A model of the BFH payments system.

I. Introduction The BFH payments system was introduced by Robert L. Greenfield and Leland B. Yeager in "A Laissez-Faire Approach to Monetary Stability" |6~. The key element of their proposal is to dispense with base money and instead tie the means of payment to a nearly-comprehensive bundle of goods and services by the institution of indirect convertibility. Their system promises to be free from inflation and several sources of recession.

While BFH was named to credit Fischer Black |1~, Eugene Fama |3; 4~, and Robert Hail |10; 11~, it must not be confused with their specific institutions or arguments. Greenfield and Yeager modified their ideas and have continued to develop the system |20; 5; 21; 8; 9~.

The purpose of this paper is to present a model of BFH consistent with simple textbook macroeconomics. Contrary to first impressions, BFH is best understood using the concept of money. But the absence of base money makes the "quantity theory" inappropriate for analysis. Instead, a simple "Keynesian" model illustrates the determination of interest rates, real income, the price level, and the quantity of money. Aggregate supply, the "IS" relationship, and money demand are conventional. Only the money supply process is unusual.

II. Money and BFH

Sophisticated Barter?

Fischer Black, Eugene Fama, and Robert Hall claimed their systems are best understood without the concept of money |1, 15; 3, 44; 11, 1553~. Greenfield and Yeager agreed, describing BFH as "a sophisticated system of barter" |6, 314~. Claiming an absence of money can cause unnecessary confusion.

Payments are made much as they are in a conventional money and banking system. Prices are quoted and contracts are made in terms a common unit of account, and this amount is written on the checks used to make payment. Sellers and creditors accept checks drawn on many banks in payment at par because the banks accept each others' checks for deposit at par. Some formal clearing arrangement allows the banks to cancel offsetting claims and settle net clearings |1, 10; 4, 10; 6, 307~.

Unusual Checkable Accounts

One reason Black, Fama, Hall, and Greenfield and Yeager may have found the concept of money inappropriate is their focus on unusual checkable accounts. Black described accounts that are similar to conventional deposit accounts if the balance is positive and similar to conventional credit card accounts if the balance is negative |1, 10-1~. While this is nothing more than the "over-draft" protection provided by conventional banks, Black assumed that any "credit card" balance is directly credited (decreased) when a customer deposits a check.

By assuming all accounts take this form, Black described a system where the quantity of money is irrelevant. For example, it would be conceivable for each person to match daily payments and receipts. The balances in what appear to be conventional deposit accounts (positive balances) would be zero each evening and morning.

Rather than pursue Black's approach, Greenfield and Yeager followed Fama and Hall, emphasizing checkable mutual fund share accounts |6, 307~. Fama went so far as to suggest that checks could be drawn on personalized security accounts |3, 41~. While the unit-of-account values of all the various assets could be summed, aggregating the demands for a variety of assets (each with a different maturity, return, and risk) to find a demand for money seems questionable.

Supply and Demand Determination of Amounts of Means of Payment

A second reason Black, Fama, Hall, and Greenfield and Yeager may have found the concept of money inappropriate is a supposed supply and demand determination of the amounts of the means of payment. Markets for the various means of payment are supposed to clear like the markets for other financial assets |1, 17; 3, 46; 6, 310-2~.

They explicitly or implicitly assumed that banks must offer an interest rate on checkable accounts so that depositors are willing to hold the amounts outstanding |1, 11; 3, 46; 6, 311~. Given this assumption, the difference between the yields on other assets and the yields on checkable accounts is a market "price" that directly adjusts so that quantities demanded and supplied are equal. In equilibrium, this "yield differential" must be equal to the marginal cost of providing intermediation services.

Their assumption is implausible, at least without further explanation (such as that given below). A single bank must pay competitive yields because it will suffer a shortage of funds if its depositors transfer their funds to competing banks. But the banking system cannot suffer a similar shortage of funds because there is no base money for depositors to withdraw.

Some Special Characteristics of Money

To understand why the concept of money is useful for understanding BFH, it is necessary to review some essential characteristics of money. Money is accepted in exchange for goods, services, and assets or in settlement of debts even when sellers or creditors have no intention of increasing their money holdings |18, 43~. They usually accept money with the intention of spending it on goods, services, or other assets.

And since money is often transacted with no intention to change money holdings, there is little reason to negotiate a price and yield on money with each transaction |18, 53~. This is convenient because it simplifies transactions. But it also implies special problems.

