Duration of Employment in Employment Discrimination Cases
Hughes, Melvin, Journal of Forensic Economics
Trout (1995) develops a model of employment duration for employment discharge cases that..."substitutes probabilities based on a very large sample for subjective assessments [of employment duration] made by an economist, an attorney, or the plaintiff." (p. 176) The likely duration of employment is also an issue in class-action employment discrimination cases. This note presents a very simple model to estimate employment duration in such cases.
In order to estimate economic damages in a class-action discrimination case, we need to estimate two types of figures: (1) The number of "wrongfully not hired" persons; and (2) The expected duration of employment at the defendant employer. We may know the identity and demographic characteristics of some plaintiffs claiming discrimination. However, we must also calculate economic damages for persons who might not be identified until after a settlement or court award has been published. In situations where the economist must calculate damages for unidentified plaintiffs, a broad, unconditional measure of employment duration is appropriate. When the identities and demographic characteristics of the plaintiffs are known, Trout's model could also be used.
The present model assumes that exit from employment follows the exponential probability distribution, so that this equation applies:
1) P([H.sub.i]) = [re.sup.-rt],
where Hi is the event that the [i.sup.th] hire exits employment, r is the parameter of the model, and t is time. In this model, the mean duration of employment is simply:
2) [E.sub.i](t) = 1/r.
It can be shown that the exponential distribution has the "no memory property," which is also a property of the classical Markov process (Goodman 1988). Two Harvard professors tested an absorbing-state Markov model to analyze intra-firm employment transitions (Churhill and Shank 1975). Based on parametric Chi-squared tests, they find that the Markovian assumptions of time-homogeneity and stationarity are met for the single employer under study.
Stephen Marston (1976) developed a Markov model of labor market transitions with a macroeconomic focus. Using Current Population Survey (CPS) data, he traced the monthly transitions of workers among the states of (1) employed; (2) unemployed; and (3) not in the labor force. Thus, we have the three-by-three transition probability matrix shown below:
Not in the To: Employed Unemployed Labor Force From: Employed Pee Peu Pen Unemployed Pue Puu Pun Not in the Labor Force Pne Pnu Pnn
Marston did not test the Markovian assumptions, and in a replication study and literature review, Coleman (1989) found that the assumptions were not met. Heckman and Borjas (1980) developed a model under relaxed assumptions to address the shortcomings of the classical Markov models. However, the model that they developed is exceedingly complex and tedious.
A series of papers used Markov-like models to study whether unemployment was primarily due to structural or frictional economic forces (Akerlof and Main 1980, 1981, 1983; Clark and Summers 1979; Summers 1986). More recently, the Monthly Labor Review periodically publishes tables of employment transition probabilities, using monthly flow data from the CPS, e.g. Howe (1990). Thus, perhaps the present model can be applied without manipulating the raw CPS data.
To illustrate how to apply the present model, let us consider data in Howe (1990). Howe calculates transition probabilities by age group, but here we will only consider total women, age 20 and over. The monthly probability of transition from employment to unemployment (Peu) is 0.0104, and the probability of transition from employment to not in the labor force (Pen) is 0.0341. The probabilities in each row of the transition probability matrix are mutually exclusive and collectively exhaustive, and thus the sum is one. …