This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: The Demand for Money: Some Theoretical and Empirical Results Volume Author/Editor: Milton Friedman Volume Publisher: UMI Volume ISBN: 0-87014-382-4 Volume URL: http://www.nber.org/books/frie59-1 Publication Date: 1959 Chapter Title: The Demand for Money: Some Theoretical and Empirical Results Chapter Author: Milton Friedman Chapter URL: http://www.nber.org/chapters/c5857 Chapter pages in book: (p. 1 - 29)
Transcript
This PDF is a selection from an out-of-print volume from the National Bureauof Economic Research
Volume Title: The Demand for Money: Some Theoretical and Empirical Results
Volume Author/Editor: Milton Friedman
Volume Publisher: UMI
Volume ISBN: 0-87014-382-4
Volume URL: http://www.nber.org/books/frie59-1
Publication Date: 1959
Chapter Title: The Demand for Money: Some Theoretical and Empirical Results
Chapter Author: Milton Friedman
Chapter URL: http://www.nber.org/chapters/c5857
Chapter pages in book: (p. 1 - 29)
The Demand for Money:Some Theoretical and
Empirical Results
MILTON FRIEDMAN
OCCASIONAL PAPER 68
NATIONAL BUREAU OF ECONOMIC RESEARCH, INC.1959
Distributed by Columbia University Press: New York and London
Reprinted from the August 1959 issue of the
Journal of Political Economy
University of Chicago, Economics Department
Library of Congress Catalog Card Number: 59-12559
Price: $1.5,O
NATIONAL BUREAU OF ECONOMIC RESEARCH, Inc.261 Madison Avenue, New York 16, N.Y.
NATIONAL BUREAU OF ECONOMIC RESEARCH1959
OFFICERS
George B. Roberts, ChairmanArthur F. Burns, President
Theodore W. Schultz, Vice-PresidentMurray Shields, Treasurer
Solomon Fabricant, Director of ResearchGeoffrey H. Moore, Associate Director of Research
William J. Carson, Executive Director
DIRECTORS AT LARGE
Wallace J. Campbell, Director, Cooperative League of the USASolomon Fabricant, New York University
Gabriel Hauge, Chairman, Finance Committee, Manufacturers Trust CompanyAlbert J. Hettinger, Jr., Lazard Frères and Company
Oswald W. Knauth, Beaufort, South CarolinaH. W. Laidler, Executive Director Emeritus, League for Industrial Democracy
Shepard Morgan, Norfolk, ConnecticutGeorge B. Roberts, Larchmont, New York
Beardsley Rumi, New York CityHarry Scherman, Chairman, Book-of-the-Month ClubBoris Shishkin, American Federation of Labor and
Congress of Industrial OrganizationsGeorge Soule, Professor Emeritus, Bennington College
N. I. Stone, Consulting EconomistJ. Raymond Walsh, New York City
Joseph H. Willits, Director, The Educational Survey, University of PennsylvaniaLeo Wolman, Columbia University
Donald B. Woodward, Vick Chemical CompanyTheodore 0. Yntema, Vice-President—Finance, Ford Motor Company
DIRECTORS BY UNIVERSITY APPOINTMENT
V. W. Bladen, TorontoArthur F. Burns, ColumbiaMelvin G, de Chazeau, CornellFrank W. Fetter, NorthwesternH. M. Groves, WisconsinGottiried Haberler, Harvard
Walter W. Heller, MinnesotaMaurice W. Lee, North CarolinaLloyd G. Reynolds, YaleT. W. Schultz, ChicagoJacob Viner, PrincetonWillis J. Winn, Pennsylvania
DIRECTORS APPOINTED BY ORGANIZATIONS
Percival F. Brundage, American Institute of Certified Public AccountantsHarold G. Halcrow, American Farm Economic AssociationTheodore V. Houser, Committee for Economic DevelopmentStanley H. Ruttenberg, American Federation of Labor and
Congress of Industrial OrganizationsMurray Shields, American Management AssociationWillard L. Thorp, American Economic AssociationW. Allen Wallis, American Statistical Association
Harold F. Williamson, Economic History Association
Moses AbramovitzGary S. BeckerGerhard BryArthur F. BurnsMorris A. CopelandFrank G. DickinsonJames S. EarleyRichard A. EasterlinSolomon FabricantMilton Friedman
RESEARCH STAFF
Raymond W. GoldsmithLeo GreblerMillard HastayW. Braddock HickmanDaniel M. HollandThor HultgrenC. Harry KahnJohn W. KendrickSimon KuznetsClarence D. Long
Ruth P. Mackuse MintzGeoffrey H. MooreRoger R. MurrayG. Warren NutterLawrence H. SeltzerRobert P. ShayGeorge J. StiglerLeo WolmanHerbert B. Woolley
RELATION OF THE DIRECTORS
TO THE WORK AND PUBLICATIONS
OP THE NATIONAL BUREAU OP ECONOMIC RESEARCH
1. The object of the National Bureau of Economic Research is to ascertain and topresent to the public important economic facts and their interpretation in a scientific andimpartial manner. The Board of Directors is charged with the responsibility of ensuringthat the work of the National Bureau is carried on in strict conformity with this object.
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5. A copy of any manuscript proposed for publication shall also be submitted to eachmember of the Board. For each manuscript to be so submitted a special committee shall beappointed by the President, or at his designation by the Executive Director, consisting ofthree Directors selected as nearly as may be one from each general division of the Board.The names of the special manuscript committee shall be stated to each Director when thesummary and report described in paragraph (4) are sent to him. It shall be the duty ofeach member of the committee to read the manuscript. If each member of the special com-mittee signifies his approval within thirty days, the manuscript may be published. If eachmember of the special committee has not signified his approval within thirty days of thetransmittal of the report and manuscript, the Director of Research shall then notify eachmember of the Board, requesting approval or disapproval of publication, and thirty addi-tional days shall be granted for this purpose. The manuscript shall then not be publishedunless at least a majority of the entire Board and a two-thirds majority of those membersof the Board who shall have voted on the proposal within the time fixed for the receipt ofvotes on the publication proposed shall have approved.
6. No manuscript may be published, though approved by each member of the specialcommittee, until forty-five days have elapsed from the transmittal of the summary andreport. The interval is allowed for the receipt of any memorandum of dissent or reservation,together with a brief statement of his reasons, that any member may wish to express; andsuch memorandum of dissent or reservation shall be published with the manuscript if heso desires. Publication does not, however, imply that each member of the Board has readthe manuscript, or that either members of the Board in general, or of the special committee,have passed its validity in every detail.
7. A COPY of this resolution shall, unless otherwise determined by the Board, be printedin each copy of every National Bureau book.
(Resolution adopted October 25, 1926
and revised February 6, 1933 and February 24, 1941)
THE DEMAND FOR MONEY: SOME THEORETICAL
AND EMPIRICAL RESULTS1
MILTON FRIEDMAN
University of Chicago and National Bureau of Economic Research
IN COUNTRIES experiencing a secularrise in real income per capita, thestock of money generally rises over
long periods at a decidedly higher ratethan does money income. Income veloci-ty—the ratio of money income to thestock of money—therefore declines secu-larly as real income rises. During cycles,to judge from the TJnited States, the onlycountry for which a detailed analysis hasbeen made, the stock of money generallyrises during expansions at a lower ratethan money income and either continuesto rise during contractions or falls at adecidedly lower rate than money income.
1 This paper reports on part of a broader studybeing conducted at the National Bureau of EconomicResearch by Anna J. Schwartz and myself. I amindebted to Mrs. Schwartz for extensive assistanceand numerous suggestions in connection with thepresent paper.
This paper has been approved for publicationas a report of the National Bureau of EconomicResearch by the Director of Research and the Boardof Directors of the National Bureau, in accordancewith the resolution of the board governing NationalBureau reports (see the Annual Report of the Na-tional Bureau of Economic Research). It is reprintedas No. 68 in the National Bureau's series of Occa-sional Papers.
1
Income velocity therefore rises duringcyclical expansions as real income risesand falls during cyclical contractions asreal income falls—precisely the reverseof the secular relation between incomeand velocity.
These key facts about the secular andcyclical behavior of income velocity havebeen documented in a number of studies.2For the United States, Anna Schwartzand I have been able to document themmore fully than has hitherto been pos-sible, thanks to a new series on the stockof money that we have constructedwhich gives estimates at annual or semi-annual dates from 1867 to 1907 andmonthly thereafter. This fuller documen-tation does not, however, dispel the ap-parent contradiction between the secularand the cyclical behavior of income ve-locity. On the contrary, as the summary
2 See in particular Richard T. Selden, "MonetaryVelocity in the United States," in Milton Friedman(ed.), Studies in the Quantity Theory of Money (Chi-cago: University of Chicago Press, 1956), pp. 179—257; and Ernest Doblin, "The Ratio of Income toMoney Supply: An International Survey," Reviewof Economics and Statistics, August, 1951, p. 201.
of our findings in the following sectionmakes explicit, it reveals an additionalcontradiction or, rather, another aspectof the central contradiction.
