4
Evolving Market Baskets: Adjusting Indexes to Account for Quality Change

The ever-changing mix and quality of products and services available in the market create difficult problems for price index construction. At a basic conceptual level, the problem is easy to understand: under either of the conceptual frameworks we have discussed, unadjusted price comparisons between an item and a non-identical replacement cannot generally be treated as equivalent to comparisons that involve an unchanged item. However, developing solutions and assessing techniques for correcting the problem is extremely complicated. Quality change has typically been considered the least tractable problem associated with the Consumer Price Index (CPI).

The pervasiveness of item replacement alone makes quality change impossible to ignore. Item replacement refers to the process whereby a Bureau of Labor Statistics (BLS) field agent must select and price a different product because the one previously included in the sample can no longer be found on the store shelf. Moulton and Moses (1997:323) estimate that, based on 1995 data, about 4 percent of price quotations on average every month involve a replacement item. Some items are replaced more than once during a year, and this translates into an annual replacement rate of about 30 percent for CPI items scheduled to remain in the sample. Although a price adjustment is not made in each case, a judgment about quality change is. In about a third of these cases—roughly 10 percent of all CPI items each year—a quality adjustment is deemed necessary. Moulton and Moses also show that, relative to continuously priced items, replacement items have a disproportionately large effect on the rate of change in the CPI.

“Quality change” can take many forms. In the research literature, the distinction is often made between quality change and new goods. Unfortunately, this



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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes 4 Evolving Market Baskets: Adjusting Indexes to Account for Quality Change The ever-changing mix and quality of products and services available in the market create difficult problems for price index construction. At a basic conceptual level, the problem is easy to understand: under either of the conceptual frameworks we have discussed, unadjusted price comparisons between an item and a non-identical replacement cannot generally be treated as equivalent to comparisons that involve an unchanged item. However, developing solutions and assessing techniques for correcting the problem is extremely complicated. Quality change has typically been considered the least tractable problem associated with the Consumer Price Index (CPI). The pervasiveness of item replacement alone makes quality change impossible to ignore. Item replacement refers to the process whereby a Bureau of Labor Statistics (BLS) field agent must select and price a different product because the one previously included in the sample can no longer be found on the store shelf. Moulton and Moses (1997:323) estimate that, based on 1995 data, about 4 percent of price quotations on average every month involve a replacement item. Some items are replaced more than once during a year, and this translates into an annual replacement rate of about 30 percent for CPI items scheduled to remain in the sample. Although a price adjustment is not made in each case, a judgment about quality change is. In about a third of these cases—roughly 10 percent of all CPI items each year—a quality adjustment is deemed necessary. Moulton and Moses also show that, relative to continuously priced items, replacement items have a disproportionately large effect on the rate of change in the CPI. “Quality change” can take many forms. In the research literature, the distinction is often made between quality change and new goods. Unfortunately, this

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes distinction does not create clear-cut categories that imply specific corrective approaches. For instance, is a cell phone an improved wired phone or an entirely new product? What about a high-definition television, a fuel cell automobile, or on-line stock trading? The line between “new” and “improved” is inevitably arbitrary. The situation is brought into focus somewhat by thinking in slightly different terms, framed by consideration of how CPI product sampling and item identification actually work in real cases. Following Armknecht et al. (1997), three distinct cases can be delineated: A new item replaces another that has been or soon will be discontinued and that will fall out of the CPI sample. Replacement goods may be substantively similar (in which case there may be no quality issue at all), or they may be improved (or possibly inferior) versions of the discontinued item. These goods replace old goods but fall into familiar CPI categories—e.g., 2001 Fords. A new “supplemental” good appears that does not replace a specific outgoing good in the CPI, but that does fit appropriately into an existing item strata category—e.g., Honey Nut Cheerios. A genuinely new item appears that does not fit into an established CPI item or strata—e.g., VCRs or wireless phones. In some sense, all of the above situations involve new goods; however, the extent of the difference between an old and a new product ranges from close to zero, to run-of-the-mill quality changes that happen on a daily basis, all the way to the appearance of radically new products that reflect what Nordhaus (1998) calls “tectonic shifts in technology.” Over time, BLS confronts situations on all points of this quality change spectrum. On the easy end, a commodity analyst may be forced to compare a 2-pound bag of rice with a 1-pound bag. Perhaps the previous 1-pound bag is out of stock or is not sold much anymore. Something like this happened with butter, which used to be sold in half-pound packets and now is more frequently sold in 1-pound packets. Most economists would simply work with per-pound prices in both cases. Of course, a 1-pound package is not identical to two half-pound packages, since the former requires longer storage, may be more likely to go bad, or may be sold with size discounts, and so on. But in many cases of this sort, per-unit prices seem likely to provide a very good approximation. The BLS apparently agrees. For instance, when the CPI went from pricing 16-ounce cans of tomato sauce to 14.5-ounce cans, all of the difference in price per ounce was attributed to pure price change (Kokoski et al., 2000:2).1 1   This is not to say that the nonlinear pricing issue is unimportant, particularly for large differences in package sizes. As a first step toward estimating its impact on the CPI, BLS could, in a straightforward manner, perform empirical research that examines how unit prices vary with package sizes. Of course, this only applies to products for which a range of sizes is typical.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes Some of the distinctions between cases can be clarified by casting them in this repackaging framework (this idea dates back at least to Fisher and Shell, 1968, 1972). This framework deals with situations in which the amount of “good” in the good has changed. It is difficult to think of actual examples other than changes in package size that correspond exactly to this framework, but imagine that gasoline has been improved so that it gives a 25 percent increase in miles per gallon for all vehicles and is otherwise unchanged. Once again, the solution seems fairly clear: the real price has fallen by 20 percent from, say, 5 cents to 4 cents a mile. One useful way of thinking about this is that the good is not gasoline but miles from fuel, and the price of the latter has fallen by 20 percent. Another example might be a new razor that yields more shaves before becoming dull. These cases converge with the butter case when one shifts from thinking of gasoline or razors to thinking of a good that more directly relates to consumer welfare. Once the good is defined appropriately—which is not trivial—and one thinks of the market good as a repackaged real good, the right way to handle quality change becomes transparent. The basic idea applies to more complicated cases, though the practicalities get harder. In most cases, there is no single obvious quantitative metric (like miles per gallon or number of shaves) to use in redefining the package, which makes it difficult to identify a simple one-to-one relationship between the real goods and the market goods. Economists and marketing specialists often think of situations of this sort in terms of characteristics, with market goods consisting of various combinations (packages) of several characteristics. Since one often does not really know the characteristics—because each good has many and because there is often no nonarbitrary way of defining them—things are rarely as simple as in the gasoline case, let alone the butter case. It is conceptually useful though to think of approaches such as hedonic techniques, which we discuss in detail below, as an attempt to redefine goods so that, by repackaging, one can factor out quality change. The really hard cases occur when a new good introduces new characteristics, in which case the repackaging idea cannot help with measuring quality change. But it is unclear that any practical technique can help in these cases or, indeed, whether radically different goods can even be appropriately discussed in the context of price measurement. For instance, in no clear sense did the introduction of cellular telephones reduce the general price level. Yet that new product did increase the well-being achievable by a subset of the population for a fixed money outlay and, in that sense, reduced the cost-of-living. Our coverage of the quality change/new goods problem follows the taxonomy outlined by Armknecht et al. (1997). First, we contrast the nature of the problem as it arises in the COGI and COLI contexts. In the next three sections, we sort though the gradations of quality change that occur along the repackaging spectrum. This discussion includes a brief review of the evidence of CPI bias presented by the Boskin commission (Boskin et al., 1996) as well as a discussion

