2. Free Banking in Theory and Practice
Lawrence H. White
George Mason University

3. Money issue by unregulated banks
How are M and ppm determined under free banking competition?
Allowed to issue currency, absent reserve requirements, etc., what economic forces if any compel banks to
limit their issues?
hold positive reserves?

4. Free banking versus Central banking
19th cent. debates
Vera Smith, The Rationale of Central Banking
L H White, Free Banking in Britain

5. Key assumptions for bank of issue
Bank-issued (“inside”) money is redeemable for some reserve (“outside”) money
Purchasing power of outside money is given to the individual bank
and to the banking system for a SMOPEC
Bank is a price taker in deposit and loan markets
Interbank par acceptance, clearing, settlement

6. Simplified balance sheet
Assets Liabilities + Equity
______________________________________
R reserves N notes in circulation
L loans and securities D deposits
K equity capital
risk-return tradeoff in reserve holding
interest-bearing vs. non-interest-bearing liabilities
Balance sheet constraint: R + L = N + D + K
assume given K

7. Profit function  = iLL ‑ iDD ‑ C ‑ Q where  = expected profit
iL = interest yield on loans and securities
iD = interest rate on deposits
C = operating cost
Q = liquidity cost
assume iL and iD are parametric (bank is a price‑taker)

8. Operating costs C
continuous (and positive) function of each of the balance sheet items:
C = f (R, L, N, D)
CR > 0, CL> 0, CN> 0, CD> 0
where
CR is the marginal cost of holding larger reserves
CL is the marginal cost of holding a larger loan portfolio, etc.

9. Expected liquidity cost Q
probability of reserve shortfall of X, times penalty for that size shortfall
Q = p(X ‑ R)  (X| N, D) dX
where
X = outflow of reserves, R = initial reserves
 (X| N, D) = probability density function over X, conditional on N and D
p = penalty cost as a percentage of shortfall,
p = 0 for X  R, p > 0 for X > R
When mean of  is zero (probability of reserve loss is .5), p must exceed twice iL (the opportunity cost of holding reserves) to motivate positive reserves
Choices of R, N, and D depend on how they influence Q

10. Expected liquidity cost Q

11. Equi-marginal conditions: #1
Equal marginal benefits to lending and holding reserves
iL ‑ CL = ‑ QR ‑ CR
LHS: marginal net revenue from making loans
RHS: marginal net benefit from holding reserves (reduction in liquidity cost minus the marginal operating costs of reserve holding)
Note: QR < 0

12. Equi-marginal conditions: #2
Marginal benefit to lending equals marginal cost of financing via note-issue:
iL ‑ CL = CN + QN
LHS: marginal net revenue from making loans
RHS: marginal cost of maintaining currency in circulation, sum of marginal operating cost and marginal liquidity cost.
Bank’s desired note circulation limited by the rising marginal cost of keeping currency in circulation (more below)

13. Equi-marginal conditions: #3
Marginal benefit to lending equals marginal cost of financing via deposits:
iL ‑ CL = iD + CD + QD
LHS: marginal net revenue from making loans
RHS: total marginal cost of maintaining and servicing deposits
interest payments
marginal operating cost
marginal liquidity cost

14. Equi-marginal conditions: #4
Marginal net benefit of holding reserves equals marginal cost of financing via note-issue:
‑ QR ‑CR = CN + QN

15. Equi-marginal conditions: #5
Marginal net benefit of holding reserves equals marginal cost of financing via deposits:
‑ QR ‑CR = iD + CD + QD

16. Equi-marginal conditions: #6
Marginal cost of expanding the bank’s note circulation equals marginal cost of expanding its deposits:
CN + QN = iD + CD + QD

17. The costs of expanding N
Cheap to print up notes and lend them into circulation
But the bank can expand its earning portfolio only if the currency stays in circulation
Bank must get clients to hold its currency, rather than redeem or deposit
Faces rising MC of cultivating such a clientele
unlimited profits not available from unlimited expansion

18. Costly ways to increase demand to hold a bank’s notes
attract more depositors
virtual note-brand discrimination
make redemption easier
open more branch offices
hire more tellers
stay open more hours
advertise
anti‑counterfeiting measures
make the currency more attractive
Is non‑price competition for customers inefficient?
No. See unit 6.