Previous attempts to reconcile thesecular and cyclical behavior of thevelocity of circulation of money haveconcentrated on variables other than in-come, such as the rate of interest or therate of change of prices. These attemptshave been unsuccessful. While such othervariables doubtless affect the quantity ofmoney demanded and hence the velocityof circulation of money, most do not havea cyclical pattern that could explain theobserved discrepancy. In any event, itseems dubious that their influence onvelocity is sufficiently great to explain solarge a discrepancy.
An alternative theoretical explanationof the discrepancy is suggested by thework I have done on consumption—arather striking example of how work inone field can have important implicationsfor work in another that has generallybeen regarded as only rather distantlyrelated. This theoretical explanation,which concentrates on the meaning at-tached to "income" and to "prices," ispresented in Sections II and III belowand turns out to be susceptible of quan-titative test. The quantitative evidencein Section IV is highly favorable. The re-suit is both a fuller understanding of theobserved behavior of velocity and a dif-ferent emphasis in the theory of the de-niand for money.
One important feature of monetary be-havior not accounted for by this explana-tion is the consistent tendency for actualcash balances, adjusted for trend, to leadat both peaks and troughs in generalbusiness. In Section V, a preliminary at-tempt is made to explore factors thatmight account for the discrepancy be-tween desired cash balances as deter-mined by income alone and actual cash
balances. Finally, in Section VI, somebroader implications of the results pre-sented in this paper are explored.
I. A SUMMARY OF THE EMPIRICAL EVI-DENCE FOR THE STATES
A full documentation of our findingsabout the secular and cyclical behaviorof the stock of money and its relation toincome and prices will be given in a near-iy completed National Bureau of Eco-nomic Research monograph by Anna J.Schwartz and myself. For present pur-poses, a brief summary of a few of ourfindings will suffice.
A. SECULAR BEHAVIOR
1. Secular changes in the real stock ofmoney per capita are highly correlatedwith secular changes in real income percapita. In order to study this relation, wehave used average values over completereference cycles as our elementary ob-servations. For twenty cycles measuredfrom trough to trough and covering theperiod from 1870 to 1954, the simple cor-relation between the logarithm of the'real stock of money per capita and thelogarithm of real income per capita is0.99, and the computed elasticity is
1 per cent increase in real income percapita has therefore, on the average, beenassociated with a 1.8 per cent increase inreal cash balances per capita and hence
The corresponding figures for cycles measuredfrom peak to peak are 0.99 and 1.7. In these andlater correlations, "money" is defined as includingcurrency held by the public, adjusted demand de-posits, and time deposits in commercial banks. Thistotal is available for the period from 1867 on,whereas the total exclusive of time deposits is notavailable until 1914. For other reasons supportingour definition see the NBER monograph now inpreparation. For income, we have used Simon Kuz-nets' estimates of net national product adjustedfor wartime periods to a concept approximatingthat underlying the current Department of Com-merce estimates, and for prices, the deflator implicitin Kuznets' estimates of net national product inconstant prices.
2
with a 0.8 per cent decrease in incomevelocity. If we interpret these results asreflecting movements along a stable de-mand relation, they imply that money isa "luxury" in the terminology of con-sumption theory. Because of the strongtrend element in the two series correlat-ed, the high correlation alone does notjustify much confidence that the statisti-cal regression is a valid estimate of a de-mand relation rather than the result ofan accidental difference in trends. How-ever, additional evidence from othersources leads us to believe that it can beso regarded.
We have investigated the influence ofboth rates of interest and rates of changeof prices. In our experiments, the rate ofinterest had an effect in the direction tobe expected from theoretical considera-tions but too small to be statistically sig-nificant. We have not as yet been able toisolate by correlation techniques anyeffect of the rate of change of prices,though a historical analysis persuades usthat such an effect is present.
2. Over the nine decades that we havestudied, there have been a number oflong swings in money income. As a mat-ter of arithmetic, these swings in moneyincome can be attributed to movementsin the nominal stock of money and invelocity. If this is done, it turns out thatthe swings in the stock of money are inthe opposite direction from those invelocity and so much larger in amplitudethat they dominate the movements inmoney income. As a result, the longswings in prices mirror faithfully the longswings in the stock of money per unit ofoutput. These long swings are muchmore marked in money income and in thenominal stock of money than in real in-come and in the real stock of money,which is to say that the long swings arelargely price swings.
3
B. CYCLICAL BEHAVIOR
1. The real stock of money, like realincome, conforms positively to the cycle;that is, it tends to rise during expansionsand to fall, or to rise at a less rapid rate,during contractions. However, the am-plitude of the movement in the real stockof money is decidedly smaller than inreal income. If we allow for seculartrends, a 1 per cent change in real incomeduring a cycle is accompanied by achange in the real stock of money in thesame direction of about one-fifth of 1 percent.
It follows that income velocity tendsto rise during cyclical expansions whenreal income is rising and to fall duringcyclical contractions when real income isfalling—that is, to conform positively.So far as we can tell from data that aremostly annual, velocity reaches both itspeak and its trough at roughly the sametime as general economic activity does.
2. Cyclical movements in money in-come, like the long swings, can be at-tributed to movements in the nominalstock of money and in velocity. If this isdone, it turns out that the movements inthe stock of money and in velocity are inthe same direction and of roughly equalmagnitude, so that neither can be said todominate the movements in money in-come.
3. Table 1 summarizes the size of thecyclical movements in the variables usedin the analysis, where the size of cyclicalmovement is measured by the excess ofthe rate of change per month duringcyclical expansions over that duringcyclical contractions.
C. THE CONTRAST
These findings are clearly in sharpcontrast. Over long periods, real incomeand velocity tend to move in oppositedirections; over reference cycles, in thesame direction. Over long periods,
changes in the nominal stock of moneydominate, at least in a statistical sense,the swings in money income, and the in-verse movements in velocity are of minorquantitative importance; over referencecycles, changes in velocity are in thesame direction as changes in the nominalstock of money and are comparable in
first instance by the monetary authori-ties or institutions and cannot be alteredby the non-bank holders of money. Thereal stock of money is determined in thefirst instance by the holders of money.
This distinction is sharpest and leastambiguous in a hypothetical society inwhich money consists exclusively of a
Six deep depression cycles:Money income .64 — .97 1.61Money stock .60 — .28 0.88Income velocity .02 — .69 0.71Implicit price deflator .16 — .44 0.60Real income .46 — .53 0.99Real stock of money 0.42 0.18 0.24* The series were analyzed as described in A. F. Burns and W. C. Mitchell, Measuring Business
Cycles (New York: National Bureau of Economic Research, 1947), pp. 197—202. Because of round-ing, cot. 3 sometimes disagrees with the difference between cols. 1 and 2. Deep depression cyclesare 1870—78,1891—94,1904—8,1919—21, 1927—32,and 1932—38. Allothersaremilddepressioncyclesexcept for war cycles 1914—19 and 1938—46, which are excluded. The basis of classification isdescribed in the NBER monograph on the money supply now in preparation. Money incomeis net national product at current prices, preliminary estimates by Simon Kuznets1 preparedfor use in the NBER study of long-term trends in capital formation and financing in theUnited States. Variant III (from 1929 based on estimates of commodity flow and services preparedby the Department of Commerce). Money stock is averaged to center on June 30 from data inthe money monograph just mentioned. Income velocity is money income divided annually by moneystock. Implicit price deflator is money income divided by real income. Real income is net nationalproduct, 1929 prices, Variant III from the same source as money income. Real stock of money ismoney stock divided by the implicit price deflator.
quantitative importance in accountingfor changes in money income. I turn toan attempted reconciliation.
