By ROSANNE COLE, Y.C. CHEN, JOAN A. BARQUIN-STOLLEMAN,ELLEN DULBERGER, NURHAN HELVACIAN, and JAMES H. HODGE

Quality-Adjusted Price Indexes for Computer Processors andSelected Peripheral Equipment

J.HIS article summarizes IBM'swork on developing quality-adjustedprice indexes for computer processorsand three types of peripheral equip-ment: Disk drives, printers, and gen-eral purpose displays.1 The first sec-tion describes three issues that arisein the application of hedonic regres-sion methods to computing equip-ment: The level of aggregation, thespecification of the characteristics,and the need to modify the hedonicfunction to deal with the problems oftechnologically induced disequilibri-um.2 The second section discusses thedata; the third, the regression results;and the fourth, the use of the resultsto construct quality-adjusted price in-dexes. The article closes with a sum-mary of the findings and their limita-tions.

I. Issues in the Application ofHedonic Methods to

Computers

Level of aggregation

The first issue concerns the level ofaggregation at which the analysisshould be conducted—complete com-puting systems or system components.The decision to develop regressionsand price indexes at the system com-ponent level was based on two consid-

1. Results for processors are from Ellen Dulberger'sdissertation in preparation, "The Application of anHedonic Model to a Quality Adjusted Price Index ofComputer Processors" for The City University of NewYork. Results for disk drives and printers are fromtwo reports in preparation: Y.C. Chen and Jaines H.Hodge, "Using Hedonics to Measure Performance: AStudy of Computer Disk Drives" and Joan A. Barquin-Stolleman, "Quality Adjusted Price Indexes for Print-ers: A Hedonic Approach."

2. The hedonic regression method was so named byAndrew Court (who applied it to automobiles) at Gen-eral Motors in the 1930's. It has been developed andapplied more generally by Zvi Griliches and others.Examples of applications to computers are: Chow;Ratchford and Ford; Stoneman; Archibald and Reece;Michaels; Fisher, McGowan, and Greenwood; and U.S.Department of Commerce, BEA. (References are at theend of the article.)

erations. First, with the evolution ofsystem modularity, most purchasesare of system components, or "boxes,"rather than of complete computingsystems. Second, the problems of ob-taining appropriate measures of char-acteristics are more tractable at thebox level.

Although working at the box levelreduces many of the problems ofmeasurement, it is important to rec-ognize that both the hardware andsoftware of a computing systemembody attributes—such as ease of in-stallation, reliability, and ease ofuse—that are not easily measured.Working at the box level is likely tounderstate the improvements thathave occurred in computing systemsover the years.

Specification of characteristics

The second issue concerns the speci-fication of the characteristics of thesystem components: If the character-istics are not specified and measuredcorrectly, the results of the regres-sions may be biased. The choice ofcharacteristics for each componentwas guided by its role in a computingsystem. The characteristics selectedreflect value to users; they also reflectresource cost.

Computer processors, henceforthcalled processors, execute instruc-tions. They house the central process-ing unit and main memory. The workdescribed in this article dealt with in-termediate- and large-size generalpurpose digital processors. Small com-puters are not included; typically,

NOTE.—The paper has benefited from discus-sions with David W. Cartwright and Jack E.Triplett of the BEA staff. It has been strength-ened by A. J. Karchere's recognition manyyears ago that work in this area requires amultidisciplinary effort and his establishmentof a small group of system performance expertsunder Y.C. Chen within the IBM economics de-partment.

they are packaged with auxiliary stor-age devices (disk drives or cassettes),and research thus far indicates thattheir analysis requires a more compli-cated technique than the one de-scribed here.3

The two key characteristics of proc-essors are the speed with which in-structions are executed and mainmemory capacity. The unit of meas-urement of memory capacity isstraightforward—megabytes.4 Manu-facturers, however, typically offer sev-eral sizes of memory for a given proc-essor. In such cases, both the largestand smallest memory configurationsfor a given processor were included inthe study.

Obtaining an appropriate measureof speed was more difficult. Previousstudies have generally used the speedof a single instruction—such as add,or multiply-—that can be comparedacross models. However, the speed ofa processor is not adequately repre-sented by the rate of executing asingle instruction.5 A weighted com-posite of all of the instruction execu-tion rates for a typical job mix (orbenchmark) is a better representa-tion. A widely used measure of this

3. When two or more components are packaged to-gether, other approaches—such as analytic models(which are designed to cope with the queueing aspectsof the interactions among the components)—may bemore efficient. See Bard and Sauer for a general de-scription of analytic models as well as other types ofcomputing system performance modeling at IBM.

4. For IBM and manufacturers of plug-compatibleprocessors, one byte equals eight bits, and a bit is abinary digit (that is, 0 or 1). For other manufacturers,memory is often expressed in words, where thenumber of bits per word must be divided by eight toconvert to bytes.

5. Two conditions must be met in order for a singleinstruction execution rate to be adequate: The proces-sors compared must have the same instruction setsand the relative instruction execution rates must notvary across processors. These conditions rarely hold.

In addition to the rate of executing a single instruc-tion, earlier studies also included memory cycle time.Others used only machine cycle time or memory cycletime. See Bloch and Galage for a first-order approxi-mation of the relationship of cycle times to the ratesof executing instructions.

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42 SURVEY OF CURRENT BUSINESS January 1986

kind is MIPS—millions of instructionexecutions per second, in which eachinstruction is weighted by its frequen-cy of use in a specific job mix. Twotypes of problems, however, arise withrespect to the use of this measure.The first problem concerns compara-bility. If two processors have differentinstruction formats or different logicdesigns, the MIPS ratings are notcomparable. They can, however, bemade comparable. Assume the MIPSrating of a given processor equalsMIPSi and that Ni equals the numberof instruction executions in processingthe job mix. If some other processorhas a rating of MIPS2 and its numberof instruction executions equals N2 forthe same job mix, then the "equiva-lent MIPS" rating equals MIPS2(Ni/N2). The second problem relates to thechoice of the job mix. It arises be-cause of the difficulty of defining atruly representative benchmark. Theadvantage of equivalent MIPS as ameasure of processor speed is realizedonly if the specified job mix is repre-sentative of the jobs expected to beperformed by the processors beingcompared.

