Spurious Volatility

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Spurious Volatility in HistoricalUnemployment Data

ChristinaRomerPriticetom ULizersitN

This paper shows that the stabilization of the unemployment ratebetween the pre-1930 and post-1948 eras is an artifact of im-provements in data collection procedures. Prewar methods are usedto construct postwar unemployment data that are consistent with thehistorical data. The constructed postwar series is nearly as volatile asthe pre- 1930 unemployment data. The constructed postwar data aresystematically more volatile than the actual postwar data because thecyclical behavior of the labor force and productivity are misspecifiedin the construction procedures. The relationship between the actualand constructed postwar unemployment series is used to constructnew historical data.

I. IntroductionA. ProblemThe unemployment rate series for 1900-1980 is not one but severalseries. Like nearly all aggregate macroeconomic series, it is a combina-tion of modern survey data and less accurate historical series. Themodern unemployment series is based on the Current PopulationSurvey, which began in 1940. The pre-1940 data, on the other hand,are pieced together from census data, industry records, and variousstate reports. With decadal census data as benchmark estimates, an-nual unemployment is calculated by various forms of interpolation.

I would like to thank Rudiger Dornbusch, Stanley Fischer, Robert j. Gordon, StanleyLebergott, N. Gregory Mankiw, David Romer, Robert Solow, and Peter Temin forextremely helpful comments and suggestions.[Journal of Political EcononN 1986, vol. 94, no. 1]? 1986 bh Thle University of Chicago. All rights reserved. 0022-3808/86/9401 -0007$0 1.50

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2 JOURNAL OF POLITICAL ECONOMYWhile such inconsistencies between the modern and historical un-employment data may not matter when this series is used to examinelong-term trends, they may be very important when the series is usedfor cyclical comparisons. This paper shows that the methods used to

construct the historical data yield an unemployment series that issystematically too volatile. The interpolation methods exaggerate cy-clical movements in the historical unemployment series. As a result,comparisons of short-term cyclical movements in the historical andmodern unemployment data are fundamentally flawed.The finding that the prewar data are excessively volatile challengesthe belief that the postwar economy is more stable than the prewareconomy. In its inconsistent form, unemployment, like most othermacroeconomic variables, is dramatically less volatile in the postwarera than in the prewar era. This can be seen in table 1, which showsthe mean, standard deviation, and average cyclical amplitude of theunemployment series over various time periods. Even during themost stable prewar period, 1900-1930, the historical unemploymentrate is much more variable than the postwar rate. However, if theprewar data are artificially volatile, this apparent stabilization mayactually be a figment of the data.B. MethodologyTo analyze the effects of the inconsistencies in the unemploymentdata I rely on unconventional methods. Typical studies of data prob-lemnsoften begin by correcting the historical data and then explain ontheoretical grounds why the correction is appropriate. The problemwith this approach is that there are many data problems for whichsolutions do not exist. Furthermore, even if one can form a prewarseries that is conceptually similar to the postwar data, the quality andavailability of base data in the prewar period are so poor that theprewar series is certainly less accurate than the postwar series. Be-cause of the inaccuracies in the prewar data, comparisons between theprewar and postwar data are flawed.The fundamental approach of my research is to do just the oppo-site of what is typically done. Because it is impossible to form prewardata that are as good as the postwar data, I begin by creating postwardata that are as bad as the prewar series. From a description of thehistorical data, it is possible to construct a series for the postwar yearsusing the same procedures that are used to create the prewar series.For example, if the historical unemployment rate is calculated byinterpolating between census years, a postwar series can be created byinterpolation as well. Doing this yields a postwar series that is trulyconsistent with the historical data.



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HISTORICAL UNEMPLOYMENT DATA 3TABLE I

SUMMARY STATISTICS OF THE UNEMPLOYMENT RATE SERIES

Standard AveragePeriod Mean Deviation Amplitude*1890-1940 8.71 6.48 6.791890-1930 6.20 4.05 5.101900-1930 4.84 2.38 4.161948-82 5.41 1.58 2.651948-73 4.77 1.10 2.23

* Amplitude is measured as the peak to trough change in the level of the unemploy-ment rate. Cycles with a peak to trotigh change of less than one percentage point areexcluded front the calculation of the mean.

This constructed postwar series is very useful. First, it permits validcomparisons of various time periods. It makes it possible to disen-tangle true economic changes from improvements in our data collec-tion procedures. Second, it allows one to see what errors the construc-tion process adds to the data. By comparing the good (actual) postwardata with the bad (constructed) postwar data, it is possible to analyzeand quantify the systematic differences between the two. One canestimate the size and other characteristics of the errors and evaluatetheir significance.While turning good data into bad is useful for pointing out possibleerrors in the constructed data, the process is most fruitful if it leads tothe ability to turn bad data into good. There is one obvious way inwhich the constructed data may be useful for such corrections. If theconstructed postwar data bear a systematic relationship to the actualpostwar data, it may be possible to derive a simple filter that can beused to correct the prewar constructed data. While one must be verycareful in imposing a postwar relationship on prewar data, suchan unabashedly ad hoc correction may improve the historical datagreatly.C. OvenriewThe organization of this paper follows the description of themethodology very closely. Section II discusses the construction of apostwar series that is consistent with the historical unemployment rateseries. Section III uses the constructed data to make accurate com-parisons between the pre-1930 and the post-1948 periods. Section IVanalyzes the behavior of the postwar constructed series and comparesit with the actual unemployment rate series. It includes a simplemodel of the relationship between the two postwar series. Section V



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4 JOURNAL OF POLITICAL ECONOMYuses this model to create a potentially more accurate historical unem-ployment rate series.II. Constructing Consistent Postwar DataA. The Historical Unemployment eriesThe first step in explaining my procedures for turning good datainto bad is to describe the historical unemployment data. The now-standard unemployment series for 1890-1940 is that created byLebergott and described in his book Manpower in Economic Growth(1964). Though Lebergott is extremely careful and detailed in hisconstruction of the historical data, his prewar series is less accuratethan modern data because of a lack of data and a narrowness ofmethod.The methods that Lebergott uses to piece together the availablebase data vary across the prewar era. I concentrate on the period1900-1930 because the methods that he uses throughout this timeperiod are roughly similar. These methods are described in detail inpart 3 of Manpower in Economic Growth.In general, Lebergott beginswith decadal census data on the labor force, unemployment, andemployment. He does some adjusting of the census data, which, forthe purposes of this study, I assume to be correct. He then calculatesintercensal estimates of the labor force and employment. Unemploy-ment in intercensal years is calculated as a residual.Labor ForceTo construct annual estimates of the labor force, Lebergott first calcu-lates labor force participation rates for various demographic groupsin census years and interpolates linearly between these observations.He then multiplies the estimated participation rates by annual popu-lation numbers to derive estimates of the labor force. Though takenas fact by this study, the annual population numbers are themselvesestimates, based on more exotic interpolation procedures.It is clear that Lebergott's labor force numbers miss cyclical move-ments in the labor force. Specifically, they do not take into account thecountercyclical fluctuations in the number of discouraged workersthat typically dominate the movements in the labor force. Other au-thors have noticed this problem. For example, Coen (1973) uses thepostwar behavior of the labor force to estimate the cyclical movementsin the labor force in the interwar period. He finds that movements inthe labor force are strongly procyclical in the postwar period. Theapplication of this relationship to the interwar period substantiallychanges Lebergott's estimates of the labor force and unemployment.



