alchian and klein - 1973 - on a correct measure of inflation

8/10/2019 Alchian and Klein - 1973 - On a Correct Measure of Inflation

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ARMEN A. ALCHIAN andBENJAT\ 1 N KLE I N

n orrect Measure o nflatione

Two commonly cited and newsworthy price indices are theBureau of Labor Statistic's Consumer Price Index and the Commerce Department'sGNP deflator. These indices have become an important part of our economic intelli-gence and are frequently considered to be the operational counterparts of whateconomists call "the price level." They, therefore, often are used as measures ofinflation and often are targets or indicators of monetary and fiscal policy. Neverthe-less, these price indices, which represent measures of current consumption serviceprices and current output prices, are theoretically inappropriate or the purpose towhich they are generally put. The analysis n this paper bases a price index on theFisherian tradition of a proper definition of intertemporal consumption and leadsto the conclusion that a price index used to measure nflation must include assetprices. A correct measure of changes n the nominal money cost of a giverl utilitylevel is a price index for wealth. If monetary impulses are transmitted to the realsector of the economy by producing transient changes in the relative prices ofservice flows and assets (i.e., by producing short-run changes n "the" real rate ofinterest), then the commonly used, incomplete, current flow price indices providebiased short-run measures of changes in "the purchasing power of money." Theinappropriate ndices that dominate popular and professional iterature and analyses

*The authors are indebted to Michael DePrano, Michael Hamburger, oseph Ostroy, EarlThompson, Jai Hoon Yang, and participants at seminars at the University of WashingtonCarleton University, and the National Bureau of Economic Research or helpful comments andto Irene Abramson or able research assistance. Financial assistance was provided by the Na-tional Bureau of Economic Research and by the Lilly Foundation, nc. grant o UCLA or thestudy of property rights. This work has not undergone he full critical review accorded Na-tional Bureau Studies and s not a National Bureau publication.

A rmen A. Alchian s professor of economics, Universit.v f California, Los Angeles;Benjamin Klein is assistant professor of economics at the University of California,Los Angeles.



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are thereby shown to result in significant errors n monetary research, heory, andpolicy.

I. AN ISO-UTILITY PRICE INDEX WITH INTERTEMPORAL CONSUMPTION

A well recognized principle s that the appropriateness f a price index depends onthe question to which an answer s sought.l For many situations we are interestedin measuring he money cost of a fixed welfare or constant utility vector of goodsas money prices change. This iso-utility price index, often called a cost-of-living orfslxed welfare index, was first discussed formally by Konus [24] . However, as earlyas 1906 Irving Fisher [9] (and others earlier, we conjecture) pointed out that aniso-utility vector included claims to future consumption. And more recently,Samuelson [31 ] elegantly restated the slgnificance of wealth-like measures insteadof current income) in comparisons of welfare. We, therefore, regard he utility or

preference ordering of any situation as a function of a vector of claims to presentand future consumption,2

U= U ([q(i, t)] ) (1)

where the q(i, t) element represents he quantity of the ith consumption service lowat time t.

Assume, initially, that markets exist for every consumption service flow to bedelivered at every moment of time. At any moment an individual s assumed o beconstrained by a scalar W(wealth), which he allocates over claims to present and

lSee, for example Frisch [15, p. 10], Mitchell [28, p. 23], Keynes [23, book II], and Ulmer[37, ch. 2]. Fisher, on the other hand, considered the problem of constructing a price indexindependent of purpose and concluded that "from a practical standpoint, it is quite unneces-sary to discuss the fanciful arguments for using 'one formula for one purpose and another foranother' in view of the great practical fact that all methods (if free of freakishness and bias)agree " [ 1 1, p. 231, his italics] . However, Fisher [ 10, ch. 10] earlier stated that the correctnessof an index depended on its purpose and he emphasized the theoretical importance of not basingan index of purchasing power to be used in long-term loan contracts solely on consumer serviceprices. Using an analysis similar to our own, he argued that:

Borrowers and lenders, in other words, may be more interested in purchasing factories,railroads, land, durable houses, etc., which yield services during a long future, then inpurchasing more or better food, shelter and entertainments, which yield immediate satis-factions. To base our index number for time contracts solely on services and immediatelyconsumable goods would therefore be illogical.

Although he asserts that the practical differences may be inconsequential, the broad-based indexwhich he concludes that it is, on the whole, it is best to use the P in his equation of exchange,which is similar to our index in terms of its inclusiveness.

2Samuelson notes that Pigou [29, p. 37] explicitly recognized that economic welfare dependsupon "total consumption" and not solely "immediate consumption." See any recent mathe-matical price theory textbook, e.g. Henderson and Quandt [19, pp. 229-240], for a formalstatement of this commonly accepted proposition.

While we consider present and future consumption as the sole elements in the utility functionand emphasize wealth as claims to future consumption, we do not deny the possibility thatindividuals are willing to hold wealth in, and of, itself. See, for example, Dewey [8] for ananalysiswhere consumption is not the sole end of economic activity. This alternative view is notinconsistent with the analysis of this paper.



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ALCHIAN AND KLEIN : 17 5

future consumption flows at present prices quoted on these markets. If at each(current and future) moment there are n consumption services, hen

Oo nWA j E qA (int) PA (i,t) dt; (2)

i=1

where WA is the individual's current nominal wealth, PA (i, t) is the current rentalprice of the ith consumption service for moment t (i.e., present prices nclude pricesof present claims to future consumption) and qA (i, t) is the magnitude of the ithconsumption service flow at moment t which at the current price wector and wealthlevel maximizes the individual's ntertemporal utility. All of these values are de-scribed as given under condition A 3

Let present flow prices, including present prices of future consumption services,change and describe this new state as condition B. The question we are asking swhether prices, measured by a constant-utility ndex, have risen or fallen. We can,in principle, compute at the new set of present prices, l[PB (i, t)], the cost of an iso-utility consumption service vector, [qB (i, t)] . If, for example, the new cost underprice condition B, WB, s greater han under the initial price condition A, we can saythat the money cost of an iso-utility vector of goods has risen.4 The iso-utility priceindex implicit in this can be represented by

J LqB (int) PB (i,t) dt

PAB--- _i= 1 - (3)}4/A ,^oo n

X EqA (i,t)pA (i,t) dto i=l -

where qB (i, t) represents he (i, t) element in the minimum cost consumption vec-tor that yields the same condition A utility at the new condition B price vector. IfPAB is greater than one, the nominal money cost of condition A utility has in-creased; an inflation has occurred.

