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Quality-adjusted price indexes for computer processors and selected peripheral equipment.

Quality-Adjusted Price Indexes for Computer Processors and Selected Peripheral Equipment

THIS article summarizes IBM's work on developing quality-adjusted price indexes for computer processors and three types of peripheral equipment: Disk drives, printers, and general purpose displays. The first section describes three issues that arise in the application of hedonic regression methods to computing equipment: The level of aggregation, the specification of the characteristics, and the need to modify the hedonic function to deal with the problems of technologically induced disequilibrium. The second section discusses the data; the third, the regression results; and the fourth, the use of the results to construct quality-adjusted price indexes. The article closes with a summary of the findings and their limitations.

I. Issues in the Application of

Hedonic Methods to


Level of aggregation

The first issue concerns the level of aggregation at which the analysis should be conducted--complete computing systems or system components. The decision to develop regressions and price indexes at the system component level was based on two considerations. First, with the evolution of system modularity, most purchases are of system components, or "boxes," rather than of complete computing systems. Second, the problems of obtaining appropriate measures of characteristics are more tractable at the box level.

Although working at the box level reduces many of the problems of measurement, it is important to recognize that both the hardware and software of a computing system embody attributes--such as ease of installation, reliability, and ease of use--that are not easily measured. Working at the box level is likely to understate the improvements that have occurred in computing systems over the years.

Specification of characteristics

The second issue concerns the specification of the characteristics of the system components: If the characteristics are not specified and measured correctly, the results of the regressions may be biased. The choice of characteristics for each component was guided by its role in a computing system. The characteristics selected reflect value to users; they also reflect resource cost.

Computer processors, henceforth called processors, execute instructions. They house the central processing unit and main memory. The work described in this article dealt with intermediate- and large-size general purpose digital processors. Small computers are not included; typically, they are packaged with auxiliary storage devices (disk drives or cassettes), and research thus far indicates that their analysis requires a more complicated technique than the one described here.

The two key characteristics of processors are the speed with which instructions are executed and main memory capacity. The unit of measurement of memory capacity is straightforward--megabytes. Manufacturers, however, typically offer several sizes of memory for a given processor. In such cases, both the largest and smallest memory configurations for a given processor were included in the study.

Obtaining an appropriate measure of speed was more difficult. Previous studies have generally used the speed of a single instruction--such as add, or multiply--that can be compared across models. However, the speed of a processor is not adequately represented by the rate of executing a single instruction. A weighted composite of all of the instruction execution rates for a typical job mix (or benchmark) is a better representation. A widely used measure of this kind is MIPS--millions of instruction executions per second, in which each instruction is weighted by its frequency of use in a specific job mix. Two types of problems, however, arise with respect to the use of this measure. The first problem concerns comparability. If two processors have different instruction formats or different logic designs, the MIPS ratings are not comparable. They can, however, be made comparable. Assume the MIPS rating of a given processor equals MIPS.sub.1 and that N.sub.1 equals the number of instruction executions in processing the job mix. If some other processor has a rating of MIPS.sub.2 and its number of instruction executions equals N.sub.2 for the same job mix, then the "equivalent MIPS" rating equals MIPS.sub.2.(N.sub.1./N.sub.2.). The second problem relates to the choice of the job mix. It arises because of the difficulty of defining a truly representative benchmark. The advantage of equivalent MIPS as a measure of processor speed is realized only if the specified job mix is representative of the jobs expected to be performed by the processors being compared.

Estimates of equivalent MIPS ratings, expressed in terms of IBM 370-equivalent MIPS, are publicly available for IBM and plug-compatible processors. MIPS ratings published for the processors of other manufacturers may not be expressed in the same terms. To be assured of a consistent and cmparable measure of speed, the work described here is based on IBM and plug-compatible processors.

Disk drives--technically, direct access storage devices (DASD)--are devices that write, store, and retrieve data. They are now the dominant auxiliary storage device. Basically, they consist of stacks of records or disks, centered on a spindle, on which data can be written or from which data can be read. A disk drive may possess one or more spindles. The component that does the actual reading and writing of data is known as the read/write head; until recently, there was one set of heads per spindle. Disk drives are random access devices--that is, they have the ability to move the head to any point on the disk so that the stored data are directly accessible. Data stored on tapes--the main competing storage medium--can be accessed only sequentially. The work described here covered large and intermediate single-density drives that do not possess explicit control functions.

