Hedonic Models in the Producer Price Index

U.S. Bureau of Labor Statistics
Producer Price Index Program
June 2011

Valuing changes in the quality of products or services is one of the oldest measurement challenges facing statistical agencies around the world. The Producer Price Index (PPI) program has developed and adopted several methodologies to respond to these quality measurement challenges, but the primary focus here will be on hedonic methods.¹ One of the most widely recognized pioneers in applied hedonic research was Griliches (1988) who stated that "...one might use regression techniques to relate the prices of different models or versions of a commodity to differences in their characteristics, and discover thereby the relative valuation of such qualities is reasonably obvious.” The terms hedonics or hedonic models are often used by economists when referring to a form of econometrics (Gujarati 1995). At its most basic, hedonics can be described as a regression designed to isolate and measure the influence on price of economically meaningful product characteristics. In other words, a product must first be disaggregated into its characteristics. For instance, a computer can be disaggregated into characteristics such as speed of processor, hard drive capacity, amount of memory, and many other defining features that influence the computer’s price. These product characteristics enter a regression as independent (explanatory) variables and the product’s selling price is entered as the dependent variable. The regression may take different functional forms, but in each form the independent variables are “regressed” against the dependent variable yielding implicit prices (regression coefficients) for each of the independent variables. A basic regression formula for a hedonic model could take the form shown in equation 1.

Equation 1

P_it = Α₀ + Β₂ X_2i + Β₃ X_3i ··· Β_k X_ki + u_i

Where:

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

Α₀  is the intercept

X_i  are the variables representing observed product characteristics

Β₂ ··· Β_k  are the regression/slope coefficients

u_i  is the residual or error term

It is the implicit prices represented by the Β s in equation 1 that provide the PPI with values that may be used in quality adjustments when product characteristics change over time. Before going further, let’s look in a more fundamental way at how the PPI attempts to adjust prices to reflect changes in quality.

Measures of Price Change

The following description of price measurement is deliberately generalized and is intended only to provide context for the use of hedonic methods as a quality valuation tool.

The PPI collects price and product specification data from producers (based on specific sample designs) to measure price change by constructing price relatives that in their most basic form can be expressed as:

Equation 2

^p_it/_pi^o

Where ^p_it is the price of product i in period t and ^p_io is the price of product i in some previous base period o. Weights and choice of index formula are not considered here.

As long as product i remains unchanged between periods o and t, measures of price change are straightforward. This situation is often referred to as the matched model in price index literature (Triplett 1983, 1986, 2003). However, the price measurement challenge becomes more complex when the inputs, including technology, used to produce product i change between periods o and t. New input requirements violate the fixed inputs assumption of the matched model and may cause biased measures of price change if unaccounted for. Essentially, when the matched model is violated, the measurement challenge is to estimate what part of price change between period o and t is due to quality change and what part is pure or market-based price change. Equation 3 more formally describes the price measurement adjustment that is attempted in the PPI when products undergo quality change.

Equation 3

^p_it - (VQA)/_pi^o

Equation 3 adds the term VQA (value of quality adjustment) to the price relative shown in equation 2. VQA is the estimate of what part of any price change between periods o and t is due to quality change. VQA may be estimated with a variety of methods including hedonics. The specific method chosen to estimate VQA is always determined (at least in part) by the type and detail of data reported to the PPI. For instance, hedonics would not be used if all reporters to the PPI could always provide estimates of the marginal cost of new input requirements that are directly tied to changes in output quality. Estimating the cost of new input requirements to value changes in quality is referred to in the PPI as the resource cost method.² To illustrate how the resource cost method can be used to estimate VQA, assume that the product in base period o is a 1 inch steel nail and that in period t the producer replaces the 1 inch steel nail with a 1 inch steel-galvanized nail. The galvanization process is a quality improvement that increases the nails corrosion resistance. Further assume that the producer raises the ^p_it price to $2.00 compared to the previous ^p_io price of $1.25. The PPI now has the information to construct a nominal price relative of:

Equation 4

Nominal price relative = ^p_it/_pi^o = ^2.00/_1.25 = 1.60

Equation 4 shows that the price of the galvanized nail ( ^p_it ) is 60 percent higher than the plain steel nail ( ^p_io ). The problem for the PPI is that the new substitute product is no longer directly comparable to the originally sampled non-galvanized nail. If the 60 percent price increase in period t is not adjusted for quality change, this nominal price measurement could be considered upwardly biased. This is where VQA is used to estimate what part of price change is the result of quality change and what part is pure price change. Using the resource cost method, the PPI attempts to obtain an estimate from the producer of the marginal cost of the new input requirements directly tied to quality change. In this example, the producer informs the PPI that the galvanization process adds 50 cents to the unit production (marginal) cost of 1 inch nails ( ^p_it ). With the cost of the new input requirements the PPI now has a value for VQA and can construct a constant quality price relative that is shown in equation 5:

Equation 5

Quality adjusted price relative = ^p_it - (VQA)/_pi^o = ^{2.00 - (0.50)}/_1.25 = ^1.50/_1.25 = 1.20

In equation 5, the period t price has been adjusted by the VQA provided by the producer. Instead of the 60 percent nominal increase shown in equation 4, the quality adjusted, or pure price change, is only 20 percent. The estimated VQA is a tool that enables the PPI to remove the ambiguity of nominal price comparisons when input requirements change and is fully compliant with the fixed quantity of inputs that is assumed in the PPI’s Fixed-Input Output Price Index (FIOPI) model.³ Another way of looking at VQA is that it enables the PPI to make price comparisons on a constant quality basis when changes in output quality occur.

The Hedonic Option

An interesting question that the PPI faces every month is what to do when the resource cost method described above is not feasible because producers are unwilling or unable to provide VQA estimates. Several non-hedonic options described in the 2004 International Monetary Fund publication Producer Price Index Manual: Theory and Practice (see references) are available to the PPI analysts.

Hedonic methods as an alternative to resource cost have been historically targeted at valuing quality change for computer products such as desktops, laptops and servers where the rate of technological change is relatively fast. The limited use of hedonics in the PPI is primarily due to constraints in both staffing and availability of appropriate data.⁴

The PPI recognized that computer technology changed so rapidly that the resource cost approach to valuing quality change would be unlikely to fully capture the dynamics of computer outputs. For example, a mainstream desktop computer that sold for $1,200 in 2004 may have included 1 gigabyte (GB) of system memory, a 60 GB hard drive, a 15-inch cathode-tube monitor as well as many other defining technological characteristics. In 2010, however, a desktop computer that still sells for $1,200 could easily have been configured with 8 GB of system memory, a 700 GB hard drive and a 21” liquid crystal display (LCD) monitor. The 2010 model also includes technologies unavailable in 2004 such as blue-ray high definition DVD players and quad-core microprocessors.⁵ In this example, the observed prices for the 2004 and 2010 computers are identical. However, technological change over this 6-year period has been remarkable: system memory has jumped 700 percent; hard drive storage capacity has increased an amazing 1000+ percent and monitor size gained 40 percent while also advancing from bulky cathode ray to relatively thin, light, and higher resolution LCD. 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. However, as mentioned earlier, the resource cost method was not feasible for this industry. 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 using hedonic methods.

Many of the hedonic models developed outside of the Bureau of Labor Statistics (BLS) explicitly identify time as an independent variable (Triplett 1986). Most of these models are based on pooled data (multiple time periods) 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 shown in equation 6.

Equation 6

                      _T

_Pit = Α₀ + _∑Δ_t D_t + Β₂ X_2i + Β₃ X_3i ··· Β_k X_ki + u_i

                    ^t-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 economically meaningful product characteristics

Β₂ ··· Β_k  are the regression/slope coefficients

u_i  is the residual or error term

Δ_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 6. For instance, the pooled approach enables maximum sample size, but is complicated by dissimilarity in computer characteristics over time due to rapid obsolescence. When product characteristics are unstable over time, a remedial strategy that may minimize the problem of rapid evolution in product characteristics 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. Ultimately, the choice is dictated by the type of product that is modeled, the rate of technological change, and the quality and detail of the available data.

Because there are many different approaches, including preferred functional form and the choice of specific 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 computer prices declined 21 percent annually, from 1960 to 1965; Gordon (1989) reported quality-adjusted mainframe computer 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. Finally, Berndt, Griliches, and Rappaport (1995) extended the previous hedonic work with a large sample of personal computer data and reported 28 percent annual decreases, on average.

