By JACK E. TRIPLETT

The Economic Interpretation of Hedonic Methods

Editor's Note—This article and the one following are parts of a three-part presentation

of the new price index for computers incorporated in the revised estimatesof the national income and product accounts (NIPA's) released in Decem-ber 1985. The new index represents a substantial step in coping statistical-ly with what is referred to as the "quality change problem," a problemcommon to many products to one degree or another but particularly pro-nounced for computer equipment because of rapid technological change.

The first article provides an introduction to hedonic methods, the econ-ometrically based approach to dealing with quality change that underliesthe new price index for computers. The second article, authored by agroup from the economics department of the IBM Corporation, describesthe results of their work on developing price indexes for computing equip-ment. Last year, following circulation of a preliminary description ofBEA's research on computer prices, IBM offered to make its researchavailable to BEA and to assist in further development of a computer price

index. BEA acknowledges the generous contribution made by the authorsand IBM.

The third article, which will appear in a forthcoming issue of theSURVEY, will describe the use of the IBM composite price indexes in thedeflation of current-dollar expenditures for computers in the NIPA's. Cor-rections to the current-dollar estimates of business purchases of computersthat were released in December will appear at the same time. Althoughwork on quantifying the error is not yet complete, it is likely that the cor-rections will raise the estimates of business purchases of computers, pro-ducers' durable equipment, and GNP for 1984 by $4 to $5 billion and theestimates for years back to 1978 by smaller amounts.

Draft versions of portions of the three-part presentation were read byZvi Griliches of Harvard University and Joel Popkin of Joel Popkin andCompany. BEA and the authors appreciate their comments and sugges-tions.

CONSTRUCTING price indexes forcomputer equipment is a challengebecause these products have exhibitedextremely high rates of qualitychange, and quality change presentsone of the most difficult problems en-countered in price index construction.Hedonic methods provide an advanta-geous alternative to conventionalprice index approaches for situationswhere quality change is encountered.

The conventional method for con-trolling for the effects of qualitychange is designated the "matched-model" method in this article. In thismethod, only prices for models, or va-rieties, that are unchanged in specifi-cation between the two periods areused in the index. Matching themodels assures that any difference be-tween the prices collected for the twoperiods reflects solely price change,rather than a change in what wasbought. Producer Price Indexes,which are used for deflating manycomponents of producers' durableequipment, are constructed with thematched-model method.1

For two reasons, price indexes con-structed with the matched-modelmethod may not completely avoid

1. See U.S. Bureau of Labor Statistics, chapter 7, fora description of the methodology for the ProducerPrice Indexes. (References are at the end of the arti-cle.)

errors that are associated with qual-ity change.

One error arises when the pricechanges observed for matched modelsdo not capture the price movementthat is taking place for all models.When models embodying an improvedtechnology are introduced, prices ofmodels embodying older technologiesare bid down; however, when theolder technology cannot successfullycompete with the new, it may simplydisappear. By following prices of es-tablished models until they disappear,the matched-model method missessome of the price change that the newtechnology engenders, particularlywhen (as is often the case) the fullpattern of discounting is not recordedin the price information used for theindex. The potential errors from in-ferring price change for unmatchedmodels from that observed formatched models, particularly whenthe matched models become obsoles-cent, have been discussed in the priceindex literature for many years.

A second error occurs when modelsthat are not identical are neverthe-less matched. Information on some ofthe specifications of the models, or onaspects of the terms of sale, may notbe available, so that some models thatappear to be matches actually differ

in some respects. Alternatively, thepricing agency may know that twomodels are not truly identical, butwhen the differences are small, mayconclude that making the match ispreferable to dropping the price infor-mation from the index. The possibilitythat unlike models are compared hasmotivated a good part of the priceindex literature on quality change.Notice that the stricter the rules foraccepting two models as a match, thegreater the number of models thatwill be excluded from the price index.This means that, with the matched-model method, the more one guardsagainst the second error, the morelikely the index will contain the firstone.2

In the BEA price measures for com-puter equipment, the matched-modelmethod has been supplemented withhedonic methods. Matched-modelcomparisons are used whenever theyare available, and hedonic methodsare used to impute missing prices fornewly introduced or discontinuedmodels to capture price change thataccompanies the turnover of modelsavailable in the market. This articleintroduces hedonic methods and

2. See Price Statistics Review Committee and Gri-liches (1971) for a discussion of the quality changeproblem in economic statistics, and Triplett (1975) fora survey of empirical research.

