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《宏观经济学 Macroeconomics》课外读物：An Experience-Weighted Measure of Employment and Unemployment Durations

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An Experience-Weighted Measure of Employment and Unemployment durations By GEORGE A AKERLOF AND BRIAN G. M. MAIN* Kim Clark and Lawrence Summers(1979) tion, SEw. It appears that although the have recently established that while most age job is of short duration, most er unemployment spells are quite short, most ment is spent in jobs of longer than av average time spent in unemployment is spent in spells duration of longer than average duration. This ap The fact that both employment and unem- parent paradox is due to the fact that the ployment fall in spells of considerably greater most common measure of the average length length than is indicated by examination of of a spell of unemployment is an average of turnover statistics, is of considerable import all spell lengths terminating in a given period, to the standing of what has come to be herein labeled Srw. In this measure, all spells known as the"new view"of the labor market. are given the same weighting irrespective of ( See Martin Feldstein; Robert Hall; George he amount of unemployment for which they Perry. )In this view the labor market is full of account. Weighting each spell by its length movement with both employment and unem- would result in an experience-weighted mea- ployment occurring in relatively brief spells sure, herein labeled SEw, which would reflect That there is a lot of movement is a fact the length of spell in which a typical week of reflected in labor market turnover statistics unemployment is spent and, hence, avoid the As our empirical work will show, however, it Clark and Summ is erroneous to take these turnover statistics Our paper motivates this alternative mea- which reflect average movement through cer- re, Sew, and observes that in the steady tain states to reflect the average experience state a reasonable measure of this experi- of persons in these states. In both employ ence-weighted spell duration is twice the ment and unemployment there appears to be official Bureau of Labor Statistics(BLS) much more permanence than the new view average duration of uncompleted spells, allows. In our view, for most purposes, the herein labeled T. When this approach is ap- existence of many short spells of employ- plied to employment statistics, in the form of ment or unemployment is of little relevance job tenures, a sharp contrast is found be- if these spells in the aggregate contribute tween the average length of a job as reflected relatively little, respectively, to total employ in turnover statistics or the terminations- ment or total unemployment. This appears in weighted spell length, STw, and as measured fact to be the case since employment-years by the experience-weighted average job dura- and unemployment-weeks are in spells which are on average quite long. Section I will explain theoretically and by analogy the meaning of the various measures of average spell lengths and present some Economics and University of facts about their relationship to each other California-Berkeley, and University of Edinburgh, re- Section II displays estimates both of the Hajime Miyazaki, Charles O'Reilly, George Per length of the average completed spell and Stephen Salant, Elaine Sorenson, Jean Vanski, Clai of the Vickery, and Janet Yellen for valuable comments and length for various populations for job tenures assistance. We also like to thank the U.S. Department of and unemployment durations. Section II Labor for generous financial support under small grant contains some concluding remarks pertaining o.91-06-79-33, administered by the Institute of B ness and Economic Research of the University of Cali- to the ramifications of these results on labor fornia-Berkeley market policy