To emphasize he intertemporal nature of this price index and the fact that it doesnot refer solely to the cost of the current moment's consumption t could less mis-

3This model, like the standard microeconomic model under which the usual price indices arederived, assumes the absence of all information or transaction costs and therefore lacks atheoretical justification for the value of a price index. (Introduction of uncertainty by the use ofcostlessly made contingency contracts (e.g., Arrow [4] ), where all transactors know the truestate of the world when it occurs, is also economically equivalent to a world of perfect informa-tion with no rationale for a price index.) We will here ignore this fundamental question andconcentrate solely on defining what is commonly considered to be a fixed welfare price index,recognizing that the usefulness of this or any other index depends crucially on the particularinformation and transaction costs assumed.

4But we cannot, with a fixed quantity weighted index say it has risen. The analysis is exactlyparallel, indeed is identical, to the standard price index theory where q is interpreted as currentservices. See Allen [ 2, pp 19 7-20 3 ] .



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leadingly be called the current "cost of life" index. Current nstantaneous prices ofcurrent consumption flows enter this index, but insignificantly.

II. FUTURES AND ASSET PRICES

Current ash prices to be paid now) for future consumption services are here calledfutures prices.5 Any price index that fails to include these current utures prices sdeficient in not including the cost of all relevant elements of the utility function.Its incompleteness can result in a severe (negative or positive) bias of indicatedchange in the money price level of "life." Prices of current services may rise whilefutures prices (present money prices of claims to future services) fall more thanenough to lower the money cost-or the opposite may happen.

The major diffslculty n making our index operational s that separate utures mar-kets or contracts do not exist for all future consumption services.6 As a result, some

futures prices required for a complete iso-utility price index will not be directlyobservable n explicit market prices. But since assets are sources of future services,asset prices provide clues to prices of present claims on future consumption. Currentwealth can be represented y the sum of all asset values, or, equivalently, nterpretedas the sum of all present valued claims to all consumption service lows over time.Symbolically, f there are m assets, wealth is denotable by:

m oo nWA E PA ]) QA /)-j E qA (i, t)PA (i,t) d (4)

j=l i=1 _

where WA s the individual's current nominal wealth and [QA (X)] s the current

sThe current utures price of the ith consumption ervice at moment , p (i l), is related o thefuture (or forward) price currently anticipated at moment t, f (i,), by an implicit market rateof interest, r (i, t); p (i, t) = f (i,) e-ris) If interest rates are assumed not to vary over differentconsumption ervice lows, equation 2) restated n terms of forward, ather han futures, pricesis therefore:

A t E qA (i,t)tA(i, t) e Jo A(t) dt d (2)'o i=l

Our terminology here may be somewhat confusing ince "futures" onventionally efers o theprice paid later but agreed to now in a futures contract on a commodity exchange, while"forward" price is also often used to refer to a price to be paid in the future upon futuredelivery but agreed to now. With apologies to our readers, and on the assumption hat fore-warned s forearmed, we use the word "futures" o denote a price agreed o now, "payable now"for services o be received n the future.

6Houthakker 21] theoretically examines why futures markets exist only for a rather nzallnumber of commodities. The answer o this important question must be based on the trans-action costs of purchasing nd selling particular ommodities. These costs are determined inpart, by the costs of obtaining nformation bout "characteristics" f assets and the distributionof such information among transactors n society (where "characteristics" s an economic andnot a physical concept) and have implications for the essential properties of money (cf.Brunner nd Meltzer 5, pp. 258-61] ).



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ALCHIAN AND KLEIN * 17 7

vector of asset quantities hat would yield his intertemporal utility maximizing con-sumption service stream, [qA (i, t)] . If assets are standardized n terms of their pres-ent and future service flows, the current vector of asset prices, [PA f)], can there-

fore be used as a proxy for current utures prices, PA (i, t).When relative prices change, one can, in principle, determine he vector of assets,

[QB X)], which will yield the minimum cost iso-utility consumption service stream[qB (i, t)] at the new set of asset prices [PB X)] and mplicit futures prices PB (i, t ).Current asset prices can therefore be used to construct our constant welfare priceindex

m

5LPB (X) QB (X)_ WB_ j=l

WA m

SPA (X)QA (j)j=l

where WB s the nominal cost of the vector of assets that will yield a flow of presentand future consumption services equal in utility to the initial condition A consump-tion service stream.

It is crucial to emphasize hat the vectors [QA (/)] and [QB (/)] must include allassets-consumer and producer, durable and nondurable, tangible and intangible,financial and nonfinancial, human and nonhuman. All sources of present and futureconsllmption services must be considered. The vectors do not represeht the actualassets held by the representative ndividual, but the asset combination that wouldyield the individual's desired consumption service flows. An individual may hold

some assets that yield the exact pattern of consumption service flows that hedemands over time, e.g., a house that yields his present and future desired housingservice flow. But, more generally, due to transaction costs individuals will holdsome assets not because they yield services that coincide with their consumptionplans, but because they are an efficient form in which to hold wealth. The servicesfrom these assets or the assets themselves are later sold and exchanged for desiredconsumption services. Human capital s the most obvious example.

