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U.S. Department of Labor Bureau of Labor Statistics November 1982 Bulletin 2135 Tables of Working Life: Th@ Increment-Decrement IMlodteS U.S. Department of Labor Raymond J. Donovan, Secretary Bureau of Labor Statistics Janet L. Norwood, Commissioner November 1982 Bulletin 2135 F o r sa le by th e S u p erin ten d en t o f D ocu m en ts, U .S. G overnm ent P r in tin g Office W a sh in g to n , D.C. 20402 - P rice $5.00 A 3. 3 P /3 J Tables of working life are a popular statistical tool by which to summarize current patterns of labor force at tachment. This bulletin discusses worklife methodology, introducing the “increment-decrement” technique re cently adopted by the Bureau of Labor Statistics. New tables of working life for men and women for 1977 are presented together with revised estimates for 1970. Increment-decrement and conventional models are compared, and differences in findings are discussed. The bulletin was prepared by Shirley J. Smith, a demo graphic statistician in the Division of Labor Force Studies, Office of Current Employment Analysis. Kenneth D. Buckley and Josephyne W. Price of the Data Services Group assisted in the preparation of the tables. Material in this publication is in the public domain and may, with appropriate credit, be reproduced without permission. © © o n te n ti Page Chapters: 1. The worklife expectancy of men and women ............................................... , ....................................... Recent changes in labor force behavior ............................................................................................... Changes in worklife estimation procedures ......................................................................................... The new estimates .................................................................................................................. ............ Trends in worklife duration ................................................................................................................... 1 1 1 2 2 2. Rates of labor force accession and separation ....................................................................................... 4 3. Increment-decrement tables of working l if e ............................................................................................. Literature on increment-decrement modeling ..................................................................................... Overview of the model ............................ ............................................................................................ Worklife expectancy of the general population ................................................................................. Worklife expectancies of persons in and out of the labor force ..................................................... Estimates of accession and separation rates .......... ............................................................................ Other measures of labor force mobility ............................................................................................... § 9 10 11 12 14 15 4. Evaluation of the increment-decrement worklife model ....................................................................... Estimates of labor force mobility rates ............................................................................................... Estimates of number of people likely to work at or beyond age x ................................................. Estimates of person years of labor force attach m en t......................................................................... Other considerations .......................................................................................................................... .. Areas for further research ..................................................................................................................... 30 30 30 ^ 31 31 31 Text tables: 1. Civilian labor force participation rates by age and sex, annual averages, 1970 and 1977 .................. 2. Worklife expectancies of the population and of active and inactive persons by ageand sex, 1977 3. Changes in life and worklife expectancies by sex, 1900-1977 ............................................................. 4. Average remaining labor force entries and exits per person at specific ages, 1977 ............................ 5. Selected indexes of working life by sex, 1970 and 1977 ....................................................................... 6. Rates of labor force mobility by age and sex, conventional model, 1970, and increment-decrement model, 1970 and 1977 ....................................................................................... 7. Population-based rates of labor force accession and separation by age and sex, 1970 and 1977 . . . 8. Net labor force transfers by age and sex, conventional model, 1970, and increment-decrement model, 1970 and 1977 ..................................................................... ................ 9. Matrix of transitions over a 1-year interval ........................................................................................... 10. Matrix of transitions used by Schoen and Woodrow to compute 1972working lifetables ............... 11. Changes in the size and composition of the cohort of menbetween exact ages 16and 1 7 ............... 12. Proportion of a standard 2,080-hour year worked by the average individual by sex, selected ages, 1977 .................................................................................................................................. Reference tables: Tables of working life for men, 1977: . 1. Derivation of the expectation of active life for the general population ............................................. 2. Sample derivation of worklife expectancies by labor force status for persons currently age 16 ...................................................................................................................................... 3. Expectation of active life by current labor force s ta tu s ......................................................................... 4. Indexes of labor force accession and separation ............................................................................. v 1 2 3 4 5 6 6 7 10 10 12 31 16 19 21 22 G ® n f@ n !s— C o n t i n u e d Page Tables of working life for women, 1977: 5. Derivation of the expectation of active life for the general population .............................................. 6. Sample derivation of worklife expectancies by labor force status for persons currently age 16 .................................................................................................................................. ... 7. Expectation of active life by current labor forces ta tu s ................................. 8. Indexes of labor force accession and separation........................................... 23 26 28 29 Figures: 1. Alternative paths of survival and labor force attachment for persons alive at time t: Potential paths over an 8-year period .................................................................................................... 8 2. Alternative paths of survival and labor force attachment for persons alive at time t Paths measured in the conventional worklife model ......................................................................... 9 3. Selected portion of the labor force status-specific Markov chain for men, initial age 16 ................ 13 Appendixes: 33 A. Revised tables of working life for men and women,1970 ..................................................................... B. The conventional working life table ......................................................................................................... 44 C. Notation .......................................................................................................................................................... 59 Bibliography ....................................................................................................................................... vi Chapter 1. The Worklife Expectancy of Mem and Women labor force attachment of men slackened somewhat in the prime ages and declined markedly above the age of 55. These participation changes contributed to a decline in the mean age of the male labor force.3 Although the par ticipation rates of women 55 and over were more stable than those of men, dramatic increases in the participation of women 16 to 54 had a similar effect on the age profile of • the female labor force. Working life tables summarize the long-term implica tions of present work patterns by modeling the lifetime experience of a hypothetical cohort which is assumed to “live through” the entire array of currently prevailing labor force rates. The experience of this synthetic cohort is used to determine how many years a person of a given age might expect to spend in the labor force, if participa tion patterns remained as they were in the reference year throughout his or her lifetime. In addition, the worklife model generates rates of labor force accession and separa tion, which describe patterns of mobility into and out of the labor market at each age. The indexes generated by these tables have a broad range of applications. Labor analysts use the worklife expectancy index to compare degrees of labor force attachment between groups and over time, and to esti mate the effects of various changes in behavior on lifetime work patterns. The index is also widely used in liability proceedings, as an indicator of work years lost and earn ings foregone by individuals whose earning capacity has been reduced or impaired, or has been truncated by death or severe disability. Labor force mobility rates are fre quently used to project replacement needs within occu pations,1 as well as to study patterns of labor turnover. T@kI table 1. Civilian labor tore® participation rat@@ by age and sen, annual averages, 1870 and 1977 Men Age group 1977 Change 1970-77 1970 1977 Change 1970-77 ........................ ........................ ........................ ........................ 56.1 83.3 96.4 96.9 61.0 85.7 95.4 95.7 4.9 2.4 -1.0 -1.2 44.0 57.7 45.0 51.1 51.4 68.5 59.5 59.6 7.4 8.8 14.5 8.5 45-54 ....................... 55-59 ........................ 60-64 ........................ 65 and over ............. 94.2 89.5 75.0 26.8 91.2 83.2 62.9 20.1 -3.0 -6.3 -12.1 -6.7 54.4 49.0 36.1 9.7 55.8 48.0 32.9 8.1 1.4 -1.0 -3.2 -1.6 16-19 20-24 25-34 35-44 Changes in wrorlclif© ©itSmiffom procedures The magnitude and character of these changes have rendered the 1970-based worklife estimates obsolete. Moreover, a careful reevaluation of the conventional worklife model has revealed some conceptual and techni cal deficiencies which have led to questionable estimates for certain population groups. For this reason, the staff of the Bureau of Labor Statistics has'undertaken a study of alternative worklife estimation procedures. The new 1977-based working life tables for the United States are the result of one such alternative method, known as the “increment-decrement” o r“multistate” life table model. It ■should be noted that these new estimates do not corre spond directly with previously published figures. They reflect not only changes in the behavior of American adults, but also several fundamental changes in modeling procedures. The increment-decrement model describes labor force attachment as a dynamic process. Members of the popu- ©h®mg©§ in S®b@r fore© fe©hiwi©r The last set of working life tables published by the Bureau of Labor Statistics was based on the work pat terns prevailing in 1970.2These patterns changed dramat ically between 1970 and 1977, the year for which new tables are being presented (text table 1). The single most striking change during this period involved young women. The participation rate of women 25 to 34 rose by 14.5 percentage points in just 7 years. Men 60 to 64 experi enced a drop in participation which was nearly as large, 12.1 percentage points. During this period, the entire age profile of participation for both sexes shifted. Young people (ages 16 to 24) became increasingly active. Older persons (55 and above) became less likely to work. The 'These projections, produced by the Bureau of Labor Statistics, incorporate a single set of separation rates for each sex, irrespective o f occupation. It may eventually be possible, using the worklife model introduced in this study, to prepare separate tables for various occupational clusters. 3The mean age of workers has also been depressed by the recent influx of babyboom cohorts into the labor force. Working life tables attempt to look past such changes—which stem from fertility fluctuations—to identify the impact of mortality and labor force changes. (See the discussion of the stationary labor force, appendix B.) However, to the extent that its numbers have indirectly affected participation rates, the baby-boom cohort may have made its mark on recent worklife estimates. 2Howard N. Fullerton, Jr., and James J. Byrne, Length o f Working Life fo r Men and Women, 1970, Special Labor Force Report 187 (Bureau o f Labor Statistics, 1976). Women 1970 1 lation are viewed as entering and leaving the labor market repeatedly during their lifetimes, with nearly all partici pating for some period during their lives. This scenario contrasts sharply with the assumptions underlying the previous model, that men enter and leave the labor force only once, and that women enter and leave only as the result of specific changes in marital and parental status. By assuming continuous participation, the conventional model tends to understate the size of the ever-active popu lation and to overstate average worklife expectancies. This bias is especially severe for groups characterized by high labor turnover, such as women. The incrementdecrement model identifies a larger group of persons over which to average total person years of work. Hence it produces somewhat lower mean work durations. Text table 2. Worklife expectancies of the population and of active and inactive persons by age and sex, 1977 [In years] Age Men Women Total Active Inactive Total Active Inactive At birth ....... 16 ................ 20 ................ 25 ................ 37.9 38.5 36.8 33.4 39.6 37.3 33.7 37.9 38.1 35.9 32.0 27.5 27.7 26.0 23.0 28.8 26.7 23.7 27.5 27.4 25.2 21.7 30 35 40 45 ................ ................ ................ ................ 29.2 24.7 20.3 15.9 29.3 24.9 20.4 16.2 27.2 21.7 16.9 12.0 19.9 16.8 13.7 10.5 20.9 17.9 14.9 11.9 18.2 14.8 11.4 8.0 50 55 60 65 70 ................ ................ ................ ................ ................ 11.7 7.8 4.3 1.9 .9 12.2 8.5 5.2 3.4 2.6 7.2 3.6 1.9 1.1 7.5 4.8 2.5 1.1 9.3 6.8 4.4 3.1 2.4 4.9 2.5 1.2 .6 .2 6 5 Tlh® m w © sim ile s The new worklife estimates, based on patterns of labor force attachment observed in 1977—and on the impor tant assumption that these remain constant in the future— are presented in tables 1-8 and summarized in text table 2. The reader should be aware that these estimates do not focus exclusively on time spent employed. They encom pass all forms of labor force attachment, including un employment. Following the long-established convention, the term “worklife” denotes the broader concept of time spent in the labor force. Members of the labor force are referred to as the “economically active” or simply “active” group. Those outside of the labor force are referred to as the “inactive” population. In 1977 the average 16-year-old man could expect to spend 38.5 years as a member of the labor force. At 16, the typical woman could anticipate a worklife of 27.7 years. At age 50, the average man could look forward to 11.7 more years of economic activity; the average woman, 7.5. It has long been recognized that persons who are al ready in the labor force are more likely to work in the future than are those not currently active. Published tables have alluded to this differential without clearly quantifying it. In the past they have displayed worklife durations for the total population and for those economi cally active. The new increment-decrement model also displays values for the missing group, those economically inactive (text table 2). The distinction between active and inactive teenagers is somewhat vague: Most enter and leave the labor force repeatedly at this age. Hence the expectancy differential by status is relatively small—about 1.5 years at age 16. It widens to about 4 years by age 45. At midlife the two groups are no longer so similar. Those out of the labor force face longer periods of inactivity associated with a diminished propensity to reenter the job market. substantial differences in the assumptions underlying the old and new models which markedly affect their out comes. To bridge the gap, figures for 1970 have been reestimated using the newer technique (appendix A). Com parisons of 1977 values with the early part of this century, 1900 to 1940, may not be seriously misleading. At that time work patterns conformed rather well with those assumed in the conventional tables. However, a growing disparity between assumed and actual behavior after World War II led to serious biases in the original 1950-70 estimates. Figures for working women were especially tenuous, overstating average work durations during that period. Apart from these values, the summary information of text table 3 gives a reasonable overview of changing work patterns during this century. In 1900, the life expectancy and worklife expectancy of men were very similar. The typical 20-year-old man could expect to spend just 4.4 years of his adult life outside of the labor force.4 Over the next 77 years, male life expect ancy at birth rose by about 23 years, with the bulk of the increase—about 17 years—being allocated to non-laborforce activities. During this entire period, male worklife expectancy at birth increased by less than 6 years. Looking at the most recent period—between 1970 and 1977—the increase in worklife expectancy was negligible. Virtually the entire increase in male life expectancy (2.2 years) was allocated to non-labor-force activities. At the turn of the century, formal labor force activities occupied a small portion of the typical woman ’s lifespan— about 6 years.5Yet as the lifespan has lengthened, most of the additional years have been spent within the labor force. Female longevity has increased by about 29 years since 1900, of which about 21 have gone to labor market activities, and less than 8 to nonmarket pursuits. The increase in labor force activity was most pronounced Trdimdte Igu workllf® duration Changes in methodology impede direct comparison between the 1977-based estimates and others previously published by the Bureau of Labor Statistics. There are 4Stuart H. Garfinkle, The Length o f Working Life fo r Males, 1900-1960, Manpower Report No. 8 (U.S. Department of Labor, Manpower Administration, 1963). 5Fullerton and Byrne, Length o f Working Life, 1970. 2 Text table 3. Changes in life and worklife expectancies by sex, 1900-1977 Life expectancy Worklife model, sex, and year Worklife expectancy All persons At birth At age 20 Conventional model: 1900 ............................................................... 1940 ............................................................... 1950 ............................................................... 1960 ............................................................... 1970 ............................................................... 46.3 61.2 65.5 66.8 67.1 Increment-decrement model: 1970 ....... ............... ....................................... 1977 ............................................................... Change: 1900 772 ........................................................ 1970 773 ........................................................ Inactive years (total population) Percent of lifespan active Ratio of female to male worklife expectancies Workers From birth From age 20 From birth From age 20 39.4 41.3 43.1 42.9 41.5 14.2 23.1 24.0 25.7 27.0 4.4 7.1 7.5 8.7 10.2 69.3 62.3 63.4 61.5 59.8 89.6 84.8 84.7 82.5 79.4 (') (') n (’) (’) 37.3 36.8 38.0 37.3 29.4 31.5 12.3 14.5 56.3 54.7 75.2 71.7 (’) 5.7 .1 -1.0 -.5 -2.1 -.7 17.3 2.1 10.1 2.2 -14.8 -1.7 -17.9 -3.5 n n 43.8 50.4 53.7 55.7 56.7 6.3 12.1 15.1 20.1 22.9 (4) 11.9 14.5 18.6 22.0 (4) (4) (4) 37.3 40.6 42.0 53.6 55.9 53.0 51.9 (4) 38.5 39.2 37.1 34.7 13.0 18.4 21 3 27.5 30.6 13.7 23.6 27 0 33.4 38.8 (4) 30.0 35.0 45.0 55.8 74.8 77.1 56.7 58.6 22.3 27.5 21.3 26.0 22.1 26.7 52.4 49.7 35.4 32.6 29.8 35.7 37.6 44.4 57.1 70.7 28.8 2.3 14.8 1.9 21.1 5.0 (3) 4.7 (3) 4.6 7.7 -2.7 (3) -2.8 22.5 5.6 30.7 6.8 (4) 13.6 At birth At age 20 At age 20 42.2 48.6 48.9 49.6 49.6 32.1 38.1 41.5 41.1 40.1 37.8 39.7 41.4 40.9 39.4 67.1 69.3 49.6 51.3 37.8 37.9 23.0 2.2 9.1 1.7 Conventional model: 1900 ................................................................ 1940 ................................................................ 1950 ........................................................ 1960 ................................................................ 1970 ................................................................ 48.3 65.7 71.0 73.1 74.8 Increment-decrement model: 1970 ................................................................ 1977 ................................................................ Change: 1900-772 ........................................................ 1970-773 ........................................................ At age 20 Men {') Women 'Not applicable. 2Based on conventional model estimates for 1900 and incrementdecrement model estimates for 1977. 3Based on the increment-decrement model. “Data not available, 14 percent for the average woman. By 1977 the figure for men had dropped to 72 percent, while that for women had risen to 44 percent. These figures do not take account of differences in hours worked, an important distinction. However, they do show that the relative roles of men and women shifted tremendously during this period. toward the end of this period. The average lifespan of women increased by 2.3 years between 1970 and 1977, yet their average duration of working life rose by 5.0 years. This was accomplished by the reallocation of time (nearly 3 years per woman) from home to market activities. It is estimated that in 1940 the worklife duration of women was just 30 percent that of men.6 By 1970 it was 57 percent, and by 1977 it had risen to 71 percent. At the turn of the century, the average 20-year-old man was likely to work during 90 percent of his remaining years, as against 6Tables o f Working Life: Length o f Working Life fo r Men, Bulletin 1001 (Bureau of Labor Statistics, 1950); Tables o f Working Life f o r Women, 1950, Bulletin 1204 (Bureau of Labor Statistics, 1957). 3 Chapter 2„ Kates ©f Labor Force Accession and! Separation men tended to complete their intermittent activity early in life. They were expected to remain 29.1 years per entry beyond the age of 25. By contrast, at 25, the expected duration per entry for women was just 8.6 years. The majority of all young people have had some labor force experience before the age of 20. In 1977, the median age of first labor force entry for men was 16.4 years, while that for women was 16.6 years. Taking all entries and reentries together, the average male entrant was 26.9 years of age. The average female entrant was slightly older, 28.7 years. An important function of a working life table is to quantify movements into and out of the labor force. In the past it has been assumed that men enter and leave the labor force only once during their lives, and that women do so only slightly more frequently in conjunction with changes in marital or parental status. The incrementdecrement model for the first time actually estimates the number of moves which take place. The conventional worklife model rested on crosssectional data from a single point in time. Differences in the labor force participation rates of successive age groups were taken as a measure of net movement into the job market (for young people) and into permanent retirement (for older workers). The increment-decrement model rests on longitudinal records of the labor force activities of specific individuals interviewed in the Current Population Survey (C P S ). A year-to-year match of these records quantifies move ments into and out of the job market, and the correspond ing transitional probabilities at each age. Following the flow of individuals between recognized states (e.g., in and out of the labor force), and discounting these flows for mortality at each age, the new model generates informa tion on the dynamics of lifetime movement between the job market and the outside world. Its results help to ex plain why the standard estimates of mobility have become increasingly unrealistic. These tables show that the average male child born in 1977 could expect to enter the laborforce 3.0 times and to withdraw from it. voluntarily 2.7 times in his lifetime (text table 4). The average female child was likely to make 4.5 such entries and 4.4 voluntary withdrawals. The timing of these entries would be more compressed for men than for women, occurring primarily below the age of 25. Thus, at 25, the average man was likely to reenter just 1.1 more times, as against an average of 2.7 additional entries for women. These figures represent a volume of mobility nearly three times that assumed for men, and well above that assumed for women in the conventional worklife procedure. The lifetime transition estimates were relatively stable between 1970 and 1977 (text table 5). So too were the expected durations in the labor force per entry, for men. The 1977 tables indicate that, over a lifetime, men aver aged 12.6 years of labor force attachment per entry. Women averaged less than half this figure, 6.1 years. But Text table 4. Average remaining laborforce entries and exits per person at specific ages, 1977 Exact age Labor force entries remaining Voluntary labor force exits remaining Men Women Men Women At b irth ............................... 1 6 ........................................ 2 0 ........................................ 2 5 ........................................ 3.0 2.6 1.8 1.1 4.5 4.3 3.4 2.7 2.7 2.7 2.2 1.7 4.4 4.4 3.9 3.2 3 0 ........................................ 3 5 ........................................ 4 0 ........................................ 4 5 ........................................ .9 .8 .7 .6 2.1 1.7 1.3 1.0 1.6 1.5 1.4 1.4 2.7 2.3 1.9 1.6 5 0 ........................................ 5 5 ........................................ 6 0 ........................................ 6 5 ........................................ 7 0 ........................................ .6 .5 .5 .4 .2 .7 .5 .3 .2 .1 1.3 1.2 1.1 .7 .3 1.3 1.0 .7 .4 .2 Grouping temporary and permanent exits, the average man leaving the labor force in 1977 was 38.7 years of age; the average woman, 33.9.7 Among persons leaving the labor force after the age of 50, the median age of exits for men was 63.4 years. Women tended to leave somewhat earlier—half of all their exits had taken place by age 60.6. Among male children born in 1977, it was expected that over one-quarter (27 percent) would die before retire ment. Only about 1 in 10 (9.5 percent) of all female chil dren was likely to die while economically active. The retirement age for both sexes appears to have dropped since 1970. This may help to explain the substantial de cline in proportions expected to die while active. 7These figures naturally reflect heavy volumes of movement at both ends of the age spectrum. They do not necessarily indicate heavy volume at midlife. 