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Revisions in BES Output per Hour SHARON DE SHA National Research Council INTRODUCTION Journalists, policy makers, business forecasters, and others watching current developments in the economy want statistics on output, employ- ment, prices, money, productivity, and other economic indicators as soon as possible. The federal agencies that produce these statistics have responded to the demands of users by publishing estimates promptly, usually a few weeks after the end of a month or a quarter. Sometimes the first publication is a final estimate, as is the case with the monthly consumer price index. More often, the agencies publish a preliminary estimate, which is revised when better and more complete data become available. This paper will assess the reliability of preliminary estimates of out- put per hour published by the Bureau of Labor Statistics (BES) in terms of the size and direction of revisions. The reliability of productivity ratios depends in part on early estimates of real GNP, which are modi- fied to form the output estimate of the productivity ratio for the private business sector (see Chapter 4, Table 4-21. The studies by Young (1974), Cole (1969), and Jaszi (1965) on the reliability of GNP estimates help us assess productivity ratios. But productivity ratios also depend on the reliability of the estimates of hours in the denominator. Since revisions in estimates of hours may reinforce or offset those in output, a separate revision analysis for output per hour seems called for. The proper way to analyze the reliability of any statistic is to estimate its measurement error. For measures such as GNP and productivity, 239

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240 PAPERS which are made up of many components and based on several samples or estimated by indirect methods, it is extremely difficult to calculate the overall error. Studies of the reliability of GNP estimates and this study of the reliability of productivity measures therefore take the form of revisions analyses. A revisions analysis begins by assuming that the latest revised esti- mate is the most accurate one and is a standard of comparison for all earlier estimates; that is, as revisions are made, measurement error is reduced. However, it is conceivable that some revisions increase mea- surement error. Cole (1969) grapples with this issue in her study of GNP revisions. She argues that if the benchmark estimates and data for a series do not deteriorate over time, it is reasonable to conclude that ''revisions could be expected to improve the accuracy of the estimates" (p. 5~. In other words, if one believes in the accuracy of the benchmark estimates from which extrapolations are made and in the integrity of the data, then the assumption that revisions reduce error is a reasonable assumption for a revisions analysis. The preceding paper by Holland and King evaluates productivity ratios by estimating measurement error directly. The authors use simula- tion and other statistical techniques to estimate the magnitude of overall error that arises from aggregating components, each of which is subject to error. However, they do not have actual measures of the errors of the components; rather they assume certain values for the errors. Until direct estimates of the errors in components can be calculated, there is a need for separate revisions analysis. The paper is organized into three sections. The first section explains how early estimates of output per hour are constructed and why revi- sions are made. The second section presents the evidence on the extent of revisions in quarterly labor productivity measures. It points out that this study has some limitations resulting from the lack of a long time series of productivity measures and from definitional changes of output. The final section summarizes the findings and draws conclusions. The major conclusion is that the revisions in preliminary quarterly measures of productivity are large and that the user of these measures should be made aware of the size of past revisions. It is recommended that the BUS extend this revision analysis and consider publication of the range of past revisions in its quarterly press releases. REASONS FOR FREQUENT REVISIONS The basic procedure for preparing preliminary quarterly estimates is to extrapolate from trends in past quarters with the data that are available