IL A SUGGESTED EXPLANATION
It is important to note at the outsetan essential difference between the de-terminants of the nominal stock ofmoney, on the one hand, and the realstock of money, on the other. The nomi-nal stock of money is determined in the
4
purely fiduciary currency issued by asingle money-creating authority at itsdiscretion. The nominal number of unitsof money is then whatever amount thisauthority creates. Holders of money can-not alter this amount directly. But theycan make the real amount of money any-thing that in the aggregate they want to.If they want to hold a relatively smallreal quantity of money, they will indi-vidually seek to reduce their nominal
TABLE 1*
CYCLICAL MOVEMENTS IN INCOME, MONEY STOCK, INCOME VELOCITY,AND PRICES: DIFFERENCE IN Mowrmx RATE OF CHANGE BETWEENREFERENCE EXPANSION AND CONTRACTION, ANNUAL ANALYSIS, 1870-1954, EXCLUDING WAR CYcLES
CHANGE PER MONTB IN REF-
ERENCE- CYCLE RELATIVES
DURING REFERENCE
Expansion Contraction(1) (2)
ExCEss oi'ExPANsIoN
OVER
CONTRACTION
(3)
cash balances by increasing expendi-tures. This will not alter the nominalstock of money to be held—if some indi-viduals succeed in reducing their nominalcash balances, it will only be by transfer-ring them to others. But it will raise theflow of expenditures and hence moneyincome and prices and thereby reducethe real quantity of money to the de-sired level. Conversely, if they want tohold a relatively large real quantity ofmoney, they will individually seek to in-crease their nominal cash balances. Theycannot, in the aggregate, succeed indoing so. However, in the attempt, theywill lower the nominal flow of expendi-tures, and hence money income andprices, and so raise the real quantity ofmoney. Given the level of real income,the ratio of income to the stock ofmoney, or income velocity, is uniquelydetermined by the real stock of money.Consequently, these comments applyalso to income velocity. It, too, is deter-mined by the holders of money, or, toput it differently, it is a reflection of theirdecisions about the real quantity ofmoney that they desire to hold. We cantherefore speak more or less interchange-ably about decisions of holders of moneyto change their real stock of money or tochange the ratio of the flow of income tothe stock of money.
The situation is more complicated forthe monetary arrangements that actuallyprevailed over the period which our datacover. During part of the period, when theUnited States was on an effective goldstalidard, an attempt by holders ofmoney to reduce their cash balances rela-tive to the flow of income raised domesticprices, thereby discouraging exports andencouraging imports, and so tended toincrease the outflow of gold or reduce itsinflow. In addition, the rise in domesticprices raised, among other things, the
5
cost of producing gold and hence discour-aged gold production. Both effects oper-ated to reduce the nominal supply ofmoney. Conversely, an attempt by hold-ers of money to increase their cash bal-ances relative to the flow of incometended to increase the nominal supply ofmoney through the same channels. Theseeffects still occur but can be and typicallyare offset by Federal Reserve action.
Throughout the period, more compli-cated reactions operated on the commer-cial banking system, sometimes in per-verse fashion. For example, an attemptby holders of money to reduce cash bal-ances relative to income tended to raiseincome and prices, thus promoting anexpansionary atmosphere in which bankswere generally willing to operate on aslenderer margin of liquidity. The resultwas an increase rather than a reductionin the nominal supply of money. Similar-ly, changes in the demand for money hadeffects on security prices and interestrates that affected the amount of moneysupplied by the banking system. Andthere were further effects on the actionsof the Federal Reserve System for theperiod since 1914.
There were also indirect effects run-ning in the. opposite direction, fromchanges in the conditions of supply ofmoney to the nominal quantity of moneydemanded. If, for whatever reason,money-creating institutions expandedthe nominal quantity of money, thiscould have effects, at least in the first in-stance, on rates of interest and so on thequantity of money demanded, and per-haps also on money income and realincome.
Despite these qualifications, all ofwhich would have to be taken into ac-count in a complete analysis, it seemsuseful to regard the nominal quantity ofmoney as determined primarily by con-
ditions of supply, and the real quantity ofmoney and the income velocity of moneyas determined primarily by conditions ofdemand. This implies that we should ex-amine the demand side for an initial in-terpretation of the observed behavior ofvelocity.
Along these lines, the changes in thereal stock of money and in the incomevelocity of circulation reflect either(a) shifts along a relatively fixed demandschedule for money produced by changesin the variables entering into thatschedule; (b) changes in the demandschedule itself; or (c) temporary depar-tures from the schedule, that is, frictionsthat make the actual stock of money de-part from the desired stock of money.The rest of this paper is an attempt tosee to what extent we can reconcile thesecular and cyclical behavior of velocityin terms of a alone without bringing inthe more complicated phenomena thatwould be involved in b and c.
One way to do so would be to regardthe cyclical changes in velocity as reflect-ing the influence of variables other thanincome. In order for this explanation tobe satisfactory, these other variableswould have to exert an influence oppo-site to that of income and also be sufh-ciently potent to dominate the move-ment of velocity. Our secular resultsrender this implausible, for we therefound that income appeared to be thedominant variable affecting the demandfor real cash balances. Moreover, theother variables that come first to mindare interest rates, and these display cycli-cal patterns that seem most unlikely toaccount for the sizable, highly consistent,and roughly synchronous cyclical pat-tern in velocity. Long-term corporate in-terest rates fairly regularly reached theirtrough in mid-expansion and their peakin mid-contraction prior to World War I.
6
Since then, the pattern is less regular andis characterized by shorter lags. Rates onshort-term commercial paper also tend tolag at peaks and troughs, though by abriefer interval, and the lag has similarlyshortened since 1921. Call-money ratescome closer to being synchronous withthe cycle, and this is true also of yieldson long- and short-term government oh-ligations for the six cycles for which theyare available. Of the rates we have exam-ined these are the only ones that haveanything like the right timing pattern toaccount for the synchronous pattern invelocity. However, neither call-mQneyrates nor government bond yields havebeen highly consistent in behavior fromcycle to cycle. Even if they had been, itseems dubious that the effects of changesin these particular rates, or other unre-corded rates like them, would be suffi-ciently more important cyclically thansecularly to offset the effects of counter-movements both in other rates and inincome. Furthermore, earlier studies thathave attempted to explain velocitymovements in these terms have had onlylimited success.4
A very different way to reconcile thecyclical and secular behavior of velocityis to regard the statistical magnitudecalled "real income" as corresponding toa different theoretical construct in thecyclical than in the secular analysis. Thispossibility was suggested by my work onconsumption. In that field, too, it will berecalled, there is an apparent conflict be-tween empirical findings for short periodsand long periods: cross-section data forindividual years suggest that the averagepropensity to consume is lower at high-income levels than at low-income levels;yet aggregate time-series data covering along period reveal no secular decline in
E.g., see Selden, op. cii., pp. 195—202.
the average propensity to consume witharise in income. It turned out that thisconflict could be reconciled by distin-guishing between "measured" income,the figure recorded by statisticians, and"permanent" income, a longer-term con-cept to which individuals are regarded asadjusting their consumption.5
According to the permanent incomehypothesis, when a consumer unit expe-riences a transitory increment of income,that is, when its measured income ex-ceeds its permanent income, this transi-tory component is added to its assets(perhaps in the form of durable consumergoods) or used to reduce its liabilitiesrather than spent on consumption. Con-.versely, when it experiences a transitorydecrement of income, it nonetheless ad-justs consumption to permanent income,financing any excess over measured in-come by drawing down assets or increas-ing liabilities.
This theory of consumption behavioris directly applicable to that part of thestock of money held by consumer unitsrather than by business enterprises. Theproblem is how to interpret money hold-ing. Much of the theoretical literature on"motives" for holding money suggestsinterpreting money holdings as one of thebalance-sheet items that act as shock ab-sorbers for transitory components of in-come; as an asset item that is increasedtemporarily when the transitory compo-nent is positive and that is drawn down,if necessary, to finance consumptionwhen the transitory component is nega-ti ye.
This interpretation may be valid forvery short time periods. However, if itwere valid for periods as long as a busi-
5 my A Theory of the Consumption Function(a publication of the National Bureau of EconomicResearch) (Princeton: Princeton University Press,1957).
7
ness cycle, it would produce a cyclicalbehavior of velocity precisely the oppo-site of the observed behavior. Measuredincome presumably exceeds permanentincome at cyclical peaks and falls shortof permanent income at cyclical troughs.Hence cash balances would be drawndown abnormally at troughs and built upabnormally at peaks. In consequence,cash balances would fluctuate morewidely over the cycle than income, andvelocity would conform inversely to thecycle, falling during expansions and ris-ing during contractions, whereas in factit conforms positively.
An alternative is to interpret money asa durable consumer good held for theservices it renders and yielding a flow ofservices proportional to the stock, whichimplies that the shock-absorber functionis performed by other items in the bal-ance sheet, such as the stock of durablegoods, consumer credit outstanding, per-sonal debt, and perhaps securities held.On this interpretation, the quantity ofmoney demanded, like the quantity ofconsumption services in general, isadapted not to measured income but topermanent income. This interpretation isconsistent with our secular results. Theincome figure we used in obtaining theseis an average value over a cycle, whichmay be regarded as a closer approxima-tion to permanent income than an annualvalue. In any case, the long time periodcovered assures that the movements inmoney are dominated by the movementsin the permanent component of income.6For the cyclical analysis, permanent in-come need not itself be stable over acycle. It may well rise during expansionsand fall during contractions. Presuma-bly, however, it will rise less than meas-ured income during expansions and fall
pp. 125—29.
less during contractions. Hence, if moneyholdings were adapted to permanent in-come, they might rise and fall more thanin proportion to permanent income, as isrequired by our secular results, yet lessthan in proportion to measured income,as is required by our cyclical results.