Estimates of equivalent MIPS rat-ings, expressed in terms of IBM 370-equivalent MIPS, are publicly avail-able for IBM and plug-compatibleprocessors. MIPS ratings publishedfor the processors of other manufac-turers may not be expressed in thesame terms. To be assured of a con-sistent and comparable measure ofspeed, the work described here isbased on IBM and plug-compatibleprocessors.

Disk drives—technically, directaccess storage devices (DASD)—aredevices that write, store, and retrievedata. They are now the dominantauxiliary storage device. Basically,they consist of stacks of records ordisks, centered on a spindle, on whichdata can be written or from whichdata can be read. A disk drive maypossess one or more spindles. Thecomponent that does the actual read-ing and writing of data is known asthe read/write head; until recently,there was one set of heads per spin-dle. Disk drives are random access de-vices—that is, they have the ability tomove the head to any point on thedisk so that the stored data are direct-ly accessible. Data stored on tapes—the main competing storagemedium—can be accessed only se-

quentially.6 The work described herecovered large and intermediate single-density drives that do not possess ex-plicit control functions.

The two key characteristics for diskdrives are capacity and the speedwith which data can be transferredbetween the device and mainmemory. Unlike processors, the meas-urement of both these characteristicsis relatively straightforward. Capacitycan be measured by the number ofmegabytes that can be stored in adevice.

The measure of speed, in units ofkilobytes per second, consists of threeelements. (1) Average seek time (ast)is the average time for the read/writehead to locate and arrive at the cor-rect track of the disk. (2) Average ro-tation delay (arotd) is the time for thedisk to rotate so that the read/writehead is lined up at the correct pointon the track. (3) The transfer rate (tr)is the time it takes to transfer thedata, once the correct position on thedisk has been located, between thedrive and main memory. The totaltime to transfer a kilobyte of data isthe sum of these three elements. Thecalculations are made under the as-sumption that the average amount ofdata transferred at one time is two ki-lobytes. Under this assumption, speedper set of read/write heads is meas-ured as the inverse of the time ittakes to transfer two kilobytes, or as:

Speed = 2 / (ast + arotd + 2/tr).If there is more than one set of headsper device, the speed of the device ismeasured as the speed per set timesthe number of sets.

Printers record the system's outputon paper. There are two broad catego-ries of printers: Impact and nonim-pact. There are two classes of impactprinters: System line printers, whichcan print an entire line of charactersat once, and serial printers, whichprint one character at a time. Serialprinters are used with personal com-puters and other workstations. Theymay use daisywheel (for letter-qualityprint) or dot matrix mechanisms.There are also two classes of nonim-pact printers: Page printers, whichare based on laser electrophotogra-phic technology, and ink jet printers.7

The study covered all of these classesof printers.

The three key characteristics forprinters are speed, resolution, and thenumber of fonts available on-line topermit automatic variation of typesize, style, and boldness. Speed ismeasured as characters per second.Resolution is measured by thenumber of dots per character.8

General purpose displays, or termi-nals, are input-output devices thatallow communication between theprocessor and a user. They possess nodata processing capability. A unit con-sists of a keyboard and a monitor—the former to enter data, the latter todisplay data. Two types of monitorsare available: Cathode ray tube (CRT)and gas panel. The study covered onlyCRT displays.

The four key characteristics for dis-plays are screen capacity, resolution,the number of colors that can be dis-played, and the number of program-mable function keys. Screen capacityis measured as the number of charac-ters that can be displayed. Resolutionis measured as the number of pictureelements per character. Displays alsodiffer in various ergonomic attributes,such as the feel and shape of the keysor tilt positions of the monitor; theseare difficult to quantify and are as-sumed to be uncorrelated with themeasured characteristics. In contrastwith processors and the other periph-eral equipment, speed is not a charac-teristic for displays. The speed withwhich information is exchanged be-tween the display and the host proces-sor can be considered essentially inde-pendent of the type of display used.The main determinants of speed, asperceived by the user, are characteris-tics of other components of thesystem.

Modification of the hedonic function

The use of hedonic regressions isbased on the premise that differencesin the prices of goods offered in thesame market at the same time mainlyreflect differences in the characteris-tics of the goods. When the market

6. See Marker et al.; Engh; and Mulvany andThompson for detailed descriptions of disk drives.

7. See Nickel and Kania and Elzinga et al. for de-tailed descriptions of printing mechanisms and tech-nology.

8. Resolution measures were not published for someprinters and were imputed using data from a refer-ence printer. In other cases, the published measureswere in terms of dots per square inch. Data from thereference printer were used to convert dots per squareinch to dots per character. See Barquin-Stolleman fora detailed description of the estimating and conver-sion procedures used in these cases.

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Table 1.—Processor and Disk Drive Technologies, 1972-84

Processors

Class code

1

2

3

4

5

6

7

8

Memory type

Magnetic core

Semiconductor, bipolar

Semiconductor, bipolar

Semiconductor, field effect transistor

Semiconductor, field effect transistor

Semiconductor, field effect transistor

Semiconductor, field effect transistor

Semiconductor, field effect transistor

Memory chipdensity

(kilobits perchip)

2 0.0025

.128

1

1

2

4

16

64

Years

Insample

1972

1972

1973-74

1973,1976-79

1974-83

1975-82

1981-84

1979-84

"Best"

1972

1973

1974

1975-78

1979-84

Large and intermediate disk drives

Class code

1

2

3 3

4 3

5

6

7 s

8

9

Type

Removable disk pack

Removable disk pack

Removable head/disk pack

Fixed disk

Fixed disk

Fixed disk

Fixed disk

Fixed disk

Fixed disk

Areadensity l

(kilobytesper square

inch)

220

776

1,691

2,694-2,705

3,071-3,084

4,191

7,705

9,707

12,192 12,939

Years

Insample

1972

1972-77

1974-77

1976-81

1976-82

1977-82

1980-84

1981-84

1981-84

"Best"

1972-73

1974-75

1976

1977 79

1980

1981-84

1. Single density only (see footnote 11 in text).2. Estimated using relative volume/megabyte from Pugh et al., table 1.3. Intermediate drives.

under study is not in long-run equilib-rium, and when the forces creatingthe disequilibrium are correlated withthe characteristics, a statistical analy-sis that fails to treat the issue explic-itly risks producing biased estimates.9

