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/ A Guide So Seasonal Adjustment ©f Labor Foroe Oaf® U.S. Department of Labor Bureau of Labor Statistics March 1982 Bulletin 2114 a , 3 ; A Guide to Seasonal Adjustment ©f Labor Fore© Data U.S. Department of Labor Raymond J. Donovan, Secretary Bureau of Labor Statistics Janet L. Norwood, Commissioner March 1982 Bulletin 2114 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402-Price $2.00, Stock No. 029-001-02643-9 < . . ■ . ?V HO Uh . id ■..■■■■■ Prd'ffil©® Each month, the Bureau of Labor Statistics issues statistics on employment and unemployment with the term “seasonally adjusted” appended to them. While there seems to be a general understanding of the meaning of employment, unemployment, and unemployment rate, the term “seasonally adjusted” may cause confu sion. This publication explains what seasonal adjustment is, how it works, and why it is important. The expla nation and the examples relate to labor force statistics collected for BLS by the Bureau of the Census in the monthly Current Population Survey. The basic princi ples, however, can help in understanding the use of seasonal adjustment for a wide variety of economic time series. For readers interested in additional information on this subject, a bibliography has been included. An ex planation of how the labor force data are collected and definitions of the terms and concepts used in the labor force data are covered in Concepts and Methods Used in Labor Force Statistics Derived from the Current Pop ulation Survey, BLS Report 463 (1976); How the Gov ernment Measures Unemployment, BLS Report 505 (1977); and the Explanatory Notes of the BLS publica tion, Employment and Earnings. This bulletin was prepared in the Office of Current Employment Analysis, Division of Employment and Unemployment Analysis, by John F. Stinson, Jr., un der the general direction of Gloria Peterson Green. Unless otherwise noted, all seasonally adjusted data in this bulletin are those published at the beginning of 1981 and reflect all revisions up to that time. Material in this publication is in the public domain and may, with appropriate credit, be reproduced with out permission. i iii Contents Page What is seasonality?...................................................................................................................... What is seasonal adjustment and why is it im portant?................................................................. How are data seasonally adjusted?............................................................. .................................. How has the seasonal adjustment process been developed?......................................................... How are the seasonally adjusted labor force data updated each y ear? ........................................ Aggregation of labor force series................................................................................................... Which labor force series are seasonally adjusted and published by the B L S ?............................. Limitations of the seasonal adjustment process............................................................................ 1 1 3 4 5 6 7 8 Chart: 1. Employment status of all civilian workers, seasonally adjusted and unadjusted, 1980 ............................................................................................................... 2 Tables: 1. Seasonally adjusted unemployment rates as originally published and as revised in subsequent years, 1977-80 .......................... 2. Current seasonal adjustment factors for the 12 major labor force components, July-December 1981......................................................................................................... Selected bibliography 6 7 10 A Guide to Seasonal Adjustment of Labor For©© Datsi What is seasonality? Over the course of a year, the size of the Nation’s labor force and the levels of employment and unem ployment exhibit sharp movements due to such season al events as changes in the weather, major holidays, reduced or expanded industrial production, harvests, and the opening and closing of schools. Some specific examples of these events are the increase in retail sales each December due to the Christmas buying rush, the decline in construction activity during the winter months, and the expansion in the labor force each June when schools close and many youth enter the labor market in search of jobs. Often these seasonal fluctuations are large and thus overshadow or obscure other movements in the data. For example, typically more than 90 percent of the monthly variation in the level of unemployment results from seasonal conditions (chart 1). Because these events follow a more or less regular pattern each year, their influence on the more important, longer term trends in the data can be eliminated by adjusting the statistics over the course of a year. Total unemployed ... Unemployment rate January 7,233,000 6.9 8,543,000 1981 8.2 DecemberJanuary change 1,310,000 1.3 The number of unemployed persons rose by over 1.3 million and the unemployment rate increased from 6.9 to 8.2 percent. Unemployment, however, always rises between December and January, as cold weather causes a cutback in outdoor jobs and as persons hired tempo rarily for the Christmas buying season are no longer needed. The important information for an economic an alyst or policymaker is whether or not the increase in unemployment was greater or less than usual. Data for the same 2 months after seasonal adjustment give a dif ferent picture: Total unemployed........... Unemployment ra te ........ December 1980 January 7,785,000 7.4 7,847,000 7.4 1981 DecemberJanuary change 62,000 Seasonally adjusted data provide a completely differ ent perspective on the employment situation. When the normal seasonal increase in unemployment is removed, via seasonal adjustment, both the number of unemployed persons and the unemployment rate show no significant change between December and January, rather than a sharp increase as indicated by the unadjusted data. This is not to deny, however, that there were actually over 8.5 million persons unemployed in January 1981, an in crease of 1.3 million from December 1980. On an indi vidual basis, the experience of unemployment was very real. But in order to interpret the movements of the unemployment time series, aggregated over many indi viduals, it is essential to recognize and adjust for the seasonality; it is important to know that a particular kind of increase or decrease always takes place at a certain time in the year. Such seasonal changes may sometimes warrant special short-term programs such as those which provide summer jobs for youth; but since What is seasonal adjustment and why is it important? Seasonal adjustment is a statistical tool that attempts to remove, or filter out, seasonal fluctuations in a time series. Once the seasonal component has been removed, the series is said to be seasonally adjusted, and nonseasonal developments such as cyclical swings in eco nomic activity are easier to observe. Without the use of seasonally adjusted data, observations of change for a particular pair of months could be compared proper ly only with those for the same pair of months in oth er years where the seasonal influences were the same. Consequently, it would be difficult to make accurate comparisons over time, such as for a 6-month period or an entire business cycle. The following examples illustrate the use of seasonal adjustment as a tool in analyzing changes in labor mar ket activity. The actual (not seasonally adjusted) data for December 1980 and January 1981 show a marked deterioration in the employment situation: December 1980 the effects o f such changes are transient, they do not portend any fundamental changes in the Nation’s employment situation. 1 Chart 1. Employment status of all civilian workers—seasonally adjusted and unadjusted,, 1980 Thousands Employed , Thousands 99000 98000 97000 96000 Thousands Unemployed Thousands 8500 8500 8000 8000 7500 7500 7000 7000 6500 6500 6000 6000 P ercen t 8.0 7=5 7 .0 6=5 6=0 1980 2 the seasonally adjusted data, from which the usual in crease caused by the influx of students into the labor market has been removed. The seasonally adjusted data reveal that the increase in employment between May and June was only a little greater than normal, about 250,000. Each of these examples illustrates the importance of using seasonally adjusted data in the analysis of labor market statistics. Without such data, it would be ex tremely difficult to determine how much of a change in a data series was due to normal seasonal patterns and how much was due to an actual change in the under lying economic conditions. Additionally, it is of crucial importance that economic policymakers, who use the employment and unemployment statistics as a guide to the health of the economy, have statistics which can be compared directly from 1 month to the next so that they can accurately follow trends in the labor market and implement the proper economic policies. The following data on the total unemployment rate for February, March, April, and May of 1980 also show how important it is to use seasonally adjusted data to interpret trends: Total unemployment rate, not seasonally adjusted ........................ Total unemployment rate, seasonally adjusted ........................ February 1980 March 1980 April 1980 May 1980 6.8 6.6 6.6 7.0 6.2 6.3 6.9 7.6 The unadjusted data indicate that, between February and April, there was a very slight improvement in the economic situation, as the jobless rate edged down from 6.8 to 6.6 percent. Unemployment, however, always declines between February and April as the weather improves and outdoor work activity increases. Once more, the important question is: Was the decline in un employment greater or less than what usually occurs? The seasonally adjusted data reveal that the decline was much less than usual; the seasonally adjusted unemploy ment rate increased sharply between February and April, rising from 6.2 to 6.9 percent. Extending this analysis through May, there was a very small increase from February to May in the unadjusted data, from 6.8 to 7.0 percent, versus a very large increase—1.4 per centage points— in the seasonally adjusted rates. The unadjusted unemployment rate in May was much high er than would have been expected, given the unadjust ed rate in February, and, in reality, there was a sharp upward trend in unemployment as a recession set in. The only way to know how much higher the rate was in May, and how severe that sharp upward trend was, is to have reliable estimates of the normal seasonal movements over those months. The seasonally adjust ed series clearly identified what was going on; looking at the unadjusted series alone without knowledge of the seasonality would have been misleading. The following data on employment, from May to June of 1979, are a further example of the importance of using seasonally adjusted data when making monthto-month comparisons: May 1979 Total employment, not seasonally adjusted ...... Total employment, seasonally adjusted ...... June 1979 How are data seasonally adjusted? Underlying the process of seasonal adjustment is the basic assumption that an economic time series can be broken down into four distinct components: The trend (T), the cyclical (C), the seasonal (S), and the irregular (I). The trend component is defined as that part of a time series which shows a smooth or regular movement over a long period of time. The cyclical component is that part which displays periodic fluctuations of a reason ably long-term nature (generally 2 to 5 years) around the trend in response to the ups and downs in business conditions. For seasonal