To put the matter differently, supposethat the demand for real cash balanceswere determined entirely by real perma-nent income according to the relation es-timated in the secular analysis and thatactual balances throughout equaled de-sired oalances. Velocity would then fallduring expansions and rise (or fall at asmaller rate) during contractions, pro-vided that it was computed by dividingpermanent iiwome by the stock of money.But the numbers we have been caffing"velocity" were not computed in thisway; they were computed by dividingmeasured income by the stock of money.Such a measured velocity would tend tobe lower than what we may call perma-nent velocity at troughs, because meas-ured income is then lower than perma-nent income and would tend to be higherat peaks, because measured income isthen higher than permanent income.,Measured velocity might therefore con-form positively to the cycle, even thoughpermanent velOcity conformed inversely.
These comments apply explicitly onlyto consumer cash balances. However,they can readily be extended to businesscash balances. Businesses hold cash as aproductive resource. The question iswhether cash is a resource like inven-tories, in which case it might be expectedto fluctuate more over the cycle than cur-rent production, or like fixed capital, inwhich case it might be expected to fluc-tuate less and to be adapted to the long-er-term level of production at which afirm plans to operate. This latter possi-bility involves a concept analogous to
8
that of permanent income. If the ob-served positive cyclical conformity ofvelocity reflects wider movements in in-come than in both business holdings andconsumer holdings, as seems likely inview of the changing importance of thesetwo components and the consistent be-havior of velocity, the answer must bethat cash balances are analogous to fixedcapital rather than to inventories andthat some other assets or liabilities serveas shock-absorbers for business as forconsumers.
The distinction between permanentand measured income can rationalize theobserved cyclical behavior of incomevelocity in terms of a movement along astable demand curve. It cannot by itselfeasily rationalize the behavior of realcash balances. Our secular analysis im-plies that real cash balances should con-form positively to the cycle with an am-plitude nearly twice that of permanentreal income. Observed real cash balancesdo conform positively, but their ampli-tude, at any rate for cycles containingmild contractions, is so small that itseems implausible to regard it as largerthan that in permanent real income. Putdifferently, it would take oniy very mod-erate changes in the index of prices, wellwithin the margin of error in such in-dexes, to convert the positive conformityinto inverted conformity.
The resolution is straightforward. Wehave not yet carried our logic far enough.If applied to both money income andreal income, the distinction betweenmeasured and permanent income imp] iesa corresponding distinction for prices. Toput the matter in terms of economicsrather than arithmetic, our analysis sug-gests that holders of cash balances deter-mine the amount to hold in light of theirlonger-term income position rather thantheir momentary receipts—this is the
justification for distinguishing measuredfrom permanent income. By the sametoken, they may be expected to deter-mine the amount of cash balances tohold in light of longer-term price move-
prices, as it were—rather than current or measured prices.Suppose, for example, prices were todouble permanently or, alternatively, todouble for day X only and then return totheir initial level and that this behaviorwas correctly anticipated by holders ofmoney. Holders of money would hardlywant to hold the same nominal cash bal-ances on day X in these two cases, eventhough prices were the same on that day.More generally, whatever the motivesfor holding cash balances, they are heldand are expected to be held for a sizableand indefinite period of time. Holders ofmoney presumably judge the "real"amount of cash balances in terms of thequantity of goods and services to whichthe balances are equivalent, not at anygiven moment of time, but over a sizableand indefinite period; that is, they evalu-ate them. in terms of "expected" or "per-manent" prices, not in terms of the cur-rent price level. This consideration doesnot, of course, rule out some adjustmentto temporary movements in prices. Suchmovements offer opportunities of profitfrom shifting wealth from cash to otherforms of assets and conversely, and theymay affect people's expectations aboutfuture price levels. Like "permanent in-come," the "permanent" price level neednot be—and presumably is not—a con-stant over time; it departs from the cur-rent price level in having a smoother andless fluctuating pattern in time but neednot go to the extreme of displaying nofluctuations.
On this view, the current price levelwould presumably fall short of the per-m.anent price level at troughs and exceed
it at peaks of cycles; hence measuredreal cash balances would tend to belarger than permanent real cash balancesat troughs and smaller at peaks. It fol-lows that measured real cash balanceswould show a smaller cyclical movementthan permanent real cash balances and,indeed, might conform inversely to thecycle, even though permanent real cashbalances conformed positively.
III. A SYMBOLIC RESTATEMENT
The distinction between permanentand measured magnitudes can thusreconcile the qualitative behavior duringreference cycles of both measured veloci-ty—its tendency to conform positively—and measured real cash balances—itstendency to show an exceedingly mildcyclical movement— with their behaviorover secular periods. The crucial questionremains whether it not only can reconcilethe qualitative behavior but does in fact
'rationalize the quantitative behavior ofthese magnitudes. After all, an interpre-tation in terms of interest rates can alsorationalize the qualitative results; we re-ject it because it appears likely to be con-tradicted on a more detailed quantitativelevel.
9
It will facilitate such a quantitativetest to restate symbolically and moreprecisely the explanation just presented.Let
V be measured aggregate in-come in nominal terms;
P be measured price level;M be aggregate stock of money
in nominal terms, measuredand permanent being takenthroughout as identical;
N be population, measuredand permanent being takenas identical;be permanent nominal ag-gregate income and perma-nent price level, respective-ly;
= V be measured aggregate in-p come in real terms;
be permanent aggregate in-come in real terms;be measured aggregatestock of money in realterms;be permanent aggregatestock of money in realterms;
be measured velocity;
be permanent velocity.
In these symbols, the demand equationfitted to the secular data can be writtenthus:
M (Y,,VNP,,
(1)
which expresses permanent real balancesper capita as a function of permanentreal income per capita, or in the equiva-lent form,
in,, = 'yN =
which expresses aggregate permanentreal balances as a function of aggregatepermanent real income and population,where 'y and a- are parameters and & wasestimated to be approximately
By definition,
m,,,
so that still a third form of the demandequation is
m =!?
'The basic analysis holds, of course, whateverthe precise form of the demand equation for money.I use this particular form for simplicity and becauseit gave a satisfactory fit to the available evidence.The whole analysis could, however, be restatedin terms of a generalized demand function whoseform was unspecified.
which expresses aggregate measured realbalances as a function of aggregate per-manent real income, population, and per-manent and measured prices.
This relation can also be expressed interms of velocity. By definition, =yp/mp. Divide successively by the twosides of equation (2). This gives
= ! !m,, yp
By definition,
so that
p_V_V vp,
F' 1 \!—6V=__1!i
In interpreting equations (1), (2), (4),(5), and (7), it should be borne in mindthat they will not, of course, be satisfiedprecisely by observed data. In conse-quence, at a later stage, I shall want to
(2) distinguish between observed values of,for example, measured velocity and the.value estimated from, say, equation (7).
IV. TESTS OF THE EXPLANATION.
It has so far been sufficient to supposeonly that the permanent magnitudes in-
income and per-manent prices—fluctuate less over the
(3)cycle, than the corresponding measuredmagnitudes. We can clearly go fartherand ask how much less the permanentmagnitudes must fluctuate in order toaccount for the quantitative, as well asthe qualitative average behavior ofvelocity and real cash balances. The an-swer may provide some internal evidenceon the plausibility of the suggested ex-planation and will also provide a startingpoint for bringing external evidence tobear.
Consider the data for the mild depres-
10
—Vpyp—-15.-
.Lp
M
Mm,, =
v— MmV — V,,_
" M m,
sion cycles shown in Table 1 and neglectthe mild cyclical movements in popula-tion, so that aggregate and per capitavalues can be regarded as interchange-able. If measured and permanent magni-tudes were treated as. identical, the in-come elasticity of 1.8 computed from thesecular data would convert the 0.57cyclical movement in real income into amovement of 1.03 in real cash balancesdemanded. The movement of 0.14 in theimplicit price index would, in turn, con-vert this into a movement of 1.17 inmoney cash balances demanded. The ac-tual movement in cash balances is 0.27,or 23 per cent as large. Hence, to recon-cile the secular and cyclical results, thecyclical movements in permanent incomeand permanent prices would each haveto be 23 per cent of those in measuredincome and measured prices—a resultthat seems not implausible. For deep de-pression cycles, the corresponding figureturns out to be 37 per cent, which isequally plausible. Moreover, it seemseminently reasonable that this figureshould be larger for deep, than for mild,depression cycles, since the deep depres-sion cycles are longer on the average thanthe mild depression cycles.8
Of course, this test of intuitive plausi-bility is a weak one. To get a strongertest, we must introduce some inde-pendent evidence on the relation ofpermanent to measured magnitudes. Onesource of such evidence is the work onconsumption that suggested the explana-tion under test. In deriving a consump-tion function from aggregate time-seriesdata, I concluded that an estimate ofpermanent income—which I called "ex-pected" income to distinguish it fromthe theoretical concept—was given by
T
yp (T) = T)y (t) dl. (8)
In words, an estimate of expected in-come at time T is given by a weightedaverage of past incomes, adjusted forsecular growth at the rate of a per centper year, the weights declining ex-ponentially and being equal towhere I is the time of the observationbeing weighted. The numerical value of
8 Let M and P be the cyclical movements asmeasured in the final column of Table 1 in thenominal stock of money and in measured prices;let in, and F, be the cyclical movements in perma-nent real balances and permanent prices. Then,to a first approximation,
M (i)
since the stock of money is the product of permanentreal cash balances and the permanent price level.Using the demand equation (2), we get
ih (ii)
where is the cyclical movement in permanentreal income (recall that we are neglecting any cycli-cal movement in population, so also equals themovement in permanent real per capita income).
