Reconciling the CPI and the PCE Deflator New analysis compares the CPI and the PCE Deflator and quantifies the effect on the inflation measures of the treatment of owner-occupied housing, the weights assigned products and services, and other factors in index number construction JACK E. TRIPLETT The Federal Government produces two major inflation Cpl . Accordingly, the basic measures of price trend for measures for consumption goods and services. The Con- most specific consumption commodities are common to sumer Price Index (CP1), published by the Bureau of La- both aggregate price measures . Differences in the move- bor Statistics, is the most widely used aggregate price ment of aggregate indexes can reflect how the basic index, as well as the major source of information on price data are used-in other words, how the aggregate price trends for individual consumption goods and ser- indexes are constructed. vices. An alternative aggregate consumption inflation Both the Bureau of Labor Statistics and the Bureau measure, the Implicit Price Deflator for Personal Con- of Economic Analysis publish alternative aggregate in- sumption Expenditures (PCE Deflator), published by the dexes, in which many of the basic price data are han- Bureau of Economic Analysis, is a by-product of the dled differently, to suit different purposes . The BLS now construction of the National Income and Product Ac- publishes two official CPI's-the CPI for all Urban counts. Consumers (CPI-U) and the CPI for Urban Wage Earners For at least a decade, users have noted that the CPI and Clerical Workers (CPI-w) . It also publishes five "ex- and the PCE Deflator often give different measures of perimental" CPI indexes that contain alternative treat- the rate of inflation . "How," these users ask, "can we ments of owner-occupied housing : these are designated reconcile the difference between the CPI and the PCE De- CPI-u-xl through CPI-U-x5 in the monthly CPI press re- flator?" This article provides an answer to that ques- lease and in the periodical, Cpl Detailed Report. tion . The BEA arranges the basic price information used in the personal consumption expenditures sector of the Alternative price measures National Accounts into three alternative aggregate price The price information used by the Bureau of Eco- measures-in addition to the Implicit Deflator for Per- nomic Analysis (BEA) in constructing its price measures sonal Consumption Expenditures are two alternatively is largely based on detailed CPI price indexes: 85 of the weighted price measures for personal consumption ex- Deflator's 115 components are taken directly from the penditures . These are described more fully later in the article. Jack E. Triplett is assistant commissioner, Office of Research and Accordingly, 10 different aggregate consumption ex- Evaluation, Bureau of Labor Statistics . penditure price measures are regularly published by the MONTHLY LABOR REVIEW September 1981 . Reconciling the cpi and the PCE Deflator Federal Government. Because several price measures are Cpi and the BEA price measures have been associated published, the analyst can use them to determine the ef- with such factors .' But recent revisions and improve- fect of particular differences in index number construc- ments in the Personal Consumption Expenditures sector tion on the measured inflation rate. of the accounts have undoubtedly greatly diminished their importance . Sources of difference in inflation rates In order to reconcile the various inflation measures The difference in the inflation rates indicated by any obtained from BLS and BEA, the present article presents two of the BLs and the BEA price measures can be at- a method for decomposing the difference between the tributed to three factors, described in the following sec- CPI-U and the BEA's PCE price measures into the factors tions. just discussed . The methodology is somewhat different from the well-known "reconciliation" tables published Owner-occupied housing. The treatment of owner-occu- quarterly by the BEA .' Its objective is to derive simple pied housing (and a few other products) varies. The two and straightforward measures of the empirical impor- official CPI's price houses and the costs of acquiring and tance of those factors-such as housing and index operating a house. All BEA price indexes (as well as the weights-that recently have become issues in the meas- CPI-U-XI index) use the CPi rent index as a measure of urement of inflation . the monthly cost of living in a house. In summary, in recent years the treatment of housing costs is the largest quantitative contributor to diver- Different index weights. Weighting differences among gence in the price measures . The difficulty of measuring BLS and BEA price measures can be broken down into costs of owner-occupied housing has been discussed at two sources: (1) weighting differences stemming from length in recent articles .' Five alternative treatments of differences in index definition and (2) weighting dif- owner-occupied