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Revisions in BLS Output per Hour 241 for the current quarter. Revisions occur both in levels and rates of change of quarterly estimates for several reasons. Some revisions occur as more data become available for past quarters, and these affect the trends on which the estimate for the current quarter is based. Other revisions occur because more data for the current quarter become avail- able and replace extrapolations or other assumptions that are used in lieu of current data. In some instances, proxy data sources are replaced by direct data, or estimates from universes replace sample estimates. A few revisions may be made because of computational errors or for other minor reasons. GNP statistics, which are adjusted and used as the output measure ire broad productivity ratios, are revised for all the reasons just given. Some components of GNP are extrapolations that weight together the data from past and current quarters. For example, the BEA prepares monthly retail sales estimates (for each of 3 months of a quarters by combining the estimates for the current month from the Census retail survey with the estimates of the rate of change in retail sales for the previous 36 months. The overall weights given to the current and past months are about 0.2 and 0.8, respectively (Bureau of Economic Analysis, 1979, Chapter 5, footnote 21. When no data are available quarterly, as in the case of proprietors' income, the BEA necessarily relies on extrapolation from past experiences and sometimes on the judgment of the estimator. In some instances, the first estimates are based on less reliable data, which are later supplanted with better data; for example, initial esti- mates of profits are made from data from the Federal Trade Commis- sion and Securities and Exchange Commission, while the revisions are based on more reliable data from the Internal Revenue Service. The BEA has a regular schedule for revisions of estimates of quarterly GNP. Preliminary estimates are released 15 days after the end of a reference quarter, followed 30 days later by the first revision.' The next major revisions of quarterly estimates come at the time of the three annual July revisions that affect estimates for three previous years. 2 When annual revisions are made. the quarterly estimates that are ex- trapolated from the annual ones are revised, as are those interpolated between annual estimates. The last time quarterly estimates are revised is where census quinquennial data sources are incorporated, because a new benchmark affects annual estimates.3 ~ BEA refers to this revision as the 45-day estimate. 2 In response to a recommendation of the GNP Data Improvement Committee the BEA has begun to publish an estimate 75 days after the reference quarter. which is based primarily on new information on corporate profits. 3 Seasonal adjustments are a further source of revisions. Since these adjustments are based on 7-years prior data. they can attect the annual and quarterly estimates For many years.

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242 PAPERS Revisions in hours estimates occur when more sample data are in- cluded in earlier estimates and at the time of employment benchmarks. In contrast to the GNP estimates, total hours have only two major com- ponents, employment and average weekly hours (AWH), both of which are estimated primarily from the survey of employers in the current employment statistics (CES) program.4 The preliminary monthly esti- mates of employment and AWH are based on early sample returns. Thirty days later, BES publishes the first monthly revision, based on a complete set of sample returns. The final, or closing, estimate comes 90 days after the end of the month. A preliminary quarterly estimate of total hours or employment is made up of three monthly estimates: the first month of the quarter is a final estimate, the second month is a first monthly revision, and the third month is a preliminary estimate. Quarterly revisions are then based on the monthly revisions. The other major source of data for average hours is the current population survey, which is also released monthly but is not revised. The monthly (and quarterly) estimates of employment are used to move forward the latest employment benchmark. When a new bench- mark year is introduced, the quarterly estimates of employment (and total hours) will be revised. The benchmark occurs only for the employ- ment component of total hours; average weekly hours estimates are based entirely on monthly sample data. The employment benchmark is scheduled for March of every year, but in recent years the benchmark adjustment has been made every 2 or 3 years (see Buso and Bennett 1968~. s Table 1 shows how frequently revisions are published in quarterly estimates of rates of change in productivity. The preliminary estimate appears under the column heading "one month after the end of a quar- ter." It is based on the 15-day GNP estimate and partial sample returns from the CES. Two months after the quarter the 45-day GNP estimate is available, as is more information from the CES. The first July revision of output is included in the estimates 16, 13, 10, and 7 months after the end of the first, second, third, and fourth quarters, respectively. One can see that there are several revisions before and after the first July revision. In the next section a few key revisions are chosen to assess the reliability of productivity estimates. 4 See Chapter 4, Table 4-4, for a breakdown of the sources of data on hours. 5As for output, seasonal adjustments are based on data for 7 prior years and are a source of revision for years to come.

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Revisions in BLS Outputper Hour EVIDENCE FROM PAST REVISIONS 243 This section examines the characteristics of revision error in estimates of quarterly change in productivity and in its major components, output and hours. It looks only at revisions in rates of change, not at levels. 6 In general, revision error is considered to be the difference between an estimate for a quarter at some point in time and an estimate made at an earlier time. Before examining the characteristics of these errors, we explain why certain revisions are chosen for analysis, how a major defini- tional change in output affects comparisons of early and later estimates, and what is meant by a mixed vintage of the latest revised estimates. There are many revisions in productivity measures (see Table 1), but this analysis examines only the more important ones, which include the preliminary, first monthly, first July, and latest revised estimates. For these four estimates, the values of quarterly rates of change from 1968 to 1977 are shown in Table 2. The first monthly estimate is interesting because it is published only 30 days after the preliminary estimate and is based on more complete monthly data sources. The first July estimate is important because it incorporates annual data sources on output and sometimes the employment benchmark.7 The latest revised estimate is, by the assumption that revisions reduce error, the "best" estimate available. In March 1976, BES changed the scope of its broadest productivity measure from the total private economy to the private business sector. The private business sector excludes some sectors for which measured productivity change is zero, and so it is a better domain for measuring productivity. Because of this change, two series of productivity estimates are shown in Table 2. BUS continues to maintain the latest revised esti- mates for both series, although it publishes current and revised esti- mates only for the private business sector. Table 2 repeats the period from the first quarter of 1975 to the first quarter of 1976, so that com 6Cole (1969) compares revisions errors in levels and rates of change in early estimates of quarterly GNP. When revisions from a benchmark affect levels more than changes, it is an indication that revision errors are due more to forecasting error than to error resulting from incomplete data sources (p. 18). It did not seem as important to examine levels for productivity measures, for the benchmark of hours estimates are generally made every few years and the benchmark adjustments to aggregate hours are small (see Buso and Bennett 1978). 7 The second and third July revisions are also interesting and have been examined in revisions study of GNP. However, these revisions are not included here because the defini- tional change complicates their comparison with earlier or later productivity revisions.