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HISTORICAL UNEMPLOYMENT DATA 5If the labor force were also procyclical in the 1900-1930 period,then it is clear that Lebergott's labor force numbers are too high inrecessions and too low in booms. This implies that the unemploymentrate calculated as a residual is artificially high in recessions and

artificially low in booms. Thus the historical unemployment rate is, byconstruction, more volatile than the truth.EmploymentTo estimate annual employment, Lebergott uses more complicatedprocedures. He estimates it as the sum of several component series onemployment in various sectors and among various classes of workers.To form these component series he begins with basic data on employ-ment in each sector in whatever base years are available. He theninterpolates each employment series using some annual variable hebelieves to be related to employment in that sector. The most com-mon interpolating variables are measures of output, fragments ofemployment data, and indexes of labor demand.While interpolating by some fragment of employment data proba-bly yields reasonably accurate estimates of sectoral employment, in-terpolating by output may lead to systematic errors in the sectoralemployment estimates. Usual interpolation procedures assume thatthe percentage deviations from trend of a given employment seriesare equal to the percentage deviations from trend of output in thecorresponding sector. The typical formula for interpolating betweenyears t = 0 and t = 10 is

emp, = .1[(10 - t)empo + tempi(1] + yt- .1[(10 - 0)yo + tylo], (1)

where emp, is the logarithm of employment, the series to be es-timated, and yt is the logarithm of output, the interpolating variable.'Lebergott correctly notes that with frequent benchmarkings, this typeof procedure captures most long-run changes in hours and produc-' . 2,tivity.2However, productivity and hours have strong cyclical movementsas well as trend movements. Productivity and hours, at least in the

l Friedman (1962) discusses this typical formula in detail. He demonstrates the statis-tical complexity of interpolation and suggests more accurate correlation procedures.2 In discussing the effects of interpolating by output, Lebergott states: "Individualemployment series for key industries will in turn tend to reflect changes in productionbecause of the method of estimate. However, the frequency of' benchmark counts ...means fairly frequent checks of' the combined productivity and hours factor inter-polated between these dates" (Lebergott 1957, pp. 222-23).



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6 JOURNAL OF POLITICAL ECONOMYpostwar period, are significantly procyclical. Firms tend to be slow tofire workers in bad years and slow to hire workers in good years.Typical interpolation procedures miss this effect entirely. They as-sume that deviations of employment from trend move one for onewith deviations of output from trend. The cyclical movements ofproductivity and hours suggest that the true relationship is muchsmaller. Thus using the basic interpolation methods leads to a system-atic overstating of the cyclical movements of those series for whichoutput is the interpolating variable.This systematic overstating of cyclical movements in employmenthas important implications for the unemployment rate. If Lebergott'sannual total employment series includes some components that ig-nore procyclical movements in productivity and hours, then employ-ment is overestimated in boom years and underestimated in slumpyears. This suggests that the employment effect will exacerbate ratherthan counteract the labor force effect. The unemployment series iseven more biased downward in booms and upward in recessions.Because of this, it is also biased toward having a larger variance andcyclical amplitude than a true unemployment series would have.It is important to note that the errors I have pointed out in Leber-gott's methods for estimating employment are due only to the mis-specification of the relationship between employment and output. Ihave assumed that the base output data that Lebergott uses are cor-rect. Thus one way of summarizing the errors I have identified inLebergott's estimates of both employment and the labor force is to saythat the Okun's law relationship between unemployment and outputis misspecified. By assuming that employment in some sectors movesone for one with output and that the labor force has no cyclical com-ponent, Lebergott's methods impose that the Okun's law coefficientfor the historical unemployment series is biased toward one and awayfrom its actual value of 2.5 or 3.While this analysis in terms of Okun's law provides a usefulframework for considering the errors in Lebergott's methods, it is notstrictly correct. Okun's law refers specifically to the aggregate rela-tionship between unemployment and gross national product (Okun1962). The errors in Lebergott's series are due to the misspecificationof the relationship between employment and various measures ofoutput at the sectoral level and to the misspecification of the cyclicalbehavior of the labor force. To express these errors in terms ofOkun's law may lead one to forget that Lebergott's unemploymentfigures are not the result of imposing a simple aggregate relationshipbut of careful calculations of the labor force and employment in manysectors.



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HISTORICAL UNEMPLOYMENT DATA 7B. Applying Old Methods to CurrentDataChanging good postwar data into bad data is a somewhat tediousprocess. However, because what I do is only an approximation toLebergott's procedures, it is important to describe my methods indetail. This is especially true because one must believe that theseprocedures are similar to Lebergott's to believe that the postwar un-employment rate series I construct is more consistent with the histor-ical data than is the actual unemployment series.Labor ForceAs mentioned earlier, Lebergott's procedures for constructing annualestimates of the labor force are relatively straightforward. He merelyinterpolates participation rates for various demographic groups be-tween census years and then multiplies them by annual populationestimates. The only difficulty in replicating Lebergott's procedures isto match his age, sex, and race classifications. Lebergott uses 36classifications that divide people according to whether they are nativewhite, foreign-born white, or black; male or female; and ages 10-13,14-19, 20-24, 25-44, 45-64, or 65 and over.

For modern benchmark estimates of the labor force for thesegroups I use information from the Current Population Survey (CPS)rather than from the Censusof Population. I do this because the CPS isgenerally thought to be the more accurate source of data on popula-tion, employment, and the labor force. Also, the CPS is the source ofthe standard annual population and unemployment data. For pur-poses of comparison later, it is very helpful to have the constructedand actual data based on the same source.The fact that the CPS provides annual data has another importantbenefit. If one were to construct a single postwar series by interpolat-ing between actual census years, one might discover biases not presentin Lebergott's series. The particular census years might be odd, andthis would be causing most of the errors. But with consistent annualdata, it is possible to get a rough estimate of the sampling propertiesof such errors. Rather than construct just one series, one can con-struct several series by imagining that censuses fell in various years.That is, in addition to creating a series by interpolating between 1950,1960, 1970, and 1980, one can create other series by interpolating

3 A Bureau of the Census publication states (1960, p. 3): "It is generally agreed afterextensive analysis that the CPS results, which are obtained through a repetitive samplesurvey with the opportunity for developing a well-trained and controlled field organi-zation, provide more accurate measures of labor force items than a census does."



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8 JOURNAL OF POLITICAL ECONOMYbetween 1951, 1961, 1971, 1981; 1952, 1962, 1972, 1982; and so on.The existence of these several series enables one to distinguish be-tween the effects of particular census years and the general effects ofthe interpolation procedures.

Because the CPS data on the labor force by race do not begin until1954, it is impossible to replicate Lebergott's procedures for the laborforce exactly for the entire postwar period. However, since the CPSdata on the labor force by sex and age, but not race, begin in 1948, Ican approximate Lebergott's procedures using a finer age-sex break-down without the race distinction. I classify people according towhether they are male or female and ages 16-17, 18-19, 20-24, 25-34, 35-44, 45-54, 55-64, or 65 and over.4 Using these classificationsI create five series of 30 observations each by imagining that censusdecades begin in 1948, 1949, 1950, 1951, and 1952, respectively.EmploymentReplicating Lebergott's procedures for estimating employment ismuch more difficult. To do exactly what Lebergott does for everyemployment series that he estimates would be nearly impossible.However, it is possible to capture some of the most important errorsof his approach. To do this, I construct employment series only forthose sectors in which I can replicate Lebergott's procedures fairlywell. For the other series I assume that Lebergott manages to estimateemployment exactly. That is, in the aggregate employment measure Iinclude the actual employment number for those sectors. Thus theerrors in the total employment measure are only ones I am reasonablycertain exist in the historical data.Replicating Lebergott's procedures when he interpolates usingsome fragment of employment data is very difficult. It is hard to guesswhat modern fragment might correspond to the fragment that Leber-gott actually uses. However, when he interpolates using a measure ofoutput, it is more straightforward to replicate his methods. Fortu-nately, from the perspective of this study, Lebergott uses output tointerpolate three of the largest and traditionally most important em-ployment series: construction, manufacturing, and trade. He doesthis because, as he notes, "the soundest procedure was to take advan-tage of the major advances in our knowledge of this period which areassociated with the names of Shaw, Fabricant, Kuznets and others

4This approximation to Lebergott's procedures is quite accurate. When one com-pares the constructed labor force numbers for the 1958, 1968, 1978 series using bothLebergott's methods and my approximation to them, the difference between the twoseries is almost always less than 0.1 percent of the actual labor force number and usuallyless than 0.025 percent.



