Modelling Incomplete Spells of Unemployment and Employment

The procedure used to analyse a data set which includes only censored or incomplete spells is examined in this paper. First of all, the distributions of the incomplete spells of employment are analysed without explanatory variables (such as age, sex, etc.), assuming that the unobserved completed spells have a Weibull distribution. The relationships between the mean of the incomplete spells and the mean of the completed spells are reported for first-job seekers, unemployed, employed, and self-employed workers. Given that the unobserved completed spells are Weibull-distributed, the unobserved heterogeneity is introduced on the scale parameter of the Weibull. The heterogeneity, considered as a variable, is analysed for a binomial or Weibull distribution. As the beginning of a spell a retrospective datum, the recall errors are modelled including the heaping effect. Using some proportional hazards models, the methodology to study the influences of explanatory variables on spell distributions is then described, once again including both the heterogeneity and the heaping effect. On this basis, the lengths of on-going spells of unemployment for first-job seekers and unemployed workers are modelled, as well as the current job tenures of employed and self-employed workers.