Quality-Adjusting Computer Prices in the Producer Price Index: An Overview
Michael Holdway

In 1991, the Producer Price Index (PPI) expanded its coverage to include the output of the computer industry.¹ Computers have consistently exhibited rapid technological change that must be taken into account to avoid biased estimates of inflation.² For example, a mainstream desktop computer that sold for $2,200 in 1993 may have included a 33 megahertz (MHz) central processing unit (CPU), 8 megabytes (MB) of dynamic random access memory (DRAM), a 210MB hard drive, a 15-inch monitor, as well as many other defining technological characteristics. In 1998, however, a desktop computer that sold for $2,200 could easily have been configured with a 450MHz CPU, 128MB of SDRAM, an 8,000MB hard drive, a 17-inch monitor, and included other advanced features unavailable in 1993, such as a DVD player and 3D-graphics capabilities. In this example the observed prices for the 1993 and 1998 computers are identical. However, technological change over this 5-year period has been remarkable: CPU speed (MHz) jumped 1,263 percent (this actually understates the change in CPU performance³), system memory increased 1,500 percent, hard drive capacity increased 3,700 percent, and monitor size increased 13 percent. A computer price index that did not account for these significant quality improvements, that is, an index that showed no price change for the period in question, would clearly have an upward bias as a measure of quality-adjusted computer prices. This difficult price measurement issue has received extensive coverage in various econometric research papers, providing some of the basic principles followed by the PPI in accounting for technological change in computers.

Before proceeding to a general description of hedonic modeling in the PPI, it is important to understand a fundamental difference between the hedonic models presented in the referenced papers and the PPI implementation. I refer to time dummy variables that are commonly used in the pooled secondary source data employed by much of the econometric research that explore price dependencies in high technology products. The PPI departs from this approach, in that it does not apply time dummy variables. In other words, cross-sectional—rather than pooled—data sources are used to construct hedonic models.

It may be helpful to provide a brief summary of computer product hedonic models, which have been developed outside of BLS that explicitly identify time as an independent variable. Most of these models are based on pooled data that are segmented with time dummy variables to enable the direct construction of a quality-adjusted price index. A variety of functional forms and model specifications have been developed over the years, but a simplified example of the underlying hedonic equation could take the form:

Equation (1)

Where:

P_it is the price of the i^th model in period t;

D_t is a time dummy variable;

X_i is a variable representing observed computer characteristics, such as CPU speed, hard drive capacity, etc.;

u_i is the residual or error term; and

d_t represents the percentage change in price across time intervals defined by D_t holding quality constant.

Different strategies can be applied to the estimation of equation 1, such as the pooled approach. Pooling enables maximum sample size, but is complicated by dissimilarity in computer characteristics between time periods due to rapid obsolescence and introduction of new technologies. Another strategy that may minimize the problem of rapid evolution in characteristics’ space is the adjacent period approach. The adjacent period approach disaggregates the pooled data spread over many years into a series of regressions that are limited to data from two or more periods. Experimentation with varying time spans may allow several adjacent periods to be pooled.

Quality adjusted price indexes that are obtained from adjacent period regressions can be generated in a variety of ways, with the most common approach using estimates of (d_t ) to construct these indexes. Other methods used to create quality adjusted price indexes involve comparison of implicit prices for characteristics over time, in which quantities of characteristics serve as weights. Diewert (1980) describes such an approach that utilizes a Fisher Ideal Index formula. Because there are many different approaches, including type of computer product modeled, preferred functional form, and selection of independent variables, the mechanics are best understood from a direct review of various research papers. Interestingly, published results from these papers are remarkably similar. Chow (1967) calculated that quality-adjusted mainframe prices declined 21 percent annually, from 1960 to 1965, Gordon (1989) reported quality-adjusted mainframe prices fell 22 percent per year from 1951 to 1984, and Triplett (1989) summarized much of the work on mainframes and reported his findings of a 27 percent annual rate of decrease from 1953 to 1972. Gordon (1990) extended his hedonic work into personal computers and found 30 percent annual declines from 1981 to 1987, and Berndt-Griliches (1990) collected a large sample of personal computer data from 1982 to 1988 and reported 28 percent annual decreases.

The Bureau of Labor Statistics began its own research into hedonic modeling of computer products in 1987. The PPI opted for a cross-sectional—rather than pooled—approach, due to limited resources and rapid technical changes in the characteristics that define computers. With cross-sectional models, the PPI does not attempt to directly construct price indexes for computers, but instead uses the model's implicit prices for computer characteristics to adjust directly reported producer prices, when technical changes are introduced.

