At What Price? Conceptualizing and Measuring Cost-of-Living and Price Indexes (2002) / Chapter Skim
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2 Conceptual Foundations for Price and Cost-of-Living Indexes
2 Conceptual Foundations for Price and Cost-of-Living Indexes
Pages 38-93
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From page 38... ...
The basket price and cost-of-living approaches to index construction are conceptually quite different. Nonetheless, for many (perhaps even most)
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From page 39... ...
Basket price indexes simply measure the cost of a fixed bundle of goods and are not designed with substitution in mind, notwithstanding the fact that a suitable choice of basket sometimes allows them to be interpreted as cost-of-living index numbers. The language is also important, at least in the eyes of policy makers and the public, even if those who make the index know that the formulas are the same.
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From page 40... ...
These criticisms, many of which derive from the literature in psychology, are also reviewed in this section. The next section presents a discussion of specific topics, such as how to relate price indexes for individuals or groups of people to indexes for the nation, how to choose the prices that are appropriately included in a consumer price index, how to use price indexes to compensate people or groups of people for price change, and how to adjust price indexes for changes in the quality of goods.
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From page 41... ...
The nature of these approximations, as well as their relationship to an exact COLI, is developed in the next section. But as is the case for basket price indexes, the calculation of the price index starts from a basket, or baskets, of goods and from lists of prices in the reference and comparison periods.
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From page 42... ...
To see the implications of this, think about the two most familiar forms of the basket price index, the Laspeyres price index and the Paasche price index. In the Laspeyres, the base period basket is priced in both base and current periods the base period is also the reference period and the price index is the ratio of the basket's cost at current prices and at base period prices.
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From page 43... ...
One simple way to do so is to calculate a basket price index. Beginning with a list of actual purchases in the base period, the total cost of this basket in the reference period can be calculated, as can its total cost in the
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From page 44... ...
If the basket is the list of goods actually purchased in the base period, this is a Laspeyres price index. If the current basket is used as the base and the price index is the ratio of the current to reference period costs of the current period basket, the result is a Paasche price index.
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From page 45... ...
Because the national index uses national expenditures as weights, and because families who spend more contribute more to the national expenditure than do families who spend less, those who spend more get a higher weight in the national index. Indeed, the national Laspeyres price index is a weighted average of the individual families' Laspeyres price indexes, with weights equal to the total expenditure on all goods by each family.
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From page 46... ...
Basket price indexes work with the cost of specific goods and services; cost-of-living indexes work with the cost of "living." Measuring the cost of living requires one to compare different baskets of goods and to say when they yield the same
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From page 47... ...
standard of living. The difference between changes in the cost of the base period basket and changes in the cost of the base period level of living plays an important part in cost-of-living index theory, as well as in this report.
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From page 48... ...
As is the case for basket price indexes for which the choice of basket matters, the choice of the base level of living will also generally matter. In consequence, it is not true, though it is often loosely claimed to be true, that the cost-of-living index lies between the Paasche and the Laspeyres.
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From page 49... ...
Although they explain the limits of basket price indexes for thinking about cost-of-living indexes or compensation, they tell nothing about how to calculate a cost-of-living index more accurately. For example, one might argue that compensating social security recipients according to a Laspeyres-based CPI ignores their ability to substitute in response to changes in relative prices and therefore overcompensates them.
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From page 50... ...
First, he went beyond the Fisher ideal index and defined a whole class of superlative indexes whose members, like the Fisher ideal index, are capable of capturing general substitution responses. All of these, like the Fisher index, can be calculated from the same information that goes into basket price indexes reference and comparison period prices and quantities.
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From page 51... ...
We have presented a theoretical concept for a cost-of-living index, described the intimate link between cost of living indexes and compensation, identified inequalities that link cost-of-living indexes to the Paasche and the Laspeyres indexes, and introduced a set of practical superlative indexes that can capture the consumer substitution effects missed by basket price indexes. But there remains one important step.
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From page 52... ...
The aggregation of index numbers over the population, or over groups, is not an issue that separates cost-of-living and basket price indexes. Not surprisingly, the over- and underestimation results linking COLIs to the Paasche and Laspeyres indexes carry through to the social (and, indeed, to the democratic)
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From page 53... ...
Theoretically, a COLI seeks to measure the amount of expenditure required for a consumer to be equally satisfied in one time period as in another, or "the minimum expenditure necessary to achieve a base period level of utility" (Boskin et al., 1998:5~. In theory, conceptualizing a COLI in terms of satisfaction or utility has the potential to avoid many of the conceptual problems addressed in this report, from substitution to taste and quality changes.
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From page 54... ...
In contrast to core assumptions of the economic theory of consumer behavior, experimental research in psychology and decision making indicates that choice, or revealed preference, is at best an imperfect measure of experienced utility. Choices are often based on erroneous assumptions, always dependent on the given context, and frequently fail to increase experienced utility even when the consumer has abundant experience with the product of choice (for a review, see Loewenstein and Schkade, 1999~.
