Longitudinal datasets with information about firms investment, employment or price decisions, among others, show how frequently firms do not respond to observed changes in costs or in the demand, and they prefer \doing nothing". Retail firms may not change their prices for several months even if wholesale prices are changing. Firms wait to renovate their capital stock even when technological change is rapidly depreciating this stock, or when significant reductions in real interest rates occur. Employment in a plant may not be reduced even if the plant is suffering significant and persistent reductions in its demand. This lack of response to sizable changes in relevant variables can be also observed in individuals' purchasing decisions of durable goods. From a theoretical point of view there are several potential characteristics of the decision problem that can explain the existence of this censoring in observed decision variables: non-negativity constraints, partial irreversibility of the decision, kinked adjustment costs, indivisibilities, or lump-sum adjustment costs, among others. Each of these sources of censoring can have different economic interpretations for each particular decision problem, e.g., regulatory or technological restrictions, or market conditions in which the agents operate.
In this paper we analyze the identification and estimation of the sources of censoring in dynamic structural models. The paper discusses different econometric issues associated to the estimation of these models and presents several approaches to overcome some of these problems. Special emphasis is placed on the identification and estimation of the parameters of interest under different assumptions on the stochastic structure of the unobservables and under different characteristics of the longitudinal dataset, like its temporal dimension, the frequency of corner solutions, or the distribution of duration spells between two consecutive interior solutions.