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes of BLS item replacement procedures and their associated biases. Chapter 5 considers separately the case when goods appear that do not fall into existing product categories. The second half of this chapter assesses the role of hedonic regression techniques in quality adjustment. We offer specific recommendations about the applicability of hedonics for adjusting observed prices or for directly constructing indexes and about approaches to selecting items for quality adjustment.2 COLI AND COGI VIEWS OF THE QUALITY CHANGE PROBLEM The general problem of changing quality can be illustrated by simple example. Consider a price index for automobiles for which, in the reference period, the dominant type of automobile has a steel dashboard and no seat belts and is a gas guzzler. Now suppose that, in the comparison period, the dominant type of automobile has leather appointments, airbags, and efficient fuel economy. Direct comparison of the nominal prices of these cars will yield little meaningful information. What does it tell us if the price of a 2002 Camry is 10 times that of a 1965 Rambler? Similarly, if this year’s computer model costs the same as last year’s but does more and does it faster, what does the observed price constancy really tell us? Nordhaus (1998:59-60) points out that a fundamental problem associated with quality change is raised by these types of comparisons because “conventional price indexes measure the prices of commodities that consumers buy rather than the cost of attaining a given level of economic well-being or utility.” The manner in which quality change and new goods problems arise depends to some extent on the index’s underlying conceptual structure whether a cost-of-goods index (COGI) or a cost-of-living index (COLI) though procedures for dealing with these problems are essentially the same in both cases. COLI The COLI requires that prices, or the index itself, be adjusted to account for effects on living standards that accompany changes in the quality of goods and services. For certain commodities, the quantitative adjustment could be straight-forward—e.g., the new automobile fuel that increases miles traveled per gallon. But in most cases, the relationship between product or product characteristics (inputs to well-being) and actual well-being created cannot be directly observed. 2   We bypass the issue of quality change as it affects nonmarket inputs to consumer well-being (things like air quality, traffic congestion, and sense of personal safety) that are not captured in conventional price indexes (see Chapter 2). In addition, while we acknowledge the theoretical validity of the Boskin commission’s observation that changes in the variety of available goods and services affect consumer well-being, we know of no useful way to deal with this issue in index construction.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes It may be impossible to measure the value, even for just one consumer, created by the change from black and white to color television, by an increase in the user friendliness of computers, or by the addition of antismog devices to automobiles. Even setting aside the problem that the value attached to changing products may differ widely among consumers, changes in the mix of items sold raise two difficult issues. First, when outgoing items are replaced, COLI calculation requires isolating a pure price component from the observed price difference between the outgoing item and its replacement, which reflects both pure price change and quality change. If the underlying index methodology is unable to disentangle the quality-driven price movement from the “pure” price movement, living standards cannot be held constant. Second, techniques must keep the composite of index items—which is in constant churn—relevant to consumers’ material well-being. The addition of new goods into the marketplace generally raises (and the elimination of goods lowers) the welfare of some consumers; until the new good is represented, this welfare change is not reflected in the price index.3 The cost-of-living approach provides a theoretical framework for thinking about problems associated with the changing nature of goods and services available in the market. If a rational consumer buys two varieties of some product— apples, for instance—in some (relatively short) period, economic theory asserts that the ratio of their prices measures their relative qualities, at least at the margin.4 The next logical step is to assume that such price ratios provide meaningful measures of relative qualities even if there are many consumers and some do not purchase both products simultaneously. This assumption may be misleading when notions of quality differ across consumers, since demographic changes may then shift relative prices without quality change. Without this assumption, however, there is no way to use market data to recognize that, for instance, replacing a low-price variety with a high-price variety can make all consumers better off if the new variety is of sufficiently higher quality. More generally, if the quality of goods improves on balance over time, a cost-of-living index will discount some of the nominal price increases that occur, and the overall price index will rise more slowly than the average of the unadjusted prices. 3   Hausman (1997) has argued that the CPI is also biased as a cost-of-living estimator because, to the extent that consumers value variety, it makes no allowance for increases in the number of choices within index categories. Conceptually, this assertion is hard to dispute—if for no other reason than greater variety permits better matching to individual tastes, which gives some people pleasure directly. On the other hand, the existence of greater variety may, in some cases, be welfare decreasing if it creates increased search costs. There is no known way to capture such effects accurately in regular index production. 4   In practice, of course, it is often a matter of judgment as to whether one is dealing with two varieties of the same product or two different products that happen to be relatively close substitutes. Also, as the number of varieties multiplies, the act of choosing itself may require more time and effort.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes Unfortunately, quality adjustment techniques seem destined always to have an ad hoc element. The aspects or characteristics of goods that determine consumers’ perceptions of quality are not consistently observable. Moreover, the quality and taste components of price change are often inexorably intertwined. On the other hand, BLS has to balance on a case-by-case basis the errors that inevitably arise in the adjustment process against the errors that would inevitably arise either from ignoring quality changes or from assuming, as is often done, that all price differences between similar items reflect quality differences. We return to these issues below. COGI In a conventional Laspeyres index, the changing set of available goods and good characteristics also creates problems. Once an index item from the reference period is replaced by a different item, a strictly defined Laspeyres index cannot be calculated, since an identical bundle can no longer be priced in the comparison period. Given the pace at which new goods are introduced in a modern economy—ranging from those with slightly modified characteristics to those that are entirely new—it would be highly restrictive to monitor price inflation solely from a bundle chosen for stability. A “Big Mac” index may lead to misleading conclusions about general price movements, particularly since stagnant and dynamic sectors of the economy are likely to display systematically different price trends. Nonetheless, in no small part because of the uses to which they are put, it seems desirable to adjust price indexes to account for changing item quality and to reflect the changing mix of goods over time. In practice, one need not be methodologically boxed in by this narrow textbook view of a Laspeyres index. And the CPI has in fact been modified—since at least 1967 when BLS began adjusting automobile prices—to address quality issues while, at the same time, maintaining its basic COGI structure. A working definition requires only that a set of market goods and services that are valued by consumers be identified for inclusion in the index. Since purchasing patterns and the set of available products have changed, the basket has been allowed to change over time. The organizing principle is the desire to cover the goods on which people spend most of their money and then to make adjustments to account for quality change. A COGI proponent is likely to argue that quality adjustment is necessary because, when the nature of goods change, prices of like items cannot be compared over time since the original bundle of goods no longer exists. A COLI proponent is likely to add that, since improved products generate higher levels of consumer satisfaction, observed prices must be adjusted to isolate changes in the cost of maintaining living standards. These differences would not affect their evaluations of alternative adjustment mechanisms. Again, the idea of repackaging helps draw some distinctions between a COGI and a COLI in handling quality change. When two half-pounds of butter are

