The CPI and the PCE Deflator: an Econometric Analysis of Two Price Measures
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This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Annals of Economic and Social Measurement, Volume 2, number 3 Volume Author/Editor: NBER Volume Publisher: NBER Volume URL: http://www.nber.org/books/aesm73-3 Publication Date: July 1973 Chapter Title: The CPI and the PCE Deflator: An Econometric Analysis of Two Price Measures Chapter Author: Jack E. Triplett, Stephen Merchant Chapter URL: http://www.nber.org/chapters/c9904 Chapter pages in book: (p. 263 - 286) Annuls of Econom iv and Social P1r'asurmenf, 2/3. 1973 THE CPI AND THE PCE DEFLATOR: AN ECONOMETRIC ANALYSIS OF TWO PRICE MEASURES BY JACK E. TRIPI.ETT AND STEPHEN M.MERCHANT* This paper shows that differences in the movement of the CPI and the PCE deflator can largely he at- tributed to different price changes recorded hr comparable individual components of the two indexes. rather than to dfJerences (such as the weighting patterns) in methods for constructing the aggregate indexes out of the micro data. The results provide a basis for choosing between alternatire price measures for consumption. Two measures of aggregate price change for consumption goods and services are in general use--the Consumer Price Index (CPI), published by the Bureau of Labor Statistics, and the Implicit Price Deflator for Personal Consumption Ex- penditures (PCE), from the Bureau of Economic Analysis. The two indexes frequently present contradictory evidence of the magnitudeand sometimes even the direction--of price movement (see Figure 1), so that index users, faced with a choice between the CPI and the PCE, frequently ask: What is the sourceof the divergence between the two series? And, which is preferable for a particularuse? Figure IQuarterly Percentage Changes (Seasonally Adjusted), Consumer Price Index and Implicit PCE Deflator, 1965-1971. PERCENT FE CENT OH N GE Oh q N GE - 3.0 cPI 2.5 - 2.1) 1 .5 .5 L 1.0 2.5 " 0.5 jO.3 0.0 1965 1956 1957 1968 1969 1970 1971 Sources: PCE: computed from data published in Survey of CurrentBustness, July 1968. p. 49, July 1969, p. 47, July 1970, p. 47. July 1971, p. 43. July,1972. p.47 (correction of errors in printed data provided by BEA). CPI : computed from BLS data. * Office of Prices and Living Conditions, U.S. Bureau of Labor Statistics.Conclusions are those of the authors, exclusively. The paper does not represent anofficial position of the Bureau of Labor Statistics nor is it necessarily endorsed by the staff of the Officeof Prices and Living Conditions, either individually or collectively. We wish to thank the following forassistance: Robert F. Gillingham. Marian L. Hall, and Brian D. Hedgesf the BLS, the reviewer for this journal, and John C. Musgrave, Bureau of Economic Analysis. 263 Determining answers to either of these questions is difficult.Although it is 'Nell known that the CIJand PCE deflator differ in patterns, and computationa, coverage, concept, weighting procedures, available publishedinformationis insufficient to determineexact details of differences between less information about them.' There is even the quantitative impact ofdifferences in construction methods on index behavior. The present article compares behavior ofthe two indexes, using methodswhich permit statistical them; results testing of relationships between suggest that divergence between thePCE and the CPI stems from sources other than those previouslyconsidered. PREVIOUS APPROACHESTO THE PROBLEM Descriptions of the PCE implicitprice deflator indicate that data exist, the CPI series wherever CPI are used as deflatingindexes.2Thus, in a simple example where only one valueseries and one CPI deflating of a PCE index appear in thecomputation component, the PCE shouldpresent an exact imageof ponents used as inputs. Thus, it the CPI com- is tempting (thoughas we show, incorrect) to conc'ude that if theaggregate PCE and CP1 do not move together, thesource of the discrepancymust lie in the different weighting schemes employed toaggregate the individualcomponents into an overall index, or in coverage differences inthe two indexes (componentswhich make up about PCE have no one-quarter of the weightofthe counterpart in the CPI), or indifferences in concept measurement of price change in employed in the certain components (housingand used cars being the best knownexamples). We believe, from examining fragmentaryremarks sprinkled through theliterature, that most index or trying to decide whichof users comparing the two indexes, them to employ ina study, have regarded weights, concept and coverage to be therelevantand, indeed, only.