4 Text table 5. and 1977 four to five times as likely to leave the job market as was the average man. The character of net flows is best seen when both entries and exits are stated as a ratio to total population (text table 7). Consider the pattern of events over a lifetime, as measured in 1977. Although the accession and separation rates of teenage men and women are roughly comparable, the net effect is a greater influx of men into the labor force by age 20. Thereafter gross entries for both sexes decline. A compensating drop in separations for men holds net entries at a high level. A rise in separations for women slows the pace of their net labor force gains. Because a larger share of the female population is outside the job market with a likelihood of entry, their labor force acces sion rates exceed those of men throughout life. Net retirements peak between the ages of 60 and 64. For men, a substantial number of these exits are temporary. Beginning at age 60, their rates of labor force reentry increase, and above the age of 65 they exceed the corre sponding rates for women. The net population flows in text table 7 document a continuous expansion of the male labor force from age 16 to age 34 and a gradual contraction from age 35 onward. The net pattern for women is more complex: An expan sion of the labor force in the teens, a net contraction in the late 20’s, renewed expansion in the 30’s, and a final con traction beginning at about age 40. The outflow in the late 20’s is often dubbed the “fertility trough” because it coin cides with a period of family formation. However, the gross flows shown in text table 7 suggest that reading the net profile as a summary of normal female experiences may lead to misconceptions about their work patterns. The modest pace of net entries for teenage women con ceals very heavy movement into and out of the job market at this age. The “trough” at ages 25 to 29 suggests an increase in labor force withdrawals, when in fact separa tions actually decline at this age. The net outflow results from even sharper declines in labor force entries. The apparent resurgence of entries at age 30 occurs despite an actual drop in female accessions. It results from an even greater decline in the pace of withdrawals. The interpreta tion of net flows is greatly facilitated by an examination of these gross flows. The pace of net labor force entries for young people of both sexes appeared to have quickened between 1970 and 1977 (text table 8). Here, too, net patterns seemed to arise from somewhat contradictory gross trends. Only a small portion of the net increase in accessions can be traced to a rise in gross entries (text table 7). For men 20 to 34, and for most women above the age of 20, the pace of entries actually slowed during this period. In stead, the determining factor appears to have been a drop in gross labor force exits among persons 16 to 24. Their increased reluctance to leave the job market resulted in a more efficient expansion process. Much of the increase in labor force participation rates for persons in this age range could be traced to this decline in labor turnover. Selected indexes of working life by sex, 1970 Worklife measure Women Men 1970 1977 1970 1977 Median age at first labor force entry ........................................................ 16.5 16.4 16.8 16.6 Mean age of all first and repeat labor force entrants ............................... 26.6 26.9 29.2 28.7 Worklife expectancy (in years): At birth ................................................. At age 25 ............................................. 37.8 34.4 37.9 33.4 22.3 19.0 27.5 23.0 Number of labor force entries per: Person born ........................................ Person age 25 .................................... 2.9 1.2 3.0 1.1 4.6 2.8 4.5 2.7 Expected duration in labor force per entry remaining (in years): At birth ................................................. At age 25 ............................................. 13.0 29.4 12.6 29.1 4.8 6.8 6.1 8.6 Number of voluntary exits from labor force per: Person born ........................................ Person age 25 ..................................... 2.6 1.9 2.7 2.0 4.5 3.3 4.4 3.3 Percent of workers expected to die while in the labor force .................. 36.3 27.0 10.8 9.5 Mean age of all persons leaving the labor force: Total first and repeat exits ................ Voluntary withdrawals ........................ Deaths of workers ............................... 38.7 36.1 57.3 38.7 37.0 55.6 33.5 32.9 58.1 33.9 33.4 56.3 Median age of persons leaving labor force at age 50 and above ....................................................... 65.0 63.4 61.4 60.6 At the aggregate level, the new tables also document a much greater volume of movement into and out of the labor force thanlias been quantified in the past (text table 6). The conventional model used totally different pro cedures to estimate these flows for men than for women. As a result, there appeared to be tremendous disparities between the male and female patterns of labor force entry and withdrawal. It was difficult to determine how much of this disparity was real, and how much simply a function of differences in procedure. The increment-decrement model utilizes a single procedure for both sexes, elimina ting most of this method-related bias. A comparison of the two sets of estimates for 1970 illustrates how this change alters our perception of the relative rates of men and women. The earlier model im plied that about seven times as many men as women entered the labor force during the teenage years. In fact, the accession rates of teenage men and women are shown to be nearly identical. The old estimates showed no men entering the labor force beyond the age of 29. The new tables indicate that they continue to do so throughout their lives, increasing the pace of reentries after age 60. The new tables do confirm the previously held view that at most ages women have higher propensities to leave and reenter the labor force than do men. Between the ages of 25 and 44, they show that the typical working woman was 5 Text table 6. Rates of labor force mobility by age and sex, conventional model, 1970, and increment-decrement model, 1970 and 1977 Labor force entries per 1,000 persons in the stationary population Conventional model, Age group 16-19 20-24 25-29 30-34 35-39 40-44 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 45-49 50-54 55-59 60-64 65-69 70-74 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ Increment-decrement model 1970 1970 1977 Men Women Men Women Men Women 476.1 84.3 12.2 66.2 22.7 6.0 10.0 12.0 7.2 191.9 145.7 72.0 27.6 14.8 13.5 204.1 164.6 102.2 90.7 83.7 72.3 211.6 136.3 54.4 23.8 14.9 15.4 207.2 158.3 109.6 88.4 75.2 66.3 1.6 1.8 2.3 2.4 2.3 .6 14.6 14.5 18.8 32.2 38.2 36.7 60.3 49.7 43.3 38.9 29.4 16.0 16.4 17.1 19.1 30.8 44.5 35.7 57.9 46.8 37.4 32.0 27.8 16.1 — — — _ — — — — — Labor force separations per 1,000 persons in the stationary labor force1 Conventional model, Increment-decrement model 1970 Men 1970 1977 Women Men Women Men Women 16-19 20-24 25-29 30-34 35-39 40-44 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 1.7 2.3 2.0 2.5 4.4 6.7 24.5 42.5 18.4 11.0 4.8 3.7 299.0 160.6 47.1 20.5 20.6 24.3 455.7 321.0 231.2 206.3 162.6 132.7 254.7 125.0 42.7 24.3 18.5 22.9 290.5 226.3 182.9 134.7 112.8 105.3 45-49 50-54 55-59 60-64 65-69 70-74 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 11.0 17.2 32.9 103.3 170.7 166.4 15.0 33.1 61.8 165.9 193.2 234.8 27.6 35.3 58.7 137.5 264.2 343.1 121.9 115.4 131.5 200.8 308.9 402.8 30.5 42.1 74.6 209.7 376.2 441.9 107.7 110.8 136.2 251.9 369.7 388.7 1Separations include both voluntary withdrawals from the labor force and deaths of economically active persons. Text table 7. Population-based rates of labor force accession and separation by age and sex, 1970 and 1977 (Per 1,000 persons in the stationary population) Accessions Year and age group Separations Net flow Men Women Men Women Men Women 1970 16-19 20-24 25-29 30-34 35-39 40-44 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 191.9 145.7 72.0 27.6 14.8 13.5 204.1 164.6 102.2 90.7 83.7 72.3 125.0 104.0 39.6 19.6 19.9 23.0 149.8 150.1 109.8 91.7 76.5 67.6 66.8 41.7 32.4 8.0 -5.1 -9.5 54.3 14.5 -7.6 -1.1 7.2 4.7 45-49 50-54 55-59 60-64 65-69 70-74 ............................................ ............................................ ............................................ ............................................ .......................................... ............................................ 14.6 14.5 18.8 32.2 38.2 36.7 60.3 49.7 43.3 38.9 29.4 16.0 25.5 31.8 49.8 97.1 113.2 74.8 63.3 58.4 60.7 71.9 62.9 35.9 -11.0 -17.3 -31.1 -64.9 -75.1 -38.1 -2.9 -8.7 -17.4 -33.0 -33.4 -19.9 1977 16-19 20-24 25-29 30-34 35-39 40-44 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 211.6 136.3 54.4 23.8 14.9 15.5 207.2 158.3 109.6 88.4 75.2 66.3 124.3 93.9 38.6 23.0 17.6 21.6 127.9 142.0 116.0 84.1 73.5 69.0 87.3 42.5 15.8 .8 -2.7 -6.1 79.3 16.2 -6.5 4.3 1.7 -2.7 45-49 50-54 55-59 60-64 65-69 70-74 ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ 16.4 17.1 19.1 30.8 44.5 35.7 57.9 46.8 37.4 32.0 27.8 16.1 28.2 37.1 59.3 113.1 92.9 56.3 68.1 63.7 66.2 77.8 52.2 27.1 -11.8 -20.0 -40.2 -82.3 -48.4 -20.6 -10.2 -16.9 -28.8 -45.8 -24.4 -11.1 6 T®nfi tab!® 8. Net labor f@ree transfers by ag© and sen, conventional model, 1®?©, and 5mer@m®mt-©]®®r@m@n8 model, 1®7® and 1077 (Per 1,000 persons in the stationary population) Men Women Increment-decrement model Increment-decrement model 1970 1977 Conventional model, 1970 1970 1977 16-19 20-24 25-29 30-34 35-39 40-44 ............................................. ............................................. ............................................. ............................................. ............................................. ............................................. 475.0 82.3 10.3 -2.4 -4.2 -6.4 66.9 41.7 32.4 8.0 -5.1 -9.5 87.3 42.5 15.8 .8 -2.7 -6.1 58.9 3.7 -.5 6.1 10.1 5.5 48.1 10.0 -8.0 -1.1 7.2 4.7 79.3 16.2 -6.5 4.3 1.7 -2.7 45-49 50-54 55-59 60-64 65-69 70-74 ............................................. .............................................. ............................................. ............................................. ............................................. ............................................. -10.4 -15.9 -29.1 -76.3 -68.8 -39.8 -11.0 -17.3 -31.1 -64.9 -75.1 -38.1 -11.8 -20.0 -40.2 -82.3 -48.4 -20.6 -5.5 -13.4 -22.4 -46.0 -30.5 -21.7 -2.9 -8.7 -17.4 -33.0 -33.4 -19.9 -10.2 -16.9 -28.8 -45.8 -24.4 -11.1 Age group Conventional model, 1970 Hence entries also declined. Despite this drop in turnover, there was a modest increase in net outward flow of women workers age 45 to 54. Those 55 to 64 in 1977 showed stronger evidence of the intent to retire: Higher rates of labor force separation were coupled with diminished rates of reentry. (The result was a drop in worklife expectancies for women 60 and above.) At the same time, the withdrawal process for persons 45 to 64 also became more efficient. An increase in the labor force separations of men outweighed (but may also have brought about) a modest increase in labor force entries at this age. Women exhibited a stronger labor force attach ment at all ages, 16 through 54. The slowdown of their separations at younger ages diminished the size of the labor reserve from which to draw older female entrants. 7 Chapter 3. Increment-Decrement Table® ©f Working Life facilitate hand calculation. One such assumption, defin ing individual labor force attachments as continuous from age of entry to age of final retirement, overlooks short-term movements into and out of the job market. As we shift our attention to questions of labor force dynam ics, this assumption masks much of the movement ana lysts would like to quantify. In contrast, the increment-decrement model explicitly focuses on labor force mobility. The key statistic under lying these tables is the transition probability, drawn from observed patterns of labor force entry and exit at each age. There are no assumptions about normal work pat terns. Instead, the model is used to estimate these norms. The increment-decrement technique is less convenient to implement than was its predecessor. It involves a much more complex model format, one which necessitates the Increment-decrement working life tables are a power ful extension of conventional worklife methodology.8 They overcome many of the limitations of the conven tional model which stem from its convenient but simplis tic design. Although the conventional model rests on a set of readily accessible data—cross-sectional rates of labor force participation—these data are not really appropriate to the study of labor force mobility. Inferring flows from stocks of workers at each age can lead to misconceptions about current labor force behavior. Furthermore, the original model was designed in the era of the desk calcula tor. Several simplifying assumptions were introduced to 8Many of the terms and functions o f the new models are direct analogs of others found in the original technique. Readers unfamiliar with the earlier model will find the discussion in appendix B helpful in understanding this chapter. 8 estimation problem to one of first entries (in the age range of net entries) and final withdrawals (in the age range of net exits). (See figure 2.) They did so at the cost of certain unrealistic assumptions about individual labor force attachments. By failing to discount for turnover and periods of midlife inactivity, their model exaggerated indi vidual worklife durations. The increment-decrement model, made feasible by the computer, provides a more complete accounting framework in which credits and debits can be appropriately recorded. use of a computer. Moreover, the detailed longitudinal data on which it rests are not universally available. How ever, its findings are relatively free of model distortion and are credible and realistic. They are easier to under stand and to explain and are more revealing of the under lying process of labor force attachment than were values based solely on labor force participation rates. The increment-decrement working life table is one variation of what is known as the “multistate life table.” A number of other forms in use today measure such phe nomena as patterns of marital and residential change. In any multistate life table, members of the stationary popu lation are assumed to move back and forth among life statuses according to prevailing age-specific probabilities of transition, until the last members finally enter the absorbing state of death. Life statuses are defined in a variety of ways, including but not limited to marital, labor force, and residential categories. The simplest multistate model describes three options for the individual passing through a given age interval: He/she may remain in the same life status throughout, may change status, or may die. Figure 1 shows that, even with a single decision point per year, this construct quick ly generates a tremendous number of potential paths. The developers of the original model avoided tracing most of these flows by disregarding temporary midlife labor force withdrawals and reentries. They reduced the Literature 00 ineremont-dleeremerit modeling The use of three-state disability tables in Europe pre dates World War I. However, social scientists first turned their attention to multistate modeling in the 1970’s. Andrei Rogers of the International Institute for Applied Systems Analysis in Laxenburg, Austria, was one of the first to exploit this technique. He expanded the basic life table to describe a multiregional system in which both migration and mortality patterns differed by location. Working alone and with Frans Willekens and others, he developed a number of interesting applications of the model, both in marital and labor force studies (see Bibliography, entries 27-36). In a second research program at the University of Copenhagen, Jan Hoem and Monica Fong explored the relationship between multistate models and the theory of 9 stochastic processes. Their Markov Chain Model o f Work ing Life Tables for the Danish labor force is an important contribution to the literature on multistate theory(15,16). Another advocate of multistate models has been Rob ert Schoen of the University of Illinois. Working with Land and Nelson, he has developed an increment-decre ment table of marital status change (39, 40). Working alone and with Karen Woodrow, he has also developed increment-decrement tables of working life for the United States for 1972 (37, 41). Willekens recently reestimated the Danish tables using his own simplified multiregional program. His program has been published both as a four-state marital status life table and as a two-state worklife model (51). Extensions of this analysis to social mobility and migration studies as well as further extensions of the marital tables have also been released (53, 54). Other important contributions to the literature include Krishnamoorthy (20), and Ledent ( 21, 22). The fact that multistate models are applied to so many areas of study attests to their versatility. So long as the “states” in question represent alternatives among which members of the population may move, their specific character is unimportant. In some tables all movement is toward an absorbing life status (e.g., moves from “single” to “ever-married”) while in others it is multidirectional (e.g., among geographic areas). All models include the ultimate absorbing state of death. fied. Hence, although the model could accommodate different mortality schedules for those in and out of the labor force, the two groups are assumed to face identical risks of death. Text tabs© 9. Total Total .................. a d g / b c e / h i k 1 Status of respondents age x + /, time 2 In labor force ....... Not in labor force . In labor force Not in labor force Dead The labor force flows shown as items d through ihave been drawn from the records of individuals responding to the Current Population Survey (CPS) for January 1977 and again in January 1978. Their matched responses give a direct picture of year-to-year changes in labor force status. The totals in column 1 represent the sum of the remaining three columns. There is a slight discrepancy between the age reference of survey data and that used in an actuarial model. Per sons interviewed in a survey are on average a half-year older than their stated (integer) age. Thus the survey documents flows during the interval between ages x + .5 and x + 1.5. Values have been adjusted slightly to center them on the period between birthdays, ages x to x + 1. The resulting matrix represents numbers of persons who change (or fail to change) status during a given year of life. Percentage distributions across the rows of this matrix yield the corresponding transition probabilities. In their increment-decrement tables of working life for 1972, Schoen and Woodrow used data from a single Cur rent Population Survey to compute transition probabili ties (41). Their source was the January 1973 CPS, which included retrospective information on persons who were employed at the time of the interview. This survey gave an incomplete picture; several cells in the transition matrix had to be pieced together from external sources. The total sample for January 1973 provided information for cells d, m, p, and g of text table 10. Ow©rei©w off tSi© model In the conventional worklife model, a comparison of numbers active at the beginning and end of an age yields a net estimate of movement into or out of the job market during that interval. The increment-decrement model reverses this inference process. Instead, probabilities of movement during the interval are used to determine the number economically active at the beginning of the next age. The key variable, a schedule of transition probabilities, is developed from longitudinal records of labor force behavior. For this study, the data have been obtained by matching records of persons interviewed at the beginning and end of calendar year 1977. Alternatively, they can be drawn from a single retrospective survey, taken at the end of the interval in question. (This approach will be dis cussed further below.) Because the tables deal with ageto-age changes, the survey interval of preference is 1 year. The working life tables for 1977 are the simplest form of a multistate model, including just two life states—in and out of the labor force. In order to compute such tables, it is necessary to obtain all of the information shown in text table 9 for every age group. Surveys seldom ' provide the mortality information needed for cells j, k, and l of this matrix. Instead, we must use vital statistics for the period to estimate the share of respondents lost through death. Differentials in mortality by labor force status have never been successfully quanti Matrix of transitions over a 1-year intoreal Status of respondents age x, time 1 Text table 10. Matrix of transitions used by Schoen and Woodrow to compute 1972 working life tables Status of persons age x, January 1973 Status of persons age jt- 1, January 1972 In labor force Total Not in labor Dead Total Employed Unemployed force T o ta l....... ... a d m P g i In labor force .. Not in labor fo rce............. b e n 9 h k c f o r i l The proportions in and out of the labor force 1 year be fore (cells b and c) were obtained from the January 1972 CPS. One-year flows for the employed (cells n and o) were estimated from retrospective data. The same column distribution was inferred for the total and unemployed 10 When men are first observed in the tables at exact age 16 (table 1, columns 11 through 13), there are 97,598 survivors of the original birth cohort, of which 27,059 are members of the labor force and 70,539 are economically inactive. Columns 2 through 9 of the table show the basic transition probabilities and transfer rates used to survive this cohort forward through life. The transition probabili ties indicate the proportion of those in a given state (i.e., economically inactive or active) at age x who will be found in each of three states (i.e., dead, inactive, or active) one year later. Because every member of the cohort takes one of these routes, the sum of the probabilities is unity. For instance, among men inactive at age 16 (columns 2 through 4): groups (cells e and /, and q and r). Mortality estimates (k and /) were derived from vital statistics, leaving cells h and i as residual values. The final 1972 worklife tables rested on the same 12 cells of information shown in text table 9 (items a through /) once again centered on ex act age intervals. Whatever the source, the transition matrix provides the driving force for increment-decrement modeling. It de scribes the flow of persons from state 1 at exact age x to state 2 at exact age x +1. Snapshots of the beginning and end of the year necessarily overlook many of the changes which occur during that period. For a more complete count of events, numbers of persons changing status must be translated into numbers of transitions occurring. This has been accomplished using the procedure outlined by Schoen and Land (39). The resulting transfer rates de scribe the full volume of movement between various cells of text table 9 during the specific age in question. The increment-decrement working life table follows a cohort of individuals through its life cycle, exposing members of that population to the risks of movement observed for each successive age. It summarizes the num ber of labor force entries and exits which would occur, the average timing of these events, and the length of time beyond any given age which would be spent in labor force activities—if prevailing rates did not change. There are few critical assumptions to this life table technique. The most important (and vulnerable) of these is the Markovian assumption: ASSUME: 1. That for any individual the probability of transition depends solely on his or her current status, sex, and exact age. It is independent of previous statuses. That is, worklife estimates do not attempt to reflect the impact of cumulative experience. A second assumption follows the life table convention of holding rates at their observed levels over the fore seeable future: ASSUME: 2. That age-specific transfer rates (i.e., of entry into and withdrawal from the la bor force and of death) are constant, at levels observed in the reference popula tion during the reference year. The model summarizes the lifetime implications of pre vailing rates. It does not attempt to project future rates. ■nd _ in’ + ina p \6 + P \6 - 1.000 p \6 .703 + .296 + .001 = 1.000 where: l 2 p - the probability that a person in life status 1 at exX • act age x would be in life status 2 at exact age x +1 i =economically inactive (i.e., not in the labor force) a - economically active • = living d =dead, and x = any given age. At certain ages, the likelihood of changing status dur ing the year is relatively high. When persons do so repeat edly within a 1-year interval, all but the last of their tran sitions is lost in year-to-year comparisons. In such cases, the real rate of transfer per thousand persons noticeably exceeds the corresponding transition probability. Trans fer rates are derived from transition probabilities using the relationship discussed by Schoen and Land (39). The rate of labor force accession or entry for me; age 16, shown in column 8, is computed as: Worklife <aKp@et®ney of the geoeraS population The model is best illustrated by the tables themselves. Tables 1 through 4, which follow this chapter, summarize male worklife experiences; tables 5 through 8 summarize female worklife behavior. In each case the tables display the lifetime mortality and labor force experiences of a stationary population into which 100,000 persons of the given sex are born each year. They spell out how this population would behave if it were exposed to the agespecific risks of death, labor force entry, and exit prevail ing for that sex in the United States in 1977. 1 a 16 nrnr16 = (> + (1 + (2) < '< ) < % ) where: lma16 =the rate of transfer of persons from the inactive to the active state during age 16. The rate of labor force withdrawal is derived by trans11 posing superscripts in the numerator and in the mx term. The high volume of turnover for men age 16 is reflected in the disparity between this group’s accession rate (.411) and its corresponding transition probability (.296). Given the mortality rates of 1977, 127 of the survivors to age 16 would die before their 17th birthday (column 18). If risks of death were equal for those in and out of the labor force, 83 of these deaths would occur among in actives, 44 among labor force members. The prevailing rates of transfer in and out of the labor force would result in 26,194 entries and 12,422 exits during the 16th year of life, for a net inward flow of 13,722. These events are summarized in text table 11. The summary values for exact age 17 form the starting point for estimates of change during the next age interval. The same set of calculations is repeated for each successive year of age. 75 + 'T X‘ - ageE= x K (5) where: T ] =remaining person years to be lived in labor force status 1 beyond exact age x, for all persons irre spective of labor force status at age x. Remaining years in each status are averaged over persons who will contribute to the cohort’s future worklife, i.e,, survivors to exact age x. Continuing our example, the average man age 16 in 1977 had a worklife expectancy of: Text tabs© 11. Changes In the sis© and composition of the cohort of men between exact ages 16 and 17 Item Survivors Inactive Active Total at exact age 16 ...................... Deaths during interval.................... Labor force accessions .................. Labor force separations ................ Total at exact age 17 ...................... 97,598 -127 70,539 -83 -26,194 +12,422 56,684 27,059 -44 +26,194 -12,422 40,787 97,471 ’e ‘e i 16 38.52 years (6) 1,604,555 ~ 97,598 16.44 years (7) outside the labor market. The results of this estimation procedure for men in 1977 are displayed in table 3, col umns 2 through 4. Work!!?