Since our asset price index is not constructed on the basis of assets actually ownedby an individual we are therefore not measuring whether the individual s better orworse off after a change in prices, only whether he requires more or less money toreach the same utility level. We must distinguish between actual shifts in the budgetconstraint with corresponding welfare changes and changes n our measure of infla-

tion WB s compared o WA o determine he change n the individual's money costof a constant utility level. The individual's ctual nominal wealth under condition Bmust be compared o WB o determine f he is better or worse off under the new setof prices. An individual, or example, may own a coal mine not because he consumesthe coal yielded by the mine over time, but because the coal mine is an efficientform in which to hold his wealth. He sells most of the coal for income to purchase



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17 8 : MONEY, CREDIT, AND BANKING

other consumption flows, and he intends to sell the mine and retire to an Hawaiianresort in a few years. If under condition B the only change is an increase n theprice of coal, the individual's current wealth will rise more than B/B; he is betteroff while he experiences an inflation. Alternatively, f the price of Hawaiian andincreases under condition B, the individual's nominal wealth remains unchanged ifhe did not own any of the land) while WB ncreases; he is worse off and experiencesan inflation. Any combination of inflation or deflation and better off or worse offis possible.

III. THE SYSTEMATIC BIAS OF CURRENT SERVICE FLOW PRICE INDICES

A money price index based on considerations we have outlined is fundamentallydifferent from the CPI, which is constructed on the basis of prices of current con-sumption ervices. The CPI considers he prices of only a part of the utility function

and is therefore inadequate n principle as a constant utility money price measure.The CPI attempts to measure changes in the cost of only the iso-utility currentconsumption flows and therefore supplies an answer to a question distinct fromwhether the present money cost of consumer utility has changed.7

Current service flow prices are related to asset prices by implicit real rates ofinterest and therefore our iso-utility price index is logically equivalent to an indexbased on current ervice low prices and a broadly defined interest rate vector. If ourrepresentative ndieridual moved to a new society where current service Row ricesare dentical but where real nterest rates are higher, our iso-utility price index wouldfall. The individual would substitute future consumption for present consumptionand his money cost of life would decrease.8

If we assume that society's equilibrium rate of time preference and real produc-tivity of investment remains constant, is there any reason to suppose that use of acurrent service flow price index provides a deceptive measure of inflation? If realinterest rates remain constant and the prices of current services and the prices ofcurrent assets move together then, as a practical matter, a current service price indexcan be used as a perfect proxy for the theoretically correct wealth price index.There s, however, reason to expect a major systematic discrepancy n the transitorymovement of a current service Row rice index and a current asset price index. Andit is this discrepancy which makes a current service fRowprice index an especiallypoor short-run ndicator and target of monetary policy.

7It is interesting to note that a major gap between a theoretically correct constant utility priceindex and the actual CPI is often said to be the improper inclusion of some consumer durableprices, such as new and used automobiles and houses, in the index. The proper price for thesedurables is said to be the current rental price or current cost of using the services from the assetand not the purchase price of the asset itself (cf., for example, Steiner [33] ). We would claim,on the other hand, that the CPI is inappropriate because of the emphasis on current prices andthe insufficient weight given to asset prices.

80n the contrary, nominal interest rates (current mortgage rates) enter the CPI positively. Anincrease in nominal interest rates due to an increase in anticipated future (or forward) priceswhich leaves real rates and current futures prices unchanged will not alter our price of wealthindex.



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Changes n the quantity of money cause a "nonadiabatic" adjustment process nthe money market which is terminated when all prices have changed proportion-ately. The initial price changes will depend upon how the monetary change is ac-

complished; but, ignoring distribution effects among individuals which may causepermanent changes in relative prices, the initial changes will "diffuse themselvesequally after a certain time through all price-levels alike," [23, p. 90]. But allprices may not change at the same rate. Keynes [23, ch. 7] emphasized he pos-sibility that price levels might not be rapidly "diffused" and that the failure ofdifferent price levels to move in the same way was a crucial element in the explana-tion of short-period fluctuations. Differential adjustment speeds among prices, ofconsumption goods and capital goods (or of service flows and durable assets) inparticular, ormed a cornerstone of his theory of the trade cycle.9

The behavior of current service flow prices relative to asset prices as a crucialelement in the transmission rocess between monetary stock changes and economicfluctuations has also been emphasized by Friedman and Schwartz [14, pp. 229-231]. They maintain that monetary changes temporarily affect real income byproducing transient changes in the interest rate structure, defined by the ratio ofcurrent rental prices of services to the price of current assets as sources of the ser-vices, i.e., by changing wealth relative to income. A decrease in the supply ofnominal money, for example, decreases he demand for and prices of financial andnon-financial assets as individuals adjust their portfolios by attempting to add totheir depleted cash holdings. This causes asset prices to fall relative o service flowprices and relative to the cost of producing new assets. (The general all in the assetprice level is a rise in "the" real interest rate; wealth falls relative to income.) Inturn, the reduced profitability of producing new assets decreases their production(i.e., leads to a fall in the rate of "investment"), and the higher nterest rate implicit

in the current rental asset price ratio stimulates asset purchases relative to rentals(i.e., leads to a rise in the rate of "saving"-in the sense that consumption of currentservices s reduced).10

If such an "interest rate" mechanism actually operates, then short-run ffects on"the purchasing power of money" of a change in the rate of growth of money willbe underestimated by a current service flow price index compared o an index thatalso includes asset prices. But, unfortunately, we have not been able to verify theexistence of such a mechanism. Very little reliable nformation exists on transactionprices of used assets and almost none on a quarterly or monthly basis.ll Given the

9Leijonhufvud's ecent interpretation of Keynes emphasizes he importance Keynes placedon an "inappropriately" ow relative price of assets (or high interest rate) as a "cause of un-employment" 26, pp. 335-338] .

lIn addition to asset prices generally adjusting more rapidly han current low prices pricesof "liquid" (low transaction costs) assets will adjust more rapidly than prices of "iliiquid"assets.