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes replaced by a 1-pound pack, a strictly defined Laspeyres index is an impossibility. However, it is possible to go forward in this framework if the item for pricing has been defined as “butter” instead of “half-pound packets of butter.” In our earlier gasoline example, a Laspeyrian working in this fashion would price “miles from fuel” and not “gasoline.” The Laspeyres approach has no difficulty pricing characteristics, provided of course that one has some way of identifying and measuring the relevant ones, a difficulty that is common to all approaches. Any Laspeyres-type approach must, however, begin with a definition of the goods (which may be characteristics) to be priced. Selection must be based on some clear notion (e.g., market share) that the set of goods represents that which people buy and what gives them utility. This is as true in a world of fixed quality as in one with changing quality. It is important not to confuse the issue of the definition of goods with the issue of a COLI versus a COGI. The arguments and recommendations in this chapter reflect the panel’s view that the CPI should be adjusted, for most categories of goods and services, to account for changing quality. In the next two sections, we review evidence on quality change bias. First, we briefly examine the Boskin commission report (Boskin et al., 1996) which focused on factors that are external to the CPI sample. We then review CPI methods for adjusting quality-changed items within its sample as well as potential biases associated with those methods, reserving the special case of hedonic adjustment methods for the following section. EVIDENCE FROM THE BOSKIN COMMISSION REPORT In accordance with its congressional charge, the Boskin commission ventured to estimate, by source and by item strata, biases in the U.S. CPI, relative to a hypothetical cost-of-living index. The commission’s report (Boskin et al., 1996) estimates quality change and new product bias (which they treat interchangeably) to be 0.612 percentage points per year—the largest component of its overall CPI bias estimate of 1.1 percentage points.5 The commission’s report has received extensive attention in the academic literature; numerous studies (both pre- and post-Boskin) corroborate the general view that quality change bias exists, though there is much debate on the size and sources of the biases. Much of the research has focused on specific index items (e.g., Berndt et al. [1996] on prescription drugs, Cutler et al. [1996] on hospital and physician services, Hausman [1997] on new cereal varieties). Shapiro and Wilcox (1996) did estimate an overall CPI bias, in the range of 0.6 to 1.5 percentage points per year, but it is extrapolated from trends for a limited number of products and not from an evaluation ranging across all CPI item categories. Unfortunately, research on the potential magni- 5   Though the Boskin commission does not attempt to identify separate quality change and new goods bias estimates, the report does make some descriptive distinctions between the two categories.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes tude of the quality change or new goods problem has not revealed broadly applicable techniques for correcting these biases. In contrast, a set of generally accepted methods has emerged for addressing other perceived index problem areas, most notably substitution bias. Shapiro and Wilcox (1996) describe solutions to the substitution component of the bias problem as harvesting the “low-hanging fruit” of the CPI bias problem. Sticking with the harvesting metaphor, solutions to quality change and new goods bias problems must be the fruit at the top of the tree, the kind that requires expensive tools to reach or that may not be reachable at all. The theoretical COLI perspective provides a rationale for tracking the value to consumers of new models and commodities and suggests why, for certain purposes, an index should be adjusted to reflect these changes. However, the COLI theory is less illuminating when it comes to directing research toward appropriate corrective techniques. Indeed, finding approaches for accurately dealing with changing goods and new goods is the most difficult obstacle to fulfilling the Boskin commission’s prescriptions for BLS to establish a cost-of-living index as its objective in measuring consumer prices. Reflecting the difficulty of the issue, the Boskin commission report did not advance any formal recommendations about how BLS could improve its measurement of quality change.6 The Boskin commission suggested perhaps that BLS should be doing more of the things it already does to correct for quality change bias, but seemed to concede that it did not have new ideas for approaching the problem. Summarizing the commission’s report, Gordon and Griliches (1997:84) write: The difficult questions posed by quality change and the continual arrival of new products . . . have been called the “house-to-house combat of price measurement.” Because the magnitude of quality-change bias differs so much across product categories, any overall evaluation must be conducted “down in the trenches,” taking individual categories of consumer expenditure, assessing quality-change bias for each category, and then aggregating using appropriate weights.” The Conference Board (1999:21) study group concurred: “In an advanced, dynamic economy like ours, there is no alternative to thorough, detailed analyses that slog through the data category by category, item by item. This is difficult, costly work, but no shortcuts are available.” Such conclusions reinforce the premise that general solutions, equivalent to the use of superlative indexes or geomeans to address substitution bias, do not exist to correct for quality change 6   In contrast, 5 of the commission’s 17 recommendations deal directly with a form of substitution bias—for which concrete options (superlative and superlative approximation indexes) exist. Individual commission members have elsewhere advocated expanding the use of hedonic regression methods to control for quality change for specific product types (see, for example, Boskin et al., 1998:14).