The two key characteristics for disk drives are capacity and the speed with which data can be transferred between the device and main memory. Unlike processors, the measurement of both these characteristics is relatively straightforward. Capacity can be measured by the number of megabytes that can be stored in a device.

The measure of speed, in units of kilobytes per second, consists of three elements. (1) Average seek time (ast) is the average time for the read/write head to locate and arrive at the correct track of the disk. (2) Average rotation delay (arotd) is the time for the disk to rotate so that the read/write head is lined up at the correct point on the track. (3) The transfer rate (tr) is the time it takes to transfer the data, once the correct position on the disk has been located, between the drive and main memory. The total time to transfer a kilobyte of data is the sum of these three elements. The calculations are made under the assumption that the average amount of data transferred at one time is two kilobytes. Under this assumption, speed per set of read/write heads is measured as the inverse of the time it takes to transfer two kilobytes, or as:

Speed = 2 / (ast + arotd + 2/tr).

If there is more than one set of heads per device, the speed of the device is measured as the speed per set times the number of sets.

Printers record the system's output on paper. There are two broad categories of printers: Impact and nonimpact. There are two classes of impact printers: System line printers, which can print an entire line of characters at once, and serial printers, which print one character at a time. Serial printers are used with personal computers and other workstations. They may use daisywheel (for letter-quality print) or dot matrix mechanisms. There are also two classes of nonimpact printers: Page printers, which are based on laser electrophotographic technology, and ink jet printers. The study covered all of these classes of printers.

The three key characteristics for printers are speed, resolution, and the number of fonts available on-line to permit automatic variation of type size, style, and boldness. Speed is measured as characters per second. Resolution is measured by the number of dots per character.

General purpose displays, or terminals, are input-output devices that allow communication between the processor and a user. They possess no data processing capability. A unit consists of a keyboard and a monitor--the former to enter data, the latter to display data. Two types of monitors are available: Cathode ray tube (CRT) and gas panel. The study covered only CRT displays.

The four key characteristics for displays are screen capacity, resolution, the number of colors that can be displayed, and the number of programmable function keys. Screen capacity is measured as the number of characters that can be displayed. Resolution is measured as the number of picture elements per character. Displays also differ in various ergonomic attributes, such as the feel and shape of the keys or tilt positions of the monitor; these are difficult to quantify and are assumed to be uncorrelated with the measured characteristics. In contrast with processors and the other peripheral equipment, speed is not a characteristic for displays. The speed with which information is exchanged between the display and the host processor can be considered essentially independent of the type of display used. The main determinants of speed, as perceived by the user, are characteristics of other components of the system.

Modification of the hedonic function

The use of hedonic regressions is based on the premise that differences in the prices of goods offered in the same market at the same time mainly reflect differences in the characteristics of the goods. When the market under study is not in long-run equilibrium, and when the forces creating the disequilibrium are correlated with the characteristics, a statistical analysis that fails to treat the issue explicitly risks producing biased estimates.

The market for computing equipment is characterized by disequilibrium caused by rapid technological change. Existing products are leap-frogged by products embodying improved technology and manufactured using improved processes. The introduction of the new products induces market disequilibrium. An important aspect of the disequilibrium is that there is a period of time when two sets of prices coexist for products possessing the same characteristics--one price for the products based on the old technology and one for the products based on the new. In this study, the hedonic function was expanded to take this aspect of disequilibrium into account for processors and disk drives by introducing measures of embodied technology into the regressions. The measures serve as proxies for technology-associated differences in production costs and for the attractiveness of technologically superior substitutes. The measures of technology are described next; the ways in which they are introduced into the hedonic regressions are described in the third section. (For printers and displays, it was not feasible to allow for disequilibrium.)

The measures used to represent technology are based on density--that is, the amount of information that can be stored on a given surface area. Semiconductor memory chip density was used for processors, and the recording, or areal density, was used for disk drives.

Semiconductor memory chip density was used for processors because much of the improvement of processors has come from advances in semiconductor technology. Greater speed and memory capacity have been achieved by packaging increased numbers of circuits closer together. With increased densities, the distance electrons travel is shortened; not only can more information be stored, but also instruction execution time is reduced. Improvements in packaging at higher levels (cards and boards) have enabled improvements in computer manufacturing (and reductions in costs) to parallel improvements in chip densities. The use of memory chip density to represent logic technology (its proprietary nature precludes direct comparison) is appropriate only to the extent that logic design is also improved by advances in semiconductor technology. The unit of measurement of memory chip density is kilobits per chip.