Let
yp=
k'P,
(iii)
(iv)
where is the cyclical movement in measured realincome and k and k' are unspecified constants tobe determined. Substituting equations (ii), (iii), and(iv) in equation (i) gives
11
1.8k3'+k'P. (v)
At first glance, it seems possible to derive bothk and k' from one set of data by deriving a similarequation starting with an identity like (i) expressingmeasured velocity in terms of permanent velocity.However, the resulting equation is identical witheq. (v), thanks to the definitional relations connect-ing velocity, money, and income.
The calculations in the text implicitly assumethat k = k' in eq. (v). Separate estimates for kand k' require two sets of data. One possibility isto assunie that k and k' differ but that each is thesame for mild and for deep depression cycles, anassumption that seems less plausible than the onemade in the text that k = k'. This calculation yieldsan estimate of 0.11 for k and 1.15 for k'. The valuefor k' contradicts the concepts of permanent andmeasured prices that underlie the analysis.
j3 was estimated to be 0.4; of a, Itis by no means necessary that the con-cept of permanent income that is rele-vant in determining total consumptionexpenditures should also be the one thatis relevant in determining cash bal-ances.'0 But it would not be at all sur-prising if it were. On the assumptionthat it is, we can get independent esti-mates of the percentages cited in theprevious paragraph by computing esti-mates of permanent real income, andpermanent prices from the correspondingobserved annual series, using the weight-ing pattern just described.
The results of these computations aresummarized in columns 1, 2, and 3 ofTable 2.11 The agreement between the
9Friedrnan, A Theory of the Consumption Func-tion, pp. 146—47.
'° See ibid., pp. 150—51.
These results at first seemed to me relevantalso to the choice between the two alternative as-sumptions used above—the one in the text thatk k' and the one noted in footnote 8, that kbut that k is the same for mild and deep depressioncycles and so is k'. On this issue, the result is un-ambiguous. The entries in col. 3. clearly speak forthe first assumption.
However, James Ford has pointed out to methat this result is largely a consequence of an as-sumption made in estimating permanent income andprices, namely, the use of the same value of fifor both. There is no independent empirical evidencefor this assumption, and hence results based on itcan give no independent evidence for the essentiallyequivalent assumption that k =
For the special case in which the measured mag-nitude is given by a sine curve, the relative amplitudeof a permanent and a measured magnitude whenthe permanent is estimated by a weighted averageof the measured is determined entirely by the valueof and the duration of the cycle. For = 0.4and a cycle 43 months in length, which is the averagelength of the mild depression cycles, the relativeamplitude for the sine curve is 0.22. For = 0.4and a cycle 47.5 months in length, the averagelength of the deep depression cycles, the relativeamplitude for the sine curve is 0.25. These resultsare fairly similar to the computed values in Table2. They differ enough, however, to suggest that thedeparture from a sine curve affects the results ap-preciably.
I am indebted to James Ford for these calcula-tions.
estimates in column 3 so obtained andthe estimates constructed above frominternal evidence alone is very good—thetwo differ by only 15—30 per cent, eventhough they are based on independentbodies of data and even though theweights used in estimating the perma-nent magnitudes directly were derivedfor another purpose and rest on stillother data. Moreover, the discrepancy isconsistent; the difference between deepand mild depression cycles is in the samedirection and of roughly the same magni-tude for both columns.
These results are sufficiently encourag-ing to justify going beyond this indirecttest and seeing how far our interpreta-tion is consistent not only with the sizeof the cyclical movement in cash bal-ances and measured velocity but alsowith their entire cyclical patterns andnot only on the average but also cycle bycycle.
In order to perform this test on a fullyconsistent basis, we first recomputed thesecular demand equation, using as theindependent variable the cycle averagesof estimated permanent income ratherthan measured income. This substitutionslightly raised the correlation coefficient,thus giving a minor bit of additional evi-dence in favor of the permanent incomeinterpretation. It also raised slightly theestimated elasticity of demand, but notby enough, to change the numericalvalue to the number of significant figuresgiven above.
The resulting calculated equation fornominal cash balances is
12
1.810M* = (0.003 23)
and, for measured velocity
NP,,, (9)
1
fy)_O.8'Oy0.00323LN
where the asterisks are used to indicatevalues computed from the equationrather than directly observed. Theseequations, it will be recalled, were esti-mated from average values over wholereference cycles.'2
From these equations, one can esti-mate for each year separately, from thecorresponding annual data, desired cash
balances and the value of measuredvelocity that would be observed if actualcash balances equaled desired balancesas so estimated. I shall call these "com-puted cash balances" and "computedmeasured velocity."3.
The estimates of computed measuredvelocity are plotted in Chart I, alongwith observed measured velocity. In
Two ESTIMATES OF CYCLICAL MOVEMENTS OF PERMANENT REAL INCOME ANDPRICES AS PERCENTAGES OF THOSE OF MEASURED REAL INCOME AND
MONTH IN REFERENCE-CYCLE PERMANENT AS PER-RELATIVES DURING REFERENCE CENTAGE or MEASURED
OVER THAT DURING RatioREFERENcE CONTRACTION Permanent Estimated
Permanent Measured Estimated from MoneyMagnitude Magnitude Separately Equations
(1) (2) (3) (4)
Twelve mild depression cycles:Real incomePrices
Six deep depression cycles:Real incomePrices
0.11 0.57 19 23.02 .14 16 23•
.29 .99 29 370.18 0.60 30 37
* The sources for the columns are as follows (cycles grouped as in Table 1):1. Permanent real income and permanent prices were estimated as described in the text, using Kuznets'
data (see note to Table 1). These data begin in 1869. To obtain an estimate of the permanent magnitudein 1869, measured figures covering the years 1858—69 are required, the weights assigned declining ex-ponentially. Measured figures were therefore extrapolated: for real income by assuming a constant rateof growth of 3.5 per cent per year; for implicit prices by assuming that in each of t4ie years 1858—68 theybore the same relation to the wholesale price index as in 1869.
2. Table 1, col. 3.3. Column 1 divided by col. 2, the figures in each case being carried to an additional place.4. Values from Table 1, col. were substituted in the expression M/(1.82 + F), where Mis money stock,
y is real income, P is implicit price deflator, and the dot on top means •'excess of chanp per month inreference-cycle relatives during reference expansion over that during reference contraction."
'2The numerical values given were computedfrom combined data for trough-to-trough and peak-to-peak averages. However, separate regressions foreach set of averages are almost identical.
To make these calculations, estimates of Y,Yr,, yr,, P,, and N are needed. Measured moneyincome, Y, was taken to be Kuznets' annual netnational product in current prices adjusted for war-time periods; Y, was computed by applying eq.(8) to this same series, except for a minor adjustmentin level; y,,, by applying eq. (8) to Kuznets' netnational product in constant prices similarly ad-justed, and again with a minor adjustment in level;F,, by applying eq. (8) to the price index implicitin computing net national product in constant prices;and N was taken as the mid-year population ofthe United States as estimated by the Census.
Equation (8) with = 0.40 and a = 0.02 impliesthat expected income is 1.05 times the weightedaverage of actual income, where the weights are
the declining exponential weights inside the integralof eq. (8), adjusted to sum to unity. When perma-nent net national product per capita in Constantprices was computed in this way, it turned out thatthe geometric mean of the ratios of the cycle bases ofreal measured net national product per capita to thecycle bases of permanent net national product inconstant prices so computed was 1.057. This factor of1.057 was used to adjust the level of the latter seriesrather than the 1.05 strictly called for by eq. (8)and was used also for permanent net national prod-uct in current prices. The logical implication ofemploying the same multiple for net national prod-uct in constant and current prices is that a wastreated as zero for prices alone. None of theseadjustments is of any moment for the present anal-ysis, since they affect only the level of the seriesand hence all. cancel out when cycle relatives arecomputed.