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HISTORICAL UNEMPLOYMENT DATA 9who have laboriously developed basic production series" (Lebergott1957, p. 222).The actual activity series that Lebergott uses for each of these sec-tors are described in detail in the Appendix. I describe them onlybriefly here. For 1900-1920, Lebergott interpolates employment inconstruction by Shaw's (1947) series on the output of constructionmaterials. For 1920-30, he uses the Commerce Department's serieson the value of new construction, deflated by the price of input mate-rials as the interpolating series.For the period 1909-19, Lebergott interpolates employment inmanufacturing by Shaw's estimates of the output of finished goodsplus construction materials. For 1899-1909, Lebergott interpolatestotal employment in manufacturing by manufacturing employmentin a sample of states. The Appendix discusses this procedure andshows that the results of this method are similar to those using output.Finally, Lebergott interpolates the number of employees in retailand wholesale trade for 1900-1929 by the number of goods sold. Heuses disaggregated data on employees in a particular line of trade andinterpolates by the real output of finished goods in the same category.For example, he interpolates the number of employees in food storesby Shaw's series on the real output of food.While there are other sectors, such as transportation and banking,in which Lebergott uses a measure of output as the interpolatingvariable, the three sectors I consider are clearly the most important.Employment in construction, manufacturing, and trade accounts for47 percent of total employment in 1972. Employment in these samesectors accounts for approximately 37 percent of total employment in1910.5 While their share is somewhat smaller in the pre-1930 era, theconstruction, manufacturing, and trade sectors clearly account for asubstantial fraction of total employment in both the prewar and post-war eras. For this reason, these are the only three employment seriesthat I attempt to construct. All the others are set equal to their actualvalues.It is useful to note that the Shaw series that Lebergott uses tointerpolate employment in these three sectors appears to provide afairly accurate measure of industrial production. Shaw's data arebased on data from various volumes of the Census of Manufactures andnumerous annual state records. Because his series relies on a largersample of base data than most of the other prewar indexes of produc-

' For 1972 this calculation is based on the ratio of wage and salary workers in con-struction, manufacturing, and trade to total employment. Data on these quantities arefrom the CPS. For 1910 the calculation is based on the ratio of employees in construc-tion, manufacturing, and trade establishments to total employment. The data are fromLebergott (1964, tables A-3, A-5).



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10 JOURNAL OF POLITICAL ECONOMYtion, it is probably more accurate than most other output measures.Another characteristic of the Shaw series is that it is somewhat lessvolatile than most of the other output measures. As a result, it is likelythat most of the excess volatility of the prewar employment numberscomes from the misspecification of the employment-output link, notfrom the underlying output data.To approximate Lebergott's procedures for the postwar period, Iuse series that are conceptually similar to Shaw's data. In general,because the various Shaw series are essentially measures of industrialproduction, I use industrial production data from the Federal Re-serve Board to construct postwar data. For employment in construc-tion I interpolate by the Federal Reserve Board index of the output ofconstruction materials. For employment in manufacturing I use theFederal Reserve Board index of the production of final products,adjusted to include construction materials, as the interpolating vari-able. For trade, I interpolate by the Federal Reserve Board index offinal products destined for consumers. This is an aggregate approxi-mation to Lebergott's procedure of estimating employment in variouslines of trade separately.The Appendix contains a detailed study of the effects of usingthese particular activity variables. I try a wide variety of variables foreach sector and find that the results described in the rest of the paperdo not depend on the choice of the activity variable.The actual construction of the employment series for construction,manufacturing, and trade is relatively straightforward. I use the for-mula given in equation (1). Following Lebergott, I interpolate be-tween 10-year benchmarks for trade and construction. For manufac-turing I interpolate between 5-year benchmarks because for 1899-1919 Lebergott has quinquennial data from the Census of Manufac-tures. The benchmark estimates I use are simply the actual data onwage and salary workers in construction, manufacturing, and tradefrom the CPS. As in the replication of Lebergott's procedures forestimating the labor force, I form five possible constructed series foremployment in each sector by supposing that benchmark intervalsbegin in 1948, 1949, 1950, 1951, and 1952.The resulting constructed series on employment in the varioussectors for each base year are combined with data on actual employ-ment for all remaining sectors and classes of workers to form con-structed series on total employment for each base year. These esti-mates of total employment are combined with the constructed laborforce numbers to form estimates of postwar unemployment that areroughly consistent with Lebergott's prewar seriesis I construct five

The actual combination of the two series is very simple because the CPS data on thelabor force, employment, and unemployment are mutually consistent and exhaustive.Because Lebergott's base data are often not exhaustive, he uses a more complicated



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HISTORICAL UNEMPLOYMENT DATA 11postwar unemployment series corresponding to the five possible com-binations of benchmark estimates. These constructed unemploymentseries, as well as the actual postwar unemployment rate series, areshown in table 2. The prefix UI denotes that the unemployment seriesis formed using both constructed labor force and employment series.The numerical suffix denotes the first base year.

III. Accurate Comparisons of VariousTime PeriodsThe most obvious use of the constructed data is to make accuratecomparisons of the prewar and postwar unemployment rate data.Because the two series are now roughly consistent, any change in thebehavior of the two series reflects true economic changes rather thanimprovements in data collection procedures. Another way to view it isthat these comparisons show what the stylized facts would have beenhad we used the same data collection procedures throughout bothperiods.In forming the consistent postwar series, I have replicated themethods Lebergott uses for the period 1900-1930. Thus the onlyvalid comparison is between the pre-1930 data and the post-1948data. While this comparison clearly excludes the very important de-cade of the 1930s, it is still useful. The notion that the prewar unem-ployment rate was substantially more volatile than the postwar unem-ployment rate does not stem from the fact that the Great Depressionoccurred in the prewar rather than the postwar era. As table 1showed, Lebergott's unemployment series for 1900-1930 is approxi-mately 50 percent more volatile than the actual postwar series. Thus acomparison of consistent unemployment data over these same pe-riods can provide useful information about whether this apparentstabilization actually occurred or is an artifact of data inconsistencies.

A. Severity of the CycleFigure 1 shows Lebergott's unemployment series for 1900-1930 andthe constructed series for the postwar period (based in 1950, 1960,1970, and 1980) for 1950-80. In terms of the overall picture, I coulduse any one of the five constructed postwar series since their basicmovements are similar. One thing is apparent from the figure: rela-tive to the period 1900-1930, there is no stabilization of the postwartwo-step procedure. He forms a preliminary unemployment series by subtracting apreliminary estimate of total employment from his series on the annual labor force. Hethen uses this series to interpolate between census observations on unemployment.



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1 2 JOURNAL OF POLITICAL ECONOMYTABLE 2

ACTUAL AN)D CONSTRUCTED UNEMPLOYMENTI RATES FOR THE POSTWAR PERIO)D

Year UA* UI48t3 UI49 UI50 UI51 UI521948 3.76 3.76 ... ... ... ...1949 5.94 7.17 5.94 ... ... ...1950 5.29 3.40 1.98 5.29 ... ...1951 3.31 2.65 1.14 4.13 3.31 ...1952 3.04 2.40 .79 3.42 2.78 3.041953 2.91 2.55 .84 3.13 2.64 2.731954 5.55 6.72 5.45 7.24 6.93 6.841955 4.38 2.96 2.16 3.50 3.32 3.041956 4.14 1.93 1.65 2.50 2.44 1.991957 4.27 3.09 3.32 3.66 3.55 3.111958 6.80 6.80 7.48 7.37 7.21 6.951959 5.47 4.41 5.47 4.89 4.67 4.571960 5.53 5.20 6.10( 5.53 5.26 5.331961 6.68 6.80 7.56 7.11 6.68 6.911962 5.54 5.44 6.10 5.75 5.25 5.541963 5.67 5.86 6.40 6.16 5.59 5.761964 5.18 5.53 5.80 5.66 5.02 5.071965 4.52 4.51 4.68 4.47 3.75 3.701966 3.79 3.41 3.47 2.84 2.40 2.221967 3.85 4.25 4.21 3.16 2.81 2.701968 3.58 3.58 3.43 1.92 1.67 1.891969 3.51 3.37 3.51 1.56 1.40 1.951970 4.95 6.76 6.80 4.95 4.84 5.661971 5.95 7.91 7.84 6.08 5.95 7.061972 5.60 6.23 6.03 4.28 4.09 5.601973 4.88 5.26 4.92 3.20 2.94 4.121974 5.61 7.03 6.87 5.29 4.97 5.701975 8.45 11.53 11.36 10.15 9.77 10.081976 7.70 9.00 8.78 7.39 7.30 7.261977 7.06 7.38 7.11 5.58 5.52 5.371978 6.07 6.07 5.74 4.09 4.07 3.571979 5.85 ... 5.85 4.11 4.12 3.291980 7.14 ... ... 7.14 7.15 6.071981 7.61 ... ... ... 7.61 6.231982 9.69 ... ... ... ... 9.69