An Experience-Weighted Measure of Employment and Unemployment Durations Kim Clark and Lawrence Summers (1979) have recently established that whle most unemployment spells are quite short, most time spent in unemployment is spent in spells of longer than average duration. This apparent paradox is due to the fact that the most common measure of the average length of a spell of unemployment is an average of all spell lengths terminating in a given period, herein labeled ST,. In ths measure, all spells are given the same weighting irrespective of the amount of unemployment for which they account. Weighting each spell by its length would result in an experience-weighted measure, herein labeled SEW, whch would reflect the length of spell in whch a typical week of unemployment is spent and, hence, avoid the Clark and Summers paradox. Our paper motivates this alternative measure, SEW, and observes that in the steady state a reasonable measure of this experience-weighted spell duration is twice the official Bureau of Labor Statistics (BLS) average duration of uncompleted spells, herein labeled T. When this approach is applied to employment statistics, in the form of job tenures, a sharp contrast is found between the average length of a job as reflected in turnover statistics or the terminationsweighted spell length, ST,, and as measured by the experience-weighted average job dura- 'London School of Economics and University of California-Berkeley, and University of Edinburgh, respectively. We thank Todd Easton, Harvey Hamel, Hajime Myazaki, Charles O'Reilly, George Perry, Stephen Salant, Elaine Sorenson, Jean Vanski, Clair Vickery, and Janet Yellen for valuable comments and assistance. We also like to thank the U.S. Department of Labor for generous financial support under small grant no. 91-06-79-33, administered by the Institute of Business and Economic Research of the University of California-Berkeley. AND BRIANG. M. MAIN* tion, SEW. It appears that although the average job is of short duration, most employment is spent in jobs of longer than average duration. The fact that both employment and unemployment fall in spells of considerably greater length than is indicated by examination of turnover statistics, is of considerable import to the standing of what has come to be known as the "new view" of the labor market. (See Martin Feldstein; Robert Hall; George Perry.) In this view the labor market is full of movement with both employment and unemployment occurring in relatively brief spells. That there is a lot of movement is a fact reflected in labor market turnover statistics. As our empirical work will show, however, it is erroneous to take these turnover statistics which reflect average movement through certain states to reflect the average experience of persons in these states. In both employment and unemployment there appears lo be much more permanence than the new view allows. In our view, for most purposes, the existence of many short spells of employment or unemployment is of little relevance if these spells in the aggregate contribute relatively little, respectively, to total employment or total unemployment. This appears in fact to be the case since employment-Years and unemployment-weeks are in spells which are on average quite long. Section I will explain theoretically and by analogy the meaning of the various measures of average spell lengths and present some facts about their relationshp to each other. Section I1 displays estimates both of the length of the average completed spell and of the experience-weighted completed spell length for various populations for job tenures and unem~lovment . < durations. section 111 contains some concluding remarks pertaining to the ramifications of these results on labor market policy

THE AMERICAN ECONOMIC REVIEW DECEMBER 198I I. Three Different Measures of Spell Length PERSON 1 A. Three Statistics Defined and Explained with Use of a diagram PERsOn 22 The different es of durations statis- PE RSON 3 ence to Figure 1(which is adapted from a similar diagram by Stephen saint Let the PERSON 4 S41 horizontal lines in Figure 1 represent the periods during which persons (labeled on the vertical axis) are unemployed. (An exactly PERSON 5 analogous figure could be drawn for job PERSON 6 Now consider three possible measures of employment duration. The first measure is Date of Interview Calendar Time the one commonly reported. Suppose that at date to a poll is taken which records how FIGURE 1 have been out of work. In terms of the iagram, Person l has been out of work for a length of time T, Person 2 for a length of time T2, Person 5 for a length of time Ts, and measure of the average length of unemploy Person 6 for a length of time T6. Persons 3 ment. This measure consists of the average and 4 are not out of work, and therefore length of all spells of unemployment, where eir unemployment durations are not re- the spells are not defined to be those in corded in the sample. An average computed progress at a given point in time, as in Sew, from the durations out of work of those but are those spells which are observed to employed at time of inte terminate over a given period of time. In such an average each spell counts exactly once, irrespective of its total contribution to T=(T1+T2+T+T6)/4 unemployment In terms of Figure I such an average would be This statistic T corresponds to the official statistics on mean duration of unemploy Srw=(S1+S2+S31+S32 ment reported by the bls There is at least one sense in which this statistic is lacking. The times T, T2, T5, and T6 do not report the completed length of the taking into account the two repeat spells of pells of persons l, 2, 5, and 6, respectively, persons 3 and 4. This statistic is represented but only the length of their interrupted spell, by the symbol STw, where TW mnemoni which is for each person an obviously shorter cally represents"termination-weighted "The phenomenon. In terms of the diagram, the time period over which these terminations verage completed length of unemployment have been averaged in the literature has com- spells of the currently unemployed is only been the calendar year(see Hyman SEw=(S1+S2+S5+S)/4. Kaitz and salant) In contrast to Srw, which weights all spells equally, the chances of sampling a given spell S is Salant's notation for completed length of at a given point in time is proportional to its spell. The subscripts EW stand for"experi- length. For this reason in steady state the ence-weighted"spell length, as shall be ex- average of completed spells at a given point in time(to for example) is equivalent to a

