Fisherian and Wicksellian Price-Stabilization Models in the History of Monetary Thought If monfg bezame scarce, as shown by a L+m&myof the price kvel to foil, mom couhi be mpphd ins&&y; and if sup.mabunhnt, some co&i be with&awn m?h fquaZpmnzpbam. 72e money management wouki thus ctit . of buying Jiechies on t&eopen mar&tJ whenever the price kveZ thmmned to fai. behw th stiiuhtcd par and selling whentxm it thrzuotenedto rise above that par. -In&g F&k f3, p. si7J Tht intmt on bommed monq isjr one rzason or another either be&m or abwe the ltx& wbhb wouki norm@ be gwemed by t&e real rate m&g at t& time /isJ a cimmtame wbkb, so hng as it hsts, must cause a pmgmsive he or fall in prim . JTZusJ thm s/w&i be a commm policy, a raising or hmihg of bank ram . jwn time to time in order to akpms tire commodityprice hel wkn it showed a &znaknqto r& and to raise it -Knuc Wiu&dZ/17, pp. 225, 223J Introduction 1940s they constituted the dominant policy models in nineteenth and twentieth century central banking Central bankers charged with the responsibility for tradition. In fact, many celebrated economists stabilizing the general level of prices need to know before Fisher and Wicksell contributed to their at least two things. First, what causes prices to deviate development. from their desired fixed target level? Secondly, what policy rule or response most effectively corrects those Given the importance of price stability as a policy deviations and restores prices to target? goal, it is useful to reexamine these historical models. As simple, stripped-down prototypes of the more Historically, proponents of price stability de- elaborate macroeconomic models employed today, veloped two basic reduced-form models to answer they reveal in sharp focus much about the mechanics these questions. One model, associated with Irving of price-level stabilization. In particular, they provide Fisher, attributes price movements to shocks information on the relative price-stabilizing powers operating through excess money supply and demand. of alternative policy feedback rules-e.g., money It calls for money-stock adjustments to keep prices stock rules versus interest rate rules. Accordingly, at their target level. The other model, associated with the threefold purpose of this article is (1) to describe Knut Wicksell, ascribes price movements to dis- the structure and logic of the two reduced-form crepancies between market and natural (equilibrium) models, (2) to sketch their evolution in the history rates of interest. It prescribes interest-rate adjust- of monetary thought, and (3) to analyze each to see ments to restore prices to target. Although both if they yield dynamic stability such that prices return models are fairly well known, their historical to target equilibrium following economic shocks. The significance has not always been fully appreciated; central message is that both models, if properly Until the Keynesian revolution of the 1930s and formulated, still provide reliable guides to policy. FEDERAL RESERVE BANK OF RICHMOND 3 The Models Outlined ‘, ’ to rise or fall the central ,bank acts to restore them to target by raising or lowering the market rate in Before tracing the historical development of the proportion to prices’ deviation from target. Stated models, it is necessary to sketch their essential mathematically: : 1 ,. ~ . .. ‘:, features so as to identify what particular contributors _‘..a. had to say about each. As presented here, both (3) dP/dt = o(r -i) reduced-form models consist ,of (1) a price-change equation relating price movements to the variables (4) di/dt = @(P APT) ’ ’ that cause them and (2) a policy-response function specifying the feedback rule the central bank follows to keep prices on target. where r denotes the natural rate, i the market rate, di/dt its adjustment, and the other symbols are as Fisherian Model defined above. The Fisherian model says that prices rise or fall These reduced-form equations, are derived from when the existing quantity of money exceeds.or falls a larger model that explains how the interest rate short of the amount people wish to hold at prevail- differential affects, (1). real investment and saving, ing prices and real ‘incomes. It also says that (2) loan supply and demand, (3) money supply and policymakers can correct deviations of prices from demand, and (4) ‘aggregate supply and demand. target by expanding or contracting the money stock Through these factors the rate differential moves the (or at least its high-powered base component) as price level. prices are below or above their target level. In symbols: Thus when the loan rate lies below the natural rate (the rate that equilibrates saving and investment) in- (1) dP/dt = &(M -kPy) vestors demand more funds from banks than savers deposit there. Assuming banks accommodate these (2) dM/dt = @(Pr -P) extra loan demands by issuing notes .a$ creating checking deposits, a monetary expansion occurs. where dP/dt denotes price change;P actual prices, Since neither real income nor prices have changed Pr their fixed target level, M the money stock, dM/dt in cashholders’ money demand functions, the addi- its change, k the inverse of money’s turnover velocity tional money constitutes an excess supply of cash or the fraction of nominal income people wish to hold that spills over into the product market in the form in money, y real income, and o and fl positive of an excess demand for goods. This excess demand constants. puts upward pressure on prices which contrnue to rise until the rate differential vanishes. Since the Thus suppose a money-control error or decrease model in its pure credit or inside money version con- in money demand .produces an excess supply of tains no automatic self-equilibrating market money. The resulting attempts by cashholders to get mechanism to eliminate the rate differential, the cen- rid of the excess cash through spending puts upward tral bank must do the job. To arrest and reverse the pressure on prices according to equation 1. As prices price rise the bank must raise the market rate until begin to rise above target, the central bank responds prices return to target. by conuacting the money stock according to the feed- back-policy rule represented by equation 2. In this Of course if the central bank knew the level of the way the central bank eventually contracts the money natural rate it could always keep the market rate there stock sufficiently to restore prices to target. Such is and no price movements would occur. But the the underlying logic of the Fisherian model. essence of the Wicksellian model is that the natural rate is an unobservable variabie. that moves around Wicksellian Model under the impact of productivity shocks, techno- The alternative Wicksellian model attributes price logical progress, factor endowment changes, and movements to the differential between the natural other real disturbances that cause it to deviate from (equilibrium) and market rates of interest. Prices rise the market rate. In such circumstances the central when the market rate is below the unobservable bank does not know what the natural rate is. It knows natural rate, fall when the market rate exceeds the only that the resulting price level movements indicate natural rate, and remain unchanged at .a stationary that the market rate is not at its natural level and must level when the two rates coincide. When prices start be changed. That is, the bank must adjust the market 4 ECONOMIC REVIEW, MAY/JUNE 1990 rate in the same direction that prices are deviating Second, the fall in domestic prices P relative to given from target, ceasing only when they finally stabilii foreign (world) prices PW would generate a uade there. balance surplus B as cheaper domestic goods out- sold dearer foreign ones at home and abroad: Historical Evolution of the Models (6) B = /3(Pw-P). Having outlined the essential features of the two price-stabilization models, one can readily uace their Third, the trade surplus would be paid for by a com- evolution in the history of monetary thought. At least pensating inflow of monetary gold from abroad: four classical and neoclassical economists conuibuted to the development of the Fisherian model: David (7) B = dM/dt. Hume (1711-1776), David Ricardo (177%1823), Irving Fisher (1867-1947), and Lloyd Mints Substituting equation 7 into equation 6 yields (1888-1989). Likewise at least four monetary economists helped advance the Wicksellian model: (8) dM/dt = B(Pw -P) Henry Thornton ( 1760- 18 1S), Thomas Joplin (c.1790-1847), Knut Wicksell (1851-1926), and which implies that the domestic money stock adjusts Gustav Cassel (1866-1945). through specie flows until domestic prices stabilize at the fured level of world prices as required for David Hume balance-of-payments and monetary equilibria. Here The Fisherian model is much older than Irving is the Fisherian model with (1) world prices replac- Fisher. The origins of the model date back at least ing target prices and (2) the balance of payments to David Hume’s 1752 essay “Of the Balance of replacing the central bank as adjuster of the money Trade.” There Hume stated the gist of the model’s stock. equations, albeit in words rather than algebraic symbols (see Waterman 115, pp. 86-71). True, as David Ricardo noted below, he substituted the world gold price of Hume applied the model to a metallic or conver- goods Pw for target prices Pr in the model’s feed- tible currency regime. Ricardo, writing almost sixty back policy rule or money adjustment equation. He years later, extended Hume’s model to an incon- also assumed that corrective money stock adjust- vertible paper currency regime with floating exchange ments were achieved through international specie rates and a variable price of gold.