19. What corrects a bank’s over-issue?
Reserve losses as notes return for redemption
“overissue”: the quantity of a bank’s currency in circulation exceeds the quantity demanded
given its optimizing expenditures on non-price competition
cause: either bank expands N, or Nd falls
What corrects over-issue?
Fullarton's (1845) flawed “law of the reflux”
correct theory: actual N converges on desired Nd as the public adjusts toward its desired portfolio of assets

20. Why excess notes return
An individual with excess note balances can respond in any of three ways
Direct redemption
causes reserve loss, N reduction, for over-issuing bank
Deposit the excess into another bank
generates adverse clearings at the clearinghouse
reserve loss, N reduction
Spending
transfers the excess to someone else; same three options
leads to direct redemption and deposit at the next stage

21. Reserve losses due to adverse clearings
Signal to the bank that reissuing the returned notes would simply lead to further reserve losses
so the bank will accept the reduction in its circulation
Reduce reserves below the bank’s desired level
prompts it to sell securities (or not roll over maturing loans) in order to increase its reserves

22. What corrects a system’s over-issue?
System-wide reserve losses: "external drain"
Direct effect: extra spending, prompted by excess supply of money (ESm), on imports
imports paid for by exporting specie
which comes out of overissuing banks’ reserves
Indirect effect via price-specie-flow mechanism
domestic P > world P
Exports depressed and imports stimulated
Balance of payments deficit again settled by exporting reserve money from bank vaults
The outflow of bank reserves signals and also corrects ESm and P divergence
Hume

23. A reserve-loss externality?
The indirect effect acting through P draws reserves from all banks, not just over‑issuer(s)
thus raises the possibility of that innocent banks may suffer reserve losses
but innocent banks will also enjoying positive clearings from expanding bank(s)
Effect on P is small relative to adverse clearings where the overissuing bank is small
Conversely, the larger the overissue relative to M, the greater will be the external drain

24. “Free banking School” policy implications
Competition (many issuers) limits the danger of a large-scale overissue
Random money-supply errors will tend to offset one another in the aggregate
Danger of large-scale overissue is greatest when a single issuer has a 100% share of the circulation
Conclusion: don’t restrict note-issue to a single institution (like BOE). Allow free entry.
Did BOE promote England’s growth? Compared to what?
J. W. Gilbart

25. What if all the banks in the world over-issue in concert?
Interbank adverse clearings won’t operate
each bank collects more to offset greater returns
External drain won’t operate
ditto for each country
Nonetheless there is a unique equilibrium system-wide volume of N, not a continuum of equilibria given system-wide R
Selgin: In-concert expansion doesn’t make any bank loses reserves
but instead increases every bank’s desired reserves
greater N means greater threat to existing reserves
Mises: drain of gold into non-monetary use as ppg falls

26. In-concert over-expansion
Selgin: increases desired reserves by increasing each bank’s threat of reserve depletion, with greater gross volume of clearings
The mean of net clearings can remain zero for each bank
but the risk of reserve depletion increases because the increase in gross clearings widens the reserve-loss probability distribution
and thus enlarges the area of the left tail beyond any given level of reserves

27. In-concert overexpansion raises Q

28. As a result of in-concert over-expansion
Each bank will feel its risk of running out of reserves too great
banks must contract their liabilities (N and/or D) to reduce illiquidity risk

29. Equilibrium volume of system liabilities
is uniquely determined by
the marginal cost functions the individual banks face for expanding demand to hold their liabilities
the volume of system reserves
the stochastic process generating adverse clearings
the level of safety each bank desires against reserve depletion
With no change in these fundamentals, in-concert expansion is inconsistent with an equilibrium in which all banks are optimizing
the same logic rules out arbitrary in-concert reserve reduction

30. What corrects a bank’s under-issue?
Suppose the actual circulation falls short of the desired circulation
Demand to hold Bank i-currency has risen without additional expenditures by Bank i
marginal operating cost (CN) is no higher
marginal liquidity cost (QN) is no higher, despite the larger volume.
The bank can profitably expand
as if customers borrow and promise to hold (not spend) additional notes

31. How does an under-issuing bank know to expand?
Customers, whose demand to hold i-currency has risen, spend it less
Fewer i-notes enter the clearing system: N “passively” expands
Bank i enjoys positive clearings
Reserves become greater than desired
Profit motive prompts lending out of undesired reserve

32. Thus the supply of money by an individual bank is “demand‑elastic”
Bank i finds it profitable to respond to a rise in demand by expanding
the reverse for a fall in demand

33. What corrects a system’s under-issue?
Suppose a general rise in the public's desired holdings of currency (across all brands)
Customers seeking to accumulate greater N in proportion to their spending
temporarily spend less or try to earn more
Spending flows fall relative to the stocks of bank-issued money and reserves
No bank systematically gains reserves from other banks, but each bank can safely and profitably expand, because its reserve-loss threat is reduced