* UA denotes the actual unemployment rate.tU148 denotes the constructed unemployment rate based on 1948, 1958, 1968, 1978; [U149 denotes the unene-ployment rate based on 1949, 1959, 1969, 1979, etc.

unemployment rate. The severity of cyclical swings is nearly identicalin both periods.Cyclical AmplitudeThis fact is easily quantified. The most common measure of the se-verity of the cycle is the average peak to trough change in theunemployment rate. Thus a simple test of the hypothesis thatthe pre-Depression and the postwar cycles are equally severe is to



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HISTORICAL UNEMPLOYMENT I)ATA 13

12-

10i-8

QC6

4

2

1900 1910 1920 1930 1950 1960 1970 1980Fic(. 1.-Consistent unemployment rate series. The series for 1900-1930 is Leber-gott's unemployment rate series. The series for 1950-80 is the constructed tilemploy-ment series UI50.

compare the peak to trough movements in the pre-1930 Lebergottseries and the post-1948 constructed series. This is done in table 3,which shows the average cyclical amplitude for Lebergott's series andall five of the constructed series. To calculate these cyclical ampli-tudes, peaks and troughs are defined as the actual turning points inthe various unemployment series. Cycles with a peak to trough in-crease in unemployment of less than one percentage point are ex-cluded from the calculation of the mean.The similarity between all the constructed series is very strong.When consistent data are used, there is no damping of the amplitudeof the business cycle. In fact, the amplitudes of the constructed post-war unemployment rate series are slightly greater than the amplitudeof Lebergott's series for 1900-1930. This is certainly a contrast to thecomparison of' Lebergott's prewar series with the actual postwar un-employment rate. When inconsistent data are used, the postwar pe-riod looks markedly more stable.Standard DeviationWhile the amplitude of the cycle is a common measure of the severityof' cyclical swings, it is in some sense an arbitrary measure. Thedefinition of a cycle is imprecise, and the cyclical amplitude may be



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14 'JOURNAL OF POLITICAL ECONOMYTABLE 3

AVERAGE CYCLICAL AMPLITUDES

AveragePeriod Series Amplitude*1900- 193() ULEB 4.161948-78 UI48 4.301949-79 UI49 4.691950-8() UI5() 4.531951-81 UI51 4.491952-82 UI52 4.821948-82 UA 2.65

* Aniplittide is mIeasIured as the peak to tioumgh change in thelvtel of the uLnemC1ploVIymellt rate.

affected by the particular definition chosen. The standard deviationof the constructed unemployment series is a more straightforwardmeasure of volatility. The standard deviations for the prewar andpostwar constructed series are shown in table 4.The results are very similar to those for the cyclical amplitudes.Whereas a comparison of Lebergott's pre-1930 series with the actualpostwar unemployment rate shows an obvious stabilization, a com-parison of' Lebergott's series with the constructed postwar seriesshows little stabilization. On average, the standard deviation of theconstructed postwar series is only approximately 10 percent less thanthat of Lebergott's series for 1900-1930. Furthermore, table Al ofthe Appendix shows that this result holds regardless of what outputvariables are used to interpolate employment in the various sectors.

TABLE 4STANDARD DEVIATIONS

StandardPeriod Series Deviation*1900-1930 ULEB 2.381948-78 UI48 2.191949-79 UI49 2.481950-80 UI50 1.9(1951-81 UI51 1.981952-82 UI52 2.141948-82 UA 1.58

* [he standard deviation of the level of the tinemnployment r-atearouLnld its ineani.



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HISTORICAL UNEMPLOYMENT DATA 15The noticeable absence of stabilization is also robust to the choice oftime period. Keynesians might argue that the supply shocks of the1970s were a unique destabilizing force and that it is only the period1948-73 that is more stable than the pre-1930 era. Even this assertion

fails when consistent data are compared. The standard deviations andamplitudes of the constructed postwar unemployment series before1974 are shown in table 5. The amplitudes of the pre-1974 series arestill very similar to the amplitude of Lebergott's pre-1930 series. Thestandard deviations of the pre- 1974 series are somewhat smaller thanthat of the pre-1930 Lebergott unemployment data but still substan-tially larger than the standard deviation of the actual postwar seriesbefore 1974. Thus a comparison of consistent unemployment datastill shows little stabilization of the postwar economy, even if oneexcludes the years after the first oil shock.B. Time-SeriesPropertiesIn addition to the severity of the cycle, a second aspect of the volatilityof the cycle is the choppiness of cyclical movements. A common per-ception is that prewar cycles are much shorter and much less pro-tracted than postwar cycles. In terms of the time-series properties ofthe various unemployment series, this translates into the perceptionthat a given shock has greater persistence in the postwar era than inthe prewar era.Standard Deviation of the Changein UnemploymentThe standard deviation of the change in the unemployment rate is asimple measure of the choppiness of the cycle. This measure shows

TABLE 5STANDARD DEVIATIONS AND AVERAGE

AMPLITUDES BEFORE 1974Standard AveragePeriod Series Deviation Amplitude

1900-1930 ULEB 2.38 4.161948-73 UI48 1.72 3.911949-73 UI49 2.19 4.251950-73 UI50 1.66 3.931951-73 UI51 1.68 3.911952-73 UI52 1.80 4.151948-73 UA 1.10 2.23



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i6 JOURNAL OF POLITICAL ECONOMYthe average size of yearly fluctuations in unemployment. It indicateswhether unemployment moves gradually through the cycle or shiftsrapidly from peak to trough. The standard deviations of the changein the actual and constructed unemployment series for various timeperiods are shown in table 6.The results show that the year-to-year volatility of the constructedpostwar unemployment series is much larger than that of the actualpostwar series. At the same time, it is also noticeably smaller than thatof the historical unemployment series. On average, the standard devi-ation of the change in the constructed unemployment rate series isapproximately 30 percent smaller than the standard deviation of thechange in the historical series.7 This finding suggests that even whenconsistent data are compared, yearly fluctuations are smaller in thepostwar era than in the prewar era. However, the decline in thechoppiness of the cycle in the consistent data is only half as large asthe apparent decline in the inconsistent data.Sample AutocorrelationsThe time-series properties of the various unemployment series can beanalyzed more generally by examining the sample autocorrelations ofeach series. The sample autocorrelations show the correlation of agiven series with itself at various lags. The pattern of these autocorre-lations can suggest the nature of the serial correlation in the various

TABLE 6STANDARD DEVIATIONS OF THE CHANGE

IN UNEMPLOYMENT

StandardPeriod Series Deviation*1900-1930 ULEB 2.861948-78 U148 2.191949-79 U149 2.151950-80 U150 2.151951-81 U151 2.111952-82 U152 2.191948-82 UA 1.22

* The standard deviation of the change in the uIMe-ployment rate arouLnd ts inean.

7 This result also holds when the sample is stopped in 1973. In this case the averagestandard deviation of the change in the constructed unemployment rate series is 35percent smaller than the standard deviation of the change in the pre-1930 Lebergottseries.



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HISTORICAL UNEMIPLOYMENT IDATA 17unemployment series. The sample autocorrelations for the first 10lags of the prewar and postwar unemployment series under consider-ation are given in table 7.The degree of first-order serial correlation is of particular interest.It is a simple measure of the persistence of shocks in the variousunemployment series. The figures in table 7 show that the degree offirst-order autocorrelation is much lower in the Lebergott unemploy-ment series for 1900-1930 than it is in the actual postwar unemploy-ment series. This is certainly consistent with the usual belief' thatcycles are much more protracted in the postwar era than in the pre-war era.The first-order sample autocorrelations of the constructed postwarseries are, in general, substantially smaller than that of the actual post-war unemployment rate series. Only one of the five constructed postwarseries (UI49) shows persistence as large as that of the actual post-war series. On the other hand, the first-order autocorrelations of theconstructed postwar series are also substantially larger than that ofthe prewar Lebergott series. In fact, on average the first-order serialcorrelation of the constructed postwar series is approximately halfwaybetween that of' the prewar Lebergott series and that of the postwaractual series.These findings suggest that prewar and postwar cycles look muchmore similar when consistent data are compared than when inconsis-tent data are analyzed. The increased persistence of shocks betweenthe prewar and postwar eras apparent in the inconsistent data is muchless pronounced in the consistent data. While even consistent datareveal somewhat more protracted and persistent cycles in the postwarera than in the pre-1930 era, the actual change in this series has beenslight rather than dramatic.

