Estimation of the Inter-occurrence Time Between Events from Incomplete Data. Analysis of Periods of Unemployment in Spain

Abstract

This work analyzes the stochastic variable representing the waiting times between two consecutive events of a stationary renewal process, such as periods of unemployment of different individuals in a specific population. This data has been obtained through cross-sectional sampling: a specific point in time t is chosen, and a random sample of the individuals who are unemployed at the time t is extracted. For each individual we are interested in the unemployment period including t. However, in practice these values are not observable, and the only fact we can ascertain is the time from the inclusion of the individual in the previous unemployment period to the sampling time t. Our data also includes the corresponding values of a certain set of covariates (for example, the time spent on employment training courses or the age of the individual). Using non parametric techniques, an estimation of the conditional mean has been obtained, given the sex and age groups of the individuals. This is a more natural approach than other methods based on the estimation of the hazard rate, thus avoiding pre-established forms for the inclusion of covariates.