adjustment purposes, the trend and cyclical components are often treated together as a single, trend-cycle (TC) component. The seasonal com ponent is that part of a time series which features the repetitive pattern of ups and downs over the course of a year caused by regular events such as changing sea sons, holidays, and school enrollment patterns. It is this component that the seasonal adjustment process is de signed to isolate and remove from a time series. The final component, the irregular, is made up of the fluc tuations in a time series that are random, unusual move ments caused by a variety of factors. These factors would include such things as extremely adverse weath er conditions, natural disasters, labor-management dis putes, civil disturbances, and other unpredictable, nonregularly recurring phenomena. Another likely source of the irregular component, however, is simply statis tical or sampling errors, differences that occur princi pally because the data are derived from a sample sur vey rather than from a complete census each month. Each of these concepts can be illustrated by break ing down the monthly time series on total employment in the United States into the four components. The trend component of total employment is the long-term May-June change 96,220,000 97,917,000 1,697,000 96,590,000 96,838,000 248,000 The data, unadjusted for seasonality, give the impres sion that the economy was doing extremely well, with total employment increasing by almost 1.7 million. Em ployment, however, always rises sharply between May and June, as large numbers of school-age youth enter the labor market. For policymaking and analytical pur poses, the important thing to know is whether or not the increase was consistent with that which normally occurs in June. This can be determined by examining 3 growth in employment that has occurred as the popu lation has expanded and as a greater proportion of the population, particularly women, have entered the labor force and found jobs. The cyclical component is repre sented by the periodic expansions and contractions of employment (around the long-term, upward trend) caused by swings in business activity. The seasonal com ponent is comprised of the predictable monthly changes in the number of jobs which tend to occur each year. Finally, the irregular component is made up of the shifts in employment caused by random, unpredictable events or by sampling errors that may be present in the data. The relationship between the original time series, (0), and its four components depends on the statistical mod el that best represents the interaction of the four com ponents. Two of the most common models used are the multiplicative and additive models. In the multiplicative model, the original series is as sumed to be the product of the trend, cyclical, season al, and irregular components. Seasonal changes in the model are assumed to be proportional to changes in the level of the series. The multiplicative model can be ex pressed as: The first step is to obtain a measure o f the trend-cycle component by calculating a centered 12-month moving average of the original data for each m onth.1 This average, which provides an approximation o f the trendcycle component, is then divided into the original time series to remove the trend-cycle component, leaving on ly the seasonal and irregular components which are ex pressed in percentage terms: 0 TCxSxI -----<=--------------= S x I TC TC The next step is to remove the irregular component by averaging the S x I ratio for each month over a number of years to get a mean value of the S x I ratio for that particular month. Since the averaging process is assumed to remove most of the irregular component, the mean values of the S x I ratio represent an estimate of the isolated seasonal component. This seasonal com ponent, or seasonal factor, is then divided back into the original time series to remove the seasonal component and yield seasonally adjusted data. The final relation ship can be expressed as: 0=TxCxSxI 0 TCxSxI _ = --------------= TC x I = Seasonally adjusted data S S In the additive model, the original series is assumed to be the sum of the trend, cyclical, seasonal, and ir regular components. In additive models, seasonal changes are assumed to be constant in magnitude. The additive model can be expressed as: This description of the seasonal adjustment process has been simplified to illustrate the basic principles of the procedure. Although most of the seasonal adjust ment methods are more complex and utilize a number of statistical techniques to smooth the data and produce reliable seasonal factors, they build on these basic principles. 0=T+C+S+I How has the seasonal adjustment process been developed? The fundamental premise of seasonal adjustment is that the seasonal component of a time series can be measured and separated from the trend, cyclical, and irregular components. While there are a number of sta tistical techniques available for isolating the seasonal component of a time series, the most commonly used is probably the ratio-to-moving average method. The Bureau of the Census X -ll seasonal adjustment pro gram, a widely used computer program for seasonally adjusting time series data, is a variation of the basic ratio-to-moving-average technique. The following discus sion of this technique assumes a basic multiplicative model, but the procedure is similar for the basic addi tive and other models. The seasonal adjustment process starts with the orig inal series: The theoretical foundation of modern seasonal ad justment techniques was developed in the first several decades of this century. Warren Persons of Harvard University is credited with being the first to decompose ' A moving average is also a time series. The values for a 12-month moving average are calculated by taking the average value o f each possible set of 12 consecutive