I. Introduction

Worklife expectancy within the Markov model remains the current paradigm employed by forensic economists to calculate time in and out of the labor force resulting from mortality and transitions into and out of activity. Its use is commonly dated to Smith (1982) and the Bureau of Labor Statistics Bulletin 2135, which announced the change from the conventional model; but the model goes back much earlier. Two living states, active and inactive, are employed and continue to be used in the worklife tables that are in most common use.

This paper updates the Skoog-Ciecka (2001a and 2001b) worklife tables, which used 1997–1998 data, and the Krueger (2004) worklife tables, which used 1998–2004 data. The present paper estimates probability mass functions introduced by Skoog and Ciecka (2001a and 2002) with data generated by the methodology in Krueger (2003). We have pooled the data beginning January 2005 and continuing through December 2009, a period of five years, using observations matched one year apart. Thus, we have roughly four times the data in the first of the previous studies, and about that of the second. We chose this period for a variety of reasons, including recency, business cycle, and trend considerations. The result is the most current and disaggregated set of worklife tables, along with extended probability calculations and statistical measures, available to forensic economists.

The paper is organized as follows. Section II contains a discussion of period and cohort tables, business cycles, and trends. Section III explains notation and recursions used to calculate worklife expectancies and other distributional characteristics of time in the labor force. Our data set and its properties are discussed in Section IV. Section V is the heart of the paper. It contains worklife expectancy tables and many other characteristics of time in the labor force by gender, age, and education. Section VI is a brief conclusion. The paper ends with an appendix analyzing pooled labor force activity data when trends may be present in the data. We prove the theorem: ignoring trend in data pooled across several years results in unbiased estimates of what would be trend-corrected transition probabilities at the mid-point of a sample.

II. Methodology and Commentary on Markov Worklife Expectancy Issues

We adopt the Markov model¹ applied to Current Population Survey (CPS) data² as our methodological vehicle. The building blocks of the Markov model are survival probabilities, taken from the latest U.S. Life Table, and transition probabilities, depicting the probability of ending up in the active state (A), conditional on having been in the active or inactive state (I) in the previous year.³ These probabilities are denoted by ^A p_x^A and ^I p_x^A, respectively, for a person age x in a particular sex-education group. Letting pp_x denote the age x labor force participation rate, these quantities are connected by the Balance Equation:

Thus, given a starting participation at an age at which a group enters the labor force, the pair of transition probabilities at this and all later ages determines that group's participation rates. The reverse is not true—roughly transition rates provide twice the information that participation rates do. Nevertheless, over time, participation rates rise when either rates of entry into activity from activity (^A p_x ^A) or from inactivity (^I p_x^A) rise, and fall in the opposite circumstances. Participation rates have received more attention than transition rates in the general economics literature and in the popular press, especially when changes in behavior are alleged to have occurred.

The Period Assumption: No Extrapolation of Trends in Mortality or Transition Probabilities (or Labor Force Participation)

Bulletin 2254, the last Bureau of Labor Statistics (BLS) worklif expectancy tab e, began with the words “It is estimated that if mortality conditions and labor force entry and exit rates held constant at levels observed in 1979 to 1980 ....” (p. 1)

This statement makes it clear that the BLS worklife methodology did not attempt to estimate trends in either mortality or in transition probabilities. We call this the period assumption, or equivalently, the constancy benchmark. We make the same assumptions about the constancy of mortality and transition probabilities in this paper.

Regarding mortality, the analogous actuarial construct is that of a period life table. We use the most recent such table, the U.S. life table, here the 2006 table, released June 28, 2010.⁴ Although we do not use them in this paper, we note that from time to time the Social Security Administration publishes cohort life tables; the ost recent are found in Study No. 120 with mortality projected to 2100 (Bell and Miller, 2005). A graphical depiction of the projection of these trends on life expectancy at birth is produced in Figure 1.⁵ Past mortality improvements cited in Study 120 include those due to improved medical care, sanitation, diet, vehicle safety, and the general standard of living. Study 120 anticipates future trends in mortality that will be influenced by factors (not necessarily all life enhancing) such as new diagnostic, surgical, and life sustaining techniques; misuse of drugs and prevalence of smoking; environmental pollutants and new diseases; health education and people assuming personal responsibility for their health; violence; and society's willingness to pay for health care. Finally, Study No. 120 notes various periods over the twentieth century when mortality changed at different rates for different subpopulations, and observes that the relatively larger mortality improvements have been for those under 65. The study projects that mortality reductions for the aged will be relatively greater than in the past, based on cause of death data for heart disease, cancer, vascular disease, violence, respiratory disease, diabetes mellitus, and other causes.