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes and new goods bias. Furthermore, there is no guarantee that even such “detailed analyses” will produce results that are suitable for inclusion in the CPI. While the Boskin commission offered no new remedies, it had much to say regarding the magnitude of quality change and new goods effects on the CPI, producing a comprehensive, categorical point estimate. Of the 27 CPI item categories evaluated for quality change by the commission, 8 were assigned a bias of zero; the other 19 were estimated to impart a positive bias on the index.7 Estimates for 6 of the 19 positive bias categories were calculated using a combination of results from existing studies of specific items and inferred figures for similar unresearched items in the category. Two upper-level CPI categories assessed in this way—appliances (including electronic) and medical services—contributed more than half the estimated overall quality bias. The commission performed original research or detailed back-of-the-envelope calculations for 4 categories. For the remaining 9 categories, empirical evidence was unavailable, and a descriptive approach discussing possible bias sources coupled with guesswork had to suffice (Moulton and Moses, 1997:310). (See “Technical Note 1” to this chapter for a review of upper-level item categories that the commission identified as contributing significantly to its overall CPI bias estimate.) BLS APPROACHES TO QUALITY CHANGE In constructing its CPI, the BLS has implemented a number of techniques to minimize perceived biases associated with its modified Laspeyres approach. For many decades—starting long before the comparatively recent calls for a cost-of-living index—BLS has been aware of problems posed by items whose quality is changing over time. In general, the agency has appealed to the cost-of-living theory in describing its efforts to confront the issue. BLS readily acknowledges that, relative to some ideal COLI, introduction of new goods and quality change of existing ones may bias the CPI in two different ways.8 First, there are biases associated with quality changes that are detected in the CPI sample and for which BLS attempts to correct. In this case the question is: “What is the bias, if any, of CPI procedures for handling quality change when quality changes appear on CPI items?” (Triplett, 1997:24). Second, there are 7   See Boskin et al. (1996) or Gordon and Griliches (1997) for the complete list of estimated bias by category; see Moulton and Moses (1997) for a detailed critique of the estimates. 8   As noted above, the distinction between a “new good” and a new variety or improved-quality good is arbitrary. In terms of CPI construction, we think of a “new good” as one that would require creation of a new item strata (or entry-level item) and that can only enter the index by initiation of a new item classification structure—the VCR is an example. Quality change refers to evolving characteristics of a good or service already included in the index and whose price can be adjusted to reflect the change at any point—a laptop computer with more memory is an example.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes factors that go unrecognized with current CPI methods that bias the index as a representation of changes in the price to consumers of attaining a given level of well-being. A COLI in its purest sense would respond even to changes in non-market goods (such as air quality or commuting time). Moreover, even in a conditional COLI, changes occur in the market—most visibly the appearance of new goods and services—that affect well-being but are not accounted for, at least not immediately, in the CPI. Estimating the extent of the first source of bias requires evaluating internal CPI quality adjustment practices. BLS uses a range of quality adjustment approaches when a new item replaces an old one in the sample; the result may add all, some, or none of an observed price change to the index. Some of these approaches implicitly adjust for quality differences; others produce direct cost-based or hedonically derived comparisons of quality that are used to adjust observed prices explicitly. The Boskin commission report emphasized the second sort of quality-related biases, those created beyond the CPI sample and outside of CPI methodology. They focused on one subcomponent: underrepresentation of new market goods in the CPI. One way of thinking about new goods in the context of a price index (due to Hicks, 1940) is to imagine that the good was always available but at such a high price that no one would buy it. When the good is introduced, one can calculate the effect on the cost of living by translating the new availability into a price reduction, from the (imaginary) price that choked off demand to the new (lower) price at which it was first sold. The CPI as calculated makes no attempt to capture this “price reduction” associated with the introduction of new goods (see Hausman, 1997). Nor does it attempt to capture the later similar “effective” price reductions that occur as more and more consumers learn about new goods and experience a reduction in the cost of living because of that knowledge. Since the CPI market basket has historically only been revised every 10 years or so, new goods often entered the basket only after a long delay, and early stages of product price cycles were missed. Other sources of index bias may go undetected, such as those associated with gradual change in the quality of services (medicine, education, airline travel) or intangible aspects of quality change, such as improved stereo sound or television picture quality. Estimates of the magnitude of quality change bias seem to be closely tied to the type of bias researchers emphasize. Triplett (1997) argues that the Boskin commission arrived at a high-end estimate of quality bias partly because it focused primarily on biases generated by new goods (such as VCRs and mobile phones) during the periods when they were outside the CPI sample. He further suggests that current BLS methods for within-sample adjustment—which occur when an old product disappears from a CPI outlet and is replaced by a new noncomparable one—may impart some downward biases (Triplett, 1997:24): “The implications of the methods used in the CPI for handling quality changes are not well understood by economists; the CPI [Boskin] Commission did not