observations from the original series. For example, in computing a 12-month moving average based on a monthly time series starting in January of some year, the first value for the moving average series would be computed by averaging the values for January through December of that year, the second value would be computed by averaging the data for February o f that year through January of the following year, and so forth. A centered 12month moving average is then calculated by computing a 2-month moving average o f the values in the 12-month moving average series, placing (centering) each result in the middle month o f the 13 months originally participating in each calculation. For example, the first re sult would involve data for January o f the first year through Janu ary of the following year and would be placed in July of the first year. 0 = TC X S XI 4 time series into their four component parts, in 1919.2 The standard ratio-to-moving-average technique was developed in the 1920’s by Frederick Macaulay at the National Bureau of Economic Research.3The early sea sonal adjustment procedures, however, were cumber some and required numerous, lengthy manual calcula tions. It was only with the introduction of high-speed electronic computers in the 1950’s that the seasonal ad justment of a large number of time series in a short pe riod of time became feasible. Research conducted by Julius Shiskin at the Bureau of the Census led to the introduction in 1954 of a com puter program for seasonal adjustment entitled the Cen sus Method I, which was essentially a refinement of the standard ratio-to-moving-average technique. This pro gram greatly expedited the seasonal adjustment proc ess, permitting the wider use of seasonally adjusted data in the statistical analysis of the economy. In 1955, this original program was replaced with a revised proce dure, the Census Method II. The X -ll variant of the Census Method II, introduced in 1965, is at present probably the most widely used seasonal adjustment program.4 The seasonal adjustment of labor force data has changed considerably over the years, keeping pace with improvements in methodology. Seasonally adjusted la bor force data were first published in the mid-1950’s and were adjusted using the Census Methods I and II. In 1960, the BLS Seasonal Factor Method,5 similar in most respects to the Census technique, was adopted as the official BLS procedure for seasonally adjusting the labor force data and was used until 1973, when a shift was made in the seasonal adjustment methodology. In 1973, data prior to 1967 that had already been season ally adjusted by the BLS Seasonal Factor Method were “frozen” and were subject to no further revision. Data for 1967 and later years, however, were now adjusted by the X -ll Variant of the Census Method II, which was capable of adjusting shorter time series than the BLS method. Use of the standard X -ll method contin ued through 1979. In January 1980, the BLS adopted the X -ll ARIMA (Auto-Regressive Integrated Moving Average) tech nique as its official method for seasonally adjusting na tional employment and unemployment data. The X-11 ARIMA method (developed under the direction of 2Warren M. Persons, “Indices o f Business Conditions,” Review o f Economics and Statistics, Vol. 1, 1919, pp. 5-107; and “An Index o f General Business Conditions,” Review o f Economics and Statistics, Vol. 1, 1919, pp. 111-205. F rederick R. Macaulay, The Smoothing o f Time Series (New York, National Bureau o f Economic Research, 1931). 4Julius Shiskin, Allan H. Young, and John C. Musgrave, The X - ll Variant o f the Census Method II Seasonal Adjustment Program, Tech nical Paper No. 15 (Bureau o f the Census, 1967). 5 The BLS Seasonal Factor Method (1966) (Bureau o f Labor Statis tics, 1966). Estela Dagum at the Canadian national statistical agen cy, Statistics Canada) is a modified version of the stand ard X -ll procedure.6The ARIMA method adds 1 year of forecasted data to the time series being adjusted and then seasonally adjusts the enlarged time series with the standard X -ll method. The forecasted data are projec ted through the use of ARIMA statistical models which have been fitted to the individual series. By including the year of forecasted data, the X -ll ARIMA proce dure is able to provide better seasonal adjustment fac tors for the year being currently adjusted than the stand ard X-11 procedure can; that is, the size of the revisions in the seasonally adjusted data is expected to be some what less when the statistics are updated and new sea sonal factors are calculated at the end of each year. At present, ARIMA models have been identified for about 75 percent of the major labor force series that are di rectly seasonally adjusted. The remaining series are still adjusted with the standard X -ll method. How are the seasonally adjusted labor force data updated each year? Twice each year, in January and July, the seasonal adjustment factors used in adjusting labor force data are updated with the X -ll ARIMA program. Each Jan uary, the original (not seasonally adjusted) data through December of the year just completed are added to the data previously used in the seasonal adjustment process and are run through the X -ll ARIMA computer pro gram, generating revised seasonally adjusted data for the previous 5 years and seasonal factors for the next 6 months. Each month, the seasonal factors for that month are applied to the newly collected original esti mates to derive the seasonally adjusted figures for the various labor force series. When a multiplicative sea sonal adjustment method is used, the unadjusted data are divided by a seasonal factor to calculate the sea sonally adjusted figure. When an additive seasonal ad justment method is used, the seasonal factor is sub tracted from the unadjusted level to calculate the sea sonally adjusted level. Then in July, the not seasonally adjusted data from January to June are incorporated into the historical data base and the data are rerun through the X -ll ARIMA seasonal adjustment proce dure. At this time, however, only new seasonal factors for the July-December period are produced, and no re visions are made in the historical data. Updating of the seasonal factors on a 6-month basis is a relatively new practice that was initiated in 1980 at the same time the X -ll ARIMA seasonal adjustment method was adopt ed. Previously, seasonal adjustment of the data was car ried out once a year, in January, and seasonal factors for all 12 months of the coming year were created. The reason for the change in procedure was that, in the past, 6Estella Bee Dagum, The X - l l ARIMA Seasonal Adjustment Meth od (Statistics Canada, February 1980). 