The overall pattern of the first several sample autocorrelations pro-vides some additional information about the various unemploymentseries. The figures in table 7 show that the prewar Lebergott seriesand the actual postwar unemployment series have very differentautocorrelation patterns. The prewar unemployment series has samn-ple autocorrelations that die out very quickly; in fact, the second auto-correlation is negative. A given shock has very little persistence in theprewar era. The actual postwar series, on the other hand, has sampleautocorrelations that die off gradually; the first five autocorrelationsare positive and progressively smaller. A given shock continues tohave a positive effect for several subsequent years.The autocorrelation patterns of the five constructed postwar unem-ployment series are very different from one another. The patternsfor UI50, UI5 1, and UI52 are very similar to that for Lebergott'sprewar unemployment series. The patterns for UI48 and UI49 are



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HISTORICAL UNEMPLOYMENT DATA 19equally similar to the autocorrelation pattern of the actual post-war unemployment data. The large difference between the five con-structed postwar series suggests that the benchmark estimates usedin the construction process may be an important determinant of thepattern of autocorrelation. Since the five series differ only in whichyears are used to determine trends, these different trends are themost plausible source of the difference in the serial correlationproperties.The fact that the five postwar constructed unemployment seriesdiffer substantially in their autocorrelation patterns makes it difficultto assess how much change has actually occurred over time. It ispossible to conclude that there has been little change or much changein the serial correlation properties of the unemployment series overtime, depending on which of the five possible extensions of Leber-gott's pre-1930 series one considers. Since it is very difficult to decidewhich of the constructed postwar series has benchmark years mostsimilar to those Lebergott uses to construct the prewar data, it is bestto leave the degree of change in the overall pattern of serial correla-tion as an unresolved issue.Despite this particular ambiguity, it is possible to draw two conclu-sions about what the stylized facts concerning the unemployment rateseries over time would be if economists used consistent rather thaninconsistent data. One new stylized fact would be that the businesscycle from 1900 to 1930 is no more severe than the cycle from 1948 to1982. The second new stylized fact would be that while even consis-tent data show more protracted cyclical movements in the postwar erathan in the prewar era, the change over time has been only about halfas large as the analysis of inconsistent data has led economists tobelieve.IV. The Behavior of the ConstructedPostwar SeriesThe preceding section showed what the stylized facts about the pre-1930 and the post-1948 unemployment rates would have been hadthe United States not revamped its data collection procedures. Thissection analyzes the behavior of the constructed series in the post-war period. It examines the difference between the actual and con-structed postwar unemployment rates. It derives and tests a model ofthe relationship between the two series and uses the results to suggestthe source of the systematic errors in the constructed series. Thissection also uses a series of counterfactual experiments to decomposethe source of the errors into those due to estimating the labor forceand those due to estimating employment.



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20 JOURNAL OF POLITICAL ECONOMYA. The Relationshipbetween heActualand ConstructedSeriesAs discussed in Section II, certain facts about the cyclical behavior ofthe labor force and employment suggest possible errors in the con-structed unemployment data. The fact that Lebergott's estimationtechniques neglect procyclical movements in the labor force, pro-ductivity, and hours implies that the cyclical movements in the con-structed unemployment rate may be exaggerated. Figure 2 suggeststhat this is indeed the case. It graphs the actual unemployment rate(UA) and the constructed unemployment rate (UI50) and shows thatUI50 is consistently more volatile. Given this qualitative evidence, it isuseful to test whether the suspected errors in the constructed seriesactually do account for the systematic differences between the actualand constructed series.

ModelTo do this I derive a model of the relationship between the twoseries. The derivation centers on the difference between the inter-polation formulas for the constructed series and the more likely re-gression formulas for the true series. For the labor force the con-struction formula is

If, = 1 fA + eo, (2)where If, is the logarithm of the constructed (interpolated) laborforce and IfA is the trend of the logarithm of the actual labor force.The error term, eo, is included to account for the fact that this interpo-lation formula is a simplification of Lebergott's procedures.

We suspect that the regression formula for the true labor forceshould be more complicated than this simple interpolation formula.Specifically, we suspect that the true labor force depends on the busi-ness cycle. Thus a likely representation of the true labor force islfA = lfA + a(y - -) + el, (3)

where lfA is the logarithm of the actual labor force, y is the logarithmof any conventional measure of output, and a is presumably positive.The deviation of output from its trend is used as a measure of thecycle.For employment, the construction procedures imply that

emp, = empA + c(y - j) + e2, (4)where emp, is the logarithm of the constructed total employmentseries and empA is the trend of the logarithm of the actual total



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HISTORICAL UNEMPLOYMENT DATA 2112

10 A8

c I I I1950 1955 1960 1965 1970 1975 1980Ftc;. 2. Actual and constructed employment rates. lfA is the actual unlemlploy-mnert rate series and U150 is the constructed tinemployenelt rate ser ies b)asedl inl

employment series. The coefficient on (y - 5) enters not because ofthe interpolation procedures but because the total constructed em-ployment series includes some actual and some interpolated series forindividual sectors. If all sectors were interpolated, c would equal oneby construction and there would be no error e2.We suspect that this interpolation formula differs from the trueregression relationship in two Ways. First, true employment is proba-bly less responsive to current output than the construction formulaimplies. Second, actual employment may depend on lagged output.Thus actual employment may be more correctly modeled as

empA = empA + boy -5) + bdy - 5)_ + e3,, (5)where b0 is positive but less than c. The coefficient on lagged output(b1) is also likely to be positive because it is capturing the fact thatemployment is a lagging indicator.From these relationships one can derive a model of the differencebetween the level of the constructed unemployment rate (UI) and thelevel of the actual unemployment rate (UA). Using the approximationln(1 -x)- -x yields the following expression for UI:

UI- -ln( 1 - UI)*-ln[1-(1 - EMPS (6)

- ln LF1 - ln EMPJ.



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2 2 JOURNAL OF POLITICAL ECONOMYHere capital letters denote variables in levels rather than logarithms.A similar relationship holds between UA and LFA and EMPA. Sub-stituting these relationships and adding an error term (e4) to accountfor the approximation yields

UI - UA = (If, - empi) - (lfA - empA) + e4= -(a + c - bo(y -) + bl(y -I- (7)

+ e( -el - e2 + e3 + e4-Using the same approximation as above one can show that

U -=lf, - empI =lfA -empA. (8)Substituting this relationship yields

UI - UI = (If, - empi) - (WfA - empA)= (If - fA)- (emp, - empA) (9)= -c (y -y) + eo -e2-

This implies thatUI- UA = (a + c- bo)(UI - UI) (10)-( 1 )(UI UI)_1 + e,

where (a + c - b))lc is positive, - (blc) is negative, and e is thecombined error term. Equation (10) shows the relationship betweenUI and UA that one might expect knowing the interpolation formulasand some stylized facts about the postwar economy.EstimationTo test whether this is indeed the relationship between UI and UA,equation (10) can be rewritten as the following estimating equation:

UI- UA = g((UI- UI) + gI(UI - UI)-1 + e. (11)If the explanatory power of this model is high, then it is likely that thesuspected sources of the errors in UI do explain the systematic devia-tions of the constructed unemployment series from the truth.This model can be estimated in two ways. One is to run the regres-sion for each of the five constructed postwar series. The other is topool all five series and constrain the response to be similar. Since theresults from the two procedures are very similar, I report only theresults from the pooled regression. In both cases I exclude some



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HISTORICAL UNEMPLOYMENT DATA 23observations to take into account the fact that, by construction, UI =UA in census years. This model is designed to explain how intercensalestimates of the constructed unemployment rate (UI) differ from theactual unemployment rate (UA), and thus it is run on data excludingcensus years.The basic results are

UI - UA = .528(UI - UI) - .136(UI - UI>1 + e;(.029) (.029) (12)S.E. = .615,

where the standard errors are in parentheses. For reference, when aconstant is included, it is not significantly different from zero, and theR2 is .77. While the explanatory power of the regression is very high,the Durbin-Watson statistic is .63. This suggests that there is serialcorrelation. To correct for this I include a lagged dependent vari-able.8 The expanded results are

UI - UA = .484(UI - UI) - .458(UI - UI)(.023) (.042) (13)+ .749(UI - UA)1 + e; S.E. = .476.