Even if relative prices are not affected by the monetary change, real ncome will be affectedif anticipations about market clearing prices lag behind changing reality-which is costly todetect and adjust o instantly. C.f., Alchian [ 1 .

1lGoldsmith nd Lipsey [ 16] have constructed n annual wealth price ndex in the context ofestimating a national and sectoral balance sheet. The components of their index, however, arenot based on transaction prices but on owner estimates of the market value of their property



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assumed importance of asset prices in the transmission of monetary changes, thisdeficiency in the data and lack of any previous systematic empirical analysis of thebehavior of asset relative to flow price is truly shocking. Some suggestive evidence

on the existence of this cyclical relative price process can be obtained, however, byexamining recent movements in common stock price indices relative to flow priceindtces and by examining movements in estimates of "the" real rate of interest.Although there are significant problems n the interpretation of the movement ofstock prtces (see section VI), they should be included in our iso-utility price indexsince they implicitly measure current prices of capital assets owned by corporationsand represent the only readily available data on current market prices of assets.And changes in the real rate of interest can be considered an indirect measure ofchanges n the relative prices of service flows to capital stocks.l2

The sharp decrease in the growth rate of money during 1969 provides a classicexample of the bias involved in measuring nflation by considering only, for exam-ple, movements n the CPI. Narrowly defined money, which had grown at a 7.6 per-cent annual rate over the two previous years, grew at only a 2.9 percent annual ratefrom January, 1969, to February, 1970. (Most of this restraint, as recorded n thefigures revised for the unusually large volume of Eurodollar bortowing in early1969, came in the second half of 1969). Although real magnitudes were clearly af-fected, this policy was generally considered to have been a failure in c1lrbing herate of inflation. The CPI, which rose at a 5.8 percent annual rate during he secondhalf of I969 showed no sign of decelerating and rose at a 6.0 percent annual rateduring the first half of 1970. Absence of any perceived response of prices in theface of rising unemployment led to the total abandonment of monetary restraintduring 1970 and early 1971 and ultimately to the imposition of wage and price con-trols. But there is some evidence that asset prices responded almost immedsatelyand quite dramaticalty o the change n policy.

Standard and Poor's Composite (500) Common Stock Price Index started to de-cline in early 1969, and by June, 1970, had fallen nearly thirty percent to the levelof early 1964. In addition, the real rate of interest as measured by the Federal Re-

(for farm real estate and for most of the single-family house data) and on construction costs(for commercial, industrial and residential structures and for producer and consumer durables).Reliance on cost data limits our indexes solely to measures of new asset prices. Over long periodsthis procedure may not yield biased price estimates of all existing assets but will most certainlyyield misleading current asset price measures in a short-run cyclical context when reproductioncosts are considerably more rigid than market prices. Grebler, Blank, and Winnick [ 17, appendixC], for example, compare the market "prices" (i.e., owner estimates) of houses with theconstruction costs for the 1890-1934 period and conclude that, although there is close confor-mity between the two series over decade-long periods, market prices fluctuate more widely thanconstruction costs and there are significant divergencies between the series over shorter periodsof several years.

Market transaction price data for used assets are available in trade publications and dealercatalogues for cars, trucks, and farm equipment; and less complete price data possibly may becollected by other trade associations.

l2It should be noted that although our discussion emphasizes that movements in asset andservice prices differ largely because of differing rates of adjustment to cyclical monetary dis-turbances there may also be a significant secular bias due to changing equilibrium real assetyields. (The apparent increase in real rates of interest over the years is ignored in our discussion.)



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serve Bank of St. Louis (the nominal corporate Aaa bond yield minus the averageannual rate of change of the GNP deRator over the previous 24 months) rose aboutone percentage point during the last half of 1969 and the Elrst alf of 1970-from

2.3 per cent in June, 1969, to 3.3 percent in June, 1970.l3 This evidence suggeststhat asset prices declined relative o Sow prices over the period and that movementsin the CPI severely underestimated the deRationary effects of the tight moneypolicy.

IV. CURRENT OUTPUT FLOW PRICES, STOCK PRlCES AND THEDEMAND FOR MONEY

Another commonly employed index of inSation is the GNP deflator, which mea-sures the price of current output Sows. This price index includes the prices of newlyproduced assets but does not include the prices of previously existing items of

wealth and therefore s conceptually distinct from our iso-utility wealth price index.Therefore, although t is useful for other purposes, a current output price index alsoprovides a biased estimate of changes in the money cost of consumer utility. Thetheoretical considerations outlined above with regards o tlle bias in the movementof the CPI compared o a wealth price index also suggest a similar systematic bias inthe movement of the GNP deflator relative to a wealth price index. Prices of al-ready produced assets will, we conjecture, generally be more Rexible than prices ofcurrently produced goods, which are based on current costs tllat are often made lessflexible by long-term contracts. And given the rigidity of current production costsrelative o asset prices, a fall in the rate of growth of money decreases he profitabil-ity (and therefore the rate) of new asset production. Concern during 1969-70 aboutthe rigidity n the rate of rise of current output flow prices should therefore be basedon the evidence this gave us on the extent of the recession, not on the extent of theinflation.l4

l3The Federal Reserve Bank of St. Louis discontinued publishing heir real rate series shortlyafter this episode. Although their measured real rate showed remarkable tability over the1960s, this unique precipitous rise should have been expected as part of the normal relativeprice reaction to monetary disturbances. What might have been misleading s that the previoustight money episode of 1966, although similar n magnitude o 1969, did not produce suchsevere relative price changes. The money stock showed no change rom April, 1966, to January1967, after rising at about a six percent annual rate over the previous year. This produced a cleardeceleration of the rate of increases n the CPI, which rose at a 4.5 percent annual rate fromJanuary o August of 1966 and only a 1.6 percent annual rate over the following six months-while stock prices, which fell more than thirteen percent rom January o August, 1966, quicklyrecovered and rose more than eight percent over the next six months, the St. Louis real rateremained ssentially unchanged over the period, rising ess than ten basis points from April toAugust 1966 and then quickly falling back to

and then below its original evel). This dramaticdifference n the relative price moveient between the two most recent contractionary pisodesmay explain why the downturn n economic activity was much milder in 1966-67 than in1969-70, but the surprising lexibility of flow prices n 1966 remains unexplained.