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shows alternative ways for using he-donic methods in price indexes.

I. The Hedonic FunctionThe hedonic nomenclature is quite

old, going back to the late 1930?s.3

The heart of the methodology is a re-gression equation, referred to as the"hedonic function," in which pricesfrom an array of different models, orvarieties, of a product are the depend-ent variable and the characteristics ofthat product are the independent, orexplanatory, variables.

For example, in the IBM study thehedonic functions for computer equip-ment took the specific form

P = A M2b2 u,

where P represents the prices ofmodels of a particular kind of comput-er equipment, M\ and M2 are twocharacteristics of that item of equip-ment, and u is an error term. The co-efficients A, bi9 and b2 are estimatedby the regression, and from the coeffi-cients one can calculate dollar valu-ations, or implicit prices, for charac-teristics.4

The number of characteristics in ahedonic function, and accordingly thenumber of implicit characteristicsprices, is a technical matter that de-pends on the product being investigat-ed. The functional form for the re-gression has usually been determinedempirically. The specific form used inthe IBM study is one of three alterna-tives frequently encountered in he-donic studies.

Interpreting the hedonic function

Hedonic methods were developed,and indeed used in price indexes, longbefore their conceptual frameworkwas understood. At one time, hedonicmethods were regarded as ad hoc ad-justments, which could not be relatedto the conceptual basis for economicmeasurement nor to the theory ofprice index numbers and real outputmeasurement.

In the last 10 years or so, an explic-it conceptual framework for hedonicmethods has been developed. The

framework is derived from the ideathat production or consumption ofheterogeneous goods (or services, forthat matter) can be analyzed by disag-gregating them into more basic, orelemental, units that better measurethe dimensions of what is bought andsold—the characteristics. Several ex-amples may help clarify the meaningof the term "characteristic."

Within the computer equipment in-dustry, it is common to refer to apiece of computer equipment as a"box." Although the sale is conven-tionally denominated in terms of"box" prices and "box" quantities,meaningful economic units, to bothbuyers and sellers, are the character-istics in the box—speed, capacity, andother measures, as presented in theIBM study. What it costs to build abox, given a technology, depends onthe characteristics the builder putsinto the box; from the user's perspec-tive as well, what matters is not thebox, but the characteristics in it. Foran airline company, the transactionunit is a flight, or an individual ticketpurchase for a flight; but a bettermeasure of an airline's output is "pas-senger miles," so passenger milescould be thought of as one character-istic of airline flights. Although abuilder sells houses, housing charac-teristics (such as square feet of floorspace, number of rooms, number ofbathrooms, and whether the househas a garage or central air-condition-ing) are a more meaningful definitionof what the builder produces, as wellas what the home buyer purchases.

These examples illustrate threeprinciples that define the term "char-acteristics." Characteristics are homo-geneous economic variables that arebuilding blocks from which heteroge-neous goods are, figuratively, assem-bled—the characteristics are "pack-aged," or "bundled," into a specificmodel. Characteristics are valued byboth buyers and sellers (indeed, onemight say this is what makes themeconomic variables), a key point inthe use of characteristics for measure-ment purposes.5 Although the charac-

3. See Court for the first use of the hedonic termi-nology in the literature.

4. In the hedonic literature, the term "implicitprice" is often used to designate the coefficients bi and62 themselves, as well as to denote the price, expressedin dollars.

5. On the buyer side, the idea that demands for het-erogeneous goods could be analyzed through demandsfor the characteristics embodied in them is developedin Lancaster and Ironmonger, though neither notedthat the hedonic function might be used to estimateprices for the characteristics. The extension to model-ing the supply of heterogeneous goods, explicitly in ahedonic framework, appears in several places, mostnotably Rosen and in the empirical work of Spady andFriedlaender.

teristics are generally not priced sepa-rately, the price for the model repre-sents the valuation of all the charac-teristics that are bundled in it—foreach characteristic, the quantity of itembodied in the model, valued by its"implicit" price.