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246 PAPERS TABLE 2 Preliminary and Revised Figures for Changes in Quarterly Output per Hour for Total Private Economy or Private Business Sector, 1968-1977 (percent changes from previous quarter at annual rate) First First Latest Monthly July Revised Quarter Preliminary Revision Revision Estimate Total Private Economy 1968 I II III IV 1969 I II III IV 1970 I II III IV 1971 I II III IV 1972 II III IV 1973 1 II III IV 1974 1.0 0.6 0.7 1.0 -0.3 -0.3 0.2 2.0 -0.6 3.1 4.6 0.5 5.3 1.7 4.3 3.5 2.1 6.0 3.7 5.3 4.7 -0.2 1.6 -1.3 1.2 0.8 0.8 1.0 -0.3 -0.4 0.8 1.6 -0.6 3.1 4.3 0.1 6.1 2.1 5.1 3.4 2.3 6.0 4.1 4.7 4.0 -0.7 1.9 -0.~8 1.2 0.9 0.5 0.9 -0.5 -1.1 1.6 0.8 -2.3 3.2 5.6 0.6 6.5 2.0 3.8 4.1 2.1 6.5 3.1 5.2 6.5 -1.6 -1.5 0.0 5.0 2.5 4.1 0.0 0.6 -1.1 -0.6 -1.1 1.8 1.8 6.6 -2.8 8.4 -0.4 5.8 0.0 4.6 3.4 2.2 6.0 5.1 -3.7 -0.8 0.2 I-5.5- 6.4- 7.6- 5.2 II0.81.40.1- 1 .4 III0.81.40.1- 1.9 IV-5.1- 5.0- 5.1- 1.1 1975 I0.6- 0.21.61.4 II2.04.3NA10.0 III9.511.0NA8.0 IV1.00.6NA-2.0

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Revisions in BLS Output per Hour TABLE 2 Continued First First Monthly July Quarter Preliminary Revision Revision Latest Revised Estimate Total Private Economy 1976 I 4.6 Private Business Sector 6.1 NA 1975 IN.A.NA1.60.9 IIN.A.NA12.711.0 IIIN.A.NA8.58.3 IVN.A.NA-1.6-2.3 1976 IN.A.NA7.65.8 II3.64.03.22.8 III3.83.13.03.2 IV1.50.50.0- 0.1 1977 I3.24.72.82.8 II-1.8- 1.4- 1.2- 1.2 III4.94.55.85.8 IV1.40.50.60.6 SOURCE: Employn~ent and Earnings. N.A. means not applicable because of the change in the scope of the broadest sector for purposes of productivity measurement from total private to private business sector. Total private economy excludes from GNP both output and hours of general government. The private business sector excludes from the total private economy both output and hours associated with rest-oi:-the-world sector, the domestic and not-for-profit sectors, and owner-occupied housing. Output of the private business sector also excludes the statistical discrepancy. See Chapter 4, Table 4.2. 247 parisons can be made between measures with the same definition of output. In the preceding section, it was argued that the latest revisions are best. However, the latest revised estimates are of mixed vintage because of the lags between the time basic data are collected and processed and the time they are available for making estimates of output and hours. For 1968-1971 the latest revisions in productivity include the benchmark of output to the 1967 economic censuses. The estimates from 1972 to 1975 include the third July revisions of output; and for 1976, only the

