Nonparametric Structural Models

The interplay between economic theory and econometrics comes to its full force when analyzing structural models. These models are used in Industrial Organization, Marketing, Public Finance, Labor Economics, and many other fields in economics. Structural econometric methods make use of the behavioral and equilibrium assumptions specified in economic models to define a mapping between the distribution of the observable variables and the primitive functions and distributions that are used in the model. Using these methods, one can infer elements of the model, such as utility and production functions, that are not directly observed. This allows one to predict behavior and equilibria outcomes under new environments and to evaluate the welfare of individuals and profits of firms under alternative policies, among other benefits. To provide an example, suppose that one would like to predict the demand for a new product. Since the product has not previously been available, no direct data exists. However, one could use data on the demand for existent products together with a structural model, as shown and developed by McFadden (1974). Characterize the new product and the existent competing products by vectors of common attributes. Assume that consumers derive utility from the observable and unobservable attributes of the products, and that each chooses the product that maximizes his/her utility of those attributes among the existent products. Then, from the choice of consumers among existent products, one can infer their preferences for the attributes, and then predict what the choice of each of them would be in a situation when a new vector of attributes, corresponding to the new product, is available. Moreover, one could get a measure of the difference in the welfare of the consumers when the new product is available. Economic theory seldom has implications regarding the parametric structures that functions and distributions may possess. The behavioral and equilibrium specifications made in economic models typically imply shape restrictions, such as monotonicity, concavity, homogeneity, weak separability, and additive separability, and exclusion restrictions, but not parametric specifications, such as linearity of conditional expectations, or normal distributions for unobserved variables. Nonparametric methods, which do not require specification of parametric structures for the functions and distributions in a model are ideally fitted, therefore, to analyze structural models, using as few a-priory restrictions as possible. Nonparametric techniques have been applied to many models, such as discrete choice models, tobit models, selection models, and duration models. We will concentrate here, however, on the basic models and, on those, indicate some of the latest works that have dealt with identification and estimation.