l4In a crude iimonetarist" model such as Anderson and Carlson's 3] changes n moneyimply changes n nominal ncome; and the movement of current output prices, which dependson past output price changes, determines he division of the nominal ncome change betweenreal income and prices. Therefore, he flexibility of current output flow prices s an importantdeterminant f cyclical economic activity.



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The GNP deflator s incorrectly sed not only as a measure f inflation, ut alsoalmost universally sed as the deflator of nominal money balances n demand ormoney studies. f, however, money s considered o be a capital asset and the de-

mand or money treated as an application f the general heory of wealth con-strained nter-temporal ortfolio choice, the purchasing ower of money s moremeaningfully easured n terms of our price of wealth ndex.15

Final choice of the proper price deflator n the demand or money, however, sconditional pon the particular tructural pecif1cation rom which he demand c)rmoney s derived. An explicit heory of the demand or money s necessary eforewe can determine he price ndex hat should be used. If money s alternatively on-sidered, or example, olely as a medium f exchange nd the demand or monetderived n the basis of an inventory-transactions-type odel, he use of the GNPdeflator as the relevant price variable n the demand or money function remainstheoretically njustified. Money s used o purchase ssets of varying urability ndage. The demand or money therefore annot be dependent olely on the prices ofcurrent utput lows which represent nly a part of what money can buy. Hence,within the context of a transactions emand ramework r a wealth portfoliochoice framework, he GNP deflator s incomplete nd the purchasing ower ofmoney could be more meaningfully easured n terms of our more nclusive riceof wealth ndex.16

If nominal money balances redeflated y our asset price ndex, hen the connec-tion between ncome not wealth) velocity of money and he demand or real cashbalances s no longer s direct as once thought. The ratio of our asset price ndex othe current utput price ndex hat s used o deflate nominal ncome now enters asan additional ariable, .e., both asset prices and current output prices enter hevelocity unction. Since asset prices are generally more lexible han output prices,if "real" balances re (incorrectly) ef1ned n terms of a current utput price ndex(and asset prices gnored), a decrease n the nominal tock of money eads o anoverestimate f the initial resultant ecline n real cash balances nd hence to an"unexplained" ncrease n velocity. Movements n the relative prices of assets oflows may explain he initial offsetting hanges f velocity n response o monetarychanges without nvoking presumption f a short-run isequilibrium i.e., slow

l50ne of the major developments in monetary theory in the postwar period has been theintegration of monetary theory with capital theory and the recognition of money as an asset inan optimum wealth portfolio (cf., e.g., Friedman [12] and Tobin [36]). Friedman'sempiricalwork explicitly takes account of the fact that money holders "judge the 'real' amount of cashbalances in terms of the quantity of goods and services to which the balances are equivalent,not at any given moment of time, but over a sizable and indefinite period" [13, p. 121] bydeflating nominal balances by "permanent" or "expected" prices. But this price variable ismerely a weighted average of current and past GNP deflators and does not properly consider

anticipated future prices as embodied in current asset prices.l6Keynes [23, ch. 6] defines two price indexes, a cash-transactions index and a cash-balancesindex, that may be superior deflators of nominal balances within these theoretical frameworks.Both of these indexes, like our iso-utility wealth price index, include all objects of possibleexpenditure, but the weights applied to the objects are significantly different. The cash-transac-tions index weights objects in proportion to the amount of money transactions to which theygive rise per unit time and the cash-balances index weights objects in proportion to the demandfor money they occasion, representing the P in the Fisher and Cambridge quantity equationsrespectively.



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adjustment). he introduction f a vector of interest ates to reflect elative ricesof current ervices ndwealth) n an ncorrectly pecified emand or "real" moneymay tlhen erve as a proxy for the more complete rice of wealth deflator. This m-

plies that use of the incomplete urrent utput price ndex as the price deflator nthe demand or money nduces, o some extent, the observed xistence of a signi-ficant nterest rate effect on the demand or "real" ash balances. If a wealthprice ndex were employed nstead, nterest ates would then implicitly nter n amore general way, while "the" observed nterest ate effect would be reduced ndpossibly }.iminated.17

The question s essentially an empirical ne of whether he commonly usedinterest ates on financial ssets are sufficient o pick up this short-run liquidity"effect of changes n money on the relative rices of existing tocks and lows.Thesignificance f the dividend ield in the demand or money cf. e.g., Hamburger[18] may, n fact, be reflecting he inability f the prices of financial ssets o com-pletely pick up this relative rice movement. The dividend ield is statistically ig-nificant n a quarterly emand or money regression ver the 1951-71 period.18

Alog Ml P) = - .0011 + .3096 d\log Y/P) - .0044 l\log S - .0359 i\log rD(4.66) (0.78) (2.87)

R2 = .295D W = 1 06SE - .0058 (1 1)

But the significance an be attributed olely to the variability f real stock pricesand not to the variability f real dividends. f we substitute tock prices deflated ythe GNP deflator or the dividend ield in the above regression where S refers o

Standard nd Poors 500 Common tock price ndex), we observe hat stock pricesactually nter slightly more significantly han the dividend ield. This mplies hat,

log (Ml P) = - .001 1 + .2914 /\log (Y/P) .0053 i\log rS(4.29) (0.95)

