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The Classical Equation of Exchange As It Is Applied Today Equates The Copyrighted Material quantity theory of money hold even less of it than they did before the infla- The classical equation of exchange as it is applied tionary process began. There is, in fact, an exact in- today equates the money supply multiplied by the verse relationship between the proportion of income velocity of circulation (the number of times the av- held as money and the velocity of circulation with, erage currency unit changes hands in a given year) say, a halving of average money holdings requiring with the economy’s gross domestic product (the that the currency circulate at double the old rate in quantity of output produced multiplied by the price order to buy the same goods as before. In the extreme level). Although the American economist Irving case of ‘‘hyperinflation’’ (broadly defined as inflation Fisher originally included transactions of previously exceeding 50 percent per month), money holdings produced goods and assets as part of the output plunge and the inflation rate significantly outstrips measure, only newly produced goods are included in the rate of money supply growth. Conversely, under present-daycalculationsof grossdomestic product.If deflation, velocity is likely to fall: people hold onto the velocity of circulation and output are both con- their money longer as they recognize that the same stant, there is a one-to-one relationship between a funds will buy more goods and services over time if change in the money supply and a change in prices. prices continue to decline. Thus money demand rises This yields a ‘‘quantity theory of money’’ under as money supply falls, again exaggerating the effects which a doubling of the money supply must be ac- of the money supply change on the aggregate price companied by a doubling of the price level (or, when level. the rate of money supply growth doubles, the rate of The demand for money is also influenced by the inflation also doubles). The Nobel Prize–winning economy’s output level. If output rises, money de- economist Milton Friedman (1956) restated this mand should rise too, as increased production gen- quantity theory of money by modifying the as- erates more income and spending power. This would sumption of constant velocity, allowing velocity to put downward pressure on prices. Just as sustained adjust in response to changes in expected inflation inflation is possible only when the rate of money and the returns available onother assetssuch asbonds growth rises above the rate of growth of output (and and equities. money demand), so too does sustained deflation The tendency for velocity to rise as expected in- occur under conditions of insufficient money flation rises reflects people’s incentive to unload a growth. According to the monetarist school, which depreciating currency before its purchasing power emphasizes the importance of the money supply as a erodes. This reinforces the effects of faster money long-run determinant of prices and gross domestic supply growth on inflation because, at the same time product, stable prices could be achieved by simply that more money is being printed, people want to tying the rate of money supply growth to the 947 Copyrighted Material quantity theory of money long-run rate of growth of output. This would keep Wallace (1973) argue that such ‘‘reverse’’ causation money demand and money supply in balance so long could arise when a government is dependent on the as velocity is stable. revenue earned by inflating away the value of its Critics, such as those of the Keynesian school, outstanding money issues. Here, higher inflation which views the effects of monetary policy as unre- produces faster rates of monetary expansion, and not liable and uncertain in practice, argue that such a the other way around. As higher expected inflation policy rule would have undesirable consequences leads individuals to reduce their real money balances, because velocity historically has been subject to this reduces individuals’ exposure to the inflation tax fluctuations that require offsetting movements in the and reduces the government’s revenue from infla- money supply. On the other hand, Friedman (1960) tion. To keep inflation tax revenue at its old level, the argued that velocity has been unstable only because government must accelerate the rate of monetary policy has been unstable and that adoption of a expansion so as to increase the inflation tax rate and constant growth rate rule for the money supply offset the decline in the inflation tax base as real would keep inflation expectations, along with ve- money balances fall. This novel, albeit controversial, locity, steady. perspective could not apply in the more usual situa- Friedman’s restatement of the quantity theory of tion where governments are able to finance their money tempers the classical prediction that money expenditures through conventional taxes and bond supply increases exert one-to-one effects on prices issues. even in the shortrun. Under the restatement, velocity The quantity theory’s predictions have also been is allowed to adjust to a new level if the inflation questioned by adherents of ‘‘backing theory.’’ Under environment changes. However, once real money this view, it is the quality rather than the quantity of holdings have adjusted to their new lower equilib- money that matters. Whereas unbacked paper rium level following a rise in inflation, the rise in money may well be as inflationary as the standard velocity should end with a one-to-one relationship quantity theory assumes, this need not be true of between money growth and inflation. Such a pattern money that is credibly backed by future taxes or other is typically observed over extended periods. More- provisions for their future retirement from circula- over Friedman’s (1992) famous proposition that tion. Pioneering analysis of the American colonies inflation is always and everywhere a monetary phe- prior to the Revolutionary War by Smith (1985) nomenon receives support from the fact that it is suggests that even large money issues might be will- hard, if not impossible, to find any episodes of sig- ingly held rather than spent—implying a fall in the nificant inflation that have not been accompanied by velocity of circulation and an absence of the infla- accelerating rates of monetary expansion. The im- tionary pressures predicted by the quantity theory— portance of this link is further illustrated by the fact provided that they were properly backed. The case of that, while a one-third money supply reduction in Maryland stands out because that colony undertook the eastern Confederate States in April 1864 dra- to accumulate funds set aside for future purchases of maticallyreducedinflationthere,inflationcontinued pounds sterling that would retire the colony’s paper to run rampant in the western portion where the money at a predetermined rate of exchange. Data monetary cutback was postponed. limitations make it hard to conclusively determine Criticisms of Quantity Theory Critics of the the practical extent to which backing reduced the quantity theory approach have questioned not only inflationary effects of the Maryland currency issues the stability of velocity and money demand but also and those of other colonies, but recent work suggests the determination of the money supply itself. That is, that Pennsylvania enjoyed the long-run constancy of a link between money and prices does not necessarily velocity, and proportional relationship between prove that money supply movements are driving money and prices, implied by the quantity theory price movements. The economists Sargent and (Grubb 2005). 948 Copyrighted Material Excess Monetary Creation Whatever predictive theory and Phillip Cagan’s pioneering analysis of money power the quantity theory approach may have over demand under hyperinflation. the long term, even its strongest adherents would ———. 1960. AProgramforMonetaryStability.NewYork: accept that short-run dynamics and adjustments Fordham University Press. Lays out Friedman’s case for militate against a one-for-one relation between a constant growth rate rule for monetary policy. money and prices in the short run. Excess money ———. 1992. Money Mischief: Episodes in Monetary Policy. creation will eventually lead to inflation, but extra New York: Harcourt Brace Jovanovich. Highly accessi- liquidity may well initially push down interest rates ble general analysis of the causes and consequences of and encourage greater output and employment. monetary expansion, both past and present, can be Until these beneficial effects are reversed, the extra found in chapters 2 and 8. money issue may ‘‘buy’’ at least the illusion of greater Grubb, Farley. 2005. ‘‘Two Theories of Money Reconciled: prosperity. This, in turn, may produce a temptation The Colonial Puzzle Revisited with New Evidence.’’ to inflate. While the continued ratcheting up of the NBER Working Paper No.11784. Washington, DC: money supply will eventually lead to hyperinflation, National Bureau of Economic Research. Available at such an extreme outcome usually occurs only when a http://www.nber.org/papers/w11784. Revisits the ap- government finds itself unable to obtain funding plicability of the quantity theory of money to the from any source other than the printing press. Such American colonial experience and finds Pennsylvania episodes, while unfortunate, have nevertheless pro- data to be consistent with the quantity theory’s predic- vided economists with ample opportunity to observe tions. not only the inflationary consequences of such Sargent, Thomas J., and Neil Wallace. 1973. ‘‘Rational
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