The PPI measures price change, by first sampling those producers whose plurality of shipments fall within a defined industry, such as Electronic Computers, SIC 3571.⁴ The probability of a firm's selection is proportionate to its employment size. Once a firm is selected, products and services within an establishment are sampled, according to the probability-proportionate-to-size method that, in turn, is based on estimated sales data by product line supplied by a company representative. Ideally, the PPI would specify a hedonic model supported by computer characteristics and prices taken directly from the PPI sample. However, due to the complexity of computers, a properly specified model can easily include 20 or more characteristics, which would require a database too large for the PPI sample to support. Sampling techniques allow the PPI to capture data from a small but representative number of computer producers (currently 30) that report monthly price and specification data for 121 products. These sampled products are disaggregated into five product categories, ranging from large-scale (host system) computers to portable computers. The most important computer category, in terms of revenue (based on value of shipments provided by the Bureau of the Census) is personal desktop computers (PCs), represented in the PPI by 37 models. The PPI's sample size is designed to accurately represent the output of the domestic computer industry, but limited resources preclude expanding the sample size to support a fully specified hedonic model. As a result, the PPI uses secondary data sources to generate hedonic models for computers. The secondary data sources are product specific. For example, the PPI constructs separate models for portable computers, personal desktop computers, entry-level/mid-range computer servers, and large-scale computers. These hedonic models are updated on a semi-annual or quarterly basis, because of the rapid technical changes that preclude the possibility of maintaining a matched model.⁵

The PPI's use of hedonics to quality adjust computer prices has evolved over the years. As recently as 1996, databases supporting PPI models were constructed from manufacturers' advertisements in Computer Shopper magazine. One of the advantages of direct producer repricing in the PPI is that the Bureau is in monthly contact with both large and small domestic computer manufacturers. This regular contact has given BLS staff the opportunity to ask specific questions about various technical inconsistencies and errors that often occur when secondary data sources are used to construct a model. In 1997, several manufacturers stated that more reliable and comprehensive technical data was available on their web pages. Many of these Internet sites include configuration utilities that calculate selling prices for a range of technical features that are available in currently shipping products. As a test, the PPI developed a hedonic computer desktop model in February 1997 entirely from producer website data that was roughly comparable to what was available from Computer Shopper magazine in the same time period. The Internet-based model provided higher precision estimators and enabled direct real-time feedback for correcting or clarifying technical descriptions that were not readily available from 3^rd party advertisements.

The regression formula used in a recent PPI hedonic model for personal desktop computers is shown in equation 2, and the corresponding June 1999 results are shown in table 1.

Equation (2)

Note that equation 2 takes a linear form and does not include a time variable, as in equation 1. The selection of functional form is evaluated in terms of statistical precision, reasonableness of absolute values, R-square and F-tests. Log-log forms are often strong candidates; but the linear form has consistently prevailed, when all of the mentioned tests are performed. Single log (on either side of the equation) has generally run a poor third. As a side note, the Log-Log form has, in fact, proven superior to the linear form in our laser printer models.⁶

 

Table 1. Hedonic model regression results for personal desktop computers, June 1999

	Coefficient	Standard error	T-statistic	P-value
Constant	619.925	81.685	7.589	0.000
CPU per MHz	3.533	0.079	44.9270	0.000
Celeron CPU*	-277.538	11.558	-24.013	0.000
SDRAM/MB	1.686	0.079	21.232	0.000
HD/MB	0.020	0.001	19.221	0.000
100MB ZIP*	96.702	11.430	8.460	0.000
DVD (4.6/6.0)*	95.459	16.039	5.952	0.000
Video/MB	5.076	0.948	5.357	0.000
Sound card and 2 Speakers*	24.184	14.070	1.719	0.086
Speakers and Sub*	77.246	12.238	6.312	0.000
Speakers and Premium Sub*	172.473	14.842	11.621	0.000
56.6 fax modem*	27.919	9.364	2.982	0.003
10/100Mbs NIC*	49.287	11.165	4.414	0.000
Monitor, 15 inch*	246.919	21.733	11.362	0.000
Monitor, 17 inch*	296.941	15.763	18.838	0.000
Monitor, 17" Trinitron*	370.599	16.135	22.969	0.000
Software Office Suite*	62.568	18.614	3.361	0.001
MS Office Suite SBE*	228.880	14.088	16.246	0.000
MS WIN NT OS*	111.235	10.911	10.195	0.000
Business Market	268.988	21.689	12.402	0.000
3-year On-Site Warranty*	155.622	16.225	9.591	0.000
Company A*	257.225	13.549	18.984	0.000
Company B*	139.632	21.100	6.618	0.000
Company C*	-121.727	18.676	-6.518	0.000
* Dummy variable