By reference to density, the study established eight classes of technology for processors, shown in table 1. The first class is magnetic core, the storage material in use before the shift to semiconductors during the early 1970's. Semiconductors, although initially expensive, reduced by a factor of 50 the space required to store a given amount of information. This new material provided the potential for future improvements in densities. The first semiconductors covered in the sample were bipolar. Of these, there are two classes: The first, introduced in 1972, had a density of 0.128 kilobits per chip; the second had a density of 1 kilobit per chip. They were replaced by field effect transistor (FET) semiconductors, which were produced at substantially lower costs. Of these, there are five classes, over which densities increased from 1 to 64 kilobits per chip.

For disk drives, manufacturers have improved speed and capacity in three ways: By decreasing the distance from the read/write head to the disk, by decreasing the head-gap length (that is, the distance between the reading and writing elements on the read/write head), and by decreasing the thickness of the recording medium on the disk. Each of these improvements makes it possible for the head to read information from a smaller area on the disk. The unit of measurement of areal density is the number of kilobytes per square inch.

The first two of the nine technology classes for disk drives consist of those designed to handle disk packs that could be removed (table 1). The first, introduced in the mid-1960's, had an areal density of 220 kilobytes per square inch; the second, introduced in 1972, had a density of 776. In the mid-1970's, separate technologies were introduced for intermediate and large disk drives. The first intermediate drives had a density of 1,691 kilobytes per square inch. This type was called the "Winchester," and it had disks and read/write heads that were packaged together in a removable unit. Other intermediate drives, as well as large drives, had fixed disks--that is, they could not be removed. The first of the large drives, introduced in the mid-1970's, had areal densities in excess of 3,000 kilobytes per square inch. The current generation of large disk drives, introduced in the early 1980's, has areal densities in excess of 12,000 kilobytes per square inch--densities 55 times greater than the densities of the devices introduced in the mid-1960's.

II. The Data

The samples for all four system components contain annual data for 1972-84. Each sample contains information on prices and characteristics for each model used in the regressions. Prices for IBM models in the samples were taken from IBM sales manuals. In general, prices for non-IBM models and information on characteristics for all models were drawn from trade and general press sources, as indicated in the descriptions of the sample data that follow.

The processor sample consists of 67 different models from 4 manufacturers. Prices refer to the central electronic complex, which includes--in addition to the central processing unit and main memory--the minimum required gear, such as standard channels, the console, and the power supply unit. For non-IBM processors, prices, main memory sizes, and information on the minimum required gear came from the trade and general press. MIPS ratings for all models appearing prior to 1981 are from "Tracking Those Elusive KOPS," in Datamation of November 1980; ratings for models introduced after 1980 are from the annual "Hardware Roundup," in Computerworld of July 1981 and August 1982, 1983, and 1984.

Average annual prices for processors were obtained by weighting the different prices prevailing within a year by their respective durations. For non-IBM processors, dates of price change were taken from the press; when no reports of change were located, prices were assumed unchanged.

The sample for disk drives consists of 30 devices marketed by 10 vendors. Characteristics and prices were compiled from a number of sources. The main ones were the series of annual reports for 1973-85 published by Datapro Research Corporation and Disk Trend Reports for 1976-84 published by J. Porter.

The printer sample consists of 480 models from 126 vendors. Characteristics and prices are from reports published by Datapro Research Corporation for 1972-84 and from Electronic Printer Industry Services, a series of reports published by Dataquest, Inc., for 1983 and 1984. The display sample consists of 772 models from 115 vendors. Characteristics and prices are from Datapro's series of annual reports, "All About Alphanumeric Display Terminals," 1973-84.

It was necessary to devise rules to determine how long a model appears in the sample. In principle, a model should appear as long as it is being produced. For IBM models, it was possible to determine this directly; other models were a problem. For non-IBM processors, a model was entered the first year it appeared in the annual tabulations of the stock of installed computers in the United States prepared by the International Data Corporation and published in EDP Industry Reports, and it was deleted the year after the stock peaked. A non-IBM disk drive model was entered in the sample in the year in which it was first shipped and deleted the second year after a new generation of technology was introduced. Non-IBM printer and display models were carried in the sample as long as they appeared in annual Datapro reports.

