Search Models and Duration Data

Many topics of interest to economists involve the passage of time. How long does a typical spell of unemployment last? Has the time between births increased in recent years as women's relative earnings increased? Answers to these questions are desired both for the purpose of sorting out various theories of social behavior and to answer questions of public policy. For example, the effects of Unemployment Insurance benefits on the duration of unemployment remains a subject on continued interest and controversy (Atkinson et al. [1984]), as does the effect of public sector dispute resolvement procedures on strike durations in collective bargaining (Butler and Ehrenberg, 1981); Schnell and Gramm, 1987). Analysis of duration data is complicated by the fact that duration data typically come in incomplete form; that is, some observations will, at the time of survey, be unfinished. Sometimes the data will consist of complete and incomplete spells, as in follow up studies of medical treatments. In other cases, such as the Occupational Mobility and Job Tenure survey that the United States Bureau of Labor Statistics conducts, employment spell lengths are incomplete of necessity: individuals are asked for the "length of time working for the present employer." The set of special methods that have been developed to deal with data with this structure are known as failure time models, that is, they deal with data that measure the time until an event occurs. Although the methods originated in industrial engineering and the biomedical sciences, where they were used to study machine breakdown and the effects of medical procedures, they had natural application to diverse social science phenomena from wars to strikes to unemployment spells, and they were rapidly adopted in economics, demography, and sociology.