As stated earlier, the PPI began its own research into hedonic modeling of computer products in 1987. The PPI opted for a cross-sectional (equation 1)—rather than pooled—(equation 6) approach, due to rapid technical changes in the characteristics that define computers. With cross-sectional models, the PPI does not attempt to directly construct price indexes, but instead uses the hedonic model to adjust prices reported to the PPI directly by producers when they indicate that product characteristics have changed. In other words, the model’s implicit prices for product characteristics are the VQAs used by the PPI to adjust reported prices for changes in quality.

Sampling and Database Issues

The PPI measures price change by first sampling those producers whose plurality of shipments fall within a NAICS defined industry, such as NAICS 34111-Electronic computer manufacturing.⁶ 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 respondent. Sampling techniques allow the PPI to capture data from a small but representative number of producers that report monthly prices and notify the PPI when sampled products change. Ideally, the PPI would specify a hedonic model supported by characteristics and prices taken directly from the PPI sample. However, with the exception of some services industries, most PPI samples at the product level are not of sufficient size to support the data requirements of a fully specified hedonic model. As a result, the PPI uses product specific secondary data sources to generate most of its hedonic models. For example, the PPI constructs separate models for portable computers, personal desktop computers, and host systems (computer servers). As recently as 1996, databases supporting PPI models were constructed from manufacturers' advertisements in Computer Shopper magazine. In 1997, several PPI reporters 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. 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.

Using Hedonic Models in the PPI

The regression formula used in a recent PPI hedonic model was based on equation 1, which is repeated here, and the results are shown in table 1.

Equation 1

P_it = Α₀ + Β₂ X_2i + Β₃ X_3i ··· Β_k X_ki + u_i

Note that equation 1 does not include a time variable, as in equation 6. The selection of functional form is evaluated in terms of statistical precision, reasonableness of absolute values, R-square, and F-tests (Gujarati 1995).

The model in table 1 is based on a cross-sectional linear functional form with the independent variables (computer characteristics) shown on the left and the implicit prices for each characteristic shown under coefficients. The remaining columns are for basic statistical diagnostics.

The regression results are derived from 2,022 observations of desktop computers 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. 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 preconfigured model that includes a 2.0GHz 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. Computer models will generally include four or more sites. After the data are acquired, data relationships are explored, various regression scenarios are run, and the results analyzed. Each database is structured to ensure that the most important PPI computer producers are included. Several dummy or qualitative variables are used in the model. For example, the coefficients (values) for the 22” and 24” LCDs in table 1 are relative to a base configuration with a 19” LCD. Company-effect dummy variables are also used, in this case referred to as Company A and B, 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. The interpretation of a company-effect variable is that it may capture otherwise unspecified price determining factors, such as name recognition, buyer loyalty, and superior marketing. These are factors that provide a limited company-specific price differentiation that go beyond the explanatory powers of the explicitly defined product characteristics. To illustrate how regression results from table 1 would be used in the PPI to obtain quality-adjusted price relatives, a hypothetical example is described below in table 2.

The example in table 2 is based on the assumption that the PPI is repricing a computer configured with 2.5GB of DDR-2 memory that sold in period (t-1) for $1,000 that the producer upgrades to 4.0GB of DDR-2 in period (t). The reporter indicates that the current period price for the upgraded model is still $1,000, and that the producer cannot provide a value for the change in production cost that is directly attributable to the additional 1.5GB of memory. If the PPI did not have a hedonic model to show the obvious quality improvement the PPI would use a standard methodology that adjusts the base price so that the item would show a price change that reflected the average price movement of all of the other items that had prices that were reported and included in the same index that month. With the implicit unit memory price generated by the hedonic model, the PPI has a method for valuing this quality change. The implicit price of $25.77 per unit (GB) of memory is obtained from the DDR-2 variable in table 1 and multiplied by the 1.5 unit increase in period (t), to yield a total quality change valuation of $38.66. As used in the PPI, this hedonic model is simply a tool that estimates the average change in price over the 2,022 observations for a unit change in a continuous variable or the absence or presence of a dummy/qualitative 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.

Additional Models

As previously mentioned, the PPI has developed multiple hedonic models for a range of computer products. In addition to the desktop model shown above, recent models for laptops, servers, and netbooks are shown in tables 3, 4, and 5 respectively.

