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Comparison of Industry Output Measures in Manufacturing JOEL POPKIN Joel Popkin and Company INTRODUCTION When in 1962 the Bureau of Economic Analysis (BEA) introduced annual measures of gross output originating by industry, the possibility arose that differences in behavior would emerge between them and the Federal Reserve Board's (FRB) industrial production indexes, which were first published in 1926. The two series have in fact moved differently, which has concerned producers as well as users of the data. Year-to-year and trend differences can be seen when the two series are compared. Year-to-year differences have been of concern recently because of speculation that the process of deriving constant-dollar series from the nominal value of shipments and the book value of inventories may be par- ticularly subject to error in a period of high inflation rates and of shifts in inventory valuation methods such high rates induce. Such concern reached its peak during the recent bout of double-digit inflation. Trend differences in the movement of the two series have also received attention as a result of concern over the apparent decline in the rate of productivity advance in the past 10 years. It has been about a dozen years since the last study of the two series was accomplished. It was prepared and presented by Gottsegen and Ziemer (1968) at an Income and Wealth Conference in 1964, the proceedings of which were published in 1968. The study dealt with differences arising between the two series due to both concepts and estimation methods, and covered the years 1947-1964. The aggregate output, as measured by FRO' 363

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364 PAPERS rose somewhat faster than that of BEA during those years, when the underlying data are standardized with respect to concept. Since then, and particularly after 1967, the gap between FRB and BEA has continued and widened. It is apparent in a similar analysis published by the FRB in connection with its 1971 revision of the industrial produc- tion index. This analysis covered the years from 1947 through 1971. Discussions with officials who prepare these indexes indicate the divergences widened further after 1971, and there was a particularly marked difference in 1974, a year of double-digit inflation. Much time has passed since the Gottsegen-Ziemer study. The purpose of this research paper will be to carry forward the investigation of the sources of differences in the movement of industrial production and real output originating in the industrial sector. The circumstances of declining trend productivity and high inflation rates, double-digit at some times, create the need for such an update. The main thrust of this paper is to examine both the FRB and BEA out- put data in some detail and attempt to understand the reasons for the divergence such as it has been. More attention will be given to statistical procedures as a source of divergence than to concept. The focus of the project is the comparison of BEA'S annual measures of the deflated value of output for the 51 manufacturing cells of the 80-order U.S. input-output table with similar measures constructed from the FRB production index system from 1963 through 1974. The time period is selected to start with a benchmark year and run through one full and one partial benchmark year, 1967 and 1972. Thus, it begins about when the Gottsegen-Ziemer study ended, to avoid duplication, and goes beyond the 1972 partial benchmark through 1974 in order to provide an assessment of the effect of the high inflation rates of 1973-1974 on the measurement of output. THE DATA SET AND TIME PERIODS To facilitate a comprehensive review and analysis of the behavior of the two series, the data set selected should be as disaggregated as possible. The FRB prepares 215 basic series for manufacturing, at a degree of detail averaging somewhat greater than 3-digit sac. But BEA prepares output measures only at the level of disaggregation of the 51 manufacturing cells of the 80-order U.S. input-output (I-O) table, on average between 2- and 3-digit detail. The degree of detail available from BEA iS determined by the level at which it calculates the change in goods-in-process and finished goods inventories necessary to transform its deflated shipments data into

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Comparison of Industry Output Measures in Manufacturing 365 gross output measures. The BEA uses these output measures to derive deflators for gross product originating calculated from the income side of the accounts; but for maximum consistency in comparing FRB and BEA data and the growing use in sectoral research of gross output rather than value added, the analysis here is based on output-side measures. The BEA provided annual data on gross output for the S1 cells for the years 1963-1974. The terminal year was dictated by the availability of data on a 1967 sac definitional basis. FRB data are currently defined on that basis. A concordance was prepared by which the 215 FRB series could be ag- gregated to correspond with the classifications used in the 1967 I-O table. FRB concorded with BEA at that level except in one instance in which FRB data cut across two I-O cells. These two cells (62 and 63) had to be col- lapsed. So the data set was reduced to SO sectors. The FRB prepared an- nual data for these 50 sectors for the same time period. The two data sets are not strictly comparable in concepts for a number of reasons. Probably most important is that FRB data were aggregated to the 50 sectors using value-added weights because gross output value weights were not available. But given the sectors employed in the study, there is not a wide variation in the ratio of value added to gross output. Another noteworthy difference is that the FRB indexes are based on 1963 weights from 1963 to 1966, 1967 weights thereafter. The BEA output measures are based largely on Bureau of Labor Statistics (B[S) price in- dexes, which are weighted by 1963 data. These factors, related to weights, would loom troublesome if the analytical findings were of small dif- ferences between the two series. But they are not important enough to give rise to widespread, large differences between years. To conduct an analysis of differences between the two series, it is necessary to divide the annual data covering 1963- 1974 into several subperiods, as well as to treat the period in its entirety. The need for subperiod analysis reflects FRB'S use of different data sources for different time spans. To measure changes between benchmark years, which coin- cide with the roughly quinquennial censuses of manufactures, FRB relies in large part on 6,000 or so production indexes calculated by the Census Bureau. These indexes are based on physical quantity measures except where they are not available or deemed inadequate. Where physical quan- tities are not the basis for the indexes, they are derived by adjusting shipments for inventory (goods-in-process and finished goods) change and deflating the resulting value of production. Deflation is based on specification-based price indexes of the BES or on unit-value indexes developed by the Census Bureau. The criteria for selection of the ap

