8
Whose Index? Aggregating Across Households

This chapter deals with the consequences for price index construction of the tremendous heterogeneity in the purchasing patterns and shopping behavior of consumers. An important part of these differences among consumers is associated with differences in their economic and demographic characteristics and their geographic location.

The existence of heterogeneity raises two important questions: First, are the rates of inflation experienced by different groups or by people in different geographic locations sufficiently different so that separate indexes should be constructed for each group or location? This issue is particularly important when indexes are used for adjusting taxes, social security benefits, and other public transfer payments: Should they be tailored to the groups to be compensated? If so, how might the data be collected that would allow us to investigate the extent to which inflation rates for particular groups differ and, if they do, to construct separate indexes?

Second, even if households face differing rates of price change, a single national index would still be needed for many purposes—for example, to provide an overall measure of inflation. But construction of a single index requires some method of averaging or aggregating across people, and there are different ways of doing that. Even with many subgroup indexes, there is still enough heterogeneity within those subgroups that the averaging issue would still have to be faced. As noted throughout this report, the Consumer Price Index (CPI) is now a plutocratic index: the weight of each household’s consumption pattern in the overall index is proportional to that household’s total consumption expenditures. Since consumer expenditures rise with income, this approach gives more influence in the con-



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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes 8 Whose Index? Aggregating Across Households This chapter deals with the consequences for price index construction of the tremendous heterogeneity in the purchasing patterns and shopping behavior of consumers. An important part of these differences among consumers is associated with differences in their economic and demographic characteristics and their geographic location. The existence of heterogeneity raises two important questions: First, are the rates of inflation experienced by different groups or by people in different geographic locations sufficiently different so that separate indexes should be constructed for each group or location? This issue is particularly important when indexes are used for adjusting taxes, social security benefits, and other public transfer payments: Should they be tailored to the groups to be compensated? If so, how might the data be collected that would allow us to investigate the extent to which inflation rates for particular groups differ and, if they do, to construct separate indexes? Second, even if households face differing rates of price change, a single national index would still be needed for many purposes—for example, to provide an overall measure of inflation. But construction of a single index requires some method of averaging or aggregating across people, and there are different ways of doing that. Even with many subgroup indexes, there is still enough heterogeneity within those subgroups that the averaging issue would still have to be faced. As noted throughout this report, the Consumer Price Index (CPI) is now a plutocratic index: the weight of each household’s consumption pattern in the overall index is proportional to that household’s total consumption expenditures. Since consumer expenditures rise with income, this approach gives more influence in the con-

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes struction of national and regional indexes to the consumption patterns and prices paid by the rich than to those of the poor. The alternative approach, for which it would be much more difficult to collect the necessary data, is a democratic index: Under this approach, we would construct individual price (or cost-of-living) indexes for a representative sample of the whole population and then average them, assigning the same weight to each person, regardless of the magnitude of their total consumption expenditures. Which kind of index is appropriate for each of the major purposes that the CPI serve? And, in practice, how would one construct the democratic counterpart of the current plutocratic CPI? Such questions arise in much the same form whether one is working with fixed-basket or cost-of-living indexes. This chapter pays particular attention to the fact that the data collection system underlying the CPI, and those employed to produce price indexes in other countries, cannot now provide important elements of the information needed to explore consequences of consumer heterogeneity and, specifically, to determine whether inflation rates do in fact differ among various groups within the population. As we pointed out in the introductory chapter, the key constraint is that information about consumers and how they budget their income is collected from a household survey, while price information is collected from retail stores; thus we cannot link the characteristics of purchasers with the prices they pay. This chapter outlines the kind of surveys that would be needed to collect price data directly from households. It explains why, using current survey techniques, acquiring such information would be extremely expensive and perhaps impossible. It suggests research options for exploring the feasibility and costs of alternative and more technologically intensive survey methods that might help solve this problem and, in the process, produce information about the inflation experience of particular groups such as the poor or the elderly. TWO KINDS OF HETEROGENEITY From the standpoint of constructing a price index, heterogeneity shows up at two stages of the process. First, people allocate their consumption budgets differently across categories of goods such as food, shelter, entertainment, and travel. Some of these differences are idiosyncratic among individuals—vegetarians and meat eaters, book lovers and sports enthusiasts, travelers and homebodies. But many of the differences are systematically related to the economic, demographic, and locational characteristics of households. The poor spend a higher fraction of their income on food and clothing than do the rich and a smaller fraction on travel and entertainment. The elderly tend to devote a smaller fraction of their budgets to durable goods and clothing and a larger fraction to travel and medical care than do non-elderly. People who live in the South spend less on heating fuel and more on air conditioning than those in the North. As we explained earlier, the Bureau of Labor Statistics (BLS) distinguishes some 218 different strata or categories of