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes discuss them adequately, and some of these methods over-adjust for quality change, so that improving quality can generate downward bias in the CPI.” Essentially, BLS methods for adjusting observed prices of items that have undergone significant quality change, as judged by a commodity analyst, borrow information about price changes observed for similar items. For example, say a new improved microwave oven replaces the old model at a CPI outlet. Under one method, BLS will assume that the pure price portion of an observed price change between the old and new models is the same, in percentage terms, as that for other microwave ovens. Any remaining price difference is attributed to quality change. Such a method would implicitly overstate the effect of quality (and impart a downward bias on the CPI) if, for instance, manufacturers tend to increase prices (beyond those that cover costs of implementing improvements) when they roll out new models. We lay out BLS quality adjustment methods and examine potential biases in greater detail below. CPI Item Replacement Methods As noted at the beginning of this chapter, the manner in which goods (and services) appear and disappear can take a number of forms: old models are replaced by new ones that are nearly identical; new models are introduced that embody clear improvements over their predecessors; models may display qualitative change in existing features or may introduce altogether new features. To accommodate some of these differences and to overcome data and procedural limitations, BLS employs alternative methods, shown in Table 4-1, for treating replacement item price quotes. For cases in which a sample item is replaced, the observed price change must be (1) considered a pure price change (e.g., simple repackaging), (2) attributed entirely to quality differences, or (3) attributed partly to price change and partly to quality change (Kokoski, 1993). Cases 2 and 3 require adjusting observed prices prior to inclusion in the index; all three require judgments by BLS commodity analysts. Case 1 results in what BLS calls “direct comparison,” which applies when the replaced and replacement items are determined to be comparable by the commodity analyst. A repackaged food item or a new color of shirt are examples. Direct comparison is essentially item replacement for cases in which adjustment to the observed price has been deemed unnecessary. As Table 4-1 indicates, this is the most common finding. According to Moulton and Moses (1997), for 1995 about 65 percent of item replacements were in this category. With direct comparison, a commodity analyst has determined that it is appropriate to treat the observed price change as pure price change. If any quality change does occur, its effect on the index is not filtered out. The Boskin commission wrote that direct comparison, which it called “comparable substitution,” likely imparts an upward bias to the index since “in practice most goods tend to

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes Recommendation 4-5: BLS should experiment with the direct characteristics method, beginning with a few, carefully selected goods. The timely availability of relevant data should be a key selection criterion. Though its statistical properties require more in-depth study, the indirect method seems at this time the most broadly applicable hedonic approach for use in the CPI. Recommendation 4-6: BLS should continue to study the value of the indirect method for a wide range of goods. A large part of its promise rests on the comparatively modest maintenance and data requirements relative to the direct methods. Different adjustment methods imply different updating intensities. Under direct methods, the hedonic regression is part of index construction and must be rerun each time the index is recalculated. Thus, data on prices, characteristics, and purchase shares of a large set of varieties are required in each period and such data must be in hand for the current period before the hedonic function can be estimated and the index computed. Under the indirect approach, results can be obtained with only periodic reestimation. Only past period estimates are required, so there is less time pressure on data collection and analysis. However, when the relationship between characteristics and price moves quickly, even the indirectly used hedonic functions must be reestimated and, when characteristic sets change, they have to be respecified if they are to remain accurate. Ideally, regression equations would be updated every month. Practical considerations all but eliminate this possibility; BLS is not equipped or adequately funded to do this on a large scale. Rerunning current models with new data may not be overly burdensome, but respecifying models is highly labor intensive. Given that data collection and model estimation requirements may impose more than a 1-month lag in many cases, it may be necessary to figure out how best to use an estimated surface based on 6-month-old data to compute hedonic functions for the most recent monthly index. There are also basic questions regarding which price data to use when estimating hedonic models. For instance, should data be collected on transaction prices or list prices? Although transaction prices seem preferable due to seasonal selling patterns, BLS has used regular list prices in hedonic modeling of apparel—the idea being to avoid looking at different points in a product’s life price cycle. The long list of unresolved issues discussed in this chapter explains why even some proponents of hedonics advocate a less aggressive expansion of its use in the CPI than BLS appears to be taking. It is important that the BLS position on hedonics be shaped by scientific corroboration of the validity of broadly applying the method across index items and not be adopted as the default method to correct for quality bias in an attempt to move the CPI closer toward a COLI ideal. There

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes is certainly no guarantee that hedonic methods always improve accuracy relative to alternative approaches. The data and specification problems discussed in this chapter are serious, and we believe that the value of hedonic methods, and of alternatives, must be determined over time on an item-by-item basis. This represents a major undertaking. Recommendation 4-7: Congress should continue to provide the BLS incremental resources to permit it to conduct in-depth and systematic analysis of quality changes across a broad range of goods and services covered by the CPI. In designing its hedonics research program, BLS should seek to develop tools for dealing with the data and specification problems discussed above. Extending the CPI improvement initiative will allow BLS to continue its experimental research into scanner data; to assess the impact of hedonics on item comparability decisions and on index performance; and to investigate the replicability of competing techniques, perhaps using outside researchers to review and attempt to reproduce BLS results. Recommendation 4-8: An independent advisory panel, consisting of econometricians, statisticians, index experts, marketing specialists, and possibly product engineers, should be formed to provide guidance on both conceptual and application issues pertaining to hedonic methods. BLS, working with the advisory panel, should assess the impact of modeling imperfections on the validity of its hedonic adjustments prior to their introduction into the index. This would provide an analytic basis for proceeding sensibly in the face of external pressures to ameliorate the perception that the CPI fails to capture improvements in rapidly evolving sectors and to proceed quickly in this area simply because it is viewed as the only option available. In addition to attempting to advance understanding of the econometric methodology underlying the estimation of hedonic functions, the proposed advisory panel should provide outside review to help guide decisions about potential new applications and about which BLS pilot studies are adequately developed to be incorporated into the index. The hedonic results should always be evaluated against BLS’s currently used alternatives (generally those associated with implicit quality adjustment techniques), as opposed to some idealized flawless solution. To improve its effectiveness, the proposed advisory panel might be charged with helping to promote a major academic research effort to address issues (like the validity of using brand-specific dummy variables in the regressions) that are suspect but are not currently being discussed in the literature. The initiative should aim to increase collaboration between BLS and outside researchers on