Banks can lend new money into existence because those receiving the new money usually intend to spend it on goods, services, or other assets. They have no reason to insist on a yield sufficient for them or anyone else to choose to hold the new money |19, 4~.

And if an excess supply of money develops, those with excess money holdings do not need to offer money for "sale" at a lower price and higher yield. They purchase goods, services, and other assets. The sellers do not insist on a lower price and higher yield on money because they intend to spend the additional funds on goods, services, and other assets.

Similarly, if there is an excess demand for money, those with deficient money holdings do not go to a money shop and offer to pay a higher price or accept a lower yield for newly-issued money. Nor do they go to banks and ask to borrow money. They sell goods, services, and other assets. And because incomes are usually paid in the form of money, they simply can refrain from customary purchases of goods, services, and other assets |18, 56~. Those who buy the assets or fail to make customary sales make up for their now deficient money holdings by also selling goods, services, or other assets and refraining from customary purchases.

Unusual Checkable Accounts and the Special Characteristics of Money

The essential characteristics of money would apply even if all means of payment were in the form of checkable mutual fund share accounts. Usually, sellers would accept checks without intending to increase their holdings of mutual fund shares, so they would have little interest in negotiating a price or yield for shares with each transaction. Mutual funds could spend new shares into existence, using checks drawn on their own account to purchase primary securities. Excessive share holdings would result in checks being written to buy goods, services, or other assets. And inadequate share holdings would result in sales and restrictions on customary purchases of goods, services, and other assets.

The prices and yields on mutual fund shares do depend on market forces, but they do not directly adjust enough to clear the "market" for checkable mutual fund shares. Instead, the supplies of and demands for the primary securities in the mutual funds' asset portfolios determine the net asset values and yields on the shares |14, 63-76~.

Even Black's unusual checkable accounts provide the advantages and suffer the disadvantages implied by the essential characteristics of money. Sellers accept checks even when they have no intention of adding to a positive or decreasing a negative balance. There is no reason to negotiate with the buyers (or some bank) about appropriate interest rates on either sort of balance when payments are made.

If the interest rates banks charge and pay are too low, customers will increase expenditures (by check) in an attempt to increase negative and decrease positive balances. And if the interest rates are too high, they will restrict expenditures in an effort to decrease negative and increase positive balances. But credits always match debits, so positive and negative balances are always equal. No shortage or surplus of funds forces the banks or anyone else to adjust interest rates.

Conventional Checkable Deposits in BFH

Unusual checkable accounts make the concept of money useless or hazy, but the problems associated with monetary disequilibrium remain. Unfamiliar institutions simply make the problems more difficult to identify. Fortunately, unusual checkable accounts are not essential to BFH.

Even in their early papers, Greenfield and Yeager noted that privately-issued banknotes and token coins would be needed for hand-to-hand currency. They added that conventional fixed-value checkable deposits might make up a small portion of the means of payment |6, 308~. Fama went further, explaining that revealed consumer preference suggests conventional checkable deposits would remain most important |4, 8-9~.

In response to Lawrence White's argument that checkable mutual fund accounts would not replace conventional deposits in a competitive setting |13, 707~, Greenfield and Yeager explained that the specific form of the checkable accounts is unimportant to BFH |8, 849~. And their emphasis has changed in later papers. They continue to mention the possibility of checkable mutual fund share accounts, but the operation of BFH mostly is described using bank notes and deposits |9~. Woolsey |14~, Schnadt and Whittaker |12~, and Dowd |2~ also describe BFH with bank notes or deposits serving as the means of payment.

III. Specific Institutions Consistent with BFH

Means of Payment

This paper will follow the more recent practice of emphasizing the more conventional means of payment. Prices are quoted and contracts are made in terms of a common unit of account called "the dollar".(1) Competing banks finance the purchase of bonds with conventional, interest-beating checkable deposits. To simplify the exposition, commercial loans, time deposits, and bank capital are ignored. And to further simplify the exposition, hand-to-hand currency is ignored. The issue of banknotes and token coins by the banks would have little effect on the operation of BFH, but the model directly applies only to some future time when all payments are by check or an electronic equivalent.(2)

Given these assumptions, the sum of the nominal amounts of the checkable deposits issued by all the banks is the quantity of money. The amount of checkable deposits the public prefers to hold is the demand for money.(3)

A Clearing Institution for BFH

Since there is no base money to settle net clearings among banks, some alternative is necessary. Greenfield and Yeager suggested gold or a list of securities specified by the clearinghouse |6, 307; 21, 104~.