© @2tpectanci©s off persons m and ®uH ®f the [labor f@re© Often in liability hearings the court applies worklife expectancies to the case of real individuals. Because cur rent and future activities are often positively related, information on labor force behavior at the time of injury or death can have a bearing on estimated worktime lost. The conventional model indicates that—at any given age—the worklife expectancy of persons in the labor force is greater than that of the general population. However, because it does not isolate expectancies for persons out side the labor force, it is difficult to apply conventional findings to cases in which the plaintiff has been economi cally inactive. By contrast, the categories of display in the increment-decrement model are exhaustive, allowing a clear definition of the active/inactive differential. Recall that, in the discussion of average worklife ex pectancies for the population, there were three steps to the calculation. These were 1) tracing a specific cohort of individuals (i.e., 100,000 persons of the same sex born at the same time) through a lifetime of labor force entries where: L a - person years of activity lived by the group passing through age x, regardless of their labor force status at the beginning of the interval, and • - persons living in all statuses (active and inactive). Estimates of person years spent in and out of the labor force during each interval are shown in columns 20 through 25 of table 1. These summarize the experience of the entire stationary population, and can be translated into average work and nonwork expectancies in the usual manner. That is, the L*and functions are cumulated from the end of the table backward to the beginning so that, for any age: 3,759,317 and could expect to spend ai16 + % 27,059 + 40,787 ---------------= ----------------------- = 33,923 (3) °Ta = X 16 97,598 This establishes the size of the stationary labor force at each exact age, a\x (shown in column 13). In the conven tional manner this function is translated into person years of activity lived by the group passing through that inter-, val, L^. For men age 16: L a16 a 75 + V 'La X age = x 12 and exits, (2) estimating how many person years this group would spend in the labor force at and beyond each age, and (3) for any given age, computing the ratio of work years remaining to persons at risk of working them (i.e., cohort members surviving to the beginning of that age). The same process can be repeated for smaller cohorts who share not only a common sex and birth date, but also a common labor force status at age x. For instance, the worklife expectancy of a man in the labor force at age 27 can be differentiated from that of another who is inactive at the same age. To accomplish this, every age/ sex/labor force status group must be modeled as a separate cohort. The increment-decrement tables repeat the entire process for each of two sexes, two initial labor force classifica tions, and 60 age (or birth cohort) groups. To develop the estimates shown in columns 5 through 10 of table 3, the basic process is.repeated 240 times. Although there is no need to display every such calculation, table 2 illustrates how status-specific estimates are derived for one such age cohort. Consider the example of men age 16. In order to dis tinguish the worklife expectancies of those in the labor force from those of persons who were not, the two groups must be treated as separate entry cohorts. According to table 1 (columns 12 and 13), at exact age 16 the 1977 stationary population included 70,539 inactive men and another 27,059 who were members of the labor force. These figures serve as the initial cohort counts of table 2 (columns 2 and 5). ' Figure 3 illustrates how cohorts are aged forward in the increment-decrement tables. Given the transition prob abilities for 16-year-olds in table 1, 70.3 percent of the inactive group will remain so classified at exact age 17, 29.6 percent will have become active, and 0.1 percent will have died before that birthday. Thus the “inactive to inactive” stream will include 49,559 men; the “inactive to active” stream, 20,889. A parallel computation for those active at 16, using the probabilities in columns 5 and 6 of table 1, is also performed. The path taken over the next age interval is a function of each person’s sex, age, and labor force status at 17. Among those inactive at 17, 73.2 percent will remain so at 18, 26.7 percent will be in the labor force by that age, and about 0.2 percent will have died. The same transition probabilities apply, regardless of status at age 16. The tables do not take account of cumulative labor force experience. There are two reasons for disregarding cumulative experience. In the first place, the number of “experience paths” increases geometrically with age. Following each stream separately would mean tracing 1,080 different paths to arrive at a single worklife expectancy for men active at 16, another 1,080 for men inactive at 16, 1,062 streams each for those active and inactive at 17, and so on. The cost and time involved would be prohibitive. A 13 who survive to a given age, as a function of their behavior at that time. second and more fundamental reason is that we do not know and cannot feasibly determine the probabilities for each of these experience-specific streams. Lacking this information, there is no choice but to employ the Markov assumption stated earlier. This assumption permits us to regroup survivors by status at each successive age, identifying them only by initial cohort and labor force status at the current age. Table 2 gives a numerical illustration. Columns 2 through 4 are a “snapshot” of the cohort of men who were inactive at exact age 16, seen at each subsequent birthday. Col umns 5 through 7 are a parallel series for those who were active at exact age 16. Persons in each labor force status at the precise age are used to estimate “person years lived” in that status during the age interval. These values are cumu lated backward from the end of the table in the usual manner (columns 15 to 20). The worklife expectancy of men active at age 16 is then simply the ratio of work years remaining to that group, over initial members. There are four status-specific expectancies for each age, computed as follows: Estimates of accession and separation rates The formula for estimating accession and separation rates by single year of age has already been introduced (equation 2). When multiplied by the stationary popula tion counts, 'l x and a\x , these rates produce estimates of the number of transfers in and out of the model labor force within each age interval (table 1, columns 14 and 15). The corresponding mortality rate is used to estimate deaths within the active and inactive model populations (columns 16 and 17). The numbers of transfers are denoted 't*X atl, atd, and x % h “ for accessions, separations, deaths of actives, and deaths of inactives, respectively. These values are used to determine expected labor force entries and exits beyond a given age, the mean and median age of movements, and related indexes (text table 5). They are also used to estab lish the labor force mobility rates of various age groups. Several variants of the labor force accession and sepa ration rates are shown for 5-year age groups 4n table 4. The first set (columns 2 through 5) are population-based rates. Entry rates are conventionally stated in this form. The entry rate is computed as: j # ( 8) x+5 / M ax 5 (9) age = x :v x ( 12) 5 where: ( 10) *Az=the population-based labor force entry rate for v persons age x to x + 5 ( 11) .L - the number of persons in the stationary popula tion who are alive in the age interval x to x + 5. In order to determine the net flow of workers into or out of the job market, withdrawal rates must also be ex pressed as a ratio to population. (This is not the usual base for published separation rates.) The population-based rate of voluntary labor force exit ( j Mx ) and of separa tions including death ( parallel the entry rate: where: 1 2 e - the expectation of life in category 2 for persons in x category 1 at exact age x 1 T 2x ~ person years of life remaining to be lived in cate gory 2 by persons in category 1 at exact age x x + 5 7 = persons alive and in category 1 at exact age x. E a 5 Together these four indexes (equations 8-11) spell out the work- and non-work-life expectancies of all persons 14 age - x ( 13) x + 5 E afyf(i, d) = age - ( V + x GO at d ) x x E age = x (14) The rate of net movement for persons within the age range # to x + 5 (^ ‘AT’ ) is then simply a residual: ‘5 M ax - a5M(i,d) 5 ( 16) Expected separations are computed in a similar manner (column 11). The number of deaths occurring to members of the stationary labor force at each successive age (atx) is dis played in table 1. The age distribution of these deaths is used to derive the mean age at which workers are likely to die (text table 5). It is also used to estimate the proportion of all persons likely to die before retirement. This index is simply the ratio of deaths of workers at and beyond age x to persons alive at that exact age. In like manner, the age profile of labor force entries and exits is used to determine the mean and median ages of such occurrences. The median age of first labor force entry is drawn from a separate Markov chain describing unidirectional flows. In this chain, survivors pass from “never active” to “ever active”, on the assumption that' first and subsequent entries are governed by the same transition probabilities. The age profile of transfers pin points the age at which half would have established their first labor force contact. The increment-decrement model sheds new light on the whole process of labor force attachment and turnover. Many of the new indexes discussed in this study are the outgrowth of gross flow estimates, which were not avail able in conventional tables. As chapter 2 illustrates, their availability may change the conclusions we draw from net mobility patterns. (15) This first set of rates describes the likelihood of an event occurring to the typical individual within a specific age group, during a single year. A slightly different perspective appears in columns 6 and 7 of the table, where events are related to persons alive at the beginning of the age interval. These rates address the likelihood of an event affecting a person as he or she passes through the entire age range. The rates in columns 8 and 9 are more focused, express ing events as a ratio to population “at risk”. Entries are related to persons outside the labor force at the corre sponding age, an unconventional but meaningful index. Separations are expressed in their normal form, as a ratio to persons who are economically active. Other measures of labor force mobility In addition to these rates, the increment-decrement table quantifies several other dimensions of labor force mobility. For instance, the average number of labor force entries likely to occur beyond a given age x (column 10) is computed as: a x 15 life fo r men, 1977: Derivation o f flh© ©npeefation @f aetiv® life fo r the general population Probability of transition between specified states during age interval x to x+1 Living to dead Inactive to inactive . d P i i pX X Inactive to active i Active to inactive Active to active 'i pX a a pX a a pX Age-specific rates of transfer per 1,000 persons in initial status during age interval x to x+1 Mortality . d m X Labor force accession i a m X Voluntary labor force separation a i m X (2) (3) (4) (5) (6) (8) (9) 0.00130 .00152 .00168 .00179 0.70257 .73158 .68082 .63115 0.29613 .26690 .31750 .36706 0.26333 .06377 .07157 .07734 0.73537 .83471 .82675 .82087 1.30 1.52 1.68 1.79 411.77 340.73 421.10 505.42 366.17 209.08 227.55 244.18 23 24 25 26 27 28 29 .00190 .00200 .00207 .00208 .00205 .00201 .00197 .00193 .00190 .00188 .60351 .59326 .59247 .58035 .56979 .56253 .56219 .56209 .56534 .58105 .39459 .40474 .40546 .41757 .42816 .43546' .43584 .43598 .43276 .41707 .03862 .01331 .09116 .07084 .05506 .04323 .03490 .02942 .02571 .02382 .85948 .88469 .90677 .92708 .94289 .95476 .96313 .96865 .97239 .97430 1.90 2.00 2.07 2.08 2.05 2.01 1.97 1.93 1.90 1.88 539.24 547.50 540.69 553.83 565.92 573.81 571.30 569.47 562.70 536.15 189.43 153.27 121.57 93.96 72.77 56.97 45.75 38.43 33.43 30.62 30 31 32 33 34 35 36 37 38 39 .00186 .00186 .00189 .00197 .00208 .00222 .00239 .00257 .00277 .00300 .59900 .61817 .65287 .67166 .68396 .70656 .73058 .75729 .75239 .75525 .39914 .37997 .34524 .32637 .31396 .29122 .26703 .24014 .24484 .24175 .02088 .01914 .01785 .01702 .01583 .01452 .01397 .01352 .01286 .01367 .97726 .97900 .98026 .98101 .98209 .98326 .98364 .98391 .98437 .98333 1.86 1.86 1.89 1.97 2.08 2.22 2.39 2.57 2.77 3.00 506.32 475.70 422.70 394.88 376.82 344.61 311.49 275.79 281.89 278.04 26.49 23.97 21.85 20.59 18.99 17.18 16.30 15.53 14.81 15.72 40 41 42 4344 45 46 47 48 49 .00325 .00355 .00388 .00425 .00467 .00512 .00562 .00618 .00681 .00751 .75589 .75147 .75617 .76275 .76568 .77441 .78118 .80524 .81482 .82414 .24086 .24498 .23995 .23300 .22965 .22047 .21320 .18858 .17837 .16835 .01518 .01606 .01603 .01698 .01821 .01879 .01930 .02150 .02383 .02452 .98157 .98039 .98009 .97877 .97712 .97609 .97508 .97232 .96936 .96797 3.26 3.56 3.89 4.26 4.68 5.13 5.64 6.20 6.83 7.54 277.19 282.83 276.31 267.50 263.46 251.81 242.70 212.09 199.87 187.80 17.46 18.54 18.46 19.49 20.88 21.46 21.97 24.18 26.70 27.36 50 51 52 53 54 55 56 57 58 59 .00828 .00910 .00995 .01081 .01171 .01263 .01366 .01491 .01647 .01826 .83035 .83867 .85595 .87234 .88380 .88826 .89527 .89801 .90035 .91071 .16137 .15223 .13410 .11685 .10449 .09911 , .09107 .08708 .08318 .07103 .02590 .02764 .02856 .03049 .03378 .03807 .04152 .04936 .06484 .08345 .96582 .96326 .96149 .95870 .95451 .94930 .94482 .93573 .91869 .89829 8.31 9.14 10.00 10.87 11.78 12.71 13.75 15.02 16.61 18.43 179.60 168.88 147.50 127.58 113.62 107.82 98.93 94.92 91.38 78.46 28.82 30.66 31.41 33.28 36.73 41.42 45.10 53.80 71.24 92.18 60 61 62 63 64 65 66 67 68 69 .02026 .02231 .02429 .02611 .02783 .02958 .03154 .03388 .03675 .04013 .91865 .91958 .91755 .91666 .91727 .91484 .91715 .91926 .91874 .91945 .06109 .05811 .05816 .05723 .05490 .05558 .05131 .04686 .04451 .04042 .11228 .14231 .16971 .19580 .22547 .25680 .27466 .28195 .29215 .29252 .86746 .83538 .80600 .77809 .74670 .71362 .69380 .68417 .67110 .66735 20.47 22.56 24.59 26.46 28.22 30.02 32.05 34.46 37.44 40.95 68.33 66.12 67.36 67.39 65.82 68.05 63.48 58.23 55.75 50.71 125.59 161.95 196.58 230.57 270.31 314.42 339.80 350.35 365.94 366.96 .04377 .04761 .05184 .05649 .06156 .06703 .91996 .91783 .91535 .91348 .91254 .89659 .03627 .03456 .03281 .03003 .02590 .03622 .29690 .30124 .30748 .31581 .31562 .32675 .65933 .65115 .64068 .62770 .62282 44.75 48.77 53.22 58.13 63.51 69.35 45.69 43.80 41.90 38.68 33.47 47.75 374.03 381.78 392.65 406.84 407.85 430.75 18 19 20 21 22 i, see appendix C. 16 .6 0 6 0 6 (7) Table 1. Continued—Table of working life for men, 1977: Derivation of the expectation of active life for the general population Stationary population living in each status at exact age x, per 100,000 persons born Number of status transfers within stationary population during age interval x to x+1 Labor force entries Labor force status Age Total Inactive a i I X I X i I a t X X a i t X Deaths Of actives d a Of inactives d i X . d t t t Total X X (11) (12) (13) (14) (15) 16 17 18 19 97,598 97,471 97,323 97,159 70,539 56,684 48,149 41,217 27,059 40,787 49,174 55,942 26,194 17,860 18,816 19,497 12,422 9,405 11,960 14,284 44 68 88 105 83 80 75 69 127 148 164 174 20 21 22 23 24 25 26 27 28 29 96,985 96,801 96,607 96,407 96,207 96,010 95,817 95,628 95,444 95,263 35,935 30,150 25,439 21,560 17,815 14,466 11,663 9,494 7,871 6,701 61,050 66,651 71,168 74,847 78,392 81,544 84,154 86,134 87,573 88,562 17,817 15,217 12,706 10,903 9,134 7,497 6,044 4,945 4,100 3,406 12,095 10,562 8,875 7,199 5,819 4,720 3,896 3,338 2,944 2,720 121 138 151 160 164 167 168 168 167 167 63 56 49 41 33 26 21 17 14 12 184 194 200 200 197 193 189 184 181 179 30 31 32 33 34 35 36 37 38 39 95,084 94,907 94,730 94,551 94,365 94,168 93,958 93,734 93,493 93,034 6,003 5,456 5,085 4,920 4,829 4,720 4,634 4,634 4,714 4,679 89,081 89,451 89,645 89,631 89,536 89,448 89,324 89,100 88,779 88,355 2,901 2,507 2,115 1,925 1,799 1,612 1,443 1,289 1,325 1,312 2,364 2,146 1,959 1,844 1,700 1,536 1,454 1,381 1,313 1,390 166 167 170 177 186 199 213 229 246 266 11 10 9 10 10 10 11 12 13 14 177 177 179 186 197 210 224 241 259 279 40 41 42 43 44 45 46 47 48 49 92,955 92,653 92,324 91,966 91,575 91,147 90,680 90,170 89,613 89,002 4,752 4,930 5,114 5,265 5,488 5,769 6,072 6,376 6,936 7,622 88,203 87,723 87,210 86,701 86,087 85,378 84,608 83,794 82,677 81,380 1,342 1,420 1,434 1,438 1,483 1,491 1,510 1,412 1,455 1,493 1,536 1,622 1,605 1,684 1,790 1,824 1,850 2,012 2,190 2,208 286 311 338 368 401 436 474 516 560 608 16 18 20 23 26 30 35 41 50 60 302 329 358 391 428 467 510 557 611 668 50 51 52 53 54 55 56 57 58 59 88,334 87,603 86,805 85,941 85,012 84,016 82,954 81,821 80,601 79,274 8,277 8,946 9,677 10,486 11,447 12,602 13,913 15,322 17,042 19,465 80,057 78,657 77,128 75,455 73,565 71,414 69,041 66,499 63,559 59,809 1,547 1,573 1,487 1,399 1,366 1,429 1,446 1,535 1,667 1,654 2,287 2,389 2,397 2,480 2,663 2,908 3,056 3,497 4,393 5,295 660 712 763 810 854 892 932 977 1,024 1,058 72 85 101 119 142 168 201 243 303 389 731 798 864 929 996 1,062 1,133 1,220 1,327 1,448 60 61 62 63 64 65 66 67 68 69 77,826 76,250 74,549 72,738 70,839 68,867 66,830 64,722 62,530 60,232 22,718 27,057 31,882 36,494 40,550 44,024 46,655 48,331 49,050 49,003 55,108 49,193 42,667 36,244 30,289 24,843 20,175 16,391 13,480 11,229 1,700 1,948 2,302 2,595 2,783 3,083 3,013 2,834 2,732 2,466 6,548 7,437 7,754 7,669 7,450 7,073 6,209 5,230 4,518 3,796 1,067 1,036 970 880 778 675 586 514 462 424 509 665 840 1,019 1,193 1,361 1,521 1,677 1,834 1,992 1,576 1,701 1,811 1,899 1,972 2,037 2,108 2,192 2,298 2,417 70 71 72 73 74 75 57,815 55,284 52,652 49,923 47,103 44,203 48,340 47,284 45,809 44,035 42,085 39,988 9,475 8,000 6,843 5,888 5,018 4,215 2,181 2,035 1,879 1,662 1,371 1,841 3,263 2,828 2,495 2,214 1,879 1,767 390 361 338 316 293 284 2,136 2,266 2,386 2,498 2,601 2,673 2,531 2,632 2,729 2,820 2,900 2,963 (10) NOTE: X Active Voluntary labor force exits For explanation of notation, see appendix C. 17 (16) (17) (18) Table 1. C o n tin u e d -T a b le of working life for men, 1977: Derivation of the expectation of active ■Bsf© for the general population Age X Total Inactive L . i L X Active a L X X Person years lived in each status beyond exact age x Total Inactive T T Active a i X T X X (20) (21) (22) (23) (24) (25) 16 17 18 19 97,536 97,398 97,242 97,073 63,613 52,417 44,684 38,576 33,923 44,981 52,558 58,497 5,363,872 5,266,336 5,168,938 5,071,696 1,604,555 1,540,942 1,488,525 1,443,841 3,759,317 3,725,394 3,680,413 3,627,855 20 21 22 23 24 25 26 27 28 29 96,892 96,704 96,506 96,307 96,108 95,913 95,723 95,536 95,353 95,173 33,042 27,794 23,499 19,687 16,140 13,065 10,579 8,683 7,286 6,352 63,850 68,910 73,007 76,620 79,968 82,848 85,144 86,853 88,067 88,821 4,974,623 4,877,731 4,781,027 4,684,521 4,588,214 4,492,106 4,396,193 4,300,470 4,204,934 4,109,581 1,405,265 1,372,223 1,344,429 1,320,930 1,301,243 1,285,103 1,272,038 1,261,459 1,252,777 1,245,491 3,569,358 3,505,508 3,436,598 3,363,591 3,286,971 3,207,003 3,124,155 3,039,011 2,952,157 2,864,090 30 31 32 33 34 35 36 37 38 39 95,002 94,824 94,647 94,464 94,272 94,065 93,849 93,616 93,366 93,097 5,730 5,271 5,003 4,875 4,775 4,677 4,634 4,674 4,701 4,720 89,272 89,553 89,644 89,589 89,497 89,388 89,215 88,942 88,665 88,377 4,014,408 3,919,406 3,824,582 3,729,935 3,635,471 3,541,199 3,447,134 3,353,285 3,259,669 3,166,303 1,239,138 1,233,408 1,228,138 1,223,135 1,218,260 1,213,485 1,208,808 1,204,174 1,199,500 1,194,799 2,775,270 2,685,998 2,596,444 2,506,800 2,417,211 2,327,714 2,238,326 2,149,111 2,060,169 1,971,504 40 41 42 43 44 45 46 47 48 49 92,801 92,486 92,142 91,768 91,358 90,904 90,415 89,882 89,298 88,658 4,841 5,022 5,189 5,376 5,628 5,920 6,224 6,655 7,278 7,949 87,960 87,464 86,953 86,392 85,730 84,984 84,191 83,227 82,020 80,709 3,073,206 2,980,405 2,887,919 2,795,777 2,704,009 2,612,651 2,521,747 2,431,332 2,341,450 2,252,152 1,190,078 1,185,238 1,180,216 1,175,027 1,169,651 1,164,023 1,158,103 1,151,879 1,145,224 1,137,946 1,883,128 1,795,167 1,707,703 1,620,750 1,534,358 1,448,628 1,363,644 1,279,453 1,196,226 1,114,206 50 51 52 53 54 55 56 57 58 59 87,976 87,212 86,380 85,484 84,522 83,459 82,361 81,185 79,911 78,523 8,612 9,312 10,082 10,968 12,026 13,253 14,613 16,177 18,247 21,084 79,364 77,900 76,298 74,516 72,496 70,206 67,748 65,008 61,664 57,439 2,163,494 2,075,518 1,988,306 1,901,926 1,816,442 1,731,920 1,648,461 1,566,100 1,484,915 1,405,004 1,129,997 1,121,385 1,112,072 1,101,990 1,091,023 1,078,997 1,065,744 1,051,131 1,034,954 1,016,707 1,033,497 954,133 876,234 799,936 725,419 652,923 582,717 514,969 449,961 388,297 60 61 62 63 64 65 66 67 68 69 77,024 75,386 73,625 71,775 69,839 67,811 65,740 63,589 61,344 58,986 24,883 29,465 34,180 38,515 42,278 45,314 47,467 48,662 48,997 48,640 52,141 45,921 39,445 33,260 27,561 22,497 18,273 14,927 12,347 10,346 1,326,481 1,249,457 1,174,071 1,100,446 1,028,671 958,832 891,021 825,281 761,692 700,348 995,623 970,740 941,275 907,096 868,581 826,303 780,988 733,521 684,859 635,862 330,858 278,717 232,796 193,350 160,090 132,529 110,033 91,760 76,833 64,486 70 71 72 73 74 75 56,454 53,873 51,192 48,417 45,557 42,644 47,731 46,464 44,838 42,975 40,950 38,542 8,723 7,409 6,354 5,442 4,607 4,102 641,362 584,908 531,035 479,843 431,426 385,869 587,222 539,491 493,026 448,188 405,213 364,262 54,140 45,417 38,009 31,655 26,213 21,607 (19) NOTE: Person years lived in each status during age x hor explanation of notation, see appendix C. 18 Tabs© 2. TabS® of working lit® for men, 1977: Sam ple derivation of w orkiife expectan cies by labor fore© status for persons currently age 18 Survivors to exact age x by labor force status at age 16 and at age x Persons inactive at 16 Age X (1) NOTE: Total at x Inactive at x i,16 . I i,16 i ! X X (2) (3) Active at x i,16 a I Person years lived by cohort members in each status during age interval x to x+1 Persons inactive at age 16 Persons active at 16 Total at x Inactive at x a,16 . I a,16 i I X X X (4) (5) (6) Active at x Total at x Inactive at x i,16 . L i,16 i L X X X (7) (8) (9) a,16 a I Active at x i,16 a L X Persons active at 16 Total at x Inactive at x a,16 . L a,16 i L X X (10) (11) (12) Active at x a,16 a L X (13) 16 17 18 19 70,539 70,448 70,341 70,222 70,539 49,559 39,678 32,274 0 20,889 30,663 37,948 27,059 27,023 26,982 26,937 0 7,125 8,472 8,944 27,059 19,898 18,511 17,993 70,494 70,394 70,281 70,160 60,046 44,618 35,974 29,686 10,448 25,778 34,307 40,474 27,041 27,003 26,960 26,913 3,564 7,799 8,708 8,890 23,477 19,204 18,252 18,023 20 21 22 23 24 25 26 27 28 29 70,097 69,964 69,824 69,679 69,534 69,392 69,252 69,116 68,982 68,851 27,099 22,315 18,638 15,708 12,940 10,489 8,447 6,871 5,694 4,846 42,997 47,649 51,186 53,971 56,594 58,903 60,805 62,245 63,289 64,006 26,889 26,838 26,784 26,729 26,673 26,618 26,565 26,512 26,461 26,411 8,836 7,835 6,801 5,851 4,875 3,978 3,216 2,623 2,177 1,855 18,053 19,003 19,983 20,877 21,798 22,641 23,348 23,889 24,284 24,556 70,030 69,893 69,751 69,607 69,463 69,322 69,184 69,049 68,917 68,787 24,706 20,475 17,172 14,324 11,714 9,467 7,659 6,282 5,270 4,593 45,324 49,418 52,579 55,283 57,749 59,855 61,525 62,767 63,647 64,194 26,863 26,811 26,756 26,701 26,646 26,592 26,539 26,487 26,436 26,386 8,335 7,318 6,326 5,363 4,426 3,597 2,920 2,400 2,016 1,759 18,528 19,493 20,430 21,338 22,220 22,995 23,619 24,087 24,420 24,627 30 31 32 33 34 35 36 37 38 39 68,722 68,594 68,466 68,337 68,202 68,061 67,909 67,747 67,573 67,386 4,340 3,944 3,676 3,556 3,491 3,412 3,349 3,349 3,407 3,389 64,382 64,650 84,791 64,781 64,712 64,649 64,560 64,398 64,166 63,997 26,361 26,312 26,263 26,214 26,162 26,108 26,050 25,987 25,921 25,849 1,663 1,512 1,409 1,364 1,339 1,308 1,285 1,285 1,307 1,300 24,698 24,801 24,854 24,850 24,823 24,799 24,765 24,703 24,614 24,549 68,658 68,530 68,402 68,270 68,131 67,985 67,829 67,660 67,479 67,285 4,142 3,810 3,616 3,523 3,451 3,380 3,349 3,378 3,528 3,281 64,516 64,720 64,786 64,746 64,680 64,604 64,479 64,282 63,951 64,004 26,337 26,288 26,239 26,188 26,135 26,079 26,019 25,954 25,885 25,810 1,587 1,461 1,386 1,351 1,324 1,297 1,285 1,296 1,353 1,259 24,749 24,827 24,852 24,837 24,811 24,782 24,734 24,658 24,531 24,551 40 41 42 43 44 45 46 47 48 49 67,184 66,965 66,728 66,469 66,186 65,877 65,540 65,172 64,769 64,328 3,434 3,563 3,696 3,805 3,966 4,170 4,389 4,609 5,013 5,509 63,749 63,402 63,032 62,664 62,220 61,708 61,151 60,563 59,756 58,819 25,771 25,688 25,596 25,497 25,389 25,270 25,141 24,999 24,845 24,676 1,317 1,367 1,418 1,460 1,521 1,599 1,683 1,768 1,923 2,113 24,454 24,321 24,179 24,037 23,867 23,671 23,457 23,232 22,922 22,563 67,075 66,846 66,598 66,327 66,032 65,708 65,356 64,970 64,548 64,086 3,499 3,630 3,751 3,886 4,068 4,279 4,499 4,811 5,262 5,746 63,576 63,217 62,848 62,442 61,963 61,429 60,857 60,159 59,286 58,340 25,729 25,642 25,547 25,443 25,329 25,205 25,070 24,922 24,760 24,583 1,342 1,392 1,439 1,491 1,561 1,642 1,726 1,846 2,018 2,204 24,387 24,250 24,108 23,952 23,769 23,564 23,344 23,077 22,742 22,379 50 51 52 53 54 55 56 57 58 59 83,845 63,316 62,740 62,116 61,444 60,725 59,958 59,139 58,257 57,297 5,982 6,466 6,994 7,579 8,274 9,108 10,056 11,075 12,317 14,069 57,862 56,850 55,746 54,537 53,170 51,616 49,902 48,064 45,939 43,229 24,490 24,288 24,067 23,827 23,570 23,294 22,999 22,685 22,347 21,979 2,295 2,480 2,683 2,907 3,174 3,494 3,857 4,248 4,725 5,397 22,196 21,807 21,384 20,920 20,396 19,800 19,142 18,437 17,622 16,582 63,580 63,028 62,428 61,780 61,084 60,341 59,548 58,698 57,777 56,774 6,225 6,731 7,288 7,928 8,693 9,585 10,568 11,700 13,198 15,252 57,355 56,296 55,140 53,852 52,391 50,756 48,980 46,998 44,579 41,523 24,389 24,177 23,947 23,698 23,432 23,146 22,842 22,516 22,163 21,778 2,388 2,582 2,796 3,041 3,335 3,677 4,054 4,488 5,063 5,850 22,001 21,595 21,151 20,657 20,097 19,470 18,788 18,028 17,100 15,928 60 61 62 63 64 65 66 67 68 69 56,251 55,111 53,882 52,573 51,200 49,776 48,303 46,780 45,195 43,534 16,420 19,556 23,044 26,377 29,308 31,820 33,721 34,932 35,452 35,418 39,831 35,555 30,838 26,196 21,892 17,956 14,582 11,847 9,743 8,116 21,578 21,140 20,669 20,167 19,640 19,094 18,529 17,944 17,336 16,699 6,299 7,502 8,839 118 1,242 2,206 2,935 3,400 3,599 3,586 15,279 13,639 11,829 10,049 8,398 6,888 5,594 4,545 3,737 3,113 55,682 54,497 53,227 51,887 50,488 49,039 47,541 45,988 44,364 42,660 17,998 21,312 24,723 27,855 30,575 32,779 34,333 35,196 35,436 35,177 37,683 33,185 28,505 24,032 19,913 16,260 13,208 10,791 3,928 7,483 21,359 20,905 20,418 19,904 19,367 18,811 18,237 17,641 17,018 16,364 6,904 8,175 9,484 685 1,728 2,574 3,170 3,501 3,593 3,494 14,455 12,730 10,934 9,219 7,639 6,237 5,067 4,139 3,425 2,870 70 71 72 73 74 75 41,787 39,958 38,055 36,083 34,044 31,949 34,939 34,176 33,109 31,827 30,418 28,902 6,848 5,782 4,946 4,255 3,627 3,047 16,029 15,328 14,598 13,841 13,059 12,255 3,402 3,110 2,701 2,209 2,627 2,218 1,897 1,632 1,391 1,168 40,872 39,007 37,069 35,064 32,996 30,878 34,555 33,638 32,462 31,114 29,650 27,892 6,318 5,369 4,607 3,949 3,347 2,985 15,678 14,963 14,220 13,450 12,657 11,845 3,255 2,903 2,452 1,935 1,373 699 2,423 2,060 1,767 1,515 1,284 1,145 1 ,6 6 8 1,087 For explanation of notation, see appendix C. 19 Table 2. C o ntinu ed — 'Tab!© ©If working life for men, 1977: Sam ple derivation of worksite expectancies by labor force status for persons currently age 16 Years remaining to be lived in each status By persons inactive at exact age 16 Age Inactive years i,16 . T i,16 i T X X Active years i,16 a T X Total years Inactive years a,16 . T a,16 i T X X Active years a,16 a T X (15) (16) (17) (18) (19) (20) 16 17 18 19 3,876,765 3,806,272 3,735,877 3,665,596 1,187,483 1,127,437 1,082,821 1,046,846 2,689,282 2,678,835 2,653,057 2,618,750 1,487,107 1,460,066 1,433,063 1,406,103 416,924 413,360 405,561 396,854 1,070,183 1,046,706 1,027,502 1,009,250 20 21 22 23 24 25 26 27 28 29 3,595,436 3,525,406 3,455,513 3,385,761 3,316,154 3,246,691 3,177,369 3,108,185 3,039,136 2,970,219 1,017,161 992,455 971,980 954,807 940,484 928,770 919,303 911,644 905,362 900,093 2,578,276 2,532,951 2,483,533 2,430,954 2,375,671 2,317,921 2,258,067 2,196,541 2,133,774 2,070,127 1,379,191 1,352,327 1,325,517 1,298,760 1,272,059 1,245,414 1,218,822 1,192,284 1,165,797 1,139,361 387,964 379,629 372,311 365,985 360,623 356,197 352,600 349,680 347,280 345,264 991,226 972,698 953,205 932,775 911,437 889,217 866,223 842,604 818,517 794,097 30 31 32 33 34 35 36 37 38 39 2,901,433 2,832,775 2,764,245 2,695,843 2,627,573 2,559,442 2,491,457 2,423,629 2,355,969 2,288,489 895,500 891,357 887,548 883,932 880,408 876,957 873,577 870,227 866,849 863,321 2,005,933 1,941,417 1,876,697 1,811,911 1,747,165 1,682,485 1,617,880 1,553,401 1,489,119 1,425,168 1,112,974 1,086,638 1,060,350 1,034,111 1,007,923 981,789 955,710 929,691 903,737 877,852 343,505 341,917 340,457 339,070 337,719 336,396 335,099 333,814 332,519 331,165 769,470 744,720 719,893 695,041 670,204 645,393 620,611 595,877 571,219 546,687 40 41 42 43 44 45 46 47 48 49 2,221,204 2,154,130 2,087,283 2,020,685 1,954,357 1,888,326 1,822,617 1,757,262 1,692,292 1,627,744 860,040 856,541 852,911 849,160 845,274 841,206 836,927 832,428 827,616 822,355 1,361,164 1,297,589 1,234,372 1,171,525 1,109,083 1,047,120 985,691 924,834 864,675 805,389 852,042 826,313 800,671 775,124 749,681 724,352 699,147 674,077 649,154 624,394 329,907 328,565 327,172 325,733 324,243 322,682 321,041 319,315 317,469 315,451 522,136 497,748 473,499 449,391 425,439 401,670 378,106 354,762 331,685 308,943 50 51 52 53 54 55 56 57 58 59 1,563,657 1,500,077 1,437,049 1,374,622 1,312,842 1,251,758 1,191,417 1,131,869 1,073,171 1,015,394 816,608 810,383 803,652 796,364 788,436 779,743 770,158 759,590 747,891 734,692 747,049 689,694 633,397 578,258 524,406 472,015 421,259 372,279 325,281 280,702 599,811 575,422 551,245 527,298 503,599 480,168 457,021 434,179 411,663 389,500 313,247 310,859 308,277 305,481 302,440 299,105 295,429 291,375 286,887 281,824 286,564 264,563 242,968 221,817 201,159 181,063 161,593 142,804 124,776 107,676 60 61 62 63 64 65 66 67 68 69 958,620 902,938 848,442 795,214 743,328 692,840 643,800 596,259 550,271 505,907 719,441 701,442 680,130 655,408 627,553 596,978 564,199 529,866 494,669 459,233 239,179 201,496 168,311 139,807 115,774 95,861 79,601 66,393 55,602 46,674 367,722 346,362 325,458 305,040 285,137 265,770 246,958 228,722 211,081 194,063 275,974 269,070 260,895 251,411 240,726 228,998 216,424 203,254 189,753 176,159 91,748 77,293 64,563 53,629 44,410 36,772 30,535 25,468 21,329 17,904 70 71 72 73 74 75 463,247 422,375 383,368 346,299 311,235 278,239 424,056 389,501 355,863 323,402 292,287 262,638 39,191 32,873 27,505 22,897 18,948 15,601 177,699 162,021 147,058 132,838 119,388 106,731 162,666 149,411 136,507 124,055 112,120 100,747 15,034 12,610 10.551 8,783 7,268 5,984 (14) NOTE: Total years By persons active at exact age 16 For explanation of notation, see appendix C. 20 Table 3. Table of working life for men, 1977: Expectation of active life by current labor force status Age Total years Inactive years . X NOTE: e Total years Active years a i e Expectancies of persons active at age x Expectancies of persons inactive at age x Expectancies of the total population i . e e Inactive years i i e Active years a i e Total years Inactive years a a e i e X Active years a a e X X X X X X X X (1) (2) (3) (4) (5) (6) (7) (8) 0) (10) 16 17 18 19 55.0 54.0 53.1 52.2 16.4 15.8 15.3 14.9 38.5 38.2 37.8 37.3 55.0 54.0 53.1 52.2 16.8 16.5 16.0 15.6 38.1 37.5 37.1 36.6 55.0 54.0 53.1 52.2 15.4 14.9 14.6 14.3 39.6 39.2 38.5 37.9 20 21 22 23 24 25 26 27 28 29 51.3 50.4 49.5 48.6 47.7 46.8 45.9 45.0 44.1 43.1 14.5 14.2 13.9 13.7 13.5 13.4 13.3 13.2 13.1 13.1 36.8 36.2 35.6 34.9 34.2 33.4 32.6 31.8 30.9 30.1 51.3 50.4 49.5 48.6 47.7 46.8 45.9 45.0 44.1 43.1 15.4 15.2 15.0 14.9 14.8 14.8 14.8 14.8 14.8 14.9 35.9 35.2 34.4 33.7 32.9 32.0 31.1 30.2 29.3 28.2 51.3 50.4 49.5 48.6 47.7 46.8 45.9 45.0 44.1 43.1 14.0 13.7 13.5 13.3 13.2 13.1 13.1 13.0 13.0 12.9 37.3 36.7 36.0 35.2 34.5 33.7 32.8 32.0 31.1 30.2 30 31 32 33 34 35 36 37 38 39 42.2 41.3 40.4 39.4 38.5 37.6 36.7 35.8 34.9 34.0 13.0 13.0 13.0 12.9 12.9 12.9 12.9 12.8 12.8 12.8 29.2 28.3 27.4 26.5 25.6 24.7 23.8 22.9 22.0 21.2 42.2 41.3 40.4 39.4 38.5 37.6 36.7 35.8 34.9 34.0 15.0 15.2 15.4 15.5 15.7 15.9 16.0 16.1 16.1 16.2 27.2 26.1 25.0 23.9 22.8 21.7 20.7 19.7 18.8 17.8 42.2 41.3 40.4 39.4 38.5 37.6 36.7 35.8 34.9 34.0 12.9 12.9 12.8 12.8 12.8 12.7 12.7 12.7 12.7 12.7 29.3 28.4 27.5 26.7 25.8 24.9 24.0 23.1 22.2 21.3 40 41 42 43 44 45 46 47 48 49 33.1 32.2 31.3 30.4 29.5 28.7 27.8 27.0 26.1 25.3 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 20.3 19.4 18.5 17.6 16.8 15.9 15.0 14.2 13.3 12.5 33.1 32.2 31.3 30.4 29.5 28.7 27.8 27.0 26.1 25.3 16.2 16.2 16.3 16.4 16.6 16.7 16.9 17.1 17.2 17.3 16.9 16.0 15.0 14.0 13.0 11.9 10.9 9.9 8.9 8.0 33.1 32.2 31.3 30.4 29.5 28.7 27.8 27.0 26.1 25.3 12.6 12.6 12.6 12.6 12.5 12.5 12.5 12.4 12.4 12.4 20.4 19.6 18.7 17.8 17.0 16.2 15.3 14.5 13.7 12.9 50 51 52 53 54 55 56 57 58 59 24.5 23.7 22.9 22.1 21.4 20.6 19.9 19.1 18.4 17.7 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 11.7 10.9 10.1 9.3 8.5 7.8 7.0 6.3 5.6 4.9 24.5 23.7 22.9 22.1 21.4 20.6 19.9 19.1 18.4 17.7 17.3 17.4 17.4 17.4 17.2 17.0 16.7 16.4 16.0 15.6 7.2 6.3 5.5 4.8 4.2 3.6 3.2 2.8 2.4 2.1 24.5 23.7 22.9 22.1 21.4 20.6 19.9 19.1 18.4 17.7 12.3 12.3 12.2 12.2 12.2 12.1 12.1 12.0 12.0 11.9 12.2 11.4 10.7 9.9 9.2 8.5 7.8 7.1 6.4 5.8 60 61 62 63 64 65 66 67 68 69 17.0 16.4 15.7 15.1 14.5 13.9 13.3 12.8 12.2 11.6 12.8 12.7 12.6 12.5 12.3 12.0 11.7 11.3 11.0 10.6 4.3 3.7 3.1 2.7 2.3 1.9 1.6 1.4 1.2 1.1 17.0 16.4 15.7 15.1 14.5 13.9 13.3 12.8 12.2 . 