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes both theoretical work and practical construction issues. The tendency to emphasize what can be most easily measured, rather than to focus on learning what characteristics are important to consumers, should be resisted. No research program can identify a universal set of criteria against which the BLS can validate its econometric procedures—there will always be a role for detailed case-by-case study. But precisely because so much judgment and knowledge of the product is involved, it makes sense to have outside review before new hedonic applications are brought into the CPI. TECHNICAL NOTE 1: BOSKIN COMMISSION ESTIMATES OF QUALITY CHANGE AND NEW GOODS BIAS In this note we briefly review the items, grouped into upper-level categories, that the Boskin commission identified as contributing significantly to its overall CPI bias estimate. We also make note of criticisms of commission methods by Moulton and Moses (1997) to illustrate the lack of consensus that exists regarding the magnitude of quality change and new goods biases—particularly at the level of disaggregated CPI component indexes. Food and Beverages The estimated bias associated with CPI pricing of fresh fruit and vegetables was the largest among components of the food and beverages category and was attributed by the commission primarily to the value to consumers of increased seasonal availability and variety. Limited by the dearth of published evidence on items in the food category, the commission was forced to lean heavily on Hausman’s (1997) work that calculated consumer surplus for a new variety of breakfast cereal as a means to quantitatively estimate the value consumers place on increased product variety. Citing data showing increased total consumption of products within the category, which they linked to increased variety and convenience, the commission arrived at an annual bias estimate of 0.6 percent for fresh fruit and vegetables. Moulton and Moses (1997) challenged this figure, showing that most of the increase in consumption over the period 1972-1995 occurred after 1985, while most of the increase in availability occurred before 1985: “Part of the increase appears to have been driven by shifts in preferences, perhaps as a response to improved knowledge about the health benefits of fresh vegetables” (Moulton and Moses, 1997:314). Shelter The Boskin commission produced detailed back-of-the-envelope calculations, based on assumptions about rental unit quality and size, to estimate a 0.25 percent annual bias for the shelter cost index. The commission’s position that CPI quality adjustments have been inadequate for shelter was deduced from the premise that newer apartments have increased significantly in quality (as reflected by improved amenities, such as central air conditioning) and in size (a

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes dimension of quality). They interpreted housing survey data as indicating that apartments increased in size by 20 percent between 1976 and 1993. Moulton and Moses (1997) countered, arguing that (1) rents generally do not increase proportionately with apartment size and (2) more importantly, that careful examination of data from the American Housing Survey and elsewhere suggests that the Boskin commission overstated historical increases in apartment sizes by perhaps a factor of three. Appliances and Electronics The commission’s bias estimates for this category are the largest—3.6 percent per year for the period 1973-1994 and 5.6 percent per year for 1994-1996. Due to the identifiable and quantifiable nature of appliance characteristics, and probably also to a priori notions about advances in the sector, research into this category of consumer spending is more extensive than for any other. Thus, the commission was able to access direct evidence, and the overall category estimate was extrapolated from items for which studies have been produced. The body of evidence included research by commission member Gordon (1990, cited in Boskin et al., 1996) of model-by-model comparisons from Consumer Reports. Moulton and Moses acknowledge that bias estimates for this category were probably the best documented by the Boskin commission: the report cites a number of academic and government studies that “develop hedonic adjustment models and find upward bias for personal computers, television, video equipment, and other items in this category” (Moulton and Moses, 1997:317). Apparel The Boskin commission used a “conservative reestimation” of figures from Gordon’s Sears catalog index, which rose less rapidly than the CPI subindex, to arrive at a 1 percent annual bias for the category. The main shortcoming of the experiment, according to Moulton and Moses (1997), is that Gordon measured year-to-year price changes only for the subset of apparel items that remained identical. The methodology links out—or deletes—the price increases associated with new product lines; the entire observed price change is assumed to reflect quality change. This approach produces misleading estimates if manufacturers are most likely to hike prices when new lines and varieties are introduced, as suggested by BLS studies. Also, apparel prices are known to be affected by lower-level substitution bias because of cross-outlet and seasonal volatility that allows consumers to find similar items at very different prices, depending on the store and on shopping times. Because methods to minimize substitution bias have been applied by BLS to apparel items, Moulton and Moses (1997:318) note that “it is unclear whether the Advisory Commission avoided double counting when sorting through these various sources of bias to produce its estimate of quality bias.” Transportation (New and Used Vehicles/Motor Fuel) On the basis of studies showing increased quality and increased service lifetime, the Boskin commission estimated an annual bias of 0.59 percent for automobiles. The esti-

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes mate was based on back-of-the-envelope calculations on the effect of increased longevity and, in turn, reduced depreciation rates, on annual operation costs. Triplett (1997), as well as Moulton and Moses, argues that the commission did not have accurate information about measures that BLS has implemented to take into account improved automobile quality. The Boskin commission also estimated a 0.25 percent annual bias associated with CPI pricing of motor fuel, which was attributed to failure of the CPI to capture convenience and time savings associated with automatic credit card readers at gas stations. Moulton and Moses offer their own back-of-the-envelope calculations, based on assumptions about the value of consumers’ time, time savings created by the machines, and average purchase size and find a bias about half as large. Medical Care The Boskin commission’s estimate of bias in the medical services index, 3.0 percent for both professional medical services and hospital and related services, is imputed largely from two empirical studies—Shapiro and Wilcox (1996) on treatment of cataracts and Cutler et al. (1996) on treatment for heart attacks. Thus, though Moulton and Moses agree that there is upward bias in the medical index, the validity of the commission’s estimate ultimately depends not only on the accuracy of these specific results but also on the extent to which the studied services are representative of the sector. Work by Berndt et al. (1996) and Griliches and Cockburn (1996) for prescription pharmaceuticals—for which the Boskin commission estimated a 2.0 percent per year bias—led BLS, in 1995, to change its method of pricing prescription drugs when generic versions become available. Also, beginning in January 1997, BLS adopted the PPI (Producer Price Index) method of pricing treatment-based bundles of hospital services. Both these measures reduced biases associated with measurement of medical service categories, although it likely did not eliminate them. Other Goods and Services The estimated biases associated with items other than those noted above were generally minor in terms of their impact on the all-item CPI. The Boskin commission suggested a 2.0 percent bias in sporting equipment and toys; small appliances such as hair dryers were assigned the same bias as large appliances, 3.0 percent per year. Personal financial services, a category for which output is extremely difficult to measure and rapid technological change (e.g., proliferation of ATMs and on-line account management) has occurred, the commission “conservatively” estimated an annual bias of 2.0 percent. The commission also discussed cellular phones but, as Moulton and Moses (1997:321) point out, it is not completely clear whether or not they included this in their estimated 1.0 percent bias for the “other utilities, including telephone” category.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes TECHNICAL NOTE 2: MATHEMATICAL DESCRIPTION OF HEDONIC METHODS In the index number context, the hedonic function pi,t = ht(zi) for a product with multiple varieties—where pi,t is the price of the ith variety in period t and zi is a vector of the ith variety’s characteristics or attributes—plays the same conceptual role as the (scalar) price plays for an undifferentiated good. In the present context, the hedonic function can be viewed as a menu from which individual consumers make choices. A typical hedonic specification for econometric estimation uses the natural logarithm of an item’s price as the dependent variable and several characteristics as the explanatory variables. The model may contain discrete variables, indicating whether or not a model has a feature, such as a CD drive on a computer, as well as continuous variables, such as the thread count of a fabric. Control variables, such as purchase location or outlet type, may also be included. When, as is typically the case, the explanatory variables are included linearly (rather than, say, logarithmically), the coefficients can be interpreted as giving proportional changes in price associated with a one-unit change in the quality characteristic or from a switch in the dichotomous variable. If explanatory variables enter non-linearly, these proportional changes depend on the values of the explanatory variables. There is a large theoretical literature on the properties of observed hedonic functions (see, e.g., Rosen, 1974; Muelbauer, 1974; Feenstra, 1995; Barry et al., 1995; Diewert, 2001). Much of this literature is concerned with the extent to which ht provides information on producers’ costs and consumers’ preferences under various assumptions about the nature of competition. This is not our concern here: in general, hedonic functions are reduced-form reflections of details of tastes, technologies, endowments, and strategic behavior in differentiated product markets. In particular, when competition is imperfect, it is generally not possible to infer marginal costs from the observed hedonic functions. We follow most of the theoretical literature and assume what Pollak (1983) calls “Houthakker’s ‘heterogeneous’ or ‘H-characteristics’” approach, which fits products for which consumers purchase one and only one variety. (The alternative, “Lancaster’s ‘linear and additive’ or ‘L-characteristics’” approach, applies when consumers purchase multiple varieties and care about the total amount of each characteristic supplied by all.) The use of hedonics in the index number context rests on being able to interpret the ht functions as summarizing the menu of alternatives faced by consumers in period t. This raises the general problem that different consumers in fact face different prices and have different stocks of information about their alternatives. Moreover, when price is not linear in the values of characteristics about which consumers care (see Muelbauer, 1974, for some relevant theory), which most hedonic studies seem to find, it follows that, even if ht is a smooth