Black hinted at a more convenient approach. While he failed to explain how the banks' net clearings are settled, he mentioned an active inter-bank loan market |1, 11~. Banks with "deposits" greater than "loans" would lend funds to banks with "loans" greater than "deposits". Apparently, he assumes that banks that would otherwise develop favorable net clearings lend and banks that would otherwise develop adverse net clearings borrow.

In this paper, the assumed clearing institution "settles" net clearings with automatic loans, but provides an incentive for banks to use offsetting market transactions. The clearinghouse gives each bank a clearing account that begins with a zero balance. As items are cleared, the clearing-house credits and debits the appropriate accounts. A bank can have a net credit or a net debit balance. Favorable clearings increase a net credit or decrease a net debit balance. Adverse clearings decrease a net credit or increase a net debit balance. The clearinghouse also provides each bank with a security account and insists banks hold bonds to provide collateral against net debt balances.

The clearinghouse pays interest on net credit balances and charges interest to net debit balances. It pays a fixed number of basis points less than the bond interest rate. It charges a fixed number of basis points more than the deposit interest rate.

Because the interest rates on clearing account balances are unattractive, banks have an incentive to use offsetting market transactions. A bank can buy bonds to offset a net credit balance and sell bonds to offset a net debit balance. Monitoring and transactions costs make it unlikely that a bank would continually offset random fluctuations caused by its depositors' payments. Still, the assumed clearing institution makes the clearinghouse interest rates endogenous and "lending" or "borrowing" through the clearinghouse irrelevant to the money supply process and macroeconomic equilibrium.(4)

The Money Supply Process

The money supply process is unusual. Banks adjust the size of their balance sheets to maximize their profits. In equilibrium, the marginal cost of intermediation services is equal to the difference between the interest rates on bonds and deposits.

Suppose a change in the cost of providing intermediation services, the bond interest rate, or the deposit interest rate leaves the marginal cost of intermediation services less than the difference between the interest rates on bonds and deposits. Each bank profits by expanding its balance sheet. It purchases bonds with checks drawn on its own account. To avoid the unfavorable interest rate on a net debit balance at the clearinghouse, it seeks matching deposits by simultaneously increasing the interest rate it pays.

When all banks increase the deposit interest rate, the intended changes in market share fail to develop. Instead, the banks shrink the difference between the bond and deposit interest rates, bringing it closer to the marginal cost of providing intermediation services.

More importantly, the checkable deposits of those from whom the banks purchased the bonds increase. Assuming the marginal cost of intermediation services is positively related to the size of each bank's balance sheet, the quantity of money increases until the marginal cost of intermediation services is equal to the difference between the bond and deposit interest rates.

Similarly, if the marginal cost of intermediation services is greater than the difference between the interest rates on bonds and deposits, each bank shrinks its balance sheet by selling bonds, intending to lose the matching deposits by paying a slightly lower interest rate. The checkable deposits of those to whom the banks sold the bonds are debited. So the increase in the difference between the interest rates on bonds and deposits and the decrease in the quantity of money and the marginal cost of intermediation services returns the banking system to equilibrium.

Indirect Convertibility

The money supply process in BFH determines the quantity of money and the difference between the interest rates on bonds and deposits, but it does not determine the price level. Instead, indirect convertibility implies a market process that effectively pegs the price level.

Indirect convertibility requires banks to redeem checks with an amount of gold (or perhaps some other settlement medium) equal in market value to a nearly comprehensive bundle of goods and services |6, 313; 20, 324; 5, 6~. Indirect convertibility also applies to clearing accounts. A bank can demand settlement of a net credit balance of one dollar (or insist on settling a net debit balance) with gold that has a market value equal to that of the bundle. The banks with the matching net debit balances are obligated to provide the gold. (Banks with net credit balances must accept gold in settlement).

Indirect convertibility implies arbitrage transactions that reverse any deviation of the price of the bundle from its defined price |21, 105-6; 8, 848-9; 9, 410-4~. Suppose the price of the bundle is greater than its defined price of one dollar. An arbitrageur can redeem a check made out for one dollar with gold that has a market value of more than one dollar. The gold can be sold for another check, which can be redeemed for even more gold, and so on. The arbitrageur profits at the expense of the banks.