The market for computing equip-ment is characterized by disequilibri-um caused by rapid technologicalchange. Existing products are leap-frogged by products embodying im-proved technology and manufacturedusing improved processes. The intro-duction of the new products inducesmarket disequilibrium. An importantaspect of the disequilibrium is thatthere is a period of time when twosets of prices coexist for products pos-sessing the same characteristics—oneprice for the products based on theold technology and one for the prod-ucts based on the new. In this study,the hedonic function was expanded totake this aspect of disequilibrium intoaccount for processors and disk drivesby introducing measures of embodiedtechnology into the regressions. Themeasures serve as proxies for technol-ogy-associated differences in produc-tion costs and for the attractiveness oftechnologically superior substitutes.The measures of technology are de-scribed next; the ways in which theyare introduced into the hedonic re-gressions are described in the thirdsection. (For printers and displays, itwas not feasible to allow for disequi-librium.)

The measures used to representtechnology are based on density—thatis, the amount of information thatcan be stored on a given surface area.

Semiconductor memory chip densitywas used for processors, and the re-cording, or areal density, was used fordisk drives.

Semiconductor memory chip densi-ty was used for processors becausemuch of the improvement of proces-sors has come from advances in semi-conductor technology. Greater speedand memory capacity have beenachieved by packaging increasednumbers of circuits closer together.With increased densities, the distanceelectrons travel is shortened; not onlycan more information be stored, butalso instruction execution time is re-duced. Improvements in packaging athigher levels (cards and boards) haveenabled improvements in computermanufacturing (and reductions incosts) to parallel improvements inchip densities.10 The use of memorychip density to represent logic tech-nology (its proprietary nature pre-cludes direct comparison) is appropri-ate only to the extent that logicdesign is also improved by advancesin semiconductor technology. The unitof measurement of memory chip den-sity is kilobits per chip.

By reference to density, the studyestablished eight classes of technologyfor processors, shown in table 1. Thefirst class is magnetic core, the stor-age material in use before the shift tosemiconductors during the early1970's. Semiconductors, although ini-tially expensive, reduced by a factorof 50 the space required to store agiven amount of information. Thisnew material provided the potentialfor future improvements in densities.

The first semiconductors covered inthe sample were bipolar. Of these,there are two classes: The first, intro-duced in 1972, had a density of 0.128kilobits per chip; the second had adensity of 1 kilobit per chip. Theywere replaced by field effect transis-tor (FET) semiconductors, which wereproduced at substantially lower costs.Of these, there are five classes, overwhich densities increased from 1 to 64kilobits per chip.

For disk drives, manufacturershave improved speed and capacity inthree ways: By decreasing the dis-tance from the read/write head to thedisk, by decreasing the head-gaplength (that is, the distance betweenthe reading and writing elements onthe read/write head), and by decreas-ing the thickness of the recordingmedium on the disk. Each of theseimprovements makes it possible forthe head to read information from asmaller area on the disk. The unit ofmeasurement of areal density is thenumber of kilobytes per square inch.

The first two of the nine technologyclasses for disk drives consist of thosedesigned to handle disk packs thatcould be removed (table 1). The first,introduced in the mid-1960's, had anareal density of 220 kilobytes persquare inch; the second, introduced in1972, had a density of 776.ll In themid-1970's, separate technologies were

9. See Rosen and Fisher, McGowan, and Greenwoodfor discussions of the conditions under which it is ap-propriate to employ the traditional hedonic approach.

10. See Seraphim and Feinberg and Bloch andGalage for discussions of the interrelationships be-tween improvements in semiconductor technology andthe design and manufacture of computers.

11. As noted earlier, the study only included single-density drives. However, classes 1, 2, and 4 also con-tain products known as double-density drives. Adouble-density drive is one in which the manufacturerhas made changes that lead to a doubling of the prod-uct's areal density, but has not changed other perti-nent parameters that affect the device's overall per-formance. These drives were not included in the studybecause they do not represent the same technologicalimprovement as the introduction of a new generationof devices for which all of the technical parametershave been changed.

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44 SURVEY OF CURRENT BUSINESS January 1986

introduced for intermediate and largedisk drives. The first intermediatedrives had a density of 1,691 kilobytesper square inch. This type was calledthe "Winchester," and it had disksand read/write heads that were pack-aged together in a removable unit.Other intermediate drives, as well aslarge drives, had fixed disks—that is,they could not be removed. The firstof the large drives, introduced in themid-1970's, had areal densities inexcess of 3,000 kilobytes per squareinch. The current generation of largedisk drives, introduced in the early1980's, has areal densities in excess of12,000 kilobytes per square inch—den-sities 55 times greater than the densi-ties of the devices introduced in theinid-1960's.

II. The DataThe samples for all four system

components contain annual data for1972-84. Each sample contains infor-mation on prices and characteristicsfor each model used in the regres-sions. Prices for IBM models in thesamples were taken from IBM salesmanuals. In general, prices for non-IBM models and information on char-acteristics for all models were drawnfrom trade and general press sources,as indicated in the descriptions of thesample data that follow.12

The processor sample consists of 67different models from 4 manufactur-ers. Prices refer to the central elec-tronic complex, which includes—inaddition to the central processing unitand main memory—the minimum re-quired gear, such as standard chan-nels, the console, and the powersupply unit. For non-IBM processors,prices, main memory sizes, and infor-mation on the minimum requiredgear came from the trade and generalpress. MIPS ratings for all models ap-pearing prior to 1981 are from"Tracking Those Elusive KOPS," inDatamation of November 1980; rat-ings for models introduced after 1980are from the annual "HardwareRoundup," in Computerworld of July1981 and August 1982, 1983, and 1984.

Average annual prices for proces-sors were obtained by weighting thedifferent prices prevailing within ayear by their respective durations.

12. The availability of a package of data and a de-tailed listing of the data sources will be announced inthe SURVEY OF CURRENT BUSINESS.

For non-IBM processors, dates of pricechange were taken from the press;when no reports of change were locat-ed, prices were assumed unchanged.

The sample for disk drives consistsof 30 devices marketed by 10 vendors.Characteristics and prices were com-piled from a number of sources. Themain ones were the series of annualreports for 1973-85 published by Da-tapro Research Corporation and DiskTrend Reports for 1976-84 publishedby J. Porter.

