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U.S. Department of Labor
Bureau of Labor Statistics
November 1982
Bulletin 2135




Tables of Working Life:
Th@ Increment-Decrement IM
lodteS
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@ fore© fe©hiwi©r
® 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

Trdim Igu workllf® duration
dte
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.
2
Based 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

Increment-decrement model

1970

1970

1977

Men
16-19
20-24
25-29
30-34
35-39
40-44

............................................
............................................
............................................
............................................
............................................
............................................

45-49
50-54
55-59
60-64
65-69
70-74

............................................
............................................
............................................
............................................
............................................
............................................

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.

in’ + ina + ■nd _ 1.000
P \6 p \6
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

n r16 =
rn
(> +

(1 +

(2)
< '< ) < % )

where:
lma =the rate of transfer of persons from the inactive
16
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!!?© @
2
tpectanci©s o persons m and ® ®f the
ff
uH
[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* atl, atd, and
X
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

/
Ma
5
x

(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)

. - the number of persons in the stationary popula­
L
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 2 ~ person years of life remaining to be lived in cate­
x
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 x
‘M a - a
5M(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

X

Active

I
X

i

I

a

t

X

X

Voluntary
labor force
exits

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:

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
■B for the general population
sf©

Age

Person years lived in each status
during age x
Total

X

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:

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)

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
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
NOTE:

70,539
70,448
70,341
70,222

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

Total
years

Inactive
years

i,16 .
T

i,16 i
T

X

Active
years

X

i,16 a
T
X

By persons active at exact age 16
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:

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

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

(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
NOTE:

X

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

Accessions

i

a

E

Voluntary
separations

a

i
E

x

X

X

O)

5

(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

(2)

Inactive
to
inactive
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:

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

X

Active

I
X

a

i

t

I

X

X

Voluntary
labor force
exits

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:

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

Person years lived in each status
during age x
Total

X

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

a
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:




X

X

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

(2)

Inactive
at x
i,16 i
I

X

(3)

Active
at x
i,16 a
I
X

(4)

Person years lived by cohort members in each status
during age interval x to x+1

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 i
L

X

a,16 a
L
X

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

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

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

24,260
24,247
24,232
24,217

0
9,751
9,402
6,263

20
21
22
23
24
25
26
27
28
29

NOTE:

a,16 .
L

Active
at x

9,877
4,577
2,833
8,435

73,943
54,153
44,458
37,552

68

X

Inactive
at x

(13)

0)

73,943
73,904
73,861
73,815

66

i,16 a
L

Total
at x

(12)

(7)

16
17
18
19

67

Active
at x

(11)

(5)

(8)

Inactive
at x

Persons active at 16

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

.

Inactive
years
i, 1 6

T

Active
years
i,16 a
T

i

T
X

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:




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

Total
years
i

.

e

e

Inactive
years
i

i

e

Expectancies of persons
active at age x

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:

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

Accessions

i

a

E

Voluntary
separations

a

i

E

x

X

X

(9)

5

(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

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

(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
NOTE:

(2)

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

Person years lived in each status
during age x
Total

X

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

Expectancies of persons
active at age x

Expectancies of persons
inactive at age x

Expectancies of the total
population
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:

. 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

Accessions

i

a

E

Voluntary
separations

a

i

E

x

X

X

0)

5

(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

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

(3)

(4)

(5)

(6).

(8)

0)

16
17
18
19

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
NOTE:

(2)
0.00057
.00065
.00068
.00070

.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)

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

(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
NOTE:

(11)

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

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

a
e

Inactive
years

Active
years

a i
e

Total
years

a a
e

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
NOTE:

X

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
W trE B g Life Table
o s ira )

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@ worklif© models
r
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 @ to® conventions! working Site table
f?
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

'

Qs = rate of total labor force separations between age
x
intervals x and x+1
Q d - rate of separations due to death, and
x

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 = < w x ~ L w x+\>
L
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:
w
DX

(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

w
.5 D X

(18)

Al
% = accession of women age x, due to the loss of a
husband
Lh - the stationary population of women age x with
x
a husband present
W°+ = the activity rate of women in all other marital
i
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:

Qr = Qs - Q d x
x
x (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 l = ( Lx ) ( l - Q x) * W + i - W
h
x
°x



jfm
c<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 cn
f

= 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
Stationary
population
at exact
age x

Deaths
between
exact ages
x and x+1

Stationary
population
in age

X

q

Age

i

d

Mortality
rate at
exact age

X

d)

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® @ working B for men, 1977: Conventional model
f
if@

Age

X

Mortality
rate at
exact age
X

q

of X

At exact
age x

I

year olds

Within
age x

L

X

D

X

X

(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

Deaths

X

(2 )

(D

Stationary population

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)

(10 )

At exact
age x

Within
age x

Iw

Lw

x

X

Person yrs.
of work
remaining
in the
population
at age x

Worklife
expectancy
of the
population
(in years)

Tw

ew

(11 )

(12 )

(13)

(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

Adjusted
activity
At exact
rate
age x
w’

X

X

Closed stationary
labor force

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:

.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)

Voluntary
retirement
r

d
Q

Q

X

(25)
0
0
0
0

138.7
67.2
76.0
56.6

0
0
0
0

41.9
30.7
28.8
25.8
16.1

0

X

X

(26)

(27)

(28)

1 ,1 1 0

56

.0
.0
.0

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

6 .0

0

1.7
1.9

1.9
1.9

7.3

0

1.7
1.9

1.9

0

0
0

0.0

1.6

2 .0
2.1
2.1
2 .0
2 .0
2 .0

10.0

0

1.4

1.6

1.9

0

0

1.4

2 .0
2.1
2.1
2 .0
2 .0
2 .0

0

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
P
^Y

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.

Q5
^

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 .......................................................

it d

Increment-decrement estimate is gross;
conventional estimate is net.

X

a(d
1X

Deaths of inactives2 .....................................................

Increment-decrement estimate is gross;
conventional estimate is net.

Sx

X

Total deaths between exact ages1 ..............................

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

X

Comments

Terms are functionally similar but
numerically different.
Terms are functionally similar but
numerically different.

Lw '

Closed labor force estimate.........................................

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

\

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)................................

• r-< Cl
j

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 .

Comments

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.




/

1

Accessions

4

Values are exactly equal.

X

63

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☆

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