5 Table 1. Seasonally adjusted unemployment rates as originally published and as revised in subseqent years, 1977-80 1977 Month January ......................................... February........................................ March ............................................ April ............................................... M ay................................................ June............................................... July ................................................ August................... ....................... September.................................... O ctober......................................... November..................................... December..................................... Origi 1978 1979 1980 1981 nally pub revision revision revision revision lished 7.3 7.5 7.3 7.0 6.9 7.1 6.9 7.1 6.9 7.0 6.9 6.4 7.4 7.6 7.4 7.1 7.1 7.1 6.9 7.0 6.8 6.8 6.7 6.4 7.4 7.5 7.4 7.2 7.1 7.2 6.9 7.0 6.8 6.8 6.7 6.3 7.4 7.6 7.4 7.2 7.1 7.2 6.9 7.0 6.8 6.7 6.7 6.2 Origi nally pub lished 6.3 6.1 6.2 6.0 6.1 5.7 6.2 5.9 6.0 5.8 5.8 1 6.0 7.5 7.6 7.4 7.2 7.0 7.2 6.9 6.9 6.8 6.8 6.7 6.3 1979 1980 1981 revision revision revision 6.3 6.1 6.2 6.1 6.1 5.8 6.1 5.9 5.9 5.8 5.8 5.9 1980 1979 1978 6.4 6.1 6.2 6.1 6.1 5.9 6.2 5.9 5.9 5.7 5.8 5.9 6.4 6.2 6.2 6.1 6.0 5.8 6.1 5.8 5.9 5.7 5.8 6.0 Origi nally pub lished 5.8 5.7 5.7 5.8 5.8 5.6 5.7 6.0 5.8 6.0 5.8 ' 5.9 1981 1980 revision revision 5.8 5.7 5.7 5.8 5.8 5.7 5.7 5.9 5.8 5.9 5.8 5.9 5.8 5.9 5.8 5.8 5.6 5.6 5.6 5.9 5.8 5.9 5.9 6.0 Origi nally pub lished 6.2 6.0 6.2 7.0 7.8 7.7 7.8 7.6 7.5 7.6 7.5 1 7.3 1981 revision 6.2 6.2 6.3 6.9 7.6 7.5 7.6 7.6 7.4 7.6 7.5 7.4 1 Never published when the seasonal factors were updated only in Janu ary, sizable revisions sometimes occurred in the data for the last half of the previous year. More reliable sea sonal factors for those last 6 months can be produced when they are updated at midyear through the incor poration of data for the first 6 months of the year. The revisions in the data, typically small even for the year just completed, generally get progressively small er over the 5-year revision span. An indication of how small the revisions can sometimes be is shown in table 1. After being revised in January 1980, the seasonally adjusted monthly total unemployment rates for 1979 were not affected at all in 9 months and changed by only 0.1 percentage point in the other 3 months. Revi sions were more extensive in 1977 and 1980, years when more sizable cyclical shifts occurred in the unemploy ment data. It would be possible to update the seasonal adjust ment of the labor force data each month when the new data became available rather than wait for the accumu lation of 6 months of new data. In fact, the National Commission on Employment and Unemployment Sta tistics recently recommended that the BLS consider us ing this technique, known as the concurrent method of seasonal adjustment, for the principal labor force series such as total employment and unemployment.7 Under this procedure, however, the seasonal factors could not be published in advance because new seasonal factors would be created each month when a new month’s data became available and were added to the data base for the seasonal adjustment process. BLS felt that any tech nical advantages gained through monthly updating might be outweighed by the possible erosion of public confidence resulting from the cessation of prior publi cation of the factors to be used. Therefore, it was de cided only to update the seasonal factors every 6 months, a procedure which improves the data for the second half of the year while still enabling the seasonal factors to be published in advance. The BLS, however, main tains and makes available to interested data users sev eral unofficial monthly data series for the total unem ployment rate seasonally adjusted by alternative meth ods, including the concurrent method. These alterna tive methods, which represent slight variations of one aspect or another of the official adjustment method, produce a range of unemployment rates that usually do not vary much from the official rate in any 1 month (typically 0.2 percentage point or less). Aggregation ©f labor force series Many labor force series are not directly seasonally adjusted but are summed or aggregated from other se ries that are directly adjusted. This aggregation proc ess is used to calculate the seasonally adjusted estimates for the overall civilian labor force, total employment, total unemployment, and the unemployment rate. The civilian labor force, for example, represents the sum of eight individually seasonally adjusted employment se ries and four individually adjusted unemployment se ries. The eight employment series are those for men and women 16-19 years of age and men and women 20 years and over employed, respectively, in agricultural and nonagricultural industries. The four unemployment series are the number of unemployed men and women 16-19 years and 20 years and over. Examples of month ly seasonal adjustment factors for each of these 12 se ries, covering the period of July to December 1981, are shown in table 2. Each month, the eight individual employment series are seasonally adjusted and then summed to arrive at the seasonally adjusted level of total employment; the same is done with the four unemployment series. The seasonally adjusted total employment and unemploy 7 National Commission on Employment and Unemployment Statis tics, Counting the Labor Force (Washington, D.C., 1979), pp. 223-25. 