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.
There are several reasons that motivate the use of a dynamic structural approach to analyze the economic implications of infrequent adjustments in individuals' decisions. First, in the presence of any of the different potential sources of censoring, an individual's decision problem becomes dynamic, even if in the absence of these factors the problem is static. Second, in the context of an axiomatic approach to individual behavior, both identification assumptions and parameters of interest have clear economic or behavioral interpretations. This makes it easier to discuss the plausibility of the assumptions or of the parameter estimates. Finally, but not less important, the estimation of a structural model allows one to implement counterfactual experiments to evaluate the effects of changes in institutional or behavioral parameters entering in the model. Section 2 characterizes the type of models that will be considered in this paper and presents the notation. In that section we also present a model of labor demand that will be used to illustrate methods and results.
There are at least two types of empirical questions that can be answered from the estimation of the sources of censoring in a dynamic decision model. First, different sources of censoring in a decision variable are associated to different institutional characteristics of the market under study. To illustrate this, consider an individual's purchasing decision of an automobile (see Bar-Ilan and Blinder, 1988, or Eberly, 1994, for examples of these models). A simple potential explanation for individuals' purchasing infrequency is the existence of indivisibilities. If that is the unique source of censoring, there are not borrowing constraints, and there are perfect competitive markets for purchasing and renting cars, an individual would be indifferent between purchasing a new car or renting it during its operative life. In such a case, purchasing infrequency would not have any implication on individuals' consumption behavior. Alternatively, consider that there exist significant informational asymmetries in the market of second-hand cars.
These asymmetries imply that the price of a car in the second-hand market is lower than the price of exactly the same car in the market of new cars. This introduces an additional source of infrequency in individuals' purchasing behavior (i.e., partial irreversibility). Another possible source of censoring would be the existence of search costs or administrative costs that could persist even in the absence of informational asymmetries or indivisibilities. It is clear that the identification of the quantitative importance of these different factors affecting infrequent purchasing behavior is of significant interest both for firms operating in the market and for regulators.
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