11.6 15.2 14.7 14.2 13.8 13.3 12.8 12.3 11.9 11.4 10.9 1.9 1.7 1.5 1.4 1.2 1.1 1.0 .9 .8 .7 17.0 16.4 15.7 15.1 14.5 13.9 13.3 12.8 12.2 11.6 11.8 11.6 11.4 11.2 10.9 10.5 10.1 9.7 9.3 8.9 5.2 4.7 4.3 4.0 3.6 3.4 3.2 3.0 2.9 2.7 70 71 72 73 74 75 11.1 10.6 10.1 9.6 9.2 8.7 10.2 9.8 9.4 9.0 8.6 8.2 .9 .8 .7 .6 .6 .5 11.1 10.6 10.1 9.6 9.2 8.7 10.5 10.0 9.6 9.2 8.7 8.3 .6 .6 .5 .5 .4 .4 11.1 10.6 10.1 9.6 9.2 8.7 8.5 8.1 7.8 7.6 7.5 7.5 2.6 2.4 2.2 2.0 1.7 1.2 For explanation of notation, see appendix C. 21 Table 4. Table of working life for men, 1977: Indexes of labor force accession and separation Annual population-based rates of labor force mobility Events per person at risk during interval Events per person alive at exact age x Events remaining per person entering interval Age Accessions i x to x+ 4 (D 16-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75+ NOTE: a Total separations a M 5 x (2 ) 0.2116 .1363 .0544 .0238 .0149 .0155 .0164 .0171 .0191 .0308 .0445 .0357 .0432 Voluntary separations (i,d ) a x 5 i M 5 • M x (4) (3) 0.1243 .0939 .0386 .0230 .0176 .0216 .0282 .0371 .0593 .1131 .0929 .0563 .1420 Net moves 0.1235 .0923 .0369 .0 2 1 2 .0151 .0179 .0225 .0283 .0472 .1003 .0845 .0496 .1353 5 (..cD M Accessions ( 'lx ,i) -.0402 -.0823 -.0484 -.0205 -.0988 0.8439 .6782 .2707 .1183 .0741 .0766 .0807 .0835 .0920 .1456 .2052 .1579 .0416 For explanation of notation, see appendix C. x (6) (5) -.0 2 0 0 fix ,a ) 22 (i,d ) Accessions per inactive person i M M 5 x 0.0873 .0425 .0158 .0008 -.0027 -.0061 -.0118 a Total separations 5 x (7) 0.4957 .4669 .1922 .1144 .0874 .1070 .1391 .1813 .2860 .5344 .4282 .2487 .1370 a Total separations per active person a m 5 x (8) 0.4133 .5474 .5654 .4384 .2983 .2731 .2163 .1446 .0927 .0669 .0591 .0409 .0478 (i,d ) m 5 Accessions i a E Voluntary separations a i E x X X O) (10) (11) 2.6473 1.8148 1.1481 .8859 .7751 .7101 .6461 .5834 .5256 .4680 .3644 .1897 .0416 2.6552 2.1764 1.7345 1.5661 1.4750 1.4181 1.3559 1.2849 1.2055 1.0554 .6574 .3191 .1306 0.2547 .1250 .0427 .0243 .0185 .0229 .0305 .0421 .0746 .2097 .3762 .4419 1.4762 TalbO® 5. T®b>S@ ®f w orking Bit® for wom en, 1977: Derivation of th® expectation of active life for !h® ganaraB population Age-specific rates of transfer during age interval x to x + 1 per 1,000 persons in initial status Probability of transition between specified states, a g e x t o a g e x -t- i Age Living to dead . d P X (D i i p X (3) Inactive to active i Active to inactive a a pX i pX (5) (4) Active to active a Mortality a pX (6) d m Labor force accession i a (7) a i m m X Voluntary labor force separation X X (8) (9 ) 16 17 18 19 0.00053 .00059 .00062 .00063 0.73236 .75581 .71538 .67869 0.26711 .24360 .28400 .32068 0.30562 .17867 .19546 .21170 0.69385 .82074 .80392 .78767 0.53 .59 .62 .63 374.54 309.00 373.81 437.33 428.54 226.64 257.27 288.70 20 21 22 23 24 25 26 27 28 29 .00064 .00065 .00066 .00066 .00067 .00068 .00069 .00071 .00073 .00076 .66272 .66480 .67447 .69094 .70834 .72338 .74021 .76015 .77631 .78934 .33664 .33455 .32487 .30840 .29099 .27594 .25910. .23914 .22296 .20990 .19141 .17455 .16531 .16111 .16039 .15667 .15198 .14597 .14114 .13622 .80795 .82480 .83403 .83823 .83894 .84265 .84733 .85332 .85813 .86302 .64 .65 .66 .66 .67 .68 .69 .71 .73 .76 457.75 449.13 430.68 403.31 376.09 352.38 326.39 296.41 272.80 254.04 260.28 234.33 219.16 210.70 207.29 200.06 191.45 180.92 172.70 164.87 30 31 32 33 34 35 36 37 38 39 .00080 .00084 .00089 .00095 .00103 .00111 .00121 .00132 .00146 .00162 .79668 .80077 .79942 .80139 .80447 .80776 .81138 .81302 .81589 .82036 .20252 .19839 .19969 .19766 .19450 .19113 .18741 .18566 .18265 .17802 .12935 .12011 .11070 .10508 .09908 .09690 .09746 .09655 .09475 .09266 .86985 .87905 .88841 .89397 .89989 .90199 .90133 .90213 .90379 .90572 .80 .84 .89 .95 1.03 1.11 1.21 1.32 1.46 1.62 243.02 236.19 236.60 233.15 228.22 223.56 218.83 216.47 212.40 206.24 155.22 142.99 131.17 123.95 116.26 113.34 113.80 112.57 110.19 107.36 40 41 42 43 44. 45 46 47 48 49 .00180 .00199 .00219 .00240 .00263 .00287 .00314 .00343 .00375 .00409 .82135 .82523 .82888 .83601 .84272 .84581 .85081 .85729 .86181 .87281 .17685 .17278 .16893 .16159 .15465 .15132 .14605 .13928 .13444 .12310 .09144 .09075 .08934 .08883 .08795 .09038 .09107 .09144 .09320 .09353 .90676 .90726 .90847 .90877 .90942 .90675 .90579 .90513 .90305 .90238 1.80 1.99 2.19 2.40 2.63 2.87 3.14 3.44 3.76 4.10 204.65 199.43 194.44 185.20 176.49 172.65 166.26 158.02 152.31 138.65 105.81 104.75 102.82 101.81 100.37 103.13 103.67 103.74 105.59 105.35 50 51 52 53 54 55 56 57 58 59 .00446 .00486 .00528 .00570 .00614 .00659 .00710 .00771 .00847 .00934 .88348 .89035 .89458 .90099 .90811 .91553 .92168 .92796 .93094 .93496 .11206 .10479 .10014 .09331 .08575 .07788 .07122 .06433 .06059 .05570 .09416 .09449 .09534 .09523 .09472 .09756 .10308 .11402 .12784 .14252 .90138 .90065 .89938 .89907 .89914 .89585 .88982 .87827 .86369 .84814 4.47 4.87 5.29 5.72 6.16 6.61 7.13 7.74 8.51 9.38 125.54 116.99 111.61 103.64 94.87 85.96 78.61 71.20 67.49 62.44 105.48 105.49 106.26 105.78 104.78 107.68 113.77 126.20 142.41 159.77 60 61 62 63 64 65 69 .01033 .01135 .01228 .01304 .01373 .01443 .01532 .01650 .01807 .02001 .93936 .94498 .94921 .95159 .95223 .95367 .95469 .95654 .95792 .95890 .05031 .04367 .03851 .03537 .03404 .03190 .02999 .02696 .02401 .02109 .16694 .18998 .21580 .23774 .25932 .27737 .29003 .29913 .30155 .29901 .82273 .79867 .77192 .74922 .72695 .70820 .69465 .68437 .68038 .68098 10.38 11.41 12.36 13.13 13.82 14.53 15.44 16.64 18.23 20.21 57.07 50.05 44.70 41.55 40.49 38.34 36.31 32.80 29.25 25.67 189.35 217.74 250.53 279.26 308.48 333.34 351.14 363.96 367.42 363.92 70 71 72 73 74 75 .02209 .02433 .02701 .03023 .03392 .03798 .95875 .95840 .95825 .95920 .95764 .95900 .01916 .01727 .01474 .01057 .00844 .00299 .30904 .31371 .30212 .27706 .25970 .37001 .66887 .66196 .67087 .69271 .70638 .59199 22.34 24.63 27.38 30.69 34.51 38.72 23.49 21.26 18.04 12.76 10.11 3.84 378.85 386.18 369.84 334.47 311.18 474.73 66 67 68 NOTE: (2) Inactive to inactive For explanation of notation, see appendix C. 23 Table 5. Continued—Table of working life for women, 1977: Derivation of the expectation of active life for the general population Stationary population living in each status at exact age x, per 100,000 persons born Number of status transfers within stationary population during age interval x to x+1 Labor force entries Labor force status Age Total Inactive a i I X I X a i t I X X a i t X Deaths Of actives a d t X Of inactives Total d d i t t X X (11) (12) (13) (14) (15) (16) 16 17 18 19 98,210 98,158 98,100 98,039 73,943 61,569 53,072 46,768 24,267 36,589 45,028 51,271 25,378 17,712 18,661 19,541 13,040 9,249 12,388 15,396 16 24 30 34 36 34 31 28 52 58 61 62 20 21 22 23 24 25 26 27 28 29 97,977 97,915 97,851 97,787 97,722 97,656 97,589 97,521 97,452 97,381 42,595 38,829 36,127 34,571 34,071 34,342 34,761 35,279 35,903 36,559 55,382 59,086 61,724 63,216 63,651 63,314 62,828 62,242 61,549 60,822 18,636 16,833 15,224 13,842 12,865 12,176 11,431 10,550 9,884 9,362 14,897 14,155 13,691 13,365 13,160 12,618 11,972 11,199 10,567 9,973 37 39 41 42 43 43 43 44 45 46 26 24 23 23 23 24 24 25 26 28 62 64 64 65 30 31 32 33 34 35 36 37 38 39 97,307 97,230 97,148 97,061 96,969 96,869 96,761 96,644 96,516 96,375 37,143 37,374 37,117 36,318 35,487 34,640 34,011 33,712 33,484 33,292 60,164 59,856 60,031 60,743 61,482 62,229 62,750 62,932 63,032 63,083 9,055 8,797 8,687 8,371 8,002 7,674 7,410 7,273 7,092 6,852 9,315 8,571 7,921 7,575 7,191 7,083 7,151 7,090 6,948 6,771 48 50 54 58 64 69 76 83 92 102 30 31 33 34 36 38 41 44 49 54 77 82 87 92 40 41 42 43 44 45 46 47 48 49 96,219 96,046 95,855 95,645 95,416 95,165 94,892 94,594 94,269 93,916 33,157 33,000 32,954 32,934 33,104 33,378 33,816 34,333 34,944 35,644 63,062 63,046 62,901 62,711 62,312 61,787 61,076 60,261 59,325 58,272 6,769 6,576 6,405 6,115 5,866 5,800 5,665 5,473 5,375 5,005 6,671 6,596 6,458 6,364 6,228 6,335 6,289 6,203 6,208 6,070 114 125 138 150 163 177 191 205 221 236 60 66 72 79 97 107 119 133 148 229 251 273 298 325 353 384 50 51 52 53 54 55 56 57 58 59 93,532 93,115 92,662 92,176 91,648 91,085 90,484 89,842 89,149 88,394 36,561 37,665 38,775 39,826 40,867 41,921 43,176 44,672 46,604 48,824 56,971 55,450 53,887 52,350 50,781 49,164 47,308 45,170 42,545 39,570 4,659 4,471 4,386 4,181 3,927 3,657 3,452 3,249 3,220 3,125 5,929 5,767 5,644 5,454 5,236 5,193 5,259 5,534 5,846 6,058 251 266 281 295 308 319 329 339 349 356 166 186 208 231 255 281 313 353 406 470 417 453 489 525 563 601 642 693 755 826 60 61 62 63 64 65 66 67 68 69 87,568 86,663 85,679 84,627 83,523 82,377 81,188 79,944 78,625 77,204 51,288 54,234 57,411 60,595 63,375 65,573 67,195 68,209 68,755 68,838 36,280 32,429 28,268 24,032 20,148 16,804 13,993 11,735 9,870 8,366 3,012 2,795 2,638 2,576 2,611 2,545 2,459 2,247 2,013 1,763 6,507 6,610 6,553 6,170 5,701 5,134 4,518 3,932 3,351 2,824 357 347 323 290 255 224 199 180 166 157 548 637 729 814 892 965 1,045 1,140 1,255 1,388 905 984 1,052 1,104 1,146 1,189 1,244 1,319 1,421 1,544 70 71 72 73 74 75 75,660 73,989 72,189 70,239 68,116 65,805 68,511 67,895 66,982 65,759 64,317 62,579 7,149 6,094 5,207 4,480 3,799 3,226 1,601 1,432 1,196 829 641 237 2,507 2,180 1,790 1,383 1,092 1,263 148 139 133 127 121 103 1,522 1,660 1,816 1,995 2,187 2,395 1,671 1,800 1,950 2,123 2,311 2,499 (10) NOTE: X Active Voluntary labor force exits For explanation of notation, see appendix C. 24 (17) 88 (18) 66 67 68 69 71 74 100 108 117 128 141 156 173 191 210 TabS® 5. Continued— Table of working life for women, 1977: Derivation of tb© expectation of active life for the general population Age X Total Inactive Active L . i L L Person years lived in each status beyond exact age x Total Inactive Active T . i T T a X X X a X X X (20) (21) (22) (23) (24) (25) 16 17 18 19 98,185 98,130 98,070 98,008 67,757 57,321 49,920 44,681 30,428 40,809 48,150 53,327 6,133,675 6,035,490 5,937,360 5,839,290 3,411,047 3,343,290 3,285,969 3,236,049 2,722,628 2,692,200 2,651,391 2,603,241 20 21 22 23 24 25 26 27 28 29 97,947 97,884 97,820 97,755 97,690 97,625 97,557 97,489 97,419 97,346 40,712 37,479 35,349 34,321 34,207 34,553 35,021 35,592 36,232 36,852 57,235 60,405 62,471 63,434 63,483 63,072 62,536 61,897 61,187 60,494 5,741,282 5,643,335 5,545,451 5,447,631 5,349,876 5,252,186 5,154,561 5,057,004 4,959,515 4,862,096 3,191,367 3,150,655 3,113,176 3,077,827 3,043,506 3,009,299 2,974,746 2,939,725 2,904,134 2,867,902 2,549,915 2,492,680 2,432,275 2,369,804 2,306,370 2,242,887 2,179,815 2,117,279 2,055,381 1,994,194 30 31 32 33 34 35 36 37 38 39 97,271 97,191 97,107 97,018 96,921 96,813 96,701 96,578 96,444 96,295 37,259 37,246 36,718 35,904 35,064 34,325 33,861 33,597 33,388 33,224 60,012 59,945 60,389 61,114 61,857 62,488 62,840 62,981 63,056 63,071 4,764,750 4,667,479 4,570,288 4,473,181 4,376,163 4,279,242 4,182,429 4,085,728 3,989,150 3,892,706 2,831,050 2,793,791 2,756,545 2,719,827 2,683,924 2,648,859 2,614,534 2,580,673 2,547,076 2,513,688 1,933,700 1,873,688 1,813,743 1,753,354 1,692,239 1,630,383 1,567,895 1,505,055 1,442,074 1,379,018 40 41 42 43 44 45 46 47 48 49 96,128 95,945 95,746 95,526 95,285 95,021 94,736 94,424 94,085 93,717 33,077 32,975 32,943 33,018 33,239 33,594 34,072 34,636 35,291 36,100 63,051 62,970 62,803 62,508 62,046 61,427 60,664 59,788 58,794 57,617 3,796,411 3,700,283 3,604,338 3,508,592 3,413,066 3,317,781 3,222,760 3,128,024 3,033,600 2,939,515 2,480,465 2,447,388 2,414,413 2,381,470 2,348,453 2,315,214 2,281,619 2,247,547 2,212,911 2,177,620 1,315,946 1,252,895 1,189,925 1,127,122 1,064,613 1,002,567 941,141 880,477 820,689 761,895 50 51 52 53 54 55 56 57 58 59 93,320 92,885 92,414 91,907 91,363 90,764 90,143 89,475 88,752 87,960 37,112 38,218 39,298 40,344 41,393 42,539 43,914 45,627 47,703 50,044 56,208 54,667 53,116 51,563 49,970 48,225 46,229 43,848 41,049 37,916 2,845,798 2,752,478 2,659,593 2,567,179 2,475,272 2,383,909 2,293,145 2,203,002 2,113,527 2,024,775 2,141,520 2,104,408 2,066,190 2,026,892 1,986,547 1,945,155 1,902,616 1,858,701 1,813,074 1,765,371 704,278 648,070 593,403 540,287 488,725 438,754 390,529 344,301 300,453 259,404 60 61 62 63 64 65 66 67 68 69 87,137 86,192 85,174 84,097 82,971 81,795 80,578 79,297 77,927 76,445 52,774 55,836 59,018 62,001 64,490 66,394 67,712 68,493 68,807 68,686 34,363 30,356 26,156 22,096 18,481 15,401 12,866 10,804 9,120 7,759 1,936,815 1,849,678 1,763,486 1,678,312 1,594,215 1,511,244 1,429,449 1,348,871 1,269,574 1,191,647 1,715,327 1,662,552 1,606,716 1,547,699 1,485,698 1,421,208 1,354,813 1,287,101 1,218,608 1,149,801 221,488 187,126 156,770 130,613 108,517 90,036 74,636 61,770 50,966 41,846 70 71 72 73 74 75 74,768 73,033 71,157 69,121 66,904 64,531 68,151 67,387 66,318 64,985 63,395 61,870 6,617 5,646 4,839 4,136 3,509 2,661 1,115,202 1,040,434 967,401 896,244 827,123 760,219 1,081,115 1,012,964 945,577 879,259 814,274 750,880 34,087 27,470 21,824 16,985 12,849 9,339 (19) NOTE: Person years lived in each status during age x For explanation of notation, see appendix C. 25 T ab le 6= Table. @? working life for wom en, 1977: Sam ple derivation of worksite expectancies by labor force status for persons currently ag© 1® Survivors to exact age x by labor force status at age 16 and at age x Persons inactive at 16 Age Total at x i,16 . i X (D i,16 i I X (3) Active at x i,16 a I X (4) Persons active at 16 Total at x a,16 . I X Inactive at x a,16 i I X (6) Persons inactive at age 16 Active at x a,16 a I X Total at x i,16 . L X i,16 i L X a,16 . L X a,16 i L X Active at x a,16 a L X 9,877 4,577 2,833 8,435 24,260 24,247 24,232 24,217 3,709 8,015 8,915 9,324 20,551 16,231 15,317 14,893 31,456 28,601 26,805 25,939 25,807 26,044 26,384 26,807 27,285 27,750 2,289 5,096 6,844 7,661 7,744 7,458 7,067 6,593 6,062 5,543 24,201 24,186 24,170 24,154 24,138 24,122 24,105 24,088 24,071 24,053 9,256 8,877 8,544 8,382 8,399 8,508 8,636 8,784 8,946 9,102 14,946 15,309 15,626 15,772 15,738 15,613 15,469 15,304 15,125 14,951 73,236 73,175 73,112 73,045 72,972 72,894 72,810 72,717 72,617 72,505 28,055 28,044 27,646 27,033 26,401 25,845 25,495 25,297 25,139 25,016 5,180 5,131 5,466 6,012 6,572 7,049 7,314 7,420 7,477 7,489 24,034 24,014 23,994 23,972 23,948 23,922 23,895 23,864 23,831 23,794 9,204 9,201 9,071 8,870 8,663 8,481 8,367 8,302 8,250 8,209 14,831 14,813 14,922 15,101 15,285 15,441 15,528 15,563 15,581 15,585 15,582 15,578 15,542 15,4£55 15,397 15,267 15,091 14,890 14,659 14,398 72,381 72,244 72,093 71,927 71,746 71,549 71,334 71,099 70,845 70,567 24,906 24,828 24,804 24,861 25,028 25,296 25,656 26,080 26,574 27,183 7,475 7,414 7,288 7,066 6,718 6,253 5,678 5,019 4,271 3,384 23,754 23,709 23,659 23,605 23,546 23,481 23,410 23,333 23,250 23,158 3,173 8,148 8,140 8,159 8,214 8,302 8,420 8,559 8,721 8,921 15,530 15,560 15,519 15,446 15,332 15,179 14,991 14,774 14,529 14,238 9,034 9,307 9,581 9,840 10,098 10,358 10,669 11,038 11,515 12,064 14,077 13,701 13,315 12,935 12,547 12,148 11,689 11,161 10,513 9,777 70,265 69,938 69,583 69,201 68,791 68,353 67,886 67,383 66,838 66,243 27,944 28,777 29,590 30,378 31,167 32,037 33,073 34,363 35,927 37,691 2,321 1,160 9,993 8,823 7,624 6,317 4,813 3,020 911 8,552 23,059 22,952 22,836 22,710 22,576 22,432 22,279 22,114 21,935 21,739 9,171 9,444 9,711 9,969 10,228 10,514 10,854 11,277 11,790 12,369 13,889 13,508 13,125 12,741 12,347 11,918 11,425 10,836 10,144 9,370 21,638 21,414 21,171 20,911 20,638 20,355 20,061 19,754 19,428 19,077 12,673 13,401 14,186 14,973 15,660 16,203 16,604 18,854 16,989 17,010 8,965 8,013 6,985 5,938 4,979 4,152 3,457 2,900 2,439 2,067 65,592 64,881 64,115 63,303 62,456 61,577 60,661 59,686 58,665 57,548 38,729 42,034 44,430 46,674 48,548 49,985 50,977 51,564 51,800 51,707 5,863 2,847 9,685 6,628 3,908 1,591 9,684 8,133 6,865 5,841 21,526 21,292 21,041 20,775 20,497 20,208 19,908 19,591 19,252 18,886 13,038 13,795 14,581 15,317 15,932 16,404 16,730 16,922 16,999 16,969 8,488 7,498 6,460 5,457 4,564 3,804 3,178 2,669 2,253 1,917 18,695 18,282 17,837 17,356 16,831 16,260 16,929 16,776 16,551 16,249 15,892 15,463 1,767 1,506 1,287 1,107 939 797 56,338 55,031 53,619 52,086 50,416 48,606 51,351 50,774 48,969 48,965 47,766 46,597 4,987 4,256 3.649 3,120 2,650 2,008 18,489 18,060 17,596 17,093 16,545 15,951 16,852 16,663 16,399 18,069 15,876 15,292 1,637 1,397 1,198 1,024 870 659 0 9,751 9,402 6,263 24,267 24,254 24,239 24,224 0 7,416 8,614 9,216 24,267 16,837 15,626 15,008 73,924 73,882 73,838 73,791 64,047 49,305 41,005 35,357 20 21 22 23 24 25 26 27 28 29 73,768 73,721 73,673 73,625 73,576 73,527 73,477 73,426 73,374 73,320 33,163 29,750 27,453 26,157 25,721 25,894 26,194 26,575 27,039 27,531 606 3,971 6,220 7,468 7,855 7,632 7,283 6,851 6,334 5,789 24,209 24,194 24,178 24,162 24,146 24,130 24,113 24,097 24,080 24,062 9,432 9,079 8,874 8,413 8,350 8,448 8,588 8,705 8,864 9,029 14,777 15,114 15,504 15,748 15,796 15,681 15,545 15,392 15,216 15,033 73,745 73,697 73,649 73,600 73,551 73,501 73,451 73,400 73,347 73,292 30 31 32 33 34 35 36 37 38 39 73,265 73,206 73,144 73,079 73,010 72,935 72,854 72,766 72,670 72,563 27,969 28,141 27,947 27,345 26,720 26,082 25,60.8 25,383 25,212 25,067 5,296 5,065 5,197 5,734 6,290 6,853 7,246 7,383 7,458 7,497 24,044 24,025 24,004 23,983 23,960 23,936 23,909 23,880 23,849 23,814 9,174 9,233 9,170 8,973 8,768 8,559 8,404 8,330 8,274 8,226 14,869 14,792 14,835 15,010 15,192 15,377 15,505 15,550 15,575 15,588 40 41 42 43 44 45 46 47 48 49 72,446 72,316 72,172 72,014 71,841 71,652 71,446 71,222 70,978 70,711 24,965 24,846 24,812 24,797 24,925 25,131 25,461 25,850 26,310 26,837 7,481 7,469 7,360 7,217 6,916 6,521 5,985 5,372 4,688 3,874 23,775 23,732 23,685 23,633 23,577 23,515 23,447 23,373 23,293 23,206 8,193 8,154 8,143 8,138 8,180 8,247 8,356 8,483 8,634 8,807 50 51 52 53 54 55 56 57 58 59 70,422 70,108 69,767 69,399 69,003 68,580 68,128 67,644 67,123 66,554 27,528 28,359 29,194 29,985 30,770 31,563 32,509 33,634 35,089 36,761 2,895 1,749 573 9,414 8,234 7,016 5,619 4,010 2,034 9,793 23,111 23,008 22,898 22,775 22,645 22,506 22,358 22,199 22,028 21,842 60 61 62 63 64 65 69 65,932 65,251 64,511 63,719 62,888 62,024 61,129 60,193 59,199 58,130 38,616 40,835 43,226 45,624 47,717 49,372 50,594 51,357 51,768 51,830 7,316 4,417 1,284 8,094 5,170 2,652 535 8,836 7,432 6,299 70 71 72 73 74 75 56,967 55,708 54,353 52,885 51,286 49,546 51,584 51,120 50,433 49,512 48,426 47,117 5,383 4,589 3,920 3,373 2,860 2,429 For explanation of notation, see appendix C. X Inactive at x (13) 0) 73,943 54,153 44,458 37,552 68 i,16 a L Total at x (12) (7) 73,943 73,904 73,861 73,815 66 Active at x Persons active at 16 (11) (5) (8) Inactive at x 16 17 18 19 67 NOTE: (2) Inactive at x Person years lived by cohort members in each status during age interval x to x+1 26 (10) Table 6. C o n tin ued -T able of working life for women, 1977: Sample derivation of worklife expectancies by labor force status for persons currently age 16 Years remaining to be lived in each status By persons active at exact age 16 By persons inactive at exact age 16 Age Total years i, 1 6 . i, 1 6 T i,16 a T i X X Total years a,1 6 . Inactive years a ,16 T i a ,16 a T T X Active years X X (15) (16) (17) (18) (19) (20) 16 17 18 19 4,618,114 4,544,190 4,470,307 4,396,470 2,594,080 2,530,033 2,480,728 2,439,724 2,024,034 2,014,157 1,989,579 1,956,746 1,515,561 1,491,301 1,467,055 1,442,823 816,892 813,184 805,168 796,253 698,669 678,118 661,886 646,569 20 21 22 23 24 25 26 27 28 29 4,322,678 4,248,933 4,175,236 4,101,587 4,027,987 3,954,436 3,880,934 3,807,483 3,734,083 3,660,736 2,404,367 2,372,911 2,344,309 2,317,504 2,291,566 2,265,758 2,239,714 2,213,330 2,186,523 2,159,238 1,918,312 1,876,023 1,830,927 1,784,083 1,736,421 1,688,678 1,641,220 1,594,153 1,547,560 1,501,499 1,418,606 1,394,405 1,370,219 1,346,049 1,321,895 1,297,757 1,273,636 1,249,531 1,225,442 1,201,372 786,929 777,673 768,797 760,253 751,871 743,472 734,963 726,327 717,543 708,597 631,677 616,731 601,422 585,796 570,024 554,286 538,672 523,204 507,900 492,775 30 31 32 33 34 35 36 37 38 39 3,587,444 3,514,208 3,441,033 3,367,921 3,294,877 3,221,904 3,149,010 3,076,200 3,003,483 2,930,866 2,131,488 2,103,433 2,075,388 2,047,742 2,020,710 1,994,309 1,968,464 1,942,969 1,917,672 1,892,533 1,455,956 1,410,776 1,365,645 1,320,179 1,274,167 1,227,595 1,180,546 1,133,232 1,085,811 1,038,334 1,177,319 1,153,284 1,129,270 1,105,276 1,081,305 1,057,357 1,033,435 1,009,540 985,676 961,845 699,495 690,292 681,090 672,019 663,149 654,485 646,004 637,638 629,336 621,086 477,824 462,993 448,179 433,257 418,156 402,871 387,430 371,902 356,340 340,758 40 41 42 43 44 45 46 47 48 49 2,858,362 2,785,981 2,713,737 2,641,645 2,569,717 2,497,971 2,426,422 2,355,088 2,283,989 2,213,144 1,867,517 1,842,611 1,817,782 1,792,978 1,768,117 1,743,089 1,717,793 1,692,137 1,666,057 1,639,482 990,845 943,370 895,955 848,667 801,601 754,882 708,629 662,951 617,932 573,662 938,050 914,296 890,588 866,929 843,324 819,778 796,297 772,887 749,554 726,304 612,877 604,703 596,555 588,415 580,256 572,043 563,741 555,321 546,762 538,041 325,173 309,593 294,033 278,514 263,067 247,736 232,556 217,566 202,791 188,263 50 51 52 53 54 55 56 57 58 59 2,142,577 2,072,312 2,002,375 1,932,791 1,863,590 1,794,798 1,726,445 1,658,559 1,591,176 1,524,337 1,612,300 1,584,356 1,555,579 1,525,989 1,495,610 1,464,443 1,432,406 1,399,333 1,364,970 1,329,043 530,278 487,956 446,796 406,803 367,980 330,355 294,039 259,225 226,205 195,294 703,146 680,086 657,134 634,299 611,588 589,013 566,581 544,302 522,188 500,253 529,121 519,950 510,506 500,795 490,826 480,597 470,084 459,230 447,953 436,162 174,025 160,136 146,628 133,504 120,763 108,415 96,497 85,072 74,236 64,091 60 61 62 63 64 65 66 67 68 69 1,458,094 1,392,503 1,327,622 1,263,507 1,200,204 1,137,748 1,076,172 1,015,511 955,815 897,150 1,291,352 1,251,624 1,209,589 1,165,160 1,118,485 1,069,938 1,019,952 968,975 917,412 865,612 166,742 140,879 118,033 98,347 81,719 67,811 56,219 46,535 38,403 31,538 478,514 456,988 435,696 414,655 393,880 373,383 353,175 333,268 313,677 294,425 423,793 410,755 396,960 382,379 367,062 351,130 334,725 317,996 301,074 284,075 54,721 46,233 38,736 32,275 26,818 22,254 18,450 15,272 12,603 10,350 70 71 72 73 74 75 839,602 783,264 728,234 674,615 622,529 572,113 813,905 762,554 711,780 661,811 612,845 565,079 25,697 20,710 16,454 12,804 9,684 7,034 275,538 257,050 238,990 221,393 204,300 187,755 267,105 250,253 233,590 217,191 201,122 185,446 8,433 6,797 5,400 4,202 3,178 2,308 (14) NOTE: Active years T X • Inactive years For explanation of notation, see appendix C. 27 Table 7. Table of working life for women, 1977: Expectation of active life by current labor force status Expectancies of persons inactive at age x Expectancies of the total population Total years Inactive years e e Active years a i X i . e e Inactive years i i e Active years i a e Total years a Inactive years a e i Active years a a e e X X X X X X X X X (2) (3) (4) (5) (6) (7) (8) O) (10) 16 17 18 19 62.5 61.5 60.5 59.6 34.7 34.1 33.5 33.0 27.7 27.4 27.0 26.6 62.5 61.5 60.5 59.6 35.1 34.7 34.2 33.7 27.4 26.8 26.3 25.8 62.5 61.5 60.5 59.6 33.7 33.0 32.7 32.3 28.8 28.5 27.8 27.2 20 21 22 23 24 25 26 27 28 29 58.6 57.6 56.7 55.7 54.7 53.8 52.8 51.9 50.9 49.9 32.6 32.2 31.8 31.5 31.1 30.8 30.5 30.1 29.8 29.5 26.0 25.5 24.9 24.2 23.6 23.0 22.3 21.7 21.1 20.5 58.6 57.6 56.7 55.7 54.7 53.8 52.8 51.9 50.9 49.9 33.4 33.1 32.9 32.6 32.4 32.1 31.9 31.6 31.4 31.1 25.2 24.5 23.8 23.1 22.4 21.7 20.9 20.2 19.5 18.9 58.6 57.6 56.7 55.7 54.7 53.8 52.8 51.9 50.9 49.9 31.9 31.6 31.2 30.9 30.5 30.1 29.7 29.3 28.9 28.5 26.7 26.1 25.5 24.9 24.3 23.7 23.1 22.6 22.0 21.5 30 31 32 33 34 35 36 37 38 39 49.0 48.0 47.0 46.1 45.1 44.2 43.2 42.3 41.3 40.4 29.1 28.7 28.4 28.0 27.7 27.3 27.0 26.7 26.4 26.1 19.9 19.3 18.7 18.1 17.5 16.8 16.2 15.6 14.9 14.3 49.0 48.0 47.0 46.1 45.1 44.2 43.2 42.3 41.3 40.4 30.8 30.5 30.2 29.9 29.6 29.3 29.1 28.8 28.5 28.3 18.2 17.5 16.9 16.2 15.5 14.8 14.2 13.5 12.8 12.1 49.0 48.0 47.0 46.1 45.1 44.2 43.2 42.3 41.3 40.4 28.1 27.7 27.3 26.9 26.6 26.2 25.9 25.6 25.2 24.9 20.9 20.3 19.8 19.2 18.6 17.9 17.3 16.7 16.1 15.5 40 41 42 43 44 45 46 47 48 49 39.5 38.5 37.6 36.7 35.8 34.9 34.0 33.1 32.2 31.3 25.8 25.5 25.2 24.9 24.6 24.3 24.0 23.8 23.5 23.2 13.7 13.0 12.4 11.8 11.2 10.5 9.9 9.3 8.7 8.1 39.5 38.5 37.6 36.7 35.8 34.9 34.0 33.1 32.2 31.3 28.0 27.8 27.6 27.3 27.1 26.9 26.6 26.4 26.1 25.9 11.4 10.7 10.0 9.3 8.7 8.0 7.3 6.7 6.1 5.4 39.5 38.5 37.6 36.7 35.8 34.9 34.0 33.1 32.2 31.3 24.6 24.3 23.9 23.6 23.3 23.0 22.6 22.3 21.9 21.6 14.9 14.3 13.7 13.1 12.5 11.9 11.3 10.8 10.3 9.7 50 51 52 53 54 55 56 57 58 59 30.4 29.6 28.7 27.9 27.0 26.2 25.3 24.5 23.7 22.9 22.9 22.6 22.3 22.0 21.7 21.4 21.0 20.7 20.3 20.0 7.5 7.0 6.4 5.9 5.3 4.8 4.3 3.8 3.4 2.9 30.4 29.6 28.7 27.9 27.0 26.2 25.3 24.5 23.7 22.9 25.6 25.2 24.9 24.5 24.1 23.7 23.2 22.6 22.1 21.5 4.9 4.3 3.8 3.3 2.9 2.5 2.2 1.9 1.6 1.4 30.4 29.6 28.7 27.9 27.0 26.2 25.3 24.5 23.7 22.9 21.2 20.8 20.4 20.1 19.7 19.4 19.1 18.8 18.4 18.1 9.2 8.8 8.3 7.8 7.3 6.8 6.3 5.8 5.3 4.8 60 61 62 63 64 65 66 67 68 69 22.1 21.3 20.6 19.8 19.1 18.3 17.6 16.9 16.1 15.4 19.6 19.2 18.8 18.3 17.8 17.3 16.7 16.1 15.5 14.9 2.5 2.2 1.8 1.5 1.3 1.1 .9 .8 .6 .5 22.1 21.3 20.6 19.8 19.1 18.3 17.6 16.9 16.1 15.4 20.9 20.3 19.7 19.0 18.4 17.8 17.1 16.4 15.8 15.1 1.2 1.0 .9 .8 .7 .6 .5 .4 .4 .3 22.1 21.3 20.6 19.8 19.1 18.3 17.6 16.9 16.1 15.4 17.7 17.3 16.9 16.4 15.9 15.3 14.7 14.1 13.5 12.9 4.4 4.0 3.7 3.5 3.2 3.1 2.9 2.8 2.7 2.6 70 71 72 73 74 75 14.7 14.1 13.4 12.8 12.1 11.6 14.3 13.7 13.1 12.5 12.0 11.4 .5 .4 .3 .2 .2 .1 14.7 14.1 13.4 12.8 12.1 11.6 14.5 13.9 13.2 12.6 12.0 11.4 .2 .2 .2 .1 .1 .1 14.7 14.1 13.4 12.8 12.1 11.6 12.3 11.8 11.2 10.8 10.6 10.7 2.4 2.3 2.2 1.9 1.5 .9 (1) NOTE: Total years Expectancies of persons active at age x For explanation of notation, see appendix C. 28 Table 8. Table of working life for women, 1977: Indexes of labor force accession and separation Events per person at