Gary R. Skoog

Probability mass functions for additional years of labor market activity induced by the Markov (increment–decrement) model

This paper finds probability mass functions for additional years of labor market activity by using recursive formulae. Empirical results are presented for parameters of some mass functions and for probability intervals around those parameters.  2002 Elsevier Science B.V. All rights reserved.

Measuring years of inactivity, years in retirement, time to retirement, and age at retirement within the Markov model.

Retirement-related concepts are treated as random variables within Markov process models that capture multiple labor force entries and exits. The expected number of years spent outside of the labor force, expected years in retirement, and expected age at retirement are computed—all of which are of immense policy interest but have been heretofore reported with less precisely measured proxies. Expected age at retirement varies directly with a person’s age; but even younger people can expect to retire at ages substantially older than those commonly associated with retirement, such as age 60, 62, or 65. Between 1970 and 2003, men allocated most of their increase in life expectancy to increased time in retirement, but women allocated most of their increased life expectancy to labor force activity. Although people can exit and reenter the labor force at older ages, most 65-year-old men who are active in the labor force will not reenter after they eventually exit. At age 65, the probability that those who are inactive will reenter the labor force at some future time is .38 for men and .27 for women. Life expectancy at exact ages is decomposed into the sum of the expected time spent active and inactive in the labor force, and also as the sum of the expected time to labor force separation and time in retirement.

Disability and the New Worklife Expectancy Tables From Vocational Econometrics, 1998: A Critical Analysis

Worklife expectancy tables using Current Population Survey data have been privately published by Vocational Econometrics, Inc. (VE) several times over the past decade. This paper examines the suitability of these data for worklife purposes and finds several flaws that preclude its use. Beyond the inappropriateness of these data, there are econometric difficulties with VEs pooling procedure. Worklife for the disabled, to the extent that it differs from the overall population, is best determined professionally on a case-by-case basis. Other (SIPP) data more accurately measures various limitations appropriately, but currently lacks sufficient size for such worklife expectancy use.

Worklife in a Markov Model with Full-time and Part-time Activity

Worklife expectancy within the Markov model, the current paradigm employed by forensic economists to calculate time in and out of the labor force from mortality and transitions into and out of labor force activity, is commonly dated to Smith (1982 and 1986) and the Bureau of Labor Statistics (BLS) Bulletin 2135, which announced the change from the conventional worklife model. Two living states, active at labor force participation and inactive at labor force participation, were used in the work of the BLS and continue to be used in common worklife tables. Methodologically, the theory holds for multiple states, but three living states is an empirical constraint to Markov worklife expectancy calculations due to the enormous longitudinal survey size needed to generate a reliable matrix of transition probabilities.1 A few papers have explored a three-state model in which the active state has been subdivided into the employed and unemployed states of labor force participation. This paper explores another three-state model in which labor force participation is divided into fulltime and part-time activity with the remaining state as not participating in the labor force. Moving from two states of labor force participation to three states provides forensic economists new information relevant to evaluating lifetime output of work-related activity. Interesting topics answered by these worklife tables are what percentage of worklife expectancy is spent in the full-time labor force or what is the difference in total worklife expectancy for those beginning an age in the part-time labor force as opposed to the full-time labor force? We sketch the theory, describe the relevant Current Population Survey (CPS) data, present calculations, and discuss the results.

Probability Mass Functions for Years to Final Separation from the Labor Force Induced by the Markov Model

The concept of a probability mass function (pmf) for labor market phenomena has been used in four recent papers (Skoog, 2002; Skoog and Ciecka, 2002; and Skoog and Ciecka, 2001, 2001a). All four papers treat additional years of labor market activity (YA) as a random variable with its pmf found through recursive formulae. The mean of this random variable is the familiar concept of worklife expectancy; but, with the pmf in hand, all the characteristics of YA (such as the median, mode, standard deviation, skewness, kurtosis, and any probability interval) can be computed. The purpose of this paper is to accomplish the same task for years to final separation (YFS) from the labor force. That is, we place the concept of YFS on a solid probabilistic foundation by treating it as a random variable. We find its pmf through recursive formulae and then calculate various measures of central tendency, shape, and probability intervals. The YA and YFS random variables differ in the sense that the former only counts time spent in the labor force and excludes time spent alive but inactive, while the latter random variable counts all time (whether active or inactive) prior to leaving the labor force through retirement or death. Section II of this paper is a literature review of the years to final separation concept. This review is factual and not intended to be a critical evaluation; such an evaluation is lengthy and the subject of another paper which has been presented before two NAFE meetings (Skoog and Ciecka, 2003 and 2004), received discussant and audience comments, and is currently under review. In Section III, we proffer the YFS random variable as well as the appropriate concept for measuring final separation from the labor force and provide recursive formulae that define its pmf. The pmf provides the theoretically correct mean and median, as any other characteristics, of YFS. Section IV contains empirical results consisting of a set of comprehensive tables for YFS. Section V is a conclusion.