housing are contained in experimental ferences associated with different periods selected for cpi indexes published monthly in the CPI press release determining the weights. and the CPI Detailed Report. cpi weights refer to expenditures by a population of ei- In addition, the article discusses the effect of ther urban wage and clerical workers (cpi-w) or of all ur- "updating" index weights from the early 1970's period ban consumers (CPI-[; and all five of the experimental to a more nearly current one. Alternative weighting cPi indexes), and all are derived from an expenditure sur- schemes show that weighting effects do make percepti- vey. The PCE consumption definition is broader than ei- ble differences in the measurement of inflation, but not ther CPI definition, adding to the expenditures of CPI-U's nearly so much as is sometimes assumed-around four- urban consumer, expenditures of rural household and tenths of a percentage point (0.4) for the double-digit expenditures by nonprofit organizations. In addition, its inflation year of 1980. The seemingly widespread im- weights are drawn from the National Accounts. pression, reported in the press and elsewhere, of a signi- With respect to differences in periods, all versions of ficantly larger weighting effect arises from making a the CPI currently use 1972-73 as the weighting period. common misinterpretation of the information in the PCE (Before January 1978, they employed weights based on Deflator. For this reason, the article includes material a 1960-61 survey.) BEA price indexes are available with on interpreting price indexes which use alternative for- weights for a variety of periods, including 1972 weights, mulas and weighting schemes. current period weights, and an index in which weights are always drawn from the period just prior to the one CPI and PCE deflator formulas for which the index is published. All versions of the CPI are computed according to what is known as a "Laspeyres formula. 114 In its purest Other factors. The price information incorporated into form, a Laspeyres price index takes its weights from the the indexes differs somewhat because the BEA price in- earlier of any two years being compared, but in practice dexes do not use a few CPI price index components and a particular weighting period is chosen and held constant include some non-CPI price data (mainly from the BLS' for several years. Currently, the CPI weights are drawn Producer Price Index and some price imputations car- from the Consumer Expenditure Survey of 1972-73. ried out by the BEA) . In any price index computation The Implicit PCE Deflator is a "Paasche formula" various technical factors may be handled differently by price index.' The Paasche index takes its weights from the compilers (for example, seasonal adjustment) . In the current period (that is, the period for which the in- some cases, the net effect of these "compilation deci- dex is computed), and for this reason, the PCE Deflator sion" differences may cause divergence in aggregate is often referred to as a "current weighted" index. At measures though it is often hard to make a comprehen- the present time, the PCE Deflator contains 115 compo- sive listing, and even harder to determine the effect of nents to which current weights are applied, an improve- each factor separately. In the past, divergences in the ment over the earlier computational system described by Gregory Kipnis', and the reference point for price on inflation measures can be obtained by comparing comparisons is always 1972 .7 The accompanying tables movements in indexes which differ only in the way own- are based on the most recent revised PCE price data, re- er-occupied housing costs are measured . The all-urban leased in April 1981 . CPI (CPI-L') and the five BLS experimental indexes differ Alternative aggregate price measures compiled by the only in their owner-occupied housing components, and of BEA use the Laspeyres price index formula . These index- the five, the relevant one for our purposes is CPI-u-xl (for es are described more fully in later sections of this arti- convenience, this designation is shortened to "CPI-xi" for cle . the remainder of the article) . In the CPI-xt index both the weight and the price measure for owner-occupied hous- Step-by-step comparison of the measures ing are determined, in principle, by assuming that the Alternative versions of the CPI and the BEA's price monthly cost of owner-occupied housing can be approxi- measures can be used to quantify the separate effects of mated by the rent that would be paid if the house were in the three factors mentioned in the introduction : (1) fact rented . This is often known as the "rental equiva- treatment of owner-occupied housing, (2) weighting dif- lence" method for measuring the cost of owner-occupied ferences associated with different weighting periods, and housing and is the concept also employed in all the BEA (3) an "all other" factor (which includes weighting dif- consumption price measures .