13
TABLE 2*
judging this figure, it should be borne inmind that the computed velocities werenot obtained by trying to fit these ob-served velocities directly. They were ob-tained from a correlation for forty-oneoverlapping cycle bases—averages ofgroups of years varying in number fromtwo to seven—plus a formula for estimat-ing permanent income derived from an
the secular ftnding. What is added bythis chart is the relation between year-to-year movements. The secular resultsin no way insure that these will cor-respond; still, if anything, the computedvelocity series mirrors the year-to-yearcycles in observed velocity even morefaithfully than it does the longer-termchanges.
CHART I
OBSERVED AND COMPUTED MEASURED VELOCITY, ANNUALLY, 1869—1957
analysis of' the relation of consumptionexpenditures to income plus a theoreticallinkage between these two, summarizedin equations (9) and (10). The high cor-relation between the cycle bases insuresa close connection between the longer-term movements in computed 'and meas-ured velocity; in this respect, Chart I issimply a repetition in a different form of
14
In order to isolate the cyclical aspectof the analysis, we have computed refer-ence-cycle patterns of computed meas-ured velocity and computed cash bal-ances, thereby eliminating entirely thepart of Chart I that repeats the secularfinding. Chart II gives the reference-cycle patterns of computed and observedmeasured velocity cycle by cycle, and
Ratio5.0
0F-.0,
0a,0,
0a,
00C.)
00.)
0 0C'J N)
r —
0 0U) U)
CHART II
OBSERVED AND COMPUTED MEASURED VELOCITY, REFERENCE-CYCLE PATTERNS, 1870-1954
100
90
NOTE: These are reference-cycle relatives computed in the course of the cyclical analysis of the datashown in Chart I (see A. F. Burns and W. C. Mitchell, Measuring Business Cycles [New York: NationaLBureau of Economic Research, 1946), pp. 197—202).
—36 —24 —12 0 +12 +24 +36Months from reference peak
Chart III gives average patterns for themild and deep depression cycles, forboth cash balances and measured ye-locity. It is clear from these that myinterpretation accounts for the bulk ofthe fluctuations in observed measuredvelocity. The average pattern of com-puted measured velocity duplicates al-most perfectly that for observed meas-
6 Deep Depression Cycles
—36 —24 —12 0 -4-12 +24 +36Months from reference peak
Cycles are grouped as in Table 1.
that this purely statistical interpretationof the findings is not valid. The cash-balance patterns agree about as closelyas the velocity patterns.
These results give strong support tothe view that cyclical movements invelocity largely reflect movements alonga stable demand curve for money andthat the apparent discrepancy between
Panel B. Measured Velocity
12 Mild Depression Cycles
6 Deep Depression Cycles
ured velocity for the mild depressioncycles and corresponds very closely tothat for the deep depression cycles. Thecycle-by-cycle patterns demonstrate thatthis coincidence is not simply in theaverages. This closeness might reflect theuse of the same values of measured in-come in both the observed and the com-puted velocities, in which case it could beregarded as largely spurious. The cash-balance patterns are included in Chart IIIto test this possibility. They demonstrate
the secular and the cyclical results re-flects a divergence between measures ofincome and of prices constructed bystatisticians for short periods and themagnitudes to which holders of moneyadjust their cash balances.
16
V. LIMITATIONS OF TIlE EXPLANATION
Important though this explanation is,it cannot be the whole of the story, sinceit fails to account for some of the mostimportant of our findings about the be-
- CHART III
OBSERVED AND COMPUTED MONEY STOCK AND MEAST.TRED VELOCITY, AVERAGE REFERENCE-CYCLE PATTERNS, MIlD AND DEEP DEPRESSION 1870—1954
ObservedComputed
Panel A. Money Stock
Cyc'es110— 110—
80 —
110—
80—
_____ _______
I I I
—36 —24 —12 0 +12 +24 +36Months from reference peak
90 —
80 —
Ito.-
100
90 —
80 —
havior of money balances. If the desiredreal stock of money were determined en-tirely by permanent real income and ifthe desired stock were always equal tothe actual stock, then, actual realstock (computed in terms of permanentprices) would have a cyclical patternthat duplicated the pattern of permanentreal income except for amplitude. Nowour evidence suggests that permanentreal income conforms . positively to thecycle and is either synchronous or lagsat the turning points. Hence real cashbalances computed at permanent priceswould do likewise. Nominal cash bal-ances equal these real cash balancestimes permanent prices, and our evi-dence suggests equally that permanentprices conform positively to the cycleeither synchronously or with a lag. Thistrain of reasoning therefore implies that,under the supposed conditions, nominaldash balances would conform positivelyto the cycle and would be either syn-chronous or lag at the turning points.Yet one of the major findings of thebroader study of which the results re-ported in this paper are a part is that thenominal stock of money, adjusted fortrend, tends to lead at both peaks andtroughs. Hence there is a residual ele-ment in the cyclical behavior of ve-locity that requires explanation.
A satisfactory analysis of this residualelement requires the use of monthlyrather than annual data. Annual dataare unduly crude for studying timingrelationships. For example, the cyclicalpatterns of the observed money stock inChart III, Panel A, reveal no averagelead; yet our more detailed analysis ofmonthly money data establish such alead, after adjustment for trend, beyondany reasonable doubt.
It may nevertheless be worth examin-ing the residual element in the annual
data as a first step. This residual elementis approximated in Chart IV by theratio of the observed measured velocityto computed measured velocity. ThisratiQ varies, very much less over thecycLe than measured velocity itself, andhence the movements it measures tendto be concealed by the movements invelocity arising out of the discrepancybetween measured and permanent in-
Yet our analysis of the stock ofmoney suggests that this residual ele-ment may play a critical cyclical role.Indeed, perhaps the major significance ofour analysis of velocity is that it enablesus to extract this residual element, toeliminate the largely spurious move-ments of velocity that have hithertomasked the• economically significantmovements.
For deep depressions, the residualelement has a clearly marked cyclical
During expansion, the residualelement at first falls, then rises, reachinga trough in mid-expansion. During con-tractions, the behavior is harder to de-terthine, because one cycle—the earliest,from 1870 to 1878—has a major influ-ence on the pattern for all cycles and thefigures for this cycle are highly dubious.'4If this cycle is. omitted, the pattern forcontractions is a mild fall from peak tomid-contraction and a sharper fall there-after.
The residual element varies much less,on the average, for mild depressioncycles than for deep depression cycles.Such cyclical movement as it does showis similar to that for deep depressioncycles during expansion and just the re-
14 problem is in the income estimates forthe early period. These are characterized by anextraordinarily rapid rate of increase from 1869 to1879. Other evidence suggests that this is at leastpartly a statistical artifact, reflecting the extremepaucity of .reliable data for estimating income forthis period.
17
CHART IV
RATIO OF OBSERVED TO COMPUTED MEASURED VELOCITY, COMPARED WITH OTHERECONOMIC VARIABLES, AVERAGE REFERENCE-CYCLE PATTERNS,
Mru AND DEEP DEPRESSION CYcLEs, 1870—1954
120 —
115 —
110—
105 —0.•
100
NOTE: Vertical scales are in reference-cycle relatives, except scale for prices in Panel C, which is inrate of change of reference-cycle relatives per month. The scale of reference-cycle relatives in Panel Bis one-fourth that in Panel A, and the scale in Panel C is two and a half times that in Panel A.
Excluding 1870—78.
— *30Panel A. Interest Rates on Private Obligations, 1870-1954
Ratio of observed to computed measured velocity 6 Deep Depression Cycles
Ratio of observed to computed measured velocity, 5 deep depression cycles0Commerciol paper roteCorporate yield
*2 Mild Depression Cycles
A.
1...
— 125
- 120
95 —
— Its
I
I
::
— Ito
105
100
95
90
85
Panel B. on Government Obligations, 1921-1954
80
Ratio of observed to computed meosured velocityYields on short-term U.S. securitiesYields on long-term U. S bonds
Panel C. Rate of Change of Wholesale 1870-1954Ratio of observed to computed measured velocityRotio of observed to computed measured 5 deep depression cycles0Weighted average rate of change in wholesale prices of all commodities
12 Mild Depression Cycles 6 Deep Depression Cycles
verse of that for deep depression cyclesduring contraction. This residual ele-ment is the cyclical component in cashbalances that cannot be explained simplyby a movement along a univariate de-mand curve in response to a cyclicalmovement in permanent income. It isperhaps not surprising that this compo-nent should be so much larger for deepthan for mild depression cycles. In themild depression cycles, there is a rela-tively small cyclical movement in gen-eral, which presumably means that thereare only relatively small movements inwhatever other variables operate to pro-duce a discrepancy between desired cashbalances as judged from aloneand actual cash balances.
What are these other variables? Theobvious candidates are measures of thereturn on other assets that could be heldinstead of money. One alternative toholding money is to hold securities; an-other, to hold physical goods. The returnto the first is measured by the rate of re-turn received on the securities. The re-
turn to the holding of physical goods ismeasured by the rate of change of pricesminus storage costs; and either of theseterms may be positive or negative—prices may rise or fall and storage ofgoods may yield a convenience return inexcess of costs of handling and mainte-nance. In either case, these returns mustbe compared with those on money, whichmay be positive, as when interest is paidon deposits, or negative, as when servicecharges are incurred.