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Similarly, the BLS, macroeconomists, labor economists, demographers, and others project future labor force participation. Every two years, the BLS issues labor force projections, the most recent of which are from November 2009 and contain projections of participation rates to 2018. Nevertheless, the BLS chose not to incorporate labor force projections into its worklife expectancy methodology. The BLS chose not to attempt to project changes in future transition probabilities or (per the Balance Equation) labor force participation rates. We agree with that decision, and we discuss our reasons in the next several paragraphs.

Two general sources of changes over time might be considered—movement during business cycles and the effects of long-term trends. To be useful, worklife tables need to apply throughout the business cycle, especially since cycles are dated well after the fact, and projecting when any current cycle might end should be left to business economists. One objection to forecasting trends is that, in the simpler demographic life tables as discussed above, cohort tables where this has been done have not met market tests, i.e., they have not been generally used or become generally accepted. Even if the market were to accept mortality projections, in light of the economic theory discussed below, it is not at all clear in which direction the associated “trend corrections” for labor force participation would or should take us. With no a priori argument for bias associated with maintaining the status quo or period assumption, we elect to maintain it. We treat business cycles first and long-run trends in labor force participation next. In an appendix, we provide econometric results which permit the interpretation and justification for our averaging methodology, viz., that it is robust to trends, in the sense that, whether trends exist or not, our methods acknowledge and capture their value at our sample mid-point, and then sensibly decline to project them into the future.

III. Notation and Recursions for the Markov (Increment-Decrement) Model⁷

Let x denote a person's exact age with BA being the youngest age at which labor force activity can occur. Everyone must have either left the labor force or died by truncation age TA. Letm ∈ {a,i}, and n ∈ {a, i, d} where a denotes active in the labor force, i enotes inactive, and d the death state. The transition probability denotes the probability that a person in state m at age x will be in state n at age x + 1. Any person alive, whether in state a or i, at age TA − 1 = 110 transitions to state d at age TA. We assume that mortality probability and activity status are independent, i.e., . Transition probabilities incorporate mortality, and the only restrictions on them are that , and .

YA_x,m denotes the random variable of future time in the labor force for a person who is in state m at age x, and p_YA(x, m, y) measures the probability that a person in state m at age x will accumulate y additional years in the labor force. That is, p_YA (x, m, y) measures the probability that YA _{x, m} = y; and the set of p_YA(x, m, y) for all possible values of y, constitutes the probability mass function (pmf) for YA_{x, m} . The pmf ultimately depends on the transition probabilities ^mp_xⁿ which are primitive to the Markov model. Transitions between states are assumed to occur at the mid-point between ages.⁸

Recursions defining p_YA(x, m, y,) consist of global conditions, boundary conditions, and main recursions. Global conditions (1a)–(1d) refer to extreme values of y and x as well as conditions that hold at all ages. Boundary conditions (2a)–(2c) deal with probabilities of future activity being either 0 or .5 of a year. Main recursions (3a)–(3b) capture probabilities of future activity for y years exceeding values defined by the boundary conditions (Skoog and Ciecka 2002).

Years of Activity Probability Mass Functions for YA_x,m = y for m ∈ {a,i} with Mid-Year Transitions

Global Conditions

(1a)  (1b)  (1c)  (1d) 

Boundary Conditions for x = BA,…,TA − 1

(2a)  (2b)  (2c) 

Main Recursions for x = BA,…,TA − 1

(3a)  (3b) 

Global condition (1a) says that future years of activity cannot be negative nor can they exceed TA –x –.5 years. The latter condition holds because everyone alive at age x dies or leaves the labor force prior to age TA. Since everyone has died prior to age TA, the probability of zero active, or inactive, time at age TA is 1.00 as expressed in (1b). Global condition (1c) expresses the assumption that transition to the death state does not depend on activity status. The last global condition, (1d) says that every person alive at age TA − 1 transitions to the death state.

Boundary condition (2a) expresses the impossibility of no future time in the labor force if a person were active at age x since at least .5 of a year of activity must accrue before any mid-year transition can occur. Condition (2b) gives the probability that a currently active person accumulates exactly one-half year of activity by either dying at age x +.5 or by transitioning to inactive and remaining inactive thereafter. Boundary condition (2c) gives the probability an inactive person accumulates no additional labor force time by either transitioning to the death state or remaining inactive after age x.