The consequence of the arbitrage is unusual. Banks have little reason to hold gold reserves, so they buy gold on the market at a higher price and "sell" it to redeem checks at a lower price |17, 7~. Even though the arbitrageurs are trading gold, their transactions have little or no direct effect on the price of gold, the quantity of money, or the bond interest rate.

Instead, the arbitrageurs force the banks to cause appropriate changes in the bond interest rate. A bank cannot purchase gold on the market with a check drawn on its own account, because with the price of the bundle greater than one dollar, the gold seller can immediately redeem the check for more gold than the amount he just sold. A bank might sell bonds on the market, receive checks drawn on other banks in payment, and use these to purchase gold. But clearing arbitrage would probably be more important, because a single bank can offset the losses imposed by arbitrageurs (or even profit) by manipulating its net clearings |17, 7~. If the price of the bundle is greater than its defined price, a bank profits from receiving gold in settlement of a net credit balance and suffers losses from settling a net debit balance with gold. So each bank has an incentive to sell bonds, obtaining items drawn on other banks to route through the clearinghouse.

Each bank intends to obtain gold from the others at a bargain price which can be paid out to arbitrageurs or sold on the market for a profit. But as all banks sell bonds, the intended favorable clearings fail to develop. Instead, the contraction in bank credit and the quantity of money cause an increase in the bond interest rate. The higher bond interest rate causes a decrease in real expenditures. As falling sales cause firms to decrease prices, the price of the bundle falls back to its defined price of one dollar.

When the price of the bundle falls below its defined price, clearing arbitrage has the opposite effect. Because of the low price of the bundle, a clearing account balance of one dollar can be settled with gold worth less than a dollar. As banks buy bonds to obtain adverse and avoid favorable clearings, the expansion of bank credit and the quantity of money cause the needed decrease in the bond interest rate. Real expenditures increase, firms raise prices, and the price of the bundle rises again to its defined price.

A Model of Indirect Convertibility?

Contrary to claims made by Norbert Schnadt and John Whittaker, indirect convertibility is not a feed-back rule |12, 15~, so a multi-period model is inappropriate. Arbitrage continues until the bond interest rate and real expenditures adjust whatever amount is necessary for the price of the bundle to return to its defined price. A formal model of the arbitrage implied by indirect convertibility is as inappropriate as a formal model of the arbitrage implied by the law of one price.

Further, arbitrage transactions are unlikely to occur. Banks and the public have an incentive to avoid capital losses or obtain capital gains by immediately selling or buying bonds. Since arbitrage will occur if the bond interest rate fails to change enough, speculation by banks and the public on the bond market directly causes the needed change in the bond interest rate. The bond interest rate, real expenditures, and the price of at least some bundle items adjust enough for the price of the bundle to remain at its defined price of one dollar. Assuming the bundle is nearly comprehensive, the price level is pegged.(5)

IV. A Simple "Keynesian" Model

The Model

The following "Keynesian" model can be used to explore BFH.

y = |y.sub.p.~ (1a)

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

The two aggregate supply functions are consistent with "New Keynesian" assumptions. (1a) applies in the long run. y represents real income and |y.sub.p.~ represents potential income. These being equal, the unemployment rate is equal to its natural level. (1b) applies in the short run. |P.sup.s.~ (|Mathematical Expression Omitted~) is a static version of the phillips curve. So P, which represents the price level, is positively related to real income. (A subscript on a function represents its partial derivative with respect to the variable.) The price level is also proportional to |alpha~, which represents aggregate supply shocks such as changes in the price of oil.

The "IS" relationship (2) is conventional. Real income is equal to real expenditure, which is represented by e (|Mathematical Expression Omitted~). Real expenditure is positively related to real income, negatively related to |r.sub.B.~ the real bond interest rate, and positively related to |beta~, which represents autonomous expenditure shocks. Such shocks would include changes in saving and investment behavior, caused by either "the fundamentals" or "animal spirits". Changes in government fiscal policy or international trade could also be included as autonomous expenditure shocks.