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes goods; we label the variation in how consumers allocate their funds among these different categories as “across-stratum” heterogeneity. Consumer behavior exhibits a second kind of heterogeneity. Within any given stratum of goods, different people buy widely different qualities and brands of goods, often shop at different kinds of retail outlets, and pay different prices for the same product. The price of housing varies a great deal from one part of the United States to another, as well as between the city and the countryside. Different patients pay widely different prices for the same medical treatment. Also, shopping outlets offer goods and services at non-identical prices; catalog stores may tailor their prices to the zip code of the purchaser. The spread of Internet shopping may bring prices closer together, because it makes arbitrage easier, or it may drive them further apart by allowing retailers to set prices more nearly in accordance with the characteristics of the shopper. These within-stratum differences, too—like those across strata—arise not only from idiosyncratic heterogeneity of tastes, but also from differences in age, income, family composition, geographical location, and other factors that have important social implications. Within almost every category of goods the poor choose less expensive and lower-quality brands, often shop in different stores, eat at different types of restaurants, and may pay different prices for the same good. Retirees are more likely to travel on group tours than take bicycling excursions and, within the BLS stratum “sporting equipment,” to buy golf clubs instead of soccer balls or skateboards. And they may get senior citizens’ discounts on many items, whose scope and value can change from time to time. It is also quite possible that the ability or willingness of an individual to substitute in response to changes in relative prices differs depending on the level of that individual’s income. In consequence, the magnitude of the substitution effect built into a cost-of-living index (COLI) may differ from one person to another, depending upon their income levels. The research on this topic contains many presumptions on how substitution varies with income, but remarkably little evidence. Some researchers argue that, precisely because of limited resources, the poor are more careful with their budgets, hunting out bargains, substituting to the maximum extent possible. Others point out that the poor buy a smaller range of goods—a phenomenon that is well documented empirically—and, therefore, have less scope for substitution among goods. Moreover, the poor consume more necessities, formally defined as goods whose demand rises less than in proportion to income, and the term suggests that at least some necessities are hard to substitute. Certainly, for such items as medical care or home heating oil, it is hard to substitute one item for another, especially in the short run. Conceivably, both of these kinds of forces could influence different aspects of the shopping behavior of people with low incomes, but there is nothing in the theory of consumer behavior that creates a presumption that the balance tips one way or the other.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes HETEROGENEITY IN PRICES PAID AND IN RATES OF INFLATION The fact that individuals and groups differ one from the other in their broad consumption patterns, in the kinds and qualities of goods they buy, and in the prices they pay is not itself enough to produce differences in the rate of inflation or the rise in the cost of living they experience. To the extent that relative prices do not change very much over time, the rates of inflation for individuals and groups cannot, of course, differ very much from each other. But relative prices are continually changing. There is some evidence that the higher the overall rate of inflation and the greater the degree of economic disruption, the larger is the variation in relative prices. Moreover, there are periods when inflation is dominated by the rapid rise in the price of one or a few commodities—oil and other energy prices in the 1970s and early1980s and, to a lesser extent, health care costs in the late 1980s and early 1990s. Yet the existence of significant alterations in relative prices will not itself produce important differences in the rate of inflation faced by different groups unless, on average, the collection of prices for the kinds and qualities of goods typically purchased by one group rises faster or slower than the collection of prices of the kinds and qualities of goods purchased by other groups. Such systematic differences do exist. Lower-income consumers in the northern states are particularly affected in the winter months by increases in the relative price of heating oil; the elderly, even with Medicare, tend to be hit hardest by above-average increases in health care costs. Unless these increases are fortuitously offset by relative price declines in other goods of which they are also especially heavy consumers, the rate of inflation they face will exceed that for the population as a whole. Some observers point out that quality improvements and technological advances, which present one of the most difficult issues in price index calculation, are more prevalent among the types of goods purchased by rich than by poor households and that the rich are the first to acquire such goods. As a consequence, an overall price index corrected for quality change runs the risk of understating inflation for the poor, even if it accurately incorporates the effect of quality change for those who can afford to buy new and improved goods. Others argue that this phenomenon may be partly offset by a “trickle-down” effect of quality change. To the extent that technology produces goods with new characteristics and lower-quality-adjusted prices, the prices of older models also cascade downward, benefitting groups with less income. In summary, different groups of consumers will experience significantly different rates of inflation whenever three conditions all occur: There are substantial differences in what consumers buy and the prices they pay; there are significant changes in the relative prices of goods; and the distribution of those changes is such as, on average, to raise or lower the prices of the collection of goods typically bought by some groups of consumers relative to the prices of those

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes bought by others. The first two conditions almost certainly occur most of the time; there is little evidence about the third. THE CONSEQUENCES OF HETEROGENEITY FOR INDEX CONSTRUCTION If inflation rates differ among people—occasionally or frequently—an overall national index, however averaged over the population, could misstate the rate of inflation for the poor, the elderly, other demographic groups, or people living in different regions of the country. An important aspect of public dialogue about national policy revolves around the changing economic fortunes of different income, age, and racial groups and different regions of the country. We typically measure these fortunes by adjusting changes in nominal incomes or consumption expenditures by a single national index of inflation, which is fine if group differences in inflation are small but misleading if they are not. Even more importantly, if inflation rates differ significantly among groups, the use of an overall CPI to index social security pensions, other public benefits, and the income tax system may overcompensate some groups in the population and undercompensate others in ways that most people would deem unfair or unjust. As a first step to address the issue, one would like to know the extent to which, in the past, a single national index would have been a reasonably close measure of inflation rates for different groups, and how often and under what economic conditions inflation rates for one or more groups differed significantly from the overall index. While the past need not repeat itself, this kind of information would certainly be valuable for making a reasoned judgment about whether a single national index is sufficient for the major uses to which it is put or whether it needs to be supplemented with one or more indexes representing the different experiences of particular groups within the population. Unfortunately, the current data collection system underlying the CPI is generated is such a way that it is impossible to produce indexes for subgroups in the population that capture the heterogeneity in the qualities of goods purchased and the prices paid among those subgroups. GROUP INDEXES: WHY THE CURRENT DATA COLLECTION SYSTEM CANNOT PRODUCE THEM Chapter 1 describes how BLS produces the CPI in two stages. At the first stage, known as the lower level, BLS collects data on monthly price changes for individual items—not from individual households, but from a sample of retail outlets throughout the nation. It groups those items into some 218 categories or strata.1 Within each stratum, BLS combines into a single-stratum index the 1   Data on housing rents are collected in a special survey.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes monthly price changes for all the individual items in that stratum. For example, within the “new passenger cars” stratum, the monthly price changes for Mercedes, Buicks, Chevys, and Hondas are all averaged together, as are those for soccer balls, hockey helmets, golf clubs, and other items in the “sporting goods” stratum. The price changes for men’s clothing purchased at Brooks Brothers and at Walmart are similarly combined in the “men’s suits” stratum index. In this process, all within-stratum heterogeneity is lost.2 And since the price changes are collected from retail stores, there is no way to assemble the data so as to make a direct link between the particular price, quality, and brand of items purchased and the economic or demographic characteristics of those who purchased them.3 At the second or upper-level stage of estimation an overall CPI is calculated as an average of the 218 stratum indexes, with each index assigned a weight equal to the proportion of total consumer expenditures devoted to purchases of the goods in that stratum, estimated from the Consumer Expenditure Survey (CEX). BLS and individual researchers have, on occasion, produced indexes for subgroups in the population—for the elderly, the poor, or, in a recent BLS report, the individual quintiles of the income distribution—by reweighting the stratum indexes with expenditure weights that represent the budget allocations of the particular demographic subgroup as determined from the CEX. Although the across-stratum weights are different in each subgroup index, the individual stratum price indexes are the same in all of them. Generally, the subgroup indexes that have been produced have not risen at a substantially different rate than the overall CPI, although at times there have been exceptions (see the second technical note to this chapter for a summary of such comparisons). But such indexes distinguish one subgroup of households from another solely by the differences in the way each one allocates its expenditures among expenditure categories. Only the across-stratum heterogeneity is accounted for. The individual stratum price indexes are averages and so do not capture within-stratum heterogeneity—the fact that those at the upper end of the scale typically buy the higher-quality items within any given category of goods are the first to acquire many types of new products, shop in high-end grocery and apparel stores, live in areas with high rents, are far more likely to be covered by medical insurance and to fly business 2   This is a highly truncated description of a more complicated process, but it accurately depicts the essence of the procedure. 3   From a TPOPS-type survey augmented with additional data on household characteristics, it would be possible to determine the average economic and demographic profile of the people who patronized each retail outlet in the BLS sample. One could then observe any differences in the extent to which price inflation varied by category of goods among stores whose patrons had different characteristics. This would provide useful information about the consequences of heterogeneity of prices paid, but in the absence of a direct link between prices paid and individual purchasers, the association between economic and demographic characteristics and prices paid would be quite indirect and partial (see below for a brief discussion of this approach).