The printer sample consists of 480models from 126 vendors. Characteris-tics and prices are from reports pub-lished by Datapro Research Corpora-tion for 1972-84 and from ElectronicPrinter Industry Services, a series ofreports published by Dataquest, Inc.,for 1983 and 1984. The display sampleconsists of 772 models from 115 ven-dors. Characteristics and prices arefrom Datapro's series of annual re-ports, "All About Alphanumeric Dis-play Terminals," 1973-84.

It was necessary to devise rules todetermine how long a model appearsin the sample. In principle, a modelshould appear as long as it is beingproduced. For IBM models, it was pos-sible to determine this directly; othermodels were a problem. For non-IBMprocessors, a model was entered thefirst year it appeared in the annualtabulations of the stock of installedcomputers in the United States pre-pared by the International Data Cor-poration and published in EDP Indus-try Reports, and it was deleted theyear after the stock peaked. A non-IBM disk drive model was entered inthe sample in the year in which itwas first shipped and deleted thesecond year after a new generation oftechnology was introduced. Non-IBMprinter and display models were car-ried in the sample as long as they ap-peared in annual Datapro reports.

The price data have serious limita-tions. First, they are list prices for aquantity of one. Because discountingis a widespread practice in the indus-try, particularly on multiple-unitsales, the prices do not representtransaction prices. Second, prices fornon-IBM peripherals refer to a pointin time rather than the full year.Point-in-time prices may distort esti-mates of year-to-year change becauseany price change occurring after thesurvey date will not be reflected untilthe following year.

III. Regression ResultsThe authors had strong views with

respect to the variables to be includedin the hedonic regressions and weakernotions with regard to the functionalform. A double-log form was triedfirst, and Box-Cox transformationswere used to test alternatives. The re-sults indicated that, for all producttypes, the double-log form is preferredto the semilog and linear forms.

Regressions were estimated for timeperiods of varying lengths, includingsingle years, groups of adjacent years,and the entire 1972-84 period. For thesake of simplicity and ease of exposi-tion, only the results for the regres-sions estimated for the entire 1972-84period are shown in table 2.

Results denoted "I" refer to a tradi-tional hedonic regression of price as afunction of characteristics and yeardummies. The estimated coefficientsfrom these regressions suggest thatspeed is more important than mainmemory capacity for processors, butthat capacity is somewhat more im-portant than speed for disk drives.Speed is the most important charac-teristic for printers, followed by reso-lution and the number of on-linefonts. The number of colors and reso-lution are almost equally importantfor displays; capacity and the numberof programmable function keys aremuch less important.

Modified regressions for processorsand disk drives

The information on technology intable 1 was used in the hedonic re-gressions in two alternative ways. Intable 2, the results of these regres-sions are denoted "II" and "III." In II,technology is represented by a set ofdummy variables for each year forthe technology classes described earli-er. For example, a processor withmemory using 4 kilobit ("4K") chipswas coded as belonging to technologyclass 6 by entering "1" for that classand "0" for the other classes.

In III, technology is represented bya set of three technology variables:Embodied, or "own," technology;"best" technology; and age of owntechnology. (1) The own technologyvariable is measured directly. For ex-ample, the value of the variable for aprocessor with memory using 4Kchips was "4" in each year. The owntechnology variable is an indicator of

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Table 2.-—Regression Coefficients for 1972-84 Pooled Regressions

Characteristics:

Speed

Capacity

Resolution

Number of:Colors

Function keys

Fonts on-line

Technology variables:

Own technology

"Best" technology

Age of own technology

Intercept

Dummies:

Portable storage

Tpchnoloffv class bv vearProduct class by year

Addenda:

R2

Standard error of estimateNumber of observations

Processors

I

0.80(35.1)

.17(6.6)

7.58(94.1)

*

.953

.062296

II

0.78(39.0)

.22(10.0)

7.94(79.1)

*'

.973

.039296

IF

0.78(41.7)

.22(10.2)

7.94(79.8)

*

.973

.038296

III

0.76(23.1)

.14(3.7)

12(-4.5)

39(-9.5)

06(-3.8)

7.88(95.1)

.900

.129296

Disk Drives

I

0.41(3.3).46

(5.8)

6.36(22.0)

*

.844

.05191

II

0.33(0.9).82

(2.4)

4.96(9.2)

*

.910

.05091

III

0.33(2.7).73

(7.9)

53(-4.6)

01(.1)

08(3.0)

8.83(23.4)

.25(2.2)

.870

.03891

III'

0.33(2.8).73

(8.0)

53(-8.9)

08(-6.0)

8.83(24.0)

.25(2.2)

.870

.03891

Print-ers

I

0.76(25.4)

.305(5.7)

.09(2.2)

3.94(10.4)

.918

.273813

Dis-plays 1

I

0.09(2.7).39

(14.9)

.40(22.5)

.07(7.6)

5.81(23.5)

*

.427

.1822,023

NOTES.—Dependent and independent variables, except age of own technology and dummies, arein natural logarithms. An asterisk denotes a set of dummies included in regressions. Technologyclasses are based on memory density for processors and on areal density for disk drives. Printercategories are line, daisywheel, dot matrix, ink jet, and page. The t statistics are in parentheses.

1. Regression for displays is estimated for 1973-84.

the sophistication of the technologyemployed in manufacturing a givenprocessor or disk drive. Because em-ployment of more advanced technol-ogies permits the same characteristicsto be produced at lower costs, thisvariable can be considered as an exog-enous "supply shifter." (2) The "best"technology is a variable that takesthe value of the greatest densityavailable in each year. It has thesame value for all processors withinany year. (In years during the transi-tion to a new technology, the value ofthe "best" technology variable wastaken as an average of the currentyear and the preceding 2 years.) Thisvariable represents the competitivepressure to lower prices that is exert-ed by technologically superior substi-tutes. (3) The age of own technologyvariable is defined as the number ofyears since introduction of the tech-nology. In any year, it has the samevalue for all models embodying thesame technology. Age is expected tobe important for at least two reasons.One is that lower costs and cheaperprices are achieved with the efficiencyin production that comes with experi-ence. The second reason is expected

obsolescence on the demand side. Theolder a technology, the less buyerswill be willing to pay because theprobability increases that new prod-ucts based on cheaper technology willsoon become available.