The remaining probability mass values are defined by the main recursions. The right-hand side of (3a) is the sum of two terms that contribute to the probability that currently active person age x will accumulate y years of future activity: (1) The first term is the product of two factors. p_YA(x+1, a,y–1) is the probability that a person active at age x + 1 will have y − 1 years of future activity and, when multiplied by , adds another year of activity at age x. (2) The second term also is the product of two factors. The latter factor p_YA (x +1,i, y −.5) is the probability that a person inactive at age x + 1 will have y − .5 years of future activity and, when multiplied by yields an additional one-half year of activity at age x. The second factors in both terms aggregate sample paths resulting from remaining active for y – 1 years and y −.5 years from age x+1, respectively; and their respective multipliers and induce an additional one whole year and one-half year of activity, respectively. The right-hand side of (3b) is the sum of two terms that contribute to the probability that an inactive person age x will accumulate y years of activity: (1) The first term is the product of two factors. p_YA(x + 1,a, y − .5) is the probability that a person active at age x + 1 will have y −.5 years of future activity and, when multiplied by , yields an additional one-half year of activity at age x since the transition to activity occurs at midyear. (2) The second term also is the product of two factors. The latter factor p_YA(x + 1,i,y) is the probability that a person inactive at age x + 1 will have y years of future activity and, when multiplied by , adds no additional activity at age x.

Our goal is to find the exact probability distribution of the years of activity random variable YA_{x, m} within the context of the Markov model and then compute its characteristics. The foregoing recursions not only accomplish that task, but they do so in a computationally efficient manner. Once transition probabilities have been estimated, these recursions yield the exact distribution of YA _{x, m} in a few seconds of computer time. The computational efficiency itself is remarkable when one considers the number of sample paths of activity, inactivity, and death that could occur; and each path makes its own contribution to the pmf of Y_{x, m}. In general, 2^TA–x–1 sample paths can occur for a person currently age x. For example, if we consider a person age x = 20, then there are 2^111–20 – 1, or approximately 2.4759x10²⁷ paths to consider. Half that many paths are possible for a person age 21, and half again as many for a person age 22, and so on.⁹

We calculate characteristics of YA_x,_m with the following formulae:

The expected value of YA_x,_m (i.e., worklife expectancy or average years of labor force activity) for people in state m (active or inactive) at age x is defined by¹⁰

(4a) 

The median value y_med of YA_{x, m} possess the property that

(4b) 

and the mode y_mode of YA_{x, m} is the value of YA_{x, m} that fulfills the inequality

(4c) 

The variance, standard deviation, skewness, and kurtosis are defined by

(4d)  (4e)  (4f)  (4g) 

Cumulative probabilities occur at values of YA_x,m where

(4h) 

for α= .10,.25,.75,.90.

IV. Data Period and Calculation of Labor Force Transition Probabilities

We utilize the U.S. labor force experience during 2005 to 2009 in our empirical work. The BLS estimates U.S. labor force participation using the Current Population Survey (CPS). The annual, non-seasonally adjusted, U.S. labor force participation rates from 2005 to 2009 are shown in Table 1. According to the Bureau of Economic Analysis, real GDP growth was 3.1% in 2005, 2.7% in 2006, 2.1% in 2007, 0.4% in 2008, and −2.4% in 2009. From 2005 to 2009, male and female labor force participation rates distinctly fell at ages 16 to 19 years. In general, male participation rates through age 49 declined during 2005 to 2009 while male labor force participation rates at ages 50 and over increased. For females, labor force participation changes were mixed during 2005 to 2009 for ages 20 to 49 and then increasing in every age group starting at age 50. Fitting with a long-term trend, the labor force participation rate for males ages 16 and over continues in its slow decline during 2005 to 2009. Female labor force participation rates for ages 16 and over have been flat since the mid-1990s. The average U.S. labor force experience from 2005 to 2009 does not present empirical anomalies which would noticeable impact worklife expectancy estimates.

Table 1 BLS Published Estimates of Labor Force Participation Rates, by Gender, Age, and Years

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Using the monthly outgoing rotations¹¹ of the CPS from January 2005 through December 2009, we were able to match 74.3% of CPS respondents' one-year-apart records of their labor force status (471,722 matching person-records). As shown in Table 2, the labor force participation and unemployment rates in the matched sample for persons ages 16 and over are the same as the BLS published averages from January 2005 to December 2009. In Table 3, we show the differences between the BLS and matched sample labor force participation rates by age and gender.