6 directly adjusted by BLS each year, hundreds of other seasonally adjusted series are derived from these com ponent series by the addition or subtraction of one or more series, dividing one series into another, or aver aging monthly data over 3-month spans to produce quarterly averages. ment series are then summed to arrive at the seasonal ly adjusted civilian labor force. The seasonally adjust ed total unemployment rate is calculated by dividing the seasonally adjusted level of unemployment by the seasonally adjusted civilian labor force. This process of directly seasonally adjusting compo nents and then aggregating these to arrive at seasonal ly adjusted totals is used because individual components often have widely differing seasonal patterns. For ex ample, the seasonal employment pattern of 16- to 19year-old men in agriculture is very different from that of men 20 years and older in nonagricultural industries because of the influence of the school year and crop cycles. Because the official seasonally adjusted employment and unemployment totals are produced by the addition of eight employment series and four unemployment se ries, they will not agree with the totals produced by summing other independently seasonally adjusted se ries, such as the number of employed and unemployed broken down by race, occupation, or the various age categories. The differences between the official season ally adjusted employment and unemployment totals and those derived by the addition of other labor force se ries, however, are usually not substantial. The process does assure that the seasonally adjusted labor force lev el for a given group will always be the sum of its em ployment and unemployment components. The total employment and unemployment series are not the only ones produced by aggregating component series. While more than 200 labor force time series are Which labor force series are seasonally adjusted and published by the BLS? Each month, BLS receives hundreds of thousands of individual data items collected in the Current Popula tion Survey. It is not technically feasible to publish each of these series, nor is it possible to seasonally adjust more than a small proportion of the total. Only the most important indicators of labor market activity are selected for seasonal adjustment. These include, in ad dition to the highly publicized data on the civilian la bor force, total employment, and total unemployment, breakdowns of these totals by important demographic characteristics such as sex, age, race, Hispanic ethnicity, and marital status as well as by full- or part-time status, occupation, industry, class of worker, and the reasons for and duration of unemployment. Numerous rates are calculated: Labor force participation rates, employ ment-population ratios, and, of course, rates of unem ployment. In addition, selected quarterly data on per sons not in the labor force are published in seasonally adjusted form. A total of about 1,800 monthly and quar terly labor force series are adjusted either directly or derived from other seasonally adjusted series. Out of this total, about 500 of the principal series are published Table 2. Current seasonal adjustment factors for the 12 major labor force components, July-Deeember 1981 July August September October November December Agricultural employment: Males, 20 years and o v e r............... Females, 20 years and o ver........... Males, 16-19 years .......................... Females, 16-19 years...................... 1.073 1.268 1.600 1.982 1.063 1.173 1.448 1.779 1.057 1.128 1.097 1.010 1.045 1.134 1.010 .883 1.001 .928 .803 .656 0.954 .831 .695 .592 Nonagricultural employment: Males, 20 years and over............... Females, 20 years and over........... 1.007 .974 1.007 .976 1.003 1.002 1.006 1.012 1.003 1.015 1.001 1.016 Unemployment: Males, 20 years and o v e r............... Females, 20 years and over........... .996 1.024 .963 1.075 .883 1.061 .883 1.022 .907 .977 .943 .929 Nonagricultural employment: Males, 16-19 years .......................... Females, 16-19 years...................... 928 677 723 481 -257 -203 -186 -68 -214 -19 -179 70 Unemployment: Males, 16-19 years .......................... Females, 16-19 years...................... 185 192 -29 50 -68 21 -73 -46 -25 -62 -46 -130 Procedure and series Multiplicative Adjustment1 Additive Adjustment1 1When the m ultiplicative seasonal adjustment method is used, seasonally adjusted data are calculated by dividing the seasonal factors into the original, or not seasonally adjusted data; when the additive seasonal adjustment method is used, seasonally adjusted data are calculated by subtracting the seasonal factors from the original data, 7 over previous years. When the seasonal pattern of the current year deviates from the average seasonal pattern of earlier years as a consequence of such factors as ex tremes of climate and shifting dates of holidays, the seasonal adjustment process will fail to capture and re move all of the seasonal movements of the time series in question, or it may remove more of the seasonal movements than is warranted. As a result, the season ally adjusted data may, at certain times, exhibit erratic behavior or lack of smoothness. These rough points are often smoothed over in subsequent years when the sea sonal adjustment program is rerun to incorporate the latest available data. An example of a problem in seasonally adjusting la bor force data caused by a possible shift