The price data have serious limitations. First, they are list prices for a quantity of one. Because discounting is a widespread practice in the industry, particularly on multiple-unit sales, the prices do not represent transaction prices. Second, prices for non-IBM peripherals refer to a point in time rather than the full year. Point-in-time prices may distort estimates of year-to-year change because any price change occurring after the survey date will not be reflected until the following year.

III. Regression Results

The authors had strong views with respect to the variables to be included in the hedonic regressions and weaker notions with regard to the functional form. A double-log form was tried first, and Box-Cox transformations were used to test alternatives. The results indicated that, for all product types, the double-log form is preferred to the semilog and linear forms.

Regressions were estimated for time periods of varying lengths, including single years, groups of adjacent years, and the entire 1972-84 period. For the sake of simplicity and ease of exposition, only the results for the regressions estimated for the entire 1972-84 period are shown in table 2.

Results denoted "I" refer to a traditional hedonic regression of price as a function of characteristics and year dummies. The estimated coefficients from these regressions suggest that speed is more important than main memory capacity for processors, but that capacity is somewhat more important than speed for disk drives. Speed is the most important characteristic for printers, followed by resolution and the number of on-line fonts. The number of colors and resolution are almost equally important for displays; capacity and the number of programmable function keys are much less important.

Modified regressions for processors

and disk drives

The information on technology in table 1 was used in the hedonic regressions in two alternative ways. In table 2, the results of these regressions are denoted "II" and "III." In II, technology is represented by a set of dummy variables for each year for the technology classes described earlier. For example, a processor with memory using 4 kilobit ("4K") chips was coded as belonging to technology class 6 by entering "1" for that class and "0" for the other classes.

In III, technology is represented by a set of three technology variables: Embodied, or "own," technology; "best" technology; and age of own technology. (1) The own technology variable is measured directly. For example, the value of the variable for a processor with memory using 4K chips was "4" in each year. The own technology variable is an indicator of the sophistication of the technology employed in manufacturing a given processor or disk drive. Because employment of more advanced technologies permits the same characteristics to be produced at lower costs, this variable can be considered as an exogenous "supply shifter." (2) The "best" technology is a variable that takes the value of the greatest density available in each year. It has the same value for all processors within any year. (In years during the transition to a new technology, the value of the "best" technology variable was taken as an average of the current year and the preceding 2 years.) This variable represents the competitive pressure to lower prices that is exerted by technologically superior substitutes. (3) The age of own technology variable is defined as the number of years since introduction of the technology. In any year, it has the same value for all models embodying the same technology. Age is expected to be important for at least two reasons. One is that lower costs and cheaper prices are achieved with the efficiency in production that comes with experience. The second reason is expected obsolescence on the demand side. The older a technology, the less buyers will be willing to pay because the probability increases that new products based on cheaper technology will soon become available.

In addition, for disk drives, another variable was added--a portable drive dummy. It was assigned a value of "1" when the product has a removable disk and a value of "0" when it has a fixed disk. Including this variable permits the intercept of the regression equations to be different for drives with removable disks and fixed disks.

Comparison of equations II and III with equation I shows that the technology information, in one specification or another, can substantially reduce the standard error of the traditional hedonic equation. For processors, the information on technology in the form of technology class by year dummies yields better results than in the form of the set of technology variables: The standard error is reduced from 0.062 in equation I to 0.039 in equation II; it is doubled to 0.129 in equation III. In contrast, for disk drives, the information on technology in the form of the set of technology variables yields better results: The standard error is reduced from 0.051 in equation I to 0.038 in equation III; it is marginally reduced to 0.050 in equation II. A likely explanation of these differences is that areal density is a better measure of technology for disk drives than memory chip density is for processors. Improvements in logic technology, though highly related to memory chip density, may not be well measured by increases in densities. Although significant for processors, the "best" technology variable was insignificant for disk drives. The results without this variable for disk drives are denoted equation III'.

For disk drives, although not for processors, the inclusion of technology variables in both specifications has a marked effect on the estimated coefficients for speed and capacity. The effect is to raise the estimated importance of capacity relative to speed. The inclusion of the technology variables gives more plausible results; one would expect capacity to be more important than speed for large- and intermediate-size storage devices.