(.084)Again, when a constant is included it is not significant, and the R2 is.86.Despite the presence of serial correlation, the key finding is that thebasic model of the systematic errors in the constructed unemploy-ment series does fit the data quite well. The errors predicted on thebasis of a knowledge of certain facts about the postwar labor marketare indeed the main errors present in the constructed data. Thissuggests that most of the errors in the constructed unemploymentseries are due to the misspecification of the output-employment linkand the failure to take into account procyclical movements in thelabor force.The fact that the specification including a lagged endogenous vari-able fits the data slightly better than the simple specification in equa-tion (1 1) suggests that there are some explanatory variables that are

8 Alternatively, one can use the Cochrane-Orcutt correction for first-order serialcorrelation. The results are very similar to those in eq. (13). The estimated equation isUI - UA = .501(UI - UI) - .087(UI - UI)l + e;(.024) (.024)

p = .819, S.E. = .498,(.056)where standard errors are in parentheses.



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24 JOURNAL OF POLITICAL ECONOMYexcluded from the model. One example of an excluded variable thatmight give rise to serial correlation is a more complicated trend term.It is very likely that the 10-year linear trend used to describe the trendof the actual employment and labor force series is too simple. Whilethe slight difference in fit of the two specifications suggests that theexcluded variables are not particularly important, their existence doesindicate that some of the systematic differences between the actualand constructed series may not be related to the business cycle.B. Decomposing he Source of SystematicErrorsThe results of the model show that the main source of the systematicerrors in the constructed unemployment rate is the misspecificationof the cyclical behavior of unemployment. However, the results donot show whether it is understating the cyclical response of the laborforce or overstating the cyclical response of employment that is themore important mistake. Counterfactual techniques, however, doprovide a way to separate and evaluate the importance of both errors.To do this one can consider two experiments. Instead of estimatingboth the labor force and employment to calculate unemployment,suppose that one knew the true level of employment. Then the unem-ployment rate (designated UL) is calculated as

UL = LF, - EMPALF,where I denotes an estimated series and A denotes an actual series. Acomparison of UL with the actual unemployment rate, UA, shows theeffect of having to estimate only the labor force.One can also suppose that the true labor force is known but thattotal employment must be estimated. The resulting unemploymentrate (designated UE) is

UE = LFA - EMP,LFAOne can compare UE with UA to see the pure effect of estimatingemployment. Furthermore, one can also compare UE with UL to seethe relative size of the labor force and employment effects.

An obvious characteristic on which to compare these series is theaverage cyclical amplitude. Table 8 shows the average peak to troughchange of the true unemployment rate (UA), the completely con-structed unemployment rate (UI), and the two new hypothetical un-employment rates (UL and UE) for all five base years. The results arequite straightforward. First, both UL and UE have substantiallyhigher cyclical amplitudes than does the actual unemployment series.



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HISTORICAL UNEMPLOYMENT DATA 25TABLE 8

AVERAGE CYCLICAL AMPLITUDES

SERIESBASE YEAR UA* UIP UL' UE? UEM111948 2.45 4.30 3.03 3.78 3.371949 2.50 4.69 3.20 4.24 3.491950 2.50 4.53 3.09 4.04 3.381951 2.50 4.49 2.97 4.18 3.641952 2.65 4.82 3.32 4.36 3.90

* UA denotes the actual unemployment rate. The amplitude of CA is calculated for the 30-year period beginningin the base year listed.UI denotes the constructed unemployment rate based on estimated labor force and employment.fL denotes the hypothetical unemployment rate based on estimated labor force and actual employment.? UE denotes the hypothetical unemployment rate based on actual labor force and estimated employment.CVEMenotes the hypothetical unemployment rate based on actual labor force, actual employment in nmanufac-turing, and estimated employment in trade and construction.

This shows that estimating either the labor force or employment us-ing Lebergott's methods raises the cyclical amplitude of the resultingunemployment rate series.Second, the two effects compound rather than counteract eachother. The difference between the amplitude of the totally con-structed unemployment rate UI and the actual unemployment rateUA is approximately equal to the sum of the differences between theamplitudes of UL and UA and the amplitudes of UE and UA. That is,

AMP(UI) - AMP(UA) [AMP(UL) - AMP(UA)]+ [AMP(UE) - AMP(UA)],

where AMP denotes amplitude. This fact makes the decomposition ofthe source of the excessive volatility of the totally constructed seriesvery easy. The ratio

AMP(UE) - AMP(UA)[AMP(UE) - AMP(UA)] + [AMP(UL) - AMP(UA)]is a measure of the amount of the exaggeration of the amplitude ofthe constructed unemployment series that is due to estimating em-ployment. For each of the five base years, this ratio is at least .70. Thisshows that estimating employment accounts for 70 percent of thecyclical exaggeration of UI, while estimating the labor force accountsfor the remaining 30 percent of this exaggeration.This finding is very important for two reasons. First, it shows thatauthors who have concentrated on the problems with Lebergott's esti-mates of the labor force have missed the more fundamental problemin the historical unemployment estimates. Estimating employment is a



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26 JOURNAL OF POLITICAL ECONOMYsource of much larger errors.9 Second, for those who believe that theunemployment rate is a poor measure of the cycle, perhaps becausethe labor force is an inherently nebulous quantity, this finding impliesthat more direct cyclical variables will show the same cyclical exagger-ation. Measures such as the deviation of employment from trend orthe employment to population ratio, when based on the constructedemployment series, will show much greater cyclical movements thansimilar measures using actual employment data.The counterfactual experiments can be taken a step further. Ifmost of the errors in the constructed unemployment rate are due toestimating employment, it is useful to discover if the total employ-ment effect is due to estimating employment in a particular sector.Specifically, this analysis has only replicated Lebergott's proceduresfor estimating employment in trade, construction, and manufactur-ing. Because the replication is roughest in manufacturing, it is impor-tant to see if the total employment error is due to the estimates ofmanufacturing employment.To check this, I run the following experiment. As in the experi-ment for UE, I suppose that the true labor force is known. I supposealso that employment in manufacturing is known, while employmentin the rest of the economy is estimated as before. The resulting unem-ployment rate (denoted UEM) can be compared with the UE seriesfrom before to see how much of the employment effect is due toestimating employment in manufacturing.The average cyclical amplitudes for UEM for all base years are alsoshown in table 8. When employment in manufacturing and the laborforce are set equal to their actual values, the resulting unemploymentseries (UEM) is still much more variable than the actual unemploy-ment rate. Furthermore, UEM is nearly as variable as UE, which setsonly the labor force equal to its actual value. This suggests that theemployment effect is not driven by estimates of employment in manu-facturing. If one compares the difference in the amplitudes of UAand UE with the amplitudes of UA and UEM, only about a third ofthe total employment effect is due to manufacturing.V. Creating Better Historical DataNow that I have derived a model of' the relationship between theactual and constructed series in the postwar period, it is natural toconsider using this model to create a better historical series. Trans-

Darbv (1976) also points out the importance of possible errors in the employmentseries. He shows that the estimates of unemployment during the Great Depressionare very sensitive to whether workers on public works jobs are counted as employed.