risk during interval Events per person alive at exact age x Annual population-based rates of labor force mobility Events remaining per person entering interval Age Accessions i x to x+4 (D 16-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75 + NOTE: a Total separations a x (2) 0.2072 .1583 .1096 .0884 .0752 .0663 .0579 .0468 .0374 .0320 .0278 .0161 .0037 (i,d ) a x 5 M M 5 Voluntary separations 5 ■ M x (4) (3) 0.1279 .1420 .1160 .0841 .0735 .0690 .0681 .0637 .0662 .0778 .0522 .0271 .0537 i Net moves 0.1276 .1416 .1156 .0836 .0726 .0675 .0659 .0607 .0624 .0741 .0499 .0252 .0521 ( ..d ) Accessions C lx .i) M 5 x (5) 0.0793 .0162 -.0065 .0043 .0017 -.0027 -.0102 -.0169 -.0288 -.0458 -.0244 -.0110 -.500 a C lx ,a ) M 5 x (6) 0.8277 .7900 .5468 .4410 .3747 .3298 .2871 .2312 .1834 .1557 .1339 .0753 .0036 For explanation of notation, see appendix C. Total separations 29 ( i,d ) Accessions per inactive person i M 5 x (7) 0.5109 .7090 .5791 .4198 .3661 .3430 .3377 .3147 .3248 .3781 .2511 .1271 .0526 a Total separations per active person a m 5 x (8) 0.3700 .4251 .2996 .2355 .2156 .1920 .1573 .1101 .0727 .0464 .0324 .0173 .0038 ( i,d ) m 5 Accessions i a E Voluntary separations a i E x X X (9) (10) (11) 4.2692 3.4497 2.6684 2.1292 1.6958 1.3300 1.0113 .7369 .5193 .3494 .2059 .0785 .0036 4.4215 3.9210 3.2246 2.6573 2.2504 1.9014 1.5829 1.2780 1.0046 .7264 .3893 .1627 .0511 0.2905 .2263 .1829 .1347 .1128 .1053 .1077 .1108 .1362 .2519 .3697 .3887 1.3017 Chapter 4= Ewalustien ®f the lner@ment"Deer®m®nt Worklife Model There are three key sets of information which any working life table must produce: 1. Estimates of the rate at which people enter and leave the labor force, 2. Estimates of the number of people likely to work at or beyond each age, and 3. Estimates of the number of person years these people will spend in the labor force. The quality of each of these estimates is important, since together they determine the outcome of the model. Even though the increment-decrement technique still requires some fine-tuning on one of these variables, its estimates have been shown to be much better than those of the conventional model. each age to determine flows within the age interval. Mobility estimates were a byproduct, having no rela tionship to worklife expectancies. The increment-decre ment technique actually uses observed patterns of move ment to determine how long people remain in the labor force. The original model included a few very crude estimates of labor force mobility, which purported to describe “net” flows. It was not clear that they did so successfully. The multistate model quantifies both net and gross labor force mobility, giving a full picture of the process of labor turnover. Estimates ©f number ©f people likely to work at or beyond age x As the denominator of the worklife expectancy index, this function is inversely related to worklife duration. Understatement of the size of the active population re sults in overstatement of worklife expectancy. The conventional model defined the size of its active population very narrowly. Only persons in the labor force at the age of peak labor force participation were viewed as workers. All others were treated as “lifetime inactives.” The high rate of turnover among working women guarantees that in any reference week or year a large number of women with work experience will be excluded from the current labor force count. The magni tude of this exclusion is striking. For instance, the 1978 Current Population Survey indicated that 91.5 percent of all American women, and 96.5 percent of those between the ages of 25 and 34, had some work experience. But because the highest single participation rate for women in 1977 was 67.3 percent, the conventional working life table for that year treated one-third of the female popu lation as permanently inactive. This huge understatement of the size of the active group — by nearly one-half— cast a serious upward bias to the worklife expectancy of active women. By contrast, the increment-decrement model treats every member of the population as a potential worker. Even those inactive at a specific age are viewed as having some future worklife. A separate Markov chain is com puted for each age/activity status group, to estimate its future labor force involvement. Drawing a larger number Estimates ©f labor f@ree mobility rates In the past, rates of “net” labor force accession or sep aration have been derived from age-to-age comparisons of labor force participation rates. Because these rates were cross-sectional, they provided no direct information about changes in status. Age effects were confounded by cohort effects, so that it was impossible to interpret the “net changes” implied. The increment-decrement model replaces this inferen tial approach with direct observations. Tables rest on longitudinal records of real people living through various age intervals. Observed changes in their labor force status are used to determine both net and gross mobility rates. The conventional model included no standard formula for computing accession or separation rates. Instead, the formula varied with the age, sex, and/or marital and parental status of the group in question. There was no single model for all women, nor were the female tables which were published an .exhaustive set. Because the estimation procedure varied from group to group, age and sex differentials in mobility rates were difficult to identify, interpret, or apply. The increment-decrement technique uses a single for mula for any given rate, regardless of age or sex. The resulting differences in group rates can be attributed to real differences in labor force behavior, rather than model bias. Provision of a summary table for all women greatly simplifies comparisons between the sexes. The conventional model used stocks of workers at 30 of individuals into the denominator of the index neces sarily lowers average worklife durations. that the amount of time actually spent in the labor force during the year varies tremendously by age and sex. In 1977 the average teenager worked no more than one-fifth of a standard year. Women averaged less than three-fifths of a full year, even at ages of peak activity. But men 30 to 45 normally worked more than 2,080 hours. If worklife durations were made to reflect the extent of these differ ences, estimates for men and women would be much more comparable. The disparity between their worklife expectancies would undoubtedly increase. It is also likely that the worklife expectancies of older workers would decrease. The increment-decrement model is flexible enough to accommodate such an adjustment. Estimates of person years of labor force attachment As the numerator of the worklife expectancy index, this function is equally important to meaningful results. Unfortunately, because there is no standard definition for “1 person year of labor force attachment”, this con cept is difficult to quantify. The life table “person year of life” is intuitively meaningful: 365 days, each lasting 24 hours, or 8,760 hours of life. Developers of the original worklife model adapted this idea to their own calcula tions. They assumed that labor force attachment was continuous from age of entry to age of permanent labor force withdrawal. Every year survived by a worker was translated into an equivalent person year of labor force attachment. There was no attempt to discount these years for periods of part-year or part-time work. The increment-decrement tables discussed in this re port correct for part of this shortcoming. Moves in and out of the job market at midlife have been identified. People who change status during the year are debited for the portion of the year spent outside the labor force, on the crude assumption that they changed status at mid year. Because a large number of women report part-year activity, this adjustment further depresses their average worklife durations. However, the tables still sidestep the issue of what a person year of labor force attachment really means. Worklife duration is a function not only of weeks (or years) of continuous activity, but also of hours worked during the week. A fully satisfactory definition of a “person year of activity” would specify a standard unit of time, such as the 2,080-hour year (i.e., 52 weeks at 40 hours per week). Each group’s time in the labor force could then be expressed in full-year equivalents, by employing information on normal work patterns for various age/sex groups of the population. Such an adjustment would greatly improve the quality of worklife expectancy data. Consider text table 12, in which average annual hours of labor force involvement are shown as a ratio to this 2,080-hour standard.9 Note Text table 12. Proportion of a standard 2,0S0-!h@ur year worked by the average individual by sex, selected ages, 19?? Age Men Women 16 20 25 30 35 ...................................................... ....................................................... ....................................................... ...................................................... ....................................................... 21.3 71.2 95.0 102.3 106.1 13.4 50.9 57.1 49.0 48.6 40 45 50 55 60 65 ....................................................... ....................................................... ....................................................... ....................................................... ....................................................... ....................................................... 103.3 100.7 97.5 91.2 72.9 31.7 52.1 51.1 47.9 43 8 34 1 13.7 Other considerations The multistate model is attractive to labor analysts for a number of other reasons. Its flexibility opens up the chance to explore other aspects of worklife. For instance, it would be possible to look at other labor force statuses, such as time spent employed and unemployed. It should also be possible to see how differentials in mortality rates (for those in and out of the job market) would affect worklife durations. Another attraction of this model is the simplicity of the premise on which it rests—the model simply spells out what would happen if people continued to enter and leave the labor force at present rates. The few assump tions underlying this technique are easy to understand and explain. And, because the mechanics of the model are straightforward, its results are both predictable and credible. Finally, the multistate model makes the “bottom line” estimates more accessible to users. It provides one sum mary set of estimates for all women, and for both sexes gives a full array of work and nonworklife expectancies, by present labor force status. ’ Hours of labor force involvement per year have been estimated from data collected in the March 1978 Current Population Survey supplement on work experience during 1977. Each adult’s labor force experience during that year has been summarized in an annual hours index, as follows: AH = (Ww + Wu - W0 ) * Hu + (W0 * Hp) where: AH = annual hours estimate Ww = weeks of work reported Areas for further research Wu = weeks of unemployment or layoff reported Future worklife studies at the Bureau of Labor Statis tics will concentrate on the following possible extensions to this model: 1. Introduction of an annual hours index, or some refinement to discount worklife for part-time employment. 2. Development of tables by educational attainment. W0 = weeks in “other” time status (i.e. part-time for those normally working full-time, or full-time for those normally working parttime) Hu = usual hours per week reported, and n p = usual hours in other status, a proxy value drawn from usual hours of persons with same age, race and sex, who normally worked the other schedule. 31 3. Extension of the tables to include differential mor tality rates. A final topic which needs to be explored is the rela tionship between data sources and model outcome. As mentioned earlier, the Current Population Survey offers two sets of information from which to develop transition probabilities: A year-to-year match of individual records (available for any period), and a retrospective question naire (used only once every 5 years). Each data set has its own advantages and disadvantages. Sample size and migration selectivity argue in favor of using retrospective data. Because of the rotation pattern of the c ps sample, only half of all respondents are eligible for a given year-to-year matched file. Of these, some are lost to follow-up due to changes in residence during the interval. On the other hand, retrospective questions are addressed to all members of the full sample who are employed at the time of the survey. Even those who have moved in the past year are interviewed in this questionnaire. The Schoen and Woodrow tables show a heavier volume of labor turnover in 1972 than is apparent in the BLS tables for 1970 and 1977. The difference is particularly evident for young people, the group we are most likely to have lost through migration; It is possible to expand the size of the matched sample simply by pooling data for several successive months. However, this does not correct for the bias of migration selectivity. Other biases are also likely to affect the data. Both retrospective and matched files are subject to response bias, particularly from those who have been reinterviewed a number of times. The retrospective data are also affected by problems of recall. A practical consideration in selecting a data source is its availability. While the retrospective file is more com plete than the matched data set, it is available at best once every 5 years. Availability of these data is contingent on continued inclusion of the relevant questions in the cps supplemental questionnaire. On the other hand, matched tapes can be used to develop transition proba bilities for any time interval, without collecting any additional information. This facilitates timely reestima tion of worklife indexes, a desirable feature in periods of rapid behavioral change. A comparison of transition probabilities from the two data sources for a single time period would probably by quite useful. Multistate models can be tailored to labor force issues in a number of ways not yet explored. They are highly adaptable and, imaginatively used, should continue to expand our understanding of labor force dynamics. 32 33 Table A-1. Table of working life for men, 1970: Derivation of the expectation of active life for the general population Age-specific rates of transfer per 1,000 Probability of transition between specified states during age interval x to x + 1 persons in initial status during age interval to x+1 Age X NOTE: Living to dead . d P X Inactive to inactive i j P X Inactive to active Active to inactive Active to active Mortality a PX a i P a a P m (7) i X X (D (2) (3) (4) (5) (6) 16 17 18 19 0.00138 .00161 .00180 .00196 0.75996 .78286 .74054 .70178 0.23866 .21553 .25766 .29626 0.29309 .19653 .20917 .21784 0.70553 .80186 .78903 .78020 20 21 22 23 24 25 26 27 28 29 .00211 .00226 .00234 .00232 .00224 .00213 .00202 .00198 .00198 .00203 .68297 .67598 .67286 .67955 .67989 .67061 .65627 .63150 .60380 .58912 .31492 .32176 .32480 .31813 .31787 .32726 .34171 .36652 .39422 .40885 .17897 .15106 .12170 .09802 .07739 .05924 .04457 .03332 .02600 .02076 30 31 32 33 34 35 36 37 38 39 .00210 .00218 .00228 .00240 .00253 .00269 .00288 .00310 .00347 .00356 .57453 .56240 .53976 .53763 .54563 .56011 .59979 .63615 .66983 .70058 .42337 .43542 .45796 .45997 .45184 .43720 .39733 .36075 .32670 .29586 40 41 42 43 44 45 46 47 48 49 .00402 .00440 .00480 .00526 .00574 .00628 .00686 .00749 .00839 .00874 .72859 .75556 .77719 .79208 .79853 .80520 .81948 .81677 .82156 .83295 50 51 52 53 54 55 56 57 58 59 .00974 .01062 .01161 .01276 .01403 .01541 .01686 .01839 .01998 .02168 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 X i a m X Voluntary labor force separation a i m X (8) (9) 1.38 1.61 1.80 1.96 325.63 271.96 336.82 399.68 399.88 247.97 273.43 293.89 .81892 .84668 .87596 .89966 .92037 .93863 .95341 .96470 .97202 .97721 2.11 2.26 2.34 2.32 2.24 2.13 2.02 1.98 1.98 2.03 419.23 422.48 419.27 402.77 397.16 406.62 424.46 459.13 500.21 521.90 238.24 198.35 157.10 124.10 96.70 73.61 55.36 41.75 32.99 26.51 .01706 .01479 .01314 .01270 .01251 .01331 .01363 .01382 .01408 .01576 .98084 .98303 .98458 .98490 .98496 .98400 .98349 .98308 .98245 .98068 2.10 2.18 2.28 2.40 2.53 2.69 2.88 3.10 3.48 3.57 544.23 563.31 600.66 603.99 590.19 566.06 501.71 445.42 395.32 351.83 21.93 19.13 17.23 16.68 16.35 17.23 17.22 17.07 17.04 18.75 .26739 .24004 .21801 .20266 .19573 .18852 .17366 .17574 .17005 .15831 .01647 .01671 .01703 .01759 .01705 .01778 .01852 .01825 .01739 .01807 .97951 .97889 .97817 .97715 .97721 .97594 .97462 .97426 .97422 .97319 4.03 4.41 4.81 5.27 5.76 6.30 6.88 7.52 8.43 8.78 312.98 276.70 248.32 229.02 220.37 211.60 193.52 196.17 189.30 175.23 19.28 19.27 19.40 19.88 19.20 19.96 20.63 20.37 19.35 20.00 .84490 .84514 .85166 .86515 .87048 .87161 .87448 .86932 .86572 .86582 .14536 .14424 .13673 .12209 .11549 .11298 .10866 .11229 .11430 .11250 .01944 .02034 .02163 .02260 .02336 .02617 .03166 .03645 .04165 .04841 .97082 .96904 .96676 .96464 .96261 .95842 .95148 .94516 .93837 .92991 9.79 10.68 11.68 12.84 14.13 15.53 17.00 18.56 20.18 21.92 160.04 158.93 150.31 133.38 125.93 123.39 118.93 123.67 126.59 125.16 21.40 22.41 23.78 24.69 25.47 28.59 34.65 40.15 46.12 53.85 .02346 .02535 .02742 .02968 .03214 .03480 .03760 .04049 .04349 .04658 .86965 .87154 .87320 .87856 .88353 .89221 .90131 .90471 .90761 .90728 .10689 .10311 .09938 .09176 .08433 .07299 .06109 .05480 .04890 .04614 .06343 .08042 .09865 .11743 .13762 .15614 .17896 .19861 .21224 .22256 .91311 .89423 .87393 .85289 .83024 .80906 .78344 .76090 .74427 .73086 23.74 25.68 27.80 30.13 32.66 35.42 38.32 41.33 44.46 47.69 119.76 116.61 113.57 105.78 98.18 85.57 72.30 65.57 58.97 56.08 71.07 90.95 112.73 135.36 160.22 183.07 211.79 237.64 255.94 270.51 .04984 .05334 .05722 .06166 .06663 .07205 .90743 .90746 .90551 .90220 .89871 .90156 .04273 .03920 .03727 .03614 .03466 .02619 .22551 .23067 .23227 .23863 .23728 .23410 .72465 .71599 .71051 .69971 .69609 .69366 51.11 54.80 58.91 63.62 68.93 74.74 52.11 48.04 45.86 44.83 43.16 32.59 275.00 282.67 285.80 296.01 295.47 291.31 For explanation of notation, see appendix C. d Labor force accession 34 x Table A-1. C©nt5nu®d=“ Tabl@ of working life for men, 1970: Derivation of the expectation of active life for the genera! population Stationary population living in each status at exact age x, per 100,000 persons bom Number of status transfers within stationary population during age interval x to x + 1 Labor force entries Labor force status Age Total Inactive a i I X X Active I X i i a a i X Deaths Of actives a d t t i X Voluntary labor force exits X Of inactives i . d (16) d t t X Total X X (17) (11) (12) (13) (14) (15) 16 17 18 19 96,781 96,647 96,491 96,317 71,421 61,710 55,176 49,501 25,360 34,937 41,315 46,816 21,675 15,894 17,623 18,C/r 12,056 9,454 12,049 14,402 42 61 79 96 92 94 94 93 134 156 174 189 20 21 23 24 25 26 27 28 29 96,128 95,925 95,708 95,484 95,262 95,049 94,847 94,655 94,468 94,281 44,938 39,852 35,410 31,164 27,482 23,931 20,261 16,621 13,097 10,023 51,190 56,073 60,298 64,320 67,780 71,118 74,586 78,034 81,371 84,258 17,773 15,899 13,956 11,811 10,210 8,985 7,828 6,822 5,782 4,613 12,777 11,541 9,789 8,196 6,716 5,362 4,225 3,327 2,732 2,262 113 132 146 153 156 155 154 158 164 173 90 85 78 68 58 47 37 29 23 18 203 217 224 222 213 202 192 187 187 191 30 31 32 33 34 35 36 37 38 39 94,090 93,892 93,687 93,473 93,249 93,013 92,763 92,496 92,209 91,889 7,654 5,872 4,604 3,656 3,106 2,823 2,782 2,895 3,080 3,318 86,436 88,020 89,083 89,817 90,143 90,190 89,981 89,601 89,129 88,571 3,681 2,951 2,481 2,042 1,750 1,586 1,424 1,331 1,265 1,238 1,913 1,694 1,542 1,501 1,474 1,553 1,546 1,525 1,514 1,654 183 193 204 216 228 243 259 277 309 315 14 9 11 13 198 205 214 224 236 250 267 287 320 327 40 41 42 43 44 45 46 47 48 49 91,562 91,194 90,793 90,357 89,882 89,366 88,805 88,196 87,535 86,801 3,721 4,158 4,596 5,040 5,493 5,825 6,176 6,591 6,873 7,043 87,841 87,036 86,197 85,317 84,389 83,541 82,629 81,605 80,662 79,752 1,233 1,211 1,196 1,206 1,247 1,270 1,235 1,321 1,318 1,258 1,685 1,669 1,663 1,687 1,612 1,659 1,694 1,653 1,552 1,585 352 382 413 448 483 523 565 610 676 696 16 19 23 28 33 38 44 51 59 63 368 401 436 475 516 561 609 661 734 759 50 51 52 53 54 55 56 57 58 59 86,042 85,204 84,299 83,320 82,257 81,103 79,853 78,507 77,063 75,523 7,312 7,708 8,091 8,539 9,078 9,612 10,249 11,166 12,162 13,232 78,730 77,496 76,208 74,781 73,173 71,491 63,604 67,341 64,901 62,291 1,202 1,255 1,250 1,175 1,177 1,225 1,274 1,442 1,607 1,734 1,671 1,722 1,795 1,827 1,843 2,017 2,373 2,654 2,933 3,277 765 821 882 950 1,022 1,096 1,164 1,227 1,283 1,334 74 84 97 113 132 154 182 216 256 304 838 905 979 1,063 1,154 1,250 1,346 1,444 1,540 1,637 60 61 62 63 64 65 66 67 68 69 73,886 72,153 70,324 68,396 66,366 64,233 61,998 59,667 57,251 54,761 14,471 16,354 18,740 21,453 24,360 27,303 30,127 32,857 35,051 36,524 59,415 55,799 51,584 46,943 42,006 36,930 31,871 26,810 22,200 18,237 1,846 2,046 2,282 2,423 2,536 2,457 2,277 2,226 2,110 2,067 4,094 4,883 5,553 6,020 6,323 6,298 6,214 5,823 5,175 4,497 1,368 1,379 1,370 1,340 1,289 1,218 1,124 1,013 899 793 366 451 559 690 844 1,017 1,207 1,403 1,591 1,758 1,733 1,829 1,928 2,030 2,133 2,235 2,331 2,416 2,490 2,551 70 71 72 73 74 75 52,210 49,608 46,962 44,275 41,545 38,777 37,196 37,139 36,578 35,534 34,145 32,442 15,014 12,469 10,384 8,741 7,400 6,335 1,937 1,771 1,654 1,562 1,437 1,030 3,779 3,230 2,733 2,389 2,029 1,687 702 626 563 513 473 433 1,900 2,020 2,124 2,217 2,295 2,361 2,602 2,646 2,687 2,730 2,768 2,794 (10) 22 NOTE: For explanation of notation, see appendix C. 35 (18) 11 3 8 8 8 8 Table A-1. Continued— Table of working life for men, 1970: Derivation of the expectation of active life for the general population Age X Person years lived in each status during age x Total Inactive Active L . i L L X Person years lived in each status beyond exact age x Total Inactive Active T . i T T a X X X a X X (20) (21) (22) (23) (24) (25) 16 17 18 19 96,714 96,569 96,404 96,223 66,565 58,443 52,339 47,220 30,149 38,126 44,065 49,003 5,154,552 5,057,838 4,961,269 4,864,865 1,410,537 1,343,972 1,285,529 1,233,191 3,744,015 3,713,866 3,675,740 3,631,674 20 21 22 23 24 25 26 27 28 29 96,027 95,817 95,596 95,373 95,156 94,948 94,751 94,562 94,375 94,186 42,395 37,631 33,287 29,323 25,707 22,096 18,441 14,859 11,560 8,839 53,632 58,186 62,309 66,050 69,449 72,852 76,310 79,703 82,815 85,347 4,768,642 4,672,615 4,576,798 4,481,202 4,385,829 4,290,673 4,195,725 4,100,974 4,006,412 3,912,037 1,185,971 1,143,576 1,105,944 1,072,657 1,043,334 1,017,627 995,531 977,090 962,231 950,671 3,582,671 3,529,039 3,470,854 3,408,545 3,342,495 3,273,046 3,200,194 3,123,884 3,044,181 2,961,366 30 31 32 33 34 35 36 37 38 39 93,991 93,790 93,580 93,361 93,131 92,888 92,630 92,353 92,049 91,726 6,763 5,238 4,130 3,381 2,965 2,802 2,838 2,988 3,199 3,520 87,228 88,552 89,450 89,980 90,166 90,086 89,792 89,365 88,850 88,206 3,817,851 3,723,860 3,630,070 3,536,490 3,443,129 3,349,998 3,257,110 3,164,480 3,072,127 2,980,078 941,832 935,069 929,831 925,701 922,320 919,355 916,553 913,714 910,727 907,527 2,876,019 2,788,791 2,700,239 2,610,789 2,520,809 2,430,643 2,340,557 2,250,766 2,161,400 2,072,551 40 41 42 43 44 45 46 47 48 49 91,378 90,994 90,575 90,120 89,624 89,086 88,501 87,866 87,168 86,422 3,939 4,377 4,818 5,266 5,659 6,001 6,384 6,732 6,961 7,181 87,439 86,617 85,757 84,854 83,965 83,085 82,117 81,134 80,207 79,241 2,888,352 2,796,974 2,705,980 2,615,405 2,525,285 2,435,661 2,346,575 2,258,074 2,170,208 2,083,040 904,008 900,068 895,691 890,873 885,607 879,948 873,947 867,563 860,831 853,870 1,984,344 1,896,906 1,810,289 1,724,532 1,639,678 1,555,713 1,472,628 1,390,511 1,309,377 1,229,170 50 51 52 53 54 55 56 57 58 59 85,623 84,752 83,810 82,789 81,680 80,478 79,180 77,785 76,293 74,705 7,510 7,899 8,315 8,809 9,345 9,930 10,708 11,664 12,697 13,852 78,113 76,853 75,495 73,980 72,335 70,548 68,472 66,121 63,596 60,853 1,996,618 1,910,995 1,826,243 1,742,433 1,659,644 1,577,964 1,497,486 1,418,306 1,340,521 1,264,228 846,689 839,179 831,279 822,964 814,156 804,811 794,881 784,173 772,509 759,813 1,149,929 1,071,816 994,964 919,469 845,488 773,153 702,605 634,133 568,012 504,415 60 61 62 63 64 65 66 67 68 69 73,020 71,239 69,360 67,381 65,300 63,116 60,833 58,459 56,006 53,486 15,413 17,547 20,097 22,906 25,832 28,715 31,492 33,954 35,788 36,861 57,607 53,692 49,263 44,475 39,468 34,401 29,341 24,505 20,218 16,625 1,189,523 1,116,503 1,045,264 975,904 908,523 843,223 780,107 719,274 660,815 604,809 745,961 730,548 713,001 692,904 669,998 644,166 615,451 583,958 550,004 514,217 443,562 385,955 332,263 283,000 238,525 199,057 164,656 135,316 110,811 90,592 70 71 72 73 74 75 50,909 48,285 45,619 42,910 40,161 37,380 37,167 36,858 36,057 34,839 33,293 31,590 13,742 11,427 9,562 8,071 6,868 5,790 551,323 500,414 452,129 406,510 363,600 323,439 477,356 440,189 403,330 367,274 332,434 299,141 73,967 60,225 48,799 39,236 31,166 24,298 (19) NOTE: For explanation of notation, see appendix C. 36 Table A-2. Table of working life for men, 1970: Expectation of active life by current labor force status Age Total years Inactive years e e Active years Total years Inactive years Active years Total years Inactive years Active years a a e a . e a i e X X X X X X X X X (1) (2) (3) (4) (5) (6) (7) (S) (9) (10) 16 17 18 19 53.3 52.3 51.4 50.5 14.6 13.9 13.3 12.8 38.7 38.4 38.1 37.7 53.3 52.3 51.4 50.5 15.0 14.5 14.0 13.5 38.3 37.8 37.4 37.0 53.3 52.3 51.4 50.5 13.4 12.8 12.4 12.0 39.8 39.5 39.0 38.5 20 21 22 23 24 25 26 27 28 29 49.6 48.7 47.8 46.9 46.0 45.1 44.2 43.3 42.4 41.5 12.3 11.9 11.6 11.2 11.0 10.7 10.5 10.3 10.2 10.1 37.3 36.8 36.3 35.7 35.1 34.4 33.7 33.0 32.2 31.4 49.6 48.7 47.8 46.9 46.0 45.1 44.2 43.3 42.4 41.5 13.2 12.9 12.7 12.6 12.4 12.2 12.0 11.9 11.7 11.7 36.4 35.8 35.1 34.4 33.7 32.9 32.2 31.5 30.7 29.8 49.6 48.7 47.8 46.9 46.0 45.1 44.2 43.3 42.4 41.5 11.6 11.2 10.9 10.6 10.4 10.2 10.1 10.0 9.9 9.9 38.0 37.5 36.9 36.3 35.7 34.9 34.2 33.3 32.5 31.6 30 31 32 33 34 35 36 37 38 39 40.6 39.7 38.7 37.8 36.9 36.0 35.1 34.2 33.3 32.4 10.0 10.0 9.9 9.9 9.9 9.9 9.9 9.9 9.9 9.9 30.6 29.7 28.8 27.9 27.0 26.1 25.2 24.3 23.4 22.6 40.6 39.7 38.7 37.8 36.9 36.0 35.1 34.2 33.3 32.4 11.6 11.5 11.5 11.6 11.7 11.9 12.2 12.5 12.8 13.1 29.0 28.1 27.2 26.3 25.2 24.1 22.9 21.7 20.5 19.3 40.6 39.7 38.7 37.8 36.9 36.0 35.1 34.2 33.3 32.4 9.9 9.9 9.8 9.8 9.8 9.8 9.8 9.8 9.8 9.8 30.7 29.8 28.9 28.0 27.1 26.2 25.3 24.4 23.5 22.7 40 41 42 43 44 45 46 47 48 49 31.5 30.7 29.8 28.9 28.1 27.3 26.4 25.6 24.8 24.0 9.9 9.9 9.9 9.9 9.9 9.8 9.8 9.8 9.8 9.8 21.7 20.8 19.9 19.1 18.2 17.4 16.6 15.8 15.0 14.2 31.5 30.7 29.8 28.9 28.1 27.3 26.4 25.6 24.8 24.0 13.4 13.7 13.9 14.0 14.1 14.2 14.4 14.4 14.5 14.6 18.1 17.0 15.9 14.9 14.0 13.0 12.1 11.2 10.3 9.4 31.5 30.7 29.8 28.9 28.1 27.3 26.4 25.6 24.8 24.0 9.7 9.7 9.7 9.6 9.6 9.5 9.5 9.5 9.4 9.4 21.8 21.0 20.2 19.3 18.5 17.7 16.9 16.1 15.4 14.6 50 51 52 53 54 55 56 57 58 59 23.2 22.4 21.7 20.9 20.2 19.5 18.8 18.1 17.4 16.7 9.8 9.8 9.9 9.9 9.9 9.9 10.0 10.0 10.0 10.1 13.4 12.6 11.8 11.0 10.3 9.5 8.8 8.1 7.4 6.7 23.2 22.4 21.7 20.9 20.2 19.5 18.8 18.1 17.4 16.7 14.6 14.6 14.6 14.5 14.4 14.2 14.0 13.8 13.6 13.4 8.6 7.9 7.1 6.4 5.8 5.3 4.8 4.3 3.8 3.4 23.2 22.4 21.7 20.9 20.2 19.5 18.8 18.1 17.4 16.7 9.4 9.4 9.4 9.4 9.3 9.4 9.4 9.4 9.4 9.4 13.8 13.0 12.3 11.6 10.8 10.1 9.4 8.7 8.0 7.4 60 61 62 63 64 65 66 67 68 69 16.1 15.5 14.9 14.3 13.7 13.1 12.6 12.1 11.5 11.0 10.1 10.1 10.1 10.1 10.1 10.0 9.9 9.8 9.6 9.4 6.0 5.3 4.7 4.1 3.6 3.1 2.7 2.3 1.9 1.7 16.1 15.5 14.9 14.3 13.7 13.1 12.6 12.1 11.5 11.0 13.1 12.9 12.6 12.3 12.0 11.7 11.4 11.0 10.6 10.2 3.0 2.6 2.3 1.9 1.7 1.4 1.2 1.1 1.0 .8 16.1 15.5 14.9 14.3 13.7 13.1 12.6 12.1 11.5 11.0 9.4 9.3 9.2 9.1 9.0 8.8 8.6 8.3 8.1 7.8 6.7 6.2 5.6 5.1 4.7 4.3 4.0 3.7 3.5 3.3 70 71 72 73 74 75 10.6 10.1 9.6 9.2 8.8 8.3 9.1 8.9 8.6 8.3 8.0 7.7 1.4 1.2 1.0 .9 .8 .6 10.6 10.1 9.6 9.2 8.8 8.3 9.8 9.4 9.0 8.6 8.2 7.8 .7 .7 .6 .5 .5 .5 10.6 10.1 9.6 9.2 8.8 8.3 7.5 7.2 7.0 6.9 6.9 7.0 3.1 2.9 2.6 2.3 1.9 1.3 i X NOTE: Expectancies of persons active at age x Expectancies of persons inactive at age x Expectancies of the total population . a e i . e For explanation of notation, see appendix C. 37 i i e a i e Table A-3. Table of working life for men, 1970: Indexes of labor force accession and separation Annual population-based rates of labor force mobility Events per person at risk during interval Events per person alive at exact age x Events remaining per person entering interval Age Accessions i x to x+4 (D 16-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75 + NOTE: 5 a M x (2) 0.1919 .1457 .0720 .0276 .0148 .0135 .0146 .0145 .0187 .0321 .0382 .0367 .0275 Total separations Voluntary separations (i,d) a x 5 a M 5 x (4) (3) 0.1250 .1040 .0396 .0196 .0199 .0230 .0255 .0318 .0498 .0971 .1132 .0748 .1970 i M 0.1243 .1026 .0379 .0174 .0169 .0184 .0185 .0212 .0341 .0776 .0959 .0621 .1854 Net moves • (-.d ) Accessions ( lx ,i) M 5 x (5) 0.0669 .0417 .0324 .0080 -.0051 -.0095 -.0110 -.0173 -.0311 -.0649 -.0751 -.0381 -.1695 a ( lx ,a ) M 5 x (6) 0.7653 .7245 .3580 .1371 .0736 .0666 .0716 .0704 .0898 .1507 .1734 .1601 .0266 For explanation of notation, see appendix C. Total separations 38 (i,d ) Accessions per inactive person i M 5 x (7) 0.4984 .5172 .1969 .0972 .0988 .1135 .1255 .1545 .2387 .4550 .5146 .3264 .1899 a Total separations per active person a m 5 x (8) 0.3298 .4137 .4490 .5741 .4460 .2533 .1925 .1447 .1237 .1094 .0668 .0469 .0326 (i,d ) m 5 Accessions i a E Voluntary separations a i E x X X 0) (10) (11) 2.6348 1.8821 1.1707 .8210 .6917 .6280 .5752 .5230 .4802 .4285 .3196 .1798 .0266 2.5351 2.0534 1.5610 1.3865 1.3153 1.2510 1.1887 1.1400 1.1002 1.0282 .7644 .4040 .1788 0.2990 .1606 .0471 .0205 .0206 .0242 .0276 .0353 .0587 .1375 .2642 .3430 1.2719 Table A-4. Table of working life for women, 1970: Derivation of the expectation of active life for the general population Age-specific rates of transfer per 1,000 Probability of transition between specified states during age interval x to x + 1 persons in initial status during age interval x to x+1 Age Living to dead . d P X NOTE: Inactive to inactive i i p X Inactive to active Active to inactive j a p a i pX X Active to active a a pX Mortality d m Labor force accession a i a i m m X Voluntary labor force separation X X (D (2) (3) (4) (5) (6). (8) 0) 16 17 18 19 0.00057 .00065 .00068 .00070 0.79044 .80352 .77437 .74897 0.20899 .19583 .22495 .25033 0.43084 .27929 .30289 .32496 0.56859 .72006 .69643 .67434 0.57 .65 .68 .70 307.51 257.04 305.86 351.71 633.95 366.58 411.82 456.56 20 21 22 23 24 25 26 27 28 29 .00071 .00074 .00075 .00077 .00079 .00081 .00084 .00087 .00091 .00095 .74191 .74797 .76209 .78084 .79759 .81290 .82888 .84239 .85181 .85754 .25738 .25129 .23716 .21839 .20162 .18629 .17028 .15674 .14728 .14151 .28862 .26142 .23762 .22179 .21114 .19907 .19089 .18767 .18569 .18461 .71067 .73784 .76163 .77744 .78807 .80012 .80827 .81146 .81340 .81444 .71 .74 .75 .77 .79 .81 .84 .87 .91 .95 354.33 338.20 311.26 280.27 254.28 230.96 208.00 189.53 176.88 169.25 397.34 351.84 311.86 284.63 266.28 246.80 233.17 226.93 223.00 220.81 30 31 32 33 34 35 36 37 38 39 .00100 .00108 .00116 .00127 .00138 .00153 .00168 .00183 .00199 .00214 .85992 .86169 .86163 .86151 .86056 .86094 .86088 .85981 .86336 .86572 .13908 .13723 .13721 .13722 .13806 .13753 .13744 .13836 .13465 .13214 .18495 .17932 .17485 .16623 .15921 .15151 .14494 .13803 .13316 .12503 .81405 .81960 .82399 .83250 .83941 .84696 .85338 .86014 .86485 .87283 1.00 1.08 1.16 1.27 1.38 1.53 1.68 1.83 1.99 2.14 166.15 163.23 162.78 161.99 162.41 161.03 160.32 160.86 155.80 151.98 220.95 213.29 207.44 196.24 187.28 177.40 169.08 160.48 154.07 143.81 40 41 42 43 44 45 46 47 48 49 .00231 .00250 .00272 .00297 .00325 .00356 .00388 .00421 .00455 .00491 .86706 .86617 .86732 .86869 .87201 .87672 .88244 .88483 .88778 .89010 .13063 .13133 .12996 .12834 .12474 .11972 .11368 .11096 .10767 .10499 .11880 .11376 .11194 .11245 .11217 .11051 .10788 .10359 .10129 .09882 .87889 .88374 .88534 .88458 .88458 .88593 .88824 .89220 .89416 .89627 2.31 2.50 2.72 2.97 3.26 3.57 3.89 4.22 4.56 4.92 149.61 150.07 148.27 146.37 142.00 135.81 128.37 124.84 120.81 117.52 136.07 129.99 127.71 128.25 127.69 125.36 121.82 116.56 113.66 110.60 50 51 52 53 54 55 56 57 58 59 .00529 .00569 .00614 .00664 .00717 .00775 .00838 .00903 .00969 .01038 .89403 .89762 .90430 .90839 .91144 .91364 .91582 .91719 .92060 ,92498 .10068 .09669 .08956 .08497 .08139 .07861 .07580 .07378 .06971 .06464 .09771 .09941 .09832 .09731 .09831 .10071 .10276 .10884 .11636 .12442 .89700 .89490 .89554 .89605 .89452 .89154 .88886 .88213 .87395 .86520 5.30 5.71 6.16 6.66 7.20 7.78 8.42 9.07 9.74 10.43 112.39 107.84 99.49 94.15 90.11 87.05 83.97 81.97 77.65 72.18 109.07 110.88 109.22 107.82 108.84 111.53 113.84 120.92 129.61 138.92 60 61 62 63 64 65 66 67 68 69 .01113 .01198 .01296 .01410 .01539 .01684 .01839 .02012 .02202 .02410 .92871 .93150 .93304 .93534 .93912 .94216 .94590 .94899 .95194 .95307 .06016 .05652 .05400 .05056 .04549 .04100 .03571 .03089 .02604 .02283 .13392 .14972 .16837 .18369 .20365 .22665 .23616 .24884 .25635 .26689 .85495 .83830 .81867 .80221 .78096 .75651 .74545 .73104 .72163 .70901 11.19 12.05 13.04 14.20 15.51 16.98 18.56 20.32 22.27 24.39 67.42 63.83 61.60 58.13 52.83 48.21 42.16 36.71 31.06 27.41 150.06 169.07 192.07 211.22 236.51 266.49 278.82 295.70 305.74 320.42 70 71 72 73 74 75 .02632 .02878 .03163 .03501 .03886 .04311 .95359 .95493 .95470 .95372 .95158 .94783 .02009 .01629 .01367 .01127 .00956 .00902 .27589 .29190 .31285 .32738 .33708 .41978 .69779 .67932 .65552 .63761 .62406 .53707 26.67 29.20 32.14 35.63 39.63 44.06 24.27 19.87 16.92 14.10 12.08 12.07 333.28 356.18 387.22 409.77 425.84 561.54 For explanation of notation, see appendix C. 39 (7) Table A-4. Continued— Table of working life for women, 1970: Derivation of the expectation of active life for the general population Stationary population living in each status at exact age x, per 100,000 persons born Number of status transfers within stationary population during age interval x to x+1 Labor force status Age Labor force entries Total Inactive i I X (10) NOTE: i;' X Active a I x i a t I X X Voluntary labor force exits a i t X Deaths Of actives a d t X Of inactives Total i d t . d t X X (11) (12) (13) (14) (15) (16) 16 17 18 19 97,581 97,525 97,462 97,396 78,389 70,230 64,055 59,720 19,192 27,295 33,407 37,676 22,851 17,258 18,929 20,521 14,735 11,126 14,637 17,813 13 20 24 27 42 44 42 41 56 63 66 68 20 21 22 23 24 25 26 27 28 29 97,328 97,259 97,187 97,114 97,039 96,962 96,883 96,802 96,718 96,630 56,972 53,916 51,658 50,187 49,596 49,574 49,732 50,223 51,049 51,964 40,356 43,343 45,529 46,927 47,443 47,388 47,151 46,579 45,669 44,666 19,645 17,853 15,850 13,983 12,608 11,468 10,395 9,597 9,110 8,866 16,629 15,634 14,417 13,430 12,626 11,666 10,928 10,467 10,072 9,760 30 33 35 36 37 38 39 40 41 42 39 39 38 38 39 40 42 44 47 50 69 72 73 75 77 79 81 84 88 92 30 31 32 33 34 35 36 37 38 39 96,538 96,441 96,337 96,225 96,103 95,970 95,823 95,662 95,487 95,297 52,807 53,498 53,799 53,793 53,397 52,750 51,962 51,091 50,081 49,284 43,731 42,943 42,538 42,432 42,706 43,220 43,861 44,571 45,406 46,013 8,832 8,757 8,757 8,682 8,620 8,431 8,261 8,137 7,741 7,425 9,575 9,116 8,813 8,354 8,046 7,724 7,476 7,220 7,043 6,665 43 46 49 54 59 67 74 82 91 99 53 58 62 68 73 80 87 93 99 105 97 104 112 122 133 147 161 175 190 204 40 41 42 43 44 45 46 47 48 49 95,093 94,873 94,636 94,379 94,099 93,793 93,459 93,096 92,704 92,282 48,419 47,527 46,553 45,759 45,217 44,913 44,778 44,765 44,616 44,480 46,674 47,346 48,083 48,620 48,882 48,880 48,681 48,331 48,088 47,802 7,177 7,060 6,844 6,658 6,399 6,090 5,747 5,579 5,382 5,218 6,397 6,203 6,175 6,252 6,242 6,115 5,909 5,619 5,449 5,271 109 119 132 145 159 174 189 203 219 235 111 118 126 135 147 160 174 189 203 219 220 237 257 280 306 334 363 392 422 453 50 51 52 53 54 55 56 57 58 59 91,829 91,343 90,823 90,265 89,666 89,023 88,333 87,593 86,802 85,961 44,315 44,262 44,411 44,723 45,058 45,453 45,916 46,410 47,049 47,939 47,514 47,081 46,412 45,542 44,608 43,570 42,417 41,183 39,753 38,022 4,978 4,781 4,434 4,226 4,078 3,977 3,876 3,831 3,688 3,501 5,159 5,183 5,022 4,860 4,799 4,795 4,758 4,894 5,040 5,141 251 267 283 300 317 334 352 367 379 386 235 253 274 299 326 355 388 424 462 506 486 520 558 599 643 690 740 791 841 892 60 61 62 63 64 65 66 67 68 69 85,069 84,122 83,114 82,037 80,880 79,635 78,294 76,854 75,308 73,650 49,073 50,395 51,992 53,751 55,471 57,269 59,026 60,382 61,401 62,015 35,996 33,727 31,122 28,286 25,409 22,366 19,268 16,472 13,907 11,635 3,353 3,268 3,257 3,175 2,978 2,803 2,517 2,236 1,917 1,702 5,232 5,482 5,705 5,671 5,650 5,548 4,983 4,492 3,905 3,412 390 391 387 381 370 354 332 309 284 260 557 617 690 775 874 988 1,108 1,238 1,374 1,515 947 1,008 1,077 1,157 1,245 1,341 1,440 1,546 1,658 1,775 70 71 72 73 74 75 71,875 69,983 67,969 65,819 63,515 61,047 62,210 61,989 61,529 60,756 59,603 58,036 9,665 7,994 6,440 5,063 3,912 3,011 1,507 1,227 1,034 849 710 690 2,943 2,570 2,227 1,839 1,474 1,447 235 211 185 160 137 114 1,656 1,803 1,965 2,144 2,331 2,518 1,892 2,014 2,150 2,304 2,468 2,632 For explanation of notation, see appendix C. 40 (17) (18) Table A-4. Continued— Table of working life for women, 1970: Derivation of the expectation of active life for the general population Age Person years lived in each status during age x Total Inactive Active L L L Person years lived in each status beyond exact age x Total Inactive Active T T T a a X X X X X X X (20) (21) (22) (23) (24) (25) 16 17 18 19 97,553 97,494 97,429 97,362 74,309 67,143 61,887 58,346 23,244 30,351 35,542 39,016 5,912,732 5,815,179 5,717,685 5,620,256 3,715,185 3,640,876 3,573,734 3,511,846 2,197,547 2,174,303 2,143,951 2,108,410 20 21 22 23 24 25 26 27 28 29 97,294 97,223 97,151 97,077 97,001 96,923 96,843 96,760 96,674 96,584 55,444 52,787 50,923 49,891 49,585 49,653 49,977 50,636 51,506 52,386 41,850 44,436 46,228 47,186 47,416 47,270 46,866 46,124 45,168 44,198 5,522,894 5,425,600 5,328,377 5,231,226 5,134,149 5,037,148 4,940,225 4,843,382 4,746,622 4,649,948 3,453,500 3,398,056 3,345,269 3,294,346 3,244,455 3,194,870 3,145,217 3,095,240 3,044,604 2,993,098 2,069,394 2,027,544 1,983,108 1,936,880 1,889,694 1,842,278 1,795,008 1,748,142 1,702,018 1,656,850 30 31 32 33 34 35 36 37 38 39 96,490 96,389 96,281 96,164 96,037 95,897 95,743 95,575 95,392 95,195 53,153 53,648 53,796 53,595 53,073 52,356 51,527 50,586 49,682 48,851 43,337 42,741 42,485 42,569 42,964 43,541 44,216 44,989 45,710 46,344 4,553,364 4,456,874 4,360,485 4,264,204 4,168,040 4,072,003 3,976,106 3,880,363 3,784,788 3,689,396 2,940,712 2,887,559 2,833,911 2,780,115 2,726,521 2,673,447 2,621,091 2,569,564 2,518,978 2,469,296 1,612,652 1,569,315 1,526,574 1,484,089 1,441,519 1,398,556 1,355,015 1,310,799 1,265,810 1,220,100 40 41 42 43 44 45 46 47 48 49 94,983 94,755 94,508 94,239 93,946 93,626 93,278 92,900 92,493 92,056 47,973 47,040 46,156 45,488 45,065 44,845 44,772 44,691 44,548 44,398 47,010 47,715 48,352 48,751 48,881 48,781 48,506 48,209 47,945 47,658 3,594,201 3,499,218 3,404,463 3,309,955 3,215,716 3,121,770 3,028,144 2,934,866 2,841,966 2,749,473 2,420,445 2,372,472 2,325,431 2,279,276 2,233,788 2,188,723 2,143,877 2,099,105 2,054,414 2,009,866 1,173,756 1,126,746 1,079,032 1,030,679 981,928 933,047 884,267 835,761 787,552 739,607 50 51 52 53 54 55 56 57 58 59 91,586 91,083 90,544 89,966 89,345 88,678 87,963 87,198 86,382 85,515 44,289 44,336 44,567 44,891 45,256 45,685 46,163 46,729 47,494 48,506 47,297 46,747 45,977 45,075 44,089 42,993 41,800 40,469 38,888 37,009 2,657,417 2,565,831 2,474,748 2,384,204 2,294,238 2,204,893 2,116,215 2,028,252 1,941,054 1,854,672 1,965,468 1,921,179 1,876,843 1,832,276 1,787,385 1,742,129 1,696,445 1,650,282 1,603,553 1,556,059 691,949 644,652 597,905 551,928 506,853 462,764 419,770 377,970 337,501 298,613 60 61 62 63 64 65 66 67 68 69 84,596 83,618 82,576 81,459 80,258 78,965 77,574 76,081 74,479 72,763 49,734 51,193 52,872 54,611 56,370 58,147 59,704 60,892 61,708 62,113 34,862 32,425 29,704 26,848 23,888 20,818 17,870 15,189 12,771 10,650 1,769,157 1,684,561 1,600,943 1,518,367 1,436,908 1,356,650 1,277,685 1,200,111 1,124,030 1,049,551 1,507,553 1,457,819 1,406,625 1,353,753 1,299,142 1,242,772 1,184,624 1,124,920 1,064,029 1,002,320 261,604 226,742 194,318 164,614 137,766 113,878 93,061 75,191 60,001 47,231 70 71 72 73 74 75 70,929 68,976 66,894 64,667 62,281 59,731 62,100 61,759 61,143 60,180 58,819 57,155 8,829 7,217 5,751 4,487 3,462 2,576 976,788 905,859 836,883 769,989 705,322 643,041 940,207 878,107 816,348 755,205 695,026 636,207 36,581 27,752 20,535 14,784 10,296 6,834 (19) NOTE: For explanation of notation, see appendix C. 41 Table A-5. Table of working life for women, 1970: Expectation ©I active life by current labor force status Expectancies of the total population NOTE: Expectancies of persons inactive at age x Total years Inactive years Active years e . i e e Total years a i e Expectancies of persons active at age x Inactive years Active years i i e i a e Total years a e Inactive years Active years a i e a a e X X X X X X X X X (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 16 17 18 19 60.6 59.6 58.7 57.7 38.1 37.3 36.7 36.1 22.5 22.3 22.0 21.6 60.6 59.6 58.7 57.7 38.3 37.7 37.1 36.6 22.3 21.9 21.5 21.1 60.6 59.6 58.7 57.7 37.1 36.3 35.8 35.2 23.5 23.4 22.9 22.5 20 21 22 23 24 25 26 27 28 29 56.7 55.8 54.8 53.9 52.9 51.9 51.0 50.0 49.1 48.1 35.5 34.9 34.4 33.9 33.4 32.9 32.5 32.0 31.5 31.0 21.3 20.8 20.4 19.9 19.5 19.0 18.5 18.1 17.6 17.1 56.7 55.8 54.8 53.9 52.9 51.9 51.0 50.0 49.1 48.1 36.1 35.7 35.3 34.9 34.5 34.1 33.7 33.2 32.7 32.2 20.7 20.1 19.6 19.0 18.4 17.9 17.3 16.8 16.4 15.9 56.7 55.8 54.8 53.9 52.9 51.9 51.0 50.0 49.1 48.1 34.6 34.0 33.5 32.9 32.3 31.8 31.2 30.7 30.1 29.5 22.1 21.7 21.4 21.0 20.6 20.2 19.8 19.4 19.0 18.6 30 31 32 33 34 35 36 37 38 39 47.2 46.2 45.3 44.3 43.4 42.4 41.5 40.6 39.6 38.7 30.5 29.9 29.4 28.9 28.4 27.9 27.4 26.9 26.4 25.9 16.7 16.3 15.8 15.4 15.0 14.6 14.1 13.7 13.3 12.8 47.2 46.2 45.3 44.3 43.4 42.4 41.5 40.6 39.6 38.7 31.7 31.2 30.7 30.2 29.7 29.3 28.9 28.4 28.0 27.7 15.5 15.0 14.6 14.1 13.6 13.1 12.6 12.1 11.6 11.1 47.2 46.2 45.3 44.3 43.4 42.4 41.5 40.6 39.6 38.7 29.0 28.4 27.8 27.2 26.7 26.1 25.6 25.1 24.5 24.0 18.2 17.8 17.5 17.1 16.7 16.3 15.9 15.5 15.1 14.7 40 41 42 43 44 45 46 47 48 49 37.8 36.9 36.0 35.1 34.2 33.3 32.4 31.5 30.7 29.8 25.5 25.0 24.6 24.2 23.7 23.3 22.9 22.5 22.2 21.8 12.3 11.9 11.4 10.9 10.4 9.9 9.5 9.0 8.5 8.0 37.8 36.9 36.0 35.1 34.2 33.3 32.4 31.5 30.7 29.8 27.3 26.9 26.5 26.2 25.8 25.5 25.1 24.8 24.4 24.1 10.5 10.0 9.5 8.9 8.3 7.8 7.3 6.7 6.2 5.7 37.8 36.9 36.0 35.1 34.2 33.3 32.4 3T.5 30.7 29.8 23.6 23.1 22.7 22.3 21.8 21.4 20.9 20.5 20.0 19.6 14.2 13.8 13.3 12.8 12.4 11.9 11.5 11.1 10.6 10.2 50 51 52 53 54 55 56 57 58 59 28.9 28.1 27.2 26.4 25.6 24.8 24.0 23.2 22.4 21.6 21.4 21.0 20.7 20.3 19.9 19.6 19.2 18.8 18.5 18.1 7.5 7.1 6.6 6.1 5.7 5.2 4.8 4.3 3.9 3.5 28.9 28.1 27.2 26.4 25.6 24.8 24.0 23.2 22.4 21.6 23.7 23.4 23.0 22.6 22.1 21.7 21.2 20.8 20.3 19.8 5.2 4.7 4.3 3.8 3.4 3.1 2.7 2.4 2.1 1.8 28.9 28.1 27.2 26.4 25.6 24.8 24.0 23.2 22.4 21.6 19.2 18.8 18.4 18.1 17.7 17.3 17.0 16.7 16.3 16.0 9.7 9.2 8.8 8.3 7.9 7.4 7.0 6.5 6.0 5.6 60 61 62 63 64 65 66 67 68 69 20.8 20.0 19.3 18.5 17.8 17.0 16.3 15.6 14.9 14.3 17.7 17.3 16.9 16.5 16.1 15.6 15.1 14.6 14.1 13.6 3.1 2.7 2.3 2.0 1.7 1.4 1.2 1.0 .8 .6 20.8 20.0 19.3 18.5 17.8 17.0 16.3 15.6 14.9 14.3 19.2 18.7 18.1 17.6 17.0 16.4 15.8 15.2 14.6 14.0 1.5 1.3 20.8 20.0 19.3 18.5 17.8 17.0 16.3 15.6 14.9 14.3 15.6 15.3 14.9 14.5 14.1 13.6 13.1 12.6 12.1 11.6 5.2 4.7 4.4 4.0 3.7 3.4 3.2 3.0 2.8 2.6 70 71 72 73 74 75 13.6 12.9 12.3 11.7 11.1 10.5 13.1 12.5 12.0 11.5 10.9 10.4 .5 .4 .3 .2 .2 .1 13.6 12.9 12.3 11.7 11.1 10.5 13.4 12.8 12.2 11.6 11.0 10.5 13.6 12.9 12.3 11.7 11.1 10.5 11.1 10.7 10.3 10.0 9.7 9.7 2.4 2.2 2.0 1.7 1.4 .8 For explanation of notation, see appendix C. 42 1.1 .9 .8 .6 .5 .4 .3 .3 .2 .2 .1 .1 .1 .1 Table A-6. Table of working life for women, 1970: Indexes of labor fore® accession and separation Annual population-based rates of labor force mobility Events per person at risk during interval Events per person alive at exact age x Events remaining per person entering interval Age Accessions i x to x+4 5 NOTE: x (2) (D 16-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75 + a M 0.2041 .1646 .1022 .0907 .0837 .0723 .0603 .0497 .0433 .0389 .0294 .0160 .0116 Total separations Voluntary separations ( i,d ) a x 5 a M 5 (3) 0.1498 .1501 .1097 .0917 .0765 .0676 .0633 .0584 .0607 .0719 .0629 .0359 .0620 i M x (4) 0.1496 .1497 .1093 .0912 .0756 .0662 .0611 .0553 .0565 .0672 .0588 .0331 .0601 Net moves ■ <.,d ) Accessions ( lx ,i) M 5 x x (6) 0.8153 .8213 .5099 .4521 .4167 .3590 .2987 .2450 .2120 .1884 .1403 .0741 .0113 For explanation of notation, see appendix C. ( lx ,a ) M 5 (5) 0.0543 .0145 -.0076 -.0011 .0072 .0047 -.0029 -.0087 -.0174 -.0330 -.0334 -.0199 -.0504 a Total separations 43 ( i,d ) Accessions per inactive person i M 5 x (7) 0.5984 .7491 .5476 .4574 .3808 .3358 .3133 .2879 .2971 .3487 .2998 .1667 .0606 Total separations per active person a a x 5 ( i,d ) m m 5 (8) 0.3040 .3091 .1945 .1633 .1581 .1473 .1255 .1007 .0805 .0605 .0369 .0175 .0121 Accessions i a E Voluntary separations a i E x X X (9) (10) (11) 0.4557 .3210 .2312 .2062 .1625 .1327 .1219 .1154 .1315 .2008 .3089 .4028 1.4367 4.3997 3.5937 2.7828 2.2829 1.8416 1.4380 1.0940 .8123 .5852 .3905 .2159 .0837 .0113 4.4883 3.9009 3.1654 2.6314 2.1895 1.8298 1.5218 1.2455 1.0036 .7608 .4644 .2037 .0588 Appendix B. The Conwentiofnall WotrEsBirag) Life Table Viewed from the vantage point of the 1980’s, the con ventional working life table seems to rest on several un warranted assumptions. Among these are the following: © That age-specific labor force participation rates never change. o That in any birth cohort, all members who will ever work have entered the labor force before any voluntarily withdraw. © That every man enters and leaves the labor force only once. © That all entries and exits of women are due to changes in marital or parental status, and that apart from final retirement they occur for no other reason. © (In a separate portion of the model) that the mari tal and parental status of women is fixed for life. However questionable they may seem, none of these assumptions was introduced arbitrarily. Each performs a specific function in the conventional worklife model. The following discussion should clarify why these as sumptions are necessary to that model, and how they affect its outcome. Actuarial Sables; The prototype f@r worklif© models The purpose of an actuarial or “life” table is to illus trate the long-term implications of prevailing mortality rates. The first such table was published in 1693, making this the oldest demographic model in use today.1 Life tables translate the mortality rates of a real population into average life expectancy values for a model popula tion. The expectancy function indicates how much longer the typical x-year-old would live, given no change in agespecific death rates during his or her lifetime. The basic life table functions are shown in table B-l. These functions underlie not only actuarial, but also working life tables. A quick review of their interrelation ships will facilitate the discussion which follows. corresponding base population during the reference year. 3. These age-specific mortality rates do not change over time. Every birth cohort loses the same number of mem bers as it passes through the age inter val X to X + 1. 4. Each birth cohort is a closed popula tion: Entrances occur only at birth, exits only through death. There are no migrants. 5. In the population as a whole, deaths exactly offset births. The size of the total population and the numbers in each age group are constant over time. Every life table rests on this same set of assumptions, differing only with respect to the specific mortality rates introduced. Because there are no immigrants or emigrants in this stationary world, the age structure of this standard pop ulation is completely determined by the age pattern of deaths. Population and vital statistics from the reference population are used to develop a schedule of death rates, denoted m vfor any age x. These are computed as: where: Dx - deaths of persons age x during a given year Px - midyear population of persons age x during the same reference year. The popular convention for identifying age is to cite the age reached at one’s last birthday. Consequently, in survey or vital statistics, the average “x year old” is actu ally x+ .5 years of age. Thus the observed rate is really a “central death rate,” describing the incidence of deaths between the ages of x + .5 and x + 1.5. Life tables model changes in behavior from one exact age to the next, or from age x to age x + 1. Central death rates are centered on the appropriate interval, and there by converted into life table mortality rates, denoted q , using the following formula: The stationary population. Central to all life table meth odology is the concept of a stationary population. This hypothetical population is characterized by several im portant features: ASSUME: 1. That each year 100,000 persons of the same sex are born into this population. 2. Each birth cohort lives through its lifespan, at every age facing age-spe cific mortality risks observed in the 44 2m = q x ----------- 2 —m (2) The life table mortality rates are displayed in column 1 of table B-l. These rates are applied sequentially to survivors of a birth cohort of 100,000 to “age” it through its lifespan until the last remaining member dies. In the life table, the function lx represents survivors alive at the beginning of each age. Deaths in that age group, denoted dx, are the product of these survivors and the probability of death during the interval: at that age. Those who die during the age are assumed to live an average of a half-year. Hence Lx quantifies not only the average number of persons alive in the age group, but also total person years lived by the group passing through that age. It is this time interpretation which enables us to esti mate the average life expectancy.3 The Lx function can be summed from any given age to the end of the table, to determine the collective number of years left to be lived by the birth cohort now aged x. Symbolically, Tx or remain ing person years of life at age x is computed as: T x = + Life expectancy. The expectation of life at age x is then simply the average number of years remaining to be lived per person alive at the beginning of the age. Figure B-l shows these functions graphically. Points along the descending survivorship curve represent sur vivors to each exact age (l*), and within the corresponding Repeating this process for each pair of ages, the life table generates a profile of survivors (1*) from a schedule of events (dx). The lx function has as its time reference the beginning of each age. For many purposes it is useful to look at survivors to the middle of each age, Lx. This function is a simple variant of the \x value, recentered on age x + .5. Assuming that deaths are evenly distributed throughout the age, half should have occurred by the midpoint of the interval.2 Therefore the average number of “x year olds” should be: ( L + lX + 1 Figure B-1. Life table functions, men, 1977 Stationary population (5) Both the lx and the Lx functions describe the stationary population. They differ only with respect to precise age reference. The Lx function is especially powerful, because it lends itself to multiple interpretations. It is first of all a.popula tion function, indicating the number of cohort survivors alive during each successive age interval. As such it pro vides a longitudinal profile of the cohort’s life experience. But, in an unchanging population, the number of persons alive in each age group is permanently fixed. Hence, Lx is also a cross-sectional profile of the full stationary popula tion at any given moment. Perhaps its most interesting application is as a measure of time. Each individual who survives through an age is said to live / person year o f life L (4) lx + • = ■ (3) = >x Deaths are subtracted from persons alive at the be ginning of the age to determine persons alive at the be ginning of the next age: + E age = 85 + 45 age interval (L*.). The area beneath the curve represents time lived by the surviving population. The heavily shaded area represents person years lived by the cohort passing through the xth interval, (L*). The entire shaded area denotes years left to be lived by the group beyond that exact age, (Tx). This calculation is possible because of the restrictive nature of the stationary population. It is closed to entries beyond birth. Everyone who will live beyond a given age is alive and counted at that precise age. Remaining person years are directly attributable to these persons. Tables of Working Life for Men, based on the labor force participation rates observed in 1940 and 1947 (48). The working life table grafted labor force participation rates (themselves new data) onto the stationary popula tion, to obtain a stationary labor force from which to esti mate worklife expectancies. The objectives were initially modest. BLS economists intended the model to reveal trends in old-age dependency, to show the impact of age structure on labor force replacement needs, and to meas ure rates of labor force growth. The expectancy values would serve as “social indicators,” documenting change. Wolfbein’s study warned that: “the table of working life... shows what might be expected for men of a given age, if the prevailing rates of mortality and of labor force partici pation should remain unchanged over their life span. Like the standard life table, it is not a forecast of future trends.” Users quickly overlooked this caveat. Because there were no official forecasts of individual work duration, the worklife expectancy index quickly filled that void. Today their primary use is in the estimation of lost earnings asso ciated with liability claims. This application takes the index well beyond its intended meaning, and assumes a higher degree of accuracy than was initially claimed. Pres sure from a growing forensic market has stimulated con tinual research in this area, and has led to many modifica tions and extensions of the model. The Department of Labor has published working life tables for both sexes, based on decennial census activity rates for 1940,1950, and 1960(7,8,9,11). The accelerated pace of change in these rates first led to mid-decade estimates, based on Current Population Survey (CPS) data in 1968 (4). Pooled CPS data for 1969 to 1971 formed the basis for the 1970 tables of working life (6). The basic worklife model has been used to explore a variety of labor force issues. Garfinkle employed it to examine trends in worklife duration since 1900, and—in conjunction with CPS data—to examine patterns of job mobility (9, 10). Fullerton adapted the model to real cohort data in his Generational Working Life Tables (5). He also used it to explore the implications of projected labor force participation rates.4 Although potential applications are numerous, a growing disparity between patterns of behavior described in the original model and those observed in real populations has prevented full exploitation of these tables. Three key life table functions. The three key variables in the basic life table are: 1) Tx , person years of life left to be lived beyond exact age x, 2) lx, the number of persons who will collectively live these years and 3) qx, the rate of withdrawal from the life table population through death. The ratio of the first two establishes life expectancy for members of the stationary population. The third is an index of mobility between alternative states (i.e., alive or dead). Evolution ©f the working Site table Although this relationship between events and time (i.e., deaths and life expectancy) was modeled nearly three centuries ago, it remains the basis for life table estimation today. Until the middle of the 20th century, researchers saw no connection between the actuarial model and labor force issues. It could be argued that it had no relevance until the human lifespan lengthened sufficiently, and the economic support system broadened enough, to facilitate retire ment. Until that time, life and worklife expectancies were nearly identical. During the early part of this century, the character of work patterns in the United States began to change. Life expectancies increased, and with them the size of the older population. The advent of social security and pension programs enabled older workers to withdraw from the job market voluntarily. Life and worklife expectancies began to diverge. Labor analysts found the “gainful worker” concept— which implied that the individual’s work status was per m anent-obsolete. They shifted their attention to “labor force” variables, measuring behavior at a specific point in time. Working life tables emerged in response to the same considerations. In 1938, Woytinsky, who was concerned with the “old age dependency problem,” used gainful worker data to develop the first estimates of “expected period of work.” (See Bibliography, entry 60.) A decade later, Durand employed the newer concept to measure the “average number of years in the labor force” (2). The connection between these indexes and life tables was finally bridged by Seymour Wolfbein of the Bureau of Labor Statistics in 1950. In that year, BLS released its first Mechanics @f? to® conventions! working Site table The conventional working life table for men for 1977 appears as table B-2. This male model is a direct extension of the actuarial model, with objectives and terms parallel ing those in the basic life table. There are two distinct sec tions to the actuarial table. One deals with mobility rates between life statuses (i.e., alive or dead), while the second deals with life expectancy. The worklife model also has two sections, one focusing on rates of labor force mobility and a second on worklife expectancies. In the convention al working life table, these two sections are independent 46 of one another, resting on somewhat contradictory as sumptions about labor force behavior. However, both build on the premises that: ASSUME: 6. The age-specific labor force participa tion rates observed in the base popula tion during the reference period (de noted w^) accurately reflect a. the individual’s probability of labor force attachment at each age x, and b. the average portion of the year spent in the labor force by per sons alive at age x. Assuming these to be true, a complete worklife model can be derived from the schedule of activity and death rates observed in the real world. The basic life table functions of table B-l are repeated in the first eight columns of the working life table. How ever, the death function, d*, and the mortality rate, qx, also appear in a new form. Whereas the life table ex pressed these functions as changes between birthdays (dx = \x - l^+i), the conventional model restates them (and other functions) in terms of changes between age groups (Dx - L x - L^+j). Actual worklife functions begin in column 10. The population of interest in this model is the stationary labor force. It follows from assumption 6a above that this labor force must be the product of survivors to any given age and the corresponding age-specific activity rate (w*). Just as there are two survival functions, 1* and L*, there are also two labor force functions, lwx and Lw*. At exact age , w x = , x ' v>x ing continuously active from entry until permanent retirement or death. 