The Consumer Price Index

Mark A. Wynne Fiona D. Sigalla Senior Economist Associate Economist Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas The Consumer Price Index Without the notion of price there the actual published value only approximates. The would be no economic science. The concept true value of the CPI is considered to be the true is of absolutely central significance. It is not cost-of-living index, and so we begin with a as easy and trivial a concept as it appears to discussion of the theory of the cost of living be at first sight. A satisfactory measurement index. We progress to the construction of the of price is, as a consequence, a difficult actual CPI as it is reported every month, following undertaking, and it is not surprising that the description of methodology in the Bureau of price statistics, abundant as they are, have Labor Statistics’ (BLS) Handbook of Methods. In to be approached with utmost caution. the remainder of the article, we consider how —Oskar Morgenstern well the CPI approximates the true cost-of-living On the Accuracy index, paying particular attention to the problems of Economic Observations of substitution, quality change, and the introduc- tion of new goods, which are generally considered to cause the CPI to overstate the rate of increase he consumer price index (CPI) is one of the in the cost of living or, alternatively, overstate the T most closely watched price statistics published rate of inflation.2 Some analysts have suggested by the federal government. As an indicator of that these measurement errors are so large that inflationary trends in the U.S. economy, the monthly CPI report undergoes intense scrutiny. For example, an upsurge in the rate of increase in the CPI in early 1993 prompted the Federal Reserve to lean toward raising interest rates in its We are grateful to Marshall Reinsdorf and Jack Triplett for detailed comments on this article. We also received helpful policy deliberations. When the inflationary surge comments from Evan Koenig, Marilyn Manser, Steven Braun, proved short-lived, the Fed reverted to a neutral Ken Emery, and Zsolt Becsi. This article is based on a longer stance.1 Movements in the CPI also have a direct paper, entitled “A Survey of Measurement Biases in Price impact on the pocketbooks of many Americans. Indexes” (Federal Reserve Bank of Dallas Research Paper For instance, the annual increase in the CPI deter- no. 9340), that was prepared for the Joint Meeting of the System Committees on Business and Financial Analysis at mines the rate at which the nominal payments to the Board of Governors of the Federal Reserve System in Social Security recipients will rise each year. The Washington, D.C., September 22–24, 1993. We thank our tax brackets that determine the income tax liability discussant at that conference, Ana Aizcorbe, for comments of most workers are indexed to the CPI as well. on that paper. In this article, we review the construction of the 1 Note that some of this increase has since been revised CPI and discuss its potential shortcomings. We away as a result of changes in the seasonal adjustment also examine how well the CPI measures what it factors used to calculate the seasonally adjusted CPI. We is supposed to measure, namely, changes in the do not review CPI seasonal adjustment procedures in this cost of living. paper. Our primary objective is to review and put 2 These problems with the CPI are common to almost all into context what is known about the potential official price indexes and have implications that extend biases in the CPI. Inherent in the concept of bias beyond the measurement of inflation to such issues as the is some notion of the true value of the CPI, which measurement of real output growth and productivity. Economic Review — Second Quarter 1994 1 CPI inflation in the 3 to 4 percent range consti- Because it is impossible to ascertain the price tutes effective price stability. We argue that there of every single good and service that is valued by is little evidence to support this belief and that, consumers, the theory of the cost-of-living index insofar as the CPI does overstate the rate of infla- as it is applied to the measurement of consumer tion, it probably does so by no more than 1 prices typically focuses on a narrower set of goods percent annually. and services, specifically, those that are purchased on markets in some time period. Focusing atten- The conceptual basis of the CPI tion on this narrower set of goods and services, t ≡ t t t which we will denote as x (q1,q 2,…,qN ), where The conceptual basis of the CPI is the theory N < M, we can define a cost or expenditure func- of the cost-of-living index.3 The cost of living is a tion for the individual as follows: unique concept for each individual and is deter- N mined by the individual’s preferences for different (2 )epu (t , )=≥ min∑ pqUqt tt : ( ) u , t i i types of goods and services and the prices at qi i =1 which that person can purchase them. We can t t t t think of the preferences of each individual as being where p = (p 1,p 2,…,pN ). The expenditure func- characterized by an intertemporal utility function tion gives the minimum cost to the individual of that is defined over all the goods and services attaining some specified level of utility, u, when consumed today as well as all the goods and faced with a set of prices, p t, for the goods and services the individual expects to consume in the services that enter that person’s utility function. future. The most general specification of this func- The true cost-of-living index is then defined on tion includes items that have a price attached to the basis of the expenditure function. Specifically, them, such as automobiles, haircuts, and bananas, it is the change in the cost of attaining some base and items that are typically consumed without a level of utility, u b, between a reference period, r, user charge, such as roads, clean air, and leisure. and a comparison period, c: Specifically, we can write epu(,cb ) ()3 , =…j 1 112 22 ……≡j rb ()1 UUqq (,,,1 2 qqqMM ,,,,1 2 q ,) Uq (), epu(,) t c r where q i denotes the quantity of the i th good or where p and p denote the prices faced by the service consumed at date t. individual in the comparison and reference periods, Calculating a cost-of-living index requires respectively. If all prices in the comparison period, that all items in the utility function be assigned a p c, are twice the reference prices, the index is 2; price. This task is relatively straightforward for if all prices in the comparison period are one-half commodities and services that have a user charge the reference period prices, the index is 0.5. If all for consumption (meaning, they are purchased on prices in the comparison period are the same as markets) but is more difficult for items such as prices in the reference period, the index is 1. The leisure and clean air that are typically consumed CPI is an approximation of this true cost-of-living without a user charge. It is also difficult for durable index. goods such as houses and cars, which are typically purchased in one period but yield services How the CPI is constructed to the consumer over several periods. The purpose of the CPI is to measure the rate of change in the cost of living for urban consumers. It does this by calculating the average change in the prices paid by urban consumers for a fixed market basket of goods and services of 3 For a general review of the theory of the cost-of-living index, see Pollak (1989). For a discussion of the theory of the cost- constant quality. Since it is obviously impossible of-living index as the conceptual basis for the CPI, see to obtain price data for all consumer transactions Gillingham (1974). in the United States, the CPI is estimated from a 2 Federal Reserve Bank of Dallas series of samples. These samples are designed earners and clerical workers (CPI–W) and all with the objective of making the CPI representa- urban consumers (CPI–U). The CPI–W is repre- tive of the prices paid by consumers in all U.S. sentative of the buying habits of about 32 percent urban areas for all goods and services. The use of of the U.S. population, while the CPI–U (which a sample, of course, introduces a source of error was introduced in 1978) covers about 80 percent into the index, but this is more than offset by the of the U.S. population. errors that sampling eliminates.4 Each year, the The prices used to calculate the CPI are BLS selects new item and outlet samples for 20 collected from about 21,000 retail and service percent of the primary sampling units on a rotat- establishments in eighty-five urban areas across ing basis, with the intention of capturing new the United States. Data on rents are collected from developments in the market for consumer goods about 40,000 landlords or tenants, and 20,000 through such rotation. owner-occupants are asked about their housing Individual commodities in the CPI are units. All price information is collected by Bureau weighted by the share of expenditure on the item, of Labor Statistics field agents through visits or as estimated in the Consumer Expenditure Survey.

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