Table 2 Comparison of Matched CPS Sample and BLS Estimates of Labor Force Participation and Unemployment Rates, by Gender, 2005–09

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Table 3 Comparison of Matched CPS Sample and BLS Estimates of Labor Force Participation Rates, by Gender and Age

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Using the matched person records from the CPS, we are able to estimate the average size of the U.S. non-institutional population by age, gender and eight educational levels by their labor force status at one-year-apart intervals ⁱN_xⁱ, ⁱN_x^a, ^aN_xⁱ, ^aN_x^a. In order to compute transition probabilities, we also require the input of the proportion of persons dying between ages x and x + 1, q_x, and the number of survivors in the population at each age x, l_x, which is computed from q_x. Since survivor data are not available by the last state participation before death or by education, we rely on the U.S. Life Tables 2006 (Arias, 2010) that gives survivor data by gender and age.

Mortality data are published for exact ages x, and they represent the probability of survival from one exact age to the next age. However, since the CPS population activity data are based on surveyed age reported in integers values only, age in the CPS has an expected value as x + ½. Therefore, when we compute the transition probabilities, we re-center the survey data to exact ages by taking the average of the surveyed population size across the range of x ± ½ by averaging two consecutive ages in the survey data (e.g., for exact age 17 transition probabilities, we use the average survey data for ages 16.5 and 17.5). Using the identities in equations (5a)–(5d), the four transition probabilities computed from the survey data for exact age x are:

(5a) 

()5b 

(5c) 

(5d) 

V. Worklife Expectancies and Other Distributional Characteristics of Time in the Labor Force

Skoog and Ciecka (2001b) provided tables for the following educational categories:

• (1) those with less than high school,

• (2) high school or a GED grouped together,

• (3) some college,

• (4) bachelor's degree,

• (5) graduate degree, and

• (6) all educational groupings combined.

Krueger (2004) provided tables for the following educational categories:

• (1) those with less than high school,

• (2) high school or a GED grouped together,

• (3) some college,

• (4) bachelor's degree or better, and

• (5) all educational groupings combined.

Since the publication of previous tables, we have learned through our work and the work of others ¹² that those who attained a GED should be separated from those who earned a high school diploma. We find that having a GED adds to worklife expectancy compared to those without a high school diploma, but that a high school diploma adds more to worklife expectancy than a GED. Further, those attending college but not earning a BA degree (“some college, no degree”) may be divided into those earning an academic associates degree and those with no degree. Finally, those attaining a college degree can usefully be divided into those earning a bachelor's degree, a master's degree, and those earning a PhD or a professional degree.

Our ability to provide these detailed breakouts without suffering an increase in the standard errors of our estimates depends on our ability to exploit more than a year of data. Indeed, the proof of this assertion is in the size of the associated standard errors, which generally are not reported.¹³ We show those standard errors in our tables, and sample size is the determinant as to whether they will be small. It is important to recognize that there are two notions of standard error, one small and one large; and we report both, although they refer to very different concepts. The standard error with which we estimate the mean or the median of additional years of activity is very small, attesting to a small “known error rate.” However, the standard error (the square root of the variance) in the population years of additional activity is intrinsically much larger—one might die tomorrow or in 50 years, and one might retire in advance of or in arrears of a traditional age such as 65.¹⁴

Tables 4–35 contain our main results.¹⁵ We utilize eight educational groups:

• (1) zero to 12 years of education but no high school diploma or GED,

• (2) GED but no high school diploma,

• (3) high school diploma but no college,

• (4) some college but no degree,

• (5) associate's degree but no bachelor's degree,

• (6) bachelor's degree but no master's or higher degree,

• (7) master's degree but no professional degree or PhD, and

• (8) professional degree or PhD.

Table 4 Characteristics for Initially Active Men with 0–12 Years of Education, No Diploma, No GED

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Tables 4–11 are for initially active men by the foregoing eight education groups. Tables 12–19 are for initially inactive men separated into the same educational groups. Tables 20–27 are for initially active women and Tables 28–35 for initially inactive women by education. Tables 36 and 37 contain worklife expectancies for men and women by education but without regard to initial labor force status. Tables begin at age 16 for groups (1) and (2), at age 17 for group (3), at age 18 for group (4), at age 19 for group (5), at age 20 for group (6), at age 22 for group (7), and at age 24 for group (8).¹⁶ Tables end at age 75 for all educational groups.