Observations = 685

Dependent variable: Price

Standard Error = 85.2

Adjusted R-Square = 0.963

F = 773.6

The regression results in table 1 are from June 1999 and include 685 observations of desktop computers obtained from producer websites on the Internet.⁷ These Internet sites have evolved over time to include online processing of direct sales from the producer to the end user. Typically, a buyer can view technical specifications and prices for a range of pre-configured computers and then complete the purchase online or through a toll-free telephone number. However, most computer producers offer buyers greater flexibility by providing a broad customization of features that can be added to, or deleted from, the pre-configured models. For instance, a pre-configured model that includes a 500MHz CPU is also available with a faster or slower CPU, more memory, or a monitor upgrade. A buyer can chose options most appropriate for their application and budget, and the producer will instantly recalculate a price based on the buyer's selection of those computer characteristics. A variety of producer websites representative of the PPI sample will typically be used to build a data base.

The number of sites used in PPI models will vary, according to the type of product. Desktop computer models will generally include five or more sites and require an average of 2 weeks of data review and entry for the industry analyst to build a completely specified model of 600 or more observations. Then, another 2 weeks are used to explore data relationships, run various regressions, and analyze the results. Proper analysis is approached from both a statistical and industry knowledge perspective. Because of the extensive resource requirements that are used to build models that are representative of the current composition of the PPI, the Bureau is only able to update the desktop computer database on a quarterly basis. Each database is structured to ensure that the most important PPI computer producers are included. (The majority of the top 10 domestic producers are represented in the PPI.) Several dummy variables are used in the model. For example, the Celeron CPU coefficient⁸ in table 1 is relative to the presence of a Pentium II CPU. Company-effect dummy variables are also used, in this case referred to as Company A through C, to avoid the possibility of disclosing companies that are in the database but also report prices directly to the PPI. Only companies that tested as statistically significant are included as dummies. The interpretation of a company-effect variable is that it may capture otherwise unspecified price determining factors, such as name recognition, buyer loyalty, and warranty policy; factors that provide a limited company-specific price differentiation that go beyond the explanatory powers of the explicitly defined characteristics. To illustrate how regression results are used in the PPI to obtain the quality-adjusted price relatives that make up the desktop computer index, a hypothetical example is described below.

Computer Reported to PPI, Period (t-1)		Computer Reported to PPI, Period (t)
Desktop personal computer		Desktop personal computer
Model 100		Model 100
Pentium II 400MHz with 512K L2 cache		Pentium II 400MHz with 512K L2 cache
32MB SDRAM system memory		64MB SDRAM system memory
4.5GB EIDE hard drive		4.5GB EIDE hard drive
4MB SGRAM video		4MB SGRAM video
20X CD-ROM		20X CD-ROM
16-bit sound card		16-bit sound card
56.6 fax-modem		56.6 fax-modem
15-inch monitor (0.26 dot pitch)		15-inch monitor (0.26 dot pitch)
Windows 95 and MS Office SBE		Windows 95 and MS Office SBE
Reported net price in period (t-1) = $1,500		Reported net price in period (t) = $1,500

 

Estimated Value of Improvement from Period (t-1) to Period (t)

System memory increase from 32MB to 64MB

32MB additional SDRAM * $1.686 (unit value from table 1) = $53.95

Quality adjusted (QA) price change = (P_(t) - QA) / P_(t-1)

= (1,500 - 53.95) / 1,500

= -3.6 percent

 

This example is based on the assumption that the PPI is repricing a computer configured with 32 megabytes of SDRAM that sold in period (t-1) for $1,500 that the producer upgrades to 64 megabytes of SDRAM in period (t). The reporter indicates that the current period price for the upgraded model is still $1,500, and that the producer cannot provide a value for the change in production cost that is directly attributable to the additional 32 megabytes of SDRAM. If the PPI did not have a hedonic model, prices would be directly compared and, in effect, would show no price change for this product despite the quality improvement. With the implicit unit memory price generated by the hedonic model, the PPI has a method for valuing this change. The implicit price of $1.686 per unit of SDRAM is obtained from the SDRAM variable in table 1 and multiplied by the 32 unit (megabyte) increase in period (t), to yield a total quality change valuation of $53.95. The hedonic model is simply a tool that estimates the average change in price for the 685 observations (minus df) for a unit change in a continuous variable or the absence or presence of a dummy variable. The remaining quality adjustment calculation is straightforward, as shown in the example. Of course, if more than one quality change had occurred; and the relevant characteristics were specified in the model, we could sum the implicit prices for these changes and calculate a multi-factor quality adjusted price relative from the nominal prices reported to the PPI.