Table 3 shows the estimated coefficients for the technology class by year dummies for processors for equation II. The coefficients in the first column are estimates of the logarithm of ratio of the price of the products embodying the "best" technology in 1972. These coefficients can be converted to index numbers, with 1972 = 100, by taking the antilog of each year's value and multiplying by 100. For example, the coefficient -0.746 in 1975 means that the price index for processors embodying the "best" technology equals 47.4 after allowing for differences in speed and storage capacity.

The coefficients in each row to the right of the double line are the estimates of the logarithm of ratio of the price of each "nonbest" technology to the price of the "best" technology in the same year. For any given year, the coefficients can be stated relative to the price of the "best" technology in that year by taking the antilog of the coefficients and multiplying by 100. For example, the coefficient 0.524 on technology class 5 for 1975 means that the price of products in this class was 168.9 percent of the "best" in 1975 after allowing for differences in speed and storage capacity. In most cases, the coefficients indicate that prices tend to be higher for "nonbest" (and usually older) technologies than for the "best." Moreover, the t statistics indicate that 16 out of 24 of these price differentials are significantly different from zero.

Comparisons across technology classes within a given year show cases where the coefficient for a "nonbest" technology is not statistically different from the coefficient of the "best" technology, of another "nonbest" technology, or of both. Formal tests of the equivalence of regression coefficients lead to a simplified version of equation II, denoted equation II', for which results are shown in the lower panel of the table. It involves two kinds of restrictions: (1) Coefficients are set equal to zero if not statistically different from zero (for example, class 4 in 1976) and (2) coefficients within a given year were constrained to be equal if they did not differ significantly from one another (for example, classes 4 and 5 in 1977). The results of equation II' similarly indicate the existence of multiple prices.

The only "nonbest" technology that sold for less was magnetic core memory in 1972. The shift to semiconductor memory took place during this period, and--because it was clear that further improvements were much more likely to come from semiconductors--core was considered obsolete.

For disk drives, all except one of the estimated coefficients for the technology class by year dummies in equation II, shown in table 4, are positive and are larger the older is the technology. However, the t statistics indicate that only four of the estimated coefficients are statistically significant. Similar but stronger results are provided by the estimated coefficients of the set of technology variables in equation III' of table 2, which suggest that multiple prices exist and that--because coefficients are negative--older technologies sell for more than newer ones. The hypothesis of multiple prices was further tested by an alternative equation containing both the technology variables and year dummies. The appropriate F tests indicate that one cannot reject the hypothesis that the coefficients on the technology variables are 0 when the year dummies are included. Thus, there is cross-sectional variation in the sample beyond that captured by speed and capacity measures, and the technology variables capture it.

In table 5, the information from the lower panel of table 3 and from table 4 is recast into the form of price indexes having the 1972 "best" = 100. This presentation makes it easy to see the course of the price changes of a given technology class. As seen by the pattern of generally declining prices reading down the columns, older technology classes have continually and rapidly falling prices in response to competitive pressure from newer technology classes.

In summary, the introduction of products embodying new technology leads initially to multiple prices, with the products based on "nonbest" technologies selling for more. The prices for older products decline rapidly, until they either match the quality-adjusted price of products based on the new technology or the products disappear. The claim that improved technology leads to reduced costs and, hence, to a lower quality-adjusted price is consistent with a competitive marketplace in which only one quality-adjusted price (the "best") ultimately prevails. It was found that in many cases price reductions permit an older technology to compete with a newer one for a limited time, but as the new technology becomes diffused, its own age-related cost and price reductions eventually drive the older technology out of production. The evidence presented here suggests that prices reflect this process of adjustment and that equilibrium is not reached within a period as short as 1 year.

Prices for characteristics of

processors and disk drives

The hedonic equations can be used to derive estimates of implicit prices for characteristics. Such prices are shown in table 6 for processors and disk drives. Each estimate is a marginal price, or price for an incremental unit, of capacity and speed. (The specific formula is presented in the footnote to the table.)

The estimated characteristics prices fell sharply between 1972 and 1984. The most dramatic drops occurred in prices of capacity. In 1984, the price of one megabyte of main memory was less than one-twentieth the 1972 price. The price of one megabyte of auxiliary storage (in the disk drive) was about one-ninth the 1972 price. Main memory was almost twice as expensive as auxiliary storage until processors embodying the 64K memory chip were introduced in 1979. After that year, the price of data storage was essentially the same, whether in main memory or in auxiliary storage.

