A Stochastic Model for the Duration of a Strike

SUMMARY This paper is a study of the nature of the frequency distribution of the duration of strikes in the United Kingdom as recorded by the Department of Employment. The settlement of a strike is regarded as a probabilistic process and the duration of a strike is treated as an observation on a random variable. A model for this random duration is created by supposing that at each point of time after the commencement of a strike there exists an index of the difference between the parties to the dispute. This index is itself regarded as a one-dimensional stochastic process in continuous time and space and determines the duration of the strike by the first point of time at which the difference index passes through an absorbing barrier representing agreement. The duration of a strike then becomes the First Passage time of a stochastic process to a single absorbing barrier. As a first approximation the index process is assumed to be simple Brownian motion with drift and in consequence the duration of a strike has the Inverse Gaussian for its probability distribution. The fit of this distribution to the observations is shown to be, with few exceptions, very close.