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes or first class on airlines even for personal trips, and so on down a long list of differences with low-income groups. A PRICE INDEX FOR THE ELDERLY? An example of the inability of the present data system to answer important questions frequently surfaces in discussions of whether the cost of living for the elderly rises at a faster or slower rate than the CPI as a whole. During the 1995 Senate Finance Committee hearings on the CPI, in response to a question from Senator Kent Conrad about a separate price index for the elderly, former BLS Commissioner Janet Norwood (1995:80) said: “The real point is that we do not know. And we do not know because we do not have prices that are collected for items that are purchased by the elderly.” The Boskin commission (Boskin et al., 1996:72), in its discussion of a separate price index for the elderly, points out that an index for the elderly calculated by using CPI prices and reweighting to match the expenditure patterns of the elderly does not differ substantially from the index for the non-elderly but recognizes that “the prices actually paid, not just expenditure shares, may differ.” Actually, for the period December 1990 to December 1995, the experimental CPI-E rose by 15.9 percent, somewhat more than the CPI-U and CPI-W, which rose by 14.7 and 14.1 percent, respectively (see www.bls.gov/news.release/cpi.br12396.a06.htm). Most of the difference can be explained by the larger expenditure share on the CPI medical care component (which increased faster than the average of other prices); a small portion of this effect was offset by a lower share by the elderly on “other goods and services,” a major expenditure group that also showed higher-than-average price growth. The Boskin commission concluded its discussion by acknowledging that “work on this subject remains to be done” (p. 72). In an article discussing the Boskin commission report, after quoting both Norwood’s testimony and the Boskin commission report, Pollak (1998:71) writes: Mention of “items that are purchased by the elderly” and “prices actually paid” turns the discussion of group indexes and representative consumers toward the items and qualities priced for the index and the outlets in which they are priced. The literature on group indexes has treated the construction of household indexes as a distinct, prior task and focused on the problem of aggregating household indexes into a group index. In practice, however, because we do not first construct household indexes and then aggregate them, our definition of the group index has implications for the items and qualities we price and the outlets in which we price them. Would a price index for the elderly behave differently than the overall CPI if data were collected on items and qualities consumed by the elderly and on the prices paid in outlets where the elderly shop? To have a definitive answer to this question, or even relevant evidence instead of speculation and conjecture, an

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes index for the elderly would have to be constructed to reflect “items that are purchased” and “prices actually paid.” By comparing such an index with one constructed by applying CPI strata prices to the expenditure pattern of the elderly, one could see whether, given the behavior of prices in a particular historical period, it would have been different. THE CONCEPTUAL BASIS FOR GROUP INDEXES One approach to the problem of how to aggregate across heterogeneous individuals starts from the concept that there exists a cost-of-goods index (COGI) and a COLI for each household, based on the prices it pays and the quantities of each good it buys. In a footnote at the beginning of its report, the Boskin commission wrote (Boskin et al., 1996:5): “In principle, if not in practice, a separate cost of living index could be developed for each and every household based on their actual consumption basket and prices paid.” Those individual indexes could be combined or averaged into many possible combinations—a single national average for all households and separate indexes for various population subgroups and geographic areas. To produce an overall national index, the indexes for the individual households could be averaged, giving equal importance to each (a democratic index) or be weighted in accordance with each household’s total expenditures on consumer goods (a plutocratic index). Currently, BLS collects monthly price data from retail outlets and other sellers and combines them with information on consumer expenditure patterns derived from separate surveys of households. But to produce individual price or cost-of-living indexes and then combine them into indexes for demographic subgroups, it would be necessary to combine, for each household, monthly information on the prices it paid, the amount expended on each item, and its basic demographic characteristics. Since retailers cannot provide information on either their patrons’ demographic characteristics or overall expenditure patterns, it would be necessary to collect the monthly price data, as well as expenditure patterns and demographic information, directly from consumers. As soon as one begins to think through the implications of collecting such data, however, it becomes increasingly difficult to support the proposition that a monthly (or even annual) price or cost-of-living index could be constructed for individual households. There are many types of goods that an individual consumer buys only at infrequent intervals, and among the goods that a consumer does buy frequently, purchases often vary among different qualities and brands of those goods. Consumers may make rental and utility payments and buy some categories of goods (e.g., food or beverages) on a monthly or more frequent basis, but a major fraction of their purchases occur at longer—in many cases much longer—intervals: How often do people buy a winter suit, a bottle of aspirin, a lawnmower, a resort vacation, a television set, or a refrigerator? For medical care,