In addition, for disk drives, anothervariable was added—a portable drivedummy. It was assigned a value of"1" when the product has a remov-able disk and a value of "0" when ithas a fixed disk. Including this vari-able permits the intercept of the re-gression equations to be different fordrives with removable disks and fixeddisks.

Comparison of equations II and IIIwith equation I shows that the tech-nology information, in one specifica-tion or another, can substantiallyreduce the standard error of the tra-ditional hedonic equation. For proces-sors, the information on technology inthe form of technology class by yeardummies yields better results than inthe form of the set of technology vari-ables: The standard error is reducedfrom 0.062 in equation I to 0.039 inequation II; it is doubled to 0.129 inequation III. In contrast, for diskdrives, the information on technology

in the form of the set of technologyvariables yields better results: Thestandard error is reduced from 0.051in equation I to 0.038 in equation III;it is marginally reduced to 0.050 inequation II. A likely explanation ofthese differences is that areal densityis a better measure of technology fordisk drives than memory chip densityis for processors. Improvements inlogic technology, though highly relat-ed to memory chip density, may notbe well measured by increases in den-sities.13 Although significant for proc-essors, the "best" technology variablewas insignificant for disk drives. Theresults without this variable for diskdrives are denoted equation III'.

For disk drives, although not forprocessors, the inclusion of technologyvariables in both specifications has amarked effect on the estimated coeffi-cients for speed and capacity. Theeffect is to raise the estimated impor-tance of capacity relative to speed.The inclusion of the technology varia-bles gives more plausible results; onewould expect capacity to be more im-portant than speed for large- and in-termediate-size storage devices.

Table 3 shows the estimated coeffi-cients for the technology class by yeardummies for processors for equationII. The coefficients in the first columnare estimates of the logarithm of ratioof the price of the products embody-ing the "best" technology in 1972.These coefficients can be converted toindex numbers, with 1972 = 100, bytaking the antilog of each year'svalue and multiplying by 100. For ex-ample, the coefficient -0.746 in 1975means that the price index for proces-sors embodying the "best" technologyequals 47.4 after allowing for differ-ences in speed and storage capacity.

The coefficients in each row to theright of the double line are the esti-mates of the logarithm of ratio of theprice of each "nonbest" technology tothe price of the "best" technology inthe same year. For any given year,the coefficients can be stated relativeto the price of the "best" technologyin that year by taking the antilog ofthe coefficients and multiplying by100. For example, the coefficient 0.524on technology class 5 for 1975 meansthat the price of products in this class

13. The results may also reflect the fact that by im-proved packaging, manufacturers may increase the ef-fective capabilities of memory chips. For example, 2Kchips have been packaged to have the effective capa-bilities of 16K chips.

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46 SURVEY OF CURRENT BUSINESS January 1986

was 168.9 percent of the "best" in1975 after allowing for differences inspeed and storage capacity. In mostcases, the coefficients indicate thatprices tend to be higher for "nonbest"(and usually older) technologies thanfor the "best." Moreover, the t statis-tics indicate that 16 out of 24 of theseprice differentials are significantlydifferent from zero.

Comparisons across technologyclasses within a given year show caseswhere the coefficient for a "nonbest"technology is not statistically differ-ent from the coefficient of the "best"technology, of another "nonbest"technology, or of both. Formal tests ofthe equivalence of regression coeffi-cients lead to a simplified version ofequation II, denoted equation IF, forwhich results are shown in the lowerpanel of the table. It involves twokinds of restrictions: (1) Coefficientsare set equal to zero if not statistical-ly different from zero (for example,class 4 in 1976) and (2) coefficientswithin a given year were constrainedto be equal if they did not differ sig-nificantly from one another (for ex-ample, classes 4 and 5 in 1977).14 Theresults of equation IF similarly indi-cate the existence of multipleprices.15

The only "nonbest" technology thatsold for less was magnetic corememory in 1972. The shift to semicon-ductor memory took place during thisperiod, and—because it was clear thatfurther improvements were muchmore likely to come from semiconduc-tors—core was considered obsolete.

For disk drives, all except one ofthe estimated coefficients for the tech-nology class by year dummies inequation II, shown in table 4, are posi-tive and are larger the older is the

14. Because the insignificance of individual t statis-tics is not sufficient to permit the set of restrictionsinvolved in equation IF, additional tests were neces-sary to support the use of equation IT. An F test indi-cates that one cannot reject the hypothesis that theset of restrictions is valid. A second F test was neces-sary to justify pooling the cross-sections into onesample. Single-year regressions of price on character-istics and the same restricted technology class by yeardummies as in equation IF were calculated. By thestandard F test (the Chow test), one cannot reject thenull hypothesis that all the single-year regression co-efficients are the same.

15. Other studies of processors have shared the un-derlying thread of coexisting multiple prices: Stone-man; Fisher, McGowan, and Greenwood; and U.S. De-partment of Commerce, BEA. The BEA study strati-fies observations by whether the model number is newor has existed in the sample previously. The BEA coef-ficients for new models and the IBM coefficients fornew technologies for 1975 and 1979, years in whichnew models also embody new technology, show similarprice differentials for new products.

Table 3.-—Regression Coefficients on Technology Class by Year Dummies for Processors

Year

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

"Best"

239(-1.8)

195(-1.6)746

(-4.3)798

(-4.6)-1.003(-7.5)-1.245(-9.3)-2.283(-13.1)-2.257(-16.7)-2.167(-17.7)-2.293(-19.0)-2.392(-20.3)-2.554(-21.0)

Technology class 1

1

-0.554(-4.4)

2 3 42 5 6 7 8

Equation II

*

0.295(2.3)284(2.3)

*

0.160(.8).318(2.4).379(2.9)1.181(6.0)

*

0.524(3.3).557(3.5).383(3.0)084

(-.7).877(5.4).537(4.6).262(2.7).147(1.0)173(1.2)

*

*

*

*

0.833(5.3).544(5.3)038

(-.4).142(1.6)

0.327(3.7).281(3.7).032(.4)-.050(-.8)

*

*

*

*

Equation II'

235(-1.8)

192(-1.6)743

(-4.3)715

(-5.1)998

(-7.5)-1.282(-10.7)2277

(-13.1)-2.250(-16.8)2172

(-18.5)2248

(-19.3)-2.273(-20.5)-2.564(-21.8)

554(-4.4)

*

.293(2.3).282(2.3)

*

0

.350(3.3).420(3.6)1.180(6.0)

*

.524(3.3).477(4.0).350(3.3)0

.851(5.7).539(5.7).273(3.0)0

0

.851(5.7).539(5.7)0

0

.338(4.1):243(3.4)0

0

*

*

NOTES.—The t statistics are in parentheses. An asterisk indicates "best" technology class.1. See table 1.2. Technology class 4, the IK field effect transistor chip, first appeared in 1973 and was replaced after only 1 year by the 2K

chip embodied in 1974 shipments of the same processor models. The IK chip was reintroduced in 1976 in new processors.