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From page 55... ...
In contrast to the assumptions of the economic theory of consumer behavior, access to more and better goods apparently fails to increase consumers' life satisfaction. Cross-national comparisons suggest a similar conclusion.
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From page 56... ...
Conversely, deteriorating circumstances would make people unhappy for some time, but only until expectations are back in line with reality, as long as basic needs are met. From this perspective, a satisfaction-based COLI would always show inflation in times of economic improvement because more goods are needed to maintain the base level of satisfaction, and it would show deflation in times of economic hardship once adaptation has set in.
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From page 57... ...
3 or more years, when data on the comparison period purchases will be available, and if there is little to choose between the two indexes on other grounds, it makes good sense to compute superlative indexes tailored to offer approximations to the COLI concept. The third question, about the varieties of goods, raises issues of quality, of whether a good is a simple irreducible "atom" on its own, or should be thought of as a bundle of characteristics.
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From page 58... ...
. Public Perception and Understanding When it comes to public understanding, basket price indexes have an advantage over cost-of-living indexes: they are simple and can be explained in seconds to almost anyone.
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From page 59... ...
The issue of substitution bias does not arise, at least if one is happy with the choice of basket. But if one has several reasonable choices of baskets and if they give different price indexes, one has to choose between them and recognize that at least part of the difference between the indexes, say the Paasche and Laspeyres, comes from consumers substituting in response to changes in relative prices.
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From page 60... ...
A CES index starts from the price relatives for each good, the ratios of the price in the current period to the price in the base period. In the Laspeyres index, these relatives are averaged, using as weights the share of the budget devoted to each good.
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From page 61... ...
In this case, there is much less scope for substitution, and the increase in the CPI ought to be much closer to the increase in the price of fuels: BLS cannot tell consumers that the CPI has not risen by much because they should drive their cars on milk or on orange juice! A superlative index can capture the difference between the two cases because it uses information on purchases after the price change and is sensitive to the fact that the shock induces a much smaller decline in demand for fuels than for imported electronics.
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From page 62... ...
We also note that, even prior to the introduction of the geomean procedure, the BLS used a seriously modified Laspeyres index that incorporated a procedure called seasoning, by which the weights come from a different period than either the reference or the comparison periods. The seasoned Laspeyres (including other modifications)
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From page 63... ...
Thus, once again, the distinctions between the two approaches are blurred. Indeed, in the judgment of the panel, the central issue in constructing quality-corrected price indexes is not the distinction between COLI and COGI approaches, but the measurement of quality change itself.
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From page 64... ...
In particular, taste change is sometimes indistinguishable from quality change. For example, becoming a vegetarian allows one to obtain the same nutrition from less food expenditure, just as would an improvement in the quality of fruits and vegetables.
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From page 65... ...
These conclusions are consistent with either a basket or cost-of-living approach to index number construction, though the arguments are different. As we shall see, the definition of a cost-of-living index needs to be modified to become a conditional cost-ofliving index (for more technical discussions, see Caves et al., 1982; Pollak, 1989; Diewert 2000a)
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From page 66... ...
One example is the construction of regional or city price indexes. Nothing in cost-ofliving theory says the base and comparison situations cannot be different places, rather than different times, and there are many situations in which such cross
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From page 67... ...
But if quality improvement comes through new technology and if a conditional COLI treats technology as an environmental variable to be held constant, the contribution of quality change to effective price reduction may be ignored or at least understated. Indeed, if one thinks of a conditional COLI as designed to prevent changes in the index level when prices are constant, then it would seem to rule out quality adjustments to price.
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From page 68... ...
Neither Laspeyres price indexes nor conditional cost-of-living indexes are likely to capture this progress; it would likely be better captured by an unconditional COLI. At present, there is probably no alternative to a selective treatment of whether or not the state of technology should be a conditioning variable for a COLI.
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From page 69... ...
The unconditional COLI essentially attaches values to different systems of tastes, something that most economists prefer to avoid. The conditional COLI is evaluating price changes according to tastes that are no longer valid, so that if tastes change rapidly and if the base period is held fixed for a long period of time, the conditional comparisons will become less and less relevant to consumers.
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From page 70... ...
It is not clear what to make of COLIs in such an environment, though one line of approach is through consideration of the literature on habit formation, according to which the cost of living increases in response to previously increased consumption because of the "needs" induced by the earlier consumption, so that the unconditional cost of living will drift upward relative to the conditional cost of living. Once again, a conditional COLI seems to be the appropriate concept for measuring the price level.
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From page 71... ...
It seems quite unlikely that it would be worthwhile in practice to try to design price indexes that deal with homeowners separately from renters, or separately for social security recipients with or without other income. Nevertheless, this discussion highlights the fact that, even in the area for which it seems best suited compensation the cost-of-living index is not as obvious a choice as at first appears.
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From page 72... ...
rate of interest into the consumer price index; user costs are higher at higher interest rates, as are both the cost-of-living and (properly computed) basket price indexes.