1004 THE AMERICAN ECONOMIC REVIEW DECEMBER 1981 I. Three Different Measures of Spell Length PERSON 1 J--- A. Three Statistics Defined and Explained with Use of a Diagram The different measures of durations statisPERSON 2 ,+ tics can be most easily explained by refer- c( ence to Figure 1 (whlch is adapted from a similar diagram by Stephen Salant). Let the PERSON 4 horizontal lines in Figure 1 represent the periods during which persons (labeled on the PERSON 5 ,75-p7 vertical axis) are unemployed. (An exactly analogous figure could be drawn for job tenures.) PERSON 6 ,* Now consider three possible measures of unemployment duration. The first measure is the one commonly reported. Suppose that at date to a poll is taken whlch records how long the persons who are unemployed at to have been out of work. In terms of the diagram, Person 1 has been out of work for a length of time TI, Person 2 for a length of time T2, Person 5 for a length of time T,, and Person 6 for a length of time T6. Persons 3 and 4 are not out of work, and therefore their unemployment durations are not recorded in the sample. An average computed from the durations out of work of those unemployed at time of interview would thus be Ths statistic T corresponds to the official statistics on mean duration of unemployment reported by the BLS. There is at least one sense in which this statistic is laclung. The times TI, T2, T,, and T6 do not report the completed length of the spells of persons 1, 2, 5, and 6, respectively, but only the length of their interrupted spell, whch is for each person an obviously shorter phenomenon. In terms of the diagram, the average completed length of unemployment spells of the currently unemployed is S is Salant's notation for completed length of spell. The subscripts EW stand for "experience-weighted" spell length, as shall be explained presently. Past F u t u r e Date of Interview Calendar TI me On the other hand, there is yet a third measure of the average length of unemployment. This measure consists of the average length of all spells of unemployment, where the spells are not defined to be those in progress at a given point in time, as in SEW, but are those spells which are observed to terminate over a given period of time. In such an average each spell counts exactly once, irrespective of its total contribution to unemployment. In terms of Figure 1 such an average would be taking into account the two repeat spells of persons 3 and 4. This statistic is represented by the symbol ST,, where TW mnemonically represents "termination-weighted." The time period over which these terminations have been averaged in the literature has commonly been the calendar year (see Hyman Kaitz and Salant). In contrast to ST,, whch weights all spells equally, the chances of sampling a given spell at a given point in time is proportional to its length. For this reason in steady state the average of completed spells at a given point in time (to for example) is equivalent to a

OL. 7I NO. 5 AKERLOF AND MAIN: EXPERIENCE-WEIGHTED MEASURES measure which weights spells according to tive jobs with each job lasting exactly one their contribution to total unemployment: year. The second person, however, is em this contribution is, of course, their com- ployed in the same job for the entire ten-year pleted length. It was for this reason that the period. At any moment of time a census of measure SEW=(S+S2+Ss +S6)/4was his population will find two persons em- named the experience-weighted spell length. ployed. One person will be in a one-year job the other will be in a ten-year job. The xplanations of Three Statistics average completed job t y Analog ently employed is, accordingly, five and one-half years. Furthermore, it should be An analogy is exact and also gives intui apparent, perhaps after a moment's reflec- tive explanation of the three statistics. Bar- tion, that, since in each and every year the ring the eat spells of average length of job in which that year's Figure I could be taken to represent not employment is spent is five and one-half length of time unemployed, but, instead, the years, so it is also true that over the entire life spans of persons over some period of period the average length of job in which time, with Person i having a life span of employment is spent is five and one-half length S, with life beginning and ending in years calendar time as indicated by the horizontal On the other hand, in the example there lines. The statistic T corresponds to the aver- are eleven spells of employment that ge age of the population; the statistic SEw terminate over the period and twenty em of the ployment years. Thus STh=20/11=1.8. The population alive at to, and Srw corresponds measure Sew weights the ten one-year jobs to the average life span of all persons who equally with the one ten-year job, according die over some period of time, or, equivalently to their respective contributions to employ in a steady state, is life expectancy at birth. ment. In contrast, Srw weights all eleven The latter statistic is smaller than the former spells equall because longer-lived persons are more apt to be seen in any given census; thus the person D. Interpretation of Data in Steady State who dies at eighty is visited by eight de- cennial censuses: the child who dies at ten is Censuses enumerate populations at given seen by only one decennial census. In de- moments of time. It is a central question in mography, life expectancy at birth(STw)is demography to use population censuses to dramatically different from the average life calculate mortality tables that show average expectancy of a population (SEw) where life expectancy at birth, or Srw. Similarly, there are high rates of child mortality. The the Bureau of Labor Statistics produces dramatic differences reported in the next sec- monthly data on the length of interrupted tion between SEw and STH for job tenures spells of unemployment and occasional ta and unemployment durations are the similar bles on the interrupted job tenure of workers result, caused by the existence of many short (see BLS, 1964, 1967, 1969, 1974). This paper job tenures and of many short spells of un- uses these census-like data to infer both the employment. average experience-weighted and the average termination-weighted unemployment dura C. A Numerical Example tions and job tenures A property of the stead A numerical example illustrates the rela- empirical estimates of Sew from reported tion between the two statistics Sew and Srw, statistics on interrupted spells. In the steady and how it may come about that Sew may be state a person who is interviewed at a ran long while Srw is short dom time will be interviewed with uniform Suppose that there are two persons who probability throughout the length of his spell are continuousl ly employed over a ten-year Thus for each person i, E(T)=S;/2, and period. The first is employed in ten consecu- with a large population SEw=2T. This fact