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366 PAPERS propriate price series have changed over the years, sometimes swinging in the direction of the BUS indexes, sometimes, the unit values. As noted, the FRB does not use the Census Bureau indexes ubiquitously. Its description of the 1976 revision of the production indexes contains the following: . . . the food, petroleum refining and primary metals industries were some of the major areas where benchmark and annual production levels for a number of series were based on averages of monthly physical quantity data. Special compilations of data made available by trade associations and other industry sources were the basis for new production levels in some industries, including fabricated structural steel and aircraft. In addition, alternative production indexes for certain portions of the textile, printing and machinery industries were compiled by the staff of the Federal Reserve Board of Governors. The changes between 1963 and 1967 in the production indexes for the 50 sectors on which the analysis is based were calculated by FRB in the manner indicated above. The annual changes between those years were in- terpolated primarily by deflated value of production data from the Census Bureau's annual surveys of manufactures. These data are more ag- gregative than those on which the intercensal-year production indexes are based. And the FRB uses measures alternative to those of the Census Bureau in the areas indicated above, where it has eschewed use of the Cen- sus production indexes. Changes during 1963-1967 constitute one subset of data that requires separate analysis. Between 1967 and 1972, another year for which a quinquennial census of manufactures was taken, the FRB has completed a "partial" bench- mark revision. The revision is termed partial because it does not yet incorporate the detailed Census production indexes. It is limited in manufacturing to expansion of the number of series, and use of more comprehensive information for measuring output in petroleum refining, chemicals, construction supplies, and motor vehicles. The revision also in- corporates throughout the index components more comprehensive annual data through 1973 and more accurate monthly series for interpolation through 1973, extrapolation thereafter. Because the data for 1967-1972 reflect partial revision and will be revised later to reflect a complete bench- marking, this subperiod will be analyzed separately. A final subperiod is that of 1973-1974. As noted, some revisions have been made in data for 1973 and in the monthly measures used to extrap- olate 1974. These two years form a subset not because of FRB methods of calculation, but rather because of interest in comparing direct output measures with those based on deflation during a time period when the deflators were accelerating rapidly.

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Comparison of Industry Output Measures in Manufacturing 367 ANALYSIS The analysis that follows is divided into four parts in line with the forgo- ing discussion of how FRB constructs its production indexes. The first part is concerned with the analysis of changes between 1963 and 1967, full benchmark years. The analysis addresses both average annual changes be- tween the two benchmark years and changes between individual years, 1963-1967, for the 50 industries. The second part of the analysis deals with changes between 1967 and 1972. The average annual changes be- tween these two years and between the intervening years are analyzed. The third part of the analysis deals with the 1973-1974 period. Here the analysis is based only on year-to-year changes because benchmarking does not enter at all. The final section deals with the results of analysis covering all years, 1963-1974. The data underlying these analyses are found in the appendix. ANALYSIS FOR 1963-1967 In Table 1 are found average annual rates of change for the 50 industry sectors from 1963 to 1967 for both the FRB and BEA series. The difference between the two series is also shown. For the FRB series, differences in the average annual rates of growth range from 7/10 of 1 percent for tobacco manufactures to 27.0 percent for electronic components and accessories. The simple average annual rate of increase of the FRB series is 7.6 percent. For the BEA series the slowest and fastest rates of growth are registered for the same two industries, although the BEA growth rate for tobacco is slightly negative and that for electronics is considerably less than the FRB index shows. For the entire period the BEA measures average 7.1 percent across all 50 sectors. Thus, the difference between the two series is 0.5 per- cent. Table 2 contains a number of regressions that were estimated using the two sets of data. The general form of the regression was to specify percent- age change in the FRB index as a function of the percentage change in the BEA gross output measure. Estimates were obtained of the intercept and slope of that relationship. Obviously, if the two measures were identical, the intercept would be zero, the slope one, and the correlation 1.00. The first regression in Table 2 is that of the average annual rates of change be- tween 1963 and 1967 for the FRB series and for the BEA series across all 50 industries. As can be seen, the slope term is 1.086, somewhat greater though not significantly larger than unity. The intercept is not signif~- cantly different from zero. In general, the observations are fairly well cor- related; the adjusted coefficient of determination is 0.88. The regression