Table 4.—Regression Coefficients on Technology Class by Year Dummies for Disk Drives,Equation II

Year

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

"Best"

0.005(.04)-.336(-1.18)-.387(-1.36)-1.033(-2.36)-1.567(-3.53)1.567

(-3.53)1.567

(-3.53)1.659

(-4.36)2015

(-3.61)-1.985(-3.56)-2.063(-4.20)-2.229(-4.26)

Technology class x

1

0.351(1.10)

2

0.123(.43).076(.26).651(1.53)1.422(3.14)

3

0.457(.79).991(1.70)

4

0.127(.40).661(2.07).559(2.02).353(1.27).306(1.09).663(2.01)

5

*

0.520(1.89).500(1.81).219(.80).169(.59).526(1.65).534(1.67)

6

*

-0.131(-.40).225(.65).387(l.H)

7

0.455(1.19).465(1.21).458(1.47).624(1.87)

8

0.282(.83)2.82(.83).229(.84).395(1.38)

9

*

NOTES.—The t statistics are in parentheses. An asterisk indicates "best" technology class.1. See table 1.

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January 1986 SURVEY OF CURRENT BUSINESS 47

technology. However, the t statisticsindicate that only four of the estimat-ed coefficients are statistically signifi-cant. Similar but stronger results areprovided by the estimated coefficientsof the set of technology variables inequation IIP of table 2, which suggestthat multiple prices exist and that—because coefficients are negative—older technologies sell for more thannewer ones. The hypothesis of multi-ple prices was further tested by an al-ternative equation containing boththe technology variables and yeardummies. The appropriate F tests in-dicate that one cannot reject the hy-pothesis that the coefficients on thetechnology variables are 0 when theyear dummies are included. Thus,there is cross-sectional variation inthe sample beyond that captured byspeed and capacity measures, and thetechnology variables capture it.

In table 5, the information from thelower panel of table 3 and from table4 is recast into the form of price in-dexes having the 1972 "best" = 100.This presentation makes it easy to seethe course of the price changes of agiven technology class. As seen by thepattern of generally declining pricesreading down the columns, older tech-nology classes have continually andrapidly falling prices in response tocompetitive pressure from newer tech-nology classes.

In summary, the introduction ofproducts embodying new technologyleads initially to multiple prices, withthe products based on "nonbest" tech-nologies selling for more. The pricesfor older products decline rapidly,until they either match the quality-adjusted price of products based onthe new technology or the productsdisappear. The claim that improvedtechnology leads to reduced costs and,hence, to a lower quality-adjustedprice is consistent with a competitivemarketplace in which only one qual-ity-adjusted price (the "best") ulti-mately prevails. It was found that inmany cases price reductions permitan older technology to compete with anewer one for a limited time, but asthe new technology becomes diffused,its own age-related cost and price re-ductions eventually drive the oldertechnology out of production. The evi-dence presented here suggests thatprices reflect this process of adjust-ment and that equilibrium is notreached within a period as short as 1year.

Table 5.—Price Indexes by Technology Class for Processors and Disk Drives[1972 "Best" = 100]

Year

197219731974 .. .197519761977

19781979198019811982 . . ..19831984

197219731974197519761977

1978197919801981198219831984

"Best"Technology class 1

I 2 3 4 5 6 7 8 9

Processors

100.079.082.547.648.936.9

27.710.210.511.410.610.37.7

57.5 100.0106.0109.4

79.0

48.952.3

42.233.4

82.580.378.852.3

27.724.018.115.010.610.3

47.648.936.9

27.724.018.111.410.6

16.013.510.37.7

10.210.511.410.610.37.7

Disk Drives

100.0100.571.567.935.620.9

20.920.919.013.313.712.710.8

142.0 100.0100.580.873.368.286.5

71.567.956.256.2

40.440.4

36.529.725.825.9

35.635.1

34.426.022.522.623.4

20.9

20.920.916.716.720.2

19.021.021.920.120.1

17.718.216.016.0

13.313.712.710.8

NOTE.—In the columns for technology classes, the index for the "best" is repeated (in italics) from the first column.1. See table 1.

Prices for characteristics ofprocessors and disk drives

The hedonic equations can be usedto derive estimates of implicit pricesfor characteristics. Such prices areshown in table 6 for processors anddisk drives. Each estimate is a mar-ginal price, or price for an incremen-tal unit, of capacity and speed. (Thespecific formula is presented in thefootnote to the table.)

The estimated characteristics pricesfell sharply between 1972 and 1984.

Table 6.—Estimated Characteristics Prices[Thousand dollars per unit]

Year

197219731974197519761977

197819791980198119821983 . ..1984

Processors

Speed, inMIPS

1,8842,2931,9061,8271,8211,385

771661419394288264220

Capacity,in

megabytes

501404332283285154

97804124262525

Disk drives

Speed, inkilobytes

persecond

758059525258

62504040433735

Capacity,in

megabytes

1881781501339060

50393434362321

NOTE.—The estimates use multiyear (1972-84) equation IFfor processors and equation III' for disk drives. Because theformulations are multiplicative, the price of the £th character-istic in year t (Pkt) is estimated as

A dPt y / Ptmt \Pkt = = bk * ( )vmt ,

8Xk V XMm '

where the overbar denotes the arithmetic mean; Pint denotesthe price of the ith model of the mth technology class in yeart; Xkim denotes the quantity of the kth characteristic in the ithmodel; vmt denotes the share of characteristics from the /nthtechnology class shipped in year t; and bk denotes the regres-sion coefficient for the kth characteristic.