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HISTORICAL UNEMPLOYMENT DATA 27forming the constructed prewar data by the estimated filter may yielda series that is closer to the true prewar unemployment rate. How-ever, imposing a relationship identified using postwar data on theprewar period is a risky step. To do so assumes that the effects of theconstruction procedures are the same in the two time periods. This isan assumption whose validity must be tested before it is imposed.A. Historical EvidenceThe analysis of Section IV showed that the main errors in the con-structed postwar data stem from the fact that employment in somesectors is assumed to move one for one with output in those sectorsand that the labor force is assumed not to vary with the cycle. Boththese assumptions are false in the postwar era, and because of this anunemployment series derived using these assumptions is excessivelyvolatile. If both these assumptions are also false in the prewar era,then it is likely that Lebergott's unemployment series is excessivelyvolatile as well. In this case, the relationship between the constructedand actual postwar unemployment series can legitimately be used tofilter the historical constructed data to form a more accurate series.In order for Lebergott's prewar unemployment series to be exces-sively volatile, prewar employment in manufacturing, trade, and con-struction must move less than one for one with output. That is, pro-ductivity and hours must be procyclical in these sectors in the prewarera. Direct empirical evidence on whether this is true is obviouslylimited because the necessary data are scarce. However, there arefragments of employment and output data that others have used toexamine the cyclical movements in productivity and hours.The most recent analysis of the cyclical behavior of productivityand hours is done by Bernanke and Powell (1984). Their study usesemployment and hours data from a monthly survey conducted by theNational Industrial Conference Board over the period 1923-39. Ber-nanke and Powell use various time-series techniques to compare thecyclical movements of productivity and hours in manufacturing overtime. Their primary measure is the coherence between movements inproductivity and hours and output. They find that for both produc-tivity and hours the coherence with output is positive and significantin both the prewar and postwar periods. They conclude that "theinterrelationship of productivity, hours, output, and employment isessentially stable between the prewar and postwar [eras]" (Bernankeand Powell 1984, p. 17).There exist other studies with the same conclusion, provided thatone defines the prewar era very loosely. The classic study by Hultgren(1960), for example, uses data that begin in 1932. Hultgren concludes



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28 JOURNAL OF POLITICAL ECONOMYthat output per hour usually rises when production rises. This showsthat for a period that is at least contiguous to the pre-1930 period,productivity is procyclical as it is in the postwar period.Both these studies apply only to manufacturing. Whether produc-tivity and hours in construction and trade are procyclical in the pre-war era as they are in the postwar era is still an open question. Unfor-tunately, there are essentially no data that can be used to answer thisquestion directly. However, on a theoretical level it seems unlikelythat labor hoarding in these sectors has increased over time. Forexample, the increase in the extent of unionism in the constructionindustry between the prewar and postwar eras is believed to haveserved mainly to raise and regulate wages (see Mills 1972, p. 120).Such stabilization of wages may have actually made productivity inconstruction less procyclical in the postwar era than in the prewar era.Similarly, the large expansion of employment in wholesale and retailtrade and the increasing reliance on secondary workers may haveweakened the ties between workers and firms in this sector. As aresult, employment in trade may move more closely with output inthe postwar period than it did in the prewar era. Both these observa-tions suggest that the assumption that employment in constructionand trade moves one for one with output is at least as bad in theprewar era as in the postwar era.Though far less crucial than the output-employment link, the rela-tionship between the labor force and output is another determinantof whether Lebergott's prewar unemployment series is excessivelyvolatile. For the prewar series to have the same errors as the con-structed postwar series, fluctuations of the labor force should be pro-cyclical in the prewar period as they are in the postwar period. Evi-dence on whether this is true, however, is very hard to find. For thepre-1930 period there does not exist even a fragment of time-seriesdata on the labor force.However, it is possible to use cross-section data to estimate thecyclical behavior of the labor force. For example, several modernstudies have tested how the labor force participation rates of variouscities are related to the unemployment rates of those cities (see, e.g.,Bowen and Finegan 1965). While Mincer (1966) has suggested severalreasons why such studies may overstate the procyclical movements inthe labor force,'0 this type of study is one of the few that can be doneon both prewar and postwar data. Furthermore, since this test is

10 Mincer (1966) suggests several possible problems with cross-section studies. One ofthe main problems is that because the labor force enters both the dependent andindependent variable, but in opposite directions, the two variables could be negativelycorrelated by construction.



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HISTORICAL UNEMPLOYMENT DATA 29designed to gauge the stability of the cyclical movement of the laborforce rather than estimate the actual sensitivity, such problems shouldnot affect the basic results.For cross-section data on the prewar labor force, I use figures fromU.S. Bureau of the Census (1932). In a special volume on unemploy-ment, the census lists the number of gainful workers and the numberunemployed by city.' ' The gainful worker numbers are only an ap-proximation to the labor force in each city because seasonal and otherworkers are treated differently in the gainful worker figures than inthe modern labor force estimates. However, Lebergott suggests thaton average the difference between the two numbers is probably small(Lebergott 1964, p. 402). Therefore, I use the gainful worker num-bers to calculate the labor force participation rates and the unemploy-ment rates of each city.To see how the labor force participation rate varies with unemploy-ment, I regress the participation rate by city (LF/POP) on a constantand the unemployment rate by city (U/LF). I use data on the 33 citiesthat had more than 200,000 inhabitants in 1930. The estimated rela-tionship is

LF _U2-~ .482 - .330 + e; R= .136, S.E. = .018, (14)POP (.013) (.149) LFwhere standard errors are in parentheses. The negative coefficientestimate on U/LF suggests that the labor force was significantly procy-clical in 1930.To see if the size of procyclical movements in the labor force is thesame pre- and postwar, I run a similar regression for 1975. I choose1975 because it is one of the few years for which data are availablethat corresponds to approximately the same point in a business cycleas 1930. When the same sample of cities as before is used, the es-timated relationship is

LF _U2pp = .473 - .298 + e R .049, S.E. = .027. (15)POP (.025) (.248) LFWhile the similarity in parameter estimates for the 1930 and 1975regressions provides some evidence that the cyclical behavior of thelabor force has indeed been stable, it is far from conclusive. Theestimated coefficient on U/LF is very unstable in the postwar period.

l Volume 1 of the 1930 Census of Unetnployment classifies the unemployed into eightclasses. To be consistent with modern unemployment data, I estimate the numberunemployed in each city as the stumof the class A unemployed (persons oltt of' a job,able to work, and looking for a job) and the class B unemployed (persons having jobsbut on layoff without pay).



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o() JOURNAL OF POLITICAL ECONOMYWhile the sign is always negative, the coefficient varies with whetherthe year is one of boom or bust.'2Nevertheless, the results on the cyclical behavior of the prewarlabor force and employment do support the notion that the construc-tion procedures have the same effects in the pre-1930 period as theydo in the postwar period. The fact that productivity, hours, and thelabor force are procyclical in the prewar period suggests that thehistorical unemployment series has errors that are similar to those inthe postwar constructed series. Thus imposing the postwar model ofthe relationship between the actual and constructed series may yield amore accurate estimate of the prewar unemployment rate.B. New Historical DataTo impose the postwar relationship is straightforward. In rearrangedform, the model of the relationship between the actual unemploy-ment rate and the constructed rate estimated in equation (13) is

UA = UI - .484(UI - UI) + .458(UI - UI)_ (16)- .749(UI - UA), l + e.Constructing fitted values for the historical period is slightly com-plicated because of the lagged UA term in the model of the relation-ship between UI and UA. To deal with this complication I use adynamic simulation to get fitted values. This process assumes that forthe first observation the error is equal to zero. While this procedure istechnically correct, it is of little consequence. As noted earlier, theinclusion of a lagged endogenous variable expands the explanatorypower of the model of the relationship between UI and UA very little.

As a result, the fitted values from the dynamic simulation are nearlyidentical to those from the simpler model that excludes the laggedendogenous variable.Constructing fitted values for the historical period is also com-plicated because it is necessary to take into account the fact thatLebergott's series is correct in census years. To deal with this secondcomplication, I impose that UI = UA in each census year and thenstart the dynamic simulation over in the first year of each decade.The results of applying these procedures are shown in table 9. Thefirst column shows Lebergott's series; the second shows the filtered12For boom years the coefficient is typically lower. For 1977, e.g., the coefficient is.70. This may show that a given change in the unemployment rate has a greaterimpact when the unemployment rate is low. This finding also explains why thecoefficient found for 1975 is lower than that found by Bowen and Finegan (1965) for1960.