+ .0369 Alog S/P) R2 = .297(291) DW= 1.03

SE = .0058 (2.1)

l7This factor is taken account of most fully in Brunner nd Meltzer's mpirical work (e.g.[S] and [27] ). I8hey, however, use a price ndex for nonhuman wealth not as a measure of thepurchasing power of money, but as a deflator of the wealth constraint. They assume therelevant deflator of nominal balances s the GNP deflator and it is therefore entered as an

additional ariable n the demand or money.l8Ml equals currency plus demand deposits, P is the GNP deflator, Y is nominal GNP, rS s thefour-to-six month commercial paper rate, rD equals Standard and Poor's dividend yield ofcorporate tock, log refers o natural ogarithm, 2 is the coefficient of determination djustedfor degrees of freedom, DW is the Durbin-Watson tatistic and SE is the standard rror ofestimate. The values n parentheses re the t-values of the estimated egression oefficient. Theregression s reported n first difference orm since rD enters a level regression ighly positivelywith a DW less than .2, indicating hat clearly a variable s missing. Even n the first differenceform the autocorrelation f the residuals emains disturbingly igh.



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if anything, hanges n dividend payments o in the i'wrong irection." Fllrther,stock prices become nsignif1cant hen the same regression s run over the sameperiod using annually veraged ata.l9 Both of these pieces

Alog M1 P) = - .0127 + .5767 i\log (Y/P) .0266 i\log S(3.36) ( 1 68)

+ .0282 i\log S/P) R2 = .429(0.98) DW= 1.01

SE = .0138 (2.1)t

of evidence uggest hat the dividend ield enters he demand or money unctionnot as a measure f the direct cost of holding money but as a proxy or the short-run movement of asset prices relative o the GNP deflator.20 n addition, hesignificance f stock prices n a short-run ut not in a long-run emand or money

regression lso provides vidence gainst he hypothesis hat stock prices nter as awealth variable s, for example, Thompson nd Pierce 35] maintain.

V. POLICY IMPLICATIONS

Nearly ifty years ago Keynes mphasized he fundamental olicymistakes iskedby the use of an inappropriate rice ndex. He claimed 22, pp. 249-25()] Church-hill returned England o the gold standard n 1925 at the prewar arity primarily

l9Our hypothesis implies that cycle average data would reduce the statistical significanceeven further. The annually averaged egression or the dividend yield indicates slightly betterresults.

alog (M1/P) = -.0129 + .5757 alog (Y/P) - .0217 alog rS - .0420alog

rDR2 = .463(3.57) (1.36) (1.42) DW=.871SE = .0134

(1.1)'

20Similarly, hanges n the quantity of money can be expected to inRuence stock prices inthe short run not, as commonly believed, because stocks are close substitutes or cash balancesor because the short run liquidity effect influences the rate at which future earnings are dis-counted but because of the differential lexibility of stock prices o the monetary change. Fisher110, ch. 9] outlined a similar mechanism n the context of the transactions ersion of thequantity theory. He emphasized hat many prices are rigid and are ikely to change ess than nproportion o monetary luctuations n the short-run nd, therefore, other prices must changemore than in proportion n the short-run or the quantity equation o hold; and he noted thatstock prices are likely to be the most "supersensitive" f these other prices to changes n thequantity of money. Since the quantity equation s now generally tated n income form where"the" price level that is determined does not include existing tems of wealth, this mechanismcannot be recognized.

2lThompson and Pierce [35] use a total public wealth variable based on Goldsmith andLipsey's work in a monthly demand for money study. But month to month changes n theirvariable are dominated by stock price changes. In addition, Thompson and Pierce fail todistinguish etween nominal and real values of wealth and money and assume (as most macromodels do) that the money market can only be cleared by movements n a small subset ofinterest ates on financial ssets, gnoring he possible hort-run djustment f a broader pectrumof asset prices.



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because Churchill was "gravely misled by his experts" who, by using the inappro-priate but commonly employed wholesale price index, significantly underestimatedthe extent of the necessary deflation.

An analogous situation may exist today. Presently employed price indices areimproper measures of the change in the money cost of an iso-utility consumptionpackage. Reliance on these biased numbers as an indicator or target of monetarypolicy makes it difficult for the monetary authorities o know what they are doing,let alone what they should be doing. And action on the basis of these numbers canlead to inappropriate decisions; policy changes will often come too late and movetoo far. Recent monetary policy provides an instructive example. The authorities'preoccupation with the movement of inappropriate low prices indices to the al-most complete exclusion of asset prices was partially responsible or a monetarypolicy that was too easy for too long a period (1967-68) and then a policy that wastoo tight for too long a period (1969) followed by a policy that was once again tooeasy (1970-early 1971). A crude modification of the CPI, with say, an index ofstock prices would have provided a much more useful indicator and target for pricelevel stability.22

Our discussion also helps explain the general reluctance of contracting parties oadopt escalator clauses. If long-term contracts were set in "real" erms, i.e., tied to"the price level," economic uncertainty would seem to be decreased.23 But "theprice level" must be made operational by a particular, arbitrary and incomplete,price index. And the fact that price indices are not generally used in long-termcontracts (or a tabular standard not adopted) provides some evidence that the in-dices are poor measures of "the price level." Only if the variance of future antici-pated price change is high will the use of, for example, a CPI price escalator clausedecrease the anticipated variance of the real pay off. This may explain the more fre-quent use of price escalators n foreign countries that have experienced great pricevariability and the recent trend towards ncreased use of price escalators n the U.S.(see [7]).

22Simons [32, p. 349], in discussing he feasibility of a monetary policy designed o stabilizea price index, notes that the particular rice ndex chesen "must be highly sensitive; therwise,the administrative uthority would be compelled o postpone ts actions unduly after significantdisturbances."