in the season al pattern is illustrated below based on initial (unrevised) seasonal adjustments: regularly on either a monthly or quarterly basis in Em ployment and Earnings. At the beginning of each year, when the seasonally adjusted data are revised, 5 years of the revised data for a few hundred of the monthly series are published in the February issue of Employment and Earnings. Also, seasonal adjustment factors for the forthcoming 6 months for the 12 labor force series used in computing the total unemployment rate are published in the Jan uary and July issues of Employment and Earnings. Ad ditionally, packages of summary sheets showing recent years of original, or not seasonally adjusted, data and the entire span of seasonally adjusted data for each of the approximately 1,800 seasonally adjusted labor force time series are made available in January of each year to interested data users. Not only have the techniques of seasonal adjustment changed over time, but the quantity of seasonally ad justed data that is published and the role that these data play in the analysis of the labor market situation have been greatly expanded. The first seasonally adjusted la bor force data series to be published was an index of the level of unemployment that appeared in the Month ly Report on the Labor Force from January 1955 to De cember 1956. Regular publication of the seasonally ad justed total unemployment rate began in June 1957, to gether with a chart showing historical data on the sea sonally adjusted levels of employment and unemploy ment. Seasonally adjusted data on the unemployment rates of men and women were added to the regularly published data in 1958, and a growing number of oth er time series were seasonally adjusted and published at the beginning of each year when the data were re vised. The quantity of seasonally adjusted data pub lished on a regular monthly basis, however, was not expanded until February 1963, when, on the recom mendation of the President’s Committee to Appraise Employment and Unemployment Statistics, BUS began publishing 5 new statistical tables containing a total of 34 seasonally adjusted data series. Since then, the quan tity of regularly published seasonally adjusted data has expanded steadily, to the point where Employment and Earnings currently has 10 monthly tables containing a total of 227 seasonally adjusted series and an addition al 10 tables with 279 series on a quarterly basis. At the same time, the role of seasonally adjusted data in labor market analysis has expanded from a secondary posi tion to where it now forms the keystone of the month ly analysis of the Nation’s employment situation. April 1980 June 1980 (in thousands) Civilian labor force, total 16 years and over, seasonally adjusted......................... Over-the-month change.. Civilian labor force, total 16 to 24 years, seasonally adjusted......................... Over-the-month change.. 104,419 105,142 723 104,542 -600 24,541 24,986 445 24,471 -515 The seasonally adjusted civilian labor force for per sons 16 years and over increased by 723,000 between April and May 1980 and then declined by 600,000 in June. A substantial portion of these changes occurred among persons 16 to 24 years of age, as a larger than usual number of school-age youth began searching for jobs in May, somewhat earlier than normal. Because the seasonal adjustment process normally adjusts for this increase of young people in June, the adjustment was thrown off by the unusual change in May. If these shifts do in fact represent a change in the seasonal pat tern (similar movements did occur in 1981) subsequent seasonal adjustments should reflect the changes more accurately. The fact that the data will be smoothed in future years is not much help to policymakers who have to make decisions based on the data currently available and cannot wait a year until the data are revised. Con sequently, much of the research in the area of seasonal adjustment of labor force data has focused on improving the quality of the current seasonally adjusted data. The changes made in the seasonal adjustment process in 1980, specifically, the adoption of the X -ll ARIMA seasonal adjustment procedure and the 6-month up dating of the seasonal adjustment factors, should help eliminate some of the problems of erratic movements in the current data. Limitations of the seasonal adjustment process It should be realized that the seasonal adjustment process has its limitations. One problem lies in the bas ic nature of seasonal adjustment. By necessity, current seasonal adjustment is an approximation based on the average seasonal movements of a particular time series May 1980 8 A second problem in the seasonal adjustment proc ess concerns sampling variability of the seasonally ad justed labor force data. Because all of the labor force data are gathered through a sample survey, they are subject to a degree of sampling variability, which is measured in terms of standard errors, or variations that occur by chance because a sample rather than the en tire population is surveyed. To cite an example, it has been determined that the standard error of the monthto-month change in the total unemployment rate is 0.19 percentage point at the 90-percent level of confidence. This means that the chances are 9 out of 10 that month ly changes in the unemployment rate of less than this magnitude could be due entirely to sampling error and may not represent an actual change in labor market conditions. Standard errors for major labor force series together with tables that provide the information needed to calculate standard errors for other labor force series are published monthly in the Explanatory Notes of Em ployment and Earnings. However, the standard errors presently reported for the employment and unemployment statistics apply to the data prior to seasonal adjustment. Applying these standard errors to