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Revisions in BLS Output per Hour 249 second July revision. Finally, the 1977 estimates are the first July revi- sions. The hours estimates are of mixed vintage also; the employment benchmarks affect hours only through 1977. Despite the problem of mixed vintage, the revision error calculated on the basis of the latest revisions gives an indication of the probable range of future revisions and is therefore used in the analysis below. CHARACTERISTICS OF REVISION ERROR Table 3 presents several summary statistics that characterize the revision error in early estimates of quarterly change in productivity and its components. These statistics indicate the direction of the error and the amount of variation in the early estimates. The mean error in produc- tivity estimates is small, only about a tenth of a percentage point for the preliminary and first monthly revisions and negligible for the first July revision. Thus, there is no tendency for early estimates to under- state or overstate productivity change. But, the average error for pro- ductivity is small because the negative average revision errors in output and hours are offsetting. The relative mean error, that is, the mean error expressed as a percent of the average of the latest revisions, is less than 10 percent in all cases. A measure of variation used in other revision studies (Jaszi 1965, Young 1974) is the mean absolute error, or dispersion. On the basis of past revisions in productivity measures, this measure indicates that one can expect on average for the absolute amount of revision to be about 1.8 percentage points regardless of sign. This is a considerable revision: it amounts to about 65 percent of the average of the latest revised esti- mates for the preliminary and first monthly estimates and narrows to around 50 percent for the first July estimates. An alternative and more common measure of variance is the standard deviation. For produc- tivity estimates it is about as large as the variation in the largest com- ponent in all cases this component is output. This result is not sur- prising because of the low correlation between the errors in output and hours:8 This statement is based on the following formula for the variance of the difference of two random variables X ~ and X2: var (X ~ -X2) = var (X; ) + var (X2) - 2 cov (X i, X2). The above formula is approximately true where eq is substituted for X~ and eh is sub- stituted for X2 (see footnotes to Table 3). The estimated covariax~ce between eq and eh is about 0.30 for the preliminary, first monthly, and first July revisions.

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Revisions in BLS Output per Hour First Monthly Estimate Percentage of successful revisions 55 63 251 First July Estimate The results thus far indicate that the first monthly revisions are not an improvement over the preliminary estimates, but the first July revi- sions are. This is confirmed by examining the percentage of successful revisions. A successful revision is one that moves the preliminary esti- mate closer to the latest revision. In 36 quarters where comparisons are possible in Table 2, the first monthly revisions of productivity have a success rate of 55 percent. The first July revision performs somewhat better, with a success rate of 63 percent. COMPARISONS WITH PREVIOUS STUDIES There are no other studies on revision error in productivity measures to compare with the results here, but there have been studies of revision error in quarterly GNP statistics that can be compared with the results in the output columns of Table 3. The scope of output defined for GNP and for productivity purposes differs (productivity estimates have output of the total private economy or private business sector in the numerator), but their rates of change are similar enough to allow com parlsons. Table 4 presents the results of studies of revision error in quarterly changes in GNP by Jaszi (1965) and Young (1974) and repeats some results from Table 3. The three studies use the same revision statistics, which are expressed in percentage points. They all use the latest revised estimates as the standard of comparison.9 Jaszi and Young calculated revision statistics for the 45-day estimates, and these are compared with the results for the first monthly output revisions (60 days after the quarter) from Table 3. Young concluded from examining his results and Jaszi's that the early estimates of GNP seem to have improved since the mid 1960s. For the period 1947-1961 (or 1963), Young's results are similar to Jaszi's. Young's study was done 9 years later than Jaszi's, and so Young's esti- mates should be based on a later set of revisions, incorporating the 1962 benchmark. If the benchmarks do not eliminate much revision error, then Young would probably be correct in concluding that ulti 9 There are also res ision studies by Zellner ( ~ 958), Stekler ( ~ 967). and Cole ( ~ 969). but they use different methodologies, and their results cannot be compared with the studies shown in Table 4.