Realization of our ignorance about movements of the appropriate soutility price ndex doesnot necessarily mply that we should adopt a monetary ule. Discretionary monetary policy canstill be based on income and employment tatistics, and, of course, the inappropriate low priceindices could be used if we knew and took cognizance of the differing ags of adjustment fprices to monetary disturbances. n this context, our discussion may supply some support orthose that believe that "money market conditions" (i.e., the behavior of interest rates) is arelevant hort-run ndicator of monetary policy. If the acceleration f the money supply s notconsidered, the inclusion of short-run nterest rate movements with price movements mayprovide a much less misleading monetary indicator than price movements alone since priceanticipations re probably relatively rigid over the short term and therefore hort-run hangesin market nterest rates will be related to short-run hanges n real rates and short-run hangesin the relative prices of assets and current lows.

23And a rationale or administrative age-price "jawboning," hat it is necessary o convincenegotiating parties that the government ntends o reduce the future rate of inflation, would beeliminated.



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VI. CAN THE ISOUTILITY PRICE INDEX BE MEASURED?

Our mprecise tatements ndicate what we think hould deallybe (1) the modifi-cation n present measurements f the impact of monetary olity on the rate ofinflation using an asset and service price ndex and (2) how they would nfluencemonetary heory and policy. Although he direction f effect seems obvious o us,our conjecture hat presently mployed umbers ield misleading onclusions an beverified nly by the construction f a superior ndex number i.e., it takes a numberto beat a number).

The desired onstant utility price ndex, however, s difficult expensive) o makeoperational. s we have already oted, without uture ontracts n all commodities,the explicit utures prices and quantities eeded or construction f a wealth priceindex are unavailable. urrent rices of assets of different ife lengths providetheoretical ubstitute ince they embody present prices of expected uture erviceflows. But both the asset prices and asset quantities ecessary or this index are

extremely xpensive o determine. We must have prices f a very broad pectrum fassets on which we presently have very ittle information. ur data must ncludeprices of generally onmarketable ssets, such as human apital, nd of assets ofvarying urability, o that we are able to produce he exact optimum urrent ndfuture consumption ervice lows by adjusting he asset mix. We may not be ableto determine ll these prices with any reasonable xpenditure f resources, utsurprisingly ittle reliable nformation xists on current rices f assets and given heassumed mportance f these prices n the transmission f monetary mpulses, omeeffort n this direction would seem o be clearly conomic. Collection f transactionprice data on land, commercial nd residential tructures, roducer nd consumerdurables nd other tangible and financial ssets and the construction f a crudequarterly ealth price ndex would probably e worthwhile.27

Determination f the asset quantity vectors s also extremely difficult. As wehave already oted, the assets actually held by an individual annot be used as anindex of the individual's esired uture onsumption. ome way of determining hecomposition f the individual's esired ntertemporal onsumption ervices, .e., ofspecifying is utility unction r fixing particular onstant sset weights must here-fore be devised. n addition, more complete pecification f the constraints n theindividual's ntertemporal ransactions s also llecessary o determine he relevantasset weights. An individual may, for example, demand particular ime stream fhousing ervices under conditions f costless perfect utures or asset markets, ut

27Stigler's price statistics committee [38, part 1, app. C. pp. 95-99] makes a similar proposal.Considering he resources expended on the collection of price data on, for example, currentfood prices, which are such a small element in the relevantly defined utility vector, a realloca-tion of funds would seem to have a payoff in terms of providing a relevant answer to thequestion of determining price level induced changes n consumer welfare. Carl Snyder's [34]attempt to measure "the general price level" (deElned ssentially as the P in the equation ofexchange) included realty values, security prices, and equipment and machinery prices inaddition o the standard ost-of-living tems was a movement n the correct direction.



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due to transactions osts actually buy and sell houses over time and consumehousing ervice low that does not coincide with this "ideal" ervice low.

And finally, even if asset prices and quantities were available, we would have

significant roblems n the interpretation f asset price changes. A change n themarket alueof an asset may reflect i) a change n the price of an unchanged utureservice low from the asset, ii) a shift in preferences or this assets ervice elativeto other assets, iii) a shift n preferences or present onsumption elative o futureconsumption, r (iv) a change n the anticipated magnitude f service low from heasset. Any or all of these changes re likely to be occurring imultaneously ndtherefore he cause of a change n a particular sset price s difficult o determine.Changes ii) and (iii) represent shift in tastes while (iv) represents change nasset quality; however, hey are not conceptually ifferent rom the problemsencountered n constructing he presently sed ndices. Changes n the preference rutility maps are ruled out in the presently sed consumption ervice ost-of-livingindices.28 And the quality change problem whereby a change n the price of a

given service low must be distinguished rom changes n the service low, is alsopresent n current ndices and has already een handled n an innovative ay fortransactions rices f used cars cf., Cagan 6] ).

For example, consider hanges n common tock prices. The prices of commonstock are ncluded n our index because whether n asset such as a house s ownedby a single proprietor r owned by him as a corporation hould have no effect onthe price of the house as manifest n the price of the stock. If the corporationrepresented ot just the house but, as s typically he case, he services f a managerwho rented and maintained he house, hen the stock price would reflect also themanager's pecific talents. Changes n the price of common tock would reflectchanging rices of two things: he house services nd he manager's alents pecificto this activity. So much he better, or we have ncluded uman and nonhumanassets; he physical ervice low being priced now has a second dimension, he flowof human ervices, nd that may change ust as a house may deteriorate. tockprices contain no more conceptual roblems han do the prices f any assets-or orthat matter of current ervice lows in which one has to separate uantity hangesand quality hanges rom price changes.