Money demand (3) is also conventional. In equilibrium, the quantity of money equals the price level multiplied by |m.sup.D.~ (|Mathematical Expression Omitted~), the real demand for money. Real money demand is negatively related to the difference between the real (or nominal) interest rates on bonds and deposits. The difference is represented by d, and the deposit interest rate by |r.sub.D~. The real demand for money is positively related to real income and proportional to |gamma~, which represents shocks to liquidity preference.(6)

Money supply (4) is unusual, because it depends on the real supply of intermediation services by the banking system. In equilibrium, the quantity of money is equal to the price level multiplied by |i.sup.S~(|Mathematical Expression Omitted~), the real supply of intermediation services. As explained above, the real supply of money is positively related to the difference between the real (and nominal) interest rates on bonds and deposits. It is also proportional to |eta~, which represents shocks to the real supply of intermediation services. These can be due to changes in the marginal cost of providing intermediation services. Those skeptical of "free banking" might use real money supply shocks to represent some inherent perversity in the banking business.

The Price Level and an Exogenous Bond Interest Rate

As argued above, clearing arbitrage or speculation leads to an increase in the bond interest rate if the price of the bundle rises above its defined price and a decrease in the bond interest rate if the price of the bundle falls below its defined price. The consequences for the price level can be illustrated using the model by treating the influence of indirect convertibility on the bond interest rate as exogenous. The short run version of the model (1b, 2, 3, 4 and an exogenous bond interest rate) shows a negative relationship between the bond interest rate and the price level.

dP/d|r.sub.B.~ = |e.sub.rB.~||P.sup.S~.sub.y/(1 - |e.sub.y.~) |is less than~ 0

Clearly, the change in the bond interest rate reverses any deviation of the price of the bundle from its defined price. Since arbitrage (or speculation) pegs the price level, the influence of indirect convertibility on the price level can be treated as exogenous. Given the pegged price level, the short run version of the model (1b, 2, 3, 4, and the exogenous price level, |P.sup.*~) shows how various shocks influence real income, the bond and deposit interest rates, and the quantity of money.

Monetary Shocks

As Greenfield and Yeager argued, shocks to the real supply and demand for money have no macroeconomic consequences. Rather than influencing the price level, real income, or even the bond interest rate, they only influence the quantity of money and interest rate on deposits.

The comparative statics for shocks to the real supply of money are as follows:

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

If the money supply shock is due to changes in the cost of providing intermediation services, the changes in the quantity of money and deposit interest rate reflect the appropriate microeconomic response. If the shock is due to some perversity in the banking business, the banks may earn less than maximum profit. Still, there are no undesirable macroeconomic consequences.

A market process consistent with these results is easy to describe. A real money supply shock appears to cause the needed change in the deposit interest rate even without indirect convertibility. For example, a decrease in the cost of intermediation services entices each bank to expand its balance sheet by purchasing bonds and increasing its deposit interest rate. Since all banks increase the interest rates they pay and new deposits match the expansion in the bond portfolios, the deposit interest rate and the quantity of money increase as implied by the comparative static results.

Since the deposits of various banks are close substitutes, an increase in any one bank's deposit interest rate sufficient to attract enough deposits to match the expansion in its bond portfolio would not amount to an increase in the deposit interest rate sufficient to cause the public to substitute away from bonds (or consumption) enough to willingly hold the entire increase in the quantity of money implied by the expansion in the banks' bond portfolios. Ignoring indirect convertibility, the purchase of bonds by the banks and those in the public with now excessive money holdings would tend to cause a decrease in the bond interest rate, an increase in real expenditures, and inflationary pressure.

Fortunately, clearing arbitrage or speculation on the bond market quickly reverses or prevents any decrease in the bond interest rate. The institution of indirect convertibility limits the increases in the quantity of money to the additional amounts the public is willing to hold as competition for market share gradually forces banks to pass on the added benefits of the lower cost of intermediation services by raising the deposit interest rate.

The comparative statics for shocks to real money demand are similar to those for shocks to the real money supply.

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

A market process similar to that implied by a real money supply shock can be described, but a real money demand shock has a perverse direct effect on the deposit interest rate. For example, a negative shock to liquidity preference causes the public to purchase bonds. The bond interest rate falls, making intermediation less profitable. Each bank attempts to shrink both sides of its balance sheet by selling bonds and decreasing the interest rate it pays to lose deposits to the other banks.

The decrease in the deposit interest rate is perverse and inconsistent with the comparative static results. It makes holding deposits even less attractive, tending to further decrease the bond interest rate, stimulate expenditures, and add to the inflationary pressure.

