market.

C.                So every day the CPI value of $1 is constant, but each day the amount of gold - or pork bellies, or human blood - you can receive in exchange for $1 fluctuates.  If public ceases to hold base money, then banks nevertheless use the same multicommodity standard to settle clearings.

D.                Inflation is virtually by definition eliminated under a sufficiently broad multicommodity standard - although if important items are difficult to include (e.g. labor) the price stabilization will be imperfect.

E.                 Main macro benefit of the (ideal) multicommodity standard: never any need for overall price level adjustments so long as all prices are denominated in terms of the multicommodity standard (or "valun").

F.                 A multicommodity standard would in practice probably be much easier for a government to get off the ground than it would be for a private banking system, since it would be necessary to effect a massive joint deviation to a new payments system.  A government-created multicommodity standard would amount to forcing the Fed to redeem current dollars for the multicommodity bundle at a fixed ratio.  Financial market arbitrage would do the rest.

1.                  Somewhat similar early proposal: Fisher's compensated dollar.

G.                Questions about multicommodity standards:

1.                  How many commodities are necessary to get close-to-perfect price level stability?

2.                  Does omission of commodities not traded in financial markets create any difficulties for multicommodity standards?

3.                  What happens under a government-administered multicommodity standard if real money demand rises?

4.                  What happens in a free banking system on a multicommodity standard if real money demand rises?

5.                  Any reasons - other than coordination failure - why multicommodity standards have never been observed?  (Is movement to single commodity a PD rather than a coordination failure?)

IX.           Other Approaches to Privatization, II: Competing Fiat Currencies

A.                 Hayek proposed a system of competing fiat currencies, in which multiple firms within a nation issue their own currency, denominated in their own "brand-name" unit.

B.                 Value of such money does not necessarily fall to equal the value of the "paper it's printed on," since issuers have monopoly over their brand names.  (Similarly, the price of Coke does not inevitably fall to equal the price of generic soda, since Coke limits the use of its brand name).

C.                Big coordination problem: How do you get the public to start taking your Hayeks, Rothbards, and Caplans?  How would anyone have any idea what one Caplan is worth?

1.                  Possible solution: Give new money a commodity jump start.  Make it initially redeemable for gold; once it is widely accepted, cut the cord.

D.                Trade-off between initial terms of exchange and subsequent rate of seigniorage (which could be negative).  Commitment to deflate currency increases real value of total stock, but hurts current revenues of fiat-money issuer.  Commitment not to hyperinflate makes private fiat money at least a reasonable alternative to government currency once the coordination problem is overcome.

E.                 Main problem with private fiat currency (apart from coordination problem): Time consistency.  Firm needs to credibly commit not to hyperinflate to get the public to accept a new currency, but once the public accepts the money, the firm can effectively expropriate the whole value by hyperinflating.

F.                 Reputation can solve time consistency problem for private fiat issuers, just like it can solve it for CB.  But: Private fiat issuers do not face elections and have no other source of new revenue other than seigniorage. 

G.                So a private issuer may be more likely to find defection worthwhile.  Which implies not that we will observe a lot of defections to hyperinflation, but rather that private fiat money won't be accepted in the first place.

H.                 Another alternative: Buyback offer (akin to buyback offers on collectors' items).  Effectively commoditizes private fiat money.

I.                     Multicommodity standard at least still allows convenient pricing in valuns.  What would menu costs look like under private fiat money?

J.                  Questions about private fiat money:

1.                  What advantages does it have over commodity (or multicommodity) base money?

2.                  What advantages does it have over government fiat money?

3.                   Why don't international currencies exchange domestically already?  (Except in pathological cases).

4.                   What about menu costs?