VOL. 71 NO. 5 AKERLOFAND MAIN: EXPERIE ZNCE- WEIGHTED MEASURES 1005 measure which weights spells according to their contribution to total unemployment; ths contribution is, of course, their completed length. It was for ths reason that the measure SEW= (S, + S, + S, + S6)/4 was named the experience-weighted spell length. B. Explanations of Three Statistics by Analogy An analogy is exact and also gives intuitive explanation of the three statistics. Barring the repeat spells of Persons 4 and 5, Figure 1 could be taken to represent not the length of time unemployed, but, instead, the life spans of persons over some period of time, with Person i having a life span of length S,, with life beginning and ending in calendar time as indicated by the horizontal lines. The statistic 7'corresponds to the average age of the population; the statistic SEW corresponds to the average life span of the population alive at to, and ST, corresponds to the average life span of all persons who die over some period of time, or, equivalently in a steady state, is life expectancy at birth. The latter statistic is smaller than the former because longer-lived persons are more apt to be seen in any given census; thus the person who dies at eighty is visited by eight decennial censuses; the child who dies at ten is seen by only one decennial census. In demography, life expectancy at birth (ST,) is dramatically different from the average life expectancy of a population (SEW)where there are high rates of child mortality. The dramatic differences reported in the next section between SEWand ST, for job tenures and unemployment durations are the similar result, caused by the existence of many short job tenures and of many short spells of unemployment. C. A Numerical Example A numerical example illustrates the relation between the two statistics SEWand ST,, and how it may come about that SEWmay be long whlle ST, is short. Suppose that there are two persons who are continuously employed over a ten-year period. The first is employed in ten consecutive jobs with each job lasting exactly one year. The second person, however, is employed in the same job for the entire ten-year period. At any moment of time a census of this population will find two persons employed. One person will be in a one-year job; the other will be in a ten-year job. The average completed job tenure of the currently employed is, accordingly, five and one-half years. Furthermore, it should be apparent, perhaps after a moment's reflection, that, since in each and every year the average length of job in which that year's employment is spent is five and one-half years, so it is also true that over the entire period the average length of job in which employment is spent is five and one-half years. On the other hand, in the example there are eleven spells of employment that terminate over the period and twenty employment years. Thus ST,= 20,' 1 1 - 1.8. The measure SEWweights the ten one-year jobs equally with the one ten-year job, according to their respective contributions to employment. In contrast, ST, weights all eleven spells equally. D. Interpretation of Data in Steady State Censuses enumerate populations at given moments of time. It is a central question in demography to use population censuses to calculate mortality tables that show average life expectancy at birth, or ST,. Similarly, the Bureau of Labor Statistics produces monthly data on the length of interrupted spells of unemployment and occasional tables on the interrupted job tenure of workers (see BLS, 1964, 1967, 1969, 1974). Ths paper uses these census-like data to infer both the average experience-weighted and the average termination-weighted unemployment durations and job tenures. A property of the steady state permits empirical estimates of SEW from reported statistics on interrupted spells. In the steady state a person who is interviewed at a random time will be interviewed with uniform probability throughout the length of his spell. Thus for each person I, E(T)=S,/2, and with a large population SEW= 2T. This fact