- In our secular analysis, we have foundthat the yield on corporate bonds is cor-related with the real stock of money andvelocity in the expected direction: a risein the bond yield tends to reduce the realstock of money demanded for a given realincome—that is, to raise velocity—andconversely. Bond yields, however, playnothing like so important and regularlyconsistent a role in accounting forehanges in velocity as does real income.The short-term interest rate was even
highly correlated with velocity thanthe yield on corporate bonds.
19
CHART I V—Continued
106—
104 —
102-0U
U,a)
U0
>
— +1.5
+ 1.0
98—
96—
94 —
I I I I
+0.5
CD
USC,0CD—0.5
—36 —24 —12 0 +12 +24Months from reference peak
-1.0
—1.5
Months from reference peak
Chart IV is designed to provide arough test whether these secular resultscarry to cyclical movements. In ad-dition to the ratio of observed measuredvelocity to computed measured velocity,which is the residual element we areseeking to explain, Chart IV also showsthe average reference-cycle patterns ofcorporate bond yields as derived fromannual data, of commercial paper ratesas derived from monthly data (PanelA),'5 and of the yields on short- andlong-term United States securities, asderived from monthly data (Panel B)Panel A covers the whole period 1870—1954, war cycles; Panel Bcovers only the six non-war cycles after1921, since, yields on United Statessecurities are not readily available forthe earlier cycles.
Short-term rates have, of course, a.
much larger cydical amplitude thanlong-term rates, which in turn have
corporate bond yield data through 1900are railroad bond yields from F. R. Macaulay, SomeTheoretical Problems Suggested by the Movements ofInterest Rates, Bond Yields and Stock Prices in theUnited States since 1856, a publication of the Na-tional Bureau of Economic Research (New York,
pp. A145—A152, col. 5, with 0.114 per centarithmetic addition to raise them to the level ofthe following segment. After 1900 the data 'are"Basic Yields of Corporate Bonds to 50 YearsMaturity," from Historical Statistics of the UnitedStates, 1789—1945 (Bureau of the Census), p. 279;Continuation to 1952 of Historical Statistics, p. 36;Statistical Abstract of the United States, annuallyhorn 1953. Commerdal paper rates in New YorkCity, monthly, through January, 1937, are from Ma-caulay, op. cit., pp. A145—A161; thereafter, monthlyaverages of weekly figures from Bank and QuotationRecord of the Commercial and Financial' Chronicle..This series was seasonally adjusted through De-cember, 1933. No seasonal adjustment has beennecessary since.
16 Yields on short-term United States securitiesare from Banking and Monetary Statistics, p. 460,and Federal Reserve Bulletin, monthly issues, May,1945, to May, 1948, and September, 1950, to Decem-ber, 1954. This series was seasonally adjusted, 1920—30, 1951—54. Yields on long-term United Statessecurities are from the sathe sources and are unad-justed.
roughly the same amplitude as theresidual element in velocity. These dif-ferences in amplitude are of no specialsignificance for our purpose except asthey reflect the consistency of the cy-clical pattern, since the effect of a changein interest rates depends not only on thesize of the change but also on theelasticity of the response of cash balancesto a change. Volatility of rate can be off-sef by a small elasticity of response andvice versa. The differences in amplitudedo, however, make it more difficult toread the chart and tend somewhat toobscure the similarity or divergence inpattern that is of major interest.
The most striking feature of the chartsis the high degree of similarity betweenthe pattern of interest rates and that ofthe residual element of velocity duringthe expansion phase of deep depressioncycles. Long and short rates and rates onprivate and public obligations all showmuch the same pattern for this phase,and the pattern of all four is similar tothe pattern in the residual element invelocity: interest rates are high at theinitial stage of expansion, and so isvelocity, which is an appropriate re-sponse to a high rate of return on non-cash assets; interest rates then decline tomid-expansion, and so does velocity;interest rates then rise to the peak of thecycle, and so does velocity.
There is no such unanimity of move-ment for the remaining phase of the deepdepression cycles or for the mild de-pression cycles. For these phases, thereis, at best, a family similarity betweenthe movements in rates and those in theresidual element in velocity. During thecontraction phase of deep depression cy-cles, short and long rates diverge, shortrates declining throughout, long ratesleveling off or recovering in mid-contrac-
20
tion. The residual element behavesrather more like short rates, if we ab-stract from the unusual behavior duringthe 1870—78 cycle, but the similarity isnot close in detail. For mild depressioncycles, the cyclical movements in shortand long rates are fairly similar, themain differences being a shorter lag incommercial paper rates at peaks andtroughs than in the corporate bond yield.For the period as a whole (Panel A), thecyclical movement in the residual ele-ment, though fairly clear, is so small thatno very precise comparison is justified;for the period since 1921 (Panel B), it isalmost non-existent, the average refer-ence-cycle pattern being dominated byan intracycle trend.
A number of empirical studies havedemonstrated that the rate of change ofprices has an important effect on thequantity of money demanded duringperiods of considerable instability ofprices—as during hyperinflations or ma-jor and long-continued inflations.'7 Thesestudies suggest, further, that the ex-pected rate of change of prices, which isthe variable that directly influences thedemand for money, can be regarded asderived largely from past experience withthe actual movement of prices and that itchanges more smoothly than actualprices; it is something like the rate ofchange in what I earlier designated"permanent" prices. These findings im-ply that any changes in the expected rateof change of prices during periods of rela-tive price stability will be small, perhapstoo small to have any appreciable effect.And this is, indeed, the conclusion
See Phillip Cagan, "The Monetary Dynamicsof Hyperinflation," in Milton Friedman (ed.),Studies in the Quantity Theory of Money, pp. 25—117.The same relation has been documented for othercountries and episodes in a number of unpublishedstudies done in the Workshop on Money and Bank-ing of the University of Chicago.
reached by Richard Selden in his studyof the behavior of velocity.18
As a further check on this conclusion,we have plotted in Chart IV, Panel C,the rate of change of prices from refer-ence stage to reference stage. This is de-rived from the nine-stage reference-cyclepatterns of the monthly wholesale priceindex,'9 by dividing the difference be-tween successive average standings bythe average time interval between them.The resulting eight rates of change permonth are plotted at the mid-points of thecorresponding intervals. Since these arethe actual rates of change, they presum-ably vary more than expected rates ofchange and, in addition, may lead thelatter in time. one might ex-pect enough similarity between theactual rates of change and the expectedrates of change to permit the detectionof any moderately close relation betweenexpected rate of change and the residualelement in velocity.
Interestingly enough, the results large-ly duplicate those for interest rates. Forthe expansion phase of the deep depres-sion cycles, there is the same strikingagreement in pattern between the rateof change of prices and the residual ele-ment in velocity as there is betweeninterest rates and the residual element.There is only slightly less similarity inpattern for the expansion phase of milddepression cycles. There is no systematicrelation for the contraction phase ofeither group of cycles.
This analysis, based as it is on annualvelocity data and on a comparison solely
2!
Selden, op. cit., p. 202.
Historical Statistics of the United Slates, 1789—1945 (Warren-Pearson series, 1870—89; B.L.S. series,1890-1945 IBureau of the Census]), p. 344; Con-tinualion to 1952 of Historical Statistics, p. 47; there-after, U.S. Department of Labor, Bureau of LaborStatistics, Wholesale Market) Price Index,monthly issues.
of average reference-cycle patterns, istoo crude to be at all decisive. Yet theresults are most suggestive. If thecyclical patterns of interest rates and therate of change in prices are comparedwith the pattern of measured velocity it-self (Chart III, Panel B), there is no clearrelation—as we noted at the outset inexplaining why an alternative reconcilia-tion of the secular and cyclical behaviorof velocity is required. When the com-parison is made instead with the residualelement of velocity—that part of themovement in measured velocity that isaccounted for neither by the effect ofchanges in permanent income on desiredcash balances nor by the discrepancy be-tween measured and permanent income—there is a striking consistency for onephase of one set of cycles, and at least afamily resemblance elsewhere, though,of course, not without considerable ir-regularity. These results are of the kindthat might be expected if the returns onalternative ways of holding assets werethe chief factor other than permanent in-come affecting desired cash balances. Ofcourse, they do not demonstrate thatthis is so. They might, for example, re-flect accidental concurrence of movementin just a few cycles. And they do not pro-vide any estimate of the quantitativestrength of the connection. But they cer-tainly justify further research in thisdirection. The main requirements forsuch research are the use of monthlydata on velocity or indicators of velocityand the examination of cycle-by-cyclerelations and not simply relations be-tween average patterns.