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252 PAPERS mately, on the basis of benchmark revisions, early GNP estimates have been improving. (See Young 1974, p. 25~. The evidence on the period 1968-1977 in Table 4 does not support that conclusion. Unless the differences between changes in GNP and output of total private economy/private business sector are considerable (which is unlikely), then the revisions in GNP are probably getting much larger. In addition, Cole (1969) found that the GNP benchmark revisions have eliminated over 60 percent of revision error for the years 1947-1961 (p. 49~. If revisions in GNP are as large as for total private economy/ private business sector output for 1968-1977 and if benchmarks con- tinue to result in substantial revisions, the early estimates of quarterly GNP since the mid-1960s may be getting less reliable. This result has implications for users both of GNP and productivity estimates. FINDINGS, CONCLUSIONS, AND RECOMMENDATIONS The major finding of this study is that there is considerable revision of the early estimates of quarterly change in productivity. The average absolute revision of preliminary and first monthly productivity measures is about 1.8 percentage points for the preliminary and first monthly estimates, or around 65 percent of the average of the latest revisions. However, these early estimates do not systematically either overstate or understate productivity change. Another finding is that the first monthly revisions of productivity estimates do not improve upon the preliminary estimates. This finding is based on the low success rate of the first monthly revision. The success rate is 55 percent, which means there is little better than a 50-50 chance that the first monthly revision will move the preliminary closer to the final estimate. Finally, we found that the early estimates of output do not appear more reliable for the period since the mid-1960s than for earlier periods. This finding is based on estimates of changes in output of the total private economy or private business sector for 1968-1977 and estimates for GNP for earlier periods. This result should be considered tentative until there is an update of Young's study. One conclusion of this study is that it would be helpful to users to have regular periodic assessments of revisions in productivity and other statistics. They might be interested to learn that the first monthly esti- mates do not systematically improve the preliminary estimates. These assessments might be done by private researchers, by the agency pro

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Revisions in BLS Output per Hour 253 ducing the statistics, or by an overseeing statistical agency like the Office of Federal Statistical Policy and Standards. Moore (1977) has suggested an ongoing review committee outside the government. What form the assessment would take depends on the statistic. Labor force statistics are based on probability samples, and a sampling error can be calculated. But for output, productivity, employment, and other com- posite statistics, analysis of revision error is one major mode of assess- ment. Another is comparison of estimates from different sources of the same magnitude (such as cPs and CES for hours). The development of other modes should be considered. A second conclusion is that revisions are substantial enough that the user of productivity measures, who reads BES press releases but who may know little about statistical quality, should be told something about the reliability of the estimates. The user might be informed that the initial estimates will be revised and how large the revisions are likely to be, using ranges based on past revisions. The BES publishes the initial and revised annual estimates, but these do not inform the user about the reliability of the quarterly estimates. The BEA has developed a revi- sion page for its press release that gives the probable size of revisions in quarterly GNP based on past revisions (however, it uses the first July revision as a standard of comparison). The BUS might consider this page as a model for its own press releases. It is recommended that BUS make its own assessment of the reliability of initial and later estimates of output per hour. The BES could study the magnitude, direction, and other characteristics of estimates of out- put per hour and, on the basis of its findings, consider publishing in its press releases a range of probable revisions (based on historical experi- ence) for initial estimates. REFERENCES Bureau of Economic Analysis (1977) Gross National Product Data Improvement Project Report. Washington, D.C.: U.S. Department of Commerce. Buso, M., and Bennett, W. C., Jr. (1978) BLS establishment estimates revised to reflect new benchmark levels and 1972 SIC. Employment and Earnings 25(10):8-12. Cole, R. E. (1969) Errors in Provisional Estimates of Gross National Product. New York: National Bureau of Economic Research. Jaszi, G. (1965) The quarterly national income and product accounts for the United States, 1942-62. In S. Goldberg and P. Deane, eds., Income and Wealth. Studies in Short-Term National Accounts and Log-Term Economic Growth. Series XI. London: Bowes & Bowes Publishers, Ltd. Moore, G. E. (1977) A continuing audit of government economic statistics. Challenge 20(4):29-33.

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254 PAPERS Stekler. H. O. (1967) Data revisions and economic forecasting. Journal of the America,' Statistical Association 62(318):470-483. Young, A. H. (1974) Reliability of the Quarterly National Income and Product Accounts of the U.S., 1947-71. Order no. COM-74-11538 (July). Springfield, Va.: National Technical Information Service. Zellner, A. (1958) A statistical analysis of provisional estimates of gross national product and its components, of selected national income components, and of personal savings. Journal of the American Statistical Association 281(53):54-65.