A Simple Model of Irving Fisher's Price-Level Stabilization
Humphrey, Thomas M., Economic Review
It is now well understood that a price-level stabilization policy is more ambitious than a zero-inflation policy. Targeting zero inflation means that the central bank brings inflation to a halt but leaves the price level where it is at the end of the inflation. By contrast, targeting stable prices means that the central bank ends inflation and also rolls back prices to some fixed target level. By reversing inflated prices and restoring them to their pre-existing level, a price-stabilization policy eradicates the upward drift of prices that can occur under a zero-inflation policy. It follows that a stable-price policy is more stringent than a zero-inflation policy.
The history of monetary thought abounds with price-level (as opposed to inflation-rate) stabilization rules. Not all of these policy rules were sound; some would have destabilized prices rather than stabilizing them. Notoriously flawed was John Law's 1705 proposal to back the quantity of money dollar for dollar with the nominal value of land. His rule guaranteed that changes in the price of land would induce equiproportional changes in the money stock. Equally flawed was the celebrated real bills doctrine advanced by the antibullionist writers during the Bank Restriction period of the Napoleonic Wars. It tied money's issue to the "needs of trade" as represented by the nominal quantity of commercial bills presented to banks as loan collateral. It failed to note that since the nominal volume of bills supplied (or loans demanded) varies directly with general prices, accommodating the former with money creation meant accommodating prices as well. Seen by their proponents as price-stabilizing, both rules in fact would have expanded or contracted the money supply in response to shock-induced price-level changes, thus underwriting or validating those changes (see Mints, 1945, pp. 30, 47-48).
Ruling out such inherently fallacious schemes leaves the remaining valid ones. These fall into two categories. The first consists of non-activist policy rules that fix the money stock or its rate of change at a constant level. Milton Friedman's k-percent rule, which would establish the money stock at a fixed level when output's growth rate is zero, is perhaps the best known example of this type of rule. The second includes activist feedback rules which dictate predetermined corrective responses of the money supply and/or central-bank interest rates to price deviations from target. The proposals of David Ricardo, Knut Wicksell and Irving Fisher exemplify this type of rule. Given England's 1810 regime of inconvertible paper currency and floating exchange rates, Ricardo (1810) advocated lock-step money-stock contraction in proportion to price-level increases as proxied by exchange-rate depreciation and the premium (excess of market price over mint price) on gold. Wicksell (1898, p. 198) proposed an interest-rate feedback rule: raise the bank interest rate when prices are rising, lower it when prices are falling, and keep it steady when prices are neither rising nor falling. Fisher suggested not one rule but two. His 1920 compensated dollar plan called for the policymakers to adjust the gold weight of the dollar equiproportionally to changes in the preceding month's general price index. In essence, he posited the relationship: dollar price of goods = dollar price of gold X gold price of goods. Official adjustments in the dollar price of gold, he thought, would offset fluctuations in the world gold price of goods (as proxied by the preceding month's general price index), thus stabilizing the dollar price of goods. His second rule (1935) was more conventional. Much like stabilization rules proposed today, it dictated automatic variations in the money stock to correct price-level deviations from target.
This article examines Fisher's second policy rule, particularly its dynamic properties. Fisher himself failed to investigate these properties. He provided no analytical model in support of his rule. …