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes function, the marginal cost to consumers of any particular characteristic varies with z. Thus, consumers who choose different varieties of some product because of differences in incomes or tastes (or both) face different “characteristics prices” at the margin, and the “characteristics prices” faced by nonbuyers are clearly not well defined. Finally, most uses of hedonics involve using an estimate of ht to, in effect, predict the price that would have prevailed in period t for a variety or model not actually offered for sale in that period. While this seems sensible, it is problematic at the theoretical level: under imperfect competition, if an additional variety or model had actually been offered for sale, the prices of other products might also have changed. In addition, smoothness and functional form assumptions are important in these exercises, and, particularly when consumers are heterogeneous, theory provides relatively little guidance regarding such assumptions (see Diewert, 2001, for a useful discussion). The Indirect Method As discussed in the body of the chapter, the indirect method is used to handle situations in which one variety of a good tracked in the CPI system—with a specific vector of characteristics z1 and price p1,t, say—disappears after period t and is replaced by another—with characteristics z2 and price p2,t+1, beginning in period t + 1. There are two basic types of indirect methods. If the hedonic function, ht(z), for period t is available, the simplest form of the forward-looking indirect method involves using p2,t+1/ht(z2) as the estimated “pure” price relative. The denominator of this ratio is an estimate of what a good with characteristics z2 would have cost if it had been available in period t, based on the empirical relation between price and characteristics in that period. If the hedonic function, ht+1(z), for period t + 1 is available, the simplest backward-looking indirect method involves using ht+1(z1)/p1t as the estimated price relative. Because it uses a bundle (of characteristics) purchased in period t + 1, the forward-looking method is Paasche-like; similarly, the backward-looking method is Laspeyres-like. Hedonic functions are typically refit only periodically, so neither the current period nor the prior period function is usually available. Thus, the backward-looking method is rarely feasible. To see how this affects the calculations under the forward-looking method, suppose the hedonic function was last estimated in period 0, with h0(z) the estimated function, and suppose one wants to calculate the “pure” price relative between periods t and t + 1. Clearly, p2,t+1/h0(z2) is a forward-looking estimate of the price relative between periods 0 and t + 1 for the bundle z2, while p1,t/h0(z1) gives a similar estimate of the price relative between periods 0 and t for bundle z1. If z1 and z2 were the same bundle, the ratio of these quantities Rt,t+1 = [p2,t+1 / p1,t][h0 (z1) / h0(z2 )] (1)

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes would give the price relative between periods 1 and 2 for that bundle. Since product 2 is being treated as a replacement for product 1, z1 and z2 must be close in some relevant sense. In any case, the BLS proceeds as if they were equal and employs Rt,t+1 as the price relative. Another way to look at (1) is that the actual price of product 2 in period t + 1 is being compared with the adjusted price of product 1 in period t—adjusted for the quality difference between products 1 and 2 using h0(z): adjusted p1,t = p1,t[h0(z2)/h0(z1)].(2) It is easy to show that these methods automatically take into account some forms of unobservable outlet-specific price differences that, along with other factors, prevent hedonic functions from fitting perfectly. Suppose, for instance, that h0(z) is the estimated marketwide base period hedonic function, as above, but prices of all varieties in some particular outlet exceed marketwide averages by a constant multiple θ. Then p2/θh0(z2) is the natural estimate of the price relative between periods 0 and 2 for the bundle z2, while p1/θh0(z1) is the natural estimate of the price relative between periods 0 and 1 for bundle z1. Neither of these is observable if θ is unknown, but their ratio, which is the quantity of interest, is given simply by equation 1, above. The Direct Time Dummy Method This method involves estimating hedonic functions of the following form: (3) where the subscript i denotes varieties or models and, as above, the βτ are constants, and δ(t,τ) equals 1, if t = τ and 0 otherwise. Note that there is no time dummy for period 0, the base period; we have arbitrarily normalized at β0 = 0 to identify the rest of the model. Specification (2) implies that in any period t the ratio of the prices of models with, say, characteristics bundles z1 and z2, p1,t/p2,t, is equal to antilog[h(z1) − h(z2)], which does not depend on time. It is thus being assumed that the prices of all (actual and potential) varieties change proportionately over time. (In light of Zvi Griliches’s seminal contributions to the theory and practice of hedonic methods, the panel believes it would be appropriate to label this the case of Griliches neutrality.) Neither theory nor empirical research provides much support for this assumption, however, particularly in industries experiencing rapid technological change. If prices of all varieties do change proportionally, though, it is simple to use the function above to produce a “pure” price relative for the product under study. For any variety i with a constant characteristic vector zi, the equation above immediately implies that for any two time periods t and u