006 THEAMERICAN ECONOMIC REVIEW DECEMBER 1981 TABLE 1-ESTIMATED MEAN COMPLETED TENURE OF CURRENTLY HELD JOBS(IN YEARS)=SEw Male 1963 966 968 1973 19661968 73 A. By Race, Date, and Sex 11612. 11.6 24 28.2 290 928.623.323.0 11.0 195 13.7 Transport/public utilities 21.823422.8 15.113.3 Service/finance 18.6 18.8 17.1 17.0 Sales workers 124 18.2 6 14. Operatives and kindred 15.6 15.7 5.0 13.8 13.1 Farm laborers and foremen 23.6 Service workers l28128133 gives a simple way of estimating the Sew interrupted job tenure to give the statistic statistic, using the steady-state assumptio reported in Table 1 as SEw, or the estimated from the official BLS statistics on in- mean completed tenure of currently held jobs terrupted spells display markable stability for each subgroup over IL. Job Tenures and Longest time; this stability for four different times Job-Unemployment Durations not all at the same phase of the business cycle, gives some confidence in the use of the ng other things, displays steady-state assumption to calculate Srw and estimates of t statistics on job tenures SEw durations SEw and Sri Table 2 reports the estimates obtained for various populations. It shows that Sew is using the steady-state assumption for mean mpirically a uniformly large multiple of Stw completed job tenures in the 1968 to 1973 both for job tenures and for unemployment period and compare durations mated experience-weighted job tenures for 1968 as obtained in Table 1. These statistic A. Job Tenures support the major hypothesis of this v.9 that the average employment-year is spent The bureau of Labor Statistics has, on a job of long tenure even though the average occasion, compiled data on interrupted job length of all jobs is quite short. For white tenures. Table I displays the estimated mean males the estimated average completed length completed tenure of currently held jobs for a of job is four years; however, the average variety of demographic, occupational, and length of job of currently employed males is ndustrial subgroups. Assuming the steady state, we doubled an estimate of the mean ce our 1979 article

1006 THE AMERICAN ECONOMIC RE VIEW DECEMBER 1981 Male Female 1963 1966 1968 1973 1963 1966 1968 1973 - - - - - - A. By Race, Date, and Sex White 17.4 18.2 18.3 17.2 11.6 Nonwhite B. By Industry, Date, and Sex Agriculture Mining Construction 14.2 24.5 19.4 10.5 14.1 28.2 18.5 11.0 14.4 29.0 20.7 12.3 14.2 30.6 19.7 11.9 11.0 22.9 - 10.0 Manufacturing-durable Manufacturing-nondurable Transport/public utilities Wholesale/retail Service/finance Public Administration 18.8 18.3 21.8 11.7 12.0 18.6 21.8 19.8 23.4 12.2 11.8 19.4 18.3 19.5 22.8 13.7 13.7 18.8 18.3 18.5 20.6 11.7 11.5 19.3 13.2 13.7 16.4 9.2 9.8 14.5 C. By Occupation, Date, and Sex Professional/technical Managers, proprietors Clerical and kindred 16.2 21.2 17.0 17.1 22.1 17.2 16.7 22.0 17.2 16.3 19.7 16.9 13.2 17.3 11.0 Sales workers 12.4 13.8 14.1 14.2 10.5 Craftsmen, foremen Operatives and kindred Nonfarm laborers 18.4 15.7 11.4 20.0 15.6 11.3 19.5 15.7 12.7 18.2 15.0 10.9 14.6 13.4 - Farm laborers and foremen 9.7 11.4 10.7 13.5 23.6 Service workers 12.8 12.8 13.3 11.6 8.4 Source: See text. gives a simple way of estimating the SEW interrupted job tenure to give the statistic statistic, using the steady-state assumption, reported in Table 1 as SEW,or the estimated from the official BLS statistics on in- mean completed tenure of currently held jobs. terrupted spells. The estimates were found to display a remarkable stability for each subgroup over 11. Job Tenures and Longest time; this stability for four different times, Job-Unemployment Durations not all at the same phase of the business cycle, gives some confidence in the use of the This section, among other things, displays steady-state assumption to calculate ST, and " estimates of the two statistics on job tenures >EWand unemployment durations SEWand ST,, Table 2 reports the estimates obtained for various populations. It shows that SEWis using the steahy-state assumption for mean empirically a uniformly large multiple of ST, completed job tenures in the 1968 to 1973 both for job tenures and for unemployment period and compares them with the estidurations. mated experience-weighted job tenures for 1968 as obtained in Table 1.' These statistics A. Job Tenures support the major hypothesis of this paper: that the average employment-year is spent in The Bureau of Labor Statistics has, on a job of long tenure even though the average occasion, compiled data on interrupted job length of all jobs is quite short. For white tenures. Table 1 displays the estimated mean males the estimated average completed length completed tenure of currently held jobs for a of job is four years; however, the average variety of demographic, occupational, and length of job of currently employed males is industrial subgroups. Assuming the steady state, we doubled an estimate of the mean 'See our 1979 article

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