8. That in any given birth cohort, movement into or out of the labor force is basically unidirectional. Prior to the age of peak labor force involvement, men enter but do not voluntarily withdraw. (A few die.) After that age, workers retire or die, but none reenters the job market. (8) whereas in the age interval x to x + 1: Lwx = L x *w x' (9) Labor force mobility rates o f men. With the addition of a third premise, these assumptions establish a stationary (i.e., unchanging) labor force. This premise is: ASSUME: 9. That the rate of labor force participa tion at each age is constant over time. In an unchanging world, the Lw* curve of figure B-2 can be interpreted both as a cross-section of the entire labor force, and as a lifetime activity profile for a single birth cohort. Playing these two interpretations against one another, estimates of the net flow of workers into and out of the labor force are derived from cross-sectional comparisons of the stock of workers at successive ages. (Flows are not estimated from data on observed changes in labor force status.) For young male workers, columns 21 through 28 illus trate the estimation procedure for labor force mobility As figure B-2 illustrates, the activity rate function w* is parabolic. When multiplied by the monotonic survival functions, it produces stationary labor force values which are also parabolic in form. That is, although the popula tion as a whole gains no entrants except through birth, the stationary labor force acquires its entire membership after the age of 16. In its phase of expansion, it is an open labor force. In fact, designers of the model constrained it to a limited entry labor force by making the following assumptions: ASSUME: 7. That there is no turnover of male workers. Every man who enters the labor force does so only once, remain 47 rates. In this limited entry labor force, all age-to-age increases in the Lwx function are interpreted as net acces sions to the labor market. Since it is assumed that all workers are active before any begin to retire and that there are no reentries once retirements commence, net entries (A* ) are completed at the age of peak labor force attachment. The conventional model makes no attempt to measure gross flows into or out of the labor market. However, in the age range of labor force expansion, the estimate of accessions includes a replacement term for young workers who have died while active, D*. shows two forms of labor force loss: Death and retire ment. Each is measured between age intervals, paralleling the Q* term. Separation functions are integrated into the notational system as follows: A * - ( L w x+l - L w x) + D™ From the age of peak labor force involvement to the end of the lifespan, the Lwx function gradually declines. All age-to-age drops are interpreted as labor force separa tions. 1 ' i ' Qsx = rate of total labor force separations between age intervals x and x+1 Q dx - rate of separations due to death, and Qx =rate of separations due to permanent retirement. ( 10) i The replacement term is simply the product of active persons multiplied by the probability of dying. S x = <L w x ~ L w x+\> Dw x L w (15) (ii) The ratio of these separations to persons alive and active in the interval is the corresponding separation rate. In the age range of net labor force entries, deaths are the only permissible form of labor force separations, S*. Therefore: (16) ( 12) For the same reason, the labor force separation rate (Q p at pre-peak ages is exactly equal to the death rate for the same age. (13) The rate of labor force entries (A*) is computed as a ratio of entries to persons alive in the given age range: For older men — beyond the peak age of labor force involvement — the stationary labor force changes from an expanding to a contracting body. The way in which it con tracts resembles, but is more complex than, the contrac tion process for the population as a whole. Recall that, in the actuarial model, population losses occurred only through death. The rate of such losses was denoted qx (for events between birthdays) or Q* (between age intervals). Among older workers, the worklife model 48 Since the denominator of this ratio includes everyone at risk of leaving the labor force in the interval, Q p s also the probability of labor force separation. By definition, total separations (S*) are the sum of deaths of workers (D*) and retirements (R*). Once the appropriate separation and death rates are established, the retirement rate follows as a residual. Because we have no statistical evidence to the contrary, it is assumed that: ASSUME: 10. The age-specific death rate for per sons in the labor force is the same as that for the population as a whole. The death rate of workers is a ratio of events (i.e., deaths of workers) to persons at risk of this event (i.e., the active population). However, certain members of the active population are not at risk of death, while working for the full year. Assuming retirements to be evenly spaced over the interval, the average retiree would be at risk of so doing for just half of the year during which he or she re tired. Therefore the rate of deaths among workers, Q^, is: D Xw (17) For the same reason, the rate of retirement, Qr, ex cludes half of the workers who die during the interval from the “at risk” base: Qx where: RX r L wX .5 D Xw (18) Al% = accession of women age x, due to the loss of a husband Lhx - the stationary population of women age x with a husband present W°+i = the activity rate of women in all other marital statuses at age x+1 W% - the activity rate of women age x with husbands present. Solving algebraically, the computational formulas for these two probabilities are: d Qx Q x ( 2 - Q x) , and (19) 2~QX The other formulas used to estimate female labor force accessions are outlined in the Tables o f Working Life fo r Women, 1950 (7). The three separate estimates of entry by cause are combined to arrive at a model estimate of the total number of labor force entries for women of the given age. Similarly, for separations, differential rates of labor force participation are used to infer numbers of labor force withdrawals associated with marriage, childbear ing, retirement, and death. For example, separations due to childbirth would be estimated as: Q rx = Q sx - Q dx -(20) Labor force mobility rates o f women. The assumption of continuous labor force attachment was never well suited to estimates of female labor force behavior. Therefore the designers of the model devised an alternative procedure for quantifying female labor force entries and exits: ASSUME: 11. That women may enter (or reenter) the labor force in response to any of the following demographic changes in their lives: Their own aging, that of their children (reaching school age), or the loss of a husband. 12. That women may leave the labor force temporarily or permanently for any of the following reasons: Mar riage, the birth of a first child, retire ment, or death. Under these conditions, rates of entry and withdrawal depend not only on age — the motivating factor for men — but also on changes in marital and parental status, and corresponding status differentials in the propensity to work. The conventional model for women estimates the number who flow between various marital and parental groupings, from one age to the next. The groups consid ered are the never-married; the ever-married (never a mother); the ever-married (children under 5); the ever-married (no children under 5); and the separated, widowed, and divorced. Transitions between these states carry with them certain implied probabilities of labor force entry or withdrawal. In regard to accessions, the model identifies just three situations associated with a woman’s entry into the labor force: Her own age, the age of her children, and the loss of a husband. There exists some differential in labor force participation between the age/ status group from which a woman passes and that into which she moves. The num ber of transitions between these two states is weighted by the magnitude of this differential to infer total changes in labor force status. For instance, in the case of a loss of a husband: A lhx = ( Lx ) ( l - Q x) * W°x + i - W j f mc<5 x+1' lym cn ( 22) where: C Sx = separations due to childbearing among women age x BRX - the birth rate for the married, nevermother population age x W y^5 = the activity rate for ever-married wo men with children under 5 years of age, when they themselves are age x WT f cn = the activity rate for ever-married wo men with no children. Here, too, the various types of exits are summed to determine the number of women who leave the job mar ket at each age. As these equations suggest, the conventional model is both more complex and more demanding of data for women than it is for men. In both cases the flow of work ers is estimated from cross-sectional comparisons of stocks of workers in successive age groups. However, because of the difference in procedures used, estimates for women are not directly comparable with those for men. The average worklife expectancy o f the population. The limited entry labor force variable lw* is useful not only in (21) 49 activity. Thus the average worklife expectancy for any person surviving to exact age x is simply: the study of accessions, but also as a clue to the average worklife duration of the total population. Recall that life expectancy is a ratio of total years of life remaining to the persons at risk of living them (equation 7, above). The worklife model includes a similar ratio, the worklife ex pectancy of the population alive at age x.s In both in stances the base of the ratio over which time is to be aver aged is persons alive at the beginning of the appropriate age, 1*. The numerator of the worklife ratio is an extension of the T* concept introduced above. Just as a person living through the year contributes 1 person year of life to the group total, a worker surviving the year in the labor force contributes 1 person year of work. Lx summarizes person years of life lived by the group in the interval, Lw* the aggregate worklife experience of the age. The latter func tion is summed from any age x to the end of the table to derive Tw*, total person years of work remaining to be lived by the group in its lifetime. The worklife expectancy of the typical person age x, ew*, is then a simple average. T wx ew = ------ years- (23) The worklife expectancy o f the active population: The closed stationary labor force. Courtroom applications of these data frequently involve adults who have or have not been working. When serious injury cuts short a worker’s economically active life, users normally want to identify a more focused value — the worklife expectancy of active persons. This index is computed by relating total worktime re maining, the Tw* function, to persons likely to work now or in the future. In life table terms, the worklife expectancy of the active population is: T w e w ' = ----- - • /w (24) X Beyond the age at which participation rates peak and net accessions end (e.g., 34 in figure B-4), the calculation is straightforward. The denominator lwx includes every one who will ever work again, and the ratio is substantive ly meaningful. The procedure is shown graphically in figure B-3. The stationary population (\x) is comprised of two groups: Those active at age x (lw*) and those not active at that age Ox - lw*). As a typical birth cohort passes through its lifespan, it traces out the labor force curve shown in figure B-3. Between any age x and the end of that lifespan, mem bers of the group will live Tw* person years of economic 50 However, the same ratio makes less sense when applied to the pre-peak ages. For instance, at age 18 many of the eventual workers (lw3 4 - lwis) are not yet active. The total worktime circumscribed by the Lw curve beyond this age (abed) includes a large component of worktime (abc) to be contributed by persons still outside the labor force. Computing a ratio of work years remaining (the entire shaded area Twig) to persons actually in the labor force at 18, lwig, would necessarily overstate the average duration of active life for this group. The numerator and denomi nator must be reconciled before a meaningful average can be computed for these younger workers. The developers of the worklife model reconciled the two by devising a “closed labor force” variable, lw'*. This “closed” labor force was defined to include everyone who would ever work during his or her lifetime. ' ASSUME: 13. That every person who will eventual ly work can be identified as a member of the “closed” labor force from age 16 until the age of permanent retire ment or death. Assumption 8 implied that nearly every member of the ever-active population would be working simultaneously at the age of peak labor force attachment. If one accepts this premise, it is a simple matter to survive the peak labor force backward to age 16. This is done by multiplying the peak participation rate, w* by survivors to each pre-peak age. The product, lw* is an estimate of the “closed labor force,” or the eventually active population (figure B-5). The Lw'* and Tw* functions follow directly from lw'*. For pre-peak ages6 equation 24 is restated as: ew ' X (25) Closing the stationary labor force in this way resolves the conflict between terms in equation 24. The adjusted functions are now read from a smoothly descending sur vivorship curve. Worktime is now averaged over the model’s best estimate of the number responsible for these years of economic activity. This solution imposes a clear order on the data. It does not, however, guarantee good worklife estimates for ac tive young men. In modifying both the numerator and the denominator of equation 24, it is not clear how the ratio has been affected. The lw* and Lw* values have been in flated (from ac to be in figure B-6). At age 18 this means ab inactive men added to the ever-active population. The shift to the Lw* function means thatTw * is also inflated. At age 18, Tw'ig includes abc additional person years of labor force attachment, “work years” which don’t really occur. The shifts in lw* and Tw* need not— and prob51 Tabi© B-1. Interpolated abridged life table for men, 1977 Age d) Deaths between exact ages x and x+1 Stationary population in age X Stationary population at exact age x q i d Mortality rate at exact age X X X (2) (3) (4) 0 1 2 3 4 5 6 7 8 9 0.01586 .00104 .00080 .00064 .00054 .00048 .00045 .00041 .00037 .00032 10 11 12 13 14 15 16 17 18 19 X Person-years of life remaining at age x Life expectancy of the population L T e X (5) X X (6) (7) 100,000 98,414 98,312 98,233 98,170 98,117 98,069 98,025 97,984 97,948 1,586 102 79 63 53 48 44 41 36 31 98,606 98,361 98,270 98,200 98,142 98,095 98,048 98,007 97,968 97,934 6,932,304 6,833,698 6,735,337 6,637,067 6,538,867 6,440,725 6,342,630 6,244,582 6,146,575 6,048,607 69.3 69.4 68.5 67.6 66.6 65.6 64.7 63.7 62.7 61.8 .00028 .00028 .00036 .00053 .00077 .00105 .00130 .00152 .00168 .00179 97,917 97,890 97,863 97,828 97,776 97,700 97,598 97,471 97,323 97,159 27 27 35 52 76 102 127 148 164 174 '.97,900 §7,873 97,841 97,798 97,735 97,650 97,536 97,398 97,242 97,073 5,950,673 5,852,773 5,754,900 5,657,059 5,559,261 5,461,526 5,363,876 5,266,340 5,168,942 5,071,700 60.8 59.8 58.8 57.8 56.9 55.9 55.0 54.0 53.1 52.2 20 21 22 23 24 25 26 27 28 29 .00190 .00200 .00207 .00208 .00205 .00201 .00197 .00193 .00190 .00188 96,985 96,801 96,607 96,407 96,207 96,010 95,817 95,628 95,444 95,263 184 194 200 200 197 193 189 184 181 179 96,892 96,704 96,506 96,307 96,108 95,913 95,723 95,536 95,353 95,173 4,974,627 4,877,735 4,781,031 4,684,525 4,588,218 4,492,110 4,396,197 4,300,474 4,204,938 4,109,585 51.3 50.4 49.5 48.6 47.7 46.8 45.9 45.0 44.1 43.1 30 31 32 33 34 35 36 37 38 39 .00186 .00186 .00189 .00197 .00208 .00222 .00239 .00257 .00277 .00300 95,084 94,907 94,730 94,551 94,365 94,168 93,958 93,734 93,493 93,234 177 177 179 186 197 210 224 241 259 279 95,002 94,824 94,647 94,464 94,272 94,065 93,849 93,616 93,366 93,097 4,014,412 3,919,410 3,824,586 3,729,939 3,635,475 3,541,203 3,447,138 3,353,289 3,259,673 3,166,307 42.2 41.3 40.4 39.4 38.5 37.6 36.7 35.8 34.9 34.0 40 41 42 43 44 45 46 47 48 49 .00325 .00355 .00388 .00425 .00467 .00512 .00562 .00618 .00681 .00751 92,955 92,653 92,324 91,966 91,575 91,147 90,680 90,170 89,613 89,002 302 329 358 391 428 467 510 557 611 668 92,801 92,486 92,142 91,768 91,358 90,904 90,415 89,882 89,298 88,658 3,073,210 2,980,409 2,887,923 2,795,781 2,704,013 2,612,655 2,521,751 2,431,336 2,341,454 2,252,156 33.1 32.2 31.3 30.4 29.5 28.7 27.8 27.0 26.1 25.3 50 51 52 53 54 55 56 57 58 59 .00828 .00910 .00995 .01081 .01171 .01263 .01366 .01491 .01647 .01826 88,334 87,603 86,805 85,941 85,012 84,016 82,954 81,821 80,601 79,274 731 798 864 929 996 1,062 1,133 1,220 1,327 1,448 87,976 87,212 86,380 85,484 84,522 83,459 82,361 81,185 79,911 78,523 2,163,498 2,075,522 1,988,310 1,901,930 1,816,446 1,731,924 1,648,465 1,566,104 1,484,919 1,405,008 24.5 23.7 22.9 22.1 21.4 20.6 19.9 19.1 18.4 17.7 60 61 62 63 64 65 66 67 68 69 .02026 .02231 .02429 .02611 .02783 .02958 .03154 .03388 .03675 .04013 77,826 76,250 74,549 72,738 70,839 68,867 66,830 64,722 62,530 60,232 1,576 1,701 1,811 1,899 1,972 2,037 2,108 2,192 2,298 2,417 77,024 75,386 73,629 71,775 69,839 67,811 65,740 63,589 61,344 58,986 1,326,485 1,249,461 1,174,075 1,100,446 1,028,671 958,832 891,021 825,281 761,692 700,348 17.0 16.4 15.7 15.1 14.5 13.9 13.3 12.8 12.2 11.6 c- 52 Table B-1. Continued— Interpolated abridged life table for men, 1977 Deaths between exact ages x and x + 1 Stationary population in age X Stationary population at exact age x q I d L X X 70 71 72 73 74 75 76 77 78 79 0.04377 .04761 .05184 .05649 .06156 .06703 .07286 .07900 .08539 .09195 57,815 55,284 52,652 49,923 47,103 44,203 41,240 38,235 35,214 32,207 2,531 2,632 2,729 2,820 2,900 2,963 3,005 3,021 3,007 2,961 80 81 82 83 84 85 .09852 .10487 .11057 .11497 .11702 1.00000 29,2,46 26,385 23,600 20,990 18,577 16,403 2,881 2,765 2,610 2,413 2,174 16,403 Age X NOTE: Mortality rate at exact age X For explanation of notation, see appendix C. X X Person-years of life remaining at age x Life expectancy of the population T e X X 56,454 53,873 51,192 48,417 45,557 42,644 39,660 36,647 33,633 30,649 641,362 584,908 531,035 479,843 431,426 385,869 343,225 303,565 266,918 233,285 11.1 10.6 10.1 9.6 9.2 8.7 8.3 7.9 7.6 7.2 27,885 25,062 22,375 . 19,863 17,570 89,881 202,636 174,751 149,689 127,314 107,451 89,881 6.9 6.6 6.3 6.1 5.8 5.5 SOURCE: U.S. Department of Health and Human Services, National Center for Health Statistics, Division of Vital Statistics. 53 TabS© B-2. TabS® @f working Bif@ for men, 1977: Conventional model Age X Mortality rate at exact age X q Deaths of X At exact age x Within age x I L X year olds D X X X (2 ) (D Stationary population (3) (4) (5) 16 17 18 19 0.00130 .00152 .00168 .00179 97,598 97,471 97,323 97,159 97,536 97,398 97,242 97,073 138 156 169 181 20 21 22 .00190 .0 0 2 0 0 96,985 96,801 96,607 96,407 96,207 96,010 95,817 95,628 95,444 95,263 96,892 96,704 96,506 96,307 96,108 95,913 95,723 95,536 95,353 95,173 .00239 .00257 .00277 .00300 95,084 94,907 94,730 94,551 94,365 94,168 93,958 93,734 93,493 93,234 .00325 .00355 .00388 .00425 .00467 .00512 .00562 .00618 .00681 .00751 Mortality rate for persons at age x Person years of life remaining at age x Life expectancy of the population (in years) Q T e X (6 ) X X (7) (8 ) 0.00141 .00160 .00174 .00186 5,363,876 5,266,340 1,698,942 1,811,700 55.0 54.0 53.1 52.2 188 198 199 199 195 190-187 183 180 171 .00194 .00205 .00206 .00207 .00203 .00198 .00195 .00192 .00189 .00180 1,884,627 1,987,735 1,991,031 1,994,525 1,958,218 1,902,110 1,876,197 1,830,474 1,804,938 1,719,585 51.3 50.4 49.5 48.6 47.7 46.8 45.9 45.0 44.1 43.1 95,002 94,824 94,647 94,464 94,272 94,065 93,849 93,616 93,366 93,097 178 177 183 192 207 216 233 250 269 296 .00187 .00187 .00193 .00203 .00230 .00248 .00267 .00288 .00318 1,784,412 1,779,410 1,834,586 1,929,939 2,075,475 2,161,203 2,337,138 2,503,289 2,699,673 2,966,307 42.2 41.3 40.4 39.4 38.5 37.6 36.7 35.8 34.9 34.0 92,955 92,653 92,324 91,966 91,575 91,147 90,680 90,170 89,613 89,002 92,801 92,486 92,142 91,768 91,358 90,904 90,415 89,882 89,298 88,658 315 344 374 410 454 489 533 584 640 682 .00339 .00372 .00406 .00447 .00497 .00538 .00590 .00650 .00717 .00769 3,153,210 3,440,409 3,747,923 4,105,781 4,544,013 4,892,655 5,331,751 5,841,336 6,401,454 6,822,156 33.1 32.2 31.3 30.4 29.5 28.7 27.8 27.0 26.1 25.3 .00828 .00910 .00995 .01081 .01171 .01263 .01366 .01491 .01647 .01826 88,334 87,603 86,805 85,941 85,012 84,016 82,954 81,821 80,601 79,274 87,976 87,212 86,380 85,484 84,522 83,459 82,361 81,185 79,911 78,523 764 832 896 962 63 98 176 274 388 499 .00868 .00954 .01037 .01125 .01258 .01316 .01428 .01569 .01737 .01909 7,643,498 8,325,522 8,968,310 9,621,930 10,636,446 10,981,924 11,768,465 12,746,104 13,884,919 14,995,008 24.5 23.7 22.9 77,826 76,250 74,549 72,738 70,839 68,867 66,830 64,722 62,530 60,232 77,024 75,386 73,629 71,775 69,839 67,811 65,740 63,589 61,344 58,986 638 757 854 936 28 71 151 245 358 532 .02127 .02331 .02518 .02697 .02904 .03054 .03272 .03530 .03844 .04293 16,386,485 17,579,461 18,544,075 19,360,446 20,288,671 20,718,832 21,511,021 22,455,281 23,581,692 25,320,348 17.0 16.4 15.7 15.1 14.5 13.9 13.3 69 .02026 .02231 .02429 .02611 .02783 .02958 .03154 .03388 .03675 .04013 70 71 72 73 74 75 .04377 .04761 ..05184 .05649 .06156 .06703 57,815 55,284 52,652 49,923 47,103 44,203 56,454 53,873 51,192 48,417 45,557 42,644 581 681 775 860 913 984 .04572 .04977 .05421 .05907 .06394 .06997 25,811,362 26,814,908 27,751,035 28,609,843 29,131,426 29,845,869 11.1 1 0 .6 10.1 .00207 .00208 .00205 23 24 25 26 27 28 29 .00201 .00197 .00193 .00190 .00188 30 31 32 33 34 35 36 37 38 39 .00186 .00186 .00189 .00197 .00208 .0 0 2 2 2 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 NOTE: For explanation of notation, see appendix C. 54 .0 0 2 2 0 22.1 21.4 2 0 .6 19.9 19.1 18.4 17.7 1 2 .8 12.2 1 1 .6 9.6 9.2 8.7 Table B-2. Continued—Table of working life for men, 1977: Conventional model Worklife duration of the economically active Worklife duration of the total population Stationary population Age Activity rate X w X 0) Within age x Iw Lw x X Worklife expectancy of the population (in years) Tw ew (11 ) (12 ) (13) Adjusted activity At exact rate age x w’ X X Closed stationary labor force (14) Within age x lw’ Lw’ X X X (15) Person yrs. of work remaining in closed labor force at age x Worklife expectancy of the active population (in years) Tw’ ew’ X X (16) (17) (18) (19) 16 17 18 19 0.445 .584 .651 .728 43,451 56,933 63,396 70,683 43,423 56,890 63,343 70,621 3,980,044 3,936,621 3,879,731 3,816,388 40.8 40.4 39.9 39.3 0.964 .964 .964 ; .964 94,124 93,997 93,855 93,699 94,064 93,931 93,780 93,617 4,186,145 4,092,082 3,998,152 3,904,372 44.5 43.5 42.6 41.7 20 21 22 .784 .826 .857 23 24 25 26 27 28 29 .912 .928 .938 .945 .951 .955 76,056 79,977 82,792 85,407 87,722 89,088 89,867 90,388 90,786 90,957 75,983; 79,897 82,706 85,318 87,631 88,998 89,779 90,301 90,700 90,871 3,745,768 3,669,786 3,589,890 3,507,185 3,421,867 3,334,236 3,245,239 3,155,461 3,065,161 2,974,462 38.6 37.9 37.2 36.4 35.6 34.7 33.9 33.0 32.1 31.2 .964 .964 .964 .964 .964 .964 .964 .964 .964 .964 93,530 93,352 93,166 92,974 92,783 92,593 92,407 92,225 92,047 91,872 93,443 93,261 93,070 92,878 92,687 92,498 92,315 92,135 91,958 91,785 3,810,755 3,717,313 3,624,052 3,530,982 3,438,104 3,345,418 3,252,920 3,160,605 3,068,471 2,976,513 40.7 39.8 38.9 38.0 37.1 36.1 35.2 34.3 33.3 32.4 30 31 32 33 34 35 36 37 38 39 .959 .960 .963 .964 .964 .963 .963 .962 .959 .959 91,157 91,092 91,197 91,185 90,977 90,693 90,444 90,135 89,697 89,383 91,078 91,012 91,117 91,101 90,888 90,594 90,339 90,021 89,575 89,252 2,883,591 2,792,513 2,701,501 2,610,385 2,519,284 2,428,397 2,337,803 2,247,464 2,157,443 2,067,868 30.3 29.4 28.5 27.6 26.7 25.8 24.9 24.0 23.1 2 2 .2 .964 .964 .964 .964 .964 .963 .963 .962 .959 .959 91,702 91,534 91,363 91,189 90,994 90,741 90,467 90,180 89,798 89,414 91,620 91,448 91,278 91,101 90,888 90,594 90,339 90,021 89,575 89,252 2,884,729 2,793,110 2,701,662 2,610,385 2,519,284 2,428,397 2,337,803 2,247,464 2,157,443 2,067,868 31.5 30.5 29.6 28.6 27.7 26.8 25.8 24.9 24.0 23.1 40 41 42 43 44 45 46 47 48 49 .957 .954 .952 .948 .943 .940 .937 .932 .927 .921 88,958 88,354 87,874 87,193 86,383 85,678 84,958 84,029 83,026 81,935 88,811 88,195 87,701 87,005 86,178 85,450 84,710 83,761 82,735 81,619 1,978,616 1,889,806 1,801,612 1,713,912 1,626,907 1,540,729 1,455,280 1,370,571 1,286,810 1,204,076 21.3 20.4 19.5 18.6 17.8 16.9 16.0 15.2 14.4 13.5 .957 .954 .952 .948 .943 .940 .937 .932 .927 .921 89,031 88,503 87,948 87,353 86,592 85,814 85,080 84,235 83,248 82,177 88,811 88,195 87,701 87,005 86,178 85,450 84,710 83,761 82,735 81,619 1,978,616 1,889,806 1,801,612 1,713,912 1,626,907 1,540,729 1,455,280 1,370,571 1,286,810 1,204,076 2 2 .2 50 51 52 53 54 55 56 57 58 59 .910 .903 .893 .883 .875 .864 .847 .832 .813 .786 80,393 79,079 1,122,458 1,042,391 12.7 11.9 .910 .903 80,843 79,397 80,067 78,726 1,122,458 1,042,391 963,665 11.1 .893 77,923 77,12 0 963,665 13.9 13.1 12.4 886,545 811,020 737,089 664,947 595,162 527,592 462,616 10.3 9.5 65,537 62,301 80,067 78,726 77,120 75,525 73,931 72,142 69,784 67,570 64,976 61,711 .883 .875 .864 .847 .832 .813 .786 76,323 74,728 73,037 70,963 68,677 66,273 63,343 75,525 73,931 72,142 69,784 67,570 64,976 61,711 886,545 811,020 737,089 664,947 595,162 527,592 462,616 60 61 62 63 64 65 .738 .687 .628 .546 .464 .404 .349 .298 .271 .250 57,436 52,414 46,839 39,729 32,869 27,850 23,290 19,268 16,946 15,052 56,844 51,820 46,261 39,204 32,405 27,423 22,910 18,930 16,624 14,741 400,905 344,062 292,241 245,980 206,777 174,371 146,949 124,038 105,108 88,484 5.2 4.5 3.9 3.4 2.9 2.5 1.9 1.7 1.5 .738 .687 .628 .546 .464 .404 .349 .298 .271 .250 59,277 54,332 49,041 42,732 35,804 29,914 25,167 20,920 17,777 15,682 56,844 51,820 46,261 39,204 32,405 27,423 22,910 18,930 16,624 14,741 400,905 344,062 292,241 245,980 206,777 174,371 146,949 124,038 105,108 88,484 5.8 5.8 5.8 5.8 5.9 5.9 5.6 .232 13,413 11,704 10,241 8,921 7,786 6,600 13,097 11,405 9,957 8,652 7,531 6,367 73,743 60,646 49,241 39,284 30,632 23,101 1.3 .232 1.1 .2 1 2 13,919 12,251 10,681 9,304 8,091 6,949 13,097 11,405 9,957 8,652 7,531 6,367 73,743 60,646 49,241 39,284 30,632 23,101 5.3 5.0 4.6 4.2 3.8 3.3 66 67 68 69 70 71 72 73 74 75 NOTE: (10 ) At exact age x Person yrs. of work remaining in the population at age x .8 8 6 .212 .195 .179 .165 .149 77,500 75,929 74,360 72,623 70,287 6 8 ,1 0 0 For explanation of notation, see appendix C. 55 8 .8 8 .0 7.3 6.5 5.8 2 .2 .9 .8 .7 .5 .195 .179 .165 .149 21.4 20.5 19.6 18.8 18.0 17.1 16.3 15.5 14.7 11.6 10.9 10.1 9.4 8.7 8 .0 7.3 6 .8 6.3 6.0 Table B-2, Continued— Table of working life for men, 1977: Conventional model Net events in the stationary population Net rates per 1,000 in the stationary population Labor force separation Labor force separations Age Labor force accessions X Total S A X Deaths Voluntary retirements w D X 16 17 18 19 13,529 6,544 7,387 5,494 133 150 163 175 133 150 163 175 4,062 2,972 2,783 2,489 1,544 957 697 572 343 371 181 191 192 192 188 183 180 176 174 165 181 191 192 192 188 183 180 176 174 165 104 274 161 172 171 176 185 294 255 318 446 323 442 172 171 176 185 199 208 224 240 258 284 94 47 94 206 65 158 616 494 696 827 728 740 949 1,026 1,116 1,552 301 328 355 388 428 459 498 543 591 624 315 166 340 439 301 281 451 484 525 927 1,341 1,606 1,595 1,594 1,789 2,357 2,214 2,595 3,264 4,868 693 747 796 846 924 940 988 1,048 1,143 648 859 799 748 865 1,418 1,227 1,546 2,155 3,725 5,023 5,559 7,058 6,798 4,983 4,512 3,980 2,306 1,884 1,643 1,168 1,156 1,090 979 881 781 696 639 615 611 3,856 4,403 5,968 5,819 4,101 3,732 3,284 1,667 1,269 1,033 0 1,692 1,448 1,305 0 1,122 573 545 518 493 459 432 1,119 903 786 629 705 390 30 31 32 33 34 35 36 37 38 39 0 0 0 0 0 0 0 40 41 42 43 44 45 46 47 48 49 0 0 0 0 0 0 0 0 0 0 50 51 52 53 54 55 56 57 58 59 0 0 0 0 0 0 0 0 0 0 60 61 62 63 64 65 0 0 0 0 0 0 66 0 67 0 68 0 69 0 70 71 72 73 74 75 NOTE: 0 0 0 0 (2 2 ) 1,164 822 (24) (23) (25) 0 0 0 0 41.9 30.7 28.8 25.8 16.1 Voluntary retirement r d Q Q X X X (26) (27) (28) 56 1.7 1.9 .0 .0 .0 1.9 1.9 1.9 1.9 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 .0 2 .0 .0 3.2 2 .0 2 .2 7.3 6 .0 0 1.7 1.9 1.9 0 0 0.0 1.6 2 .0 2.1 2.1 2 .0 2 .0 2 .0 10.0 0 0 1.4 1.6 1.9 0 0 1.4 2 .0 2.1 2.1 2 .0 2 .0 2 .0 0 0 1 ,1 1 0 138.7 67.2 76.0 56.6 0 0 0 0 0 For explanation of notation, see appendix C. Deaths X (2 1 ) 23 24 25 26 27 28 29 Q A (2 0 ) 20 Total s R X X 21 22 Labor force accessions 3.6 3.9 1.1 2.9 1.7 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 2 .8 3.5 5.0 3.6 4.9 6.9 5.6 7.9 9.5 8.5 8.7 1 1 .2 12.3 13.5 19.0 16.7 20.4 20.7 2.3 2.5 2.7 2.9 3.2 3.4 3.7 4.1 4.5 5.0 5.4 5.9 6.5 7.1 7.6 21.1 11.2 24.2 32.7 31.7 38.4 50.2 78.9 12.5 13.0 14.2 15.5 17.1 18.5 88.4 107.3 152.6 173.4 153.8 164.5 173.7 20.5 22.3 23.6 25.0 21.2 1 2 1 .8 129.2 127.0 131.0 129.6 154.5 129.2 43.8 47.8 52.1 56.9 60.9 67.8 .0 .0 .0 .0 .0 1.8 3.5 1.9 3.9 5.1 3.5 3.3 5.3 5.8 6.3 11.4 8.1 113.3 111.5 .0 2.3 .7 10.9 10.4 9.9 11.7 19.7 17.6 22.9 33.2 60.4 .0 .0 .5 1.0 9.5 10.3 .0 .0 .0 .0 .0 .0 1.0 8 .6 28.5 30.4 33.8 37.0 41.4 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 67.8 85.0 129.0 148.4 126.6 136.1 143.3 88.1 76.3 70.1 85.5 79.2 79.0 72.7 93.6 61.3 ably do not— offset one another. The slower the group’s true entry into the labor force (or the more gradual the ac slope) the more fictitious worktime is likely to be added to the numerator. This tends to narrow real group or tempo ral differentials in worklife behavior. The worklife expectancy o f active women. The extension of the model to active women is still more complex. The “fertility trough” of the female age profile (figure B-7 ) implies that, assumptions 7 and 8 notwithstanding, wo men do leave and reenter the job market during midlife. Smoothing this function into a simple monotonic curve would totally distort the information which it conveys. Figure B-7. been that of continuous labor force attachment. Every age-sex group experiences some amount of disallowed turnover during the year. The greater the volume of turn over, the more seriously the annual average participation rate, wx, understates the proportion active during the year. The discrepancy between these two indexes is as much as 1 0 percentage points or more for young men and women of most ages (table B-3, columns 2 and 3). Tabia B-3. Comparison of labor foree participation rat©s, proportions aetsv® during the year, and the average proportion of a year spent active, by sex, seleeted ages, 1077 profil® ©f th@ stationary labor force,, women,'1977 Sex and age Stationary labor force Annual average Proportion active labor force during year participation rate Average percent of year1 spent active by the group (2 ) (3) (4) 1 6 '....................... 