A simile clarifies, on the one hand,the relation between the price of amodel and the prices of the character-istics embodied in it and, on theother, the role of the hedonic functionas a "disaggregator."6 Suppose thatgrocers, rather than placing theirwares on shelves with unit pricesmarked on them, loaded various as-sortments of groceries into grocerycarts, attaching prices to each of thepreloaded carts. Buyers would select apreloaded cart and pay the specifiedprice for the collection of groceriesthat it contains. Suppose further thata hedonic function were estimated onthe grocery cart data. The dependentvariable (which in hedonic regressionsis normally the price of models ofsome product, such as automobiles) inthis regression consists of the pricescharged for the various preloadedcarts of groceries. The independentvariables (which in the usual hedonicstudy are measures of characteristics)are here the quantities of various gro-ceries in the available preloadedcarts. Thus, groceries found in thecarts may be regarded as characteris-tics of the "grocery bundle." The esti-mated regression coefficients provideimplicit prices for groceries. One cantherefore think of the hedonic func-tion as showing what prices of indi-vidual groceries would have been, hadthey been stocked on the shelves inthe customary way. Whether on theshelf or in the carts, prices of individ-ual grocery items will be determinedby the forces of supply and demandthat always determine prices in amarket economy.

A heterogeneous good is a bundle ofcharacteristics, similar to those cartloads of groceries. Once the character-istics in the bundle have been identi-fied and measured, the hedonic func-tion is interpreted as a function thatdisaggregates the price of the goodinto the implicit prices and the quan-tities of the characteristics, and itprovides estimates of prices for thecharacteristics. Because the prices

6. The following passage is adapted from Triplett(1976).

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must be estimated, rather than direct-ly observed, they are usually termed"implicit" prices.

Interpreting the implicit prices

Estimated implicit prices for char-acteristics are the most important em-pirical results from a hedonic func-tion. Implicit prices have many prop-erties that are similar to those of or-dinary prices. As with ordinaryprices, an implicit price measureswhat the seller receives for a charac-teristic when it is sold as well as whatthe buyer pays for it. As with ordi-nary prices, implicit prices for charac-teristics are proportional to marginalvaluations for users, and they are alsoproportional to marginal costs for pro-ducers—but only (as is so well known)when there is competition on the rele-vant side of the market.7 The valuesof implicit prices will reflect theinterplay of supply and demand forcharacteristics, and in the long runcompetition will push each character-istic price to the cost of producingthat characteristic.

Characteristics prices also differ incertain respects from ordinary prices.(1) Because of bundling, the character-istics prices must be estimated withthe hedonic function; they can seldombe observed directly, as can ordinaryprices. (2) Because the characteristicsare purchased as part of a tied sale,in bundled form, relations among thecharacteristics prices are more com-plex than what is usually assumed forprices of goods.8

Economically meaningful character-istics.—-If the characteristics prices es-timated from the hedonic function areto be economically meaningful andnot just a statistical artifact of a mul-tiple regression, the variables chosenas characteristics must themselves bemeaningful. The variables will bemeaningful if they represent what abuyer desires in purchasing the prod-uct and if they represent what ab-sorbs resources in production.9 Alter-natively, one can say that the varia-

7. Rosen discusses a competitive equilibrium inwhich buyers and sellers exchange bundles of charac-teristics and behave as if characteristics prices repre-sented prices for individual characteristics in thebundle.

8. For example, when the hedonic function is notlinear, buyers of different bundles will pay differentprices for characteristics, and sellers of different bun-dles will receive different prices for them, even incompetition. See Rosen and Triplett (1976 and 1983,pp. 40-45).

bles in the regression are economical-ly meaningful when they representthe inputs used by buyers and theoutputs of producers.