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes it is unlikely most people will experience the same major procedure more than once a lifetime.4 Even for those categories of goods that are purchased frequently, many households may switch purchases among products that possess somewhat different qualities and are available at different prices, occasionally or often buying different kinds of green vegetables, meat, fish, shampoo, cosmetics, beer, and the like from week to week and month to month (quite apart from substitutions among products driven solely by changes in relative prices). But construction of the current CPI involves the measurement of period-to-period changes in the prices of goods of the same quality purchased in stores that provide the same services to shoppers. BLS goes to great pains to price the identical item each month in each retail store from which it is collecting prices. When that item disappears from a store and BLS must substitute another similar item to price, it devotes substantial resources in an effort to separate the difference in price between the old item and the new item into a component that represents quality changes, which it does not include in the index, and a component of “pure” price change, which it does include (see Chapter 4). And when new outlets are introduced into the sample of stores from which it collects prices the BLS “links” them in, so that any difference in prices is attributed to differences in the quality of service and does not cause a change in the price index. All in all, it would be impossible—even through observing a high-frequency series of prices paid by an individual household (monthly or even annually)—to calculate an index that measures the rate of inflation or the rise in the cost of living that the household has experienced. An Alternative Approach A less ambitious but more feasible approach to the aggregation problem would be to exploit the fact that an important part of the heterogeneity among households in consumption patterns and prices paid is systematically related to differences in their economic and demographic characteristics and in their geographic location. The nearest approximation to a homogenous unit that could form the building block for purposes of aggregation across households might, therefore, be an index of the prices of specific goods actually paid by a group of 4   In theory one might treat all goods which satisfied a consumer’s wants for any period longer than, say, a month as a durable good. Durable goods so defined might then account for 90 percent or more of aggregate consumer purchases. But that wouldn’t simplify the problem. Simply to calculate for a single individual household the user cost or opportunity cost of the monthly flow of services, for all of the services consumed by that household from the “durable” goods it owned, one would have to collect monthly data on prices paid from a group of households sufficiently large to furnish a statistically valid sample of price quotes for each of those durable goods.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes households ideally defined in terms of a number of characteristics—age, race, income, and family composition, as well as geographic location—with the prices weighted by the group’s budget shares allocated to the purchase of each of those goods. The sample of households within each subgroup would have to be large enough to ensure that a continuing series of price observations could be collected on individual items, including long-lived items only occasionally purchased by individual households. Moreover, the collection system would have to identify the attributes of the items purchased with sufficient detail to allow BLS to determine—as it now does—whether the particular items that are priced month to month were comparable and to make appropriate substitutions when they were not. No individual household, during the time interval covered, would itself have bought more than a fraction of the type and quality of goods whose prices are included in a subgroup index. But the index would reflect the distribution of the relevant qualities and prices of goods that were available to individual households in the subgroup, given their income, location, and other characteristics, and the conversion of that opportunity set into a distribution of prices actually paid by households who followed the average search strategy and shopping behavior of the group. Subgroup indexes stratified by income, by age, or by other characteristics would incorporate not only differences among population groups based on the allocation of their budgets among broad expenditure categories but also differences in the prices and qualities of items purchased and in the kind of outlets at which they were purchased. Indexes could then be calculated for groups classified by income level (e.g., income deciles or quintiles) and combined to give equal importance to each income so as to approximate a democratic index. And, of course, if individual group indexes, say for the elderly or the poor, frequently moved differently from an overall national index, they could be used for indexing public transfer payments going to those groups. Although the sorting of households into separate subgroups by income, or age, or location is likely to remove a good bit of the heterogeneity—and especially the kinds of heterogeneity that have the most social significance—each index for a group classified by one or two characteristics is still an average across individuals who have differences associated with other characteristics and with idiosyncratic tastes. An index for the elderly would combine rich and poor people, and the index for the poor would combine the old and the young. And, in any classification, the weights implicitly assigned to the prices paid by smokers and nonsmokers, vegetarians and meat eaters, represent an average across the remaining heterogeneity. Yet if data were collected in a way which linked prices paid to the characteristics of individuals, it would be possible to produce special indexes for groups with observable differences in tastes—e.g., those for whom a succession of monthly reports shows no purchases of cigarettes or meat—with the data possibly cross-classified by income group.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes Our ability to reduce the heterogeneity problem through the use of group indexes is unfortunately limited by the practical problem of costs. To produce true subgroup indexes, one would have to collect both price and quantity data directly from individuals so that prices and individual characteristics could be linked. Once income data are collected from individuals, it is relatively easy to add simple information on a number of other characteristics, such as age, race, and family composition. But, as we explain below, the size of the sample from which data have to be collected rises rapidly as one increases the number of characteristics that demarcate subgroups. A very large and expensive survey would be necessary in order to produce subgroup indexes cross-classified by many characteristics—e.g., elderly, Hispanic, New England households in the third income quintile, although there may be ways to reduce the size of the required sample (see below). HOW MIGHT DATA FOR SUBGROUP INDEXES BE ASSEMBLED AND WHAT WOULD IT COST? Currently, data on prices are collected by BLS in a separate operation from the survey that yields the expenditure patterns used to provide the weights for combining strata indexes into the overall CPI. At the lower (within-stratum) level, the separate Telephone Point-of-Purchase Survey (TPOPS) provides data on the distribution of consumer purchases across retail outlets and on consumer purchases for each of more than 200 relatively detailed categories of goods (see Chapters 1 and 9). But as we have repeatedly stressed, the stratum price index (e.g., for “men’s suits and sports coats”) that goes forward to the upper-stage indexes is based on price data furnished by retail stores, from Neiman-Marcus to J.C. Penney. In order to construct indexes that reflect individual circumstances and shopping behavior, specific households must be tied to specific items, prices, and outlets. To do so, the current system would have to be radically revised so that data on prices and expenditures for specific identifiable items are principally collected not from sellers but from individual households, so that their demographic and locational characteristics can be linked to the prices they pay. The first problem to be faced in producing these kinds of subgroup indexes lies in the feasibility of collecting monthly data on prices paid from a panel of households. For certain kinds of purchases, such as utilities, panel reporting should be feasible. BLS already conducts a housing survey to obtain rental prices, which might relatively easily collect periodic economic and demographic household information. But with current interview, telephone, or diary survey techniques, the burden of continuous reporting over a period of months and associated problems of reliability and product identification may well be such that for many categories of goods and services it would prove infeasible. However, there are various, more technologically advanced methods, some of which have been used by private survey firms, that could be investigated to determine whether

