Expanding the Markov Chain Toolbox: Distributions of Occupation Times and Waiting Times.

Markov models are important tools for quantitative social research. In this article, new methods for discrete Markov chains are presented. These methods allow us to calculate the distribution of the occupation time in a subset of the state space, the distribution of the waiting time to first entry into a subset of the state space, and the distribution of the waiting time to final exit from a subset of the state space. To demonstrate the usefulness of these methods, we apply them to working life tables for Spanish males to assess how the recent financial crisis affected the length of working life. The results show that the duration of working life decreased considerably, a pattern that can largely be explained by later entry to and earlier exit from the labor market. The findings also indicate that inequality in the length of working life increased. [ABSTRACT FROM AUTHOR]