Many hedonic studies have depart-ed from the meaningfulness rule, em-ploying variables that are directly in-terpretable neither as producers' out-puts nor as buyers' inputs. For exam-ple, early hedonic studies on automo-biles employed weight as a variable,even though weight has little to do di-rectly with the usefulness of an auto-mobile or with its production cost.10

In the automobile studies, weightstood as a proxy for the true charac-teristics, Use of a proxy variable,however, introduces the possibility oferror whenever the relation betweenthe proxy and the true variableschanges, and one can never be entire-ly sure whether such shifts have oc-curred.

Determining the characteristics of aparticular product requires a greatdeal of technical information, an un-derstanding of what is produced aswell as how it is used. It has notalways been easy to assemble thetechnical knowledge. Nevertheless,good design of a hedonic investigationrequires that the choice of variablesbe based on technical considerationsabout the production and use of theproduct under investigation.

Resource cost and user value

With hedonic methods, one inter-prets the variables chosen to repre-sent characteristics both as outputs(which therefore absorb resources)and as inputs (which therefore gener-ate value to the user). What assur-ance can be obtained that the theoret-ical interpretation meshes with em-pirical reality?

Perhaps one can best explore thequestion by asking: Under what cir-cumstances would either input oroutput interpretations of characteris-tics—that is, either resource-cost oruser-value interpretations of charac-teristics prices—be invalid?

A characteristic that represents re-source cost, but not user value.—Themajor cases where a characteristic

can only, or primarily, be associatedwith the cost side of the market in-volve government regulation. The in-corporation of legally mandated smogcontrol devices (as well as analogousnoise suppression and safety equip-ment) would in principle show up in ahedonic function as a characteristic,with a characteristic price (in a com-petitive situation) approximating itsresource cost. In this case, however,the characteristic cannot be interpret-ed as an input. A smog control deviceclearly does not provide transporta-tion services.11 Hence, the device isnot an input characteristic when themotor vehicle data are interpreted asinvestment, or as part of the capitalstock, or as consumer durables, eventhough it is a characteristic of theoutput of the industries that producetransportation equipment. The implic-it characteristic price is interpretableas the resource cost of the outputcharacteristic on the seller side, butas equivalent to a tax on transporta-tion on the buyer side.

A characteristic price can be identi-fied with user valuation, but not re-source cost.—Typically, markets aremore concentrated on the seller side.If price differentials among modelsare set by sellers on the basis of theirestimates of demand elasticities forcharacteristics, rather than on thebasis of cost, then estimated implicitprices for characteristics will reflectuser valuations, but not resourcecost12

In this case, unlike the first one,the presumption is that the character-istic itself is both an output and aninput. It is only the interpretation ofthe characteristic price that differsfrom the one presented earlier. Note,however, that the interpretation ofthe characteristics price under imper-fect competition is exactly parallel tostandard treatments of goods pricesunder imperfect competition.

A characteristic price that can beidentified with neither user value norresource cost— This case is the "false"characteristic, a variable that is corre-lated with price (and presumably

9. This statement may be somewhat too strong inthe sense that variables that are related to, or in someway stand for, the true "contents of the box" mightalso yield acceptable results under some circum-stances. See the following paragraph.

10. These studies are listed in the bibliography inGriliches (1971).

11. Some have argued there is a joint product—transportation and clean air—so that the amount ofsmog control equipment on the vehicle measures itsproduction of clean air.

12. One often hears this conclusion stated backward(and incorrectly): That deviations from competition onthe seller side mean that hedonic results do not reflectbuyers' marginal valuations.

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therefore with the true characteris-tics), but from the technical point ofview can be identified neither with anoutput of the producing industry norwith an input of the using industry.As an example of such a variable, thenumber of ice-cube trays providedwith a refrigerator was among thestatistically best variables in oneanalysis of refrigerator prices. Thenumber of ice-cube trays was actingas a statistical proxy for the truecharacteristics of a refrigerator, withwhich it happened to be correlated.Obviously, use of estimated implicitprices for ice-cube trays (the estimat-ed implicit price of ice-cube trays wasfar higher than what they sell forwhen purchased individually) wouldyield valid economic measurementsfor refrigerators only by accident. Theuse of weight as a variable in automo-bile hedonic studies provides anotherexample that has already been noted.Such variables typically have been in-troduced into hedonic functions eitherbecause the researcher ignored theprinciple that variables in the hedon-ic function should have a technical in-terpretation, did not understand thetechnology sufficiently to specify itcorrectly, or perhaps lacked data onthe true characteristics. Such resultsshould, however, be regarded more aserrors in the application of hedonicmethods than as limitations on theresource-cost or user-value interpreta-tion of hedonic results.