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes aggregated into a single official price index? When are different price indexes for specific population subgroups needed? And how should data to produce such subgroup indexes be collected? (2) When a single overall index is produced, how should the costs of living of individual households be combined into a single national index? Should equal weight be given to each household’s cost of living or, as is now the case, should the individual costs of living be weighted by the overall consumption spending of each household? The Consumer Expenditure Survey indicates the extent to which various economic and demographic groups allocate their budgets differently among categories of goods and services. However, substantial variation may also exist among different groups of households with respect to the particular types and qualities of goods they purchase and the prices they pay within each category. But because the price data used to produce the CPI are collected from retail stores and not directly from households, it is impossible to associate the economic and demographic characteristics of buyers with the items they buy and the prices they pay. As a consequence, it is impossible to investigate satisfactorily the two major aggregation issues we identified: To what extent does inflation or changes in living costs differ among the various economic and demographic groups? And to what extent would a democratic index behave differently from a plutocratic one? With current survey techniques and methods, collecting price as well as expenditure data from households on a scale sufficient to produce the CPI and an array of group indexes would be extremely expensive and possibly even infeasible. We therefore propose something more modest: Recommendation 8-1: BLS should pursue an exploratory research program that would, initially only on a small scale, investigate and assess several alternative approaches—including, but not limited to, the use by survey respondents of handheld scanners and computers—for collecting prices in a way that allows them to be associated with household characteristics. A first objective might be the production of indexes for a few commodity categories and several demographic groups. TECHNICAL NOTE 1: AGGREGATION AND THE “REPRESENTATIVE CONSUMER” The concept of the “representative consumer” frequently comes up in discussions of COLIs and of price indexes more generally. Indeed, it is often difficult to discuss COLIs with non-economists, policy makers, or the public at large without some sort of appeal to the concept. Sometimes the use is ambiguous or implicit: For example, a COLI might be presented in terms of the amount of money needed to keep consumers, or even “the consumer,” as well off as before the price change. Or it might appear in thinking about the change in expenditure that would

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes be necessary to offset the effects of inflation on “consumer living standards.” Similar phrases are often used to describe substitution effects in response to price changes. Sometimes the language refers explicitly to the representative consumer, sometimes to a “typical” or “average” consumer. Pollak (1981), in a paper on social cost-of-living index numbers, showed how to define an aggregate or average COLI without any appeal to the existence of a representative agent. For example, there is a well-defined COLI for each person or family, and one can average them. This would be a democratic COLI and could be approximated by a democratic Laspeyres index (for example). Or one could work with a plutocratic COLI in which the amounts of money needed to hold living standards constant are added up over all consumers and compared with the sum of actual expenditures for all consumers. Neither of these constructions involves representative consumers of any sort, and neither is very difficult to understand, certainly not the former. Nevertheless, the idea of a representative agent is often appealed to, though we have tried hard to avoid it in this report. One danger of the usage is that it is easy to fall into the trap of thinking of the welfare of the representative agent as representing the welfare of everyone. For example, when one talks about the COLI as being calculated (and perhaps paid, as in social security) so as to keep “consumer living standards” constant, it might be taken to mean that everyone’s living standards are being held constant. Instead, the best one can hope for is that some average of living standards is being held constant, with some people gaining and some losing. These distribution effects of price changes can sometimes be important. Another danger of the idea of a representative consumer is that it distracts attention from the need to think explicitly about how to aggregate over different people and families. The economic theory of consumer behavior is a theory of individuals, not of groups, and the analytical results that come with it are results about individual behavior. The theory provides many insights about such topics as substitution effects, the cost of living, and welfare. It provides an apparatus to think about substitution effects and why, when price goes up, demand goes down, as well as some less obvious results, such as the equality between good i’s substitution response to the price of good j and good j’s substitution response to the price of good i. But these results are for individual consumers, not for the aggregate or average of consumers. As we discuss in Chapter 2, the theory can be used to think about cost-of-living index numbers for groups or nations, but the transition from the individual to the group is not straightforward, and it requires a good deal of explanation. So it is sometimes tempting to avoid the complications, and to apply the theory to average or aggregate behavior, thinking about the country as a whole as a “representative consumer.” In this technical note we discuss two issues. First, what has to be true for the representative consumer to exist, in the sense that the analytic fiction will give the same answers as working with the underlying individuals and thinking about the