34. The open-economy case: PSFM
The banking system enjoys net positive clearings against the rest of the world
The public's attempt to build up its money balances curtails its spending on imports relative to exports
Reserves flow in from abroad to settle the positive balance of payments
Domestic banking system gains additional reserves

35. What if all the banks in the world under-issue in concert?
Flip side of the world-wide over-issue case
The banks' desired reserves fall below actual
Reduced spending per unit of currency, as people try to build up N balances
Reduces banks’ liquidity costs by reducing the chance of reserve depletion for any initial R
Banks will expand their liabilities, raising desired reserves, until desired reserves again match the given stock of reserves.

36. The supply of money by the banking system as a whole is “demand‑elastic”
Banks as a group
find it profitable to respond to a general rise in demand for bank-issued money by increasing its volume
the reverse for a fall in demand
Does this kind of monetary expansion distort the interest rate and thus dis-coordinate the intertermporal market?

37. “Needs of trade” doctrine, valid version
competitive note-issuer can’t persist long in over-issue, assuming
redeemability
(virtual) note-brand discrimination

38. The volume of bank-issued money is governed by the public’s demand under free banking
“A single bank … will be able to circulate more fiduciary media only if there is a demand for them even when the rate of interest charged is not lower than that charged by the banks competing with it.
Thus the banks … increase and decrease their circulation pari passu with the variations in the demand for money, so far as the lack of a uniform procedure makes it impossible for them to follow an independent interest policy. But in doing so, they help to stabilize the objective exchange value of money.
--Ludwig von Mises, Theory of Money and Credit, p. 347 (1980 ed.)

39. “Needs of trade” doctrine, invalid versions
“Real Bills Doctrine”: No bank (not even monopoly issuer) can over- issue by lending on “real bills” (making the right kind of loans)
confuses demand for currency with demand for credit
confuses quantity of currency with quality of credit
makes gold redeemability a “fifth wheel”; esp. dangerous for fiat issuer
harmless for a single small bank
dangerous as a guide to central bank policy
Fullarton’s reflux: any ES of notes returns to repay loans
also neglects redeemability, purports to limit even monopoly issuer (who can increase QD of credit by i), even in SR
(Opposing “Currency Principle”: ΔN should match ΔG)

40. Demand-elasticity of bank-issued money promotes nominal income stability
a fall in the velocity (turnover) of bank-issued money
leads to an offsetting change in the stock of bank-issued money by raising the money multiplier
velocity =df the ratio of spending to money balances (V = Py/M)
Rise in the demand to hold bank-issued money balances relative to spending implies a fall in velocity
Fall in velocity → reduced turnover of bank-issued money → reduced probability of adverse clearings → bank can keep more liabilities in circulation for a given quantity of reserves
The rise in (N + D) restores equilibrium by pushing back up the representative bank’s marginal benefit of holding reserves (QR)
Nice result: helps stabilize MV (=Py), i.e. aggregate demand

41. Market-based money in history
gold standard before WWI
gold MOA and MOR, PSFM operates
plus
free banking prevailed before state central banks took over
FB = free competition in redeemable currency and deposit issue
Central banks, often established for fiscal reasons, came to
centralize note issue and gold reserves
restrict commercial banks
assume “lender of last resort” role
over-ride automatic gold standard mechanism with discretionary policy
Source: Juliette Healey in Richard Brearley et al., eds., Financial Stability and Central Banks: A Global Perspective (London: Routledge, 2001), p. 22.

42. Ignacio Briones and Hugh Rockoff, Volume 2, Issue 2, August 2005
1995
1936 / 1990
1992
2015
Ignacio Briones and Hugh Rockoff, Volume 2, Issue 2, August 2005

43. A fiduciary currency ostensibly convertible into the monetary commodity is therefore likely to become over-issued from time to time and convertibility is likely to become impossible. Historically, this is what happened under so-called ‘free banking’ in the United States and under similar circumstances in other countries.
-- Milton Friedman, A Program for Monetary Stability (New York: Fordham University Press, 1960), p. 6.