The estimated prices of speed fell less rapidly. In 1984, the price of executing one million instructions per second was about one-ninth the 1972 price. The price of transferring one kilobyte of data per second from the disk was about one-half the 1972 price.


Further tests of the hedonic equations were conducted. The hypothesis that the characteristics coefficients sum to one could not be rejected for any of the four types of equipment. The finding that the implicit characteristics prices for these products are probably homogeneous to the first degree is appealing. Homogeneity implies that the valuation of characteristics quantities equals the observed price of the product.

IV. The Price Indexes

The price index used as a deflator to convert current-dollar values to constant-dollar values is a Paasche formula index, (1) I.sub.o,t = [sigma][sigma] where, for model i, and denote prices in the current and base periods, respectively, and denotes the quantity purchased in the current period. The problem encountered in constructing such an index for products experiencing rapid change is that models purchased in the current period may not have existed in the base period.

Matched-model index

The most frequently used approach for dealing with the problem uses observations only for the models that exist in both period t and in period 0. Models that exist only in the current period are ignored. Such an index may be referred to as a "matched-model" index.

Because computing equipment changes so rapidly, it was not possible to calculate a matched-model index using equation (1). Instead, matched models for 2 adjacent years were used to calculate an index where the base period is the first of the 2 years (that is, t -- 1): (2) I.sub.t-1,t = [sigma][sigma]P.sub.i,

An index for the entire period is calculated as a multiplicative "chain" of the adjacent-year indexes: (3) I.sub.o,t = I.sub.o1 X I.sub.12 X . . . X I.sub.t-1,t.

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

The assumption underlying the matched-model procedure is that the mean price change associated with the introduction of new models (or the discontinuance of old ones) equals the mean price change observed for models that are common to both periods. In terms of the analysis of technological disequilibrium presented earlier in this article, one can state this assumption in an alternative and illuminating way: Use of the matched-model procedure assumes that prices of models embodying old technology adjust instantaneously, so that their quality-adjusted prices are equal to those of the models embodying improved technology. If the assumption holds, the price change in the matched models equals the unobserved price change implicit in the introduction of new models (or the discontinuance of old ones).

Three hedonic indexes

Use of hedonic methods does not require the assumption that the observed price change in the matched models equals the unobserved price change. Hedonic methods make use of all the price information. They can be employed in a number of ways. The present study explored three alternatives.

The composite index. --The "composite" index uses prices from the matched-model approach whenever models exist in both current and base periods and hypothetical prices for the models that did not exist in the base period from hedonic equations. If an "overlap" model (one that exists in both periods) is designated "i" and a model present in period t but not in period 0 is designated "j," then the composite index is: (4) I.sub.ot = [sigma]i + [sigma]j P.sub.jt.Q.sub.jt./[sigma]i + [sigma]j

In this formula, denotes the estimate, taken from the hedonic equation, of the hypothetical price that the "missing" model would have commanded in the base period. Note that when 1982 is the base (as it is for all the present calculations) and a year subsequent to 1982 is "year t," then is the hypothetical price for a new model. When a year earlier than 1982 (such as 1977) is "year t," then is the hypothetical price for a discontinued model.

When there are multiple prices in the base period, some convention must be adopted in estimating because there is more than one price prevailing for any specified set of characteristics. In this study, the dominant technology--that is, the technology embodied by the majority of models shipped in the base period (1982)--was used to determine the hypothetical price In 1982, for processors, the majority of models shipped were from technology class 8; for disk drives, the majority were from technology class 4.

The characteristics price index. --In hedonic studies, one can identify more than one kind of price. The conventional concept is that of the price of the model. A second concept is that of the prices of the "characteristics." One can use the estimated characteristics prices--such as those shown in table 6--to construct a price index.

Given the formulation of the hedonic functions, the implicit dollar price of the kth characteristic possessed by the ith model of the mth technology class would be: (5) P.sub.kimt = b.sub.k P.sub.imt./, where b.sub.k is the regression coefficient for the kth characteristic (estimated as constant for all years of the study), denotes the quantity of the kth characteristic possessed by model i, and P.sub.imt is the price for model i, of technology class m, at time t.