Allocation of Worklife Expectancy and the Analysis of Front and Uniform Loading with Nomograms

Years of worklife expectancy (WLE) computed for the commonly used Markov model need not be consecutive and immediate. Theoretically correct decomposition or allocation, as of the injury date, for which both forward and backward algorithms were given, appeared in Skoog (2001) and (2002). Unfortunately the underlying transition probabilities are required, and these are not generally published. The only current exception is Krueger (2004) who supplies inter-year labor force status tables which, when combined with mortality probabilities, enable a user to calculate transition probabilities.1 The required calculations are more amenable to a subroutine or macro, and essentially require the user to re-create the worklife expectancy calculation. In practice, forensic economists often either front-load (assume that the WLE comes immediately) or uniformly load (spread the WLE over a larger number of years, such as to age 65, 66 or 67). It is then natural to ask about the biases or corrections to be associated with these two loading methods of allocation. This paper reviews the theory in Section II and extends it in Section IV, providing closed form mathematical expressions (as opposed to computational programming code) involving the primitives of the problem, one step transition probabilities. Most readers will prefer Section III, the extensive middle part of the paper, however. For each of the two commonly employed allocation methods, charts, or nomograms,2 are offered which allow forensic economists to visually make a correction to the nearest half percent, or argue that an offsetting correction has been introduced already in a calculation. In practice the necessary corrections vary with active versus inactive status and the age, sex, and education of an individual. Use of these corrections obviates performing more complex and data-intensive analysis of the exact decomposition, where there is no ageearning profile; if present, such a profile would require further study or the more exact methods.

Worklife Expectancy via Competing Risks/Multiple Decrement Theory with an Application to Railroad Workers

A key concept in economics, and arguably the key concept in forensic economics, worklife expectancy, has been treated by actuaries, demographers and forensic economists with different models. The Markov or multiple increment/multiple decrement model has been employed by all three groups, while multiple decrement theory (also known as competing risks in biometrics) represented an earlier approach and a special case, in which transitions into the measured state are disallowed. As discussed in Skoog-Ciecka (2004), in some cases, e.g., railroad worker worklife expectancy Skoog-Ciecka (1998 and 2006), hybrids of these two approaches may prove fruitful, given appropriate but only occasionally available data. In this paper we develop and extend these ideas to allow a look at worklife expectancy in occupations where actuarial data provides longitudinal records of transitions. Beyond worklife expectancy, we also develop probability mass functions (pmf’s) which enable us to calculate any other distributional characteristic of time devoted to a specific occupation. We note that occupation-specific worklives provide especially useful information when money earnings and fringe benefits vary by occupation and when people change occupations throughout their worklives. We make an extended application utilizing data for railroad workers and show much lower worklives than previously calculated by others and ourselves. We have in mind four reasons persons engaged in an occupation exit the occupation: death, disability, retirement, and withdrawal (to another occupation, or out of the labor force). Ideally, we would have such data by year on individuals working in the railroad or other crafts in a region covered by a multiemployer pension plan, e.g., carpenters, ironworkers or laborers in a metropolitan area. We would observe a first year in which contributions are made on their behalf into a pension fund. We would follow them over time and record whether they remain in the occupation and region the next year, or whether they have transitioned from active to inactive due to one of the four causes above. Likewise, when a person who was disabled, retired or withdrawn in the previous period becomes active, we observe a record, whereas when such a person remains inactive for a second period, we observe that event by the non-existence of a record. In this way, an increment-decrement model may be constructed from event-history data that an actuary would maintain. However, in practice, we often do not have access to such detailed event-history data; rather

An Essay on the New Worklife Expectancy Tables and the Continuum of Disability Concept

The New Tables are costly and proprietary. The Very New Tables (tm) may be freely used by anyone with fair use copyright access to The Journal of Legal Economics (Winter 1999-00) through membership in the American Academy of Economic and Financial Experts or by anyone who is a patron of a library subscribing to that journal. Further, the bases of The Very New Tables have been subject to peer review.

Transitions Into and Out of Census Disability

This paper examines disability as measured and reported in three Census surveys: the American Community Survey (ACS), the Current Population Survey (CPS), and the Survey on Income Program Participation (SIPP). We focus on whether person-specific disability, as measured by the Census, is a permanent or a transitory condition. Survey data results regarding the incidence of Census-measured disability are shown both cross-sectionally and longitudinally. It is found from longitudinal CPS and SIPP responses that Census-measured disability is largely transitory. That finding empirically confirms the longstanding theoretical objections to the use of Census cross-section disability data along with a permanent disability assumption in worklife expectancy models; hence, any worklife expectancy model which assumes that Census disability measures are permanent conditions is misspecified and empirically invalid. Instead of using the permanent disability assumption, we use actual longitudinal disability transition probabilities and life table analysis to quantify the lifetime duration of disability as measured by the Census in total life years and working life years. We show that the realistic feature of disability transition dramatically lowers the effect of disability on worklife expectancy.

Markov work life table research in the United States

Prior to 1982, work life tables in the United States could be viewed as the labor force counterpart of life tables. Most work in this area emanated from the US Bureau of Labor Statistics (BLS) and was based on the assumptions that men entered and left the labor force only once in their lives and women only entered and left the labor force as a result of a change in their marital or parental status. The work life model for men especially was demographic in nature since departure from the labor force was akin to death in a life table in the sense that labor force reentry was not possible, just as reentry into a life table cannot occur after death. We now refer to this type of construct as the conventional model of work life. Tables produced by Fullerton and Byrne (1976), using data from 1970, illustrate this approach to work life expectancy (WLE).