-consjderj5 However, previous investigations which haveexplored weighting and differences have failedto resolve discrepancies concept approach involves reweighting between the two indexes.One the PCE accordingto constant weightsof base period, thusConverting it into some a fixed-weight type of index(as is the CPI). Substantial divergences betweenthe reweighted PCE Unexplained3 and the CN haveremained Another approach thathas been tried is to delete, from both indexes,a few components known (or thought)to differ in concept, and then to examinethe aggregate behavior of theremainder. Removing Housing example, often seems from both indexes,for to reduce the differencesin the aggregates.aa problem with thisapproach is that there is The major no systematic way toassure oneself Standard documentation ofthe CPI is U.S. Department 'The Consumer Price Index: of Labor, Bureau of LaborStatistics History and Techniques,"Bulletin No 1517, Government Printing Office (1964).To our knowledge, the Washington, D.C.: U.S. det)ator is Gregory Kipnis, most thorough description ofthe PCE "Implicit Price Index (lPI),"Appendix C, in U.S Congress, Committee Subcommitteeon Economic Statistics, "Inflation Joint Economic 2nd Session (July, 1966). and the Price Indexes."89th Congress. 2 As Indicated above, ourmajor source of information Kipnis op cii., pp. 104-105. on the PCE was Kipnis,op. cit. Allan H. Young andClaudia Harkins, Price Change for GNp,"Surrey of Current Business, "Alternative Measures of Sut'ey of Current Business, March 1969, vol 49, No.3, pp. 47-52, also, August 1970,pp. 12-13; Survey of Current Business, Theappcn August 1971, pp. 23-26. comains an analysis of the behaviorof the Housing components of both indexes 264 that the few components deleted are the only ones which behave differently. Moreover, simple inspection is the only technique readily employable with either approach, and when there are large quantities of data, it is difficult to learn much from simple inspection. A NEW APPROACH Ihe present investigation commenced by posing a different question, namely: Is it really true that those components of the implicit PCE deflator which in- corporate CPI data as deflating indexesbehaveas if they were based on the CPI? Unless they do, exploring the impact of different weighting patterns, etc., does not strike us as particularly interesting (and interesting or not, the exploration cannot be carried out very effectively without knowledge of any behavioral differences that exist among the various components of the two indexes). There are two reasons for exploring the matter: (1) the inability to account for CPI-PCE differences with approaches used previously suggests searching for an explanation along different lines, and (2) computing the national accounts is a far more complex process than what is usually depicted in simple textbook examples, and the deflator is a by- productofthat process. Accordingly, we set out to analyze the behavior of com- ponents of the two series, in order to isolate where problems arise, and to indicate which components need to be studied more closely. Another way to describe the approach we use is the following. We want to design a test to determine where discrepancy between the two price measures originates. We compare, statistically, behavior of counterpart components from the two indexes. If we find that comparison of matched series from PCE and CPI indicates that all's well at that point, then index users and others interested in the behavior of the two indexes may confidently turn to consideration of weighting patterns, or PCE components not derived from the CPI, as the explanationof index differences, and act accordingly. If, on the other hand, we find (as we do) that even matched components of the PCE and the CPI differ in movement, then the question becomes oneofdetermining why this should be so, and users should be alerted to a different set of factors which must be considered before choosing between the two indexes. THE STATISTICAL MODEL AND THE DATA If a CPI component is used alone as the deflating index in constructing a componentofthe PCE, then the process for computing the national accounts, and the implicit price deflator, implies values for regression coefficients in the relation (1) L\PCE = c + fJ(ACPI) -I- r. There are two hypotheses to be tested. First, we test4 the joint hypothesis that [El [01 the values of the regression parameters are[] = [j,The second hypothesis By means of the F-test outlined in: Franklin A. (iraybill, An introduction to Linear Stwstica1 Models, Vol. 1, pp. 128-133. 265 I refers to the fit of theregression. It is nor enough to find between a PCE that there is some relation component and the CPI. Sincemost of the questions posed by deviations between the PCE and the CPI have to do withthe variability of short- term movements (ratherthan trcnd behavior), testing excessive degree of variablity the components foran is of equal importanceto testing values of there- gression parameters TheFisherz-statistic5may be adapted to provide appropriate test of theR2. an The z-statis(ic approachesinfinity as the correlation coefficient approachesunity, so it is not possible, strictlyspeaking, to test the hypothesis R= I; we can, however, use the 2-statistic R to test the hypothesis that takes on some arbitraryvalue close to (but chose R not actually equal to) unity. We = 0.95 (or R2 = 0.90) as a reasonablevalue for testing.6 What we will hereafter refer to as our "generalhypothesis" is: Components of the PCE deflatorare reflecting the measure of price counterpart series in the CPJ used change obtained from the as an input for the PCEmeasure.