James E. Ciecka

Competitive Balance in the Aftermath of the 1994 Players’ Strike

A new interseasonal measure of competitive balance in a sports league is presented. It is based on a Markov model of a team’s probability of qualifying for postseason play given the performance of the team in the previous season. Transitional probabilities are estimated for Major League Baseball teams before and after the 1994 players’ strike. The results indicate that there has been a significant deterioration in competitive balance for the seasons following the strike. Probability density functions for the prestrike and poststrike eras are also presented.

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.

The Postseason Value of an Elite Player to a Contending Team

This paper suggests the possibility that a superstars ability to propel a team into the playoffs may make him particularly valuable—pushing his salary beyond that which would otherwise be expected. Whereas a team in Major League Baseball (MLB) could play as many as 11 additional home games by the time it concludes the World Series, the number of home-field playoff games is a random variable with a mean of about 4 extra home games. Using reasonable assumptions, this implies that the expected increase in a MLB teams revenues associated with making the playoffs is about

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

11 million. The analysis shows that contending teams pay elite players (on average) an extra

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

2.8 million—a 40% bonus—to lure superstars to their rosters.

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

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.

State lotteries and externalities to their participants

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.

Estimation of Economic Losses to the Agricultural Sector from Airborne Residuals in the Ohio River Basin Region

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

The degree of participation in state lotteries can either increase or decrease expected returns. It is theoretically possible for unfair bets to become more than fair as participation in lotteries changes. In addition, the purchase of every combination of numbers can be more than a fair bet and such a purchase may increase the expected return to other lottery players.