Table 5 Characteristics for Initially Active Men with GED, No Diploma

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Table 6 Characteristics for Initially Active Men with High School Diploma

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Table 7 Characteristics for Initially Active Men with Some College, No Degree

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Table 8 Characteristics for Initially Active Men with Associate's Degree

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Table 9 Characteristics for Initially Active Men with Bachelor's Degree

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Table 10 Characteristics for Initially Active Men with Master's Degree

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Table 11 Characteristics for Initially Active Men with Professional or PhD Degree

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Table 12 Characteristics for Initially Inactive Men with 0–12 Years of Education, No Diploma, No GED

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Table 13 Characteristics for Initially Inactive Men with GED, No Diploma

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Table 14 Characteristics for Initially Inactive Men with High School Diploma

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Table 15 Characteristics for Initially Inactive Men with Some College, No Degree

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Table 16 Characteristics for Initially Inactive Men with Associate's Degree

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Table 17 Characteristics for Initially Inactive Men with Bachelor's Degree

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Table 18 Characteristics for Initially Inactive Men with Master's Degree

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Table 19 Characteristics for Initially Inactive Men with Professional or PhD Degree

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Table 20 Characteristics for Initially Active Women with 0-12 Years of Education, No Diploma, No GED

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Table 21 Characteristics for Initially Active Women with GED, No Diploma

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Table 22 Characteristics for Initially Active Women with High School Diploma

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Table 23 Characteristics for Initially Active Women with Some College, No Degree

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Table 24 Characteristics for Initially Active Women with Associate's Degree

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Table 25 Characteristics for Initially Active Women with Bachelor's Degree

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Table 26 Characteristics for Initially Active Women with Master's Degree

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Table 27 Characteristics for Initially Active Women with Professional or PhD Degree

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Table 28 Characteristics for Initially Inactive Women with 0-12 Years of Education, No Diploma, No GED

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Table 29 Characteristics for Initially Inactive Women with GED, No Diploma

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Table 30 Characteristics for Initially Inactive Women with High School Diploma

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Table 31 Characteristics for Initially Inactive Women with Some College, No Degree

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Table 32 Characteristics for Initially Inactive Women with Associate's Degree

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Table 33 Characteristics for Initially Inactive Women with Bachelor's Degree

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Table 34 Characteristics for Initially Inactive Women with Master's Degree

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Table 35 Characteristics for Initially Inactive Women with Professional or PhD Degree

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Table 36 Worklife Expectancy and Bootstrap Estimates for Men without Regard to Initial State

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Table 37 Worklife Expectancy and Bootstrap Estimates for Women without Regard to Initial State

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Table 37 continued Worklife Expectancy and Bootstrap Estimates for Women without Regard to Initial State

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To illustrate the results reported in Tables 4–35, consider 35-year-old men with bachelor's degrees but without graduate degrees in Table 9. Such men have worklife expectancies of 27.52 years. The median additional time in the labor force is 28.50 years, and the mode is 29.50 years. The distribution of additional labor force time shows negative skewness with a value of −.63 as would typically be the case when the mode exceeds the median which exceeds the mean (WLE).¹⁷ Kurtosis is 4.06 indicating a pmf that has more probability mass around its peak and in its tails, but less probability mass between the peak and tails, than a normally distributed random variable. The standard deviation is 7.34 years. This is the standard deviation of additional time in the labor force—the usual measure of dispersion around the mean. Table 9 also shows the 10^th (18.50 years), 25^th (23.50 years), 75^th (32.50 years), and 90^th (35.50 years) percentile points. The interpretation is, for example, that only 25% (i.e., 1 − .75) of 35-year-old men with bachelor's degrees will be in the labor force for 32.50 years or more. We use Table 38 to illustrate the detailed calculations that underlie the forgoing results, keeping in mind that a table similar to Table 38 underlies each single row in Tables 4–35. Columns A and B of Table 38 comprise the pmf for 35-year-old active men with bachelor's degrees as illustrated in Figure 3. Column C is the accumulation of the probabilities in Column B, and we note the sum is 1.0000. Entries in Column A and C that yield the 10^th, 25^th, 50^th, 75^th, and 90^th percentile points, as well as the mode, are highlighted (see 4b, 4c, and 4h). Column D contains the products of y and p_YA(x, m, y); and their sum, worklife expectancy, is highlighted on the bottom of Column D (see 4a). Columns E, F, and G develop the variance (4d), standard deviation (4e), skewness (4f), and kurtosis (4g), all highlighted at the bottom of the table.