the seasonally adjusted data assumes that the seasonal adjustment process does not affect the accuracy of the estimates, an assumption that may not be correct. Despite its smoothing effect, the seasonal adjustment process probably adds to the errors associ ated with the unadjusted statistics. Thus, if standard er rors were available for the seasonally adjusted current data, they might exceed the standard errors published for the unadjusted data by as much as 10 to 20 percent.8 9 The reports of both the President’s Committee to Ap praise Employment and Unemployment Statistics in 1962 and the National Commission on Employment and Unemployment Statistics in 1979 urged the Bureau of the Census, the agency responsible for computing stand ard errors for CPS labor force data, to undertake the research necessary to calculate errors for the seasonal ly adjusted statistics. To date, techniques have not been devised to take seasonal adjustment into account in the estimation of standard errors.9 While the seasonal adjustment process has limitations, it does, with rare exceptions, adequately remove the normal seasonal fluctuations from the labor force data. The process is constantly monitored to make sure it continues to perform adequately. And, as improvements are made in the techniques of seasonal adjustment, these new methods are routinely tested on the labor force data to determine if they increase the quality of the seasonal adjustments.10 If they meet this test, they are incorporated into the official seasonal adjustment methodology. 8Ibid., p. 227. 9For an attempt at such a calculation, see Lawrence H. Summers, “Unemployment in the 1980 Recession,” an unpublished paper pre sented at the October 2, 1980, meeting o f the Brookings Panel on Economic Activity. 10The principal criterion that BLS uses to evaluate the quality of alternative seasonal adjustment methods is revision error; i.e., how close do the initial seasonally adjusted estimates come to later revi sions? The method which produces smaller revision errors is deemed to be better. S@l@©Sedl ®ilblD©gr@p[hif Bregger, John E. “ Unemployment Statistics and What They Mean,” Monthly Labor Review, November 1971. Pierce, David A. “ A Survey of Recent Developments in Seasonal Adjustment,” The American Statistician, Vol. 34, August 1980. Brittain, John A. “ A Regression Model for Estimation of the Seasonal Component in Unemployment and Other Volatile Time Series,” Review o f Economics and Statistics, Vol. 44, February 1962. President’s Committee to Appraise Employment and Unemployment Statistics. Measuring Employment and Unemployment. Washington, D.C., 1962. Brittain, John A. “ Testing For and Removing Bias in the Seasonally Adjusted Unemployment Series,” Brookings Papers on Economic Activity, 1:1976. Shiskin, Julius. Electronic Computers and Business Indicators. Occasional Paper No. 57. New York, National Bureau of Economic Research, 1957. / Shiskin, Julius. “ Time Series: Seasonal Adjustment,” in International Encyclopedia o f the Social Sciences. New York, Macmillan Publishing Co., Inc., 1968. Dagum, Estela Bee. “ Seasonal Adjustment Methods for Labor Force Series,” in Data Collection, Processing and Presentation: National and Local. Appendix Vol. II, Counting the Labor Force. National Commission on Employment and Unemployment Statistics. Wash ington, D.C. 1979. Shiskin, Julius, and Plewes, Thomas J. “ Seasonal Ad justment of the U.S. Unemployment Rate,” The Statistician, Vol. 27, Nos. 3 and 4, 1979. Dagum, Estela Bee. “ On the Seasonal Adjustment of Economic Time Series Aggregates: A Case Study of the Unemployment Rate,” in Data Collection, Processing and Presentation: National and Local. Appendix Vol. II, Counting the Labor Force. National Commission on Employment and Unem ployment Statistics. Washington, D.C., 1979. Shiskin, Julius; Young, Allan; and Musgrave, John. The X - ll Variant o f the Census Method II Seasonal Adjustment Program. Technical Paper No. 15. Bureau of the Census, U.S. Department of Com merce. Washington, D.C., 1967. Dagum, Estela Bee. The X - ll ARIM A Seasonal Adjust ment Method. Statistics Canada, Catalogue No. 12-564E. February 1980. U.S. Department of Commerce, Bureau of the Census. Seasonal Analysis o f Economic Time Series. Eco nomic Research Report, ER-1. Washington, D.C., 1978. Lovell, Michael C. “ Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis,” Journal o f the American Statistical Association, Vol. 58, December 1963. U.S. Department of Labor, Bureau of Labor Statis tics. The BLS Seasonal Factor Method (1966). Washington, D.C., 1966. Mclntire, Robert J. “ Revision of Seasonally Adjusted Labor Force Series,” Employment and Earnings, January 1981. U.S. Department of Labor, Bureau of Labor Statistics, and U.S. Department of Commerce, Bureau of the Census. Concepts and Methods Used in Labor Force Statistics Derived from the Current Population Survey. BLS Report 463, and Current Population Reports, Series P-23, No. 62. Washington, D.C., 1976. National Commission on Employment and Unemploy ment Statistics. Counting the Labor Force. Wash ington, D.C., 1979. U.S. Department of Labor, Bureau of Labor Statistics. How the Government Measures Unemployment. BLS Report 505. Washington, D.C., 1976. Newman, Morris J. “ Seasonal Variations in Employ ment and Unemployment During 1951-75,” Monthly Labor Review, January 1980. U.S. Department of Labor, Bureau of Labor Statistics. Employment and Earnings, Washington, D.C., monthly. Lovell, Michael C. “ Least Squares Seasonally Adjusted Unemployment Data,” Brookings Papers on Eco nomic Activity, 1:1976. * II. S. GOVERNMENT ORINTING OFFICE 1982 361-270/4906 10 Bureau of Labor Statistics RegiosiaS Offices R egion i 1603 JFK Federal Building Government Center Boston, Mass. 02203 Phone: (617) 223-6761 R eg io n IV 1371 Peachtree Street, N.E. Atlanta, Ga. 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