In this paper we analyse methods which allow us to estimate and identify the sources of censoring in dynamic models. We explicitly take into account the existence of corner solutions by considering a discrete-time-discrete-choice dynamic structural model. The availability of microeconomic datasets allows us to focus on decisions at the individual level and directly exploit the information contained in the corner solutions. We show how a discrete decision process (DDP) represents a natural framework within which to analyse agents' behaviour when optimal inaction generates censoring in observed decisions. A discrete decision process is characterised by a control variable which only takes a finite number of values. Some problems are naturally discrete, such as the optimal engine replacement or job the search problem in which the individual decides whether or not to accept a job offer. Other problems may be described very efficiently by a discrete decision problem. This is clear in the case of fixed costs of adjusting inputs which imply the discrete decision of whether or not to vary the production factor.