It is common to have situations in which the sampling process and the maintained assumptions of a theoretical model are consistent with a set of parameter vectors, rather than a single parameter vectors. These econometric models are called partially identified models. The focus of the economic analysis then becomes the set of admissible values for the parameter vector of interest. However, while identification in these models focuses on sets and not on single points, estimation and inference have so far relied on techniques designed for point identified models. This is because econometricians have lacked tractable tools to estimate and test models with set identified parameters. Unfortunately, as economists attempt to analyze increasingly complex social phenomena, partially identified set models are being encountered. This research will provide a methodology to extend the conceptual shift from single valued to set valued objects to estimation and hypothesis testing. The methodology the PIs propose is based on mathematical tools that were originally introduced by economic theorists, and are intensely researched in the recent mathematical and statistical literature, although not used in the econometrics literature.
The results of this research should allow economists to conduct estimation and testing for partially identified models in a way that is completely analogous to how estimation and testing are conducted for point identified models. This is a huge contribution to economic science. Partially identified models are ubiquitous in the recent theoretical and empirical economics. Examples include theoretical studies of incomplete models for English auctions, empirical studies of oligopoly entry models with multiple equilibria, and of the changes in the distribution of male and female wages accounting for employment composition. The results of this research will provide a methodological framework for estimating and testing these models as well as provide software to apply this ethodology to conduct estimation and inference when full identification is not available. The results of this research will allow researchers (both theoretical and empirical) to investigate increasingly complex phenomena that had hitherto only been analyzed at the theoretical level. Policies based on such studies will be more realistic.
