Academic journal article
By Rosenbaum, David I.
Journal of Forensic Economics , Vol. 13, No. 3
In a recent Equal Employment Opportunity Commission class action suit, a company was charged with discriminating against applicants age 40 and over. During the first phase of the trial the company was found guilty of age discrimination. The second phase of the trial involved determining damages to be awarded to a class of approximately 152 members age 40 or over. Part of the damage calculation required estimating the amount of time members of the class would have been employed, absent the discrimination.
The employer in this case argued that there was a link between age and job tenure, and that if older workers had been hired, the company's experience suggests that they would not have been employed as long as the pool of current younger workers. Therefore, in calculating damages, it is important to examine the tenure/age relationship.
Information about current and previous employees is used to predict the relationship between age and tenure. For previous employees, company records indicate the date of hire and the date of termination. For those employees tenure is calculated as the number of weeks from hire to termination. For current employees, however, the calculation is not as straightforward. The date of hire is known. But, since each is employed at the time of sampling, termination has to occur at some unknown time in the future. Therefore, each current employee's true job tenure is underestimated, starting at the date of hire and ending at the date of sampling. This is a classic censoring problem.
One way to address the censoring problem may be to remove the censored observations from the sample. This would leave a subsample of just uncensored observations, each with known job tenure. However, if the censored observations come from a different population than the uncensored observations, using only the uncensored observations for statistical analysis will lead to biased predictions. This means that a statistical procedure will have to account for censoring. Fortunately, a procedure exists to estimate job tenures when censoring is an issue. This procedure is called duration modeling.
A duration model is developed that accounts for censored data. The model allows for specifying tenure as a function of age. The model is estimated for a sample of 170 current and previous employees. The results indicate that tenure is decreasing in age. Someone starting employment at age 24, for example, would have an expected job tenure of 166 weeks. Someone starting employment at age 40 would have an expected tenure of 129 weeks.
The next section of this paper describes duration modeling. This is a statistical technique that can be used to estimate tenure as a function of age when censoring occurs. Section III describes the data related to this particular case. Results of the estimation are shown in section IV. These results are compared to results generated either by omitting censored observations or by using all observations but not accounting for censoring. This is followed by a conclusion.
II. Duration Estimation with a Censored Sample
Duration models can be used to estimate tenure when there is a censoring problem. The simplest form of the duration model makes tenure solely a function of time. Let T represent someone's tenure or duration in a job. Some employees will have a relatively short duration in a job. Others may have a relatively long duration in a job. Therefore, the duration or tenure variable, T, has some distribution associated with it. Let f(t) be the probability distribution associated with T.
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This is just the probability that a particular individual's duration in a job is less than t weeks. Conversely, the probability that someone survives at least t weeks in a job is S(t) = 1 - F(t). Not surprisingly, this is called a survival function. Putting the probability function and the survival function together, it is possible to estimate the probability that someone who has already lasted t weeks in a job, leaves before the next week is out. …