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Table 38 Distributional Characteristics of Active Men Age 35 with BA Degrees

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Bootstrap estimates of worklife expectancies and their standard errors are shown in the last two columns of Tables 4–35.¹⁸ Each bootstrap estimate is based on our CPS matched sample sizes by age, gender, educational attainment, labor force status, and an assumed sample size of 10,000 for mortality. We used 100 bootstrap replications for each row in Tables 4–35. Continuing to use 35-year-old initially active men with bachelor's degrees as an illustration, Table 9 shows 27.55 as the bootstrap estimate of worklife expectancy, a number quite close to the reported mean of 27.52 years. The bootstrap standard error of the worklife expectancy is .29 years. We draw a sharp distinction between the standard deviation of years of activity (7.34 years) and the standard error of estimated worklife (.29). The former refers to variation in years of activity itself while the latter measures variation in the sample mean (worklife expectancy). Said differently, years of time in the labor force can differ from worklife by several years, but there is little variation in the estimate of worklife.

Tables 36 and 37 contain worklife expectancies, bootstrap worklife expectancies and bootstrap standard errors for men and women by age and education but without regard to initial labor force status.¹⁹ We can think of these worklife expectancies as weighted averages of their age, gender, education, and initial status counterparts where the weights are participation rates for initial actives and one minus participation rates for inactives. Bootstrap standard errors are based on 100 replications and our CPS matched sample sizes.

We conclude our tabulated results with some comparisons between our current work and two commonly used worklife studies. Table 39 contains worklife expectancies for initially active and initially inactive men and women with less than high school educations taken from Skoog and Ciecka (2001b), Krueger (2004), and the present study.²⁰ Worklife expectancies in the present study for initially active men exceed those reported by Skoog-Ciecka; the range being approximately .3 years to 1.4 years depending on age. Relative to Krueger, the present study has worklife expectancies approximately .6 years smaller to .9 years larger. For initially inactive men with less than high school, the present paper has bigger worklife expectancies than Skoog-Ciecka by as much as approximately 1.8 years for men in their late 30s. Relative to Krueger, differences range from .8 years to .3 years. For initially active women with less than high school, worklife expectancies in the present study differ from Skoog-Ciecka by .8 years to .6 years; the range relative to Krueger is .3 years to .7 years. For inactive women, the range is 1.1 years to .8 years with Skoog-Ciecka and −.5 years to .8 years relative to Krueger.

Table 39 Worklife Expectancies in 1997-98, 1998-2004, and 2005-09 for Men with Less Than High School^*

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Table 40 shows worklife expectancies for initially active and initially inactive men and women with Bachelor's, but not higher, degrees as reported by Skoog-Ciecka and in the present study. For initially active men, the present study contains worklife expectancies uniformly smaller than Skoog-Ciecka but the range is only approximately zero to .3 years. Almost all of the differences in worklife expectancies are negative for initially inactive men with a range of approximately .1 year to 1.2 years. Falling worklife expectancies for men are contrasted with increasing worklife expectancies for women in Table 40. Women's worklife expectancies increased at all ages for both initially active and inactive women with increases being in the range of 1.0 to 1.5 years from the youngest ages to approximately age 60.

Table 40 Worklife Expectancies in 1997–98 and 2005–09 for Men and Women with Bachelor's Degrees^*

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VI. Conclusion

We produced extended tables of labor force activity by age and gender based on the Markov model. Tables contain three measures of central tendency (mean or worklife expectancy, median, and mode), three measures of shape (standard deviation, skewness, and kurtosis), and four percentile points (10^th, 25^th, 75^th, and 90^th). Tables also contain bootstrap estimates of worklife and their standard errors. The pooled matched sample data, upon which our results are based, yield estimates of participation rates and unemployment rates that are in close agreement with their nationally reported counterparts, thereby providing a measure of consistency of our sample data and nationally reported labor force statistics. We discussed the relationship between our empirical work and period and cohort tables, business cycles, and trends. We also proved a new theorem: pooling data across several years but ignoring trend still produces unbiased estimates of what would be trend-corrected transition probabilities at the mid-point of a sample. We believe this work is the most current and disaggregated set of worklife tables, along with extended probability calculations and statistical measures, available to forensic economists.