Summary

The interpretation of hedonic func-tions is generated from the idea thatheterogeneous goods are a bundle ofcharacteristics. The price of anymodel of a heterogeneous good canthus be disaggregated into prices andquantities of characteristics. A hedon-ic function makes this disaggregationexplicit, and provides a set of estimat-ed characteristics prices.

The variables representing charac-teristics in the hedonic function (ifthey are properly chosen) and the im-plicit prices estimated for characteris-tics are—as are any quantities andprices—economic variables that haveinterpretations on both sides of themarket. The characteristics representthe economic units that are being ex-changed in the transaction—that is,they are at the same time outputs forthe producer and inputs for thebuyer. The implicit prices measure

value on both sides of the market, asdo any prices.

II. Using Hedonic Methods toCalculate Price Indexes

Key data for constructing quality-adjusted price indexes are the esti-mated implicit prices for characteris-tics. There are at least four ways touse the information from a hedonicfunction to construct a price index.

Making an explicit quality adjust-ment—Suppose the classic case ofquality change: An "old" model is re-placed by a "new" one, the twomodels differ in the characteristicsquantities embodied in them, and acomparison of the prices of the newand the old is needed for a priceindex. For any characteristic, i, thedifference in the quantity of the char-acteristic embodied in "new" (Cm) and"old" (Go) models can be valued bythe implicit characteristic price, pi, toyield the "adjustment": pi (Cm —do).13 This adjustment can be addedto or subtracted from either the priceof the new model or the price of theold one, as appropriate, and the ad-justed price is then available for usein a conventional price index con-structed by the matched-modelmethod. An example of this applica-tion of hedonic functions to a compo-nent of the Producer Price Index isTriplett and McDonald.

Imputing a "missing" price.—Thehedonic function can be used toimpute a price in period t for a modelthat existed in period s, but not inperiod t. The imputed price permits asynthetic match, so it is then possibleto construct a price index withmatched-model methods. In the IBMstudy, such an index is designated the"composite." An early example of thecomposite index is the computer proc-essor price index produced by Chow;Fisher, Griliches, and Kaysen performa similar imputation, although for adifferent purpose. Imputing a missingprice and computing an explicit qual-ity adjustment ,(the first method) aresimilar in that the hedonic adjust-ment or imputation is applied only tomodels that exhibit quality change,while the remainder of the prices

13. With some forms of the hedonic function, plac-ing a value on the ratio Ctn/Cto is the appropriate cal-culation.

gathered for the price index are han-dled in the conventional matched-model approach.

Calculating a "characteristics priceindex. "—Because the hedonic func-tion provides estimates of the implicitprices of characteristics, it is naturalto think of price index numbers thatare defined directly on the character-istics and calculated from characteris-tics prices and quantities. In the gro-cery cart simile, for example, onceone had estimated the prices of gro-ceries on the shelves, a grocery priceindex could be constructed from shelfprices, rather than from the prices onthe preloaded grocery carts. The firstconstruction of a characteristics priceindex appears in a study by Griliches(1964), who computed Laspeyres andPaasche price indexes for automobilecharacteristics, as well as the associ-ated characteristics quantity indexes.Characteristics price indexes for fourtypes of computer equipment are pre-sented in the IBM study. The PriceIndex of New One-Family HousesSold is constructed as a characteris-tics price index that estimates thecost, in the current period, of the baseperiod's quantities of housing charac-teristics (square footage put in place,and so forth), using characteristicsprices from the housing hedonic func-tion. This is the only other hedonicprice index used for deflation in thenational income and product ac-counts.