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes pit / piu = antilog[log (pit)-log(piu)] = antilog [ßt-ßu], (4) for all i. Thus the expression on the right gives the price relative between periods u and t for the product under study. The Direct Characteristics Method Let ht(z) be the hedonic function in period t, Ct be the set of varieties available—with characteristic vectors zi,t, (average) prices pi,t, and quantities sold qi,t. The direct characteristics method computes price relatives using these data without necessarily imposing the assumption (which underlies the time dummy method) that ratios of hedonic functions are independent of the point in characteristics space at which they are evaluated. If some coefficients of the hedonic function are constant over time, of course, estimation efficiency can be improved by imposing constancy and using data from multiple periods in estimation. Alternatively, if the assumption that all slope coefficients are stable over time (i.e., the assumption of Griliches neutrality that underlies the time dummy method) is rejected by statistical test, some use of some version of the direct characteristics method would seem to be in order. As noted in the text, the natural way to use the hedonic functions to compute a single price relative in, say, periods 1 and 2, with different sets of products available in each, is to use the hedonic functions to price constant bundles of characteristics over time. The literature suggests two ways of doing this. The first follows Diewert (2001) and uses the average bundles consumed as reference characteristics vectors: (5) Then Laspeyres-, Paasche-, and Fisher-type indexes, which give alternative measures of price relative between periods 1 and 2, can be defined, respectively, as follows: (6a) (6b) F12= [L12 P12]½. (6c) Note that (6a) requires only lagged quantity weights, while both (6b) and (6c) require current quantity data. Note also that all these measures are equal, and all equal the results of the time dummy method, if the ratio h2(z)/h1(z) is independent of z. The second approach follows Feenstra (1995), with some modifications by Diewert (2001). Let C* be the set of varieties available in both periods, and let be the set of varieties that are available only in period t. One can use the period 1 hedonic function to “predict” the period 1 prices of those varieties available only in period 2, and one can use the period 2 hedonic function similarly:

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes pi1´ = h1(zi2), zi2 ∈ C2´, (7a) pi2´ = h2(zi1), zi1 ∈ C2´, (7b) One can then compute a Laspeyres-like measure by taking a weighted average, using period 1 sales shares as weights, of the (actual and “predicted”) price ratios of the varieties available in period 1: L12 = ∑C* wi(pi2/pi1) + ∑C1′ wi(pi2′/pi1) = [∑C* qi1pi2 + ∑C1′ qi1pi2′]/∑C1 qi1pi1, (8a) where, as usual, wi = qi1pi1/∑C1 qi1pi1. Similarly, using period 2 sales shares of the various varieties as weights and “predicting” the period 1 prices of varieties available only in period 2 yields a Paasche-like measure: P12 = ∑C* wi(pi2/pi1) + ∑C2′ wi(pi2/pi1′) = [∑C2 qi2pi2]/[∑C* qi2pi1 + ∑C2′ qi2pi1′], (8b) where wi = qi2pi1/[∑C* qi2pi1 + ∑C2′ qi2pi1′] for zi2∈C*, and wi = qi2pi1′/[SC* qi2pi1 + SC2′ qi2pi1′] for zi2ŒC2′. One can combine these, as in (6c), to obtain a Fisher-like measure of the price relative for this product. Note again that if price ratios for all varieties are the same, as assumed by the time dummy method, all of these measures are equal. To see the sense in which these two approaches give Laspeyres-like and Paasche-like measures, it is instructive to follow Pakes (2001) and consider a single consumer with income y in periods 1 and 2, with prices the same in both periods for all goods but widgets. In period 1, the consumer has available a set of varieties C1, the prices of which are given by the known hedonic function h1(z), and she purchases variety z1. In period 2, the consumer faces choice set C2 and known hedonic function h2(z), and she chooses variety z2. Suppose this consumer is given h2(z1) − h1(z1) additional income in period 2. Is this greater or less than the compensating variation, the period 2 income increase that would leave her exactly as well off as in period 1? If z1∈C2, buying variety z1 in period 2 would leave her with y + h2(z1) − h1(z1) − h2(z1) = y − h1(z1) to spend on other goods, exactly as in period 1. So h2(z1) − h1(z1) is at least equal to the compensating variation. But because the two hedonic functions are different, it may be possible for the consumer to do even better by choosing some z2′ π z1 in C2. Thus h2(z1) − h1(z1) is greater than or equal to the compensating variation, depending on whether such a z1′ exists or not. Similarly, suppose instead that the consumer’s period 1 income is reduced by h2(x2) − h1(x2). Is this greater or less than the equivalent variation, the period 1 income reduction that would leave her exactly as well off as in period 2? If z2∈C1, buying variety z2 in period 1 would leave her with y + h1(z2) − h2(z2) − h1(z2) = y − h2(z2) to spend on other goods, exactly as in period 1. So this income

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes reduction will leave the consumer no worse off. She will be better off in the (new) first period if she can afford some z1′∈C1 that she prefers to z2. Thus h2(z2) − h1(z2) is less than or equal to the equivalent variation, depending on whether such a z1´exists or not. For our single consumer, the price relative could naturally be computed as either h2(z1)/h1(z1) or h2(z2)/h1(z2). The former is a Laspeyres approach and, as above, relates to the compensating variation. The latter is a Paasche approach and relates to the equivalent variation. In the usual sense, and with all the usual caveats plus the requirement that z1 and z2 be available in both periods, in this simple case these two measures bound the true, preference-dependent, change in the cost of living.