VI. CONCLUSION
The results summarized in this paperhave implications for the theory ofmoney, the study of business cycles, and
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the conduct and possibilities of monetarypolicy.
In the theory of money, much em-phasis has been placed on different "mo-tives" for holding money—the "transac-tions" motive, the "speculative" motive,and the "assets" or "precautionary"motive being the three commonly dis-tinguished. The transactions motive isoften regarded as implying something ofa quasi-mechanical relation between cashbalances and the flow of payments and isfrequently given priority of importanceas well as place. Our results cast seriousdoubt on the acceptability of this em-phasis. In the first place, the cyclical re-suits make it clear that changes in cashbalances over short periods are adaptedto magnitudes less volatile than thevolume of transactions. In the secondplace, the secular decline in income ye-locity is hard to explain in terms oftransactions. It is dubious that there hasbeen any secular increase in the ratio oftransactions to income large enough toexplain the growth in the ratio of moneybalances to income that has occurred.Further, improvements in transportationand communication, let alone in financialorganization, have almost surely reducedany mechanical requirement for cashbalances per unit of transactions—in-deed, it was on these grounds that IrvingFisher implied nearly half-a-century agothat velocity was likely to increasesecularly and that others have since ex-pressed views.20
Our findings equally cast doubt on theimportance of the so-called speculativemotive. One would expect this motive tobe subject to wide cydical variationsand hence, if it dominated the demandfor money, to lead to correspondingly
20 Irving Fisher, The Purchasing Power of Money(rev. ed.; New York, 1913), pp. 79—88.
wide cyclical variations in desired cashbalances, whereas we observe the reverse.
The assets or "precautionary" motiveis in a different state. Permanent incomecan be regarded as a concept closelyallied to wealth and indeed as an index ofwealth, provided that we count both hu-man and non-human sources of incomeas components of total wealth. Alongthese lines, our results can be interpretedin either of two ways. One is that therelevant asset motive is equivalent to aconsumption or income motive. As per-manent income, which is to say, totalwealth, rises, consumer units expandtheir expenditures on some items dispro-
term these items "lux-uries." On this interpretation, the serv-ices rendered by money can be includedamong these luxuries. The other interpre-tation is more nearly an asset motiveproper. It is that the holdings of cash arelinked not to total wealth but primarilyto non-human wealth and that, as per-manent income rises, the total value ofnon-human wealth rises more rapidlythan permanent income, either becausesuch a more rapid rise is a necessarycondition for a rise in income or becauseit corresponds to the preferences ofindividuals as their total wealth rises.Unfortunately, the available evidenceon the secular or cyclical behavior of theratio of non-human wealth to income isinadequate to provide a test of thisexplanation.2' On either interpretation,however, our results suggest that moti-vations and variables linked with assetsare the most fruitful category to explore—that the most fruitful approach is toregard money as one of a sequence ofassets, on a par with bonds, equities,
21 Raymond Goldsmith's estimates in A Studyof Savings (Princeton, N.J., 1955) suggest that,if anything, the ratio of non-human wealth to incomehas declined secularly rather than risen.
houses, consumer durable goods, and thelike.
Our results have a bearing on anotheraspect of the so-called precautionary mo-tive, namely, the view that the amountof cash balances held is highly sensitiveto "the" or "a" rate of interest, at leastfor some range of rates of interest. If thiswere so for rates of interest within therange observed during the period ourdata cover, it would imply that real cashbalances and the ratio of income tomoney would be highly variable, bothsecularly and cyclically, since smallmovements in interest rates would beaccompanied by large movements in de-sired cash balances. The highly stablesecular behavior of velocity is evidenceagainst this view. So is our inability tofind any close connection betweenchanges in velocity from cycle to cycleand any of a number of interest rates. Soalso is our finding that most of thecyclical movement in income velocity asordinarily measured can be accountedfor by the use of measured rather thanpermanent income in the numerator. Theremaining movement in velocity, thoughcharacterized by a consistent cyclicalpattern and though, on the basis of ourtentative explorations, it may well beaccounted for by movements in interestrates, is much too small to reflect anyvery sensitive adjustment of cash bal-ances to interest rates.
Some of these comments about the im-plications of our results for the theory ofmoney have their direct and obviouscounterparts for the empirical study ofbusiness cycles. The most important ad-ditional implications are two that have todo with the interpretation of cyclicalmovements in velocity. The fact thatvelocity changes have been about as im-portant as changes in the stock of money
23
in accounting, in an arithmetic sense, forthe movements in money income, to-gether with the small amplitude ofcyclical movements in the stock ofmoney, has. . fostered the view thatchanges in the stock of money cannot bethe prime mover, oreven of major inde-pendent importance, in cyclical change.This view may of course be correct, butit needs re-examination in light of ourfinding that most of the velocity move-ment is, from one point of view, "spuri-ous," as well as a possible consequence ofthis finding, discussed more fully below,that measured income may be highlysensitive to changes in the stock ofmoney. The other important implicationfor the study of cycles is that the cyclicalpattern of velocity changes that needsstudy and explanation is very differentfrom what it has been supposed to be.Measured velocity has a cyclical patternroughly synchronous with that in generalbusiness, tending to rise relative to itstrend from reference trough to referencepeak and to fall from reference peak toreference trough. But when this patternis corrected for the deviation of measuredincome from permanent income, theresidual movement is very different, andit is the residual movement that needsexplanation.
The most interesting implication ofour analysis for monetary policy is high-iy speculative and involves taking ourfindings more seriously in detail than Ican fully justify. It may nonetheless beworth recording if only in the hope ofstimulating further work. Suppose oneaccepts fully both the reasonably well-supported finding that money holdingsare adapted to permanent magnitudesand also the much more questionable andtentative suggestion that the economicactors derive their estimates of perma-nent magnitudes from prior measured
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magnitudes by implicitly constructingsome kind of weighted average of them.It will then follow that, given a stabledemand function for money, measuredincome will be highly sensitive in shortperiods to changes in the nominal stockof money—the short-run money multi-plier will be large and decidedly higherthan the long-run money multiplier.22To illustrate with some figures based onour tentative results: In the long run, ifwe take real income as given, a $1 in-crease in the stock of money would im-ply an annual level of money incomehigher than otherwise by $1 times thevelocity of circulation, or, at currentlevels of velocity, about $1.50 higher—the long-run money multiplier equals thevelocity of circulation. In the short run,however, an increase of $1.50 in meas-ured income would be inadequate, sincethat much of a rise in measured incomewould raise permanent money income bydecidedly less than $1.50 and hence de-sired cash balances by less than $1. Ifwe take a year as our unit and acceptthe numerical weights we have used inestimating permanent income frommeasured income, measured incomewould have to rise by roughly $4.50 forestimated permanent income to rise by$1.50, the rise required to raise desiredcash balances by $1 for given real in-come—the short-run money multiplier isthus triple the long-run multiplier.
The story does not, of course, endhere. There would be carry-over effectsinto future years, as estimated perma-nent income continued to be revised inthe light of measured income. Thesewould make the initially assumed rise inmoney income not sustainable withoutfurther rises in the stock of money andhence would give rise to a cyclical reac-
This point was first suggested to me by GaryS. Becker.
tion in measured income. Further, theassumed change in money income wouldpresumably be associated with changesin output and in prices that would affectthe relation of desired cash balances tothe change in measured money income.These further complications requiremuch more study than I have giventhem. They do not, however, affect themain point—the sensitivity of measuredincome to changes in the stock of moneythat is implied by our results if they areaccepted at face value.
It is interesting that the permanent-income hypothesis should have suchcontrasting implications for the sensitiv-ity of the economy to changes in thestock of money and to changes in invest-ment—the major other factor regardedas a prime mover in cyclical change. Thepermanent-income hypothesis impliesthat the economy is much less sensitiveto changes in investment than it wouldbe if consumption were adapted tomeasured rather than permanent in-come—the short-run investment multi-plier is decidedly smaller than the long-run multiplier.23 On the other hand, we
23 See A Theory of the Consumption Function,p. 238.
have just seen that the economy is muchmore sensitive to changes in the stock ofmoney than it would be if money bal-ances were adapted to measured ratherthan permanent income.
A corollary for policy is that the effectsof monetary policy may be expected tooperate rather more than would other-wise be supposed through the direct ef-fects of changes in the stock of money onspending, and rather less through indi-rect effects on rates of interest, thence oninvestment, and thence on income. An-other corollary is to emphasize the po-tency of relatively small changes in thestock of money—a potency, needless tosay, for good or evil. Relatively smallchanges in the stock of money, properlytimed and correct in magnitude, may beadequate to offset other changes makingfor instability. On the other hand, rela-tively small changes in the stock ofmoney, random in timing and size, mayequally be an important source of in-stability. If the reaction mechanism Ihave described is in any substantialmeasure valid, the system may not havea large tolerance for mistakes in mone-tary management.