2 0 ....................... 25 ....................... 30 ....................... 35 ....................... 44.5 78.4 92.8 95.9 96.3 6 6 .8 91.2 95.9 97.7 96.9 21.3 71.2 @5.0 102.3 106.1 40 45 50 55 60 65 @5.7 @4.0 91.0 86.4 73.8 40.4 98.9 94.0 93.1 87.8 78.5 43.5 103.3 100.7 07.5 91.2 72.9 31.7 16 ............. a ........ 2 0 ........................ 25 ....................... 30 ........................ 35 ....................... 36.4 64.2 65.6 57.9 58.5 56.0 79.7 74.1 6 6 .0 68.1 13.4 50.9 57.1 49.0 48.6 40 45 50 55 60 65 60.3 58.8 55.8 50.6 40.7 68.3 67.3 61.9 54.1 42.9 23.4 52.1 51.1 47.9 43.8 34.1 13.7 (1 ) Men ....................... ....................... ....................... ....................... ........................ ........... ........... Women Age ........................ ....................... ........................ ....................... ....................... ....................... 20.1 ’ Proportion of a 2080-hour year. Therefore Garfinkle devised an alternative procedure for estimating the worklife expectancy of active women. He broke the female population into marital and parental classes, many of which (e.g., the single, the separated, the widowed or divorced, and the ever-married without chil dren) had unimodal age profiles of participation, like those of men. For each such group he replicated the male model, closing the stationary labor force as in figure B-5. No worklife estimates were prepared for the total female population, or for groups which failed to pass the uni modality test. Ura)St®tS®ns ©f th© conventional worklll© m@d©l Many of the assumptions underlying this model have adversely affected its findings. The most troublesome has This bias leads to undercount of the stationary labor force, lw'x , which in turn upwardly biases the worklife expectancy of the active population, ew* (equation 25). The looser the group’s labor force attachment, the more its worklife expectancy is overstated. The steady influx of women into the job market—often in part-yearly capacities — has upwardly biased the worklife duration estimates for active women. The sex differ ential in worklife expectancy has been unduly narrowed by this bias, to the point where the worklife derations of men and certain groups of women appear to be nearly identical. External evidence refutes this conclusion and indicates that the conventional measures are a misleading basis for such comparisons. A second assumption which has discredited model findings is that of constant participation rates over time. In reality these rates are continually changing, yet the 57 expected durations are based on behavior as it was in a specific year. Furthermore, even the yearly summaries are unpre dictable. A change in the age profile of participation can result in illogical, unwarranted findings. Conventional tables for women in 1977 are a case in point. Between 1970 and 1977, the total female participation rate rose by more than 5 percentage points. Yet because young women were responsible for a disproportionate share of this increase, the worklife expectancy of active women appeared to drop by more than 3 years! As an illustration, consider women active at age 25. In 1970 their worklife duration was estimated to be: Tw '2 5 point to the need for a more flexible worklife model. So too do the gaps in the female worklife record. The conventional model shows no summary table for all wom en, and omits one of the largest groups in the population— those with small children. The estimates it does present are difficult to interpret, since they rest on an assumption of constant marital status. Given present rates of divorce, remarriage, and widowhood, they have little practical application. A final problem also stems from overreliance on par ticipation rates. The conventional model uses these rates as a proxy for time spent in the labor force (i.e., a 60- per cent rate is interpreted as meaning that 60 percent of the group’s time was spent active). External data sources show no such consistent relationship between these func tions. Table B-3 juxtaposes the active rates for 1977 with an index of time in the labor force (columns 2 and 4, re spectively). This time index is a ratio of the group’s aver age annual hours of participation to a standard 2080-hour work year. 7 The CPS records for 1977 indicate that at that time prime-age men tended to work more than the con ventional 52 week, 40 hour per week schedule. Activity rates understated their average “person year” contribu tion to the labor force. On the other hand, the average time commitment for women was less than 60 percent of the standard. Activity rates consistently overstated their contribution. Together, these biases further obscured the sex differential in worklife duration. In sum, recent trends in labor force attachment have violated nearly all of the underlying assumptions of the conventional worklife model. In the absence of these con ditions, the model cannot accurately describe or contrast the work patterns of various groups of the population. 2,046,385 ew 2 5 = 7 * ^ 2 5 = 35-8years- During the next 7 years the size of this young active popu lation increased by 13 percent, while the estimate of worklife years remaining grew by just 4 percent. Hence in 1977 the corresponding expectancy was: 2,128,185 64,738 32.9 years. Although mathematically correct, these findings are substantively meaningless. They illustrate the dangers of using a static model to describe a dynamic system, and FOOTNOTES TO AP P E N D IX B *The first life table was developed by Halley on the basis of birth and death registration data for the city of Breslau during the years 1687 to 1691. under the Occupational Outlook program at BLS. 5The term “worklife expectancy” is somewhat misleading on two counts. As noted earlier, the “expectancies” are merely a summary of behavior at various ages in a given year—they are not projections of what will actually occur. Secondly, the phrase “worklife” is conveniently used to describe a broader state of economic activity, including periods of unemployment. 2Table B -l, from the National Center for Health Statistics, uses a nonlinear distribution for certain age groups. However, equation 5 closely approximates the normal relationship among these functions. 3The term “expectancy” can be misleading. This index summarizes death patterns in a single year. It is derived without regard to projected mortality rates. Expectancy values can only be interpreted as a projection if one assumes present conditions will continue indefinitely. 4These data were used to estimate projected openings in various occupations, 6Beyond the age of peak participation, w'x = wx > Lw'x = Lwx , and Tw'x = Twx at all ages. 7For an explanation of this index, see footnote 9 of chapter 4. 58 Appersdfe C. Notation The notation system used in the increment-decrement tables is an extension of basic life table notation. Whereever possible, standard conventions have been maintained. Where changes have been called for, the following princi ples govern the development of new symbols. by two superscripts, the first indicates the base of the rate. Trailing subscripts. Subscripts following the basic vari able identify current age. The subscript x denotes any age. Subscripts and superscripts used. The characters used to indicate these states are as follows: Trailing superscripts. One or more superscripts following the variable indicate the status of the group in question during or at the conclusion of the interval. Leading subscripts. For variables having an interval ref erence, a numerical subscript preceding the variable indi cates the length of the interval in question (in years). When no leading subscript is shown, the implied interval is 1 year. x a i d • r s w nw Leading superscripts. The superscript preceding the vari able indicates the status of persons in question at the beginning of the interval. When the variable is preceded 59 = = = = = = = = = any age x economically active economically inactive dead all survivors (active or inactive) retirement (voluntary) separation workers nonworkers Table C-1. Notations! systems for increment-decrement and conventional models Worklife variable Conventional model notation Incrementdecrement notation Comments Transition probabilities:1 Probability of: Dying.............................................. Values are exactly equal in the two models. (a ,i) Surviving.......................................... Remaining inactive....................... Values are exactly equal. 1p I No equivalent variables in conventional model, but these two values sum to p . Becoming active............................ *x V Becoming inactive....................... No equivalent variables in conventional model, but these two values sum to p . Remaining active......................... a x a PY ^ Rat@§ of transfer: Population-based rates of: Labor force accession2 .................. A^ ' K Total labor force separation1 . . . . a M Voluntary labor force separation1 . aM [ ( ‘> d ) Increment-decrement estimate is gross; conventional estimate is net. No equivalent variable in conventional model. No equivalent variable. Net labor force mobility1 .............. No equivalent variable. Rates per person alive at exact age x. 1 Accessions..................................... Total separations.............................. rix .i) M No equivalent variable. r l x ' a) M (i.d ) No equivalent variable. X Labor fore® status-based rates:2 Accession3 ................................................................. 1m ° Total separation4 .......................................................... a m j * ‘^ No equivalent variable. Q 5^ See footnotes at end of table. 60 Increment-decrement estimate is gross; conventional estimate is net. Table C-1. Continued — Notational systems for increment-decrement and conventional models Worklife variable Voluntary separation 4 Incrementdecrement notation <7 / X Deaths of active persons4 ............................................ Deaths of all persons4 a m d X •m Conventional model notation Comments Qr.Y Increment-decrement estimate is gross; conventional estimate is net. Qd This value exactly equals the total death rate in both models. Values are exactly equal. X Qx W -Y Labor fore© participation rat©5 ........................................... No equivalent variable in increment-decrement model. Number of transfers In the stationary population: * Accessions2 Increment-decrement estimate is gross; conventional estimate is net. lt a X Total separations2 ....................................................... a . (i,d) X Voluntary separations 2 R Deaths of actives2 ....................................................... a(d 1X Deaths of inactives2 ..................................................... it d X Total deaths between exact ages1 .............................. Increment-decrement estimate is gross; conventional estimate is net. Sx Increment-decrement estimate is gross; conventional estimate is net. X Increment-decrement estimate is gross; conventional estimate is net. Kw Values are exactly equal. dx Total deaths of x year olds6 ......................................... Increment-decrement estimate is gross; conventional estimate is net. No equivalent variable shown in the increment-decrement model. Dx Stationary population: At exact age x by labor force status: 1 Total............................................................................ ■/ Inactive........................................................................ '■/ .V Active.......................................................................... Values are exactly equal. 'x Inw X lw x Closed labor force....................................................... Iw / X These terms are functionally similar to but numerically different from one another. Terms are functionally similar but numerically different. No equivalent variable in incrementdecrement model. During age x (persons alive and person years lived) by labor force status:6 Total (persons, years)................................................ See fo o tn o te s at end of table. 'L x Lx Values are exactly equal. Table C-1. Continued — Notational systems for increment-decrement and conventional models Incrementdecrement notation Worklife variable Conventional model notation Inactive (years lived by all persons).......................................... Active (years lived by all persons).............................. Lnwx Lw • n Closed labor force estimate......................................... X \ Terms are functionally similar but numerically different. Terms are functionally similar but numerically different. Lw ' No equivalent variable in incrementdecrement model. Values are virtually equal. X At and beyond exact age x (persons alive and person years lived) by labor force status:6 Comments i, Total (persons, years).............................. ................ ' T X‘ T Inactive (years lived by all persons).............................. •T ' Tnwx Terms are functionally similar but numerically different. Active (years lived by all persons)................................ • rj-< Cl Twx Terms are functionally similar but numerically different. X 1 X Closed labor force estimate.......................................... X Tw ' X No equivalent variable in incrementdecrement model. Survival chain for persons in status 1 at exact age.v : 7 Survivors in status 2 at exact age x 1 ............................ 1, V/ 2 No equivalent variable in conventional model. . ' X Person years lived by group in status 2 during age x 6 .......................................................... 1, v , 2 No equivalent variable. X Person years lived in status 2 at and beyond exact age x 6 .............................................. No equivalent variable. \,y T2 ‘ X Expectancies for: Total population alive at exact age x. Life............................................................................ ' e'x Inactive life 'e 1 ' ' Active life ex ’' enw Values are exactly equal. Terms are functionally similar but numerically different. e<x ew Terms are functionally similar but numerically different. 1e'x e Values are exactly equal. Population economically inactive at exact age x. Life S ee fo o tn o te s at end of table. 62 Table C-1. Continued — Notational systems for increment-decrement and conventional models Incrementdecrement notation Worklife variable Inactive life Conventional model notation No equivalent variable in conventional model. ‘• i Active life..................................................................... Population economically active at exact age x . No equivalent variable. 1 Life............................................................................... e Inactive life enw X Terms are functionally similar but numerically different. Active life..................................................................... ewx' Terms are functionally similar but numerically different. Events remaining per person alive at exact age x : 1E a / No equivalent variable in conventional model. X Voluntary separations No equivalent variable. 1 Changes stated in terms of the / function, or over the interval between exact ages x and x + I 2 The age or time reference for this variable differs between models. Increment-decrement values are stated in terms of change between exact ages x and x + I (using the / term).Conventional values describe changes in the stationary population, IT from the midpoint of one age to the midpoint of the next. 3 The base of this rate is the stationary inactive population. 5 In the conventional model the same function is applied to the interval between exact ages and that between (the midpoint of) successive ages to obtain stationary labor force values, Iw^ and Lw ^ respectively. 6 This variable is stated in terms of the interval between (the midpoint of) successive ages, or in terms of the L function. 7 The age interval referred to is retrospective, beginning at age y (where ,v«=jr) and ending at current age x The base of this rate is the stationary labor force. Values are exactly equal. X 1 Accessions 4 Comments 63 Bibliography 1. Dublin, Louis I., and Alfred J. Lotka. The Money Value o f a Man. Ronald Press, 1930. 14. —. “A Markov Chain Model of Working Life Tables,” Scandinavian Actuarial Journal, vol. 1, 1977. 2. Durand, John D. Labor Force in the United States, 1890-1960. New York, Social Science Research Council, 1948. 15. —, and Monica Fong. A Markov Chain Model o f Working Life Tables: A New M ethod fo r the Construction o f Tables o f Working Life. Working Paper No. 2. Copenhagen, Laboratory of Actuarial Mathematics, University of Copenhagen, 1976. 3. —, and Ann R. Miller. Methods o f Analyzing Census Data on Economic Activities o f the Population. ST/SOA/Series A /43. New York, United Nations, 1968. 16. —, and Monica Fong. A Markov Chain Model o f Working Life Tables: Illustrative Tables Based on Danish Labor Force Surveys, 1972-1974. Supple ment to Working Paper No. 2. Copenhagen, Laboratory of Actuarial Mathematics, University of Copenhagen, 1976. 4. Fullerton, Howard N., Jr. “A Table of Expected Working Life for Men, 1968,” Monthly Labor Review, June 1971. 5. —. “A New Type of Working Life Table for Men,” Monthly Labor Review, July 1972. 17. Keyfitz, Nathan. Introduction to the Mathematics o f Population. Reading, Mass.: Addison-Wesley, 1968. 6. —, and James J. Byrne. “Length of Working Life for Men and Women, 1970,” Monthly Labor Review, February 1976. 18. Multidimensionality in Population Analysis. RR-8033. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1980. 7. Garfinkle, Stuart H. Tables o f Working Life fo r Women, 1950. BLS Bulletin 1204. U.S. Department of Labor, Bureau of Labor Statistics, 1957. 19. Koesoebjono, Santo. Nuptiality Tables fo r the Female Population o f The Netherlands, 1978: An Application o f Multidimensional Demography. Working Paper No. 20. Voorburg, The Netherlands, Netherlands Interuniversity Demographic Institute, 1981. 8. —. “Table of Working Life for Men, 1 9 6 0 Monthly Labor Review, July 1963. 9. —. The Length o f Working Life fo r Males, 1900-1960. Manpower Report No. 8. U.S. Depart ment of Labor. Manpower Administration, 1963. 20. Krishnamoorthy, S. “Classical Approach to Incre ment-Decrement Life Tables: An Application to the Study of the Marital Status of United States Females, 1970,” Mathematical Biosciences, vol. 44, 1979. 10. Job Changing and Manpower Training. Manpower Report No. 10. U.S. Department of Labor, Manpower Administration, 1967. 11. —. Work Life Expectancy and Training Needs o f Women. Manpower Report No. 12. U.S. Department of Labor, Manpower Administration, 1967. 12. —. “The Lengthening of Working Life and Its Implications,” World Population Conference, 1965, vol. IV. New York, United Nations, 1967. 21. Ledent, Jacques. Some Methodological and Empirical Considerations in the Construction o f IncrementDecrement Life Tables. RM-78-25. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1978. 13. Hoem, Jan. “Estimation of Forces of Transition in Demographic Models,” Journal o f the Royal Statistical Society, series B, vol. 33, 1970. 22. —. “Multistate (Increment-Decrement) Life Tables: Movement Versus Transition Perspectives,” Environ ment and Planning A, vol. 12, 1980. 64 37. Schoen, Robert. “Constructing Increment-Decrement Life Tables,” Demography, vol. 12, No. 2, 1975. 23. Oechsli, F. “A General Method for Constructing Increment-Decrement Life Tables that Agree With the Data,” Theoretical Population Biology, vol. 16, 1979. 38. —. “Calculating Life Tables by Estimating Chiang’s a from Observed Rates,” Demography, vol. 15, 1978. 24. Rees, P.H. “Increment-Decrement Life Tables: Some Further Comments From a DemographicAccounting Point of View,” Environment and Planning A, vol. 5, 1973. 39. —, and Kenneth Land. “A General Algorithm for Estimating a Markov-Generated Increment-Decrement Life Table With Applications to Marital Status Patterns,” Journal o f the American Statistical Association, vol. 74, No. 368, 1979. 25. —. “Multistate Demographic Accounts: Measure ment and Estimation Procedures,” Environment and Planning A, vol. 12, 1980. 40. —, and V. Nelson. “Marriage, Divorce and Mortal ity: A Life Table Analysis,” Demography, vol. 11, 1974. 26. —, and A.G. Wilson. Spatial Population Analysis. London, Edward Arnold, 1977. 41. —, and Karen Woodrow. “Labor Force Status Life Tables for the United States, 1972,” Demography, vol. 17, 1980. 27. Rogers, Andrei. “The Multiregional Life Table,” The Journal o f Mathematical Sociology, vol. 3, 1973. 42. Shryock, Henry; Jacob Siegel; et. al. The Methods and Materials o f Demography. Bureau of the Census, 1973. 28. —. “The Mathematics of Multiregional Demographic Growth,” Environment and Planning, vol. 5, 1973. 43. Smith, Shirley. “Liability Cases and the Use of Working Life Tables in Court.” Paper presented at the annual meeting of the Population Association of America, St. Louis, 1977. 29. —. Introduction to Multiregional Mathematical Demography. New York, I. Wiley and Sons, Inc., 1975. 30. —, ed. Migration and Settlement: Selected Essays. RR-78-6. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1978. 44. —. “Tables of Working Life for the United States, 1977: Substantive and Methodological Implications.” Paper presented at the annual meeting of the Population Association of America, Denver, 1980. 31. —. The Formal Demography o f Migration and Redistribution: Measurement and Dynamics. RM 78-15. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1978. 45. —. “New Work Life Estimates Reflect Changing Profile of Labor Force,” Monthly Labor Review, March 1982. 32. —, ed. “Essays in Multistate Mathematical Demo graphy,” Environment and Planning A, vol. 12,1980, 5. Special issue. 46. Struyk, Albert. “A Transition from Actual AgeSpecific Labour Force Participation Rates Analyses to Increment-Decrement Working Life Tables in The Netherlands.” Spontaneous Research Note, General Conference of the International Union for the Scien tific Study of Population, Manila, 1981. 33. —, and L. J. Castro. Model Multiregional Life Tables and Stable Populations. RR-76-09. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1976. 47. U.S. Department of Health, Education, and Welfare, National Center for Health Statistics. Vital Statistics o f the United States. Various years. 34. —, and Jacques Ledent. “Increment-Decrement Life Tables: A Comment,” Demography, vol. 13, 1976. 35. —; R. Raquillet; and L.J. Castro. “Model Migration Schedules and Their Applications,” Environment and Planning A, vol. 10, 1978. 48. U.S. Department of Labor, Bureau of Labor Statistics. Tables o f Working Life: Length o f Working Life fo r Men. BLS Bulletin 1001, 1950. 36. —, and Frans Willekens. Migration and Settlement: Measurement and Analysis. RR-78-13. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1978. 49. Willekens, Frans. “Sensitivity Analysis in Multi regional Demographic Growth Models,” Environ ment and Planning A, vol. 9, 1977. 65 55. —, and Andrei Rogers. Computer Programs for Spatial Demographic Analysis. RM-76-58. Laxen burg, Austria, International Institute for Applied Systems Analysis, 1976. 50. —. The Demography o f Labor Force Participation. RM-78-17. Laxenburg, Austria, International Insti tute for Applied Systems Analysis, 1978. 51. —. Computer Program fo r Increment-Decrement Multistate Life Table Analysis: A User’s Manual to LIFEINDEC. WP-79-102. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1979. 56. —, and Andrei Rogers. Spatial Population Analysis: Methods and Computer Programs. RR-78-18. Laxenburg, Austria, International Institute for Applied Systems Analysis, 1978. 52. —. “Multistate Analysis: Tables of Working Life,” Environment and Planning A, vol. 12, 1980. 57. —; I. Shah; J.M. Shah; and P. Ramachandran. “Multistate Analysis of Marital Status Life Tables: Theory and Application,” Population Studies, March 1982. 53. —. Multiregional Population Analysis fo r Urban and Regional Planning. Working Paper 18. Voorburg, Netherlands Interuniversity Demographic Institute, 1981. 58. Wolfbein, Seymour. “The Length of Working Life,” Population Studies, vol. 3, 1949. 59. Woodrow, Karen; D.W. Hastings; and E.J. Tu. “Rural-Urban Patterns of Marriage, Divorce, and Mortality,” Rural Sociology, vol. 43, 1970. 54. —. Multidimensional Population Analysis with Incomplete Data. Working Paper 19. Voorburg, Netherlands Interuniversity Demographic Institute, 1981. 60. Woytinsky, W.S. Labor in the United States. New York, Social Science Research Council, 1938. ☆ 66 U.S. GOVERNMENT PRINTING OFFICE : 1982 0 - 3 8 1 - 6 0 8 (3874) Bureau ©f Labor Statistics Regional Offices Region I 1603 JFK Federal Building Government Center Boston, Mass. 02203 Phone: (617) 223-6761 Region IV 1371 Peachtree Street, N.E. Atlanta, Ga. 30367 Phone: (404) 881-4418 Region ¥ Region IS Suite 3400 1515 Broadway New York, N.Y. 10036 Phone: (212) 944-3121 Region SIS 3535 Market Street P.O. Box 13309 Philadelphia, Pa. 19101 Phone: (215) 596-1154 9th Floor Federal Office Building 230 S. Dearborn Street Chicago, III. 60604 Phone: (312) 353-1880 Region ¥! 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