Is there a paradox of indirect convertibility?

• Author: Woolsey, W. William

1. Indirect Convertibility

   A paradox allegedly plagues systems in which money is only indirectly, not directly, convertible (or redeemable; we use the words interchangeably). Knut Wicksell, W. William Woolsey, John Whittaker and Norbert Schnadt, Tyler Cowen and Randall Kroszner, and Hans-Michael Trautwein have described scenarios in which indirect convertibility would have catastrophic consequences [21; 23; 17; 18; 19; 3; 20].

   Currency, deposits, and checks are indirectly convertible when they are not redeemed directly in the medium of account. (The latter term is Niehans's; it means the commodity or commodity bundle of which some specified quantity defines the unit of account [16, 1].) Money is redeemable, instead, in some redemption medium--some other commodity or even some security--in amounts equal in value to the quantity of medium of account defining the unit.

   Recent proposals combine indirect convertibility with free banking, promising to stabilize the price level and avoid monetary disequilibrium that would disturb income and employment [13; 12; 25; 26; 27; 28; 4]. In this BFH system (so named, perhaps misleadingly, to acknowledge ideas borrowed, altered, and recombined from writings of Fischer Black, Eugene Fama, and Robert Hall), government money is forbidden. Only competing private banks issue notes, coins, and checking accounts.

   Earlier proposals assumed government issue of currency. Simon Newcomb and Aneurin Williams advocated money convertible into whatever variable amount of gold, as redemption medium, had a fixed general purchasing power [15; 22]. Irving Fisher, citing their proposals, argued that the dollar could be stabilized through convertibility into an amount of gold equal in value to a bundle of goods [10, 331-2]. (Indirect convertibility is not the same as Fisher's better-known proposal for a "compensated dollar" [8, 337-47; 10, 494-502; 11, 95-7]. In place of his earlier brief suggestion for indirect convertibility, Fisher later envisaged periodic discrete adjustments in the gold content of the dollar, that is, in the official price of gold, prompted by deviations of a price index from target. The reader should be careful to distinguish indirect convertibility from the compensated dollar.)

   Advantages of indirect convertibility, including lessened danger of panicky scrambles for the redemption medium, are beginning to command attention [5]. Allegedly, though, a paradox blocks achieving them.

   We will describe Wicksell's version of the paradox. We believe that his scenario points to a serious problem. If the actual market price of the medium of account was somehow shocked away from its "official" price, the changes in the quantity of money and total spending necessary to reverse that deviation could impinge on output and employment. That impact would be especially severe if the price of the medium of account was "sticky". Wicksell, however, glosses over that pedestrian macroeconomic concern and instead describes extreme fluctuations in the price of the redemption medium. We believe that part of his paradox scenario is implausible.

2. Wicksell on the Paradox

   Anderson's System

   The paradox of indirect convertibility appears first, to our knowledge, in Knut Wicksell's reply to an attack on the quantity theory of money (one whose details need not concern us) mounted by Benjamin Anderson [21; 1, 150-51]. Anderson had postulated a dollar defined by a fixed weight of gold. None is coined, however. Government paper dollars are redeemable not in gold but in whatever (changeable) amount of silver has a market value actually equal to that of the dollar-defining amount of gold. In the other direction, the government issues a new paper dollar against that amount of silver. The dollar always remains worth the specified unit amount of gold. Anderson finds total quantities of redemption medium and money irrelevant to the dollar's value. (In other versions of indirect convertibility, some composite good is the medium of account. The reader should pay close attention, in the examples that follow, to what is the redemption medium and what is the medium of account.)

   Wicksell's Critique

   Besides scoring other points, Wicksell argued that Anderson's system of indirect convertibility would collapse in the face of an increase in the relative price of gold. He supposed that the dollar-defining unit quantity of gold is initially worth 30 times as much--30 weight-units of--silver. Now a change in demand for or supply of gold doubles the price of its unit amount to $2 in paper money. (The reader may be bothered already, but that is what Wicksell supposes.) Accordingly, a dollar bill becomes redeemable in and issuable against 2 times 30 = 60 units of silver. The implied great cheapening of silver spurs its industrial consumption, which draws on the government's reserves. The prices of all commodities except silver remain nearly unchanged for the time being. Even though gold supposedly defines the dollar, Wicksell's scenario has it temporarily continuing to command its new market price of $2, which is worth 120 units of silver, since the government is delivering 60 units per dollar redeemed. This situation now forces the government to raise its redemption and issue price of the dollar bill to 120 units of silver, making 1 unit of gold become worth approximately 240 units of silver on the market, and so on.

   Each new cheapening of silver further spurs its use, perhaps even for cookware. On Wicksell's assumptions about the elasticity of industrial demand for silver and about the government's silver reserves relative to the money supply, the reserves would run out before the paper-money circulation, and with it the prices of gold and other things, had fallen by more than a few percent. The government would have to abandon the system and leave paper money irredeemable. Its attempt to restore the dollar to parity with appreciated gold would have failed.

   The system would fare less badly in the face of an initial decline in the value of gold, say to haft a dollar. The government would accordingly reduce the amount of silver delivered in each redemption and required against newly issued money. A self-reinforcing rise in the government's price of silver would spur the melting of silver objects and delivery of silver to the government for newly issued money. The resulting great monetary expansion would raise prices in general until a unit of gold, though rising in price less sharply than other things, was eventually worth 1 full dollar again, as before the disturbance. (Indirect, like direct, convertibility works asymmetrically: there is a limit, namely zero, to how low reserves of the redemption medium can fall but no definite limit to how high they can rise. At the new equilibrium price level in the second case, although gold has been restored to its money value implied by the dollar's definition, it remains cheaper relative to goods and services in general than before the postulated fundamental shift in its supply or demand.)

   If the initial supply or demand shift affected the market value of silver, the redemption medium, rather than the value of gold, the complications described would not occur. The government could allow the price used in its calculations at the redemption window to change to reflect the new fundamentals in the silver market.

   Differences Between Direct and Indirect Convertibility

   Wicksell's scenario points to an important distinction between direct and indirect convertibility. When gold serves as medium of account as well as redemption medium, two processes tend to fix the price of gold. First, the government can directly offset any shift tending to raise the price of gold by releasing enough gold from its reserve to correct the resulting shortage at the "official" price. Second, the withdrawal of currency from circulation simultaneously contracts the quantity of money and tends to restrain spending. That restraint indirectly corrects the shortage of gold by gradually decreasing its demand at the official price.

   In Anderson's scheme, in which gold remained the medium of account but silver served as the redemption medium, the government could not directly correct a shortage of gold at its "official" price by releasing silver reserves. That release of reserves instead would lower the...