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380 PAPERS trend rates of growth. And it runs counter to a frequently alleged price in- dex inadequacy, the so-called list-transaction price problem. This prob- lem arises from the notion that the BES iS able to obtain only list prices of commodities and that actual (transaction) prices fluctuate procyclically about such list prices. If that were so, and the evidence, mainly that of Stigler and Kindahl (1970), is not conclusive, BEA deflation would overstate output during cyclical expansions, understate it during contrac- tions. Then one would expect BEA to fluctuate more, cyclically, than FRB rather than the other way around as seems to be the case. In looking at possible reasons for the cyclical pattern, it is interesting to note that in their study of quality adjustment in refrigerator prices, Triplett and McDonald (1977) find a cyclical component in quality change, which if not reflected in price indexes, would tend to reduce the amplitude of fluctuations in the output of refrigerators derived by defla- tion. The cyclical aspects of quality change as they might affect price and directly measured quantity indexes need to be explored further. Were it not for this finding, the likely place one would look in seeking to understand the cyclical differences in the two measures would be constant-dollar inventory change, which must be calculated in the BEA ap- proach. Such calculations must split the change in total inventories into its stage-of-fabrication components, because deflated shipments must be adjusted by the change in finished goods inventories and part, usually half, of the change in goods-in-process inventories. The latter tends to fluctuate procyclically. Finished goods inventories are generally assumed to fluctuate anticyclically initially, reflecting involuntary accumulation or liquidation, procyclically, subsequently, in the absence of perfect foresight. The difficulty of measuring inventory change is well known and has been and is being addressed in several research projects. More needs to be known about the possible cyclical biases in measuring inventory change by stage-of-fabrication. The third major finding of this analysis relates to the behavior of the two output measures during the 1973-1974 period of double-digit infla- tion, years for which the FRB indexes have not been constrained to bench- marks and the mix of monthly series physical quantity, kilowatt hours, and labor hours have been used to measure output. There are large dif- ferences between the two series during this period. The findings of cyclical differences are even more vivid during 1973-1974, perhaps related to high and generalized inflation, and there seems to be no correlation between the two series when the FRB index declines, only a constant gap in the direction pointing to symmetry in the cyclical relationship, i.e., when the FRB index falls, it does so by more than the BEA measure. In contrast, the data sources of the FRB measure seem to matter little. Again, these results appear to suggest that inventory-change measures be assessed.

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Comparison of Industry Output Measures in Manufacturing 381 SUMMARY RECOMMENDATIONS The general recommendation arising from this study is that in seeking to reconcile FRB and BEA output measures, research should focus on the question of why the size and direction of the difference in behavior has a cyclical character. It might be asked why this strategy is recommended, rather than one designed to explain trend differences. The cyclical dif- ferences come through robustly in this analysis. The trend differences, though present, are smaller and potentially much more difficult to understand by direct analysis, given the many reconciliation items like weight and sac differences that would have to be considered at the outset. Furthermore, just as there is an interaction between trend and cyclical forces in an economy, so too, is there likely to be a similar link with respect to the measurement of economic variables. So discovering the reasons for the cyclical behavior of the FRB-BEA gap, may well provide in- sights about the reasons for the trend differences. Three specific recommendations follow from the general recommenda- tion. One appears to fall within the domain of each of three of the statistical organizations involved directly or indirectly in the calculation of the FRB and BEA output measures. 1. FRB should undertake to determine the potential sources of cyclical quality change bias and seek to test empirically for their existence where possible. 2. BUS should engage in a similar undertaking with respect to its price indexes, particularly those components of the producer and consumer price indexes that BEA uses for deflation of shipments and inventories. 3. BEA should undertake an assessment of the way in which it calculates inventory change in general and for purposes of deriving gross product originating by industry in particular. This assessment should focus on whether or not the methods employed and the data (other than price indexes) used in estimating inventory change by stage-of-fabrication contain the potential for imparting cyclical bias, and if so, attempt to quantify it. REFERENCES Gottsegen, Jack J., and Ziemer, Richard C. (1968) Comparison of federal reserve and OBE measures of real manufacturing output 1947-1964. Pages 225-347 in John W. Kendrick, ea., The Industrial Composition of Income and Product. Veil. 32 in Studies in Income and Wealth. New York: National Bureau of Economic Research. (Distributed by Columbia University Press.)

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382 PAPERS Stigler, George J., and Kindahl, James K. (1970) The Behavior of Industrial Prices. New York: National Bureau of Economic Research. (Distributed by Columbia University Press.) Triplett, Jack E., and McDonald, Richard J. (1977) Assessing the quality error in output measures: the case of refrigerators. Review of Income and Wealth Series 23(2):137-156.

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