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes aggregation explicitly? Second, if the conditions are satisfied, and one computes a COLI for a representative agent, what relationship does this COLI bear to the COLIs of the underlying consumers? Conditions for the Existence of a Representative Consumer We begin with a definition. The representative consumer of consumer theory is not defined to be representative of tastes or of levels of living but of behavior. The economic theory of consumer behavior works with a single person who is assumed to be greedy (always wants more), to make consistent choices, and to do the best to satisfy his or her desires within a fixed budget at a fixed set of prices. As a result of doing the best he or she can, each person will have demand functions that relate the amount demanded of each good to income and to the prices of all the goods. Because different people have different tastes and live in different socioeconomic and physical environments, these demand functions will generally differ from person to person, even if they have the same level of income and face the same prices. For the economy as a whole, one can sum (or average) the demand functions of each person to get the aggregate (or average) demand for each good in the economy as a function of prices and the incomes of each person in society. The representative consumer exists if this aggregate can be thought of as coming from a single consumer whose behavior replicates the aggregate of all consumers. Note again that this definition is in terms of behavior, not tastes or welfare. In general, this construction cannot work, and for a very obvious reason. According to the theory of individual behavior, demand is a function of income and all the prices. But aggregate demand is a function of all the incomes and all the prices. The distribution of income between people matters for the aggregate but has no part in the theory of individual behavior. The representative consumer demands goods according to her representative income and the prices, and there is generally no way in which all the possible effects of the distribution of income can be captured through a single representative income. So the representative consumer cannot exist in general. There are special cases where the distribution of income has no effect on aggregate demands: when each consumer spends his or her marginal dollar in exactly the same way. If so, taking a dollar from A will shrink A’s demands for goods in exactly the same way as giving the dollar to B will expand B’s demands for goods. As a result, the total demand for each good in the economy depends only on total income, not on who owns that income. Total income will work as representative income, and the representative agent exists. How realistic is this condition? For it to hold exactly is clearly absurd; no one would seriously claim that everyone in the economy spends an additional dollar in exactly the same way so that, at the margin, all consumers are identical. A more serious question is whether, at the level of aggregation in the CPI (about

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes 200 goods), the approximation is good enough. However, the equal spending condition has (at least) one unpalatable consequence. It can only be satisfied if everyone buys every good. If A does not smoke, and B does and would smoke more if he had more money, then redistributing money from A to B will change the demand for tobacco, and such behavior cannot be accommodated with only a representative consumer. It does not require any sort of econometric analysis, or appeal to the data in the CEX, to know that people consume different subsets of goods (even at the 200-plus commodity level), so that aggregate demand must depend on the distribution of income. If one insists on the fiction of the representative agent, one will be blind to changes in the social cost of living that are brought about by changes in the distribution of income. Conversely, one will also be blind to changes in the distribution of income that are brought about by changes in relative prices. An increases in the price of tobacco redistributes real income from (relatively poor) smokers to (relatively rich) nonsmokers. The representative consumer approach does not recognize such a possibility. Whose Cost of Living Does the Representative Consumer Represent? Suppose, contrary to the argument above, that the conditions hold that allow one to construct the analytic fiction of a representative consumer. One then constructs a COLI for this fictitious person to compare prices in period 1 with prices in period 0. Because the representative consumer’s behavior is the average of the behavior of each consumer in the economy, one might hope that the representative agent’s COLI is the average of the COLIs for the individual consumers. Note that nothing in the construction guarantees this. The representative consumer was constructed to represent average behavior, not the average cost-of-living index. And, in fact, the result is not true. The COLI for the representative agent is the plutocratic COLI obtained by averaging the individual COLIs with weights proportional to individual incomes. That this should be the case is intuitively clear from the fact that the representative consumer is constructed to represent average demand and that the rich contribute more to the average than do the poor, simply because they are richer and so spend more. Even though the representative consumer’s purchases of each good is a simple average of individual purchases, the representative agent’s COLI is not the simple average of the individual COLIs. Consequently, the use of a representative consumer framework in the context of plutocratic weights assigns more importance in the overall index to changes in the cost of living facing the rich than to those facing the poor. There are alternative definitions of the representative consumer that get around the plutocratic bias. For example, one could average, not the quantities purchased by each consumer, but their budget shares, defined as the fraction of their budget allocated to each good. One could then ask whether it is possible to construct a representative agent with a representative level of income whose budget shares are always equal to the average of the budget shares for each

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes consumer in the economy. The existence of such a representative agents has been investigated by Muellbauer (1975, 1976). In many ways, the conditions to make this story work are less restrictive than those for the original representative consumer, and indeed Muellbauer’s representative consumer has a representative income that depends on the distribution of income as well as on its mean. However, it is unclear whether the additional complexity of these formulations would commend them to those seeking straightforward interpretations of the COLI concept of a price index. Technical Derivation of the Representative Agent COLI Unless we place restrictions on the distribution of income, the existence of a representative agent requires that individual h has preferences that can be represented by cost functions of the Gorman “polar form” (Gorman, 1959): ch(uh, p)=ah(p)+ uhb(p), (1) where uh is utility, p is a vector of prices, and ah(p) and b(p) are nonnegative linearly homogeneous and quasi-concave functions of p. Taste variation is permitted in the function ah(p) but not in b(p). The representative agent has a cost function that is the average of (1), which is c(u, p) =a¯(p) + ub(p). (2) Denote by xh the total expenditure of h. Suppose that the two price vectors to be compared in the COLI are p1 and p0. The base-period COLI for h, is written (3) while the representative consumer’s COLI is (4) where is the population mean of xh0. Straightforward computation then confirms that (5) so that the representative consumer’s COLI is the plutocratic average of the individual COLIs, (6)