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From page 73... ...
All panel members find it difficult to think about the definition of goods and about quality change without considering what it is that consumers value, and we agree that it is impossible to think about substitution behavior without the concept of a constant standard of living that allows price changes to be converted into a monetary equivalent. For all these issues, especially the last, the cost-of-living framework is central.
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From page 74... ...
q, which denotes the sum of the element by element product of the vectors, in this case the total amount of money spent on q when it is bought at prices p. Armed with only this notation, we can introduce the two most important f xed-basket price indexes or cost-of-goods indexes, or COGIs.
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From page 75... ...
The Paasche and Laspeyres price indexes are the two most familiar fixedbasket price indexes that can be used to measure price change going from period O to t. As we have presented them, there is no strong reason to prefer one over the other.
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From page 76... ...
However, while the Laspeyres price index requires information on base period expenditure shares, the s A, the Paasche index requires information on current period expenditure shares, the s t. With present methods of data collection, it is not possible to have accurate information on current period expenditure shares in a timely manner.
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From page 77... ...
Paasche and Laspeyres indexes can be equally well constructed using individual baskets or aggregate (or average) baskets.
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From page 78... ...
Both individual and aggregate Laspeyres indexes are weighted averages of the same price relatives, and the formulas (10)
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From page 79... ...
Note finally that the arguments in the second section can be repeated in the present context leading, for example, to the use of the plutocratic Fisher ideal index as a good candidate for combining the information in the plutocratic Paasche and Laspeyres indexes into a single measure of the change in prices from O to t. Cost-of-Living Indexes In the economic theory of consumer behavior, each household (or person)
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From page 80... ...
Cost-of-living index numbers are defined directly from the cost function. Suppose that the base period level of living is us.
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From page 81... ...
It is EV = chug, pt ~ - chug, pi ~ (23) and bears the same relationship to the cost-of-living index for the current period level of living ut as does the compensating variation to the cost-of-living index for the base period level of living us.
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From page 82... ...
In general then, we can expect cost-of-living indexes to depend on the level of living on which they are based, so that the base period cost-of-living index will be different from the current period cost-of-living index, and cost-of-living indexes will be different for the poor and for the rich. It is only under homotheticity that it is possible to talk about the "true" cost-of-living index, since it is only then that it will be unique, and it is only then that it can be correctly asserted that the "true" cost-of-living index always lies between the Paasche and the Laspeyres (or even that the Laspeyres is always greater than the Paasche)
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From page 83... ...
must be estimated, which involves estimating the derivatives of each demand function with respect to total expenditures and the prices of all goods, not to mention the other factors that condition consumer behavior. In practical price indexes, there are a large number of goods, so this is a formidable undertaking.
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From page 84... ...
, then the Fisher ideal index (8) is exact in the sense that if we calculated the cost function associated with (29)
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From page 85... ...
Indeed, superlative indexes always require both current and base period quantity information. Intuitively, their ability to capture the substitution effects of prices has to be based on observation of the effects of the price change, which requires data on demand both before and after the change.
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From page 86... ...
Conditional COLIs, Quality Change, and Health As we emphasize in the main text, the use of COLIs as price indexes often requires us to ensure that a COLI changes only when prices change, and not when there are changes in the myriad other factors that affect the cost of living. In the text, this is what we refer to as the "domain" issue, that the COLI be a function of the prices of the goods and services that people buy, and not change with such things as the provision of public goods, people's tastes, their family composition, the crime rate, the ambient temperature, or the number of years that they can be expected to live.
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From page 87... ...
It is a routine exercise to check that all of the results and apparatus developed so far apply to these concepts, including the bounding relationships, the construction of superlative indexes, and the aggregation of price indexes to the national level. The results that involve a utility level intermediate between us and ut, for example, for superlative indexes in the nonhomothetic case, now involve intermediate levels of both e and u.
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From page 88... ...
gives their effective prices, p and PmlO~, as well as the effective budget available to fund them, x + Pm/ Given this, we can immediately see that the unconditional cost function the minimum cost of reaching u (including both health status and consumption) at prices Pm and p can be written in the form cot, Pm, p)
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From page 89... ...
is the conditional cost function that would be used to calculate the conditional COLI price index, by insertion into equation (35)
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From page 90... ...
This term is also not taken into account under any of the proposals we are considering and, if present, would further exacerbate the understatement of the cost of living through the sort of effects discussed in the previous paragraph. Taylor Series Approximations to Cost-of-Living Indexes Although superlative indexes are better approximations, the Laspeyres index is often itself a useful approximation to the base period cost-of-living index.
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From page 91... ...
We leave the details to the reader. CES Price Indexes Suppose that the consumer's cost function takes the form , >1/(1—o)
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From page 92... ...
, but it is more flexible than the zero substitutability utility function that is exact for the Laspeyres and Paasche price indexes. The base period cost-of-living index associated with (47)
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From page 93... ...
import and export price indexes. For alternative methods for estimating, see Balk (2000)
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