Although ome of the conceptual roblems n constructing wealth price ndexare similar o those encountered n presently sed flow price ndexes, he practicalproblems n the interpretation f asset price movements re more difficult. Whatwould one do, for example, with the drop n common tock prices f 1969-70? Didit reflect claims o reduced eal future services a decrease n quality), or lowerprices of unchanged lows of future services a deflation), or a shift in demand

towards more present consumption elative o future consumption ue to higherreal rates of interest brought about by "tight" monetary olicy or by increaseduncertainty eading o an increase n the rate of time preference), r perhaps

28This is not to say that there is in principle no computable ndex, for there s. One needs toknow the equivalent utility vectors under the shifted preference map. But the base weightedindices (and all other for that matter) no longer can be interpreted as they are now. Thedifficulty posed by shifting preferences s no greater han for the present ncomplete ndices.



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combination of all of these forces? For business corporation stocks, the pricedecrease reflects, at least in part) reduced or deferred outputs of future services.Fewer future cars will be produced or more will be deferred. The stockholder may

think of anticipated uture money earnings; hey have fallen not necessarily becausefuture i.e. forward, prices (not futures) are expected to fall but possibly because ofreduced anticipated profitability-much as if a tree would be expected to yield fewerapples as less fertilizer s applied in the coming years with lower demarld xpectedfor apples. If, however, all prices were expected to be lower in the futureS hereduced earnings reflected in lower present stock prices would be truly a reducedprice level of unchanged eal claims. We conjecture both factors were present n thestock price fall-a reduction in present prices of given future services and a reduc-tion in the future anticipated output and earnings elative to what it was before.29In other words real future services are reduced and also the present price of a unitof future service has decreased. t is the latter we want to measure.

We can attemr)t to approximate the division of an asset price change into these

two components by estimating changes in real rates of interest. A rise in the realrate would indicate a fall in future prices relative to current service prices. But weobserve only nominal interest rates, which reRect the anticipated future rate ofinflation. Market estimates of changes n the currently expected rate of change offuture prices can be obtained by examining the ratio of stock prices of net mone-tary neutral 1rms to bond prices.30 Alternatively, we could examine the movementof money interest rates relative o forward price spreads, quoted on commodity ex-changes. The usefulness of these suggestions for obtaining market measures ofanticipated nflation can only be determined by further empirical work.

The empirical problems nvolared re enormous. But whatever efforts may be madein this direction and whatever the results,: we believe it is an error to assign all ofthe change in common stock and other asset prices to changes n anticipated utureservice flows with no change n present prices of such future flows. . . which is whatis implicitly done now in commonly used price indices that ignore asset prices.

It may be cheaper to make empirical judgments about quality and quantitychanges of current than for future service flows. But what has been added isessentially a significantly arger number of items that should be priced; and weightsfor assets in the "typical' man's portfolio of possession of claims must be ascer-tained. This is not a new theoretical problem-it is an enlargement of an existingtask. And we believe that the marginal cost of improving a price index along theselines is less than the marginal gains of improved monetary and fiscal policy con-sequent to less misleading ndicators of inflation.

29These two Xctors are related. Since the prices of primary actors (especially abor) pur-chased by a firm are generally he most rigid, an unexpected decrease n the prices of futureservices old by the flrm will reduce uture anticipated arnings.

30Movements n the stock price to bond price ratio will not, however, represent solely achanging price anticipations effect. If the change in the anticipated rate of change of pricesalters the demand for and quantity of real cash balances and hence the savings unction, realinterest rates will change. Stock prices of net monetary neutral irms will therefore not remainunchanged but will move in the same direction as the anticipated rate of price change move-ment.



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23. . A Treatise n Money. Vol. I. London: Macmillan 1930). (1938 reprint).24. Konus, A. A. "The Problem of the True Index of the Cost of Living," Econo-

metrica, 7 (Jan. 1939), 10-29, (first published n Russian n 1924).25. Kramer, G. H. "Short-Term luctuations n U.S. Voting Behavior, 1896-1964,"

A merican Political Science Review, (March, 1971), 131 43.26. Leijonhufvud, A. On lU:eynesian conomics and the Economics of Keynes: A

Study in Mone ary Theorv. New York: Oxford University Press, 1968.27. Meltzer, A. H. "The Demand or Money: The Evidence rom the Time Series,"

Journal of Political Economy (June, 1963), 219-246.28. Mitchell, W. C. The Making and Using of Index Numbers. 3d ed. Washington:

U.S. Bureau of Labor Statistics, Bulletin no. 656, 1938.29. Pigou, A. C. The Economics of Welfare. th ed. (1932), London, 1960.30. Ruist, E. "Index Numbers: Theoretical Aspects," International Encyclopedia

of the Social Science, 7, New York (1968), 154-159.31. Samuelson, P. A. "The Evaluation of 'Social Income': Capital Formation and

Wealth," n F. A. Lutz and D. C. Hague, eds.. The Theor.y f Capital, London,

1961.Pp.32-57.32. Simons, H. C. "Rules Versus Authorities in Monetary Policy," in F. A. Lutzand L. W. Mints, Readings in Monetar.y Theor.y. Homewood, Ill.: 1951. Pp.337-368.

33. Steiner, P. O. "Consumer Durables n an Index of Consumer Prices," n U.S.Congress, Joint Economic Committee, Government Price Statistics, part 1,The Price Statistics of the Federal Government: Review, Appraisal and:Recommendations, 05-335.

34. Snyder, C. "The Measure of the General Price Level," Review of EconomicStatistics (February, 1928), 40-52.

35. Thompson, T. D. and J. R. Pierce, "A Monthly Model of the Financial Sector,"presented at the Konstanzer Seminar on Monetary Theory and Policy,Konstanz, West Germany, June 1971.

36. Tobin, J. "Money, Capital, and Other Stores of Value," American EconomicReview, (May, 1961), 26-37.

37. Ulmer, M. J. The Economic Theory of Cost of Living Numbers. New York:1949.

38. U. S. Congress Joint Economic Committee, Government Price Statistics, 2parts. Washington: 1961.


alchian and klein - 1973 - on a correct measure of inflation

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