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HISTORICAL UNEMPLOYMENT DATA 31TABLE 9

OLD AND NEW HISTORICAL DATA

Year ULEB* UA' Year ULEB* UA1890 3.97 3.97 1911 6.72 6.271891 5.42 4.77 1912 4.64 5.251892 3.04 3.72 1913 4.32 4.931893 11.68 8.09 1914 7.92 6.631894 18.41 12.33 1915 8.53 7.181895 13.70 11.11 1916 5.10 5.631896 14.45 11.96 1917 4.62 5.231897 14.54 12.43 1918 1.37 3.381898 12.35 11.62 1919 1.38 2.951899 6.54 8.66 1920 5.16 5.161900 5.00 5.00 1921 11.72 8.731901 4.13 4.59 1922 6.73 6.931902 3.67 4.30 1923 2.41 4.801903 3.92 4.35 1924 4.95 5.801904 5.38 5.08 1925 3.22 4.921905 4.28 4.62 1926 1.76 4.021906 1.73 3.29 1927 3.28 4.571907 2.76 3.57 1928 4.21 5.021908 7.96 6.17 1929 3.25 4.611909 5.11 5.13 1930 8.94 8.941910 5.86 5.86

ULEB denotes Lebergott's original series. These unemployment rates are calculated by dividing Lebergott'sseries on total unemployment by his series on the civilian labor force. The series are from Lebergott (1964, table A-3[for 1900- 19301 and table A- 15 [for 1890-991).t denotes the new filtered version.

series UA. In addition to filtering the 1900-1930 data, I also applythe correction filter to Lebergott's series for 1890-1900. This applica-tion is much more dubious than that for the later period both becauseI am less certain that the necessary relationships hold in this periodand because the procedures Lebergott uses to construct data for thisdecade are slightly different from those he uses for the later period.Nevertheless, it is interesting to see how the new data changeour perception of the pre-Depression economy. For example, thedownswing of the 1890s now appears to be a much milder cycle.Rather than assuming near-Great Depression severity, the depres-sion of the 1890s looks more like the 1982 recession. The 1920s alsolook much different. Rather than being a roaring boom, the twentiesactually look no more prosperous than the rest of the early 1900s andless prosperous than the roaring sixties. This smoothing out of thebusiness cycle fluctuations of the early 1900s has the effect of makingthe Great Depression stand out as a great anomaly. Instead of beingthe largest of several very severe prewar recessions, the Great Depres-sion appears to be a complete collapse of what had previously been areasonably stable economy.



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32 JOURNAL OF POLITICAL ECONOMYVI. ConclusionWhile I have tried to suggest that the methods used to create the newprewar unemployment rate series are valid, it is important to notethat the new series presented in table 9 is still very rough. It is pro-vided mainly to suggest how different the prewar business cyclewould look if the systematic biases were removed from Lebergott'sseries. Although the new estimates may be useful for certain cyclicalcomparisons over time, their accuracy is questionable enough thatthey should not be used in any applications where the actual pointestimates of unemployment are crucial.While the construction of more accurate prewar unemploymentdata is an important task, this activity is to some degree peripheral tothe main point of this study. I view this work much more as puttingLebergott's own footnotes back on the historical unemploymentseries. By demonstrating the direction and magnitude of the system-atic errors imposed by the data construction procedures, I haveshown the dangers of making cyclical comparisons between the con-structed prewar unemployment data and the more nearly accuratepostwar data.The main danger of making such comparisons may be to overesti-mate how much the economy has changed. This is especially true ofthe issue of the stabilization of the postwar economy. Whereas theinconsistent unemployment data show a marked decline in the am-plitude of the business cycle between the pre-1930 and the post-1948periods, the consistent data show no such decline. By naively assum-ing that the first comparison was valid, economists may have mis-judged both the effectiveness of stabilization policy and the long-runchanges in the economy.

It is natural to ask whether the results I have identified for theunemployment data also hold for the other macroeconomic series aswell. Because the excess volatility of the unemployment series comesprimarily from particular errors in the specification of the output-unemployment link, it seems unlikely that other series have identicalerrors. However, the types of assumptions and interpolations thatLebergott had to make are not unique to the unemployment series.The builders of various output and industrial production series hadto make similar assumptions about the behavior of many variables inorder to piece together the available fragments of data. While theexact effect of these assumptions is still an open area of research, it ispossible that critical analysis of these data will also resurrect the toot-notes of Simon Kuznets and the Federal Reserve Board on the limita-tions of the historical output series.



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HISTORICAL UNEMPLOYMENT DATA 33AppendixThis Appendix tests the robustness of the results in the text to the choice ofthe variables used to interpolate employment. For each sector I describe theseries and methods Lebergott uses to construct annual employment estimates.I then suggest various postwar extensions of the series Lebergott uses and testto see if the choice of series affects the employment estimates.The test that I use is to construct several employment series and the corre-sponding constructed unemployment rates and compare them. For the sam-ple period 1960-80 I construct nine estimates of total employment based onnine combinations of interpolating variables. Combining these estimates of totalemployment with the constructed labor force numbers for 1960-80, I createnine constructed unemployment series. The 1960-80 sample period is chosenbecause this is the earliest time pelnod for which all the interpolating series exist.1. Series and Methods Usedfor Various SectorsConstructionPre-1930.-For employment in construction, Lebergott (1964) has data ontotal employment and activity in 1899 and 1929. The interpolating series for1899-1920 is Shaw's (1947) series on the output of construction materials,deflated by the related price series. The interpolating series for 1920-38 isthe Commerce Department series on the nominal value of new construction.Lebergott creates a price series that he uses to deflate this series.The method Lebergott uses reduces to the usual interpolation formula. Hedescribes forming the ratio of employment to activity for 1899 and 1929 andinterpolating linearly. He then multiplies the resulting fitted values by theannual activity series. In logarithms this procedure is identical to the formulaemp, = emp + yt -Y.Post-] 948. -There are several possible activity series for the postwar periodthat are similar to those chosen by Lebergott. The most obvious is that chosenfor the main text: the Federal Reserve Board index of the output of construc-tion materials (abbreviated CM). A second candidate is the Commerce De-partment series on the value of new construction. Using the gross nationalproduct (GNP) deflator for structures, one can construct a series very similarto that used by Lebergott for the 1920s. This series is designated in whatfollows as CONST. A third candidate is real GNP in construction (designatedGNPC). While conceptually different from Lebergott's series, real GNP isarguably the most natural output series to use.TradePre-1930.-Lebergott's method for estimating employment in trade is com-plicated. He begins by constructing benchmarks for employment in trade in1900, 1910, 1920, and 1930. He also constructs benchmarks for a sample ofcomponent series for the same years. That is, he forms benchmarks for thenumber of employees in the food trade, the furniture trade, and so on. Hethen interpolates each of these component series by Shaw's series for the realoutput of finished commodities in the corresponding sector. For example, heinterpolates the number of employees in drugstores by Shaw's series on theoutput of drugs. These constructed component series are combined and usedto interpolate the total employment series.



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34 JOURNAL OF POLITICAL ECONOMYPost-1948.-The most obvious postwar series to use is one similar to the oneLebergott uses. For 1960-80, I construct a preliminary employment series bysumming seven constructed employment series. Following Lebergott, I formthe component series by taking employment in a particular line ot trade andinterpolating by the corresponding Federal Reserve Board index of the out-put of finished goods in that line of trade. The resulting interpolating series isdesignated ETRADE.This series is not a viable interpolating series for the entire postwar periodbecause annual data on employment in various types of stores are not avail-able from the (PS for most lines of trade before 1958. An aggregate approxi-mation to Lebergott's procedure is to interpolate total employment in tradeby the Federal Reserve Board series on the output of final goods destined forconsumers. This series, which is used in the main text, is designated as CG intable Al.Two other interpolating series are of'interest. Conceptually, real retail salesmight be the activity series most closely related to employment in trade. Forthis reason I include the Commerce Department series on retail sales deflatedby the personal consumption deflator (designated RSALES) as an interpolat-ing series. I also try real GNP in trade (GNPT) as an interpolating series.

ManufacturingPre-1930.-For 1899-1909 Lebergott interpolates employment in manufac-turing by an index of manufacturing employment in a sample of states. Theindex is based on the five largest manufacturing states, which in 1904 ac-counted for 50 percent of all manufacturing employment.For 1909-19 the interpolating series is Shaw's estimates of' the output of'finished goods in constant dollars. Lebergott adjusts this series to includeconstruction materials and to exclude nonmanufactured foods.For 1919-29 Lebergott adopts Fabricant's series on employment in manu-facturing. For this period the Census of Manufa

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