But clearing arbitrage or speculation on the bond market cause banks to decrease the quantity of money enough to quickly reverse or even prevent any decrease in the bond interest rate, so to prevent any deviation of the price of the bundle from its defined price. The lower quantity of money implies a lower marginal cost of intermediation services. Competition for market share forces banks to pass on the additional earnings by increasing the deposit interest rate. Indirect convertibility allows for a market process that overcomes any perverse direct consequences of shocks to the real demand for money and is consistent with the comparative static results.

So Black, Fama, Hall, and Greenfield and Yeager were correct. As shown by the comparative statics, there is a supply and demand determination of the quantity of money. Even though direct changes in the deposit interest rate fail to correct shortages or surpluses of money, indirect inconvertibility provides the needed market process.

Autonomous Expenditure Shocks

Not only does BFH prevent "monetary" shocks from having macroeconomic consequences, it also prevents autonomous expenditure shocks from influencing the price level, real income, or the quantity of money. Instead, the shocks only influence the interest rates on bonds and deposits.

|Mathematical Expression Omitted~

Again, a plausible market process is easy to describe. A positive autonomous expenditure shock is usually matched by an excess supply of bonds which tends to directly cause the appropriate increase in the bond interest rate. The increase in the bond interest rate immediately increases the difference between the interest rates on bonds and deposits, making this difference greater than the marginal cost of providing intermediation services. But if the banks purchase bonds and expand the quantity of money, they will soon be forced to reverse course. Clearing arbitrage or speculation cause the increase in the bond interest rate needed to keep real expenditure equal to potential income. Competition forces banks to pass on their added interest income by increasing the interest rate they pay on an unchanged quantity of deposits.

The analysis of autonomous expenditure shocks show that BFH is consistent with the "classical" conventional wisdom, even in the short run. Saving and investment behavior have no impact on real expenditures, real income, or employment. Instead, they determine "the" interest rate. While detailed discussion is beyond the scope of this paper, changes in "thrift" or "productivity" would lead to the change in the interest rate necessary to properly coordinate the allocation of resources between the production of consumer and capital goods. And even without the implausible Ricardian equivalence theorem, the interest rate changes whatever amount necessary to cause full nominal (as well as real) crowding out of fiscal policy.

Shocks to the Price Level

Unfortunately, aggregate supply shocks have less desirable consequences in the short run. The price level remains pegged, but real income, the bond interest rate, the quantity of money and the deposit interest rate all change.

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

The short run decrease in real income resulting from an adverse aggregate supply shock (a positive shock to the price level) is the most serious disadvantage of any "price" rule for monetary policy. In BFH, clearing arbitrage or speculation in the bond market cause the bond interest rate to increase enough for real expenditures to decrease the amount necessary to keep the price level pegged. The quantity of money decreases because the decrease in real income implies a decrease in the real demand for money. The deposit interest rate increases because the increase in the bond interest rate implies an increase in bank revenues and the decrease in the quantity of money implies a decrease in the marginal cost of providing intermediation services.

V. Diagrammatic Exposition of the BFH Payments System

Figure 1 illustrates the short run model. The upper left quadrant shows a conventional Keynesian short run aggregate supply curve. "Aggregate demand" is horizontal at the implied price level. The lower left quadrant shows a conventional Keynesian "IS" curve. There is no "LM" curve. The "money market" is shown in the lower right quadrant. The supply and demand curves for money relate the quantity of money supplied and demanded to the difference between the bond interest rate and the deposit interest rate.

Shocks to the real supply or demand for money are easily analyzed since they only involve the lower right quadrant. The reader can easily imagine appropriate shifts in the curves. Given the price level, a real shock to money supply or demand implies a nominal shock that is represented by a horizontal shift of the appropriate curve. The quantity of money and the deposit interest rate adjust so that the quantities of money supplied and demanded remain equal.

Autonomous expenditure shocks are slightly more complicated, involving both lower quadrants. Still, the reader can imagine appropriate shifts in the curves. As in a conventional Keynesian model, the shocks are represented by a horizontal shift in the "IS" curve. Since real income is given by aggregate supply and the pegged price level, the new "IS" curve determines a new bond interest rate. The new bond interest rate must be carried over to the lower right quadrant, implying an equal vertical shift in the supply and demand for money curves. The result is an equal change in the deposit interest rate and an unchanged quantity of money.