The characteristics price index is: (6) I.sub.ot = [sigma]k[sigma]m[sigma]i (P.sub.kimt) ( Q.sub.imt.)/[sigma]k[sigma]m[sigma]i (P.sub.kimo) ( Q.sub.imt.), where Q.sub.imt denotes the quantity of the kth characteristic possessed by model i of the mth technology class in period t.

The regression index. --The regression index was created from the year dummies in the regressions. The price index number formula for the regression index is based on the expression for the regression coefficients for the year dummies.

Regression indexes may produce indexes that differ from alternative indexes that use hedonic methods. (In the present case, for example, the regression index is unweighted, whereas the composite and characteristics price indexes employ shipments weights.) Several econometric shortcomings of the regression index have been pointed out. However, because the regression index is so frequently encountered in other hedonic studies (including those for computing equipment), it was calculated in this study for purposes of comparison.

The four price indexes

In calculating the three hedonic indexes, the results from equation II' were employed for processors and the results from equation I for printers and displays. For disk drives, results from equation III' were used for the composite and characteristics price indexes; the regression index was based on equation II results. It was necessary to develop estimates of quantities shipped for the products in which models were distinguished by class. For processors, the quantity shipped of each model was approximated from the annual tabulations of the stock of installed computers prepared by the International Data Corporation. For disk drives, no information on shipments by model was available. Estimates of shipments by technology class were developed from information from International Data Corporation's studies and from Disk Trend Reports, published by J. Porter, for 1976-84. For printers, estimates were developed by class from information published by Dataquest, Inc. Except for processors where shipments were available by model, the prices for models within a class were averaged to obtain the estimated price for the class.

Table 7 shows the four price indexes calculated for each of the four products. The matched-model indexes decline much less than the three hedonic indexes. For processors, the matched-model index declines at an annual rate of 8.5 percent from 1972 to 1984, compared with declines in the hedonic indexes ranging from 17.6 percent to 19.2 percent. For disk drives, the matched-model index declines at an annual rate of 6.9 percent, compared with declines ranging from 12.6 percent to 16.9 percent. For printers and displays, the matched-model indexes decline much less than one-half as much as the hedonic indexes.

In the case of processors, the matched-model index does not reflect the introduction of semiconductor technology nor its subsequent rapid price declines. It also continued to miss the price declines associated with major improvements in the semiconductor technology during the 1978-80 period. All four indexes move roughly together in 1983-84, when no new technologies were being introduced. In the case of disk drives, the matched-models index does not reflect the adjustment to new technologies in 1975-78 and 1982-84. All four indexes move similarly during 1972-75 and 1978-82. In the case of printers, the four indexes move together through 1982. From 1982 to 1984, however, the hedonic indexes dropped 70 to 80 percent and the matched-model index only 10 percent. The latter misses the surge of the low-priced serial printers, the majority of which were imports. The matched-model index for displays shows little movement over the entire period.

V. Conclusion

Although there may be widespread agreement that the present procedure for deflating expenditures on computing equipment is inadequate, a completely satisfactory alternative is not readily devised. Such a claim is certainly not made for the present study. Rather, it is more in the nature of a first step.

One deficiency of the study, and there are several, relates to its scope. Price indexes for personal computers and small disk drives were not produced. While work is underway on these products, the results are too tentative to report at this time. Another deficiency, and one less easily corrected, relates to the use of list rather than transaction prices. Ideally, a price index requires transaction prices. In particular, a thoroughly convincing case for the presence or absence of multiple prices requires the use of transaction prices.

The study demonstrated the inappropriateness of a matched-model index for computers. Even where there are no major technological shifts, such as for printers or displays, the matched-model index understated movements in prices. This understatement occurs because the matched-model index misses the replacement of old, higher priced models by new models, manufactured by improved methods and introduced at lower quality-adjusted prices.

In the authors' view, hedonic methods--applied at the system-component level, employing appropriate measures of characteristics, and expanded to deal with the problem of technologically induced disequilibrium--are useful for constructing quality-adjusted price indexes and represent an improvement over the present procedure for deflating expenditures on computing equipment.
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Title Annotation:IBM's work on developing quality-adjusted price indexes; see also revised estimates of national income and product accounts
Author:Cole, Rosanne; Chen, Y.C.; Barquin-Stolleman, Joan A.; Dulberger, Ellen; Helvacian, Nurhan; Hodge, J
Publication:Survey of Current Business
Date:Jan 1, 1986
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