The most dramatic drops occurred inprices of capacity. In 1984, the priceof one megabyte of main memory wasless than one-twentieth the 1972price. The price of one megabyte ofauxiliary storage (in the disk drive)was about one-ninth the 1972 price.Main memory was almost twice as ex-pensive as auxiliary storage untilprocessors embodying the 64Kmemory chip were introduced in 1979.After that year, the price of data stor-age was essentially the same, whetherin main memory or in auxiliary stor-age.

The estimated prices of speed fellless rapidly. In 1984, the price of exe-cuting one million instructions persecond was about one-ninth the 1972price. The price of transferring onekilobyte of data per second from thedisk was about one-half the 1972price.

HomogeneityFurther tests of the hedonic equa-

tions were conducted. The hypothesisthat the characteristics coefficientssum to one could not be rejected forany of the four types of equipment.The finding that the implicit charac-teristics prices for these products areprobably homogeneous to the firstdegree is appealing. Homogeneity im-plies that the valuation of character-istics quantities equals the observedprice of the product.

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48 SURVEY OF CURRENT BUSINESS January 1986

IV. The Price IndexesThe price index used as a deflator

to convert current-dollar values toconstant-dollar values is a Paascheformula index,

(1) Io,t =

where, for model i, Pu and Pio denoteprices in the current and base peri-ods, respectively, and Qu denotes thequantity purchased in the currentperiod. The problem encountered inconstructing such an index for prod-ucts experiencing rapid change is thatmodels purchased in the currentperiod may not have existed in thebase period.

Matched-model index

The most frequently used approachfor dealing with the problem uses ob-servations only for the models thatexist in both period t and in period 0.Models that exist only in the currentperiod are ignored. Such an indexmay be referred to as a "matched-model" index.

Because computing equipmentchanges so rapidly, it was not possibleto calculate a matched-model indexusing equation (1). Instead, matchedmodels for 2 adjacent years were usedto calculate an index where the baseperiod is the first of the 2 years (thatis, t-l):

(2)

An index for the entire period is cal-culated as a multiplicative "chain" ofthe adjacent-year indexes:

(3) I0,t = 7oi X /ia X . . . X -It-ijt -

This index is referred to as a "chainindex of matched models."

The assumption underlying thematched-model procedure is that themean price change associated withthe introduction of new models (orthe discontinuance of old ones) equalsthe mean price change observed formodels that are common to both peri-ods. In terms of the analysis of tech-nological disequilibrium presentedearlier in this article, one can statethis assumption in an alternative andilluminating way: Use of thematched-model procedure assumesthat prices of models embodying old

technology adjust instantaneously, sothat their quality-adjusted prices areequal to those of the models embody-ing improved technology. If the as-sumption holds, the price change inthe matched models equals the unob-served price change implicit in the in-troduction of new models (or the dis-continuance of old ones).

Three hedonic indexes

Use of hedonic methods does not re-quire the assumption that the ob-served price change in the matchedmodels equals the unobserved pricechange. Hedonic methods make use ofall the price information. They can beemployed in a number of ways. Thepresent study explored three alterna-tives.

The composite index.—The "compos-ite" index uses prices from thematched-model approach whenevermodels exist in both current and baseperiods and hypothetical prices forthe models that did not exist in thebase period from hedonic equations. Ifan "overlap" model (one that exists inboth periods) is designated "i" and amodel present in period t but not inperiod 0 is designatedcomposite index is:

essors, the majority of models shippedwere from technology class 8; for diskdrives, the majority were from tech-nology class 4.

The characteristics price index.—Inhedonic studies, one can identify morethan one kind of price. The conven-tional concept is that of the price ofthe model. A second concept is that ofthe prices of the "characteristics."One can use the estimated character-istics prices—such as those shown intable 6—to construct a price index.

Given the formulation of the hedon-ic functions, the implicit dollar priceof the kth characteristic possessed bythe ith model of the mth technologyclass would be:

"y," then the

(4) Iot =2 PuQu + 2i 3

2 PioQit + 2i i

In this formula, PJO denotes the esti-mate, taken from the hedonic equa-tion, of the hypothetical price thatthe "missing" model would have com-manded in the base period. Note thatwhen 1982 is the base (as it is for allthe present calculations) and a yearsubsequent to 1982 is "year t" thenPJO is the hypothetical price for a newmodel. When a year earlier than 1982(such as 1977) is "year t" then Pjo isthe hypothetical price for a discontin-ued model.

When there are multiple prices inthe base period, some conventionmust be adopted in estimating PJQ be-cause there is more than one priceprevailing for any specified set ofcharacteristics. In this study, thedominant technology—that is, thetechnology embodied by the majorityof models shipped in the base period(1982)—was used to determine the hy-pothetical price PJO. In 1982, for proc-

(5)£ A PimtPkimt = Ok >

Xkim

where bk is the regression coefficientfor the &th characteristic (estimatedas constant for all years of the study),Xkim denotes the quantity of the kthcharacteristic possessed by model i,and Pimt is the price for model i, oftechnology class m, at time t.

The characteristics price index is:

(6) lot =

222 (Pkimt) (XkimQimt)k m i

222 (Pkimo) (Xkim Qimt)k m i

where XkimQimt denotes the quantityof the kih characteristic possessed bymodel i of the mth technology class inperiod t.

The regression index.—The regres-sion index was created from the yeardummies in the regressions. The priceindex number formula for the regres-sion index is based on the expressionfor the regression coefficients for theyear dummies.

Regression indexes may produce in-dexes that differ from alternative in-dexes that use hedonic methods.16 (Inthe present case, for example, the re-gression index is unweighted, whereasthe composite and characteristicsprice indexes employ shipmentsweights.) Several econometric short-comings of the regression index havebeen pointed out.17 However, becausethe regression index is so frequentlyencountered in other hedonic studies(including those for computing equip-

16. See Triplett and McDonald.17. See Griliches.

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January 1986 SURVEY OF CURRENT BUSINESS 49

ment), it was calculated in this studyfor purposes of comparison.

