## Understanding the Meaning of Remaining Work-Life Expectancy

On more than one occasion I have been asked to explain the concept of remaining work-life expectancy to an attorney during a deposition. It is clear from their questions that the concept is often mistakenly believed to represent a projection to the date the worker will retire from the work force. This is not the case.

Work-life expectancy is derived by summing the probability of a worker being alive and in the labor force during each year from his/her current age through age 75 (this will be explained further below). Said probabilities account for transitions into and out of the work force for such reasons as, for instance, periods of unemployment, extended illness or injury, caring for a relative, and other non-earning periods during which the worker could have earned wages. Given such possible events, in any given year a worker faces a measurable probability of working only a portion of that year. Additionally, as individuals age they experience an increasing probability each subsequent year of being out of the labor force for a portion of the year. In other words, the probability of working through an entire year tends to decrease as we grow older.

Intuitively, it is reasonable to expect (and the data show) that the rate of decrease is more pronounced for some occupations than others, for instance, workers employed in construction or mining or fishing. Research also indicates that workers with higher levels of education tend to experience higher probabilities of working through an entire year than workers with lower levels of education. Similarly, women in general are in and out of the labor force over the course of their work life with greater frequency than men.

So how do these probabilities relate to expected work-life? (Before we answer that, it is important to note that the word “expected” as used here is a mathematical term that indicates a statistical expectation, the value of a random variable that is more likely than others. It is not used in accord with a more everyday definition relating to considering an event as likely or certain, or something that is anticipated or hoped for.)

Perhaps a simplified, hypothetical example can best illustrate the derivation of a work-life expectancy value. Suppose workers categorized as male, who are currently active in the labor force, have a bachelor’s degree, and will be 45 years of age during a given year have a probability of remaining active in the labor force through their 45th year equal to 95% (which equals 0.95). In other words, there is a 95% probability that the worker will work the entire year. However, if we ask the question “What portion of the year would we expect such a worker to work?,” it is not reasonable to conclude the answer is 100%. Indeed, the answer is 0.95, which equal 95% of one whole year. This value is called (using mathematical/statistical terminology) the expected value.

Now suppose that workers similarly categorized as our typical worker above but age 46 exhibit a probability equal to 90% (i.e., 0.90), while for those age 47 the probability equals 85% (i.e., 0.85). To keep things simple here, let’s ignore all subsequent potential years in the labor force and the corresponding probabilities (expected values), that is, through age 75. If we add together 0.95, 0.90 and 0.85, we get 2.70. This latter value – 2.70 – identifies the expected work life. In other words, the statistical expectation is that a typical worker classified as male, currently active in the labor force, with a bachelor’s degree, and 45 years of age will work 2.70 years (of the three years we have considered here).

It should be clear from the example of our typical worker above that the number of years of work-life expectancy is not equivalent to the number of years to retirement. More generally, work-life expectancy identifies the sum of the portion of each year the worker can expect to work totaled over all years starting with the worker’s current age through age 75. In contrast, the number of years to retirement counts whole years, not portions of years, since it does not account for periods when a worker is not active in the labor force. Thus, it is not reasonable to use the number of years to retirement in a calculation of lost wages in a personal injury lawsuit because that would imply that the worker would work 100% of each year from the date of injury through the date he/she retires. Such an assumption is in contradiction to pervasive empirical evidence.

**If the reader would like assistance obtaining an article discussed herein, please contact Dr. Boisso at 214-394-3165 or Dale@BoissoAndAssociates.com.**