Aggregate supply shocks are most complex, involving all three quadrants. Figure 2 provides an illustration of a positive shock to the price level. The shock implies a vertical increase in the aggregate supply curve, shown in the upper left quadrant. Given the pegged price level, the result is a decrease in real income. The lower left quadrant shows that the new real income and the "IS" curve determine a higher bond interest rate. In the lower right quadrant, the increase in the bond interest rate imply equal vertical increases in the supply and demand for money curves. But the decrease in real income also implies a left-ward horizontal shift in the money demand curve. The result is a higher deposit interest rate and a lower quantity of money.

VI. BFH in the Long Run

The long run model implies little change in most of the comparative static relationships. The price level remains pegged by indirect convertibility. Shocks to real money supply and demand have no macroeconomic consequences and influence the deposit interest rate and the quantity of money exactly as they do in the short run.(7) Similarly, autonomous expenditure shocks have no influence on the price level, real income, or the quantity of money and influence the interest rates on bonds and deposits exactly as they do in the short run.

In the long run, an aggregate supply "shock" is a change in potential income. It influences the bond interest rate, the quantity of money, and the deposit interest rate.

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

VII. Conclusion

BFH uses indirect convertibility to peg the price level in both the short run and the long run. It is free from inflation. Further, "monetary" and autonomous expenditure shocks cause no disturbance to real income. BFH is free from sources of recession such as incompetent monetary policy. unstable banking, balance of payments difficulties. changes in savings or investment fundamentals. "animal spirits", or government fiscal policy.

A possible disadvantage of BFH follows from the "tightness" of its control of the price level. Aggregate supply shocks could result in large changes in real income. Further research is needed to find institutions that keep the advantages of BFH while avoiding this possible disadvantage.

1. Greenfield and Yeager use "Unit", but if their system were ever implemented. changing the word used to quote prices, make contracts, and keep accounts would be pointless.

2. Private hand-to-hand currency confuses many readers because of its similarity to base money. See Woolsey |16~ for a discussion of bank notes and token coins.

3. Checkable deposits are demanded because calculating the amount of bonds to be tendered would be inconvenient. Bonds are demanded because they provide a higher yield.

4. A better approach would make the interest rates on clearing account balances unattractive compared 10 overnight loans. A discussion of "reserveless" clearing institutions is provided in Woolsey |15~.

5. This assumes the price of the bundle is measured continuously. If the price of the bundle is measured periodically and settlements, were made according to the most recent measurement, the result would be disastrous. In correspondence, Yeager has suggested adjusting current settlements according to the subsequent measurement.

6. (2) and (3) imply a net supply of bonds to the banking system. Greenfield and Yeager |7~ explicitly model the net supply of bonds to the banking system.

7. If entry into and exit from the banking industry cause the marginal cost of intermediation services to adjust to a constant minimum long run average cost |d.sup.*~, then |r.sub.D~ = |r.sub.B~ - |d.sup.*~, dM = |P.sup.*~d|gamma~ and dM = |P.sup.*~||m.sup.D~.sub.y~d|y.sub.p~ in the long run.

References

1. Black, Fischer, "Banking in a World Without Money: The Effects of Uncontrolled Banking." Journal of Bank Research, Autumn 1970.9-20.

2. Dowd, Kevin. The State and the Monetary System. Hertfordshire: Philip Allan, 1989.

3. Fama. Eugene E, "Banking in the Theory of Finance." Journal of Monetary Economics, January 1980, 39-59.

4. -----, "Financial Intermediation and Price Level Control." Journal of Monetary Economics. July 1983, 7-28.

5. Greenfield, Robert L. "Further Thoughts on the Black-Fama-Hall System." Presented at the annual meetings of the Southern Economics Association in Dallas, November 1984.

6. ----- and Leland B. Yeager. "A Laissez-Faire Approach to Monetary Stability." Journal of Money, Credit, and Banking. August 1983, 302-15.

7. -----. "Direct Equilibration in the Market for Media of Exchange." Appendix from 1983, Available from Robert L. Greenfield, Fairleigh Dickinson University, Madison. N.J. 07940.

8. -----, "Competitive Payments Systems: Comment." American Economic Review. September 1986, 848-49.

9. -----, "Can Monetary Disequilibrium Be Eliminated?" Cato Journal. Fail 1989, 405-21.

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11. -----, "Monetary Trends in the United States and the United Kingdom: A Review from the Perspective of New Developments in Monetary Economics." Journal of Economic Literature. December 1982. 1552-56.

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