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes If we had started from the current period COLI, holding utility at period 1’s utility, instead of using base utility from period 0, the relationship between the representative agent’s COLI and the individual COLIs is given by (7) where the tilde denotes a current base COLI. Note that (6) and (7) also hold for both Laspeyres and Paasche indexes. In (6), if the indexes on the right-hand side are replaced by the individual Laspeyres indexes, the index on the left is the plutocratic Laspeyres, and in (7) the same holds true for the individual and plutocratic Paasche indexes. Indeed, these indexes would be the obvious choices to approximate the “true” COLI concepts if one wanted to measure them. TECHNICAL NOTE 2: DO INFLATION RATES DIFFER BY AGE OR INCOME GROUP? Since price indexes are used to adjust benefits paid to well-defined demographic groups, such as the elderly or the poor, it is important to consider the extent to which inflation rates for individuals in these categories differ from those faced by the general population. If purchasing patterns diverge widely and if the prices of goods and services that mark this divergence change at significantly different rates, the idea of creating group-specific subindexes becomes compelling. If consumption bundles are proportionally similar or if price changes across group-differentiated bundles consistently balance out, index disaggregation may be superfluous. Because of the obvious policy implications, age and income-specific subindexes have been given the most attention. This emphasis is reflected in both the academic literature and BLS policy research. BLS produces an experimental index for the elderly as a means to assess the validity of using the CPI-W to index social security benefits.17 Attention has also been given to separate indexes for the poor and, more generally, to price index variation by income group. Empirical studies of the income-price inflation relationship often bear, at least indirectly, on the closely related issue of plutocratic versus democratic indexes discussed above. This technical note reviews empirical literature that assesses price variation across subpopulation groups. 17   It is worth noting that not all elderly citizens receive social security, while many non-elderly do receive benefits. Nonetheless, it is curious that social security is indexed to CPI-W, which specifically excludes households whose primary source of income is from retirement and pension accounts (the CPI-U, in contrast, includes all urban consumers, including those who are retired).

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes Subindexes for the Poor Government poverty programs and guidelines are regularly adjusted for inflation. The Census Bureau poverty thresholds and the Department of Health and Human Services poverty guidelines, food stamp programs, low-income housing, and home energy assistance programs are all adjusted using the CPI-U. However, because the CPI is plutocratic, the representative household is upper middle class, which means that price changes—as captured by the CPI—are potentially very different than price changes faced by “average” low-income households. Early on, in work for the Joint Economic Committee, Arrow (1958) pointed out that separate subindexes for different income groups might be appropriate for certain policy applications. He reasoned that observed consumption patterns, most notably the proportion of necessities to luxury goods, are likely to be quite different for low- versus high-income households. Subsequent research has been directed toward generating empirical evidence to ascertain whether or not divergent group consumption patterns do translate into significantly different group inflation rates. Snyder (1961) pioneered work contrasting the growth rates of experimental indexes for high- and low-income groups. For the period 1936-1955, she estimated Laspeyres indexes for food items—categorized by income and income-food commodity elasticity—purchased by population subgroups. Price growth for low-income (and low-income elasticity) items was generally greater than price growth of middle- or high-income items. However, she also constructed a Paasche index series from 1955 Department of Agriculture food expenditure data that revealed no significant variation across income groups. Snyder showed that, during the period’s recessions, prices of items that constituted high-expenditure shares for the poor declined more slowly than did prices of goods in general. During expansions or periods characterized by high inflation, the price growth of low-income items outpaced the price growth of items purchased proportionately more by middle- or higher-income households. Kuznets (1962) corroborated a specific component of this relationship, documenting a time trend indicating that, as income rises, food prices rise relatively faster than prices of manufactured goods. Deaton and Muellbauer (1980) estimated that in Britain during the high-inflation period 1975-1976, the inflation rate was 2 percentage points higher for the poor than for the general population. More recently, BLS has tracked price inflation for the poor using item share weight-adjusted indexes. Garner et al. (1996) report results derived from the BLS experimental price index. The stated goal of the program is “to determine whether such an index would be lower than, higher than, or equal to the current CPI-U” (p. 32). In constructing the index, CEX data are used to calculate item category expenditure weights that reflect consumption patterns of the poor. The poor are defined three ways: by program participation, by household expenditure levels, and by income. The authors compute weights using each definition and then

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes compare trends for experimental Laspeyres, Paasche, and Fisher price indexes for 1984-1994. Garner et al. (1996) found only slight differences between price trends produced by the experimental price index for the poor and the full sample CPI-U. Using 1984 as the base year, the 1994 all-consumer unit Laspeyres is 141.1; the reweighted indexes for the poor range from 139.8 to 140.7, depending on which definition is used. The Paasche and Fisher indexes vary from the all-consumer index by a similar magnitude.18 The authors conclude that “the poor and the general population have faced similar trends in relative prices over the last several years” (p. 41). In addition to being time specific, they further qualify the results to acknowledge data limitations—e.g., the large share of rural poor do not figure into the calculations and the possible existence of asymmetric substitution opportunities in poor versus high-income consumption bundles. Michael (1979) empirically examined the effect of demographic factors on price indexes and estimated the statistical significance of the correlation between the two. Using individual-level records from the 1960-1961 CEX, he regressed Laspeyres index values against household demographic characteristics. The equation produced a number of significant coefficients, but no clearly discernable variation between the inflation rates faced by specific income groups and the population sample as a whole. There was no obvious relationship between household income and relative position in the distribution of index values over time. In a similar study, Hagemann (1982) looked at group variation in Laspeyres indexes. The study generated some evidence indicating slightly higher inflation for poorer households, but, again, the results were generally statistically insignificant. In additional BLS research, Kokoski (1987) constructed a superlative Tornqvist index in order to examine income-specific effects for the period 1972-1980. Differences across groups were generally small and insignificant. Blank and Blinder (1986) round out the available evidence. As part of their investigation into income distribution and poverty and commodity purchase patterns by the poor, they conclude that price inflation faced by the poor was similar to that faced by the general population over the period 1947-1982. The balance of the evidence, then, points to either modest or no variation in inflation rates faced by different income groups, particularly for more recent periods. Consumption patterns—specifically the relative weights of necessity versus luxury items—may be different, but the differences do not translate into consistently bifurcated subindex growth rates. Even if there is wide-ranging price 18   The paper also includes estimates of substitution bias, computed as the difference between the Fisher ideal and Laspeyres indexes. Substitution bias was estimated to be 1.99 percent for all consumer units, 1.75 percent for the income poor, 2.01 percent for the expenditure poor, and 0.25 percent for the program participation poor.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes inflation for item categories that are weighted very differently across subindexes, there may be no clear pattern in which specific price changes would tend to cancel one another out. It is also possible that the available household data are simply inadequate to tease out a significant income-inflation rate relationship. Of course, the bulk of the research identified here is empirical; there is no obvious theoretical basis to assume that the relationship between inflation rates and income group will diverge more or less in the future. Future research may be productively directed toward examining the extent to which suspected index biases correlate to household income. For instance, economists have long argued that quality change and, hence, quality change bias may be more prominent among luxury goods (which would presumably give CPI-type indexes an upward bias for high-income groups). Boskin et al. (1998) challenge the notion that benefits from quality improvements and new products accrue disproportionately to the wealthy; however, there is little empirical documentation to forcefully support either assertion. Subindexes for the Elderly Social security is by far the largest government outlay directly adjusted using the CPI. This, along with the perception that the elderly are more vulnerable to adverse affects associated with price inflation, has stimulated research emphasizing this group. Also, the CPI for medical care, a comparatively important component of elderly expenditures, has increased more rapidly that has the overall CPI in recent years; however, measuring medical care costs is extremely complicated and it is hard to assess the accuracy of this CPI component. The most systematic evidence on inflation faced by the elderly has evolved from a 1987 congressional directive to BLS to develop an experimental index for the population over age 62. In testimony to Congress, Mason (1988) reported the first set of results calculated under the program. For the period 1982-1987, the CPI-U, which captures spending habits of approximately four-fifths of the U.S. population, rose 18.2 percent; the CPI-W, which captures a subset of about one-third of the population rose 16.5 percent; the experimental index for the elderly (CPI-E) rose a slightly higher 19.5% (Amble and Stewart, 1994). Amble and Stewart updated the results for the ongoing indexing program. For the period 1987-1993, the CPI-U rose 26.3 percent, the CPI-W rose 25.5 percent, and the experimental index for the elderly rose slightly more, 28.7 percent. Stewart and Pavalone (1996) completed the series through 1995, producing similar results. For the period 1990-1995, the CPI-U rose 14.7 percent, the CPI-W rose 14.1 percent, and the CPI-E rose 15.9 percent. BLS’s experimental index consistently produced slightly higher inflation rates for the elderly during the 1980s and 1990s. However, this does not necessarily mean that the elderly have truly faced more rapid increases in living costs. To understand potential inaccuracies of the CPI-E as a true cost-of-living index for