Technical descriptions of the characteristics for the various computers shown in tables 1 and 3-5 are not important for the purpose of this review. The primary interest here is that the description in table 2 of how a hedonic model is used in the PPI to adjust prices for quality change is exactly the same for each of the different models. It should also be clear that there are significant differences between each of the computer types represented in tables 3-5, which is why separate models had to be researched and developed rather than a single model for all computer products. In other words, to be a useful quality valuation tool, each model must be focused on a specific product type. One would never try to build a hedonic model for transportation by combining bicycles, motorcycles, cars, trucks and 747 jumbo jets, though all are examples of transportation. It is the responsibility of PPI industry analysts to determine the parameters of a model’s specification.

Final Thoughts

Depending on how quickly a product’s characteristics change, a hedonic model used in the PPI may be updated as frequently as quarterly. As new technologies replace old technologies, the specification of a hedonic model must also change in order to continue to reflect current market conditions. One of the challenges for the PPI is to update models in a timely fashion in a real-time monthly production environment. At this time (and for the last 20 years), the primary use of hedonic models in the PPI has been to value quality change for computer products. Currently, the PPI is researching the feasibility of developing hedonic models for new product categories. This research effort may result in an expanded ability for the PPI to value quality change when more traditional methods are not available. However, the detailed data requirements and staff resources required to build and maintain these models will almost certainly limit the expansion of hedonics in the PPI to a few select products for the foreseeable future.

References

Berndt, E. R., Z. Griliches, and N.R. Rappaport. "Econometric Estimates of Price Indexes for Personal Computers in the 1990's." Journal of Econometrics 68, no. 1 (1995), pp. 243-268.

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

Diewert, W. E. “Aggregation Problems in the Measurement of Capital.” edited by D. Usher, 433-528. Chicago, IL: The University of Chicago Press, 1980.

Griliches, Z. “Hedonic Price Indexes and the Measurement of Capital and Productivity: Some Historical Perspectives.” NBER Working Paper 2634 (June 1988), Pg. 1.

Gordon, R. J. "The Postwar Evolution of Computer Prices." Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau, 77-125. Cambridge, MA: MIT Press, 1989.

Gujarati, Damadar. Basic Econometrics. 3rd Edition. McGraw-Hill Inc. 1995.

International Monetary Fund. Producer Price Index Manual: Theory and Practice. Washington D.C.: International Monetary Fund, Publication Services, 2004.

Nelson, R. A., C. D. Patterson, and T. L. Tanguay, "A Quality-Adjusted Price Index for Personal Computers." Journal of Business and Economic Statistics, no. 1, (January 1994), pp. 23-31.

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

Triplett, Jack. "Concepts of Quality in Input and Output Price Measures: A Resolution of the User-Value Resource-Cost Debate." Studies in Income and Wealth, 47. Edited by Murray F. Foss, 269-312. University of Chicago Press for the National Bureau of Economic Research, 1982.

Triplett, Jack. Database Issues in Estimating Hedonic Computer Price Indexes: Comparison of Hedonic Model Specifications. Contracted Report for Eurostat, 2003.

Triplett, Jack. "Economic Interpretation of Hedonic Models." Survey of Current Business 66, no. 1 (January 1986), pp. 36-40.

Footnotes

1 The referenced methodologies are described in “BLS Handbook of Methods, Chapter 14, Producer Price Indexes”, pgs 3-4 and can be accessed at https://www.bls.gov/opub/hom/pdf/homch14.pdf.

2 Cost as referenced here means cost plus the producer’s standard markup.

3 The FIOPI model is one example of a theoretical construct for output based producer price indexes that assume fixed technology and inputs. Such an index is designed to reflect changes in revenue from the sale of the same set of products—though not necessarily the same mix of products. The key assumptions of a FIOPI model is that changes to the price index arise solely from change in output prices that are unaffected by changes in inputs. See Triplett 1983 for more details.

4 The PPI provides measures of price change for more than 600 industries and over 5,000 product categories.

5 Consumers commonly focus on CPU clock speed when judging a computer's performance potential, quoted in gigahertz (GHz). This single number is more confusing than enlightening in today's environment of multiple competitive processors; one processor running at a particular GHz can significantly outperform another processor rated at the same GHz, and processors based on different architectures with multiple cores are difficult to compare, without objective benchmarking.

6 As defined by the 2012 North American Industrial Classification System (NAICS).

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 NAICS 334111.

Last Modified Date: October 21, 2015