Estimating the price index directlyfrom the regression.—Perhaps themost common hedonic price index inthe literature is an index estimateddirectly from a regression: Year, orperiod, dummy variables are intro-duced into a regression on two ormore periods' data. The resulting re-gression coefficient is an estimate ofthe residual (mean) price change be-tween two periods that cannot be as-sociated with changes in the quanti-ties of characteristics. The implicitprices are in effect used to factor outthe value of the change in character-istics quantities from the total changein value. The IBM study presentsdirect regression indexes for fourtypes of computer equipment.

Sometimes the term "hedonic priceindex" has been thought to implythat the price index must be calculat-ed by the direct regression method.

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However, each of these four calcula-tions provides a hedonic price indexin the sense that each uses hedonic

methods in the construction of theindex. The four calculations are alter-natives that have differing practical

advantages and usually—but notalways—will produce price indexesthat show similar patterns of pricechange.

REFERENCES

Chow, Gregory C. "Technological Change and the Demand for Comput-ers." American Economic Review 57 (December 1967): 1117-1130.

Court, Andrew T. "Hedonic Price Indexes with Automotive Examples."In The Dynamics of Automobile Demand, pp. 99-117. New York: GeneralMotors Corporation, 1939.

Fisher, Franklin; Griliches, Zvi; and Kaysen, Carl. "The Costs of Auto-mobile Model Changes Since 1949." The Journal of Political Economy 70(October 1962): 433-451.

Griliches, Zvi. "Notes on the Measurement of Price and QualityChanges." In Models of Income Determination, pp. 381-418. Conferenceon Research in Income and Wealth, Studies in Income and Wealth, vol.28. Princeton: Princeton University Press for the National Bureau ofEconomic Research, 1964.

—, ed. Price Indexes and Quality Changes: Studies in NewMethods of Measurement. Cambridge: Harvard University Press, 1971.

Ironmonger, D.S. New Commodities and Consumer Behavior. Universi-ty of Cambridge, Department of Applied Economics Monographs: 20.Cambridge: Cambridge University Press, 1972.

Lancaster, Kelvin. Consumer Demand: A New Approach. New York:Columbia University Press, 1971.

Price Statistics Review Committee. The Price Statistics of the FederalGovernment. Printed as: U.S. Congress, Joint Economic Committee. "Gov-ernment Price Statistics." Hearings, Part I. 87th Congress, 1st Session,January 24, 1961. Also printed as: National Bureau of Economic Re-search, General Series, no. 73, 1961.

Rosen, Sherwin. "Hedonic Prices and Implicit Markets: Product Differ-entiation in Pure Competition." Journal of Political Economy 82 (Janu-ary/February 1974): 34-55.

Spady, Richard H., and Friedlaender, Ann F. "Hedonic Cost Functionsfor the Regulated Trucking Industry." Bell Journal of Economics (Spring1978): 159-179.

Triplett, Jack E. "The Measurement of Inflation: A Survey of Researchon the Accuracy of Price Indexes." In Analysis of Inflation, pp. 19-82.Edited by Paul H. Earl. Lexington, Massachusetts: Lexington Books,1975.

. "Consumer Demand and Characteristics of ConsumptionGoods." In Household Production and Consumption, pp. 305-324. Editedby Nestor E. Terleckyj. Conference on Research in Income and Wealth,Studies in Income and Wealth, vol. 40. New York: National Bureau ofEconomic Research, 1976.

-. "An Essay on Labor Cost." In The Measurement of LaborCost, pp. 1-60. Edited by Jack E. Triplett. Conference on Research inIncome and Wealth, Studies in Income and Wealth, vol. 48. Chicago: Uni-versity of Chicago Press for the National Bureau of Economic Research,1983.

Triplett, Jack E., and McDonald, Richard J. "Assessing the QualityError in Output Measures: The Case of Refrigerators." Review of Incomeand Wealth 23 (June 1977): 137-156.

U.S. Bureau of Labor Statistics. BLS Handbook of Methods, vol. 1.Washington, DC: U.S. Government Printing Office, 1982.

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