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes the elderly, one must review the BLS index construction method. For the CPI-E, BLS identifies expenditure patterns for the sample of elderly from CEX data. The standard modified Laspeyres index is calculated using a reweighted consumption basket that reflects those patterns. However, as Amble and Stewart (1994:141) report: “The experimental price index for older consumers is a weighted average of price changes for the same set of item strata and [is] collected from the same sample of urban areas used in calculating the CPI-U and CPI-W.” Thus, the selection of outlets, as well as the selection of specific item categories to price, may not be representative of those used by the urban population age 62 and over.19 The BLS reports also note that, relative to the CPI-U, the CPI-E has a higher sampling error since it is constructed from a smaller sample. Also, the CPI-E does not capture the effect of nonfixed percentage senior citizen price discounts. Nor does it account for higher rates of home ownership among the elderly. Boskin et al. (1998) argue that, because of the rental equivalency indexing method, homeowners are, in effect, getting compensated for capital gains on their homes. Out-of-pocket medical care expenses account for the majority of the growth rate differences between the CPI-E and the CPI-U; and many economists believe that the medical care component is among the most biased item categories (if the goal is a cost-of-living indicator), due to omitted quality effects and output definition problems. The Boskin commission argued that widespread and systematic quality improvements in the health care sector are not captured by the CPI, creating a significant upward bias in the medical care component—about 3 percent per year when weighted by out-of-pocket expenditures. In short, though the CPI-E has risen more rapidly than the CPI-U, one still cannot estimate relative cost-of-living trends. To summarize, BLS research shows that the CPI-E series rose slightly faster than the general CPI. However, the CPI-E is computed using a comparatively small CEX sample, and the differences are generally not statistically significant. Also, the growth differential between the CPI-E and CPI-U is attributable to increased weighting of a few item categories, most notably medical services, an item category economists agree has poorly captured improved quality and new item effects. The non-BLS literature generally concludes that there is a lack of measurable divergence between elderly and general population price inflation trends. Using the reweighted Laspeyres index approach, Boskin and Hurd (1985) found little difference in the cost of living faced by the elderly and the general population during the early 1980s. Jorgenson and Slesnick (1983) arrived at a similar conclu- 19   Of course, this says nothing of the more general problem that, to the extent that price changes faced by the rural elderly are different than those faced by the urban elderly, inaccuracies are compounded.

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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes sion using a method that attempts to estimate changes in cost of living directly from sets of demand curves representing different demographic groups.20 Berndt et al. (1998) looked at actual transactions data involving purchases of pharmaceuticals (antidepressants, calcium channel blockers, and antibiotics). For the period 1990-1996, the authors showed that, relative to younger age groups, the elderly faced rates of price inflation that were slightly higher for antibiotics, slightly lower for antidepressants, and about the same for calcium blockers. Conclusions To date, researchers have been unable to compellingly support claims that age- and income-defined population subgroups face significantly different rates of price inflation relative to the general population. On the contrary, during the short period for which reliable data exist, little divergence has been found. However, there is no theoretical rationale to assume that these trends must remain constant over time. It is important to note that, for the most part, data have been available for research that tracks group indexes differentiated only by item category weights. The Jorgenson and Slesnick article, which estimates separate systems of demand equations for different demographic groups, is an exception. On balance, little is known about exactly how quality and substitution biases in current measures may affect subindexes differently. Thus, it is difficult to assess group-specific cost-of-living trends using currently available experimental index measures. 20   This approach is unfortunately prohibitive at any detailed level of disaggregation since the number of parameters in the system to be estimated rises proportionately with the square of the number of items in the index. Another method for estimating substitution bias that allows for detailed item disaggregation is used by Garner et al. (1996). The method entails comparing Laspeyres indexes, which assume no substitution bias, with Paasche indexes, which weight item categories using the most recent period’s consumption and probably overstate substitution.