44. Historically, producers of money have established confidence by promising convertibility into some dominant money, generally, specie. Many examples can be cited of fairly long-continued and successful producers of private moneys convertible into specie.
-- Milton Friedman and Anna J. Schwartz, “Has Government any Role in
Money?,” Journal of Monetary Economics 17 (1986), pp. 45, 49-50

45. Some historical free banking systems
Scotland Canada Sweden New England
… and 50+ more

46. Scotland
1716 to 1844: free entry of unlimited liability joint-stock banks
Minor restrictions: minimum note denomination, no “option clauses” on notes after 1765
Stability and competitive performance
heyday:
Many (c. 20) competing banks, well capitalized, extensively branched
1-2% spread between deposit and loan rates
Banks mutually accepted one another’s notes at par
Bank of England did not act as LOLR

47. Canada 1867-1914, liberal granting of bank charters (with min. K req.)
B&R: “like the Scottish system and parts of the American system, was clearly a successful case of lightly regulated banking.”
Stability and competitive performance
Low failure rate
1-2% spread between deposit and loan rates
Many (c. 24) competing banks, branched nationwide
Banks mutually accepted one another’s notes at par
Canadian system “did so well that a central bank was not established until 1935”
Even then not because the system was unsatisfactory

48. United States
, New England region the least restricted, most competitive, and soundest system in the United States
Suffolk Bank of Boston, then Bank for Mutual Redemption, ran note clearing system that kept various banks’ notes at par region-wide
So-called “free banking” laws in other states opened up entry, but imposed collateral restrictions on note issue and maintained branching restrictions
“Wildcat banking” stories exaggerated (Rockoff 1974)
Failure problems in some states were due to poorly designed collateral restrictions (Rockoff 1974; Rolnick and Weber 1983, 1984)

49. Sweden
: free entry into redeemable note-issue by competing enskilda banks
Notes circulated widely at par
Reserve requirement of 5%, never binding
minimum note denomination (5 riksdaler)
Remarkably low failure rate, unlimited liability
Large numbers of partners, up to 1000 in some cases
Provided seasonal elasticity to payments and credit (Hortlund SEHR 2007)
Paliament’s bank, the Riksbank, also issued notes, but did not outcompete them
Lakomaa (2007): “Notes from private banks seemed to be preferred by the public to the Riksbank notes”
Enskilda banks’ market share > 50% during
B&R: “the combination of the two maintained convertibility and provided an efficient means of payment for the Swedish economy.”

50. Some other studied episodes
Switzerland
see: EJ Weber 1992; Fink 2014; versus Neldner 1998
Chile
see: Couyoumdjian, ed., 2018
Australia
see: Dowd 1992
Colombia
see: Meisel 1992
Ireland
see: Bodenhorn 1992
Post-revolution France 1796–1803
see: Nataf 1992)
1992 = Kevin Dowd, ed., The Experience of Free Banking

51. Summary of free banking’s record
Economies of scale, but not too few banks for competitive performance
Fostered efficiency and innovation in payments practices and intermediation
Thereby boosting growth: see Adam Smith on Scotland
Not prone to excess expansion, inflation, or suspension/devaluation
Not panic-prone
Contrast Canada to United States, where legal retrictions weakended banks
Contrast pre-1832 Scotland to England, ditto

52. Why did central banking win politically?
In some places (e.g., London) free banking never received a trial
Rent-seeking by privileged bank
Central banks mostly arose, directly or indirectly, from fiscal legislation
Seigniorage from monopoly issue
In the form of cheap loans when the central bank was privately owned (BoE, BoF)
Sometimes (e.g. United States) central bank was created to remedy weaknesses caused by earlier (often fiscally motivated) restrictions on banking

53. Is central banking a “natural development”?
CAE Goodhart, The Evolution of Central Banks (1985):
the public has a “need for quality control and supervision” of banks by some third party, and
the banks need a lender of last resort
a government central bank can play these roles more efficiently, because more impartial, than a private clearinghouse association
CHA will ask the government to step in
Doubtful because
In the least restricted free-banking systems (Scotland, Canada, Sweden, New England) quality control was not a chronic problem
CAEG cites Friedman (1960) claim that free-banking systems over-issue, but not Friedman-Schwartz (1986) reconsideration
No evidence that partiality undermined clearinghouse LOLR role
In no historical case, as recounted in Goodhart’s own appendix, did CHAs ask government to step in

54. Gold + free banking = strict pre-commitment
Value of monetary policy pre-commitment (Kydland and Prescott 1977)
Classical gold standard = semi-strict pre-commitment (see: Bordo and Kydland 1995)
+ free banking (no central bank tempted to devalue) and stricter still
Free banking systems had a better track record than central banks for not devaluing
Gold + Free banking privatizes and decentralizes currency pre-commitments, making them more trustworthy