The PPI continues to use Internet-based data sources to update computer models, because of the improved accuracy of technical descriptions and pricing data. However, the PPI maintains its traditional index construction methods that are based on directly reported producer prices for specified products sold under specified terms. The PPI does not attempt to use hedonic models for any purpose other than to obtain valuations (implicit prices) for changes in specific computer technical characteristics reported to the PPI.

 

Michael Holdway is an economist with the Office of Prices and Living Conditions at the Bureau of Labor Statistics.

References

Berndt, E. R., and Griliches, Z. (1990), "Price Indexes for Microcomputers: An Exploratory Study," Working Paper 3378, National Bureau of Economic Research, Cambridge, MA.

Berndt, E. R., Griliches, Z., and Rappaport, N. R., "Econometric Estimates of Price Indexes for Personal Computers in the 1990's," Journal of Econometrics, 68, 1995, pp. 243-268.

Chow, G. C. (1967), "Technological Change and the Demand for Computers," American Economic Review, 57, 1117-1130.

Diewert, W. E. (1980), "Aggregation Problems in the Measurement of Capital," ed. D. Usher, Chicago: The University of Chicago Press, pp. 433-528.

Gordon, R. J. (1989), "The Postwar Evolution of Computer Prices", in Technology and Capital Formation, editors D. W. Jorgenson and R. Landau, Cambridge, MA; MIT Press, pp. 77-125.

Nelson, R. A., Patterson, C. D., and Tanguay, T. L., "A Quality-Adjusted Price Index for Personal Computers," Journal of Business and Economic Statistics, January 1994, pp. 23-31.

Triplett, J. E. (1989), "Price and Technological Change in a Capital Good: A Survey of Research on Computers," in Technology and Capital Formation, editors D. W. Jorgenson and R. Landau, Cambridge, MA; MIT Press, pp. 127-213.

Triplett, J. E. (1986), "Economic Interpretation of Hedonic Models," Survey of Current Business, January 86, pp. 36-40.

Notes

1 On an experimental basis, computer price indexes were calculated by the PPI from 1987 to 1990. The PPI introduced computer price indexes on an operational basis, effective December 1990. See James Sinclair and Brian Catron, "An experimental price index for the computer industry," Monthly Labor Review, October 1990, pp. 16-24.

2 Biased index movement in the PPI can directly introduce bias into other measures of economic performance, such as gross domestic product (GDP) and productivity.

3 Consumers commonly focus on CPU clock speed when judging a computer's performance potential, quoted in megahertz (MHz). This single number is more confusing than enlightening in today's environment of multiple competitive processors; one processor running at a particular MHz can significantly outperform another processor rated at the same MHz, and processors based on different architectures are difficult to compare, without objective benchmarking. Relative to 1993, current-generation CPUs have larger caches, much deeper pipelines, branch prediction, out-of-order execution, and several other architectural enhancements that allow more instructions to be executed per clock cycle.

4 As defined by the Standard Industrial Classification System (SIC) that in turn, is based on research provided by the multi-agency Technical Committee on Industrial Classification (TCIC) chaired by the Office of Management and Budget (OMB).

5 Berndt, Griliches, Rappaport, in Econometric Estimates of Price Indexes for Personal Computers in the 1990's, referred to the matched model problem in their database. They describe an index based on the matched model premise as including only "…those models which survive unchanged year-to-year, any incremental improvements in a particular model (e.g., a faster processor) disqualify it from the index." They also discovered that a matched model index for computers is impractical. Their database included computer observations from 1989 to 1992. Only 8 percent of the 1989 models survived in 1990, using the matched model restriction. The situation worsened in 1992, when only 3 percent of the 1991 models were intact. Personal desktop computers in the PPI experience about a 3-month average life expectancy, based on the matched model definition.

6 The PPI has also developed models that are used to quality-adjust the rapidly growing disk storage array product category (PPI code 3572-1145).

7 Computer resellers (retail or wholesale) that market computers through online stores are excluded from our databases. This type of transaction is out-of-scope for the PPI's coverage of SIC 3571.

8 Which is why the coefficient for the Celeron dummy variable has the correct negative sign. (See table 1.)

 

Last Modified Date: October 16, 2001