The four price indexes

In calculating the three hedonic in-dexes, the results from equation II'were employed for processors and theresults from equation I for printersand displays. For disk drives, resultsfrom equation III' were used for thecomposite and characteristics price in-dexes; the regression index was basedon equation II results. It was neces-sary to develop estimates of quantitiesshipped for the products in whichmodels were distinguished by class.For processors, the quantity shippedof each model was approximated fromthe annual tabulations of the stock ofinstalled computers prepared by theInternational Data Corporation. Fordisk drives, no information on ship-ments by model was available. Esti-mates of shipments by technologyclass were developed from informa-tion from International Data Corpora-tion's studies and from Disk TrendReports, published by J. Porter, for1976-84. For printers, estimates weredeveloped by class from informationpublished by Dataquest, Inc. Exceptfor processors where shipments wereavailable by model, the prices formodels within a class were averagedto obtain the estimated price for theclass.

Table 7 shows the four price index-es calculated for each of the fourproducts. The matched-model indexesdecline much less than the three he-donic indexes. For processors, thematched-model index declines at anannual rate of 8.5 percent from 1972to 1984, compared with declines in thehedonic indexes ranging from 17.6percent to 19.2 percent. For diskdrives, the matched-model index de-clines at an annual rate of 6.9 per-cent, compared with declines rangingfrom 12.6 percent to 16.9 percent. Forprinters and displays, the matched-model indexes decline much less thanone-half as much as the hedonic in-dexes.

In the case of processors, thematched-model index does not reflectthe introduction of semiconductortechnology nor its subsequent rapidprice declines. It also continued to

Table 7.—Price Indexes[1982=100]

Year

1972 . . . . . .19731974197519761977

1978197919801981198219831984

Average annual rate ofchange:1972 771977 341972-84

1972197319741975 . . . .19761977

1978197919801981198219831984...

Average annual rate ofchange:1972 771977-84 . . .1972-84

Matchedmodel

Hedonic

Compos-ite

Character-istics Regression

Matchedmodel

Hedonic

Compos-ite

Character-istics Regression

Processors Disk drives

214.1214.6219.9228.9223.6183.5

147.3136.4115.4111.1100.089.773.7

-3.0122

-8.5

855.9865.8788.6703.7665.3473.6

242.0204.9147.2118.6100.093.980.8

-11.2223

-17.8

816.9924.5780.0721.0711.8505.3

283.3242.8148.0125.4100.092.780.6

-9.223 1

-17.6

990.11,047.5

814.8792.1778.2499.0

262.4242.6177.2112.9100.090.177.2

-12.823 4

-19.2

201.7200.9154.5143.4134.0133.5

131.1107.791.092.9

100.086.585.1

79-6.2

6.9

324.0313.4237.3222.0176.6144.3

133.7108.492.292.6

100.074.464.4

149-10.9-12.6

321.9326.6272.1260.2197.8156.7

140.4111.793.994.1

100.070.463.6

134-12.1-12.6

427.4429.5345.3313.2291.5150.0

147.0111.096.296.6

100.054.346.9

-18.9-15.5-16.9

Printers Displays

138.3139.0141.4140.1130.8121.4

117.3107.1106.4101.9100.094.290.3

-2.6-4.1-3.5

158.5152.6157.1142.9124.2116.4

118.4109.5103.1102.6100.033.027.0

-6.0-18.8

137

139.9136.2144.6129.0111.3111.6

120.9106.8109.298.5

100.044.637.8

44-14.4

104

155.6155.9156.9134.0121.4119.7

128.3103.6102.498,9

100.027.120.5

-5.1-22.3-15.5

105.7105.9104.8105.0105.1103.6

102.0101.4100.399.6

100.097.589.8

04-2.0

13

176.5176.9171.6158.5144.7143.3

127.5111.098.394.7

100.086.271.4

-4.19.5

-7.3

204.8205.3203.3198.7181.9174.6

157.0124.1107.3101.0100.093.378.7

-3.1-10.8-7.7

195.7196.1188.4178.2162.7159.6

142.5122.0106.3100.6100.091.878.6

-4.0-9.6-7.3

miss the price declines associatedwith major improvements in the semi-conductor technology during the1978-80 period. All four indexes moveroughly together in 1983-84, when nonew technologies were being intro-duced. In the case of disk drives, thematched-models index does not reflectthe adjustment to new technologies in1975-78 and 1982-84. All four indexesmove similarly during 1972-75 and1978-82. In the case of printers, thefour indexes move together through1982. From 1982 to 1984, however, thehedonic indexes dropped 70 to 80 per-cent and the matched-model indexonly 10 percent. The latter misses thesurge of the low-priced serial printers,the majority of which were imports.The matched-model index for displaysshows little movement over the entireperiod.18

18. Only price observations for three display modelswere available for 1972. All four price indexes, there-fore, use the price relatives for these models to movethe index from 1972 to 1973.

V. ConclusionAlthough there may be widespread

agreement that the present procedurefor deflating expenditures on comput-ing equipment is inadequate, a com-pletely satisfactory alternative is notreadily devised. Such a claim is cer-tainly not made for the present study.Rather, it is more in the nature of afirst step.

One deficiency of the study, andthere are several, relates to its scope.Price indexes for personal computersand small disk drives were not pro-duced. While work is underway onthese products, the results are tootentative to report at this time. An-other deficiency, and one less easilycorrected, relates to the use of listrather than transaction prices. Ideal-ly, a price index requires transactionprices. In particular, a thoroughlyconvincing case for the presence orabsence of multiple prices requiresthe use of transaction prices.

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50 SURVEY OF CURRENT BUSINESS January 1986

The study demonstrated the inap-propriateness of a matched-modelindex for computers. Even wherethere are no major technologicalshifts, such as for printers or displays,the matched-model index understatedmovements in prices. This understate-ment occurs because the matched-

model index misses the replacementof old, higher priced models by newmodels, manufactured by improvedmethods and introduced at lowerquality-adjusted prices.

In the authors' view, hedonic meth-ods—applied at the system-componentlevel, employing appropriate meas-

ures of characteristics, and expandedto deal with the problem of techno-logically induced disequilibrium—areuseful for constructing quality-adjust-ed price indexes and represent an im-provement over the present procedurefor deflating expenditures on comput-ing equipment.

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